A NOVEL EQUATION-OF-STATE TO MODEL MICROEMULSION …

The Pennsylvania State University

The Graduate School

Department of Energy and Mineral Engineering

A Dissertation in

A NOVEL EQUATION-OF-STATE TO MODEL MICROEMULSION PHASE

BEHAVIOR FOR ENHANCED OIL RECOVERY APPLICATIONS

Energy and Mineral Engineering

by

Soumyadeep Ghosh

2015 Soumyadeep Ghosh

Submitted in Partial Fulfillment

of the Requirements

for the Degree of

Doctor of Philosophy

December 2015

ii

The dissertation of Soumyadeep Ghosh was reviewed and approved* by the following:

Prof. Russell T. Johns

Professor of Petroleum and Natural Gas Engineering

Program Chair for Petroleum and Natural Gas Engineering

Pennsylvania State University

Dissertation Advisor

Chair of Committee

Luis F. Ayala H.

Professor of Petroleum and Natural Gas Engineering;

Associate Department Head for Graduate Education


Zuleima T. Karpyn

Associate Professor of Petroleum and Natural Gas Engineering;

Quentin E. and Louise L. Wood Faculty Fellow in Petroleum and Natural Gas

Engineering;


Andrew Belmonte

Professor of Mathematics and Materials Science and Engineering


*Signatures are on file in the Graduate School

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ABSTRACT

Surfactant-polymer (SP) floods have significant potential to recover waterflood residual oil in

shallow oil reservoirs. A thorough understanding of surfactant-oil-brine phase behavior is critical

to the design of chemical EOR floods. While considerable progress has been made in developing

surfactants and polymers that increase the potential of a chemical enhanced oil recovery (EOR)

project, very little progress has been made to predict phase behavior as a function of formulation

variables such as pressure, temperature, and oil equivalent alkane carbon number (EACN). The

empirical Hand’s plot is still used today to model the microemulsion phase behavior with little

predictive capability as these and other formulation variables change. Such models could lead to

incorrect recovery predictions and improper flood designs. Reservoir crudes also contain acidic

components (primarily naphthenic acids), which undergo neutralization to form soaps in the

presence of alkali. The generated soaps perform synergistically with injected synthetic surfactants

to mobilize waterflood residual oil in what is termed alkali-surfactant-polymer (ASP) flooding.

The addition of alkali, however, complicates the measurement and prediction of the

microemulsion phase behavior that forms with acidic crudes.

In this dissertation, we account for pressure changes in the hydrophilic-lipophilic

difference (HLD) equation. This new HLD equation is coupled with the net-average curvature

(NAC) model to predict phase volumes, solubilization ratios, and microemulsion phase

transitions (Winsor II-, III, and II+). This dissertation presents the first modified HLD-NAC

model to predict microemulsion phase behavior for live crudes, including optimal solubilization

ratio and the salinity width of the three-phase Winsor III region at different temperatures and

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pressures. This new equation-of-state-like model could significantly aid the design and forecast

of chemical floods where key variables change dynamically, and in screening of potential

candidate reservoirs for chemical EOR. The modified HLD-NAC model is also extended here for

ASP flooding. We use an empirical equation to calculate the acid distribution coefficient from

the molecular structure of the soap. Key HLD-NAC parameters like optimum salinities and

optimum solubilization ratios are calculated from soap mole fraction weighted equations. The

model is tuned to data from phase behavior experiments with real crudes to demonstrate the

procedure. We also examine the ability of the new model to predict fish plots and activity charts

that show the evolution of the three-phase region. The modified HLD-NAC equations are then

made dimensionless to develop important microemulsion phase behavior relationships and for use

in tuning the new model to measured data. Key dimensionless groups that govern phase behavior

and their effects are identified and analyzed.

A new correlation was developed to predict optimum solubilization ratios at different

temperatures, pressures and oil EACN with an average relative error of 10.55%. The prediction

of optimum salinities with the modified HLD approach resulted in average relative errors of

2.35%. We also present a robust method to precisely determine optimum salinities and optimum

solubilization ratios from salinity scan data with average relative errors of 1.17% and 2.44% for

the published data examined.

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TABLE OF CONTENTS

Glossary ................................................................................................................................... vii

List of Figures .......................................................................................................................... x

List of Tables ........................................................................................................................... xxiii

Acknowledgements .................................................................................................................. xxv

Chapter 1 Introduction ............................................................................................................. 1

1.1. Surfactants and Interfacial Tensions ......................................................................... 2 1.2. Winsor’s R-Ratio and the C-Layer ........................................................................... 3 1.3. Effect of Salinity on R-Ratio ..................................................................................... 5 1.4. Microemulsions ......................................................................................................... 6 1.5. Types of Microemulsions in Surfactant-Oil-Brine (SOB) systems and their

significance in EOR ................................................................................................. 7 1.6. Research Goals .......................................................................................................... 10 1.7. Organization of the Dissertation ............................................................................... 10

Chapter 2 Literature Review .................................................................................................... 17

2.1. The Equivalent Alkane Carbon Number and its Relevance to Microemulsion

Phase Behavior ......................................................................................................... 17 2.2. Effect of Temperature, Pressure and Solution Gas on Microemulsion Phase

Behavior ................................................................................................................... 19 2.3. Role of Alkali in Surfactant Enhanced Oil Recovery Processes ............................... 23 2.4. The Surfactant Affinity Difference ........................................................................... 24 2.5. The Hydrophilic – Lipophilic Difference.................................................................. 25 2.6. The HLD-NAC model............................................................................................... 27

2.6.1. Radii and Curvatures of Micelles in Solubilized Systems ............................. 27 2.6.2. The Average Curvature Equation ................................................................... 28 2.6.3. The Net Curvature Equation .......................................................................... 29 2.6.4. Flash Calculations using HLD-NAC .............................................................. 29

2.7. Summary ................................................................................................................... 35

Chapter 3 Development of a Modified HLD-NAC Equation-of-State to Predict

Surfactant-Oil-Brine Phase Behavior for Live Oil at Reservoir Pressure and

Temperature ..................................................................................................................... 39

3.1. Extension of The HLD Equation to Include Pressure ............................................... 39 3.2. New Relations for Prediction of Optimum Solubilization Ratio .............................. 42 3.3. Modifying the HLD-NAC Model ............................................................................. 44

3.3.1. Accounting for Surfactant Volume Fraction in The Average Curvature

Equation............................................................................................................ 44 3.4. Determining The Surfactant Length Parameter ........................................................ 46 3.5. Results ....................................................................................................................... 48

3.5.1. Example 1: Skauge and Fotland (1990) Experiments .................................... 48

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3.5.2. Example 2: Roshanfekr and Johns (2011), and Roshanfekr et al. (2013)

Experiments ...................................................................................................... 51 3.5.3. Example 3:Austad and Strand (1996) and Austad and Taugbol (1995)

Experiments ...................................................................................................... 54 3.6. Discussion ................................................................................................................. 57 3.7. Conclusions ............................................................................................................... 61

Chapter 4 A Modified HLD-NAC Equation of State to Predict Alkali-Surfactant-Oil-

Brine Phase Behavior ....................................................................................................... 83

4.1. Soap Formation Model .............................................................................................. 83 4.2. Equilibrium Constants and Their Dependence on the Molecular Structure of

Petroleum Acids ....................................................................................................... 85 4.3. Flash Calculations Including the Alkali Component ................................................ 86 4.4. Results ....................................................................................................................... 90

4.4.1. Case A from Mohammadi (2008), and Mohammadi et al. (2009) ................. 91 4.4.2. Case B from Mohammadi (2008), and Mohammadi et al. (2009) ................. 93

4.5. Conclusions ............................................................................................................... 97

Chapter 5 Dimensionless Solutions to Microemulsion Phase Behavior .................................. 108

5.1. Solubilization Ratio Relationships in Two-Phase Regions ....................................... 108 5.1.1. Dimensionless Solutions for Type II- Microemulsions.................................. 110 5.1.2. Dimensionless Solutions for Type II+ Microemulsions ................................. 111

5.2. Solubilization Ratio Relationships in The Three-phase Region ............................... 111 5.3. Two-phase Limits and Stability Criteria for Dimensionless Equations .................... 114 5.4. Results ....................................................................................................................... 117

5.4.1. Interpretation of Phase Behavior Experiments ............................................... 117 5.4.2. Analysis .......................................................................................................... 120 5.4.3. Dimensionless Solutions Applied to Temperature and Pressure Scans ......... 121 5.4.4. Interfacial Volume Ratio for Surfactant Mixtures.......................................... 123

5.5. Conclusions ............................................................................................................... 124

Chapter 6 Conclusions and Recommendations ........................................................................ 143

6.1. Conclusions ............................................................................................................... 143 6.2. Recommendations for Future Research .................................................................... 146

Appendix A Effect of Pressure on the Surfactant Affinity Difference and the

Hydrophilic-Lipophilic Difference .................................................................................. 148

Appendix B Alkalinity of Aqueous Sodium Carbonate Solution ........................................... 153

Appendix C Salinity Scan Experiments at Atmospheric Pressure .......................................... 155

References ................................................................................................................................ 160

vii

Glossary

Roman

As = Total interfacial area occupied by surfactant (Å2)

A1 = Constant slope for σ* vs 1/ΔHLD linear trend (dimensionless)

A2 = Constant intercept for σ* vs 1/ΔHLD linear trend (dimensionless)

B1 = Constant slope for lnS* vs 1/σ* linear trend (dimensionless)

B2 = Constant intercept for lnS* vs 1/σ* linear trend (dimensionless)

ai = Activity coefficient of surfactant in phase i. (dimensionless)

asurf = Area per surfactant molecule (Å2)

asoap = Area per soap molecule (Å2)

bi = constant value of partial derivative of µi* for a phase i with respect to a HLD

variable (dimensionless)

C1 = Constant slope for lnS* vs Xsoap linear trend (dimensionless)

C2 = Constant intercept for lnS* vs Xsoap linear trend (dimensionless)

Cc = Characteristic curvature of surfactant (dimensionless)

D1 = Constant slope for 1/σ* vs Xsoap linear trend (dimensionless)

D2 = Constant intercept for 1/σ* vs Xsoap linear trend (dimensionless)

EACN = Equivalent alkane carbon number (EACN unit)

f(A) = Function of alcohol type and concentration (dimensionless)

Ha = Average curvature (Å-1)

Hen = Net curvature (Å-1)

HLD = Hydrophilic lipophilic difference (dimensionless)

K = Slope of logarithm of optimum salinity as a function of EACN (per EACN unit)

viii

L = Surfactant length parameter (Å)

Lc = Maximum chain length of surfactant tail (Å)

nc = Effective number of carbon atoms in the tail of the surfactant

P = Pressure (bars)

RI = Radius of component i in the microemulsion (Å)

R = Universal gas constant (J mol-1 K-1 )

S = Salinity (g/100ml)

SAD = Surfactant affinity difference (J mol-1)

T = Temperature (°C or K)

Vi = Volume of component i (cm3)

Xi = HLD variable (mnemonic)

xi = Fraction of total system composition of surfactant in phase i.(dimensionless)

Xsoap = Soap mole fraction

Surfactant = Surfactant mole fraction

Greek

α = Temperature coefficient (°C -1 or K-1 )

β = Pressure coefficient (bar-1)

σ = Solubilization ratio (dimensionless)

ϕi = Fraction of component i in the microemulsion (dimensionless)

µi = Chemical potential of surfactant in phase i (J mol-1)

µi* = Reference state chemical potential of surfactant in phase i (J mol-1)

ξ = Correlation length (Å)

ξ* = Critical correlation length (Å)

χ = Overall composition parameter (dimensionless)

ix

Subscripts

U = Upper limit corresponding to a phase transition from type III to type II+ or vice

versa

L = Lower limit corresponding to a phase transition from type II- to type III or vice

versa

o = Oil

w = Water

s = Surfactant

ref = Reference state

Superscripts

* = Optimum state unless mentioned otherwise.

0 = Initial condition

x

List of Figures

Figure 1-1 : Schematic of forces acting (in dynes or N) on unit length (e.g. 1 cm or m) on

an interface. The force per unit length is the interfacial tension (dynes/cm or N/m). ..... 13

Figure 1-2: Oil droplet with radius R suspended in water, separated from the oil bulk

phase. Adapted from Acosta et al. (2003). ....................................................................... 13

Figure 1-3: Interaction energies in the C-layer that govern the R-ratio. Adapted from

Bourrel and Schechter (2010). ......................................................................................... 14

Figure 1-4: Schematic of microemulsion formation. Adapted from Tadros (2006). ............... 14

Figure 1-5: Pseudo ternary diagram of a type II- system. (Lake et al., 2014) ......................... 15

Figure 1-6: Pseudo ternary diagram of a type II+ system. (Lake et al., 2014) ........................ 15

Figure 1-7: Pseudo ternary diagram of a type III system. (Lake et al., 2014) ......................... 16

Figure 2-1: Flowchart showing the protocol followed for the HLD-NAC model described

by Acosta et al. (2003). .................................................................................................... 38

Figure 3-1: Optimum salinity as a function of pressure for experiments reported for the

SAS surfactant (Skauge and Fotland 1990). The slope is the β factor for the HLD

equation. ........................................................................................................................... 68

Figure 3-2: Optimum salinity as a function of pressure for experiments reported for the

SDBS surfactant (Skauge and Fotland 1990). The slope is the β factor for the HLD

equation. ........................................................................................................................... 68

Figure 3-3: A schematic showing the trend lines for the optimum salinity, and the upper

and lower salinity limits. The width of the three-phase Winsor III region is shown. ..... 68

Figure 3-4: Reciprocal of optimum solubilization ratios as a function of logarithm of

optimum salinity. Red, green and blue represent data at 20°C, 50°C and 90°C

respectively. Oils used were heptane, octane and decane. B1 = 0.15 and B2 =-0.22.

Data from Sun et al. (2012). ............................................................................................. 68

Figure 3-5: Flowchart of the modified HLD-NAC Equation-of-State. .................................... 69

Figure 3-6: Phase volume fractions after tuning as a function of salinity for the SAS

surfactant. The value for interfacial area per molecule after tuning was 180 Å2. Data

from Skauge and Fotland (1990)...................................................................................... 70

xi

Figure 3-7: Phase volume fractions after tuning as a function of salinity for the SDBS

surfactant. The value of interfacial area per molecule after tuning was 97 Å2. Data

from Skauge and Fotland (1990)...................................................................................... 70

Figure 3-8: Logarithm of optimum salinity as a function of EACN for experiments

reported for SAS surfactant. The slope of the trend line gives the slope K for the

HLD equation. Data obtained from Skauge and Fotland (1990). ..................................... 70

Figure 3-9: Logarithm of optimum salinity as a function of EACN for experiments

reported for SDBS surfactant. The slope of the trend line gives the slope K for the


Figure 3-10: Logarithm of optimum salinity as a function of reciprocal of optimum

solubilization ratio for experiments reported for SAS surfactant from the EACN

trend. B1 = 0.24 and B2 = -0.24. Data obtained from Skauge and Fotland (1990). .......... 71


solubilization ratio for experiments reported for SDBS surfactant from the EACN

trend. B1 = 0.18 and B2 = -0.02. Data obtained from Skauge and Fotland (1990). .......... 71

Figure 3-12: logarithm of optimum salinity as a function of temperature for experiments

reported for SAS surfactant. The slope of the trend line gives the α factor for the


Figure 3-13: logarithm of optimum salinity as a function of temperature for experiments

reported for SDBS surfactant. The slope of the trend line gives the α factor for the


Figure 3-14: Optimum solubilization ratio as a function of pressure for experiments

reported for SAS surfactant. The HLD equation and equation from Figure 3-10 was

used for prediction. Data obtained from Skauge and Fotland (1990). ............................. 72

Figure 3-15: Optimum solubilization ratio as a function of pressure for experiments

reported for SDBS surfactant. The HLD equation and equation from Figure 3-11 was


Figure 3-16: Optimum solubilization ratio as a function of temperature for experiments

reported for SAS surfactant. The HLD equation and equation from Figure 3-10 was


Figure 3-17: Optimum solubilization ratio as a function of temperature for experiments

reported for SDBS surfactant. The HLD equation and equation from Figure 3-11

was used for prediction. Data obtained from Skauge and Fotland (1990) ....................... 72

Figure 3-18: Tuned result for solubilization ratios as a function of salinity for octane. Red

represents oil solubilization ratios. Blue represents water solubilization ratios. The

solid lines are model results from HLD-NAC obtained by tuning as. .............................. 73

xii

Figure 3-19: Tuned result for solubilization ratios as a function of salinity for decane.

Red represents oil solubilization ratios. Blue represents water solubilization ratios.

The solid lines are model results from HLD-NAC obtained by tuning as. ...................... 73

Figure 3-20: Tuned result for solubilization ratios as a function of salinity for dodecane.

Red represents oil solubilization ratios. Blue represents water solubilization ratios.

The solid lines are model results from HLD-NAC obtained by tuning as. ...................... 73

Figure 3-21: logarithm of optimum salinity as a function of EACN. A mixture of tridecyl

alcohol propoxylate and C13-C18 internal olefin sulfonate was used along with iso-

propanol as cosurfactant. Data obtained from Roshanfekr et al. (2011). ......................... 73


solubilization ratio from experiments with varying EACN. B1 = 0.08 and B2 = 0.02.

Data obtained from Roshanfekr et al. (2011). .................................................................. 74

Figure 3-23: Prediction of phase behavior for dead oil at elevated pressure (68.95 bars)

using data from pure alkane series and estimated β factor of 7.71×10-4/bar. Red

represents oil solubilization ratios. Blue represents water solubilization ratios. .............. 74

Figure 3-24: Prediction of phase behavior for dead oil at atmospheric pressure using data

from pure alkane series. Red represents oil solubilization ratios. Blue represents

water solubilization ratios. The solid lines are model results from HLD-NAC. .............. 74

Figure 3-25: Prediction of phase behavior for live oil at high pressure using estimated β

factor of 7.71×10-4/bar. Red represents oil solubilization ratios. Blue represents

water solubilization ratios. The solid lines are model results from HLD-NAC. .............. 74

Figure 3-26: Phase volume fractions as a function of salinity using 0.5 wt. % dodecyl

orthoxylene sulfonate. The tuned as value was 98 Å2. Solid lines represent model

outputs with tuned alpha values. Circles represent experimentally obtained values.

Blue represents ................................................................................................................. 75

Figure 3-27: Comparison of tuned result (solid lines) and actual values (circles) for dead

oil temperature scan at 50 bars. Red represents oil solubilization. Blue represents

water solubilization. Data from Austad and Strand (1996). ............................................. 75










xiii







Figure 3-33: Comparison of tuned result (solid lines) and actual values (circles) for live

























oil pressure scan at 55°C. Red represents oil solubilization. Blue represents water

solubilization. Data from Austad and Strand (1996). ....................................................... 78




xiv




























Figure 3-52: Variation of α with increasing pressure. Blue squares represent tuned α

values for dead oil. Red squares represent tuned α values for the live oil. Data

obtained by analysis of experimental results reported by Austad and Strand (1996). ..... 81

Figure 3-53: Variation of β with increasing temperature. Blue squares represent tuned β

values for dead oil. Red squares represent tuned β values for the live oil. Data

obtained by analysis of experimental results reported by Austad and Strand (1996). ..... 81

Figure 3-54: linear correlation of the optimum solubilization ratio inverse of the three-

phase region width and the inverse of the three-phase region width. The points

represent results from both live and dead oil at all pressures and temperatures

reported. A1 = 2.54 and A2 = 4.28. Data obtained by analysis of experimental

results reported by Austad and Strand (1996). ................................................................. 82

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Figure 3-55: A schematic showing the shifts in optimum salinity trend line due to

pressure. The shifts in the intercepts are caused by the β factor and the difference

between the pressure of interest and the reference pressure. The black dot shows the

optimum salinity at the reference condition. The green circles show the correct

interpretation of the shift due to pressure. The red circles show the incorrect

interpretation made in Jang et al. (2014). ......................................................................... 82

Figure 4-1: Linear relationship between the number of carbon atoms in the alkyl group of

a carboxylic acid and pKd for water-heptane systems. Data obtained from Smith &

Tanford (1973). ................................................................................................................ 101

Figure 4-2: Linear relationship between mole fraction of soap formed and log of optimum

salinity (in meq/ml) for Case A. Value of n used was 13. Data obtained from

Mohammadi (2008). ......................................................................................................... 101

Figure 4-3: Linear relationship between mole fraction of soap formed and inverse of

optimum solubilization ratio in cc/cc for Case A. Value of n used was 13. Data

obtained from Mohammadi (2008). ................................................................................. 101

Figure 4-4 Match of tuned HLD-NAC model (solid lines) for Case A at 50% oil overall

concentration (v/v). Red represents σo while blue represents σw. The tuned value of

asurf was 195 Å2. Circles are experimental data and dashed lines show UTCHEM

output reported by Mohammadi (2008). .......................................................................... 101

Figure 4-5: Match of tuned HLD-NAC (solid lines) model for Case A at 30 % oil overall

concentration (v/v). Red represents σo while blue represents σw. The tuned value of

asurf was 215 Å2. Circles are experimental data and dashed lines show UTCHEM

output reported by Mohammadi (2008). .......................................................................... 102

Figure 4-6: Prediction of solubility ratios using tuned HLD-NAC model for Case A at

10 % oil overall concentration (v/v). Red represents σo while blue represents σw. The

value of asurf used was 205 Å2. The green circle represents the optimum

experimentally measured by Mohammadi (2008). This point was used in tuning. ......... 102

Figure 4-7: Prediction of solubility ratios using tuned HLD-NAC model for Case A at

20 % oil overall concentration (v/v). Red represents σo while blue represents σw. The

value of asurf used was 205 Å2. The green circle represents the optimum

experimentally measured by Mohammadi (2008). This point was used in tuning. ......... 102

Figure 4-8: Prediction of solubility ratios for tuned HLD-NAC model for Case A at 40 %

oil overall concentration (v/v). Red represents σo while blue represents σw. The value

of asurf used was 205 Å2. The green circle represents the optimum experimentally

measured by Mohammadi (2008). This point was used in tuning. .................................. 102

Figure 4-9: Phase volume fraction diagram based on flash calculations for 10 % oil

concentration for Case A. Each bar represents a fixed sodium carbonate

concentration. Red represents excess oil phase, blue excess brine, and green the

microemulsion phase. ....................................................................................................... 103

xvi

Figure 4-10: Phase volume fraction diagram based on flash calculations for 40 % oil

concentration in Case A. Each bar represents a fixed sodium carbonate

concentration. Red represents excess oil phase, blue excess brine, and green the

microemulsion phase. ....................................................................................................... 103

Figure 4-11: Activity map for Case A. Solid lines represent prediction from the model

used in this dissertation. Green represents type II-, red type III and blue type II+

regions found experimentally. The dashed lines show the three-phase window used

in the UTCHEM model by Mohammadi et al. (2009). .................................................... 103

Figure 4-12: Linear relationship between mole fraction of soap formed and log of

optimum salinity (in meq/ml) for Case B. Value of n used was 14. Data obtained

from Mohammadi (2008). ................................................................................................ 103

Figure 4-13: Linear relationship between mole fraction of soap formed and inverse of

optimum solubilization ratio in cc/cc for Case B. Value of n used was 14. Data

obtained from Mohammadi (2008). ................................................................................. 104

Figure 4-14 Match of tuned HLD-NAC model (solid lines) for Case B at 30 % oil overall

concentration (v/v) and 0.3 wt.% surfactant concentration. Red represents σo while

blue represents σw. The tuned value of asurf was 16 Å2. Circles are experimental data

and dashed lines show UTCHEM output reported by Mohammadi (2008). .................... 104

Figure 4-15: Match of tuned HLD-NAC model (solid lines) for Case B at 50 % oil overall

concentration (v/v) and 0.3 wt.% surfactant concentration. Red represents σo while

blue represents σw. The tuned value of asurf was 45 Å2. Circles are experimental data

and dashed lines show UTCHEM output reported by Mohammadi (2008). .................... 104

Figure 4-16: Prediction of tuned HLD-NAC model (solid lines) for Case B at 30 % oil

overall concentration (v/v) and 0.6 wt.% surfactant concentration. Red represents σo

while blue represents σw. Circles are experimental data and dashed lines show

UTCHEM output reported by Mohammadi (2008). ........................................................ 104


overall concentration (v/v) and 0.6 wt.% surfactant concentration. Red represents σo




overall concentration (v/v) and 1 wt.% surfactant concentration. Red represents σo



Figure 4-19: Phase volume fraction diagram based on flash calculation results for Case B

at 30 % oil overall concentration (v/v) and 0.6 wt.% surfactant concentration. Each

bar represents a sodium carbonate concentration. Red represents excess oil phase,

blue represents excess brine, and green represents microemulsion phase. ...................... 105

xvii

Figure 4-20: Phase volume fraction diagram based on flash calculation results for Case B

at 50 % oil overall concentration (v/v) and 1 wt.% surfactant concentration. Each

bar represents a sodium carbonate concentration. Red represents excess oil phase,

blue represents excess brine, and green represents microemulsion phase. ...................... 105

Figure 4-21: Activity map for Case B with 0.3 wt.% surfactant. Solid lines represent

prediction from the model used in this dissertation. Green represents type II-, red

type III and blue type II+ regions found experimentally. The dashed lines show the

window used in the UTCHEM model by Mohammadi (2008). ....................................... 106

Figure 4-22: Activity map for Case B with 0.6 wt.% surfactant. Solid lines represent




Figure 4-23: Activity map for Case B with 1 wt.% surfactant. Solid lines represent




Figure 4-24: Example of a fish diagram showing types of microemulsions with no alkali

for a pure surfactant. Only Nalco concentration in brine is varied. Model parameters

were obtained from Case A. Red shows the upper salinity limit and blue the lower

salinity limit. Dashed line shows the optima. .................................................................. 106

Figure 4-25: Fish diagrams using model parameters obtained from Case A. Red shows

the upper salinity limit and blue the lower salinity limit. Solid lines show the fish

diagram with 1.0 wt.% Na2CO3 and dashed lines show fish diagram in absence of

alkali. ................................................................................................................................ 107

Figure 4-26: Fish diagrams using model parameters obtained from Case B. Red shows the

upper salinity limit and blue the lower salinity limit. Solid lines show the fish

diagram with 1.0 wt.% Na2CO3 (fixed) and Nalco concentration varying. Dashed

lines show the fish diagram in absence of alkali. ............................................................. 107

Figure 4-27: Fish diagram using model parameters tuned for Case A. Red shows the


diagram with Na2CO3 concentration varying (brine concentration fixed). Squares

indicate experimental data from Mohammadi (2008). ..................................................... 107

Figure 4-28: Fish diagram using model parameters tuned for Case B. Red shows the


diagram with Na2CO3 concentration varying (brine concentration fixed). Squares

indicate experimental data from Mohammadi (2008). ..................................................... 107

Figure 5-1: An example showing the linear relationship between the inverse of oil

solubilization ratios and HLD for type II- microemulsions. Data obtained from

Sheng (2010). ................................................................................................................... 130

xviii

Figure 5-2: An example showing the linear relationship between the inverse of water

solubilization ratios and HLD for type II+ microemulsions. Data obtained from

Sheng (2010). ................................................................................................................... 130

Figure 5-3: An example showing the linear relationship between the inverse of

solubilization ratios (red for oil, blue for water) and HLD for type III

microemulsions. Data obtained from Sheng (2010). ........................................................ 130

Figure 5-4: An example showing the linear relationship between the inverse of

solubilization ratios and HLD. Red represents inverse of oil solubilization ratios.

Blue represents inverse of water solubilization ratios. (WOR=1, σ* = 13.5 cc/cc and

I-ratio = 0.129). ................................................................................................................ 131

Figure 5-5: Tuned phase behavior (solid lines) compared to data (circles) for experiments

with NaCl and SDS+SDBS+IBA surfactant mixture at 40 °C. Red represents oil

solubilization ratios. Blue represents water solubilization ratios. I-ratio = 0.21, σ* =

7.35 cc/cc and S*= 1.47 meq/ml. Oil used was heptane. .................................................. 131

Figure 5-6: Tuned phase behavior (solid lines) compared to data (circles) for experiments

with NaCl and SDS+SDBS+IBA surfactant mixture at 40 °C. Red represents oil

solubilization ratios. Blue represents water solubilization ratios. I-ratio = 0.34, σ* =

4.56 cc/cc and S*= 2.52 meq/ml. Oil used was dodecane. ............................................... 131

Figure 5-7: Tuned phase behavior (solid lines) compared reported data (circles) for

experiments with NaCl and SDS surfactant at 20 °C. Red represents oil

solubilization ratios. Blue represents water solubilization ratios. Data from (Aarra et

al., 1999) .......................................................................................................................... 132


experiments with KCl and SDS surfactant at 20 °C. Red represents oil solubilization

ratios. Blue represents water solubilization ratios. Data from (Aarra et al., 1999) .......... 132


experiments with CaCl2 and SDS surfactant at 20 °C. Red represents oil


al., 1999) .......................................................................................................................... 132


experiments with MgCl2 and SDS surfactant at 20 °C. Red represents oil


al., 1999) .......................................................................................................................... 132




al., 1999) .......................................................................................................................... 133

xix


experiments with KCl and SDS surfactant at 35 °C. Blue represents water

solubilization ratios. Data from (Aarra et al., 1999) ........................................................ 133


experiments with CaCl2 and SDS surfactant at 35 °C. Red represents oil


al., 1999) .......................................................................................................................... 133


experiments with MgCl2 and SDS surfactant at 35 °C. Red represents oil


al., 1999) .......................................................................................................................... 133




al., 1999) .......................................................................................................................... 134


experiments with KCl and SDS surfactant at 50 °C. Red represents oil solubilization



experiments with CaCl2, and SDS surfactant at 50 °C. Red represents oil


al., 1999) .......................................................................................................................... 134


experiments with MgCl2, and SDS surfactant at 50 °C. Red represents oil


al., 1999) .......................................................................................................................... 134


experiments with NaCl and AAS surfactant at 20 °C. Red represents oil


al., 1999) .......................................................................................................................... 135


experiments with KCl and AAS surfactant at 20 °C. Red represents oil solubilization



experiments with CaCl2, and AAS surfactant at 20 °C. Red represents oil


al., 1999) .......................................................................................................................... 135


experiments with MgCl2, and AAS surfactant at 20 °C. Red represents oil

xx


al., 1999) .......................................................................................................................... 135




al., 1999) .......................................................................................................................... 136







al., 1999) .......................................................................................................................... 136




al., 1999) .......................................................................................................................... 136




al., 1999) .......................................................................................................................... 137







al., 1999) .......................................................................................................................... 137




al., 1999) .......................................................................................................................... 137

Figure 5-31: Average tuned interfacial volume ratios for experiments using SDS

surfactant at 20°C (Blue), 35°C (Red), 50°C (Green). Black lines represent average

interfacial volume ratios for each salt. ............................................................................. 138

Figure 5-32: Average tuned interfacial volume ratios for experiments using AAS

surfactant at 20°C (Blue), 50°C (Red), 90°C (Green). Black lines represent average

interfacial volume ratios for each salt. ............................................................................. 138

xxi

Figure 5-33: Width of the three-phase region as a function of the optimum solubilization

ratio and the interfacial volume ratio (I) for a fixed overall concentration of

ϕo=0.495, ϕw=0.495 and ϕs=0.01. ................................................................................... 138

Figure 5-34: Example of a modified fish diagram (interfacial volume ratio (I)=0.2). Red

shows the upper salinity limit and blue the lower salinity limit. Type III

microemulsions can only exist when χ is larger than σ* and, HLD is within the upper

and lower critical limits HLDU* and HLDL

* . ................................................................... 138

Figure 5-35: Locus of the invariant type III microemulsion composition in a ternary

space. (σ*= 3 cc/cc) ......................................................................................................... 139

Figure 5-36: Locus of the invariant type III microemulsion composition in a ternary

space. (σ*= 10 cc/cc) ........................................................................................................ 139

Figure 5-37: Locus of invariant type III microemulsion composition in a ternary space

(σ*= 30 cc/cc). ................................................................................................................. 139

Figure 5-38: Inverse of oil solubilization ratios as a function of pressure at different

constant temperatures using dead oil. Data from Austad and Strand (1996) ................... 140

Figure 5-39: Inverse of water solubilization ratios as a function of pressure at different

constant temperatures using dead oil. Data from Austad and Strand (1996) ................... 140

Figure 5-40: Inverse of oil solubilization ratios as a function of pressure at different

constant temperatures using live oil. Data from Austad and Strand (1996) ..................... 140

Figure 5-41: Inverse of water solubilization ratios as a function of pressure at different

constant temperatures using live oil. Data from Austad and Strand (1996) ..................... 140

Figure 5-42: Inverse of oil solubilization ratios as a function of temperature at different

constant pressures using dead oil. Data from Austad and Strand (1996). ........................ 141

Figure 5-43: Inverse of water solubilization ratios as a function of temperature at

different constant pressures using dead oil. Data from Austad and Strand (1996). ......... 141


constant pressures using live oil. Data from Austad and Strand (1996). ......................... 141


different constant pressures using live oil. Data from Austad and Strand (1996). ........... 141

Figure 5-46: Interfacial volume ratio for a surfactant mixture (sodium laurate and sodium

oleate) as a function of laurate soap mole fraction using Eq. (5.32). ............................... 142


different constant pressures using dead oil. Data from Austad and Strand (1996). ......... 142

ZEqnNum272146

xxii


constant pressures using live oil. Data from Austad and Strand (1996). ......................... 142

Figure C-1: Schematic of readings measured from a phase behavior pipette scan. O: oil,

W: water and ME: microemulsion. Total volume capacity of each pipette is 5 ml. ........ 159

xxiii

List of Tables

Table 1-1: General classification of micelles, microemulsions and macroemulsions.

(Tadros, 2006) .................................................................................................................. 12

Table 1-2: Summary of effects of SOB system variables on microemulsion phase

behavior. ........................................................................................................................... 12

Table 3-1: Summary of prediction of optima at various temperatures for SAS surfactant.

Predictions for S* were made by taking S* at 20°C as reference and using α = 0.0031

K-1. Data obtained from Skauge and Fotland (1990). ...................................................... 63

Table 3-2: Summary of prediction of optima at various pressures for SAS surfactant.

Predictions for S* were made by taking S* at 20°C and atmospheric pressure as

reference. β is 0.0006 bar-1. Data obtained from Skauge and Fotland (1990). ................. 63

Table 3-3: Summary of prediction of optima at various temperatures for SDBS surfactant.

Predictions for S* were made by taking the S* at 20°C as reference. α is 0.0077 K-1.

Data obtained from Skauge and Fotland (1990). ............................................................. 64

Table 3-4: Summary of prediction of optima at various pressures for SDBS surfactant.

Predictions for S* were made by taking S* at 20°C and atmospheric pressure as

reference. β is 0.0008 bar-1. Data obtained from Skauge and Fotland (1990). ................. 64

Table 3-5: Summary of results obtained by matching pressure scans for dead oil. Data

obtained from Austad and Strand (1996). ........................................................................ 65

Table 3-6: Summary of results obtained by matching pressure scans for live oil. Data


Table 3-7: Summary of results obtained by matching temperature scans for dead oil. Data


Table 3-8: Summary of results obtained by matching temperature scans for live oil. Data


Table 3-9: Summary showing β values obtained from tuning. Data from Skauge and

Fotland (1990), Roshanfekr and Johns (2011) and Austad and Strand (1996). ............... 67

Table 4-1: : Summary of optima for experiments for crude oil case A. Data from

Mohammadi, (2008). ........................................................................................................ 99

Table 4-2: : Summary of model parameters for Case A. ......................................................... 99

xxiv

Table 4-3: Summary of optima for experiments for crude oil case B. Data from

Mohammadi, (2008). ........................................................................................................ 100

Table 4-4: Summary of model parameters for Case B. ............................................................ 100

Table 5-1: Summary of optima and tuned interfacial volume ratio (I) for experiments

using SDS surfactant reported by Aarra et al. (1999) ...................................................... 126

Table 5-2: Summary of optima and tuned interfacial volume ratio (I) for experiments

using AAS surfactant reported by Aarra et al. (1999) ...................................................... 127

Table 5-3: Summary of interfacial volume ratio at different temperatures from analysis of

pressure scans reported by Austad and Strand (1996). .................................................... 128

Table 5-4: Summary of interfacial volume ratio at different pressures from analysis of

temperature scans reported by Austad and Strand (1996). ............................................... 128

Table 5-5: Statistical summary of interfacial volume ratio data obtained from pressure

and temperature scans reported by Austad and Strand (1996). ........................................ 129

Table C-1: Summary of observations and calculations in a salinity scan. Total volume

capacity of each pipette is 5 ml. ....................................................................................... 158

xxv

Acknowledgements

I would like to thank my advisor Prof. Russell T. Johns for the support and guidance I received

from him during the course of this research. His insightful questions and perseverance helped

expand this research and make it impactful. He has constantly shown faith in my ability and has

encouraged me to excel in both academic and professional environments. I have learned a lot

from him and it has been an honor to have him as my PhD mentor.

I would also like to thank the rest of my committee, Prof. Luis Ayala, Prof. Zuleima

Karpyn, and Prof. Andrew Belmonte. Their insightful comments and critique helped me to

significantly improve my research. Special thanks to Prof. Turgay Ertekin for his guidance, which

provided me with much needed direction at the nascent stages of my graduate school experience.

Special thanks to my friends Sarath Ketineni, Taha Husain and Vaibhav Rajput for the

stimulating discussions, for the sleepless nights we were working together before deadlines, and

for all the fun we have had in the last four years. Victor Torrealba, Pooya Khodaparast, Bahareh

Nojabaei, Liwei Li and Saeid Khorsandi ensured that the office we shared was full of life. I thank

them for their camaraderie. Special thanks to Atriya Ghosh, Phani Kiran, Manasi Kamat and

Sagnik Ray Choudhury for their support.

I am grateful to Sophany Thach for gifting me Bourrel and Schechter’s book

“Microemulsions and related systems: formulation, solvency, and physical properties.” It was a

gift that proved to be crucial in the development of this research. I also thank Adwait Chawathe

for being a strong moral support. I greatly acknowledge the members of the EOR industry

affiliates program at PennState and the US Department of Energy for their financial support.

Last but not least; I thank my family; my parents and my brother, for believing in

me. The unconditional love from my family has been a pillar of strength for me

xxvi

throughout my life. This dissertation would not have been possible without their

encouragement.

1

Chapter 1

Introduction

Capillary forces resist viscous forces during a waterflood, which causes significant trapping of oil

in pores. Trapping occurs at a small capillary number, where the capillary number is defined as

the ratio of viscous forces to capillary forces. One form of the capillary number is

/

w

c

o w

µ qN

. (1.1)

An increase in capillary number reduces the residual oil saturation (Foster, 1973).

Viscous forces must overcome capillary forces to improve oil recovery (Healy and Reed, 1977).

Enhanced oil recovery processes involving surfactants aims at achieving high capillary number

by reducing the oil and water interfacial tension (γo/w) to ultra-low values. Viscous forces are also

increased by using water-soluble polymers, which increases the viscosity of drive water (µw).

Typical capillary numbers using Eq. (1.1) are on the order of 10-6 during a waterflood.

Estimates for Berea sandstone showed that in order to recover 50% of the residual oil after a

waterflood, the capillary number must increase by three orders of magnitude to about 10-3 (Foster,

1973). Typical oil-brine interfacial tensions lie in the range of 20-30 dynes/cm. Thus ultra-low

interfacial tensions (less than 10 -3 dynes/cm) are desirable.

Surfactants are compounds that have an ability to seek an interface between two

immiscible fluids and alter the interfacial tension. The phases formed due to the presence of

surfactants in the system and the degree of interfacial tension alteration is critical to enhanced oil

recovery.

2

1.1. Surfactants and Interfacial Tensions

Surfactants contain polar groups (known as “heads”) and non-polar groups (known as “tails”).

The head groups attract polar molecules like water and are hence are known as hydrophiles. Due

to polarity, heads have a tendency to repel non-polar molecules (in oils or lipids) and hence are

also known as “lipophobes”. The hydrophilic head may be negatively charged (anionics),

positively charged (cationics) or neutral (non-ionics). Anionic surfactants are most effective for

IFT reduction as they are less expensive and have smaller retention/adsorption on negatively

charged surfaces like sandstones. The tail groups mostly consist of hydrocarbon chains that have

an affinity towards non-polar molecules in oils. Tails are thus known as “lipophiles”.

Consequently, lipophiles repel polar molecules in an aqueous phase and are hence also known as

“hydrophobes.”

The word “surfactant” comes from the term “surface active agent.” As defined by Rosen

(2004), a surfactant is “a substance that, when present at low concentration in a system, has the

property of adsorbing onto surfaces or interfaces of a system and of altering to a marked degree

the surface or interfacial free energies of those surfaces (or interfaces).” An interface is the

boundary separating two different phases. An interface may form between an insoluble solid and

a liquid as occurs in rock and fluid systems. An interface may also form between two immiscible

liquids (microemulsion phase behavior). Interface formation between a liquid and an insoluble

gas occurs in foams. Interfacial free energy is defined as the minimum work Wmin required to

create an interface with area A. Interfacial tension is defined as the interfacial free energy per unit

area. Hence, for an oil-water interface, when an incremental area of ΔA is created,

min /o wW A . (1.2)

3

From Eq. (1.2), it is evident that interfacial tensions will have units of force per unit length and

are commonly reported in N/m or dynes/cm.

Now consider an oil-water interface that is planar (ignoring curvature). The equal and

opposite force experienced by a line of unit length on such an interface is the force (see Figure

1-1) that contributes to the interfacial tension.

Oil may also be suspended in aqueous solution as a droplet with radius R. Such a

simplification (see Figure 1-2) was considered by Acosta et al. (2003). The oil has a molar

volume of vo. The interfacial energy of such a spherical interface would hence be

2

/4excess o wG R . (1.3)

The chemical potential change associated with transfer of an oil molecule from the bulk phase b

to the droplet d is obtained by averaging the excess free energy per mole of oil present in the

droplet. Hence,

2

/ /, , 3

4 3

4 / 3 (1/ )

o w o w oo d o b

o

R v

R v R

. (1.4)

Therefore, from Eq. (1.3) in order to determine interfacial tensions (IFT), the excess free energy

at the interface must be known. Also, the radius of the solubilized oil droplet (oil in water

micelle) is an important factor as shown in Eq. (1.4).

1.2. Winsor’s R-Ratio and the C-Layer

Winsor (1954) was the first to explain the R-ratio. Surfactants seek the oil-water interface.

Therefore, in a surfactant-oil-water system, three distinct regions exist: an aqueous region (W), a

4

non-polar oleic region (O) and an amphiphilic or bridging region (C). The interfacial zone (C) has

a definite composition separating the oil and water bulk phases (Bourrel and Schechter, 2010).

This interfacial region, also known as the C-layer, has a defined thickness. In addition to

amphiphiles (surfactants), the C-layer also contains some oil and water molecules and also co-

solvents such as short-chain alcohols. The interaction energies between the molecules in the C-

layer determines its stability.

Consider surfactant in the C-layer (see Figure 1-3) that contains hydrophiles “H” and

lipophiles “L”. The interaction energy between molecules is represented as “A”. The interaction

between oil molecules and the C-layer (ACO) is contributed by both H and L. Hence,

CO LCO HCOA A A . (1.5)

Similarly, the interaction between water molecules and the C-layer is contributed by both H and L

such that,

CW LCW HCWA A A . (1.6)

Interaction energy amongst oil molecules is represented by AOO and, amongst water

molecules by AWW. Interaction energy between hydrophobes is represented by ALL and, between

hydrophiles, by AHH. The R-ratio is then defined as,

CO OO LL

CW WW HH

A A AR ratio

A A A

. (1.7)

5

As interaction between the amphiphile and the oil molecules (ACO) increases, the

surfactant shows greater affinity to the oleic phase. This results in an R-ratio greater than one and

the surfactant becomes increasingly oil soluble. The converse is true for ACW. As ACW increases,

the R-ratio becomes less than unity and the affinity of the surfactant towards the water phase

increases. For an R-ratio equal to unity, the surfactant has equal affinities towards the oil and

water regions. This occurs at optimum conditions, which is explained in more detail in the next

section. In practice, interaction energies at the molecular level cannot be calculated from phase

behavior experiments.

1.3. Effect of Salinity on R-Ratio

Anionic surfactants have an ionic head that attracts counter ions. Addition of salt (like NaCl)

produces more counter-ions (Na+) in the aqueous phase. Anionic surfactants are typically

available as sodium (or potassium) salts. For an undissociated surfactant salt molecule, charge on

the hydrophile is neutralized by the metallic counter-ion and so the ionic character of the

molecule is reduced. Therefore, undissociated surfactant salts are oil soluble. Dissociated

anionic surfactants in aqueous solutions have negatively charged head groups. The ionic nature

of dissociated anionic surfactants makes them water soluble. An increase in salinity results in a

greater number of counter-ions (cations) in the aqueous solution resulting in a decrease of the

anionic surfactants’ degree of ionization. Thus, an increase in salinity in the aqueous phase

typically decreases the water solubility of anionic surfactants. From an R-ratio perspective, the

counter-ion neutralizes the hydrophile, which decreases the interaction of the C-layer with water.

Hence, the R-ratio increases with salinity, which gives an increase in the surfactant’s affinity to

the oleic phase.

6

1.4. Microemulsions

Microemulsions are homogeneous solutions consisting of surfactant, oil and brine (SOB).

The term “microemulsion” was first introduced by Hoar and Schulman (1943) who found that by

titration of a milky emulsion containing potassium oleate (a soap) with a medium-chain alcohol

(pentanol or hexanol), a stable oil-in-water emulsion was produced. The components did not

separate on settling. The emulsions produced were transparent or translucent. Winsor (1948)

later described microemulsions as “swollen micellar solutions.” Broadly, micelles (surfactant

aggregates in aqueous solution), macroemulsions (or simple emulsions), and microemulsions

(also known as micellar solutions) can be categorized by their dimensions (Tadros, 2006).

Table 1-1 shows a summary of the classifications.

Tadros (2006) further explained that microemulsion classifications solely based on size

or appearance is not adequate. He defined thermodynamic criteria for formation of

microemulsions by considering a system as shown in Figure 1-4. Consider oil being introduced

into an aqueous phase. A1 is the interfacial area of the oil bulk phase. A2 is the total interfacial

area of the dispersed oil droplets. Interfacial area increases as an emulsion is formed. Hence, the

surface free energy increases (from Eq. (1.2)) by γ (A1-A2). Formation of an oil dispersion

introduces a large number of oil droplets in the system. The degree of randomness therefore

increases and so does the entropy of the system. From the second law of thermodynamics, the

free energy of emulsion formation (ΔGm) is,

mG A T S . (1.8)

The magnitude of the free energy of emulsion formation determines if the resulting mixture will

form a macroemulsion or a microemulsion.

7

In macroemulsions, interfacial tensions are not low enough. Therefore, γ ΔA is larger

than TΔS. This results in a positive ΔGm. Hence macroemulsion formation is not a spontaneous

process. External energy (agitation or mixing) is required in order to facilitate such processes.

In microemulsions, the interfacial tensions are desired to be ultra-low. Such low

interfacial tensions result in γ ΔA being smaller than TΔS. Therefore ΔGm is negative, which

implies microemulsions are formed spontaneously and are thermodynamically stable.

In summary, macroemulsions and microemulsions can be differentiated on the basis of

thermodynamics. Reduction of residual oil saturation requires ultra-low interfacial tensions as

discussed and hence microemulsions are important in EOR applications. As a consequence,

microemulsions are the subject of interest in this dissertation.

1.5. Types of Microemulsions in Surfactant-Oil-Brine (SOB) systems and

their significance in EOR

The salinity of the aqueous phase affects the R-ratio and thus the microemulsion phase behavior.

The phase behavior observed in surfactant-oil-brine systems were first described by Winsor

(1948). Healy et al. (1976) and Nelson and Pope (1978) who applied Winsor’s characterization to

specific EOR chemicals. The phase behavior is expressed using ternary diagrams in which the oil,

brine and surfactant/cosurfactant mixture are treated as three pseudo-components. The formation

of different microemulsion systems at different salinities has been well represented schematically

using ternary diagrams by Lake et al. (2014).

At low salinities, the anionic surfactant has good water solubility. Thus, the system will

exhibit two phases: an excess oil phase, which is assumed to be pure oil component and a water-

external (with respect to the micelle) microemulsion. This microemulsion has brine, surfactant

and a low amount of solubilized oil. Microemulsions of this type are classified type II- (system

8

has two-phases with ternary tie lines having a negative slope). They are also referred to as lower-

phase microemulsion as the microemulsion phase settles below the excess oil phase at

equilibrium.

At high salinities, the anionic surfactant prefers the oil phase. The system again exhibits

two-phases: an oil-external microemulsion and an excess brine phase. The microemulsion phase

consists of oil, surfactant and a low amount of solubilized oil. Microemulsions of this type are

classified as type II+ (system has two phases with ternary tie lines having positive slopes). They

are also referred to as upper phase microemulsions since (being less dense) they form above the

excess brine phase.

As salinity is increased, the system moves from a type II- to a type II+ microemulsion

system. However the transition typically takes place through a third system at intermediate

salinities. The system here exhibits three-phases: excess oil, excess brine and a microemulsion,

which contains surfactant, solubilized oil and, solubilized water. Microemulsions of this type are

classified as type III (system has three-phases). They are also referred to as middle-phase

microemulsions. The composition of this microemulsion is invariant at a particular salinity within

the tie triangle according to the Gibbs phase rule as explained by Bourrel and Schechter (2010).

There are two interfacial tensions under consideration in this type of system (γ o/m and γ m/w).

Optimal salinities and optimal solubilization ratios relevant to surfactant flooding are encountered

in this region making this system particularly important.

Irrespective of the brine salinity, a single phase may form at high surfactant

concentrations. The single phase formed is known as a type IV microemulsion. Type IV

microemulsions are typically encountered in EOR processes. However, type IV microemulsions

are of importance in other chemical engineering applications. This thesis will discuss the criteria

that lead to formation of single phase systems.

9

In an ideal surfactant flooding process at optimum conditions, an excess oil bank forms in

front of the microemulsion slug as injection continues, which in turn is followed by a polymer

drive. Since all three-phases are immiscible, it is desirable for the microemulsion slug to

effectively displace oil at the front while the microemulsion itself (which contains oil) is

effectively displaced by brine (Healy and Reed, 1977). Minimal trapping of the oil or

microemulsion phase is desirable. Thus, a condition where interfacial tensions (IFT) γo/m and γm/w

are both ultra-low and equal is required and the salinity at which this occurs is known as optimum

salinity (denoted henceforth as S*).

Consequently, from Eq. (1.9) when the water and oil solubilization ratios are equal to

each other, the minimum optimal IFT is reached. Phase behavior experiments known as salinity

scans are done to obtain these solubilization ratios.

Equation (1.2) shows the relationship of excess free energies to interfacial tensions.

However, excess free energies are difficult to measure and hence interfacial tensions are

determined by using tensiometers. Alternatively, interfacial tensions can be easily calculated

from solubilization ratios by using Huh’s correlation (Huh 1979). Huh’s equation replaced the

need for cumbersome IFT measurements. Solubilization ratios can be obtained from phase

behavior scans. Solubilization ratio of a component i (σi) is defined as the ratio of the volume of

component i solubilized to the volume of surfactant in the microemulsion (m) phase. Hence,

/ 2i m

i

c

(1.9)

where c is a constant specific to a surfactant, typically around 0.3 and,

σ ( / )i i msV V . (1.10)

10

Component i can be oil (o) or water (w). The microemulsion phase and its types are explained in

the next section.

1.6. Research Goals

The objectives of this research are to:

1. Develop a novel, physically-based equation-of-state (EOS) to predict Winsor II-, II+,

and III microemulsion phase behavior at different pressures, temperatures, oil

compositions and overall compositions.

2. Extend the model to phase behavior with acidic oils in presence of alkali by

understanding soap formation mechanisms in such systems.

3. Identify key dimensionless groups that affect microemulsion phase behavior and to

analyze the impact of such groups.

1.7. Organization of the Dissertation

Chapter 1 gives a brief review of microemulsion phase behavior considerations that are important

when designing an effective EOR flood. Chapter 2 reviews the literature on the key concepts of

hydrophilic lipophilic difference (HLD) and net-average curvature (NAC) theory. Both are

important tools to predict microemulsion phase behavior. The effects of salinity, temperature,

pressure, solution gas and alkali content on phase behavior are explained. This dissertation

extends the HLD-NACs capabilities to fulfill the research objectives.

Chapter 3 presents a new HLD-NAC based equation-of-state approach to predict

surfactant-oil-brine (SOB) phase behavior for live oil at reservoir pressure and temperature. The

11

approach brings in a new pressure dependency to the HLD equation. Key empirical relationships

between lnS* and 1/σ* are developed. Experimental data from available literature are analyzed.

Chapter 4 presents a modified HLD-NAC equation of state to predict alkali-surfactant-

oil-brine phase behavior. The model developed in Chapter 3 is coupled with a pH dependent

soap formation model. A relationship between the soap to surfactant mole fraction ratio,

optimum salinity and optimum solubilization ratio is established. The model is then validated

using published data and experimental results.

Chapter 5 develops a dimensionless solution to microemulsion phase behavior. The net

and average curvature equations are used to develop a set of dimensionless equations. This

results in identification of key dimensionless groups that impact microemulsion phase behavior.

Chapter 6 summarizes the important contributions of this research. It contains overview

of this research, results, conclusions, and recommendations for future research.

12

Type

Radius in nm

Appearance

Micelles

(surfactant aggregates in

aqueous solutions)

< 5 Scatter little light, transparent

Microemulsions / Micellar

Solutions 5-50

5-10 nm: Transparent

10-50 nm: Translucent

Macroemulsions >50 Opaque or Milky

Table 1-1: General classification of micelles, microemulsions and macroemulsions. (Tadros,

2006)

Increasing Variable

Oil Solubility of

Surfactant

Water Solubility of

Surfactant

Phase Behavior

Change

Salinity Increases Decreases Towards type II+

Oil EACN Decreases Increases Towards type II-

Temperature

Decreases for

anionics

Increases for

nonionics

Increases for

anionics

Decreases for

nonionics

Towards type II-

Towards type II+

Pressure Decreases Increases Towards type II-

Solution Gas Content

(Addition of lower EACN

volatile components at

constant pressure in under

saturated oils)

Increases Decreases

Towards type II+

Table 1-2: Summary of effects of SOB system variables on microemulsion phase behavior.

13

Figure 1-1 : Schematic of forces acting (in dynes or N) on unit length (e.g. 1 cm or m) on an

interface. The force per unit length is the interfacial tension (dynes/cm or N/m).

Figure 1-2: Oil droplet with radius R suspended in water, separated from the oil bulk

phase. Adapted from Acosta et al. (2003).

F F

Top View

of an

interface

14

Figure 1-3: Interaction energies in the C-layer that govern the R-ratio. Adapted from

Bourrel and Schechter (2010).

Figure 1-4: Schematic of microemulsion formation. Adapted from Tadros (2006).

A1 A

2

γ γ

Initial condition Dispersion

15

Figure 1-5: Pseudo ternary diagram of a type II- system. (Lake et al., 2014)

Figure 1-6: Pseudo ternary diagram of a type II+ system. (Lake et al., 2014)

16

Figure 1-7: Pseudo ternary diagram of a type III system. (Lake et al., 2014)

17

Chapter 2

Literature Review

This chapter consists of a detailed literature survey that explains the basic concepts presented in

this dissertation. First, the equivalent alkane carbon number and its impact on microemulsion

phase behavior is discussed. Then, a review of temperature, pressure and alkali effects on

surfactant-oil-brine (SOB) is presented. The concept of surfactant affinity difference (SAD) along

with the dimensionless form of SAD, the hydrophilic lipophilic difference (HLD) is discussed.

Finally, net and average curvature equations are given, which relate micelle curvatures in

solubilized microemulsion systems as a function of the state variable HLD.

2.1. The Equivalent Alkane Carbon Number and its Relevance to

Microemulsion Phase Behavior

One of the first concepts developed for characterizing the oil phase and matching it with a

preferred surfactant is equivalent alkane carbon number (EACN). Crude oils are complex

mixtures of various hydrocarbon species and thus are not easy to characterize. The EACN

provides a way to characterize a complex fluid (like oil) by using just one parameter. Oils with

the same EACN should have the same phase behavior (at the same state conditions) if all

components partition equally.

Cayias et al. (1977) first studied oils with different EACNs using petroleum sulfonates.

The aqueous phase used had constant salinity (1 wt.% NaCl) and a constant surfactant

concentration of 0.2 wt.%. Hydrocarbons from three homologous series; alkanes, alkyl benzenes

and alkyl cyclohexanes were used. Interfacial tensions between the aqueous solution and oil

consisting each of hydrocarbons from these homologous series were then plotted against

increasing alkyl chain carbon number. An interfacial tension minimum was observed for an alkyl

18

chain carbon number of eight in all cases except for the alkyl cyclohexanes, which showed a

minimum at four. Since the alkane and alkyl benzene curves showed the minimum at the same

point, it was concluded that the aromatic character of a molecule played no role in phase behavior

for their system. It was also concluded that since the cyclohexanes produced a minimum at four,

the cyclohexane ring mimics a carbon chain with four carbon atoms. The following empirical

rule was developed for calculating EACN and is still widely used today (Solairaj, 2011),

– 2 – 4 / 3C R DBEACN N N N , (2.1)

where NC is the number of carbon atoms in the molecule, NR is the number of rings in the

molecule and NDB is the number of double bonds in the molecule.

Cash et al. (1977) used the empirical equation successfully to calculate EACNs of binary

mixtures. He found that the EACN followed a mole-fraction weighted formula for mixtures such

that,

avg i i

i

EACN EACN X . (2.2)

where EACNi is the EACN and Xi is the mole fraction of the i-th component. The authors first

carried out experiments by mixing hydrocarbons from a single homologous series and used them

as the oil phase for interfacial tension measurements. They then used binary mixtures containing

components from two different homologous series.

Salager et al. (1979 a.) found that the natural log of optimal salinity for a particular

surfactant formulation with constant alcohol concentration increased linearly with EACN of a

single component oil. Salager et al. (1979 b.) then confirmed the linear dependence of the natural

log of optimal salinity on the EACN using binary mixtures of alkanes and alkyl benzenes. Cayias

19

et al. (1976) and Cayias et al. (1977) showed that a particular surfactant formulation has a

preferred ACN (PACN) value at which it gives a minimum interfacial tension. EACN is an oil

property while PACN is the EACN of the oil that a surfactant prefers in an EACN scan (an

optimum EACN).

The affinity of a surfactant towards the oil is lowered as the EACN of the oil is increased.

Therefore, the optimum salinity increases with EACN. This implies that a system is likely to

move towards a type II- phase behavior if the oil EACN is increased.

2.2. Effect of Temperature, Pressure and Solution Gas on Microemulsion

Phase Behavior

Nelson (1983) was the first to study the effect of pressure on microemulsion phase behavior with

and without methane. Stock tank oils and synthetic oils were used for the experiments. He found

that pressure alone had negligible effect on microemulsion phase behavior when a stock tank oil/

iso-octane blend was used. For the synthetic oil, he observed that pressure alone caused the phase

behavior to shift towards type II–. Subsequent researchers have validated this phase behavior

shift. Pressurization of the stock tank oil using methane resulted in a shift towards the type II+

side, which is associated with greater oil solubilization ratios in the microemulsion phase.

However, when he used methane to pressurize the synthetic oil, he observed a phase behavior

shift towards type II–. Additionally, the shifts reported in all cases were small. However,

subsequent researchers have found substantially greater shifts depending on the fluids used.

Austad et al. (1990) used a single anionic surfactant system with no cosurfactant. For an

n-decane/surfactant/brine system, an increase in pressure or temperature led to shifts towards type

II –. Live oil phase behavior was then studied using methane and decane. They measured

solubilization parameters of oil and water while increasing pressure and temperature. A shift

20

towards II- was again observed further validating the findings of Nelson (1983). Austad and

Staurland (1990) studied the microemulsion phase behavior of live oil from the North Sea. Again

an increase in pressure led to a shift towards the type II- region. This was also confirmed by

Austad and Strand (1996), but they did not study the impact of solution gas content with pressure.

Austad et al. (1996) used different types of oils in order to study the effect of oil

composition on phase behavior as pressure or temperature is increased. They confirmed that the

trend towards type II- with increasing pressure was not affected by oil composition. However, an

anomaly was observed for temperature scans of a crude oil, brine and single component

surfactant system. Contrary to the findings by Austad et al. (1990), they observed that the crude

oil showed a tendency to move towards type II+ as temperature was increased. They concluded

that the presence of resin-type polar components are capable of establishing ionic interactions

with the surfactant, which is responsible for such a trend. This effect was also observed when

aromatic live oil was used in Austad and Staurland (1990). They observed that the surfactant

showed a tendency to migrate into the excess oil phase as temperature increased.

Kahlweit et al. (1988) and Sassen et al. (1991) both confirmed phase behavior changes

towards type II- with increasing pressure. However, contrary to the conclusions made by Austad

et al. (1990), both reported a phase behavior shift towards the type II+ side as temperature of the

oil/brine/surfactant system was increased. This behavior is attributed to the nonionic surfactants

(as opposed to anionics studied before) used in their experiments. Water solubility of nonionic

surfactants decreases with increasing temperature (Karlstrom and Lindman, 1992). Such a

behavior has also been observed for some alkyl alkoxylated sulfonates (Puerto et al., 2012) even

though they are typically classified as anionic surfactants. The effect is particularly pronounced

for highly ethoxylated anionics where the non-ionic character of the surfactant contributed by the

polyoxyethylene chain dominates over the anionic character of the head group (Velasquez et al.,

2010).

21

Skauge and Fotland (1990) reported an increase in interfacial tension between the

microemulsion-oil interface and a decrease in the microemulsion-water interfacial tension as the

pressure of a surfactant-oil-brine system increased. This is in good agreement with conclusions

made by other authors that an increase in pressure leads the phase behavior of a system towards

the II- type microemulsion. Importantly, they measured the variation of optimal salinity with

increasing oil-phase density. They found that optimal salinity increased with oil phase density.

Later, Roshanfekr and Johns (2011) found that for pure components (pure hydrocarbons), the

natural logarithm of optimal salinity varies linearly with oil phase density. However, this linear

behavior was not shown for hydrocarbon mixtures.

Skauge and Fotland (1990) also presented a thermodynamic explanation for the effect of

pressure on microemulsion phase behavior. They explained that the change in partial molar

volume of the surfactant upon micellization is positive. Therefore, the critical micelle

concentration increases with increasing pressure from Le Chatelier’s principle. This suggests that

the surfactant’s preference to remain in the aqueous phase in its dissociated monomeric form

increases with pressure. Hence, as pressure increases, a phase behavior shift towards the type II-

side is preferred.

Puerto and Reed (1983) used methane to pressurize a dead crude oil. Subsequent phase

behavior experiments were carried out in order to determine the change in optimal salinity with

respect to the change in the oil molar volume as the oil was saturated with methane at different

pressures. Addition of methane lowered the oil molar volume as expected. However, a decrease

in optimal salinity was also observed. The live oil was prepared by saturating dead oil with

methane at 1000 and 2000 psig. Thus only two other data points other than that of the dead crude

were available for comparison. In another set of experiments, phase maps of salinity and alkane

carbon numbers were also presented in order to observe phase behavior changes with increasing

22

temperature. Linear alkanes were used in these experiments and a shift towards the type II- side

was observed.

Further investigation of the effect of pressure, temperature and solution gas on

microemulsion phase behavior systems for surfactant-polymer flood applications have been

reported (Roshanfekr et al., 2012; Roshanfekr et al., 2009). They used resin cured tubes to make

salinity scans at high pressures. They concluded that an increase in pressure alone causes a phase

behavior shift towards type II-, however, addition of solution gas at the same pressure and

temperature lowered the EACN, which subsequently resulted in a phase behavior shift towards

type II+. Reduction in oil phase EACN increases the oil phase solubility of an anionic surfactant.

They mentioned that both of these effects must be taken into consideration. They also gave a

thermodynamic explanation of the linear dependency of the logarithms of solubilization ratios on

pressure and the inverse of temperature.

Roshanfekr and Johns (2011) also presented a procedure to predict optimal salinities and

optimal solubilization ratios at reservoir pressure. Their procedure used data at atmospheric

pressure, which were then corrected to reservoir conditions using an oil phase density correlation.

They used PR78 Peng-Robinson equation of state (Robinson and Peng, 1978) to calculate the

densities. They eliminated the need for performing cumbersome high pressure phase behavior

experiments.

Attempts at studying live-oil microemulsion phase behavior for ASP flood applications

have been made (Southwick et al., 2010). However, reported results show that the crude oil used

for the phase behavior experiments had a low total acid number. Optimal salinity did not change

for different water to oil ratios. Thus, the alkali added (sodium carbonate) acted more like a salt

rather than a saponifying agent.

A comprehensive list of effects on microemulsion phase behavior due to changes in

salinity, oil EACN, temperature, pressure and solution gas is included in Table 1-2.

23

2.3. Role of Alkali in Surfactant Enhanced Oil Recovery Processes

Hydrocarbons are believed to be formed from diagenesis of organic matter at high temperature.

Such processes can produce polar compounds, including a large fraction of oxygenated polar

compounds called carboxylic acids (Seifert, 1975). A majority of the carboxylic acids are

naphthenic acids that have straight or branched paraffinic chains (cyclopentane or cyclohexane

type). Such acids are known as naphthenic acids.

Nelson et al. (1984) initiated research on injection of alkali (a caustic agent) with

synthetic surfactants in a chemical slug for enhanced oil recovery (EOR). Alkali reacts with

acidic compounds in the crude oil (such as naphthenic acids) to produce soaps. The soaps cause

an in-situ emulsification of the crude oil (Castor et al., 1981; Johnson Jr, 1976; Sheng, 2010).

These soaps act as surfactants and aid in lowering interfacial tensions. The synthetic surfactants

along with the in-situ soaps were able to produce low IFTs. Soaps with injected synthetic

surfactant can synergistically contribute to achieve near 100% oil displacement efficiency.

Formation of in situ soap by injecting relatively inexpensive alkali can significantly

reduce the amount of expensive synthetic surfactants needed in the EOR process (Shuler et al.

1989). In such processes, polymers may be added to the aqueous phase for mobility control to

improve sweep. With all these chemicals injected, the process becomes an alkali-surfactant-

polymer (ASP) flood.

A wide variety of caustic agents have been used for field trials (Gogarty, 1983) including

sodium carbonate (Jackson, 2006), ammonium carbonate, sodium hydroxide and ammonium

hydroxide. The amount of soap formed as a result of saponification depends on many factors

including the alkali and oil concentration. Thus, alkali complicates the phase behavior present in

an ASP flood and has not been well understood or predicted.

24

2.4. The Surfactant Affinity Difference

Winsor’s R-ratio is a measure of the surfactant’s preference to be in the oil or water phase. The

R-ratio evaluates the preference by considering interaction energies between the oil region, water

region and the C-layer as discussed in Chapter 1. Alternatively, chemical potential of the

surfactant can also be analyzed in order to understand surfactant partitioning as shown by Salager

(1988).

Consider first the chemical potential of the surfactant in phase j to be µsj where j may be

either oil or water. Now, consider these chemical potentials at some reference state to be µsj*.

The equations for chemical potentials of the surfactant component in the water and oil phases can

therefore be expressed as

* ln( )sw sw sw swRT x a , (2.3)

and,

* ln( )so so so soRT x a , (2.4)

where xso and xsw represent relative concentrations of the surfactant in oil and water, respectively.

Activity coefficients of the surfactant in oil and water phase are represented by aso and asw

respectively. At equilibrium, the chemical potentials of the surfactant component are equal to

each other. The difference between the reference state chemical potentials of the surfactant in the

water and the oil phase at equilibrium is the surfactant affinity difference. The dimensionless

form of the SAD is the hydrophilic lipophilic difference. Therefore,

* * ln( / )sw so so so sw swSAD RT x a x a , (2.5)

25

and,

SADHLD

RT . (2.6)

In high quality formulations (those that have the potential to achieve ultra-low IFTs), the

concentration of the surfactant in the excess oil and water phases (Cso and Csw) is very small. This

implies that the activity coefficients are equal to 1 in those phases. Therefore, activities can be

replaced by concentrations (Cso and Csw) in the SAD equation. Equations (2.5) and (2.6) become,

ln( / )so swHLD C C . (2.7)

Furthermore, at optimum salinity, the concentrations of surfactant in the excess oil and water

phases are equal. Hence the SAD (and the HLD) at optimum condition is zero.

2.5. The Hydrophilic – Lipophilic Difference

Salager et al. (1979 a.) derived an empirical relation from experimental data at optimum

conditions for oil-water-brine systems in the presence of an anionic surfactant as,

*ln ( ) 0refS K EACN f A T T Cc (2.8)

where S* is the optimum salinity expressed as grams per 100 ml, EACN is the equivalent alkane

carbon number, f(A) is a function of alcohol type and amount, and Cc is a surfactant-dependent

parameter called the characteristic curvature (Acosta et al., 2008). The parameter K is the slope

26

obtained from the observed linear relationship between the logarithm of optimum salinity and the

EACN. That is, when all other formulation variables are fixed we have,

*lnconstant

SK

EACN

(2.9)

Similarly, the constant α is derived from the observed linear dependence of lnS* with temperature

(all other formulation variables are fixed):

*lnconstant

S

T

(2.10)

Equation (2.8), which is valid for microemulsion systems at optimum conditions, was also

extended to the concept of surfactant affinity difference (SAD). As discussed, SAD is the

difference between the standard chemical potential of the surfactant in the water and oil phases,

which relates directly to the partitioning of the surfactant between the water and oil phases

(Marquez et al., 1995; Marquez et al., 2002). The HLD is therefore a state function that accounts

for phase behavior changes owing to compensating effects of formulation variables (Salager et

al., 2005; Salager et al., 2000), and when coupled with Eq. (2.8) gives,

ln ( )refHLD S K EACN f A T T Cc (2.11)

where HLD is zero at optimum conditions (see Eq.(2.8)). Appendix A shows that there is a

thermodynamic basis for Eq. (2.11) where formulation variables like salinity are treated

independently of the other variables.

27

Pressure effects have been ignored in the SAD and HLD equations by previous

researchers. Chapter 3 adds a pressure term to the HLD equation, which is a key contribution of

this research.

2.6. The HLD-NAC model

The use of net and average curvature (NAC) of solubilized micelles to model a microemulsion

phase behavior scan was first introduced by Acosta et al. (2003). The theoretical premise of this

model has been well explained by these authors for the three pseudo-component system of oil (o),

water (w) and surfactant (s). The model assumes that the microemulsion phase is ideal, which

implies that there is no change in the total volume of the system upon mixing. The model also

assumes that the micelles formed are spherical. Such an assumption is good from the type II- and

type II+ regions, but is not true in the type III region. Nevertheless, spherical micelles are

assumed in all regions as a first approximation. The model developed by Acosta et al. (2003) is

not predictive outside the range of their measured data, but was shown to fit data from salinity

scans well.

2.6.1. Radii and Curvatures of Micelles in Solubilized Systems

The reciprocal of a spherical micelle radius is taken to be curvature of the solubilized component.

The micelle radii containing component i (oil or water) can be obtained from the volume of

component i solubilized (Vi,m) and the interfacial area occupied by the surfactant molecules at the

interface (As). The parameter As is dependent on the moles of surfactant in the system (ns) and

surface area per molecule of surfactant (as). For a mixture of surfactants, the term As is a

28

summation of the area contributed by every surfactant molecule (Avogadro’s number times nsas)

so that,

, ,

236.023 10

3 3i m i m

i

s ss

V VR

A n a

(2.12)

2.6.2. The Average Curvature Equation

The average curvature (Ha) can be expressed by the average radii of oil (Ro) and water (Rw)

micelles (or droplets) in the microemulsion phase and the characteristic or correlation length (ξ)

as defined by DeGennes and Taupin (1982). That is,

1 1 1 1

2a

o w

HR R

(2.13)

.

The correlation length ξ is equivalent to the average micelle diameter (Buijse et al., 2012) in

simple microemulsions with spherical micelles. As a consequence, the average curvature

describes the amount of oil and water solubilized in micelles in the microemulsion phase.

Equation (2.12) can be substituted into Eq. (2.13) to derive an expression for the

correlation length. The volume of surfactant (Vs,m) can be obtained from the concentration of the

surfactant and by assuming surfactant component density equal to water. The correlation length

(ξ) can then be expressed in terms of volume of surfactant (Vs,m) in the microemulsion, volume

fraction of oil, surfactant and water in the microemulsion (ϕo, ϕs and ϕw), and their solubilization

ratios (σo and σw) as reported by Buijse et al. (2012). The expression becomes,

29

6 6

1

s o w s o w

s s s o w

V V

A A

(2.14)

However, this expression has been updated and modified in Chapter 3 in order to account for the

surfactant component volume, which was previously ignored.

2.6.3. The Net Curvature Equation

The curvature of the surfactant interface is described by the net curvature (Hn). The net curvature

is related to the radii of oil (Ro) and water (Rw) micelles, the surfactant length parameter (L), and

to HLD (Acosta et al., 2003; Acosta et al., 2008). The net curvature was found to be proportional

to the HLD of the system with 1/L as the proportionality constant. Therefore, the parameter HLD

translates the changes in formulation variables into the NAC model as,

1 1n

o w

HLDH

R R L . (2.15)

At optimum, the oil and water curvatures (hence radii) are equal to each other. This is consistent

with the fact that oil and water solubilization ratios are equal to each other at optimum. This

satisfies the condition that HLD is zero at optimum in Eq. (2.15).

2.6.4. Flash Calculations using HLD-NAC

This section describes the flash calculation protocol required for the HLD-NAC to model

microemulsion phase behavior where two and three-phase regions may be present. The

30

procedure for flash calculation is modified in Chapter 3 so that it becomes predictive outside the

range of experimental conditions.

2.6.4.1. HLD-NAC to Model Type II- Microemulsions

For a high quality formulation, the excess phases should be pure oil or water component

depending on the type of excess phase. In the type II- region the oil micelles are assumed to be

dispersed in the continuous aqueous phase (oil in water microemulsion). Therefore, all water is

in the microemulsion phase and the volume of the water component solubilized (Vw,m) in the type

II- microemulsion is equal to the total volume of water component present in the system, which is

known from the initial composition of the system. Equation (2.12) can then be used to calculate

an effective Rw, which is hypothetical in that only oil micelles (and hence oil radii) exist in a

continuous water phase in such systems. Vw,m is therefore equal to the total volume of water in the

system Vw, so that,

,3 3w

s

m w

w

s

V VR

A A . (2.16)

The curvature of solubilized water component calculated is negative since the microemulsion

phase is of type II- (water external). Only absolute values of curvatures are used in the NAC

model. Using Eq.(2.12), Ro can then be obtained based on the HLD value of the formulation.

Equation (2.15) can now be used for the oil component to calculate the amount of oil solubilized

(Vo,m).

,

1

3

3

/ 3

1o m

w

s

s

s w

VHLD HLD

L V L V

A

A

A

(2.17)

31

Furthermore, we assume excess phases to be pure. Hence, all surfactant component is contained

only in the microemulsion phase. This implies,

,s m sV V . (2.18)

Therefore, with volumes Vo,m, Vw,m, and Vs,m known, σw (Vw,m / Vs,m ) and σo (Vo,m / Vs,m ) can be

calculated.

2.6.4.2. HLD-NAC to Model Type II+ Microemulsions

An analogous procedure is followed for type II+ microemulsions. In type II+ microemulsions, Ro

is known from the overall oil composition, where curvature is negative and oil is external to the

micelles (oil is continuous) so that,

,3 3o

s

m o

o

s

V VR

A A . (2.19)

Equation (2.15) can now be used to calculate the amount of water solubilized (Vw,m) in the

microemulsion. That is,

,

1

3

3

/ 3

1w m

o

s

s

s o

VHLD HLD

A

A

AL V L V

. (2.20)

32

2.6.4.3. HLD-NAC to Model Type III Microemulsions

Oil and water micelles coexist within the bi-continuous middle phase (type III microemulsion).

The optimum solubilization ratio (σ*) for type III is equal to σo and σw at the optimum salinity.

The correlation length at optimum conditions (ξ*), therefore, can be calculated using Eq. (2.14)

and an experimentally obtained (or predicted, as shown in the modified flash calculation

procedure in Chapter 3) value of σ*. The correlation length (and the average curvature) remains

constant and equal to ξ* for the type III microemulsion phase. That is, in type III microemulsions,

*

1 1 1 1

2a

o w

HR R

(2.21)

where,

*2*

*

6

1 2

s

s

V

A

. (2.22)

In the three-phase systems, two excess phases (oil and water) and one microemulsion exist. The

oil and water curvatures, are calculated by solving Eqs. (2.15) and (2.21) simultaneously.

*

1

2

1

o

HLD

R L (2.23)

and,

*

1

2

1

w

HLD

R L . (2.24)

Using Eq. (2.12) in Eqs. (2.23) and (2.24), solubilized volumes Vo,m and Vw,m can be obtained as,

33

,

*

2

33s

w m

AV

HLD

L

(2.25)

and,

,

*

33

2

s

o m

AV

HLD

L

. (2.26)

2.6.4.4. Phase Volumes

The phase volumes for excess oil (Voo), excess water (Vww) and microemulsions (Vm) are

calculated once the solubilized volumes Vo,m and Vw,m have been determined. That is,

,oo o o mV V V , (2.27)

,ww w w mV V V , (2.28)

and,

m total ww ooV V V V , (2.29)

where,

total w o sV V V V . (2.30)

With volumes of excess phases and solubilized components known, densities of surfactant, oil

and water components can then be used to compute molar and mass compositions.

34

2.6.4.5. Stability Criteria to Determine Two and Three-phase regions

The inverse of the average curvature is equal to ξ* at the two- and three-phase transition limits:

between type II- and type III, and type III and type II+ (Acosta et al. 2003). This criteria is used

to obtain the HLD values at which the correlation lengths ξ in the type II- and II+ environments

are equal to the critical correlation length ξ*. In the two-phase regions, the oil and water radii are

used in the average curvature equation Eq. (2.13) to obtain the correlation length ξ. Therefore

upper and lower HLD limits, HLDU and HLDL can be determined as follows,

*3 3

12 s

L

w

ALHLD

V

, (2.31)

and,

*

2

3

1

3

s

U

o

ALHLD

V

(2.32)

The stability criteria that determines if the system will form a type II-, type II+ or type III

microemulsion is as follows:

Case 1: If HLDL < HLDU,

HLD > HLDU , a type II+ microemulsion exists (two-phase system).

HLD < HLDL , a type II- microemulsion exists (two-phase system).

HLDL ≤ HLD ≤ HLDU a type III microemulsion exists (three-phase system).

Case 2: If HLDL = HLDU

The system will transition from type II- to type II+ as HLD increases, encountering a three-phase

region only at HLD = HLDL = HLDU. At that HLD, ξ is equal to the critical correlation length ξ*.

Case 3: If HLDL > HLDU,

35

The system will transition from type II- to type II+ as HLD increases, without

encountering a three-phase region.

HLD < HLDU , a type II- microemulsion exists (two-phase system).

HLD > HLDL , a type II+ microemulsion exists (two-phase system).

HLDL ≥ HLD ≥ HLDU a type IV microemulsion exists (single phase system).

2.7. Summary

The net curvature equation brings the state function HLD into the phase behavior model. Hence,

the effect of net curvature as formulation variables change can be modeled this way. Figure 2-1

shows a flowchart of the steps followed to perform a flash calculation using the original HLD-

NAC model. The following input parameters are required in HLD-NAC as described by Acosta

et al. (2003):

Overall composition (from surfactant concentration and water-oil ratio),

Interfacial area per molecule of surfactant,

Surfactant length parameter,

Optimum solubilization ratio, and,

HLD of the system.

The surfactant concentration and water-oil ratio are known in experiments. However, the

surfactant length parameter and the surfactant interfacial area per molecule are obtained from the

literature. The optimum solubilization ratio and optimum salinity are determined from a single

salinity scan. The flash calculation methodology explained in this chapter is based on the state-

of-the-art prior to this research.

The HLD-NAC flash calculation procedure has the following limitations:

36

1. There was no reliable way to predict σ* as a function of changing formulation variables.

From Eq. (2.14), it can easily be inferred that the value of ξ* is governed by the value of

σ*. The HLD-NAC described could only be used after determining σ* experimentally.

Therefore, the current HLD-NAC model cannot predict phase behavior outside the range

of experimental conditions.

2. Pressure effects are not accounted for in the HLD equation. Therefore, prior to this

research, the HLD-NAC was incapable of predicting changes in microemulsion phase

behavior as a function of pressure.

3. The surfactant length parameter L is not well known for different surfactants.

4. Interfacial area per molecule of the surfactant (as) used in HLD-NAC must also be

obtained from experimental results reported in the literature.

5. Surfactant volume fraction in the microemulsion phase is ignored while calculating the

correlation length (ξ).

We address the issues listed above in subsequent chapters. Chapter 3 presents a novel approach to

predict σ* and hence, ξ* , thereby modifying the existing HLD-NAC model and making it into a

true equation of state where relationships can be found between temperature, pressure and

volume. In this research, we include a pressure term similar to the functional form of the

temperature term in the HLD equation. Chapter 3 also presents a way to estimate the surfactant

length parameter L. The method is empirical. We estimate L parameters for complex surfactants

for which reliable experimental data is not available. In Chapter 3, we use the area parameter to

tune and match phase behavior data. Our method provides a way to obtain as for complex

surfactant formulations for which experimental data are not available. We also update the average

curvature equation to include the surfactant volume fraction in the microemulsion phase. In

Chapter 4, we extend the modified HLD-NAC approach to model phase behavior for systems

with acidic oils in presence of alkali. In Chapter 5, we rearrange the equations in the modified

37

HLD-NAC and make them dimensionless. We identify and study key dimensionless groups that

impact surfactant-oil-brine phase behavior.

38

Figure 2-1: Flowchart showing the protocol followed for the HLD-NAC model described by

Acosta et al. (2003).

HLD = ln (S/S*)

Initial

compositions

Vo, Vw , Vs

σ* from a

salinity scan

experiment

S*

from a

salinity scan

experiment

Salinity S at

which flash

is to be

performed

L from

literature as from

literature

Obtain HLDL and HLDU

If HLDL ≤ HLDU If HLDL > HLD

U :

HLD < HLDL

Type II-

HLDL < HLD <

HLDU

Type III

HLDU < HLD

Type II+

HLDL < HLD

Type II+

HLDU < HLD <

HLDL

Type IV

HLD < HLDU

Type II+

Solubilized

component

volumes

Vom and Vwm

Phase volumes Voo,

Vww and Vm

Solubilization ratios

σw and σo

39

Chapter 3

Development of a Modified HLD-NAC Equation-of-State to Predict

Surfactant-Oil-Brine Phase Behavior for Live Oil at Reservoir

Pressure and Temperature

Chapter 1 reviews the effect of formulation variables on microemulsion phase behavior. In this

Chapter, a robust physically-based methodology that uses the HLD-NAC model and associated

empirical equations to predict Winsor II-, II+, and III microemulsion phase behavior at different

pressures, temperatures, and varying oil compositions (with varying amounts of solution gas) are

developed. The concept of hydrophilic-lipophilic deviation (HLD) is used and empirically

established HLD equations are modified to account for pressure changes for anionic surfactants.

The new HLD equation is coupled with the net-average curvature (NAC) model to predict, after

tuning with limited experimental data, phase volumes, solubilization ratios, optimum conditions,

and phase transitions at conditions other than those that were measured. This research study

greatly expands the applicability of the HLD-NAC model to predict microemulsion phase

behavior for oils where many formulation variables are changing simultaneously.

3.1. Extension of The HLD Equation to Include Pressure

Experiments used to develop the empirically derived HLD equation were mostly carried out at

atmospheric pressure. This is likely because experiments at low pressure are relatively easy to

perform and experiments in the chemical engineering literature focused on the effect of large

temperature changes in their applications, not large pressure changes. Thus, the effect of

pressure, which may be needed for high-pressure petroleum engineering applications, has largely

40

been neglected in the literature. This research is the first to include the effect of pressure in the

HLD equation.

An increase in pressure (and temperature) shifts the microemulsion phase behavior

towards type II- as has already been discussed in the introduction. Further, like temperature, lnS*

exhibits a linear dependence with pressure. Skauge and Fotland (1990) for example made

pressure scans for pure heptane using the surfactants secondary alkane sulfonate (SAS) and

sodium dodecyl benzene sulfonate (SDBS). Figure 3-1 and Figure 3-2 show the linear

dependence of lnS* with pressure for these surfactants, where linear regression gives excellent R2

- values of 0.956 and 0.996 respectively. Thus, the effect of pressure on phase behavior can be

treated analogously to temperature in the HLD equation. That is, we introduce a new constant

factor β in the HLD equation to account for pressure changes as,

ln ( ) ( )HLD S K EACN f A T T P P Ccref ref

, (3.1)

where Tref and Pref are at reference conditions, typically at the conditions that are measured in a

standard salinity scan (reservoir temperature and atmospheric pressure). For optimum salinity,

where the HLD is equal to zero, Eq. (3.1) yields,

*ln 0ref refS K EACN f A T T P P Cc , (3.2)

where the pressure coefficient is defined as,

.

*ln

constant

S

P

. (3.3)

41

With all formulation variables now accounted for in Eq.(3.2), however, a more general

notation would be to indicate that all formulation variables are at optimum when HLD is zero.

Thus, optima can be defined in terms of optimum pressure or temperature, not just in terms of

optimum salinity. With this new way of thinking about optimum, the HLD equation for a salinity

scan will therefore be more strictly defined as,

, , , ( ), *| lnT P EACN f A Cc

SHLD

S . (3.4)

Similarly, the HLD equation for a temperature scan is,

*

, , , ( ),| S EACN P f A CcHLD T T , (3.5)

where T* is the optimum temperature. The HLD equation for a pressure scan,

*

, , , ( ),| S EACN T f A CcHLD P P , (3.6)

where P* is the optimum pressure. An even more general expression would be to allow all three

primary variables to change simultaneously, which leads to

* * *

* *

*, ( ), , , ,( , , ) | ln ( ) ( )

EACN f A Cc S P T

SHLD S T P T T P P

S . (3.7)

In Eq. (3.7), we assumed that the oil composition is fixed, along with the type and amount of

surfactant(s) and alcohol(s). However, Eq. (3.7) holds true for all oil compositions and anionic

surfactant formulations. For example, one could change the branching of a surfactant to shift the

optimum to the desired salinity, temperature, and pressure. The equation shows the hydrophilic

lipophilic deviation from a particular optimum state of (S*, T*, P*) that satisfies Eq. (3.2). When

42

all three formulation variables are at an optimum (S*, T*, P*) in Eq. (3.7) , HLD is zero. Equation

(3.7) shows that a particular value of HLD (including zero at an optimum condition) is

represented by a plane in (lnS, T, P) space.

3.2. New Relations for Prediction of Optimum Solubilization Ratio

The HLD equation can be used to determine the deviation of the state of an oil-surfactant-brine

system from the optimum condition. However, the HLD equation offers no explanation of how

oil and water solubilization in the microemulsion phase vary with salinity. The literature

provides insight into how one could link the optimum variables such as S* to the optimum

solubilization ratio (σ*) using the HLD concept. In particular,

Optimal salinity has been observed to increase with an increase in the oil EACN, while

optimum solubilization ratio decreases (Barakat, Fortney, Schechter, et al., 1983; Graciaa

et al., 1982). The change in logarithm of optimal salinity follows a linear trend with

EACN as has been already discussed.

Salager et al. (1979) showed that as the oil EACN is increased, the range of salinity over

which a type III microemulsion is formed also increases. This range can be expressed as

ΔEACN or ΔlnS (see Figure 3-3).

Similar to optimum salinities, the natural logarithms of the upper and lower salinity limits

also form linear trends with EACN (Salager, 1988). Such a linear trend was also used by

Roshanfekr et al. (2013).

Barakat, Fortney, Lalannecassou, et al. (1983) showed that σ* is proportional to the

inverse of the width of the three-phase region irrespective of temperature and oil EACN.

Bourrel and Schechter (2010) further demonstrated that,

43

* EACN d , (3.8)

where the dimensionless proportionality constant d is a constant value of 5.5 for alkyl

benzene sulfonates, 24.7 for alpha olefin sulfonates and 40.3 for ethoxylated oleyl

sulfonates. The value of d can also be determined from experiments for particular

surfactant-oil-brine systems.

Graciaa et al. (1982) showed that σ* is proportional to the inverse of the width of the

three-phase region in terms of the difference of the hydrophilic lipophilic balance

(ΔHLB). Salager et al. (2005) suggested replacing HLB by HLD because it is easier to

determine from the empirical equations.

Barakat, Fortney, Lalannecassou, et al. (1983) also found that a relationship for S* and σ*

exists that is unique to surfactant type. This means, irrespective of oil EACN or

temperature, such a relationship is always satisfied.

Based on these observations and conclusions, a new empirical relationship is proposed to relate

the optimum solubilization ratio with the width of the type III region expressed in terms of

ΔHLD. That is,

1*

2AH

A

LD

, (3.9)

where A1 and A2 are dimensionless constants. Further, from Figure 3-3, the width of the Winsor

III three-phase window (ΔEACN or ΔlnS) increases linearly with lnS*(or EACN).

.

*ln S EACN . (3.10)

That is, lnS*, like ΔEACN, should be inversely related to σ*. That is,

44

1 2

*

*

1lnB S B

. (3.11)

.

The dimensionless constants B1 and B2 can be determined by a linear regression of lnS* and 1/σ*

available from experiments. Subsequent sections show that tuning these constants yields

excellent predictions of optimum solubilization ratio from optimum salinities.

Figure 3-4 shows an example of the validity of Eq. (3.11) where we use data reported by

Sun et al. (2012). The experiments were conducted using a commercial internal olefin sulfonate

with pure alkanes; n-heptane, n-octane and n-decane (EACNs of 7, 8 and 10 respectively) at

temperatures of 20°C, 50°C and 90°C. The figure shows a clear linear correlation of lnS* with

1/σ* where a linear regression gives an R2-value of 0.96.

3.3. Modifying the HLD-NAC Model

3.3.1. Accounting for Surfactant Volume Fraction in The Average Curvature

Equation

The microemulsion phase consists of three components namely, oil (o), water (w) and surfactant

(s). Component volume fraction is the ratio of the volume of the component (Vi) solubilized in the

microemulsion to the total volume of the microemulsion phase (Vme). The summation of

component volume fractions (ϕi) in a phase is equal to unity, which implies,

1o w s . (3.12)

Hence, adding the inverse of the water and oil volume fractions, we obtain the expression,

11 1 s

o w w o

. (3.13)

45

Dividing Eq. (3.13) by the volume of microemulsion phase Vm we get,

, ,

11 1 s

o m w m m w oV V V

, (3.14)

where, Vo,m and Vw,m are solubilized volumes of the oil and water components in the

microemulsion phase. Acosta et al. (2003) assumed the solubilized micelles to be spherical. As

shown in Chapter 2, the radii of the spheres (and hence curvatures) are related to the total

interfacial area (As) and the solubilized volumes (Vi,m),

, ,

23

3 3

6.023 10

i m i m

i

s s s

V VR

n a A

, (3.15)

Hence, the average curvature equation can be expressed as

(1 )1 1 1

2 6

s s

o w me w o

A

R R V

. (3.16)

The NAC theory as presented by Acosta et al. (2003) relates the average curvature to the inverse

of the DeGennes correlation length ξ (DeGennes and Taupin, 1982). Hence, from Eq. (3.16) , the

correlation length can be redefined as

6

(1 )

me w o

s s

V

A

(3.17)

46

The correlation length in prior research (Acosta et al., 2003; Acosta and Bhakta, 2009; Buijse et

al., 2012), was not a function of the surfactant content in the microemulsion. This was probably

because the surfactant volume component was assumed to be negligible owing to low overall

surfactant concentrations in typical formulations. However, the NAC model assumes the excess

phases to be pure, which constrains the entirety of the surfactant component to be contained in the

microemulsion phase only. Therefore, as the overall surfactant concentration increases, ϕs

becomes increasingly significant.

The HLD-NAC model at its prior state of development is constrained by the knowledge

of the value of optimum salinity and solubilization ratio. From Eqs. (3.4) - (3.6) it can be seen

that the HLD values used in the net curvature equation are constrained by the optimum HLD

variable (for example, S* in a salinity scan). ξ* in the average curvature equation for type III

microemulsions is constrained by the optimum solubilization ratio σ*. This dissertation, therefore

presents a way to predict these optimum values at different oil EACNs, pressures, and

temperatures to extend the HLD-NAC’s modeling capabilities. Equation (3.2) is used to predict

optimum salinities. Equation (3.11) is then used to predict optimum solubilization ratios from

predicted optimum salinities. Surfactant concentration and water-oil ratio are known in

experiments. Estimation of the surfactant length parameter is explained in the next section. The

interfacial area of surfactant molecule can be obtained by tuning the phase behavior model to fit

experimental data. This procedure fully defines all input variables required for the HLD-NAC

model and presents a true equation-of-state like approach.

3.4. Determining The Surfactant Length Parameter

One of the required parameters in the model is the average surfactant length. The surfactants

considered here have anionic moieties so that only the HLD equation applicable for anionics is

47

considered in this dissertation. The approach could be easily extended to nonionic surfactants as

well (Salager et al., 2000). The surfactant length parameter L in the net curvature equation is

approximately 1.2 times the surfactant tail length (Lc in Å) for anionics and 1.4 times Lc for

nonionics (Acosta et al., 2003; Acosta and Bhakta, 2009; Acosta et al., 2008). We determined Lc

from the effective number of straight chain carbon atoms (nc) using the equation for maximum

chain length (Acosta et al., 2008; Tanford, 1980):

1.5 1.265c cL n . (3.18)

Equation (3.18) is convenient for simple surfactants with tails consisting of linear carbon chains.

In order to calculate the equivalent carbon numbers (or effective chain lengths) of surfactants

with complex hydrophobes, we use rules of equivalence as reported in Rosen (2004). These rules

apply to characterization of surfactant hydrophobes with respect to their critical micelle

concentrations (CMC). For a branched hydrophobe, the carbon atoms on the branch (shorter

secondary chain) have one-half the hydrophobic effect of the primary chain. For extended

surfactants like ethoxylates or propoxylates, the carbon atoms between the oxygen atoms

contribute half the effect that would have existed if the oxygen atoms were absent. A benzene

ring and an orthoxylene group have a net contribution of 3.5 and 2.5 carbon atoms, respectively.

Using these rules, nc can be obtained. If a mixture of surfactants is used, the surfactant length

parameter is obtained by using a surfactant mole fraction averaged mixing rule. One could also

tune this parameter to the available experimental data, but in this dissertation tuning on a

minimum number of parameters was preferred.

48

3.5. Results

In this section three examples using experimental data are given to demonstrate the validity of the

methodology presented. Matched results of tuning the HLD-NAC models to the experimentally

measured data are reported. The new model’s prediction capability is demonstrated by

comparing predictions to data not used in the tuning process.

3.5.1. Example 1: Skauge and Fotland (1990) Experiments

Very limited data is reported with both temperature and pressure changing simultaneously, and

often data that is reported does not give sufficient information regarding the experiments in the

analysis that follows. One of the best data sets reported in the literature for our purposes is that

by Skauge and Fotland (1990). In their experiments they used sodium dodecyl benzene sulfonate

(SDBS) and a mixture of C13 to C18 secondary alkane sulfonate (SAS) along with the co-solvent

n-Butanol. One salinity scan for each surfactant formulation at atmospheric pressure and 20°C

using heptane were reported. They then measured optimum salinities and solubilization ratios at

different temperatures, but at atmospheric pressure. Similarly, they measured optima at different

pressures keeping the temperature fixed at 20 °C. The following steps were followed in our

analysis of their data:

1. The surfactant length parameter was calculated based on surfactant structure. Other key

parameters such as surfactant concentration, S*, and σ* were known at 20°C and 1.01

bars from standard salinity scans they reported using n-heptane. The only unknown for

the HLD-NAC model, the interfacial area per molecule of the surfactant (as), was used as

a tuning parameter to match the phase fraction vs salinity data reported within the upper

49

and lower salinity limits. Equation (3.4) was used to determine HLD for use in the net

curvature equation.

2. Using the measured change in optima (S* and σ*) with respect to EACN (at 20°C and

atmospheric pressure), the following were calculated:

a. The slope (K) of the lnS* vs EACN trend.

b. The constants B1 and B2 based on the linear trend of lnS* vs 1/σ*.

3. Skauge and Fotland (1990) varied pressure keeping the temperature constant at 20°C and

reported optima at different pressures. They held pressure constant at 1.01 bars

(atmospheric) and varied temperature to show the change in optima due to increasing

temperature. The α and β factors in Eq. (3.2) were obtained from the linear dependence of

lnS* with temperature and pressure based on their elevated T and P data with all other

parameters constant (such as EACN).

4. Using the α and β factors from step (3), optimal salinities were calculated at different

pressures and temperatures from the value at atmospheric pressure and 20°C.

5. Using the slopes from the linear correlations from step (2), σ* at different temperatures

(pressure constant at atmospheric conditions) and pressures (temperature constant at

20°C) were predicted from the value of optimum solubilization ratio at atmospheric

pressure and 20°C.

6. The calculated values and actual experimental values were compared.

The surfactant length parameters calculated for sodium dodecyl benzene sulfonate

(SDBS) and secondary alkane sulfonate (SAS) surfactants were 23.05 Å and 25.33 Å

respectively. The tuning process using the HLD-NAC model gave a tuned as value of 97 Å2 for

SDBS and 180 Å2 for SAS. Figure 3-6 and Figure 3-7 compare experimental data and tuning

results. Acosta et al. (2008) reported a value for as of 50 Å2 for SDBS. The larger value

50

obtained from tuning can directly be attributed to use of n-butanol as a cosurfactant by Skauge

and Fotland (1990), which is known to seek the interface and make the surfactant layer at the

interface less rigid.

The slopes (K) for the linear dependence of lnS* on EACN were 0.12 (R2 - value 0.99)

and 0.14 (R2 - value 0.99) for SAS and SDBS respectively (Figure 3-8 and Figure 3-9). Figure

3-10 and Figure 3-11 show the linear regression of lnS* as a function of 1/σ* along with the

constants B1 and B2. The constants B1 and B2 as defined by Eq. (3.11) for SAS are 0.24 and -0.24

respectively. B1 and B2 for SDBS are 0.18 and -0.02 respectively. The R2 - values obtained for

SAS and SDBS was 0.99 and 0.98 respectively showing good linear correlations between lnS*

and 1/σ*.

Using the optimum salinities reported by Skauge and Fotland (1990) at different

pressures, β was found from the linear trends already discussed previously. However, all of these

experiments were conducted at 20°C. Therefore we could not determine any dependence of β on

temperature. Similarly, α was determined (Figure 3-12 and Figure 3-13) from experiments where

temperature changed at fixed atmospheric pressure. The β factors obtained from linear fits were

6×10-4 bar-1 (R2 - value 0.96) and 8×10-4 bar-1 (R2 - value 0.99) for SAS and SDBS respectively.

The α values obtained from linear regression were 3.1×10-3 K-1 (R2 - value 0.90) and 7.7×10-3 K-1

(R2 - value 0.97) for SAS and SDBS respectively.

Using the α and β values, optimum salinities were predicted for heptane from the

optimum at atmospheric pressure and 20°C. The average relative error in calculation of optimal

salinities is 2.35%. Using the predicted optimum salinities, optimum solubilization ratios were

predicted. As shown in the comparison of Figure 3-14 and Figure 3-15, the predicted and actual

values agree well up to pressures of 200 bars. The use of constant β under-predicts optimum

solubilization parameters somewhat beyond this range. However, constant α gives a very good

51

prediction of changing optimum solubilization ratios with increasing temperature (compare

Figure 3-16 and Figure 3-17). The average relative error in prediction of optimum solubilization

ratio is 10.55%. Table 3-1 to Table 3-4 summarize the prediction of optima using the procedure

described previously in this dissertation and the corresponding relative errors. For both errors, the

total number of data points considered was 24.

This section demonstrates that our new HLD equation with all constants known is a

powerful tool to determine optimum conditions in terms of temperature, pressure, oil EACN and

salinity for a given surfactant formulation. This is the first time optimum solubilization ratios

have been predicted at different temperatures and pressures using a simple empirical correlation.

3.5.2. Example 2: Roshanfekr and Johns (2011), and Roshanfekr et al. (2013)

Experiments

Measurements reported by Roshanfekr and Johns (2011), Roshanfekr et al. (2013) and

Roshanfekr (2010) were used to predict dead and live oil phase behavior by estimation of input

parameters for the HLD-NAC model. They used a mixture of tridecyl propoxylated alcohol

sulfate and a C13-C18 internal olefin sulfonate along with isopropanol as a cosolvent. All

experiments were performed at 25°C (77°F). They reported salinity scans using the same

surfactant formulation for three pure alkanes; octane, decane and dodecane. They also reported

salinity scans for a dead crude at atmospheric pressure, dead crude at elevated pressure (1000 psi

/ 68.95 bars) and live crude with 17 mole % of methane solubilized at the same elevated pressure.

WOR was reported to be 1.0. The following steps were taken to analyze their experimental data:

1. The surfactant length parameter was first estimated. A mole fraction averaged length

parameter was obtained based on the surfactant mole fractions

52

2. Salinity scans of octane, decane and dodecane were matched by tuning interfacial area

per molecule (as) using the values of S* and σ* reported. Tuning was done to fit the

experimentally obtained solubilization ratios as a function of salinity. An average tuned

value of the interfacial area obtained from three matches was used in the HLD-NAC

model to predict phase behavior for dead and live oils. Equation (3.4) was used to

determine HLD in the net curvature equation.

3. We estimated the β factor from optimum salinities of the dead oil at atmospheric pressure

and elevated pressure.

4. The constant K for the HLD equation was estimated from the EACN trend for pure

alkanes. Using K, the β factor, and known EACNs of the dead and live oils, optimum

salinities were estimated.

5. The linear dependence of lnS* on 1/σ* was found using data from pure alkane

experiments. The optimum solubilization ratios for the dead and live crudes were

estimated from the optimum salinities predicted in step (4).

6. Last, we used the surfactant length parameter from step (1), average tuned value of as

from step (2), estimated optimum salinities from step (4) and estimated optimum

solubilization ratios from step (5) to predict the phase behavior for live and dead oils. We

did not use the density correlations found in Roshanfekr and Johns (2011) for this

prediction.

Tridecyl alcohol has an effective carbon number of 12.9 (Hammond and Acosta, 2012).

Using the rules already discussed, each polyoxyethylene (POE) group was considered to have an

effective linear carbon contribution of 1.5 carbon atoms. The surfactant length parameter was

therefore calculated to be 50.98 Å. The internal olefin sulfonate was a mixture of surfactants

consisting of tails between 15 and 18 carbon atoms. An average effective carbon number of 16

was hence considered. The surfactant length parameter for this carbon number was estimated to

53

be 26.88 Å. The mixture consisted of 1.5 wt. % TDA propoxylated sulfate (molecular weight of

1059 g/mol) and 0.5 wt. % of the internal olefin sulfonate (average molecular weight of 232

g/mol from Barnes et al. (2010). The mole fraction averaged length parameter was therefore

35.96 Å. Using the L parameter from step (1) and reported values of S* and σ*, as was tuned and

phase behavior of the three pure alkanes (octane, decane and dodecane) were matched (see Figure

3-18 to Figure 3-20). The tuned values of interfacial area per molecule of surfactant (as) were 225

Å2, 163 Å2 and 114 Å2 respectively. The average value was 167.33 Å2.

The β factor was calculated to be 7.71×10-4 bar-1 based on the values of optimum

salinities of the dead oil at atmospheric and elevated pressure (1000 psi / 68.95bars). The constant

K as defined by Eq. (3.2) was found to be 0.18 (see Figure 3-21) by using pure alkane data only.

Figure 3-21 shows a linear regression of lnS* and EACN with an R2 - value of 0.98. This K value

was used in order to predict phase behavior of the crude oil A, which was reported to have an

EACN of 9.9. The optimum salinity for the crude oil was predicted to be 2.33 g / 100 ml

(compared to the actual measured value of 2.3 g / 100 ml) at atmospheric conditions. From the β

factor, optimum salinity for dead oil at high pressure was calculated to be 2.45 g / 100 ml

(measured value is 2.35 g / 100 ml).

The live oil contained 17 mole % of methane. The EACN follows a mole-fraction

weighted formula for mixtures (Cash et al. 1977). The EACN of the live oil, as reported by

Roshanfekr and Johns (2011) was 8.4 where they considered EACN of methane to be 1. Using

the modified HLD equation, the predicted optimum salinity for the live oil is 1.88 g/100 ml

(measured value is 1.98 g/100ml).

The linear relationship for lnS* and 1/σ* are shown in Figure 3-22. The constants B1 and

B2 as defined by Eq. (3.11) are 0.08 and 0.02 respectively. Figure 3-22 shows a linear regression

with an R2- value of 0.91. The regression was used to predict optimum solubilization ratios for

the predicted optimum salinities from step (4). For the dead oil at atmospheric pressure, optimum

54

solubilization ratio was estimated to be 10.84 cc/cc (measured value is 11 cc/cc). For dead oil at

high pressure, the estimated optimum solubilization ratio was 11.32 cc/cc (measured value is 11.2

cc/cc). For live oil at high pressure, the estimated optimum solubilization ratio was 14.22 cc/cc

(measured value is 13 cc/cc).

The average length parameter L (35.96 Å), average interfacial area per molecule of

surfactant as (167.33 Å2), and the predicted optimum values were then used in the HLD-NAC

model in order to predict the salinity scans of the crude at dead and live conditions. Figure 3-23 to

Figure 3-25 show the predicted salinity scans and the actual data for comparison.

This example shows that if the β factor and EACN of the crude are known, salinity scans

using pure alkanes at atmospheric conditions are enough to predict phase behavior at high

pressures (with or without solution gas). Thus, no measurements with solution gas at high

pressure are necessary, except to verify the claims of our new modified HLD-NAC model.

3.5.3. Example 3:Austad and Strand (1996) and Austad and Taugbol (1995)

Experiments

Austad and Strand (1996) measured pressure and temperature scans using dead and live synthetic

oils in a PVT cell. Salinity and overall composition of the system were kept constant, but

pressure and temperature were varied to assess their effect on solubilization and optimum

conditions. Temperatures in their experiments ranged from 55°C to 120°C while pressures ranged

from 50 bars to 200 bars. The surfactant used was a dodecyl-ortho xylene sulfonate. Austad and

Taugbol (1995) used the same surfactant where they reported a salinity scan using n-heptane at

50°C. To analyze their data we performed the following steps:

1. The surfactant length parameter was first calculated. Using this value, the salinity scan

(phase fraction vs salinity) at atmospheric pressure and 50°C reported by Austad and

55

Taugbol (1995) was matched. The interfacial area per surfactant molecule (as) was again

used as a tuning parameter.

2. The HLD equations applicable to temperature and pressure scans (Eqs. (3.5) and (3.6))

were used in the net curvature equation.

3. Using the reported values of surfactant concentration and optimum variables (σ*, T* and

P*), matches to experimental results were obtained by tuning α for temperature scans and

β for pressure scans.

4. All “scans” were matched using the modified HLD Eqs. (3.5) and (3.6) coupled with the

NAC model. The width of the three-phase regions for each scan was estimated in HLD

units (ΔHLD). Eq. (3.9) was then validated.

The surfactant length parameter was 23.8 Å. The tuning process was completed and

Figure 3-26 shows the match obtained for the salinity scan reported by Austad and Taugbol

(1995). The tuned value of as was 98 Å2. The modified HLD equations Eqs. (3.5) and (3.6) were

then coupled with NAC to tune temperature and pressure scans reported by Austad and Strand

(1996). The calculated length parameter and tuned as value of 23.8 Å were used in the HLD-NAC

model.

Figure 3-27 to Figure 3-40 show matches obtained for temperature scans of live and dead

oils by tuning α. Figure 3-41 to Figure 3-51 show matches obtained for pressure scans of both

live and dead oils by tuning β. The matches obtained were excellent, which affirms the inclusion

of the factor β in the HLD equation. However, since only experimental data within the type III

window were available, we were unable to match data in the type II- and II+ regions. Table 3-5 to

Table 3-8 summarize the tuning results.

An interesting observation was made during the process of tuning these data. The tuned α

values, which affect the system’s temperature dependence on HLD, decrease with increasing

pressure (see Figure 3-52). This is a new observation since all α values reported previously were

56

obtained by analyzing experimental data obtained at atmospheric pressures. This result suggests

that the effect of temperature on microemulsion phase behavior as expressed by the HLD

equation decreases with an increase in pressure. Also, Salager et al. (1979 a.) concluded that the

surfactants they considered showed an average α value of 0.01 K-1. However, they could only

estimate α from experiments at atmospheric pressures. From Figure 3-52, it can be seen that the

tuned α values converge towards a value that is similar to their observation at atmospheric

pressures. However not much can be concluded about the dependence of β on temperature (see

Figure 3-53). The constant β is smaller than α so it is more noisy given experimental uncertainty.

The upper limit is defined at the transition between the type III and the type II+ regions

(type II+ microemulsions are also known as upper phase microemulsions). Similarly the lower

limit is defined at the transition between type II- and type III regions (type II- microemulsions are

also known as lower phase microemulsions). Since with increasing pressure, the system shifts

towards type II- (HLD decreases as pressure increases), the upper pressure limit is always lower

than the lower pressure limit. This is contrary to the traditionally popular salinity scans, where an

increase in salinity causes the phase behavior to shift towards type II+. The same is true for

temperature scans. Furthermore, we calculated the width of the three-phase regions using the

HLD equations. From Eq. (3.5), for a temperature scan, the ΔHLD in terms of the upper

temperature limit (TU) and lower temperature limit (TL) can be expressed as:

L UHLD T T . (3.19)

Similarly, for a pressure scan, from Eq. (3.6), the ΔHLD in terms of the upper pressure

limit (PU) and lower pressure limit (PL) can be expressed as:

L UHLD P P . (3.20)

57

Figure 3-54 shows the dependence of the optimum solubilization ratio on 1/ΔHLD (R2 -

value 0.99) and shows the validity of Eq. (3.9). Constants A1 and A2 are 2.54 and 4.28

respectively. The correlation satisfies all conditions of temperature and pressure for both dead and

live oils. These results provide new understandings of microemulsion phase behavior and suggest

that correlations exist that are unique to a particular surfactant, but are independent of oil

composition, temperature and pressure.

3.6. Discussion

The results show that the modified HLD coupled with NAC is a valuable tool for prediction of

microemulsion phase behavior of oils with different EACNs at different conditions of

temperature, pressure, and salinity. Furthermore, it is an excellent tool to interpret PVT

experiments like the ones conducted by Austad and Strand (1996). Such PVT experiments are

easier and faster to make compared to the traditional salinity scans at high pressures like the ones

reported by Roshanfekr and Johns (2011) and Jang et al. (2014). High pressure salinity scans

require sophisticated equipment and furnish phase behavior data at only one condition of

temperature and pressure. Alternatively, a PVT experiment furnishes data over a wide range of

temperatures and pressures and gives vital information required for proper interpretation of the

HLD factors α and β.

The effect of pressure on microemulsion phase behavior is also more important than

previously recognized. From the HLD equation for optimum conditions (Eq. (3.2)), it can be

seen that the linear trend of lnS* vs EACN translates by a factor of β(ΔP) where ΔP is the

difference between the pressure of interest and the reference pressure. Hence, a family of

58

parallel lines of different pressures (see Figure 3-55) results when lnS* is plotted as a function of

EACN. This is analogous to the family of parallel lines obtained at different temperatures but

constant pressure (Sun et al. 2012). Hence the method adopted by Jang et al. (2014), which

forced optimum salinities of lnS* vs EACN to lie on the same straight line could lead to an

incorrect interpretation. They did include the change in optima due to changing EACN as

solution gas is introduced into the oil phase. However, the effect of the translation based on

β(ΔP) was not included so they adjusted the EACN of methane to 10. Using the data reported by

Roshanfekr and Johns (2011), for example, if we forced the lnS* value for live oil on the EACN

trend at atmospheric pressure (see Figure 3-55), the EACN of the live oil would be 9, as compared

to the reported value of 8.2. Based on this value of EACN for the crude, the EACN of methane

must be incorrectly adjusted to 4.6 to lie on the same trend and to satisfy the approach presented

by Jang et al. (2014). From Figure 3-55, the error in EACN of methane will increase as pressure

increases owing to the shift of β(ΔP). Our approach shows that using the traditionally accepted

value of 1.0 for the EACN of methane, the entire phase behavior (not just optima) of live crude

can be predicted.

The EACN concept must also be used with caution. The traditionally used empirical rule

that determines the EACN of alkyl benzenes has been found to give inconclusive results (Puerto

and Reed, 1983). Queste et al. (2007) recently revisited the EACN rule and found that using fish

diagrams, the values of EACNs of alkyl benzenes can be drastically different from the ones

obtained from the traditional empirical equation. They also describe the limitations of

determining the EACNs of lower alkyl benzenes like benzene and toluene. Hence the dilution of

crude oils using toluene while assuming the toluene EACN to be 1.0 can lead to an error in

calculation of the crude oil EACN. Queste et al. (2007) suggested that EACN of toluene is -3,

but at the same time cautioned readers on the use of this value since it was obtained by

extrapolation and not by actual experiments. Therefore use of surrogate oils to match the

59

optimum salinity of a live oil is potentially an incorrect way to characterize the crude in a

microemulsion system. It is strongly recommended to use pure alkanes to obtain crude oil EACN.

Since the EACN concept attempts to scale the crude to an alkane, our recommendation will

potentially minimize errors in analysis of experimental results.

From the results obtained, we observe that β factors are approximately one-tenth of α

values. This does imply that pressure has a weak effect on phase behavior in comparison to

temperature if the magnitude of change in temperature is same as the change in pressure. But the

difference in pressures between atmospheric and reservoir conditions is larger than that for

temperature and therefore pressure effects can be equally significant when designing a

formulation for enhanced oil recovery. For example, if α is 0.01 K-1 and β is 0.001 bar-1, the

phase behavior change caused by a change of 20°C is about the same as that caused by 200 bars

(2900.8 psi). These differences in temperature and pressure might be representative of the

difference between laboratory and reservoir conditions and therefore, surfactant EOR

formulations must be optimized for both temperature and pressure.

The present research also demonstrates that in addition to the existence of an optimum

salinity at a particular temperature and pressure for a particular surfactant formulation, optimum

pressures and temperatures also exist. A scan can be performed experimentally by varying one

HLD variable while keeping all other variables fixed. The optima in a P, T and EACN space can

be determined easily if the HLD equation (Eq. (3.1)) is known. Therefore if relevant correlations

are known, phase behavior at different HLD values can be predicted using one single salinity scan

as a reference.

Reasonable estimates based on α values are available in the literature. This dissertation

provides reasonable estimates for β values as well (see Table 3-9). Similarly an estimate of K can

be made from the type of surfactant used. Salager et al. (1979) estimated K to be 0.16 (±0.01) for

the sulfonates used in their research. Acosta and Bhakta (2009) reported that a broad range of

60

surfactants have K values ranging from 0.1 to 0.2 with most surfactants having an average K

value of 0.17. Thus from one phase behavior experiment, using Eq. (3.2), a rough estimate of

optimum salinities can be made for different oils at any pressure and temperature. However for a

more robust flood design, we recommend the following steps to be followed to characterize

microemulsion phase behavior:

1. Salinity scans at atmospheric pressure and a reference temperature must be done using

pure alkanes. At least three experiments using alkanes of different EACNs should be

used. This provides the value for constant K and the constant intercept from in the HLD

equation. Additionally, a salinity scan of the oil of interest must be done under the same

conditions in order to assess its EACN by fitting its optimal salinity to the alkane trend.

Alternatively, the crude of interest may be diluted by two pure alkanes. Salinity scans

using these two model oils and the crude by itself can then be performed. The EACN of

the crude can be found iteratively by fitting the linear relationship between logarithm of

optimum salinity and EACN as shown by Roshanfekr and Johns (2011). Both approaches

also give a correlation between optimum solubilization ratios and optimum salinities that

satisfy Eq. (3.11).

2. Interfacial area per surfactant molecule and the surfactant length parameter can be

obtained from step (1). The HLD-NAC model can be tuned to match the salinity scan

experiments using the procedure described in this dissertation.

3. PVT experiments similar to the ones performed by Austad and Strand (1996) should then

be done at dead and live oil conditions at constant salinity of interest for a particular

reservoir. Matching procedures described in this dissertation can then be followed to

obtain α and β.

4. The HLD equation, now complete with pressure, temperature and EACN effects, coupled

with the NAC model becomes an equation of state (EOS) like tool that can be easily used

61

in simulators.

It is also worth pointing out that in our research we did not consider the effect of EACN,

temperature and pressure on as. The interfacial area parameter was always held constant.

However, Rosen (2004) reported a list of published results that show that as can vary with oil type

and temperature. Incorporating a model that captures changes in the area per surfactant molecule

due to pressure, temperature and EACN can potentially make the approach described in this

dissertation more accurate.

3.7. Conclusions

A new HLD-NAC based model for microemulsion phase behavior was developed. The approach

was validated by using available published data. The following conclusions are made:

1. Microemulsion phase behavior depends on pressure changes. The logarithm of optimum

salinity varies linearly with pressure.

2. The existing HLD equation was updated to include a new β factor to account for the

change in HLD due to pressure.

3. We confirm that temperature dependence on the HLD equation can be modeled by the α

factor, as defined by Salager et al. (1979 a.).

4. The optimum solubilization ratio depends inversely on the width of the three-phase

window expressed in HLD units. This dependence can be used to obtain a relationship

between optimum salinities and solubilization ratios. Based on salinity scans using

different pure alkanes, these relationships can be easily determined and used for

prediction.

5. The modified HLD equation we developed can be coupled with NAC and used to

interpret temperature and pressure scans.

62

6. PVT experiments like those reported by Austad and Strand (1996) are critical in

understanding the effect of pressure and temperature on phase behavior. They provide a

quick and easy way to obtain phase behavior data, specifically α and β in the HLD

equation, over a wide range of temperature and pressure. In comparison, salinity scans at

high pressures give limited information and are more cumbersome and expensive.

7. It is important to understand the implications of using surrogate oils to analyze high

pressure microemulsion phase behavior. Pressure and solution gas both affect phase

behavior and in a compensating manner. Therefore ignoring either one of them can lead

to errors. We do not recommend the use of surrogate oils or forcing the EACN of

methane to be values other than 1.0.

63

Table 3-1: Summary of prediction of optima at various temperatures for SAS surfactant.

Predictions for S* were made by taking S

* at 20°C as reference and using α = 0.0031 K

-1.

Data obtained from Skauge and Fotland (1990).

T in °C S* in g/100 ml S* in g/100 ml σ* in

cc/cc σ*

in cc/cc % relative error in S*

% relative error in σ*

Actual Predicted from α

Actual Predicted

20.00 4.60 4.60 7.60 7.55 0.72 55.00 4.89 5.13 6.00 6.61 4.96 10.25 65.00 5.08 5.29 5.70 6.37 4.16 11.77 80.00 5.29 5.54 5.20 6.02 4.79 15.81 85.00 5.43 5.63 4.90 5.91 3.74 20.62 90.00 5.84 5.72 5.50 5.80 2.04 5.46 Average 3.94 10.77

Table 3-2: Summary of prediction of optima at various pressures for SAS surfactant.


* at 20°C and atmospheric pressure as reference. β

is 0.0006 bar-1

. Data obtained from Skauge and Fotland (1990).

P in bars

S* in g/100 ml S* in g/100 ml σ* in

cc/cc σ*



Actual Predicted from β

Actual predicted

1.01 4.60 4.60 7.60 7.55 0.72 197.30 5.48 5.18 6.90 6.54 5.58 5.20 250.77 5.69 5.35 7.10 6.29 6.01 11.38 395.78 5.92 5.83 7.50 5.66 1.55 24.51 480.36 6.26 6.14 7.30 5.32 1.98 27.09 553.31 6.47 6.41 7.30 5.04 0.99 30.90 Average 3.22 16.63

64

Table 3-3: Summary of prediction of optima at various temperatures for SDBS surfactant.

Predictions for S* were made by taking the S

* at 20°C as reference. α is 0.0077 K

-1. Data

obtained from Skauge and Fotland (1990).

T in °C S* in g/100 ml S* in g/100 ml σ* in

cc/cc σ*



Actual Predicted from α

Actual predicted

20.00 2.10 2.10 7.90 8.46 7.14 35.00 2.29 2.36 7.20 7.31 2.90 1.56 45.00 2.49 2.54 6.60 6.70 2.09 1.55 50.00 2.58 2.64 6.70 6.43 2.68 3.97 55.00 2.64 2.75 6.00 6.19 4.02 3.10 60.00 2.83 2.86 6.00 5.96 0.83 0.73 65.00 3.05 2.97 5.20 5.74 2.64 10.43 Average 2.53 4.07

Table 3-4: Summary of prediction of optima at various pressures for SDBS surfactant.


* at 20°C and atmospheric pressure as reference. β

is 0.0008 bar-1

. Data obtained from Skauge and Fotland (1990).

P in bars

S* in g/100 ml S* in g/100 ml σ* in

cc/cc σ*



Actual Predicted from β

Actual predicted

1.01 2.15 2.15 8.30 8.22 1.01 138.69 2.37 2.40 7.70 7.17 0.91 6.88 284.49 2.63 2.69 7.40 6.32 2.47 14.64 350.15 2.80 2.84 7.20 5.99 1.49 16.75 421.00 2.99 3.00 7.20 5.68 0.48 21.10 Average 1.34 12.07

65

Table 3-5: Summary of results obtained by matching pressure scans for dead oil. Data

obtained from Austad and Strand (1996).

T in °C P* in bars σ*

in cc/cc

β in bars-1 ΔHLD PU in bars PL in bars

55.00 291.65 16.07 7.70E-04 0.22 148.79 434.51

60.00 247.16 14.31 7.60E-04 0.26 76.11 418.21

65.00 201.37 13.01 7.30E-04 0.30 -2.74 405.48

70.00 154.91 11.67 7.10E-04 0.35 -88.75 398.57

75.00 101.45 10.51 8.30E-04 0.40 -137.10 340.01

80.00 45.00 9.45 9.80E-04 0.45 -186.63 276.63

85.00 -9.26 8.39 1.00E-03 0.53 -273.26 254.74

Table 3-6: Summary of results obtained by matching pressure scans for live oil. Data


T in °C P* in bars σ* in

cc/cc β in bars-1

ΔHLD PU in bars PL in bars

70.00 612.37 20.15 2.50E-04 0.15 304.37 920.37 75.00 528.00 18.03 3.80E-04 0.18 285.90 770.11 80.00 478.38 16.27 3.00E-04 0.22 118.38 838.38 85.00 394.06 14.48 3.70E-04 0.26 48.11 740.00 90.00 318.57 12.85 2.90E-04 0.30 -205.57 842.71

66

Table 3-7: Summary of results obtained by matching temperature scans for dead oil. Data


P in bars T* in °C σ* in

cc/cc α in K-1 ΔHLD TU in °C TL in °C

50.00 79.75 9.61 8.90E-03 0.45 54.69 104.80 100.00 75.23 10.58 8.30E-03 0.39 51.50 98.97 150.00 70.47 11.61 7.70E-03 0.35 47.87 93.07 200.00 65.17 13.01 6.40E-03 0.30 41.89 88.45 250.00 59.75 14.42 5.90E-03 0.26 37.89 81.62 300.00 53.97 16.37 5.00E-03 0.21 32.57 75.37

Table 3-8: Summary of results obtained by matching temperature scans for live oil. Data


P in bars T* in °C σ* in

cc/cc α in K-1 ΔHLD TU in °C TL in °C

600.00 70.37 20.06 3.20E-03 0.15 46.31 94.43 500.00 77.61 17.07 5.10E-03 0.20 58.00 97.22 450.00 82.11 15.80 4.20E-03 0.23 55.21 109.02 400.00 84.71 14.71 4.40E-03 0.25 56.30 113.12 300.00 91.01 12.75 6.40E-03 0.31 67.11 114.92 250.00 93.87 12.40 5.40E-03 0.32 64.43 123.32 200.00 96.33 11.79 7.30E-03 0.34 73.04 119.62 100.00 98.87 10.30 8.40E-03 0.41 74.58 123.15

67

Table 3-9: Summary showing β values obtained from tuning. Data from Skauge and

Fotland (1990), Roshanfekr and Johns (2011) and Austad and Strand (1996).

Source β in bars-1

Example 1: SAS data from Skauge and Fotland (1990) 6.00E-04

Example 1: SDBS data from Skauge and Fotland (1990) 8.00E-04

Example 2: Roshanfekr and Johns (2011) 7.71E-04

Example 3: Dead oil pressure scan at 55°C (Austad and Strand 1996) 7.70E-04







Example 3: Live oil pressure scan at 70°C (Austad and Strand 1996) 2.50E-04





Average 6.36E-04

Standard Error 6.55E-05

68

Figure 3-1: Optimum salinity as a function of

pressure for experiments reported for the SAS

surfactant (Skauge and Fotland 1990). The slope is

the β factor for the HLD equation.

Figure 3-2: Optimum salinity as a function of

pressure for experiments reported for the SDBS

surfactant (Skauge and Fotland 1990). The slope is

the β factor for the HLD equation.

Figure 3-3: A schematic showing the trend lines

for the optimum salinity, and the upper and lower

salinity limits. The width of the three-phase

Winsor III region is shown.

Figure 3-4: Reciprocal of optimum solubilization

ratios as a function of logarithm of optimum

salinity. Red, green and blue represent data at

20°C, 50°C and 90°C respectively. Oils used were

heptane, octane and decane. B1 = 0.15 and B2 =-

0.22. Data from Sun et al. (2012).

y = 0.0006x + 1.56 R² = 0.9555

1.5

1.6

1.7

1.8

1.9

0 200 400 600

ln S

*

Pressure (bars)

y = 0.0008x + 0.76 R² = 0.9958

0.6

0.8

1

1.2

0 100 200 300 400 500

ln S

*

Pressure (bars)

y = 0.15x - 0.22 R² = 0.96

0.04

0.12

0.2

1.8 2 2.2 2.4 2.6

1/σ

* (c

c/c

c)

lnS* (g/100 ml)

E

nS

Δ EACN Δ lnS

69

Figure 3-5: Flowchart of the modified HLD-NAC Equation-of-State.

HLD from

Eq.(3.1)

Initial

compositions

Vo,Vw,Vs

σ* from

Eq. (3.11)

Constants K,

α, β, f(A), Cc

Salinity

Oil EACN

Temperature

Pressure

Lc from Eq.

(3.12)

Tuned

as

Obtain HLDL and HLDU If HLDL ≤ HLDU

If HLDL > HLD

U :

HLD < HLDL

Type II-

HLDL < HLD <

HLDU

Type III

HLDU < HLD

Type II+

HLDL < HLD

Type II+

HLDU < HLD <

HLDL

Type IV

HLD < HLDU

Type II+

Solubilized

component

volumes

Vom and Vwm

Phase volumes Voo,

Vww and Vm

Solubilization ratios

σw and σo

lnS* from

Eq.(3.2)

Constants B1

and B2

nc of

surfactant

component

L=1.2Lc

70

Figure 3-6: Phase volume fractions after tuning as

a function of salinity for the SAS surfactant. The

value for interfacial area per molecule after tuning

was 180 Å2. Data from Skauge and Fotland (1990).

Figure 3-7: Phase volume fractions after tuning as

a function of salinity for the SDBS surfactant. The

value of interfacial area per molecule after tuning

was 97 Å2. Data from Skauge and Fotland (1990).

Figure 3-8: Logarithm of optimum salinity as a

function of EACN for experiments reported for

SAS surfactant. The slope of the trend line gives

the slope K for the HLD equation. Data obtained

from Skauge and Fotland (1990).


function of EACN for experiments reported for

SDBS surfactant. The slope of the trend line gives

the slope K for the HLD equation. Data obtained

from Skauge and Fotland (1990).

2 3 4 5 6 7 80

0.2

0.4

0.6

0.8

1

Salinity in g/100 ml

Ph

ase v

olu

me f

racti

on

Type II+

Type II-

Excess

oil

Type III

Excess

water

0 1 2 3 4 50

0.2

0.4

0.6

0.8

1


Ph

ase v

olu

me f

racti

on

Type II+

Type III

Type II-

Excess

oil

Excess

water

y = 0.12x + 0.69 R² = 0.99

1

1.5

2

2.5

6 8 10 12

ln S

* (g

/100 m

l)

EACN

y = 0.14x - 0.18 R² = 0.99

0.4

0.8

1.2

1.6

6 8 10 12 14

ln S

* (g

/100 m

l)

EACN

71


function of reciprocal of optimum solubilization

ratio for experiments reported for SAS surfactant

from the EACN trend. B1 = 0.24 and B2 = -0.24.

Data obtained from Skauge and Fotland (1990).



ratio for experiments reported for SDBS

surfactant from the EACN trend. B1 = 0.18 and B2

= -0.02. Data obtained from Skauge and Fotland

(1990).

Figure 3-12: logarithm of optimum salinity as a

function of temperature for experiments reported

for SAS surfactant. The slope of the trend line

gives the α factor for the HLD equation. Data




for SDBS surfactant. The slope of the trend line

gives the α factor for the HLD equation. Data


y = 0.24x - 0.24 R² = 0.99

0.10

0.15

0.20

0.25

0.30

1.40 1.60 1.80 2.00 2.20

1/σ

*

ln S* (g/100 ml)

y = 0.18x - 0.02 R² = 0.98

0.08

0.13

0.18

0.23

0.28

0.60 0.80 1.00 1.20 1.40 1.60

1/σ

*

ln S* (g/100 ml)

y = 0.003x + 1.45 R² = 0.8819

1.40

1.50

1.60

1.70

1.80

15.00 35.00 55.00 75.00 95.00

ln S

* (g

/100 m

l)

Temperature in °C

y = 0.0077x + 0.56 R² = 0.9682

0.6

0.8

1

1.2

15 35 55 75

ln S

* (g

/100 m

l)

Temperature in °C

72

Figure 3-14: Optimum solubilization ratio as a

function of pressure for experiments reported for

SAS surfactant. The HLD equation and equation

from Figure 3-10 was used for prediction. Data



function of pressure for experiments reported for

SDBS surfactant. The HLD equation and equation

from Figure 3-11 was used for prediction. Data




for SAS surfactant. The HLD equation and

equation from Figure 3-10 was used for

prediction. Data obtained from Skauge and

Fotland (1990).



for SDBS surfactant. The HLD equation and

equation from Figure 3-11 was used for

prediction. Data obtained from Skauge and

Fotland (1990)

73

Figure 3-18: Tuned result for solubilization ratios

as a function of salinity for octane. Red represents

oil solubilization ratios. Blue represents water

solubilization ratios. The solid lines are model

results from HLD-NAC obtained by tuning as.


as a function of salinity for decane. Red represents

oil solubilization ratios. Blue represents water

solubilization ratios. The solid lines are model

results from HLD-NAC obtained by tuning as.


as a function of salinity for dodecane. Red

represents oil solubilization ratios. Blue represents

water solubilization ratios. The solid lines are

model results from HLD-NAC obtained by tuning

as.


function of EACN. A mixture of tridecyl alcohol

propoxylate and C13-C18 internal olefin sulfonate

was used along with iso-propanol as cosurfactant.

Data obtained from Roshanfekr et al. (2011).

0.5 1 1.5 20

5

10

15

20

25

30

Salinity in gms/100 ml

So

lub

iliz

ati

on

rati

o (

cc/c

c)

1.4 1.6 1.8 2 2.2 2.4 2.6 2.80

5

10

15

20

25

30


So

lub

iliz

ati

on

rati

o (

cc/c

c)

2.8 3 3.2 3.4 3.6 3.8 4 4.20

5

10

15

20


So

lub

iliz

ati

on

rati

o (

cc/c

c)

y = 0.18x - 0.91 R² = 0.98

0.4

0.8

1.2

7 9 11 13

ln S

* (g

/100 m

l)

EACN

74



ratio from experiments with varying EACN. B1 =

0.08 and B2 = 0.02. Data obtained from

Roshanfekr et al. (2011).

Figure 3-23: Prediction of phase behavior for dead

oil at elevated pressure (68.95 bars) using data

from pure alkane series and estimated β factor of

7.71×10-4/bar. Red represents oil solubilization

ratios. Blue represents water solubilization ratios.

Figure 3-24: Prediction of phase behavior for dead

oil at atmospheric pressure using data from pure

alkane series. Red represents oil solubilization


The solid lines are model results from HLD-NAC.

Figure 3-25: Prediction of phase behavior for live

oil at high pressure using estimated β factor of

7.71×10-4/bar. Red represents oil solubilization


The solid lines are model results from HLD-NAC.

y = 0.08x + 0.02 R² = 0.91

0.04

0.06

0.08

0.1

0.12

0.14

0.4 0.6 0.8 1 1.2 1.4

1/σ

*

lnS* (g/100 ml)

2 2.2 2.4 2.6 2.80

10

20

30


So

lub

iliz

ati

on

rati

o (

cc/c

c)

2 2.5 3 3.5 4 4.50

10

20

30


So

lub

iliz

ati

on

rati

o (

cc/c

c)

1.5 2 2.5 3 3.50

10

20

30


So

lub

iliz

ati

on

rati

o (

cc/c

c)

75

Figure 3-26: Phase volume fractions as a function

of salinity using 0.5 wt. % dodecyl orthoxylene

sulfonate. The tuned as value was 98 Å2. Solid

lines represent model outputs with tuned alpha

values. Circles represent experimentally obtained

values. Blue represents

Figure 3-27: Comparison of tuned result (solid

lines) and actual values (circles) for dead oil

temperature scan at 50 bars. Red represents oil

solubilization. Blue represents water

solubilization. Data from Austad and Strand

(1996).






(1996).






(1996).

2 2.5 30

0.2

0.4

0.6

0.8

1


Ph

ase v

olu

me f

racti

on

Type

II-

Excess

oil

Type III

Excess water

Type

II+

65 70 75 80 85 90 95 1000

10

20

30

40

Temperature in oC

So

lub

iliz

ati

on

rati

o (

cc/c

c)

60 65 70 75 80 85 90 950

10

20

30

40

Temperature in oC

So

lub

iliz

ati

on

rati

o (

cc/c

c)

55 60 65 70 75 80 85 900

10

20

30

40

Temperature in oC

So

lub

iliz

ati

on

rati

o (

cc/c

c)

76






(1996).






(1996).






(1996).


lines) and actual values (circles) for live oil




(1996).

50 55 60 65 70 75 80 850

10

20

30

40

Temperature in oC

So

lub

iliz

ati

on

rati

o (

cc/c

c)

45 50 55 60 65 70 75 800

10

20

30

40

Temperature in oC

So

lub

iliz

ati

on

rati

o (

cc/c

c)

45 50 55 60 65 700

10

20

30

40

Temperature in oC

So

lub

iliz

ati

on

rati

o (

cc/c

c)

80 90 100 110 1200

10

20

30

40

Temperature in oC

So

lub

iliz

ati

on

rati

o (

cc/c

c)

77






(1996).






(1996).






(1996).






(1996).

80 90 100 110 1200

10

20

30

40

Temperature in oC

So

lub

iliz

ati

on

rati

o (

cc/c

c)

70 75 80 85 90 95 100 1050

10

20

30

40

Temperature in oC

So

lub

iliz

ati

on

rati

o (

cc/c

c)

70 75 80 85 90 95 100 1050

10

20

30

40

Temperature in oC

So

lub

iliz

ati

on

rati

o (

cc/c

c)

70 75 80 85 90 95 1000

10

20

30

40

Temperature in oC

So

lub

iliz

ati

on

rati

o (

cc/c

c)

78






(1996).






(1996).






(1996).



pressure scan at 55°C. Red represents oil



(1996).

70 75 80 85 90 950

10

20

30

40

Temperature in oC

So

lub

iliz

ati

on

rati

o (

cc/c

c)

60 65 70 75 80 85 900

10

20

30

40

Temperature in oC

So

lub

iliz

ati

on

rati

o (

cc/c

c)

60 65 70 75 80 85 900

10

20

30

40

Temperature in oC

So

lub

iliz

ati

on

rati

o (

cc/c

c)

240 260 280 300 320 340 3600

5

10

15

20

25

30

Pressure in bars

So

lub

iliz

ati

on

rati

o (

cc/c

c)

79






(1996).






(1996).






(1996).






(1996).

200 220 240 260 280 3000

5

10

15

20

25

30

Pressure in bars

So

lub

iliz

ati

on

rati

o (

cc/c

c)

140 160 180 200 220 240 2600

5

10

15

20

25

30

Pressure in bars

So

lub

iliz

ati

on

rati

o (

cc/c

c)

0 50 100 150 200 2500

5

10

15

20

25

30

Pressure in bars

So

lub

iliz

ati

on

rati

o (

cc/c

c)

0 50 100 150 2000

5

10

15

20

25

30

Pressure in bars

So

lub

iliz

ati

on

rati

o (

cc/c

c)

80






(1996).






(1996).






(1996).






(1996).

0 50 100 1500

5

10

15

20

25

30

Pressure in bars

So

lub

iliz

ati

on

rati

o (

cc/c

c)

500 520 540 560 580 6000

5

10

15

20

25

30

Pressure in bars

So

lub

iliz

ati

on

rati

o (

cc/c

c)

500 520 540 560 580 6000

5

10

15

20

25

30

Pressure in bars

So

lub

iliz

ati

on

rati

o (

cc/c

c)

300 350 400 450 500 550 6000

5

10

15

20

25

30

Pressure in bars

So

lub

iliz

ati

on

rati

o (

cc/c

c)

81






(1996).






(1996).

Figure 3-52: Variation of α with increasing

pressure. Blue squares represent tuned α values

for dead oil. Red squares represent tuned α values

for the live oil. Data obtained by analysis of

experimental results reported by Austad and

Strand (1996).

Figure 3-53: Variation of β with increasing

temperature. Blue squares represent tuned β

values for dead oil. Red squares represent tuned β

values for the live oil. Data obtained by analysis of

experimental results reported by Austad and

Strand (1996).

340 360 380 400 420 440 4600

5

10

15

20

25

30

Pressure in bars

So

lub

iliz

ati

on

rati

o (

cc/c

c)

100 200 300 400 5000

5

10

15

20

25

30

Pressure in bars

So

lub

iliz

ati

on

rati

o (

cc/c

c)

y = -1E-05x + 0.0089 R² = 0.8672

0

0.005

0.01

0.00 200.00 400.00 600.00 800.00

α (

K-1

)

Pressure (bars)

0.00E+00

4.00E-04

8.00E-04

1.20E-03

40 60 80 100

β (

bar-

1)

Temperature (°C)

82

Figure 3-54: linear correlation of the optimum

solubilization ratio inverse of the three-phase

region width and the inverse of the three-phase

region width. The points represent results from

both live and dead oil at all pressures and

temperatures reported. A1 = 2.54 and A2 = 4.28.

Data obtained by analysis of experimental results

reported by Austad and Strand (1996).

Figure 3-55: A schematic showing the shifts in

optimum salinity trend line due to pressure. The

shifts in the intercepts are caused by the β factor

and the difference between the pressure of interest

and the reference pressure. The black dot shows

the optimum salinity at the reference condition.

The green circles show the correct interpretation

of the shift due to pressure. The red circles show

the incorrect interpretation made in Jang et al.

(2014).

y = 2.54x + 4.28 R² = 0.99

0.00

5.00

10.00

15.00

20.00

25.00

1.00 2.00 3.00 4.00 5.00 6.00 7.00

σ*

(cc/c

c)

1/ΔHLD EACN

lnS

*

Pref, Tref

P1, T

ref

P2, T

ref

83

Chapter 4

A Modified HLD-NAC Equation of State to Predict Alkali-Surfactant-

Oil-Brine Phase Behavior

This chapter discusses tuning of the model and modifications that were made to the flash

calculation procedure to allow for two or more surface active agents; one or more synthetic

surfactants, and the soap formed in-situ as a result of saponification. The model parameters are

dependent on the soap mole fraction and can be obtained by simple mixing rules developed here.

A variety of examples show that the model is capable of predicting complex phase behavior

diagrams such as ternary diagrams, activity charts and fish plots. The pH dependent soap

formation mode is introduced, where petroleum acids are represented by one pseudo component

labeled HA. The mole fraction of soap is then included in the hydrophilic-lipophilic difference

(HLD) and net-average curvature (NAC) model. The required inputs and the approach to tuning

of experimental data are discussed, followed by an illustration of the flash calculation procedure.

4.1. Soap Formation Model

The acid number (AN) of oil is defined as the milligrams of potassium hydroxide required to

neutralize one gram of oil (ASTM, 2005). Specifically for EOR applications, the acid number of

reservoir crude is a measure of its acid content at equilibrium with the reservoir brine. The model

of deZabala et al. (1982) predicts soap formation as a function of the equilibrium acid content in

the oil using equilibrium partition coefficients. We use the soap formation model presented by

84

Sharma and Yen (1983), where the equilibrium partition constants are dependent on the structure

of the acid pseudo component.

The unsaponified acid species HA partitions between the oil (o) and water (w) phase.

Hence the distribution equilibrium constant (Kd) can be represented by,

and W

O

HA

O W d

HA

CHA HA K

C (4.1)

where Ci represents concentration of species i. Dissociation of the acid in the aqueous phase at

equilibrium forms the soap. The dissociation constant Ka is dependent on the aqueous H+

concentration (pH) of the system. More soap is formed at high pH such that,

and

W

H AW a

HA

C CHA H A K

C

. (4.2)

From mass conservation, Sharma and Yen (1983) showed that the concentration of the

dissociated acid A- (soap) is dependent on the equilibrium constants Ka and Kd by,

0

1 1

o

oHA

w

A

w OH d o

a w

SC

SC

K C K S

K S

(4.3)

where Kw is the dissociation constant for water and So and Sw are oil and water saturations

respectively. C0HAo is the initial acid concentration in the oil phase, which is calculated from the

acid number. Rock-fluid reactions associated in alkali processes are beyond the scope of this

85

dissertation, but could be coupled by including the pH and chemical species concentrations in Eq.

(4.3).

4.2. Equilibrium Constants and Their Dependence on the Molecular

Structure of Petroleum Acids

The equilibrium reaction constants are dependent on the molecular structure of the acids present

in the oil. Furthermore, the distribution of acids between the oil and water phases is dependent on

additional factors like oil type and temperature. Temperature will also affect the dissociation

reaction. Values of equilibrium constants are traditionally assumed owing to lack of sufficient

data. Mohammadi (2008) and Mohammadi et al. (2009) for example, used fixed values of Kd

=10-4 and Ka =10-10, but in this dissertation we use empirical trends in estimating these

equilibrium constants.

Smith and Tanford (1973) examined partitioning of straight-chain paraffinic acids in

heptane-water systems at 25°C. They found that the free energy involved in the transfer of

carboxylic acids between the oleic and aqueous phases is a linear function of the number of

carbon atoms in the aliphatic tail (n). Consequently, they concluded that the negative logarithm

of the distribution constant (pKd) is nearly a linear function of n. We fit their data and obtained

the following linear relationship (see Figure 4-1),

0.601 3.389dpK n . (4.4)

With limited data for reservoir crudes at high temperature, Eq. (4.4) is useful for estimating more

physical values of the partitioning coefficient.

Smith and Tanford (1973) and Goodman (1958) showed that the pKa values of fatty acids

are independent of the alkyl chain length. This is a reasonable assumption because the pKa values

86

are strong functions of the acidic functional group, which for naphthenic acids is the carboxylic

group. Consequently, we use a pKa of 4.76 as reported by Smith and Tanford (1973) for all

calculations in this dissertation. This value of pKa does not agree with the fixed value used by

Mohammadi (2008).

4.3. Flash Calculations Including the Alkali Component

This section describes coupling of the soap formation equations with modified HLD-NAC using

the same flash calculation protocol described previously in Chapter 3. From Eq. (4.3), the

amount of soap formed is calculated from the acid content in the oil (AN), the concentration COH-

(the pH or pOH) of the aqueous phase, the distribution coefficient of the undissociated acid HA

(from pKd), the dissociation constant of HA (from pKa), and the water-oil ratio (ratio of water and

oil saturations). The molecular weight contribution of the –COOH group is 45.016 g/mol. The

molecular weight contribution of the CH3- and CH2- group is 15.034 g/mol and 14.026 g/mol,

respectively. Hence, for a given value of n, the molecular weight (in g/mol) of a carboxylic acid

is,

60.05 14.026( 1)HAMW n . (4.5)

The total volume of the surfactant pseudo component (Vs) is a function of the moles of

soap formed and the molecular weight of soap. Also, for a given value of n, pKd is calculated

using Eq. (4.5), while pKa is fixed at 4.76 as discussed previously. Hence, the concentration of the

soap formed in our approach becomes solely dependent on

1. the acid number of the oil, which is generally known from laboratory experiments;

87

2. the water-oil ratio from the initial overall composition (or from saturations in a grid

block);

3. Density of oil (to calculate C0HAo), which is also generally known from laboratory

experiments;

4. the pH, which is a function of alkali concentration; and

5. n, which is dependent on the structure of the acidic pseudo component.

Key HLD-NAC model parameters are taken as functions of the soap concentration

formed. The L parameter for soap (Lsoap) and synthetic surfactant (Lsurfactant) are calculated from

the effective number of carbon atoms (n) in the tail using the methodology described by Ghosh

and Johns (2014). They estimated the tail length for synthetic surfactant by calculating the

effective carbon number using rules established by Rosen (2004) and Tanford (1980). The

interfacial area per molecule for the -COO – head group is taken to be 60 Å2 based on the value

reported for oleic acid soap (asoap) by Acosta et al. (2008). The interfacial area per molecule for

the synthetic surfactant (asurf) is relatively unknown and is used as a tuning parameter in this

dissertation.

Acosta et al. (2008) applied HLD-NAC to mixtures of anionic surfactants. This

dissertation follows their procedure and lumps the soap and synthetic surfactant into one

surfactant pseudo component. They used a mole fraction weighted linear mixing rule in order to

calculate the L parameter. Hence,

soap soap surfactant surfactant

1

N

i i

i

L X L X L X L

, (4.6)

88

where N is the total number of surface active agents. In this research, two or more synthetic

surfactants are lumped into one surfactant pseudo component and distinguished from the soap.

That is,

soap surfactant

1

1N

i

i

X X X

. (4.7)

Similarly, the area term As can be obtained by adding the area contributions of the soap

and surfactant based on their concentrations. The surfactant pseudo component volume Vs is also

obtained by adding the volume contributions of all the surface active agents in the system. That

is,

23

soap soap surfactant surfactant6.023 10 ( )SA n a n a , (4.8)

and,

soap surfactantSV V V . (4.9)

Mole fraction based mixing rules are also used for calculating optimum salinities (Acosta

et al., 2008; Liu et al., 2010; Mohammadi et al., 2009; Salager et al., 1979 a.) as expressed by,

* * * *

soap soap surfactant surfactant

1

ln ln ln lnN

i i

i

S X S X S X S

. (4.10)

Equations (4.7) and (4.10) imply,

*

soapln S X . (4.11)

89

The logarithm of S* is also proportional to the inverse of optimum solubilization ratio (Ghosh

and Johns, 2014) so that,

* *ln 1/S . (4.12)

Hence, from Eqs. (4.11) and (4.12), the inverse of the optimum solubilization ratio is also

proportional to the soap mole fraction. That is,

*1/ soapX , (4.13)

and,

soap surfactant

* * * *1soap surfactant

1 Ni

i i

X X X

. (4.14)

Equations (4.13) and (4.14) are new relationships presented in this dissertation, which are

different from traditionally used linear and logarithmic mole fraction averaged rules

(Mohammadi, 2008). Equations (4.11) and (4.14) can be written using Eq. (4.7) as

*

1 soap 2ln S C X C , (4.15)

and,

1 soap 2*

1D X D

, (4.16)

where C1, C2, D1 and D2 are constants. The values of S* and σ* obtained are therefore dependent

on the amount of soap formed. These constants can be determined by having at least two points

90

at different alkali concentration (likely one of these is without alkali so that only synthetic

surfactant exists). Additionally, adding Eqs. (4.15) and (4.16) gives,

*

1 1 soap 2 2*

1ln ( ) ( ) 0S C D X C D

. (4.17)

Equation (4.17) represents a plane in the ( lnS*, 1/ σ*, Xsoap ) space.

The density of oil, acid number, pH of the solution and n determines Xsoap. Once the

constants in Eqs. (4.15) and (4.16) are known, the same flash calculation procedure used in

Chapter 3 is followed with an adjustment of several input parameters to account for Xsoap, namely

the L, AS, and HLD. For example, Eq. (4.15) is used to calculate the value of the HLD parameter

as a function of salinity. The constants (K, α, β and Cc) in the HLD equation would also follow a

mole fraction averaged rule (Acosta et al., 2008). Acosta et al. (2008) particularly mentioned

that the constant K, which varies over a small range from 0.1 to 0.19 for surfactants, can be

assumed to be independent of the surfactant mole fraction. This allows the model to perform

general flash calculations for all possible varying input parameters, such as salinity, temperature,

pressure, or oil composition (EACN).

4.4. Results

We demonstrate our modified HLD-NAC model using experimental data in the literature. We

further demonstrate how our model can be tuned and used to predict complicated phase behavior

in the presence of soap and synthetic surfactant. Solubilization ratios in phase behavior

experiments for alkali surfactant systems are typically reported in terms of volume of synthetic

surfactant because soap formation is unknown.

91

4.4.1. Case A from Mohammadi (2008), and Mohammadi et al. (2009)

These experiments were done using a blend of two anionic surfactants, C22-24 internal olefin

sulfonate (0.1 wt. %) and a branched C16 alkyl benzene sulfonate (0.1 wt. %). We calculated the

mean molecular weight of the surfactant blend to be 408.61 g/mol. Diethylene glycol butyl ether

was used as a cosolvent. The oil had an acid number of 0.5 mg of KOH/g of oil. Synthetic

brine at 0.6 wt.% NaCl concentration (0.103 meq/ml) was used. Scans using sodium carbonate as

the alkali were done for concentrations varying from 0 to 50,000 ppm. Experiments were

conducted for five different, evenly spaced oil concentrations (volume basis) ranging from 10 to

50%. The pH for sodium carbonate (alkali) in aqueous solution was calculated. All experiments

were performed at 62°C and atmospheric pressure.

4.4.1.1. Determinination of Soap Model Parameters

Mohammadi (2008) assumed values of equilibrium constants to calculate soap mole fractions.

Contrarily, in this research, the alkyl carbon number of the acid n is used to calculate Kd in a more

deterministic approach. The values of reported optimum solubilization ratios and salinities are

shown in Table 4-1. A linear fit to their data (see Eqs. (4.15) and (4.16)) gives the required

coefficients C1, C2, D1, and D2. The density of oil was assumed to be 0.9 g/cc to calculate C0HAo

from the acid number. The pH is calculated from the concentration of sodium carbonate in the

aqueous phase (see Appendix B). The initial composition and hence water-oil ratios are also

known. Therefore, only a simple iteration on n is needed to complete the soap formation model.

As discussed, the parameter n governs the distribution coefficient, molecular weight, and tail

length of the soap, thereby reducing the number of tuning variables. Excellent R2-values of 0.96

and 0.997 for n equal to 13 were obtained from linear regression of σ* and lnS*as a function of

92

Xsoap, respectively (see Figure 4-2 and Figure 4-3). Constants C1 and C2 were -1.19 and 0.001,

respectively, while D1 and D2 were -0.053 and 0.059, respectively.

4.4.1.2. Tuning the Phase Behavior Model

The modified HLD-NAC model was tuned to available experimental data, using only one tuning

parameter. All other parameters were calculated or known. The experimental data fit are

sodium carbonate scans for oil volume concentrations of 50% and 30% as reported by

Mohammadi. The length parameter L for the synthetic surfactant is 32.92 Å according to the

procedure described by Ghosh and Johns (2014). For the soap with an alkyl carbon number of

n=13, the length parameter L is calculated to be 21.53 Å. The area per molecule of the soap

(asoap) is 60 Å2 as discussed previously. Thus, the only adjustable parameter remaining is the

area per molecule of surfactant (asurf) since it is relatively unknown. This parameter is adjusted so

that the model matches the measured phase behavior data. Figure 4-4 shows the tuned result for

the case with 50% (v/v) oil concentration. The tuned value of asurf was found to be 215 Å. For

30% (v/v) oil concentration, the tuned value of asurf was found to be 195 Å (see Figure 4-5),

which is very close to the value for 50% oil concentration. Because the results for the area

parameter were consistent, we used an average value of asurf (205 Å) for predictions with our

modified HLD-NAC model. Comparisons between our tuned model and UTCHEM results

reported by Mohammadi are also shown in the figures, which show a better overall fit of the data

with our modified HLD-NAC model. The large value of asurf is likely due to the use of co-solvent

in the formulations.

93

4.4.1.3. Phase Behavior Predictions

Phase behavior diagrams were generated by making flash calculations with the modified HLD-

NAC model. The input parameters for Case A are summarized in Table 4-2. The first diagrams

generated are solubilization curves for various oil concentrations. Figure 4-6 shows the

predicted curves for 10% oil concentration, while Figure 4-7 is for 20% oil concentration and

Figure 4-8 for 40% oil concentration. Only the optima for these experiments were reported.

Flash calculation results for the 10% and 40% oil concentration cases at different sodium

carbonate concentrations can be seen in Figure 4-9 and Figure 4-10, respectively.

A common phase behavior diagram reported in the literature is activity maps. Activity

maps show the evolution of the three-phase region as a function of overall oil concentration and

salinity. UTCHEM uses parameters CSEU (upper salinity limit) and CSEL (lower salinity limit)

as input parameters for the Hand’s rule based model. CSEU and CSEL are determined from

experimental data using the procedure described in Sheng (2010). The limits for other

experiments are derived using a mixing rule similar to Eq.(4.10) . One of the main advantages of

using a modified and tuned HLD-NAC is that the three-phase salinity limits are calculated by the

model itself and can vary depending on the input parameters, such as temperature, pressure and

EACN. Figure 4-11 shows the activity map predicted by our model and compares it with the

tuned result reported by Mohammadi (2008). The results show that the new model is capable of

predicting well the evolution of the type III microemulsion window in the compositional space.

4.4.2. Case B from Mohammadi (2008), and Mohammadi et al. (2009)

The procedure followed for experiments in Case B was identical to Case A. Experiments

reported in Case B were done using an oil with a higher acid number (1.5 mg of KOH/ g of oil)

94

and a density of 0.93 g/cc. The surfactant formulation was different from Case A. In Case B,

equal quantities (weight basis) of tridecyl alcohol polyethoxy sulfate (7PO) and a C20-24 internal

olefin sulfonate was used. The surfactant concentration of this blend was varied from 0.3 wt.% to

1 wt.%. The molecular weight of the surfactant blend was reported to be 450 g/mol. Sodium

carbonate was again used as the alkali and concentrations were varied in a range from 0 to 60,000

ppm. Synthetic brine composition was provided and its salinity was calculated to be 0.072

meq/ml. A summary of the optima for the experiments in Case B is presented in Table 4-3. All

experiments were performed at 46°C and atmospheric pressure.

4.4.2.1. Determination of Soap Model Parameters

Iterations were done on n in order to obtain the constants for the linear Eqs. (4.15) and (4.16). The

value of alkyl carbon number of the acid component was found to be 14. The R2-values after

fitting Eqs. (4.15) and (4.16) were 0.95 and 0.99 respectively. Constants C1 and C2 were found to

be -1.52 and 0.48 respectively (see Figure 4-12). Constants D1 and D2 were found to -0.06 and

0.09 respectively (see Figure 4-13).

4.4.2.2. Tuning the Phase Behavior Model

The length parameter L for the surfactant was estimated to be 37.21 Å, while for the soap (n=14)

23.05 Å. Parameter asoap remained fixed at 60 Å2. The area per molecule of surfactant (asurf)

was tuned to fit the phase behavior data at 0.3 wt.% surfactant concentrations. There were two

experiments at different oil concentrations. For 30% oil concentration (v/v) asurf was tuned to 16

Å2 (see Figure 4-14). For 50% oil concentration (v/v) asurf was tuned to 45 Å2 (see Figure 4-15).

95

Both figures also compare UTCHEM phase behavior results reported by Mohammadi with our

model results. An average value of asurf (30.5 Å2) was considered for predictions.

4.4.2.3. Phase Behavior Predictions

Table 4-4 shows a summary of input parameters for Case B. With the model parameters known,

phase behavior for cases with 0.6 wt.% and 1 wt.% surfactant concentrations were predicted and

compared with experimental data. Figure 4-16 to Figure 4-18 show solubilization ratio

predictions for Case B. The results using tuned values of asurf agree well with experimental

values. Figure 4-19 shows flash calculation results at different sodium carbonate concentrations

for an oil volume concentration of 30%. Figure 4-20 shows flash calculation results for oil

volume concentration of 50%.

Mohammadi (2008) also reported activity maps generated from UTCHEM at the three

surfactant concentrations considered in Case B. Figure 4-21 to Figure 4-23 show the activity

maps predicted by the new model in comparison to UTCHEM results. Deviation from the

UTCHEM model can be seen as surfactant concentration is increased. However, as discussed

previously, UTCHEM employs a logarithmic mixing rule to predict the upper and lower limits,

while the new model predicted these limits.

4.4.2.4. Fish diagrams for alkali-surfactant systems

Activity maps are important to describe the evolution of the three-phase regions (salinity limits)

as a function of oil composition (or water-oil ratio) of the system. Fish (also known as gamma)

diagrams however, have been traditionally used to determine three-phase salinity limits in terms

of formulation variables (temperature, salinity, etc.) as a function of the total surfactant

96

concentration in the system (Salager, Forgiarini and Bullon, 2013; Salager, Forgiarini, Marquez,

et al., 2013; Salager et al., 2005). Fish diagrams are typically made for a water-oil ratio (WOR)

of one. Typically, pure surfactants tend to produce near symmetric fish diagrams (see Figure

4-24) as opposed to surfactant mixtures (or commercial surfactant blends) that form asymmetric

fish plots. Here, evolution of fish diagrams applicable to alkali-surfactant systems as a function of

lnS have been investigated using the model parameters determined for cases A and B. Fish

diagrams for different overall surfactant concentrations at unit WOR were generated.

Without alkali, the model predicts symmetric fish diagrams as shown in Figure 4-25 and

Figure 4-26. This is because the optimum does not change as a function of surfactant

concentration given other constant input parameters and the synthetic surfactant is assumed to be

pure. However, at a fixed alkali concentration of 1 wt.% sodium carbonate with NaCl

concentration varying, the optima are a function of the mole fraction of the soap formed. Thus,

the fish diagram becomes asymmetric as explained by Salager, Forgiarini, and Bullon (2013) and

Salager, Forgiarini, Marquez, et al. (2013). For a constant water-oil ratio of one, as the overall

surfactant concentration increases, the width of the three-phase region decreases. The point at

which the limits intersect is the beginning of the region where type IV microemulsion (single

phase) is formed.

Figure 4-27 and Figure 4-28 show fish diagrams where alkali concentrations were varied

keeping the brine concentration fixed for cases A and B. The results from the tuned models are

in agreement with measured data.

Typical values of surfactant concentration in EOR are less than 2 wt.%. The figures

show surfactant concentrations ranging up to 15% in order to show the fish tail and the full extent

of the three-phase region.

97

4.5. Conclusions

A modified HLD-NAC equation of state to model and predict microemulsion phase behavior

applicable to alkali-surfactant EOR was developed. The approach was validated by using

available published data. The following conclusions are made:

1. The soap formed under in-situ conditions is dependent on the alkyl carbon number

and molecular weight of the petroleum acid pseudo component.

2. The alkyl carbon number of the acid can be used to estimate distribution coefficients,

soap tail length, and soap mole fractions thereby reducing the number of input/tuning

variables.

3. The inverse of optimum solubilization ratio (1/σ*) is a linear function of the soap

mole fraction (Xsoap). This empirical relationship is new to this research.

4. The relationship between inverse of optimum solubilization ratio, lnS*, and mole

fraction of soap formed can be represented by a plane in three-dimensional

coordinates.

5. Relationships to predict optima can be used to constrain the soap model and

determine an effective alkyl carbon number for the acid pseudo component.

6. Flash calculations using the modified HLD-NAC model are non-iterative, fast, and

robust. Flash calculations were extended to model soap as a second component

lumped in the surfactant pseudo component. Additional synthetic surfactants can also

be added.

7. Only two tuning parameters are required (n and asurf). In comparison, the UTCHEM

model has seven input parameters that require tuning (Sheng, 2010) which can be

reduced to five if excess phases are assumed to be pure.

8. The new model predictions are in good agreement with un-tuned experimental data.

98

9. Activity maps can be predicted easily by our model without the need to fit three-

phase windows from experiments.

10. Fish diagrams for alkali-surfactant system are asymmetric, which is in agreement

with published literature.

Chapter 5 presents a dimensionless form of the modified HLD-NAC model developed so far.

Important design criteria with respect to dimensionless groups have then been presented.

99

Table 4-1: : Summary of optima for experiments for crude oil case A. Data from

Mohammadi, (2008).

Oil Volume % S* in meq/ml

Na2CO3 ppm at

optimum σ

* (cc/cc)

10% 0.80 37000 19.51

20% 0.72 32700 23.01

30% 0.65 29100 26.01

40% 0.54 23000 31.96

50% 0.46 19000 38.04

Table 4-2: : Summary of model parameters for Case A.

Input Parameter Value Units

Acid number 0.5 mg of KOH/g of oil

pH Dependent on alkali

concentration -

N 14 -

C1 -1.187 -

C2 0.001 -

D1 -0.053 cc/cc

D2 0.059 cc/cc

Oil density 0.9 g/cc

Lsurf 32.92 Å

Lsoap 21.53 Å

asurf 205 Å2

asoap 60 Å2

WOR 1 to 9 -

Surfactant concentration 0.2 wt. %

Surfactant molecular

weight 408 g/mol

100

Table 4-3: Summary of optima for experiments for crude oil case B. Data from

Mohammadi, (2008).

Oil

Volume

%

Surfactant

concentration

(wt.%)

S* in meq/ml Na2CO3 ppm at

optimum σ

* (cc/cc)

30% 0.6 0.86 41700 16.07

40% 0.6 0.67 31900 17.89

30% 0.3 0.66 31100 18.42

50% 0.3 0.49 22200 23.53

50% 1 0.69 32500 17.55

Table 4-4: Summary of model parameters for Case B.

Input Parameter Value Units

Acid number 1.5 mg of KOH/g of oil

pH Dependent on alkali

concentration -

n 14 -

C1 -1.789 -

C2 0.821 -

D1 -0.06 cc/cc

D2 0.09 cc/cc

Oil density 0.93 g/cc

Lsurf 37.21 Å

Lsoap 23.05 Å

asurf 30.5 Å2

asoap 60 Å2

WOR 1 to 9 -

Surfactant concentration 0.3,0.6, and 1 wt. %

Surfactant molecular

weight 450 g/mol

101

Figure 4-1: Linear relationship between the

number of carbon atoms in the alkyl group of a

carboxylic acid and pKd for water-heptane

systems. Data obtained from Smith & Tanford

(1973).

Figure 4-2: Linear relationship between mole

fraction of soap formed and log of optimum

salinity (in meq/ml) for Case A. Value of n used

was 13. Data obtained from Mohammadi

(2008).


fraction of soap formed and inverse of optimum

solubilization ratio in cc/cc for Case A. Value of n

used was 13. Data obtained from Mohammadi

(2008).

Figure 4-4 Match of tuned HLD-NAC model

(solid lines) for Case A at 50% oil overall

concentration (v/v). Red represents σo while

blue represents σw. The tuned value of asurf was

195 Å2. Circles are experimental data and

dashed lines show UTCHEM output reported

by Mohammadi (2008).

y = 0.601x - 3.389 R² = 0.999

0

1

2

3

4

5

6

7

8

9

10

5 7 9 11 13 15 17 19 21 23

pK

d

Number of carbon atoms in alkyl chain (n)

y = -1.187x - 0.001 R² = 0.965

-0.9

-0.8

-0.7

-0.6

-0.5

-0.4

-0.3

-0.2

-0.1

0

0 0.2 0.4 0.6 0.8

lnS

*

Xsoap

y = -0.053x + 0.059 R² = 0.997

0

0.01

0.02

0.03

0.04

0.05

0.06

0 0.2 0.4 0.6 0.8

1/σ

*

Xsoap

0 1 2 3 4 5

x 104

0

10

20

30

40

50

60

70

Na2CO

3 concentration in ppm

So

lub

iliz

ati

on

rati

os (

cc/c

c)

102

Figure 4-5: Match of tuned HLD-NAC (solid lines)

model for Case A at 30 % oil overall concentration

(v/v). Red represents σo while blue represents σw.

The tuned value of asurf was 215 Å2. Circles are

experimental data and dashed lines show

UTCHEM output reported by Mohammadi (2008).

Figure 4-6: Prediction of solubility ratios using

tuned HLD-NAC model for Case A at 10 % oil

overall concentration (v/v). Red represents σo

while blue represents σw. The value of asurf used

was 205 Å2. The green circle represents the

optimum experimentally measured by

Mohammadi (2008). This point was used in

tuning.

Figure 4-7: Prediction of solubility ratios using


overall concentration (v/v). Red represents σo while

blue represents σw. The value of asurf used was 205

Å2. The green circle represents the optimum

experimentally measured by Mohammadi (2008).

This point was used in tuning.

Figure 4-8: Prediction of solubility ratios for


overall concentration (v/v). Red represents σo

while blue represents σw. The value of asurf used

was 205 Å2. The green circle represents the

optimum experimentally measured by

Mohammadi (2008). This point was used in

tuning.

0 1 2 3 4 5

x 104

0

10

20

30

40

50

60

70

Na2CO


So

lub

iliz

ati

on

rati

os (

cc/c

c)

0 1 2 3 4 5

x 104

0

10

20

30

40

50

Na2CO


So

lub

iliz

ati

on

rati

os (

cc/c

c)

0 1 2 3 4 5

x 104

0

10

20

30

40

50

Na2CO


So

lub

iliz

ati

on

rati

os (

cc/c

c)

0 1 2 3 4 5

x 104

0

10

20

30

40

50

Na2CO


So

lub

iliz

ati

on

rati

os (

cc/c

c)

103

Figure 4-9: Phase volume fraction diagram based

on flash calculations for 10 % oil concentration for

Case A. Each bar represents a fixed sodium

carbonate concentration. Red represents excess oil

phase, blue excess brine, and green the

microemulsion phase.

Figure 4-10: Phase volume fraction diagram

based on flash calculations for 40 % oil

concentration in Case A. Each bar represents a

fixed sodium carbonate concentration. Red

represents excess oil phase, blue excess brine,

and green the microemulsion phase.

Figure 4-11: Activity map for Case A. Solid lines

represent prediction from the model used in this

dissertation. Green represents type II-, red type III

and blue type II+ regions found experimentally.

The dashed lines show the three-phase window

used in the UTCHEM model by Mohammadi et al.

(2009).


fraction of soap formed and log of optimum

salinity (in meq/ml) for Case B. Value of n used

was 14. Data obtained from Mohammadi

(2008).

0 1 2 3 4 5

x 104

0

20

40

60

80

100

Na2CO


Vo

lum

e (

cc)

0 0.5 1 1.5 2 2.5 3 3.5 4

x 104

0

20

40

60

80

100

Na2CO


Vo

lum

e (

cc)

0 10 20 30 40 50 600

1

2

3

4

5

6x 10

4

Na 2

CO

3 c

on

cen

trati

on

in

pp

m

Oil concentration in volume %

y = -1.519x + 0.479 R² = 0.953

-0.8

-0.7

-0.6

-0.5

-0.4

-0.3

-0.2

-0.1

0

0.3 0.5 0.7 0.9

ln S

*

Xsoap

104


fraction of soap formed and inverse of optimum

solubilization ratio in cc/cc for Case B. Value of n

used was 14. Data obtained from Mohammadi

(2008).

Figure 4-14 Match of tuned HLD-NAC model

(solid lines) for Case B at 30 % oil overall

concentration (v/v) and 0.3 wt.% surfactant

concentration. Red represents σo while blue

represents σw. The tuned value of asurf was 16

Å2. Circles are experimental data and dashed

lines show UTCHEM output reported by

Mohammadi (2008).

Figure 4-15: Match of tuned HLD-NAC model




represents σw. The tuned value of asurf was 45 Å2.

Circles are experimental data and dashed lines

show UTCHEM output reported by Mohammadi

(2008).

Figure 4-16: Prediction of tuned HLD-NAC

model (solid lines) for Case B at 30 % oil

overall concentration (v/v) and 0.6 wt.%

surfactant concentration. Red represents σo

while blue represents σw. Circles are


UTCHEM output reported by Mohammadi

(2008).

y = -0.056x + 0.087 R² = 0.985

0.03

0.04

0.05

0.06

0.07

0.3 0.5 0.7 0.9

1/σ

*

Xsoap 0 1 2 3 4 5 6

x 104

0

10

20

30

40

50

60

70

Na2CO


So

lub

iliz

ati

on

rati

os (

cc/c

c)

0 1 2 3 4 5 6

x 104

0

10

20

30

40

50

60

70

Na2CO


So

lub

iliz

ati

on

rati

os (

cc/c

c)

0 1 2 3 4 5 6

x 104

0

10

20

30

40

Na2CO


So

lub

iliz

ati

on

rati

os (

cc/c

c)

105

Figure 4-17: Prediction of tuned HLD-NAC model




represents σw. Circles are experimental data and

dashed lines show UTCHEM output reported by

Mohammadi (2008).

Figure 4-18: Prediction of tuned HLD-NAC

model (solid lines) for Case B at 50 % oil

overall concentration (v/v) and 1 wt.%

surfactant concentration. Red represents σo

while blue represents σw. Circles are


UTCHEM output reported by Mohammadi

(2008).

Figure 4-19: Phase volume fraction diagram based

on flash calculation results for Case B at 30 % oil

overall concentration (v/v) and 0.6 wt.% surfactant

concentration. Each bar represents a sodium

carbonate concentration. Red represents excess oil

phase, blue represents excess brine, and green

represents microemulsion phase.

Figure 4-20: Phase volume fraction diagram

based on flash calculation results for Case B at

50 % oil overall concentration (v/v) and 1 wt.%

surfactant concentration. Each bar represents

a sodium carbonate concentration. Red

represents excess oil phase, blue represents

excess brine, and green represents

microemulsion phase.

0 1 2 3 4 5 6

x 104

0

10

20

30

40

50

60

70

Na2CO


So

lub

iliz

ati

on

rati

os (

cc/c

c)

0 1 2 3 4 5 6

x 104

0

10

20

30

40

50

60

70

Na2CO


So

lub

iliz

ati

on

rati

os (

cc/c

c)

3 3.5 4 4.5 5

x 104

0

20

40

60

80

100

Na2CO


Vo

lum

e (

cc)

2 2.5 3 3.5 4 4.5 5

x 104

0

20

40

60

80

100

Na2CO


Vo

lum

e (

cc)

106

Figure 4-21: Activity map for Case B with 0.3

wt.% surfactant. Solid lines represent prediction

from the model used in this dissertation. Green

represents type II-, red type III and blue type II+

regions found experimentally. The dashed lines

show the window used in the UTCHEM model by

Mohammadi (2008).

Figure 4-22: Activity map for Case B with 0.6

wt.% surfactant. Solid lines represent

prediction from the model used in this

dissertation. Green represents type II-, red

type III and blue type II+ regions found

experimentally. The dashed lines show the

window used in the UTCHEM model by

Mohammadi (2008).

Figure 4-23: Activity map for Case B with 1 wt.%

surfactant. Solid lines represent prediction from

the model used in this dissertation. Green

represents type II-, red type III and blue type II+

regions found experimentally. The dashed lines

show the window used in the UTCHEM model by

Mohammadi (2008).

Figure 4-24: Example of a fish diagram

showing types of microemulsions with no alkali

for a pure surfactant. Only Nalco

concentration in brine is varied. Model

parameters were obtained from Case A. Red

shows the upper salinity limit and blue the

lower salinity limit. Dashed line shows the

optima.

0 10 20 30 40 50 600

1

2

3

4

5

6

7x 10

4

Na 2

CO

3 c

on

cen

trati

on

in

pp

m


0 10 20 30 40 50 600

1

2

3

4

5

6

7x 10

4

Na 2

CO

3 c

on

cen

trati

on

in

pp

m


0 10 20 30 40 50 600

1

2

3

4

5

6

7x 10

4

Na 2

CO

3 c

on

cen

trati

on

in

pp

m

Oil concentration in volume %0 5 10 15

-0.4

-0.3

-0.2

-0.1

0

0.1

0.2

0.3

ln (

Na+

) co

ncen

trati

on

in

meq

/ml

w t % of synthetic surfactant in aqueous solution

Type II+

Type III

Type II-

Type IV

107

Figure 4-25: Fish diagrams using model

parameters obtained from Case A. Red shows the

upper salinity limit and blue the lower salinity

limit. Solid lines show the fish diagram with 1.0

wt.% Na2CO3 and dashed lines show fish diagram

in absence of alkali.

Figure 4-26: Fish diagrams using model

parameters obtained from Case B. Red shows

the upper salinity limit and blue the lower

salinity limit. Solid lines show the fish diagram

with 1.0 wt.% Na2CO3 (fixed) and Nalco

concentration varying. Dashed lines show the

fish diagram in absence of alkali.

Figure 4-27: Fish diagram using model parameters

tuned for Case A. Red shows the upper salinity

limit and blue the lower salinity limit. Solid lines

show the fish diagram with Na2CO3 concentration

varying (brine concentration fixed). Squares

indicate experimental data from Mohammadi

(2008).

Figure 4-28: Fish diagram using model

parameters tuned for Case B. Red shows the


limit. Solid lines show the fish diagram with

Na2CO3 concentration varying (brine

concentration fixed). Squares indicate

experimental data from Mohammadi (2008).

0 5 10 15

-0.6

-0.4

-0.2

0

0.2

ln (

Na+

) co

ncen

trati

on

in

meq

/ml


0 5 10 15-0.8

-0.6

-0.4

-0.2

0

0.2

0.4

0.6

ln (

Na+

) co

ncen

trati

on

in

meq

/ml


0 1 2 3 4 5 6 7

-1.5

-1

-0.5

0

ln (

Na+

) co

ncen

trati

on

in

meq

/ml


0 2 4 6 8 10-1.2

-1

-0.8

-0.6

-0.4

-0.2

0

0.2

ln (

Na+

) co

ncen

trati

on

in

meq

/ml


108

Chapter 5

Dimensionless Solutions to Microemulsion Phase Behavior

This chapter develops the dimensionless form of our modified HLD-NAC EOS to interpret phase

behavior of surfactant-oil-brine systems. As discussed in Chapter 1, Huh (1979) found a

correlation between solubilization ratios and the interfacial tensions. The relationship made it

easier to deduce interfacial tensions from phase behavior experiments and eliminated the need for

performing cumbersome IFT measurements. Since then, phase behavior experiments known as

salinity scans have been routinely done with the primary goal of determining oil and water

solubilization ratios as a function of salinity. Therefore, prediction of solubilization ratios is of

high importance.

The solubilization ratio is a dimensionless term. The following sections revisit the net

and average curvature equations to provide useful relationships for oil and water solubilization

ratios as a function of the HLD.

5.1. Solubilization Ratio Relationships in Two-Phase Regions

This section illustrates the use of the net curvature equation to derive useful relationships between

the solubilization ratios and the HLD of the system. The net curvature equation relates the oil and

water curvatures to the HLD of the system and the surfactant length parameter L. From (3.15) and

the net curvature equation,

1 1

3

s

o w

A HLD

V V L

. (5.1)

109

Multiplication of Eq. (5.1) by the volume of surfactant in the system (Vs), and rearranging the

terms we get the relationship,

1 1

3( )( )o w

I HLD

, (5.2)

where,

s

s

VI

LA . (5.3)

I, referred to as the interfacial volume ratio henceforward, is a dimensionless group that is a ratio

of the volume of the surfactant component to the volume of the interface. The interface is defined

with a thickness L contributed by the surfactant length parameter and As, which is the total area of

all surface active molecules at the interface. The volume of the surfactant at the interface is LAs.

A large I indicate the surfactant is well packed at the interface. I must be less than one.

As discussed in Chapter 3, the HLD in a traditional salinity scan is expressed by,

, , , , ( ) *

( ) | lnEACN T P Cc f A

SHLD S

S . (5.4)

Hence, (5.2) provides a simple mathematical relationship between the solubilization ratios and the

salinity of the system in a salinity scan. Similar relationships can be developed for temperature

and pressure scans.

Chapter 2 introduced equations to calculate solubilized component volumes in type II-

and type II+ microemulsions. The excess phases were assumed to be pure. Hence from Eq. (5.2),

110

dimensionless solutions for the microemulsions in the two-phase regions can be developed as is

done next.

5.1.1. Dimensionless Solutions for Type II- Microemulsions

The system consists of an excess oil phase and a microemulsion where water is the continuous

phase. This implies Vw,m is equal to Vw of the system. Dividing this by the surfactant volume

(Vs), which by assuming pure excess phases, is equal to Vs,m, we obtain a constant water

solubilization ratio of Vw/Vs in the type II- microemulsion for a fixed overall composition,

regardless of the value of HLD (as long as the criteria for formation of type II- microemulsions

are satisfied as discussed in Section 5.3). The constant water solubilization ratio in type II-

microemulsions is henceforward denoted as σ0w. Therefore, in type II- microemulsions,

0

1 13

o w

IHLD

. (5.5)

Specifically, for a salinity scan, from Eq. (5.4),

* 0

1 13 ln

o w

SI

S . (5.6)

Therefore, the inverse of solubilization ratios varies linearly with the logarithm of the aqueous

phase salinity. This is an important new result of this research. The slope of this line is always

equal to -3I. Figure 5-1 shows evidence of a linear trend between the inverse of oil solubilization

ratios (from experiments) and HLD in the type II- region. Experimental data used here was

reported by Sheng (2010).

111

5.1.2. Dimensionless Solutions for Type II+ Microemulsions

For type II+ microemulsions, Vo,m is equal to Vo in the system. Dividing by the surfactant volume

(Vs), we obtain a constant oil solubilization ratio of Vo/Vs in the type II+ microemulsion for a

particular overall composition, regardless of the value of HLD. The constant oil solubilization

ratio in type II+ microemulsions is σ0o. Hence, in type II+ microemulsions,

0

1 13 ( )

w o

I HLD

. (5.7)

Specifically, for a salinity scan, from Eq. (5.4),

* 0

1 13 ln

w o

SI

S

. (5.8)

This result is similar to Eq. (5.6). However, the slope of the linear relationship between the

inverse of water solubilization ratio and logarithm of salinity is +3I (as opposed to -3I in Eq.

(5.6)). Figure 5-2 shows inverse of water solubilization ratios (from experiments) are linearly

related to the HLD of the system in the type II+ region. Experimental data used here was

reported by Sheng (2010).

5.2. Solubilization Ratio Relationships in The Three-phase Region

The type III system consists of three-phases, an excess oil phase, an excess brine phase and the

middle phase microemulsion. As explained in Chapter 2, neither σw nor σo in type III

microemulsions are constrained by the overall composition alone. Therefore, Eq. (5.2) is not

sufficient to determine the composition of type III microemulsions. In this section we derive a

112

second dimensionless equation from the modified average curvature equation Eq.(3.16) to

calculate the solubilization ratios.

In type III microemulsions, the correlation length is constant at ξ*. This is a good

assumption for type III microemulsions where the oil and water both form continuous planar

micelles (spheres with large radii of curvatures), but not necessarily true near the two phase

boundaries where cylindrical micellar structures may exist. Furthermore, at optimum, the oil and

water component volume fractions in the microemulsion are equal. Therefore, at optimum,

o w (5.9)

and,

*

o w . (5.10)

Consequently, from Eq. (3.17) , ξ* can be expressed as

2 ** 6 6 3 3

( ) (2 )

me w o me w w s

s w o s w s s

V V V V

A A A A

. (5.11)

Since the average curvature of the type III microemulsion is always constrained to be

equal to the inverse of ξ*, from Eq. (3.16) and Eq. (5.11),

*

1 1 2

o w . (5.12)

.

Equation (5.12) hence shows that the solubilization ratios in the type III microemulsion are

always constrained by the optimum solubilization ratio, a key screening factor in phase behavior

113

studies. In order to determine the values of the oil and water solubilization ratios, Eq. (5.2) and

Eq. (5.12) are solved simultaneously. Therefore in a type III microemulsion,

*

1 3 1

2o

IHLD

, (5.13)

and,

*

1 3 1

2w

IHLD

. (5.14)

.

Specifically for a salinity scan,

* *

1 3 1ln

2o

I S

S

, (5.15)

and,

* *

1 3 1ln

2w

I S

S

. (5.16)

Here again we see a linear correlation between the inverse of solubilization ratios and logarithm

of salinity in a typical salinity scan. The inverse of the solubilization ratios will also vary linearly

as a function of other HLD factors like EACN, T and P. However, the slope of the linear

relationship (1.5I) is half of that in the two-phase regions (3I). Figure 5-3 shows evidence of a

linear relationship between solubilization ratios (from experiments) and HLD in the type III

region. Experimental data used here was reported by Sheng (2010).

114

5.3. Two-phase Limits and Stability Criteria for Dimensionless Equations

Chapter 2 discussed the stability criteria used in HLD-NAC. Similar criteria applicable to

dimensionless equations can be developed. At the lower HLD limit (HLDL), both Eq. (5.5) and

Eq. (5.12) need to be satisfied. Therefore,

0 *

1 1 23 L

w w

IHLD

. (5.17)

However, σw = σ0w in type II- microemulsions. Hence,

0 *

2 1 1

3L

w

HLDI

(5.18)

Similarly, for the upper HLD limit (HLDU),

* 0

2 1 1

3U

o

HLDI

. (5.19)

Equations (5.18) and (5.19) both show that a decrease in interfacial volume ratio (I) increases the

upper and lower HLD limits. The width of the three-phase region expressed in terms of HLD for a

constant overall composition can be expressed as,

0 0 * 0 * 0

* 0 0 * 0 0

22 2 1 1 2

3 3

o w w o

o w o w

HLDI I

. (5.20)

115

At the invariant point representing the type III microemulsion composition, the width of the

three-phase zone is zero. The invariant composition is also the point of transition between type III

and type IV microemulsions. Hence, from Eq. (5.20) at the invariant point,

0 0 * 0 * 02 0o w w o , (5.21)

or,

* 2

( )

w o

s w o

V V

V V V

. (5.22)

Equation (5.22) expressed in terms of component volume fractions in the microemulsion

becomes,

* 2

( )

w o

s w o

. (5.23)

Equation (5.23) represents the locus of the invariant point of the tie-triangle in the compositional

space (ϕo, ϕw, ϕs). We define a new parameter χ, which determines the presence of a three-phase

region as,

2( )

w o

s w o

. (5.24)

The lower HLD limit HLDL, as defined in Eq. (5.18) marks the transition from type II- to

type III microemulsion for a particular overall composition constrained by σ0w. Thus, HLDL gives

the point of transition between the two-phase lobe (type II-) and the tie triangle (type III region).

116

However, a critical lower HLD limit (HLDL*) exists below which a type III microemulsion cannot

exist. The model assumes excess phases to be pure. The critical lower HLD limit (HLDL*) is

obtained by finding HLDL as the overall surfactant concentration goes to zero. Therefore HLDL*

is obtained when the inverse of σ0w is set to zero. Hence, from Eq. (5.18),

*

*

2 1

3LHLD

I

(5.25)

Similarly, a critical upper HLD limit (HLDU*) exists above which, a type III

microemulsion cannot exist. HLDU* is obtained by setting the inverse of σ0

w to zero. Hence.

From Eq. (5.19),

*

*

2 1

3UHLD

I

(5.26)

The limits and the transition zones can be described using fish plots as shown later in

section 5.4.2.2. Based on the upper and lower limits of HLD, the modified stability criteria are as

follows.

Case 1: If HLD < HLDL* , type III and type II+ microemulsions cannot exist.

HLD ≥ HLDU , a type IV microemulsion exists (single phase microemulsion).

HLD < HLDU , a type II- microemulsion exists (two-phase system).

Case 2: If HLD > HLDU* , type III and type II- microemulsions cannot exist.

HLD ≤ HLDL , a type IV microemulsion exists (single phase microemulsion).

HLD > HLDL , a type II+ microemulsion exists (two-phase system).

Case 3: If HLDL* ≤ HLD ≤ HLDU

* and,

if χ ≥ σ* ,

117

o HLD < HLDL , a type II- microemulsion exists (two-phase system).

o HLD > HLDU , a type II+ microemulsion exists (two-phase system).

o HLDL ≤ HLD ≤ HLDU a type III microemulsion exists (three-phase system).

If χ ≤ σ*,

o HLD > HLDL , a type II+ microemulsion exists (two-phase system).

o HLD < HLDU , a type II- microemulsion exists (two-phase system).

o HLDL ≥ HLD ≥ HLDU, a type IV microemulsion exists (single phase system).

5.4. Results

This section discusses key outcomes of the dimensionless equations developed applicable to

microemulsions across both two and three-phase regions. This dissertation is the first to clearly

define a robust way to calculate optimum solubilization ratios and optimum salinities. Chapter 3

and Chapter 4 uses the area term (as) as a tuning parameter after empirically estimating the length

term L. The dimensionless solutions eliminate the need to treat both as and L separately. Instead,

we use the interfacial volume ratio (I) as the single tuning variable. Figure 5-4 shows an example

(WOR=1, σ* = 13.5 cc/cc and I = 0.129) of the linear relationship between the inverse of

solubilization ratios and the HLD in the two-phase and three-phase regions.

5.4.1. Interpretation of Phase Behavior Experiments

Salinity scan experiments were conducted using sodium dodecyl benzenesulfonate (SDBS) and

sodium dodecyl sulfate (SDS) as surfactants. Iso-butyl alcohol (IBA) was used as a co-solvent.

The oils used were pure hydrocarbons (heptane and dodecane). Experiments were done at a

constant temperature of 40 °C. The experimental procedure is described in Appendix C.

118

Salinity scans reported by Aarra et al. (1999) have been used in this section. They

investigated the effect of different monovalent and divalent cations on microemulsion phase

behavior. The scans were done using NaCl, KCl, CaCl2 and MgCl2 as salts. Two different

surfactant systems were considered, one with sodium dodecyl sulfate (SDS) and the other with a

blend of an alkyl aryl sulfonate and dodecyl ethoxy sulfonate (AAS). The experiments were

conducted at different temperatures.

5.4.1.1. Prediction of Optimum Solubilization Ratios

Equation (5.12) suggests that the optimum solubilization ratio σ* is always equal to the harmonic

mean of the oil and water solubilization ratios (σo and σw) in a type III microemulsion. Therefore,

the optimum solubilization ratio can be estimated from a single pipette in a scan with a type III

microemulsion, irrespective of that pipette being at optimum salinity. Traditionally, optimum

solubilization ratios are obtained by manually finding the intersection of the oil and water

solubilization ratios. Alternatively, the harmonic mean approach is far more robust. If more than

one type III microemulsion data is available for a particular scan, the harmonic means of the

solubilization ratios could be averaged.

5.4.1.2. Prediction of Optimum Salinities

Equations (5.15) and (5.16) suggest that the inverse of optimum solubilization ratios vary linearly

with the logarithm of salinity. Therefore, using experimental data in the type III region, a linear

regression is done for lnS plotted against 1/σo and 1/σw. The intersection of the lines occurs at

lnS*. This is again a systematic way to predict the optimum salinity. The HLD is then calculated

from the optimum salinity using Eq. (3.4).

119

5.4.1.3. Tuning the Interfacial Volume ratio (I) to Match Phase Behavior Data

With the optima known, iteration is done on the interfacial volume ratio (I) to match

experimentally obtained solubilization ratios at different salinities. Therefore for every salinity, a

tuned interfacial volume ratio (I) is obtained. However, due to experimental uncertainties,

multiple values of interfacial volume ratios are obtained at various salinities. An average

interfacial volume ratio (I) that satisfies all data points reasonably is then calculated by

eliminating outliers (outside the range from 0 to 1). Data within the physical range of 0 to 1 was

considered, while the others were discarded in estimating the average tuned interfacial volume

ratios.

Table 5-1 and Table 5-2 shows a summary of the optima and the average tuned interfacial

volume ratios for different salinity scans. The σ* predicted for 24 salinity scans using the

harmonic mean approach had an average relative error of 2.18% and 2.7% as compared to the

optima reported by Aarra et al. (1999). This shows that the harmonic mean approach is highly

reliable. Furthermore, the optimum salinities calculated using the intersection method is also in

very good agreement with the reported values with the average relative error being less than

1.5%. The tuned interfacial volume ratios have also been reported.

Figure 5-5 and Figure 5-6 show the tuning results for the experiments described in

Appendix C. Figure 5-7 to Figure 5-30 show the tuning results for all 24 salinity scans reported

by Aarra et al. (1999). The results indicate that the dimensionless solutions are reliable and can

easily be used to match phase behavior data. Figure 5-31 and Figure 5-32 show the summary of

average interfacial volume ratios for all reported salinity scans. From the figures, it can also be

concluded that the type of salt does not significantly affect the interfacial volume ratio.

120

5.4.2. Analysis

This section qualitatively explains the effect of each dimensionless group on the phase behavior.

Key formulation design criteria are presented.

5.4.2.1. Design Criteria for a Wide Three-phase Region

Equation (5.20) shows that the width of the three-phase region is a function of the overall

composition, the optimum solubilization ratio and the interfacial volume ratio (I). Figure 5-33

shows that smaller interfacial volume ratios (I) gave a thicker width of the three-phase zone.

However, the width of the three-phase zone also decreases with increasing σ*. For good oil

recovery, high solubilizations and a wide three-phase region is desirable. Hence, EOR

formulations must be designed to have low interfacial volume ratios (I) with high σ*.

5.4.2.2. Modified Fish Diagrams Using χ

As shown in Chapter 4, fish diagrams are traditionally represented at a water-oil ratio of one

(fixed overall composition). The three-phase limits are then expressed as a function of the total

surfactant content in the system. χ as shown in Eq. (5.24) considers compositional effects of

both WOR and surfactant volume. Hence, the new parameter χ is a more appropriate variable to

represent fish plots. Figure 5-34 shows an example of a fish plot with an interfacial volume ratio

(I) of 0.2 and σ* equal to 10 cc/cc. The composition at which χ becomes equal to σ* is the

invariant point of the three-phase region. In chemical engineering applications, this point is

marks the beginning of the “fish-tail.” The invariant point marks the beginning of the type IV

region. Therefore, three-phase systems cannot exist when χ is less than σ*. This is an important

121

result from this research. The figure also clearly shows the critical upper HLD limit (HLDU*) and

critical lower HLD limit (HLDL*). A type III microemulsion can only exist when conditions for

both χ and HLD are satisfied. It is also important to note that the HLDU and HLDL curves

intersect and flip (HLDU becomes less than HLDL) when χ is less than σ*. The various limits and

regions in the fish plot corresponds to the stability criteria discussed in section 5.3.

5.4.2.3. The Tie-Triangle Locus

The model developed assumes excess phases to be pure. Hence in a ternary diagram, the base of

the tie triangle in a three-phase system is always fixed with vertices at excess phase compositions

representing pure oil and water components. Under the constraints of these assumptions, the tie

triangle evolves from the base of the ternary diagram with type III microemulsion composition

beginning at the excess brine phase and ending at the excess oil phase as the HLD increases.

Equation (5.23) can be used to find a locus of the invariant point representing the microemulsion

composition. The locus is solely a function of the optimum solubilization ratio σ*. Figure 5-35 to

Figure 5-37 show the locus for three different values of σ*, 3 cc/cc, 10 cc/cc and 30 cc/cc. The

height of the locus decreases with increasing σ*. Physically, such a result is true because

solubilization ratio is inversely proportional to the volume of surfactant in the microemulsion.

Hence the height of the locus (which is directly proportional to the surfactant concentration)

decreases.

5.4.3. Dimensionless Solutions Applied to Temperature and Pressure Scans

The inverse of solubilization ratios varies linearly with the HLD of the system. HLD, as

explained in Chapter 3, varies linearly with temperature and pressure depending on the value of α

122

and β respectively. Data from Austad and Strand (1996) was used in Chapter 3 to match pressure

and temperature scans for dead and live oil. The same dataset can be used to show that the

inverse of solubilization ratios is a linear function of temperature and pressure. Austad and

Strand (1996) reported temperature and pressure scan data for type III microemulsions.

Therefore, for a pressure scan of a type III microemulsion,

*

3 ( )1 1

2

ref

o

I P P

, (5.27)

and,

*

3 ( )1 1

2

ref

w

I P P

. (5.28)

.

Hence, the slope of 1/σ vs pressure line is dependent on the product Iβ. Similarly, for a

temperature scan (type III),

*

3 ( )1 1

2

ref

o

I T T

, (5.29)

and,

*

3 ( )1 1

2

ref

w

I T T

. (5.30)

The slope of 1/ σ vs temperature is dependent on Iα. Thus, the slopes are scaled by either α or β.

123

Figure 5-38 to Figure 5-41 show the linear dependence of 1/ σ on pressure for both dead

and live oil systems. Figure 5-42 to Figure 5-45 show the linear dependence of 1/σ on

temperature. A summary of the slopes obtained and the interfacial volume ratios obtained are

presented in Table 5-3 and Table 5-4. The mean interfacial volume ratio was 0.25. Table 5-5

shows that the interfacial volume ratio can be considered to be constant with temperature and

pressure.

5.4.4. Interfacial Volume Ratio for Surfactant Mixtures

As discussed in Chapter 4, the total volume of surfactant pseudocomponent, L and as is dependent

on the mole fractions of the surfactants present in the mixture. Therefore, the interfacial volume

ratio is also dependent on the surfactant mole fraction. For a surfactant pseudocomponent, from

Eq. (5.3),

s

s a s

MWI

LN a (5.31)

where, MWs is the molecular weight of the surfactant pseudocomponent, ρs is the surfactant

pseudocomponent density (which is traditionally taken to be equal to density of water) and Na is

Avogadro’s number. Equation (5.31) applied to a surfactant mixture with n number of surfactant

components becomes,

1

1 1

ni

i si

n n

a i i i i

i i

X

I

N X L X a

. (5.32)

124

where �̅�si is the molar density of the surfactant i .

Figure 5-46 shows I for a mixture consisting of two surfactants, sodium oleate and

sodium laurate. The dependence of I on the mole fraction of sodium laurate in a mixture with

sodium oleate is shown as an example. The molecular weights, L and as for soaps were

calculated using the equations discussed in Chapter 4. The alkali phase behavior data used in

Chapter 4 was then used in order to obtain the average tuned interfacial volume ratios. Figure

5-47 and Figure 5-48 show the tuned interfacial volume ratio as a function of the soap mole

fractions.

Therefore, to use dimensionless solutions developed in this chapter, the following key

relationships are needed:

1. Equation (4.15), which accounts for the changes in lnS* due to Xsoap.

2. Equation (4.16), which accounts for the changes in 1/σ* due to Xsoap.

3. Equation (5.32), which accounts for the changes in the interfacial volume ratio as a

function of Xsoap.

The soap formation model described in Chapter 4, along with these three equations can then be

used in the dimensionless equations.

5.5. Conclusions

Dimensionless solutions to represent microemulsion phase behavior were established. The

following conclusions can be made:

1. Inverse of oil and water solubilization ratios vary linearly with HLD and hence, lnS.

2. The slopes of the linear relationships are determined by the interfacial volume ratio (I).

The slope in the two-phase regions are twice that of the slopes in the three-phase region.

125

3. The optimum solubilization ratio σ* is the harmonic mean of σo and σw in the type III

microemulsion. This property should be used to infer optima from phase behavior

experiments.

4. The intersection of the linear trends of lnS as a function of 1/σw and lnS as a function of

1/σo gives an accurate estimate of the optimum salinity.

5. The type III microemulsion window is dependent on the upper and lower HLD limits and

the value of the χ factor.

6. The χ factor represents fish diagrams better as opposed to considering the effects of

WOR and Vs separately.

7. Based on the data available to date, the type of cations do not affect the interfacial

volume ratio (I) significantly. However, salinities should be expressed in terms of

equivalents and not in terms of weight %.

8. The locus of the type III microemulsion composition is represented by χ = σ*.

9. The interfacial volume ratio is independent of temperature and pressure.

10. For surfactant mixtures, the interfacial volume ratio is dependent on the individual

surfactant mole fraction ratios.

126

Table 5-1: Summary of optima and tuned interfacial volume ratio (I) for experiments using

SDS surfactant reported by Aarra et al. (1999)

Salt Temperature

in °C

S* in

meq/ml

Reported

by Aarra

et al.

(1999)

S* in

meq/ml

Predicted

from

Eqs.(5.15)

and (5.16)

σ*

in cc/cc

Reported

by Aarra et

al. (1999)

σ*

in cc/cc

Predicted

from

Eq.(5.12)

% relative

error in

S*

%

relative

error in

σ*

Average

Tuned

I

NaCl 20.00 1.55 1.53 6.20 6.18 1.07 0.28 0.20 35.00 1.57 1.56 6.00 5.91 0.77 1.52 0.28 50.00 1.69 1.68 5.80 5.73 0.56 1.23 0.28 KCl 20.00 1.09 1.09 6.00 6.23 0.15 3.87 0.21 35.00 1.17 1.16 5.80 5.94 0.76 2.46 0.22 50.00 1.33 1.32 5.70 5.85 0.76 2.68 0.23 CaCl2 20.00 0.97 0.93 4.70 4.88 3.78 3.78 0.10 35.00 0.95 0.90 4.80 4.93 4.71 2.68 0.10 50.00 0.97 0.97 4.80 4.82 0.15 0.45 0.12 MgCl2 20.00 1.29 1.26 5.00 5.19 2.26 3.82 0.12 35.00 1.29 1.27 5.00 5.14 2.03 2.79 0.13 50.00 1.39 1.38 5.00 5.03 0.82 0.62 0.15

Average 1.49% 2.18%

0.18

±0.02 (std.

error)

127

Table 5-2: Summary of optima and tuned interfacial volume ratio (I) for experiments using

AAS surfactant reported by Aarra et al. (1999)

Salt Temperatur

e in °C

S* in

meq/ml

Reporte

d by

Aarra et

al.

(1999)

S* in

meq/ml

Predicted

from

Eqs.(5.15)

and (5.16)

σ*

in cc/cc

Reported

by Aarra

et al.

(1999)

σ*

in

cc/cc

Predicte

d

from

Eq.(5.12)

%

relative

error in

S*

%

relative

error

in σ*

Average

Tuned

I

NaCl 20.00 0.358 0.355 8.10 7.90 0.79 2.49 0.20 50.00 0.444 0.428 7.00 7.13 3.64 1.82 0.17 90.00 0.564 0.560 5.00 5.03 0.77 0.66 0.26 KCl 20.00 0.240 0.242 8.30 7.93 0.54 4.51 0.28 50.00 0.327 0.323 7.30 7.43 1.17 1.75 0.19 90.00 0.491 0.481 5.30 4.93 2.06 7.02 0.28 CaCl2 20.00 0.070 0.070 12.10 11.89 0.53 1.77 0.41 50.00 0.077 0.077 9.30 9.16 0.13 1.46 0.33 90.00 0.086 0.086 7.10 6.65 0.11 6.36 0.49 MgCl2 20.00 0.092 0.092 9.60 9.64 0.43 0.47 0.27 50.00 0.102 0.102 8.60 8.39 0.03 2.48 0.29 90.00 0.117 0.117 5.70 5.79 0.03 1.62 0.26

Average 0.85% 2.7%

0.29

±0.03

(std.

error)

128

Table 5-3: Summary of interfacial volume ratio at different temperatures from analysis of

pressure scans reported by Austad and Strand (1996).

Temperature in

°C

Oil type β from

Table 3-5 and

Table 3-6

Tuned βI Interfacial

volume ratio I

55

60

65

70

75

80

85

70

75

80

85

90

Dead

Dead

Dead

Dead

Dead

Dead

Dead

Live

Live

Live

Live

Live

7.70E-04

7.60E-04

7.30E-04

7.10E-04

8.30E-04

9.80E-04

1.00E-03

2.50E-04

3.80E-04

3.00E-04

3.70E-04

2.90E-04

2.48E-04

2.60E-04

2.65E-04

2.90E-04

2.82E-04

2.89E-04

2.96E-04

1.18E-04

1.26E-04

1.23E-04

1.29E-04

1.15E-04

0.21

0.23

0.24

0.27

0.23

0.20

0.20

0.31

0.22

0.27

0.23

0.26

Average 6.14E-04 2.12E-04 0.24

Table 5-4: Summary of interfacial volume ratio at different pressures from analysis of

temperature scans reported by Austad and Strand (1996).

Pressure in bars Oil type α from

Table 3-7 and

Table 3-8

Tuned αI Interfacial

volume ratio I

50

100

150

200

250

300

600

500

450

400

300

250

200

100

Dead

Dead

Dead

Dead

Dead

Dead

Live

Live

Live

Live

Live

Live

Live

Live

8.90E-03

8.30E-03

7.70E-03

6.40E-03

5.90E-03

5.00E-03

3.20E-03

5.10E-03

4.20E-03

4.40E-03

6.40E-03

5.40E-03

7.30E-03

8.40E-03

3.55E-03

3.19E-03

2.97E-03

2.60E-03

2.39E-03

2.33E-03

1.62E-03

1.49E-03

1.66E-03

1.72E-03

2.00E-03

2.00E-03

2.75E-03

2.69E-03

0.266

0.256

0.257

0.271

0.270

0.311

0.338

0.195

0.264

0.260

0.208

0.247

0.251

0.214

Average 5.91E-03 2.29E-03 0.262

129

Table 5-5: Statistical summary of interfacial volume ratio data obtained from pressure and

temperature scans reported by Austad and Strand (1996).

Statistic Interfacial volume ratio I

Mean

Standard Error

Standard Deviation

Sample Variance

Minimum

Maximum

0.250

0.007

0.037

0.001

0.195

0.338

130

Figure 5-1: An example showing the linear

relationship between the inverse of oil

solubilization ratios and HLD for type II-

microemulsions. Data obtained from Sheng (2010).


relationship between the inverse of water

solubilization ratios and HLD for type II+

microemulsions. Data obtained from Sheng (2010).

Figure 5-3: An example showing the linear relationship between the inverse of solubilization ratios (red

for oil, blue for water) and HLD for type III microemulsions. Data obtained from Sheng (2010).

y = -0.49x - 0.02 R² = 0.94

0

0.1

0.2

0.3

0.4

0.5

0.6

0.7

0.8

-1.5 -1 -0.5 0

1/σ

o

HLD

y = 0.47x + 0.03 R² = 0.95

0

0.05

0.1

0.15

0.2

0.25

0.3

0 0.2 0.4 0.6

1/σ

w

HLD

y = 0.18x + 0.059 R² = 0.99

y = -0.21x + 0.06 R² = 0.96

0

0.02

0.04

0.06

0.08

0.1

0.12

-0.2 -0.1 0 0.1

1/σ

HLD

131


relationship between the inverse of solubilization

ratios and HLD. Red represents inverse of oil

solubilization ratios. Blue represents inverse of

water solubilization ratios. (WOR=1, σ* = 13.5

cc/cc and I-ratio = 0.129).

Figure 5-5: Tuned phase behavior (solid lines)

compared to data (circles) for experiments with

NaCl and SDS+SDBS+IBA surfactant mixture at

40 °C. Red represents oil solubilization ratios. Blue

represents water solubilization ratios. I-ratio =

0.21, σ* = 7.35 cc/cc and S*= 1.47 meq/ml. Oil used

was heptane.

Figure 5-6: Tuned phase behavior (solid lines) compared to data (circles) for experiments with NaCl and

SDS+SDBS+IBA surfactant mixture at 40 °C. Red represents oil solubilization ratios. Blue represents

water solubilization ratios. I-ratio = 0.34, σ* = 4.56 cc/cc and S*= 2.52 meq/ml. Oil used was dodecane.

0.8 1 1.2 1.4 1.6 1.8 2 2.20

5

10

15

20

NaCl concentration in meq/ml

So

lub

iliz

ati

on

rati

os (

cc/c

c)

1 1.5 2 2.5 3 3.50

5

10

15

20


So

lub

iliz

ati

on

rati

os (

cc/c

c)

132


compared reported data (circles) for experiments

with NaCl and SDS surfactant at 20 °C. Red


water solubilization ratios. Data from (Aarra et

al., 1999)



with KCl and SDS surfactant at 20 °C. Red



al., 1999)



with CaCl2 and SDS surfactant at 20 °C. Red



al., 1999)



with MgCl2 and SDS surfactant at 20 °C. Red



al., 1999)

1 1.2 1.4 1.6 1.8 20

5

10

15

20


So

lub

iliz

ati

on

rati

os (

cc/c

c)

0.7 0.8 0.9 1 1.1 1.2 1.3 1.40

5

10

15

20

KCl concentration in meq/ml

So

lub

iliz

ati

on

rati

os (

cc/c

c)

0.4 0.6 0.8 1 1.2 1.4 1.6 1.80

5

10

15

20

CaCl2 concentration in meq/ml

So

lub

iliz

ati

on

rati

os (

cc/c

c)

0.8 1 1.2 1.4 1.6 1.8 20

5

10

15

20

MgCl2 concentration in meq/ml

So

lub

iliz

ati

on

rati

os (

cc/c

c)

133






al., 1999)



with KCl and SDS surfactant at 35 °C. Blue

represents water solubilization ratios. Data from

(Aarra et al., 1999)



with CaCl2 and SDS surfactant at 35 °C. Red



al., 1999)



with MgCl2 and SDS surfactant at 35 °C. Red



al., 1999)

0.8 1 1.2 1.4 1.6 1.8 2 2.20

5

10

15

20


So

lub

iliz

ati

on

rati

os (

cc/c

c)

0.8 1 1.2 1.4 1.6 1.8 20

5

10

15

20


So

lub

iliz

ati

on

rati

os (

cc/c

c)

0.2 0.4 0.6 0.8 1 1.2 1.4 1.6 1.80

5

10

15

20


So

lub

iliz

ati

on

rati

os (

cc/c

c)

0.5 1 1.5 20

5

10

15

20


So

lub

iliz

ati

on

rati

os (

cc/c

c)

134






al., 1999)



with KCl and SDS surfactant at 50 °C. Red



al., 1999)



with CaCl2, and SDS surfactant at 50 °C. Red



al., 1999)



with MgCl2, and SDS surfactant at 50 °C. Red



al., 1999)

0.8 1 1.2 1.4 1.6 1.8 2 2.2 2.40

5

10

15

20


So

lub

iliz

ati

on

rati

os (

cc/c

c)

0.8 1 1.2 1.4 1.6 1.8 20

5

10

15

20


So

lub

iliz

ati

on

rati

os (

cc/c

c)

0.2 0.4 0.6 0.8 1 1.2 1.4 1.6 1.80

5

10

15

20


So

lub

iliz

ati

on

rati

os (

cc/c

c)

0.5 1 1.5 20

5

10

15

20


So

lub

iliz

ati

on

rati

os (

cc/c

c)

135



with NaCl and AAS surfactant at 20 °C. Red



al., 1999)



with KCl and AAS surfactant at 20 °C. Red



al., 1999)



with CaCl2, and AAS surfactant at 20 °C. Red



al., 1999)



with MgCl2, and AAS surfactant at 20 °C. Red



al., 1999)

0 0.1 0.2 0.3 0.4 0.5 0.6 0.70

5

10

15

20


So

lub

iliz

ati

on

rati

os (

cc/c

c)

0 0.1 0.2 0.3 0.4 0.5 0.6 0.70

5

10

15

20


So

lub

iliz

ati

on

rati

os (

cc/c

c)

0.06 0.065 0.07 0.075 0.08 0.0850

5

10

15

20

25

30


So

lub

iliz

ati

on

rati

os (

cc/c

c)

0.08 0.09 0.1 0.11 0.12 0.130

5

10

15

20

25

30


So

lub

iliz

ati

on

rati

os (

cc/c

c)

136






al., 1999)






al., 1999)






al., 1999)






al., 1999)

0.1 0.2 0.3 0.4 0.5 0.6 0.7 0.80

5

10

15

20


So

lub

iliz

ati

on

rati

os (

cc/c

c)

0.25 0.3 0.35 0.40

5

10

15

20

25

30


So

lub

iliz

ati

on

rati

os (

cc/c

c)

0.065 0.07 0.075 0.08 0.085 0.09 0.0950

5

10

15

20

25

30


So

lub

iliz

ati

on

rati

os (

cc/c

c)

0.08 0.09 0.1 0.11 0.12 0.130

5

10

15

20

25

30


So

lub

iliz

ati

on

rati

os (

cc/c

c)

137






al., 1999)






al., 1999)






al., 1999)






al., 1999)

0.4 0.5 0.6 0.7 0.80

5

10

15

20

25

30


So

lub

iliz

ati

on

rati

os (

cc/c

c)

0.25 0.3 0.35 0.4 0.45 0.5 0.55 0.6 0.650

5

10

15

20

25

30


So

lub

iliz

ati

on

rati

os (

cc/c

c)

0.075 0.08 0.085 0.09 0.095 0.1 0.105 0.11 0.1150

5

10

15

20

25

30


So

lub

iliz

ati

on

rati

os (

cc/c

c)

0.09 0.1 0.11 0.12 0.13 0.14 0.15 0.16 0.170

5

10

15

20

25

30


So

lub

iliz

ati

on

rati

os (

cc/c

c)

138

Figure 5-31: Average tuned interfacial volume

ratios for experiments using SDS surfactant at

20°C (Blue), 35°C (Red), 50°C (Green). Black lines

represent average interfacial volume ratios for

each salt.

Figure 5-32: Average tuned interfacial volume

ratios for experiments using AAS surfactant at

20°C (Blue), 50°C (Red), 90°C (Green). Black lines

represent average interfacial volume ratios for

each salt.

Figure 5-33: Width of the three-phase region as a

function of the optimum solubilization ratio and

the interfacial volume ratio (I) for a fixed overall

concentration of ϕo=0.495, ϕw=0.495 and ϕs=0.01.

Figure 5-34: Example of a modified fish diagram

(interfacial volume ratio (I)=0.2). Red shows the


limit. Type III microemulsions can only exist when

χ is larger than σ* and, HLD is within the upper

and lower critical limits HLDU*

and HLDL* .

0.00

0.10

0.20

0.30

0.40

0.50

0.60

SodiumChloride

PotassiumChloride

CalciumChloride

MagnesiumChloride

Tu

ned

I-R

ati

o

0.00

0.05

0.10

0.15

0.20

0.25

0.30

SodiumChloride

PotassiumChloride

CalciumChloride

MagnesiumChloride

Tu

ned

I-R

ati

o

0.5

1 1020

30

0

1

2

3

4

5

*

I-ratio

H

LD

HLDU*

HLDL

*

σ *

139

Figure 5-35: Locus of the invariant type III

microemulsion composition in a ternary space.

(σ*= 3 cc/cc)

Figure 5-36: Locus of the invariant type III

microemulsion composition in a ternary space.

(σ*= 10 cc/cc)

Figure 5-37: Locus of invariant type III microemulsion composition in a ternary space (σ*= 30 cc/cc).

0

20

40

60

80

0 20 40 60 80

0

20

40

60

80

Oil

Surfactant

Brine 0

20

40

60

80

0 20 40 60 80

0

20

40

60

80

Oil

Surfactant

Brine

0

20

40

60

80

0 20 40 60 80

0

20

40

60

80

Oil

Surfactant

Brine

140

Figure 5-38: Inverse of oil solubilization ratios as a

function of pressure at different constant

temperatures using dead oil. Data from Austad

and Strand (1996)

Figure 5-39: Inverse of water solubilization ratios

as a function of pressure at different constant

temperatures using dead oil. Data from Austad

and Strand (1996)


function of pressure at different constant

temperatures using live oil. Data from Austad and

Strand (1996)


as a function of pressure at different constant

temperatures using live oil. Data from Austad and

Strand (1996)

0

0.02

0.04

0.06

0.08

0.1

0.12

0.14

0.16

0 100 200 300 400

1/σ

o

Pressure in Bars

55 °C

60 °C

65 °C

70 °C

75 °C

80 °C

85 °C

90 °C0

0.02

0.04

0.06

0.08

0.1

0.12

0.14

0.16

0 100 200 300 400

1/σ

w

Pressure in Bars

55 °C

60 °C

65 °C

70 °C

75 °C

80 °C

85 °C

90 °C

0

0.02

0.04

0.06

0.08

0.1

0.12

0.14

50 250 450 650

1/σ

o

Pressure in Bars

70 °C

75 °C

80 °C

85 °C

90 °C

95 °C

100 °C

110 °C

0

0.02

0.04

0.06

0.08

0.1

0.12

0.14

50 250 450 650

1/σ

w

Pressure in Bars

70 °C

75 °C

80 °C

85 °C

90 °C

95 °C

100 °C

110 °C

141


function of temperature at different constant

pressures using dead oil. Data from Austad and

Strand (1996).


as a function of temperature at different constant


Strand (1996).



pressures using live oil. Data from Austad and

Strand (1996).




Strand (1996).

0.04

0.06

0.08

0.1

0.12

0.14

0.16

50 70 90

1/σ

o

Temperature in °C

300 bars

250 bars

200 bars

150 bars

100 bars

50 bars

0

0.02

0.04

0.06

0.08

0.1

0.12

0.14

50 70 90

1/σ

w

Temperature in °C

300 bars

250 bars

200 bars

150 bars

100 bars

50 bars

0

0.02

0.04

0.06

0.08

0.1

0.12

0.14

65 85 105

1/σ

o

Temperature in °C

600 bars

500 bars

450 bars

400 bars

300 bars

250 bars

200 bars

100 bars0

0.02

0.04

0.06

0.08

0.1

0.12

0.14

65 85 105

1/σ

w

Temperature in °C

600 bars

500 bars

450 bars

400 bars

300 bars

250 bars

200 bars

100 bars

142

Figure 5-46: Interfacial volume ratio for a

surfactant mixture (sodium laurate and sodium

oleate) as a function of laurate soap mole fraction

using Eq. (5.32).




Strand (1996).




Strand (1996).

0.23

0.24

0.24

0.25

0.25

0.26

0.26

0.27

0 0.1 0.2 0.3 0.4 0.5 0.6 0.7 0.8 0.9 1

Inte

rfacia

l V

olu

me R

ati

o

Xlaurate

0

0.05

0.1

0.15

0.2

0.25

0 0.2 0.4 0.6 0.8

Tu

ned

I-R

ati

o

Xsoap

0

0.1

0.2

0.3

0.4

0.5

0.6

0.7

0.8

0.9

1

0 0.2 0.4 0.6 0.8 1

Tu

ned

I-R

ati

o

Xsoap

143

Chapter 6

Conclusions and Recommendations

6.1. Conclusions

The effects of solution gas, pressure, temperature and alkali on the phase behavior of systems

consisting of surfactant, brine and crude oil have been examined. For the first time, a new HLD-

NAC based EOS model for microemulsion phase behavior was developed that can account for

changes in different formulation variables. This research has shown how to estimate the optimum

salinity and solubilization ratio under most conditions. We demonstrate that simple PVT data of

such systems eliminate the need to perform salinity scans at high pressures and temperatures. The

following conclusions are made:

1. Microemulsion phase behavior depends on pressure changes. The logarithm of optimum

salinity varies linearly with pressure. The existing HLD equation was updated to include

a new β factor to account for the change in HLD due to pressure.

2. The optimum solubilization ratio depends inversely on the width of the three-phase

window expressed in HLD units. This dependence can be used to obtain a relationship

between optimum salinities and solubilization ratios. Based on salinity scans using

different pure alkanes, these relationships can be easily determined and used for

prediction.

3. The modified HLD-NAC developed in this dissertation is the first phase behavior model

that was successfully used to interpret temperature and pressure scans.

4. PVT experiments like those reported by Austad and Strand (1996) are critical in

understanding the effect of pressure and temperature on phase behavior. They provide a

144

quick and easy way to obtain phase behavior data, specifically α and β in the HLD

equation, over a wide range of temperature and pressure. In comparison, salinity scans at

high pressures give limited information and are more cumbersome and expensive.

5. Pressure and solution gas both affect phase behavior and in a compensating manner.

Therefore ignoring either one of them can lead to errors. We do not recommend the use

of surrogate oils (using toluene to mimic live oil composition) or forcing the EACN of

methane to be values other than 1.0.

We then extended the modified HLD-NAC equation of state to model and predict

microemulsion phase behavior applicable to alkali-surfactant EOR. The approach was validated

by using available published data. The following conclusions are made:

1. The soap formed under in-situ conditions is dependent on the alkyl carbon number and

molecular weight of the petroleum acid pseudocomponent. The alkyl carbon number of

the acid can be used to estimate distribution coefficients, soap tail length, and soap mole

fractions thereby reducing the number of input/tuning variables.

2. The inverse of optimum solubilization ratio (1/σ*) is a linear function of the soap mole

fraction (Xsoap). This empirical relationship is new to this research. The relationship

between inverse of optimum solubilization ratio, lnS*, and mole fraction of soap formed

can be represented by a plane in three-dimensional coordinates. This relationship to

predict optima can be used to constrain the soap model and determine an effective alkyl

carbon number for the acid pseudocomponent.

3. Flash calculations using the modified HLD-NAC model are non-iterative, fast, and

robust. Flash calculations were extended to model soap as a second component lumped in

the surfactant pseudocomponent. Additional synthetic surfactants can also be added.

4. Only two tuning parameters are required (n and asurf) to model alkali-surfactant-oil-brine

phase behavior. In comparison, the Hand’s model approach has seven input parameters

145

(five if excess phases are assumed to be pure) that require tuning (Sheng, 2010). The new

model predictions are in good agreement with un-tuned experimental data.

5. Activity maps can be predicted easily by our model without the need to fit three-phase

windows from experiments as done in UTCHEM.

6. Fish diagrams for alkali-surfactant system are asymmetric, which is in agreement with

published literature.

Dimensionless solutions to represent microemulsion phase behavior were then established by

correcting the average curvature equation. The NAC equations were made dimensionless in order

to identify key dimensionless groups that govern microemulsion phase behavior. The following

conclusions can be made:

1. Inverse of oil and water solubilization ratios vary linearly with HLD and hence, lnS. The

slopes of the linear relationships are determined by the interfacial volume ratio (I). The

slope in the two-phase regions are twice that of the slopes in the three-phase region.

2. The optimum solubilization ratio σ* is the harmonic mean of σo and σw in the type III

microemulsion. This property should be used to infer optima from phase behavior

experiments. The intersection of the linear trends in the type III region gives an accurate

estimate of the optimum salinity.

3. The type III microemulsion window is dependent on the upper and lower HLD limits and

the value of the χ factor. The χ factor scales fish diagrams better as opposed to

considering the effects of WOR and Vs separately.

4. The type of cations do not affect the interfacial volume ratio (I) significantly. However,

salinities should be expressed in terms of equivalents and not in terms of weight %.

5. The locus of the type III microemulsion composition (invariant point) is a function of σ*

alone.

146

6.2. Recommendations for Future Research

In this section, we present recommendations that can help to better understand the phase

behavior of microemulsion and its impact on oil recovery in chemical EOR floods. We

recommend the following tasks:

1. PVT experiments similar to the ones analyzed in this dissertation can be done for

alkali-surfactant-oil-brine systems. The modified HLD-NAC model explained in

Chapters 3 and 4 is fully capable of capturing the effects of different formulation

variables like alkali, pressure and temperature. Such experimental data do not

exist in the published literature and are therefore, highly desirable.

2. Bourrel and Schechter (2010) showed that the constants in the linear relationship

between the width of the three-phase region and the optimum solubilization ratio

are unique for each type of surfactant. Therefore, the constants for lnS* vs 1/σ

*

relationship can be made a function of the surfactant structure properties like alkyl

chain length, number of ethoxy units, number of propoxy units and type of head

group. Hammond and Acosta (2012) showed that the Cc parameter in the HLD

equation is a function of the surfactant structure. Combining HLD and the

optimum solubilization ratio equations, a robust screening model can be

developed where surfactants with different structures can be screened to cater to

phase behavior requirements for a particular crude oil.

3. A complex geochemical model can be integrated with the modified HLD-NAC in

Chapter 4. This would allow simulators to capture phase behavior changes as a

function of rock-fluid interactions.

147

4. The model developed here assumes that the solubilized micelles are spherical in

shape. However, Acosta et al. (2003) showed that such an assumption is a

simplification. In reality, the shape of micelles are spherical in the two-phase

regions, but they transition to rod-like micelles near the two-phase and three-

phase boundaries. The bi-continuous type III microemulsion often consists of

lamellar structures with alternating layers of solubilized oil and water. A shape

factor can be introduced in the definition of the curvature in the NAC equations to

see how the shape factor changes as a function of HLD.

5. Integration of the models discussed in this dissertation with a reservoir simulator

is highly desirable. Different flood scenarios can be investigated and oil recovery

can be analyzed. Current simulators are not equipped to deal with the changes in

formulation variables other than WOR and salinity. Pressure and temperature

variations across a reservoir during an EOR flood impacts oil recovery.

148

Appendix A

Effect of Pressure on the Surfactant Affinity Difference and the

Hydrophilic-Lipophilic Difference

In this appendix, we show the thermodynamic premise behind the inclusion of the β factor in the

HLD equation by first elaborating on the concept of the surfactant affinity difference (SAD),

followed the description of the method by Salager (1988).

Consider the chemical potential of the surfactant in phase j to be µsj where j may be either

oil or water. Now, consider these chemical potentials at some reference state to be µsj*. The

equations for chemical potentials of the surfactant component in the water and oil phases can

therefore be expressed as

* ln( )sw sw sw swRT x a (A-1)

and,

* ln( )so so so soRT x a . (A-2)

where xso and xsw represent relative concentrations of the surfactant in oil and water, respectively.

Activity coefficients of the surfactant in oil and water phases are represented by aso and asw

respectively. At equilibrium, the chemical potentials of the surfactant component are equal to

each other. The difference between the reference state chemical potentials of the surfactant in the

149

water and the oil phase is the surfactant affinity difference. The dimensionless form of the SAD is

the hydrophilic lipophilic difference. Therefore,

* * ln( / )sw so so so sw swSAD RT x a x a , (A-3)

and,

SADHLD

RT . (A-4)

For high quality formulations, the concentration of the surfactant in the excess oil and

water phases is very small. This implies that the activity coefficients are equal to 1.0 in those

phases. Therefore, activities can be replaced by concentrations in the SAD equation. Furthermore,

at optimum salinity, the concentrations of surfactant in the excess oil and water phases are equal.

Hence the SAD (and the HLD) at optimum condition is zero.

When pressure and salinity are changed in the system, the change in reference state

chemical potentials cause the SAD and the HLD to change. Therefore, we form the following

differential equations similar to those derived by Salager (1988) for changes in EACN and lnS*:

* *

* *

*ln

ln

so so

sod dP d SP S

, (A-5)

and,

* *

* *

*ln

ln

sw sw

swd dP d SP S

. (A-6)

150

Now, salinity causes changes in µsw* alone (Salager, 1988) and does not affect µso

*.

Therefore,

*

* so

sod dPP

. (A-7)

Additionally, the change in µsw* is dominated by the change in salinity. Therefore, the

effect of pressure on µsw* can be assumed to be weak as compared to the strong influence of

salinity. Neglecting the pressure effect in Eq. (A-6) yields,

*

* *

*ln

ln

sw

swd d SS

. (A-8)

As shown empirically in this dissertation, the logarithm of optimum salinity and pressure

are linearly dependent. Therefore,

*ln S P C , (A-9)

where C is a constant. Thus,

*lnd S dP . (A-10)

151

At optimum conditions, SAD is always zero. This means the changes in µsw* and µso

* due

to changes in formulation variables must compensate each other at optimum conditions.

Therefore, dµsw* and dµso

* are equal. Hence combining (A-7), (A-8) and (A-9),

* *

*ln

so sw

P S

. (A-11)

This result is analogous to the one expressed by Salager (1988) for compensating changes

in EACN and lnS*. Furthermore, SAD is a function of formulation variables that are independent.

This is shown as follows. Since µsw* and µso

* are functions of different variables, the partial

derivatives must be constant. That is,

* *

1 2* and

ln

so swb bP S

, (A-12)

where, b1 and b2 are constants. Therefore by generalizing this result for other HLD variables,

*

*d ( d ) ( d )sj

sj i i i

i

X b XX

, (A-13)

where, every Xi is a HLD variable with bi as a relevant constant (the partial derivative). Linear

expressions of µw* and µo

* can be obtained by integration. The difference between µw* and µo

*

then forms a linear expression for SAD. That is,

* * ( )sw so i iSAD b X . (A-14)

152

Hence pressure, just like the other variables considered by Salager (1988), should also

form a linear (and independent) term in the SAD equation. In this dissertation, we show the

similarity between the pressure and temperature effects. Hence we adopted a linear term for

pressure that has a similar functional form to the term for temperature, which was already present

in the equation. We updated the SAD and HLD equations to include the pressure effects as

follows:

ln ( ) ( )ref ref

SADHLD S K EACN f A T T P P Cc

RT . (A-15)

153

Appendix B

Alkalinity of Aqueous Sodium Carbonate Solution

This section describes in more detail, the reactions and equilibrium constants used in this

dissertation to calculate the pH of sodium carbonate solutions. Aqueous sodium carbonate

solutions are alkaline in nature. Sodium and carbonate ions are formed as a result of dissolution.

The carbonate ion reacts with water to form bicarbonate and hydroxyl ions such that,

3

23

2

3 2 3 1andHCO OH

CO

C CCO H O HCO OH K

C

(B-1)

However, the molar concentrations of bicarbonate and the hydroxide ions are equal.

Hence,

23 3

1

1OH HCO COC C K C , (B-2)

where, C1OH- is the hydroxyl ion concentration from Eq. (B-1). The bicarbonate ion is also in

equilibrium with water, carbonic acid and hydroxyl ion,

2 3

3

3 2 2 3 2and H CO OH

HCO

C CHCO H O H CO OH K

C

. (B-3)

Again, since concentrations of carbonic acid, and hydroxyl ions are equal,

154

3

2

2OH HCOC K C . (B-4)

where C2OH- is the hydroxyl ion concentration from Eq. (B-3). Therefore, the total concentration

of hydroxyl ions will be,

2 23 3

1 2 1/4

1 2 1( )OH OH OH CO CO

C C C K C K K C . (B-5)

In this dissertation, we considered K1 to be 2.08×10-4 M and K2 to be 2.22×10-8 M (Lister,

2000). We then used the total hydroxyl ion concentration COH- in Eq. (3) to calculate the soap

content as a function of sodium carbonate concentration. The concentration of hydroxyl ions is

used to calculate pH and pOH.

155

Appendix C

Salinity Scan Experiments at Atmospheric Pressure

This section describes the procedure to conduct salinity scans at atmospheric pressure. Salinity

scans are typically done by mixing surfactant-oil-brine mixtures in sealed graduated pipettes in a

controlled environment (constant temperature oven). The pure oils used in the experiments were

heptane and dodecane. Surfactants used were sodium dodecyl benzenesulfonate (SDBS) and

sodium dodecyl sulfate (SDS). Iso-butyl alcohol (IBA) was used as a cosolvent. The procedure is

as follows:

1. Borosilicate pipettes were prepared by sealing the narrow end with a MAP gas flame

torch.

2. A salt stock solution (NaCl) was then prepared by adding salt to DI water. The

concentration of the stock solution needs to be high in order to obtain the desired range

and resolution in a salinity scan. A magnetic stirrer was used to dissolve the salt into DI

water. The salt solution is prepared on weight basis such that,

Weight of salt( )Salt Concentration( %) 100

Weight of salt( ) Weight of water( )

gwt

g g

. (C-1)

3. A surfactant stock solution was prepared by mixing equal amounts of SDS and SDBS.

The aqueous surfactant solution in each pipette contained 1 wt.% SDS, 1wt% SDBS and 3

wt.% of IBA. The concentrations of SDS, SDBS and IBA in the stock solution were four

times that of the desired aqueous surfactant solution concentration. The dilution of the

surfactant stock with the brine solution would eventually give the desired surfactant

concentrations in the pipettes.

156

4. The desired amounts (by weight) of surfactants and co-solvent (IBA) were added to DI

water to prepare the surfactant stock solution such that,

Weight of surfactant( )Surfactant Concentration( %) 100

Weight of surfactant( ) Weight of water( )

gwt

g g

.

(C-2)

A magnetic stirrer was used to dissolve the chemicals in DI water.

5. An array of pipettes was then prepared to create a salinity gradient. Each pipette was

labelled to show the salt content and the chemicals used.

6. Correct proportions of brine, surfactant solution and DI water were sequentially added to

each pipette to obtain the desired salinity and surfactant concentration. The resultant

solution in the pipette constitutes the aqueous volume. For our experiments the aqueous

volume was 2 ml.

7. Oil was then added to the pipette (the oil was dyed with a red dye). In the experiments

described here, 2 ml of oil was added.

8. An Argon stream was used to strip out the air from top of the pipette. This helps to

minimize the impact of gas on the phase behavior and also creates an inert environment

in the pipette addressing a potential fire hazard.

9. The top end of each pipette were then sealed using a flame torch.

10. The fluids were then mixed. Each pipette was checked for leaks.

11. All pipettes were then allowed to equilibrate for one day at 40 °C in a constant

temperature oven.

12. The fluids were then mixed at the desired temperature and allowed to settle for one day.

13. Readings of the interfaces formed in each pipette were measured and recorded every

three days (See Figure C-1). The final readings were obtained after two weeks.

157

14. Oil and water solubilization ratios are then calculated by measuring the volume of oil and

water solubilized in the microemulsion.

15. A list of experimental observations and calculations has been included in

158

Table C-1: Summary of observations and calculations in a salinity scan. Total volume

capacity of each pipette is 5 ml.

Variable name Quantity measured with units Calculation / Observation

A Salinity

(meq/ml) Salinity of pipettes prepared

B Initial aqueous level

(ml) See Figure C-1

C Initial oil level

(ml) See Figure C-1

D Top of microemulsion phase

(ml) See Figure C-1

E Bottom of microemulsion phase

(ml) See Figure C-1

F

Volume of surfactant in the

system

(ml)

(5-B) × (aqueous surfactant

concentration in wt. %)

Surfactant density is assumed to be

equal to water. Hence, volume % is

equal to weight %.

G Solubilized oil

(ml) G = B – D

H Solubilized water

(ml) H = E – B

I Oil solubilization ratio

(dimensionless) I = G / F

J Water solubilization ratio

(dimensionless) J = H / F

K

Volume fraction of excess oil

phase

(dimensionless)

K = (D – C) / (5 – C)

L

Volume fraction of

microemulsion

(dimensionless)

L = (5 – D) / (5 – C) for type II-

L = (E – D) / (5 – C) for type III

L = (E – C) / (5 – C) for type II+

M

Volume fraction of excess water

phase

(dimensionless)

M = 1– K – L

159

Figure C-1: Schematic of readings measured from a phase behavior pipette scan. O: oil, W:

water and ME: microemulsion. Total volume capacity of each pipette is 5 ml.

O

W

O

ME

O

W

ME

W

ME

Tota

l V

olu

me

= 5 -

Oil

L

evel

Argon

/ Air

Argon

/ Air

Argon

/ Air

Argon

/ Air R

ead

ings

incr

ease

0 t

o 5

ml

Oil level (C)

Aqueous

level (B)

Top of ME

Bottom

of ME

Oil

Solubilized

Water Solubilized

Initial Type II- Type III Type II+

160

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VITA

Soumyadeep Ghosh was born in Ramachandrapuram, India on 6th May 1989. He holds a

Bachelor of Technology degree in Oil, Oleochemical and Surfactant Technology from the

Institute of Chemical Technology, Mumbai, India (2011). He earned his PhD student in Energy

and Mineral Engineering (Petroleum and Natural Gas Engineering option) at The Pennsylvania

State University. His research interests include enhanced oil recovery, surfactant science,

thermodynamics, fluid phase behavior and reservoir engineering. He is currently working for

Chevron Corporation as a Reservoir Simulation Engineer in the improved oil recovery/enhanced

oil recovery (IOR/EOR) unit in Chevron Energy Technology Company.

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