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Digital Rock Physics for Coreflooding Simulations
Mahesh Avasare
Thesis to obtain the Master of Science Degree in
Petroleum Engineering
Thesis Supervisors:
Mr. Pedro Romero Fernandez
Prof. Maria João Correia Colunas Pereira
Examination Committee:
Chairman: Prof. Amílcar de Oliveira Soares
Supervisor: Prof. Maria João Correia Colunas Pereira
Member of the Committee: Mr. Victor Alcobia
November 2016
i
Dedication
Dedicated to
My Ever-Supportive Parents,
Grandfather, Sister
And
My Country: India.
ii
Abstract
In the era of low oil prices, economic viability of oil fields strongly relies on accurate technical
analysis and predictions. Detailed core analysis is one of the most reliable information about in-
situ conditions; results are further used for reservoir management and optimization. After
extracting petrophysical properties with core characterization, corefloodings are performed to
evaluate dynamic fluid responses by cores. This work has formalized a method to understand and
tackle uncertainties associated with coreflooding results.
Cores undergo routine core analysis to extract global porosity, permeability and water saturation.
But generally the cores possess local micro-heterogeneities. Patterns of preferential path of flow
or inaccessible pore volumes are distinctly visible when most of the cores are split opened. Such
heterogeneities cause deviation from expected behavior of the flooding. As a result, properties or
techniques predicted through corefloodings might be misleading. To avoid such uncertainties,
computational simulation of corefloodings can be performed along with experimental floodings.
This work explains detailed development steps of coreflooding computational model in association
with Digital Rock Physics. Static model for this simulation is based on computed tomography (CT)
scan results; whereas the dynamic model is developed with a black-oil simulator. After
establishing basic understanding of mathematical model behind the black oil simulators,
simulation results have been analyzed in detail. With sensitivity analysis of various parameters,
boundary conditions have been tested too.
Stepwise dynamic coreflooding model development has been explained in this work. History
matching has been performed by altering mainly the local permeability distribution and relative
permeability curves. The reference model developed achieved good results within the boundaries
of established simulation constraints.
Keywords: Digital Rock Physics, Coreflooding Simulations, Coreflooding Uncertainties,
Petrophysical Model of Core, Dynamic Coreflooding Model
iii
Acknowledgements
First and foremost, I would like to thank Compañía Española de Petróleos, S.A.U. (CEPSA) and
Instituto Superior Técnico (Lisbon) for offering me internship opportunity at R&D center of
CEPSA. The internship gave me a platform to apply my theoretical knowledge developed while
pursuing masters as well as bachelors, into practical case studies. Also, I am most thankful to
Erasmus Mundus consortium for complete financial support throughout my master program.
I am grateful to my guide, Mr. Pedro Romero Fernandez, for his constant technical as well as
personal guidance throughout my internship. He acted an ideal guide during our professional
interactions; whereas a close friend during our casual interactions. I am also grateful to my
academic guide, Prof. Amílcar de Oliveira Soares, for his support and motivation. I would also
like to thank Prof. Maria João Correia Colunas Pereira and Prof. Leonardo Azevedo Guerra
Raposo Pereira for their constant support throughout the master program.
I would also like to thank the project team; Ms. Maria Rosario Rodriguez Pardo, Mr. Jesus Montes
Ruiz, Mr. Arjen Rolf and Mr. Enrique Yuste Caro for sharing their great depth of technical
expertise with me. Along with their technical support, their patience and down to earth attitude
helped me to get the project in a good shape.
I express my gratitude to complete Exploration and Production team at R&D Center of CEPSA:
Mr. Raul Rodriguez Martin, Mr. Nicolas Blin, Mr. Jose Maria Gomez Castro, Ms. Marta Bregua
de la Sotilla, Ms. Elena González Fernández, Ms. Maria Flor Garcia Mayoral, Mr. Francisco
Daniel Trujillo España, Mr. Asier Panadero Ruiz and Mr. Juan Jose Suñer Lopez. Their assistance
and support have been greatly appreciated and saved many hours of boredom. I would like to thank
rest of R&D Center family for making my stay there a great memory, to be cherished forever.
I would like to express my special gratitude to Ms. Rogéria Bingre do Amaral for always being
there for me. Finally, I would like to thank my family and all my friends for providing me the
strength and moral support I always needed for getting through a very special phase of my life.
iv
List of Abbreviations & Symbols
1D : One Dimentional
3D : Three Dimentional
AP : Alkali and Polymer
ASP : Alkali, Surfactant and Polymer
CEPSA : Compañía Española de Petróleos, S.A.U
CT : Computed Tomography
DRP : Digital Rock Physics
ED : Displacement Efficiency
EOR : Enhanced Oil Recovery
Ero : Oil Recovery Efficiency
Evo : Vertical Sweep Efficiency
IFT / σ : Interfacial Tension
K : Permeability Distribution
Kr : Relative Permeability
Kro,wi : Oil Relarive Permeability at Initial Water Saturaion
Krw / Kro : Water / Oil Realtive Permeability
Krw,ro : Water Relarive Permeability at Residual Oil Saturaion
ME : Microemulsion
No / Nw : Corey Index of Oil / Water
PV : Pore Volumes (for the plug / core)
R&D : Research And Development
RT1/2/3/4 : Rock Type 1/2/3/4
SCAL : Special Core Analysis Lab
Soi / Swi : Initial Oil / Water Saturation
Sor : Residual Oil Saturation
μ : Fluid Viscosity as per subscript
φ : Porosity
v
DEDICATION............................................................................................................................................. I
ABSTRACT ................................................................................................................................................ II
ACKNOWLEDGEMENTS .................................................................................................................... III
LIST OF ABBREVIATIONS & SYMBOLS .......................................................................................... IV
LIST OF FIGURES ................................................................................................................................ VII
LIST OF TABLES ................................................................................................................................ VIII
1 INTRODUCTION .............................................................................................................................. 1
1.1 CONTEXT ................................................................................................................................. 1
1.2 OBJECTIVE ............................................................................................................................... 1
1.3 WORK STRUCTURE .................................................................................................................. 2
2 LITERATURE REVIEW .................................................................................................................. 3
2.1 ENHANCED OIL RECOVERY ..................................................................................................... 3
2.2 CHEMICAL EOR (ASP) ............................................................................................................ 4
2.3 COREFLOODING: INTRODUCTION ............................................................................................ 6
2.4 COREFLOODING: MATHEMATICAL MODELING ....................................................................... 7
2.5 DIGITAL ROCK PHYSICS ........................................................................................................ 12
3 EXPERIMENTAL COREFLOODING ......................................................................................... 14
3.1 COREFLOODING PROCEDURE ................................................................................................ 14
3.2 COREFLOODING SETUP .......................................................................................................... 15
4 1D COREFLOODING SIMULATION.......................................................................................... 16
4.1 CARACARA OIL FIELD ........................................................................................................... 16
4.2 1D STATIC MODEL ................................................................................................................ 17
4.3 INITIAL AND BOUNDARY CONDITIONS OF 1D DYNAMIC MODEL .......................................... 17
4.4 HISTORY MATCHING OF 1D DYNAMIC MODEL .................................................................... 19
4.5 SENSITIVITY ANALYSIS OF 1D DYNAMIC MODEL ................................................................ 21
5 3D STATIC MODEL ....................................................................................................................... 25
5.1 CT SCAN RESULTS ................................................................................................................ 25
5.2 ATTENUATION MODEL TO DENSITY MODEL ........................................................................ 26
5.3 DENSITY MODEL TO POROSITY MODEL ................................................................................ 27
5.4 POROSITY MODEL TO PERMEABILITY MODEL ...................................................................... 28
6 3D DYNAMIC MODEL .................................................................................................................. 30
6.1 INITIATION ............................................................................................................................. 30
6.2 GOAL, METHODS & CONSTRAINTS ....................................................................................... 34
6.3 DEVELOPMENT ...................................................................................................................... 35
vi
7 SENSITIVITY ANALYSIS ............................................................................................................. 56
7.1 ANALYSIS 1: WETTABILITY VARIATIONS OF RT2 MIXED WET & RT3, RT4 OIL WET ........ 56
7.2 ANALYSIS 2: WATER INJECTION RATE VARIATION .............................................................. 58
7.3 ANALYSIS 3: INJECTION WELL AREA VARIATION ................................................................ 59
7.4 ANALYSIS 4: INJECTION GEOMETRY VARIATION USING EXPERIMENTAL SHAPE ................. 61
8 RESULTS AND DISCUSSION ....................................................................................................... 64
9 FUTURE WORK ............................................................................................................................. 67
REFERENCES .......................................................................................................................................... 68
vii
List of Figures
Figure 1 Fingering Effect due to Poor Mobility Ratio (Olajire, 2014) ........................................... 5
Figure 2 Standard Relative Permeability Curve ........................................................................... 10
Figure 3 Idealized Type I ternary phase environment .................................................................. 11
Figure 4 Idealized Type II ternary phase environment ................................................................. 11
Figure 5 Idealized Type III ternary phase environment ................................................................ 11
Figure 6 Typical Digital Rock Physics Analysis Procedure (Kalam, 2012) ................................. 13
Figure 7 Simplified Schematics of Coreflooding Setup (Courtesy: R&D Center, CEPSA) ........ 15
Figure 8 Simplified Stages of coreflooding (Courtesy: R&D Center, CEPSA) ........................... 15
Figure 9 Location of Caracara Sur Field (Bozorgzadeh, et al., 2015) .......................................... 16
Figure 10 Comparison of Kr Curves: Lab and Modified (1D Model) .......................................... 19
Figure 11 Oil Recovery and Injection Pressure History Match (1D Model) ................................ 20
Figure 12 Results of sensitivity analysis for Injection Rate (1D Model) ..................................... 22
Figure 13 Result of sensitivity analysis for IFT Concentration (1D Model) ................................ 23
Figure 14 Results of sensitivity analysis for Polymer Concentration (1D Model) ....................... 24
Figure 15 Processed CT Scan Results (Attenuations) .................................................................. 25
Figure 16 Average Attenuation vs Average Density Correlation (Courtesy: E&P, CEPSA) ...... 26
Figure 17 Porosity Model Generated & Corresponding Univariate Distribution ......................... 27
Figure 18 Permeability vs Porosity Correlation with Rock Type Classification .......................... 28
Figure 19 Permeability Model Distribution Histogram ................................................................ 29
Figure 20 Well Geometry 3D Model ............................................................................................ 30
Figure 21 Optimized Timestep Scheme ........................................................................................ 31
Figure 22 Different Kr Curves Tested in Simulations .................................................................. 32
Figure 23 Comparative Results for Different Relative Permeability Curves ............................... 33
Figure 24 Results of Manual Permeability Distribution Alteration (Model 1) ............................. 36
Figure 25 Permeability Distribution Comparison (Step2) ............................................................ 37
Figure 26 Results of Permeability Distribution Alteration with Co-kriging (Step 2) ................... 38
Figure 27 Permeability Distribution Comparisons (Step 3) ......................................................... 39
Figure 28 Results of Permeability Distribution Alteration with Co-kriging (Step 3) ................... 40
Figure 29 Comparison of Relative Permeability Curves (Step 4) ................................................ 41
Figure 30 Results of Relative Permeability Curve with Corey Exponents (Model 4) .................. 42
viii
Figure 31 Comparison of Relative Permeability Curves (Step 5) ................................................ 43
Figure 32 Results of Relative Permeability Curve with Higher Water Mobility (Step 5) ............ 44
Figure 33 Permeability vs Porosity Correlation with Rock Type Classification .......................... 45
Figure 34 Permeability Distribution with all Rock Types (Step 6) .............................................. 46
Figure 35 Results of Permeability Distribution Model with All Rock Types (Step 6) ................. 47
Figure 36 Permeability Distribution Comparison (Step 6 and Step 7) ......................................... 48
Figure 37 Results of Permeability Distribution Model with All Rock Types (Step 7) ................. 49
Figure 38 Different Kr curves for different Rock Types (Kr_Mix1 | Step 8) ............................... 50
Figure 39 Results of different Kr Curve for Different Rock Types (Kr_Mix1 | Step 8) .............. 51
Figure 40 Water Saturation Distribution Models (Reference Model) .......................................... 52
Figure 41 Oil Production and Pressure Gradient History Match for Reference Model ................ 53
Figure 42 History Match of Zonal Water Saturation Profile (Reference Model) ......................... 54
Figure 43 Experimental Zonal Water Saturation Profiles with X-Ray Diffraction ...................... 55
Figure 44 Simulation Generated Zonal Water Saturation Profile (Reference Model) ................. 55
Figure 45 Sets of Kr Curves for Varied Oil Wettability (Analysis 1) .......................................... 56
Figure 46 Result of sensitivity analysis of wettability (Analysis 1) ............................................. 57
Figure 47 Results of Injection Rate Variation (Sensitivity Analysis 2) ........................................ 58
Figure 48 Well Models Created for Injection Area Sensitivity Analysis ..................................... 59
Figure 49 Injection Well Area Alteration Results (Analysis 3) .................................................... 60
Figure 50 Lab injection face in the coreholder (Courtesy: E&P, CEPSA) ................................... 61
Figure 51 Experimental Well Geometry Integration (Analysis 4)................................................ 61
Figure 52 Results of Inject Geometry Variations (Analysis 4) ..................................................... 62
Figure 53 Zonal Water Sat. for Real Injection Geometry & Reference Model (Analysis 4) ....... 63
List of Tables
Table 1 Caracara Sur Field Characteristics (Bozorgzadeh, et al., 2015) ...................................... 16
Table 2 Dynamics of Flooding (1D Model) ................................................................................. 18
Table 3 Sensitivity Analysis Parameters Summary ...................................................................... 21
1
1 Introduction
1.1 Context
Experimental corefloodings have proved to be an important tool for decades of research in oil
exploration and production. Accurate and high quality coreflooding results are integral part for
reservoir performance prediction and effective reservoir management.
But achieving such high quality flooding measurements in the laboratory is by no means an easy
task. Apart from financial viability of the experimental corefloodings, they are time consuming
and the results have uncertainties associated. These uncertainties arise from manual errors,
instrumental errors and unrepresentativeness of rock, fluid or reservoir conditions. Also, laboratory
limitations make it difficult to test extreme flooding techniques.
Meanwhile, Digital rock physics (DRP) has received attention as a possible future alternative to
laboratory core analysis. DRP includes CT scanning of reservoir cores to generate a virtual
petrophysical model. Further the model virtually undergoes with coreflooding techniques with the
use of advanced software to estimate experimental coreflooding response. The rapid rise of DRP
in coreflooding simulations can be attributed to higher computational power, advanced scanning
techniques and rise of EOR projects.
Currently the technology is relatively immature level, and quite far from being a complete
replacement for laboratory measurements. If the technology evolves as expected, it can realize
significant investment savings. So the technology has a potential to be considered as one of the
biggest breakthrough in oil industry in upcoming years.
1.2 Objective
Ultimate objective of this work is to reduce uncertainty for the petrophysical properties extracted
from laboratory corefloodings. This should be achieved by generating a robust dynamic
coreflooding simulation model, which can be used together with experimental floodings.
Also, the dynamic model should help to qualitatively understand extremities of corefloodings, by
implementing sensitivity analysis of various parameters.
2
1.3 Work Structure
In order to achieve the objectives defined above, a petrophysical model from DRP is integrated
into dynamic coreflooding simulation model with ECLIPSE 100. The work structure can be
described in following steps:
Initially, literature review was done to understand advances of coreflooding simulations across
the industry. The state of the art analysis also helped to understand major models and
methodologies used by different simulators.
Hands on experimental corefloodings helped to understand the laboratory data.
Further, a simplified 1D simulation model was generated to be history matched with
experimental conditions by altering relative permeability curves.
3D static petrophysical models were generated from results of DRP.
The 3D static model was integrated into dynamic model to generate a base simulation model.
The base simulation model was further history matched with relative permeability curve and
permeability distribution to generate a reference model.
Sensitivity analysis was performed to check extremities of the flooding techniques, results
analyzed and conclusions drawn.
This work structure was developed and executed during internship at R&D Center of CEPSA
(Madrid) between November 2015 and July 2016. The foundation of the work was laid down by
Exploration and Production division, CEPSA. They have been a key stakeholder of the project,
supporting and promoting technically.
3
2 Literature Review
2.1 Enhanced Oil Recovery
Over past two centuries, the industry has developed many techniques for oil extraction; categorized
mainly into Primary, Secondary and Tertiary Recovery. Primary recovery is the recovery obtained
with natural drive from the reservoir. Secondary recovery is achieved by forced imbibition with
water or gas. Tertiary recovery, also known as Enhanced Oil Recovery (EOR), is achieved by
altering properties of rock or oil to make the oil more mobile.
Ultimate aim of EOR process is to increase final oil recovery, which is a combined function of
microscopic and macroscopic efficiencies.
Oil Recovery Efficiency (Ero) =
Cummulative Oil Produced
Original Oil in Place
(1)
Ero = Volumetric Sweep Efficiency (EVO) ∗ Displacement Efficiency (ED) (2)
Here, Evo is a macroscopic efficiency factor, representing the effective volume reached by the
displacing fluid. And Ed represents microscopic efficiency factor, considering effectiveness of
displacing fluid at microscopic level.
ED =
Initial Oil Saturation (SOi) – Final Oil Saturation (SOr)
Initial Oil Saturation (SOi) (3)
And
Evo = Arial Sweep Efficiency ∗ Vertical Sweep Efficiency (4)
Still the average oil recovery in the world is around 30% only. Even with extensive laboratory
tests, choosing an appropriate EOR method is difficult, mainly attributed to vast number of
variables involved and uncertainties generated. As a result, most of the companies tend to apply
the most common and known techniques in the real fields.
Advanced computational power and extensive simulators have decreased the risk by generating all
possible scenarios. This was clearly observed with positive correlation between new improvements
in EOR techniques and increasing computational power over the time.
4
2.2 Chemical EOR (ASP)
Chemical EOR processes have gained attention in the last few decades owing to the significant
improvement in oil recovery provided by them.
These processes involve the use of chemicals such as alkali, surfactant and polymer (ASP) for
enhancing the recovery of oil over waterflood. Role of each component in ASP floods is discussed
below.
2.2.1 Role of Alkali in ASP flooding
Concept of using alkali to increase oil production was introduced by Frederick Squires in 1917
(Squires, 1917). He observed that the higher oil recovery can be achieved from oil sands if water
is flooded in presence of alkalis.
Till mid-twentieth century, the exact mechanism of alkali enhancing oil recovery was not clear. It
was assumed that the alkalis react with organic acids to generate in-situ soap which decreases oil-
water interfacial tension.
Later, Johnson Jr. (1976) summarized the mechanism as follows:
Emulsification and entrainment
Wettability reversal (oil wet to water wet state or vice-a-versa)
Emulsification and entrapment
2.2.2 Role of Polymer in ASP flooding
In case of waterflooding in heavy oil reservoirs fingering effect is observed. This is caused by
higher mobility of the water compared to the heavy oil. As a result, preferential path of water
created from injection well to production well, leaving behind lot of oil volume unswept; as show
in Figure 1.
So, the objective of polymer flooding, as a mobility control agent, is to provide better displacement
and volumetric sweep efficiencies during a waterflood (Lake, 1989). Due to higher understanding
with use of polymers at relatively low cost, higher number of fields have been flooded with
polymers.
5
Figure 1 Fingering Effect due to Poor Mobility Ratio (Olajire, 2014)
2.2.3 Role of Surfactant in ASP flooding
Basis of surfactant use in oil extraction is similar to use of detergent to remove oily stains from
utensils. Surfactants are molecules which will naturally tend to accumulate at interface of oil and
water. Normally they have a polar ‘head’ group and a non-polar ‘tail’ group, which have different
affinities for polar and non-polar solutions.
These accumulated molecules reduce the interfacial tension (IFT) between oil and water, as a result
the capillary force gets reduced and additional oil can be mobilized. But this is achieved with very
small concentration of surfactants; in range of 1000 ppm to 3000 ppm. As surfactant is the most
costly component of the ASP flood, different techniques are used to enhance the effectiveness of
surfactants. The most common techniques are the use of pre-flux of AP drive, the use of co-
surfactant and co-solvents, or synergy of alkalis-surfactant.
6
2.3 Coreflooding: Introduction
Core is a piece of reservoir collected during drilling wells. But as the core extraction is a costly
process, sometimes an outcrop rock with similar properties as reservoir rock is used. A small
cylindrical sample taken out of the core is called “Core plug” or just “Plug”. Plugs are
approximately 1.5 inch in diameter and up to 3.125 inch long.
After extracting petrophysical properties with core characterization, corefloodings are performed
to evaluate fluid behaviors in the given core or plug. Also the production methodologies are tested
on plugs to predict the response of the reservoir. The results from coreflooding are a very important
source of petrophysical data for reservoir engineering.
The cores from field can have local geological heterogeneities; originating from in-situ
heterogeneity or improper core extraction and transportation methods. Due to such heterogeneities,
experimental tests show deviation from real results. To minimize such uncertainties, computational
simulation of corefloodings will be helpful tool.
2.3.1 Uncertainties and Constraints
Unrepresentative of in-situ conditions:
o During extraction or transportation, core’s petrophysical properties might be modified
o Evaporation of light components or asphaltenes precipitation will change fluid properties
o Cleaning and aging can alter rock-fluid interactions (like wettability)
Limitations in up-scaling to reservoir level
o High geological-variability inside reservoirs increases uncertainty of petrophysical
properties extracted from core to large geological area in the reservoir
o Up-scaling of EOR methodologies is limited with many external parameters like raw
material availability, government rules, economic profitability, on field consistency etc.
o Huge difference in modeling scale from core to reservoir possesses technical challenges
Experimental Errors
o Minor errors from lab setup create high impact on results due to small size of plugs
7
2.4 Coreflooding: Mathematical Modeling
Even though the modeling equations are the same for reservoir modeling and pore level modeling,
there are fundamental differences in pore level simulations and reservoir simulations modeling
(Blunta, et al., 2013). Many pore scale simulators have been developed worldwide, but the
practical use of these simulators is limited due to extreme complexity at micro-scale and
difficulties in obtaining data to calibrate these models. Though this study explored pore scale
modeling to certain extent, Black Oil Simulator (ECLIPSE 100) was used further for all simulation.
This section derives basic petro-physical equations used by simulators. Most of the equations are
simplified just to oil-water system at isothermal conditions.
2.4.1 Mass Conservation
Let’s assume that the reactive system has J fluid species (Cj), K solid species (Ck), I rock adsorbed
cations (Ci), and M micelles-associated cations (Cm). And all these species are made up of N
elements.
So there are (J+K+I+M) unknown equilibrium concentrations. Therefore, as many numbers of
independent equations as number of unknown are needed to solve the system. The mass balance
equations for N elements are as follows (Veedu, 2013):
𝐶𝑛𝑇 = ∑ hnjCj
𝐽
𝑗=0
+ ∑ gnkCk
𝐾
𝑘=0
+ ∑ fniCi
𝐼
𝑖=0
+ ∑ enmCm
𝑀
𝑚=0
(5)
For each n = 1 to N
Here h, g, f and e are equivalent masses in j, k, i, m phase, respectively.
Along with this mass balance equation, there is one more basic question of charge balance. As the
total charge in the system is zero, summation of individual charges should be zero too.
As the system has J fluid phases, apart from N elements, every other constituent must be in its
reaction equilibrium. This will generate another set of (J – N) equations.
Each solid species must be in equilibrium with its dissociated phase in the liquid. This will generate
K equations.
8
Rock adsorbed cations will give I equations, as anion exchange equations. Similarly, there will be
M anion exchange equations resulting from M cations in micelle form.
This completes the needed (J + K + L + M) set of equations to know the system conditions at each
point. This set of huge numbers of equations is solved by Newton-Raphson method.
Simplifying the System
Though the most accurate system of equations is as showed above, from point of view of this case
study, let us assume following assumption to understand basic equation:
Only two phases (oil & water) and three components (oil, water & surfactant) are considered.
Only the surfactant component is partitioned in two phases and the equilibrium component
relation is given by:
𝐾𝑒𝑞𝑢𝑖𝑙𝑖𝑏𝑟𝑖𝑢𝑚 =𝑦𝑠𝑢𝑟𝑓
𝑤𝑎𝑡𝑒𝑟
𝑥𝑠𝑢𝑟𝑓𝑜𝑖𝑙
(Where, y and x are diffusion fractions of surfactant in water and oil respectively)
Isothermal condition in reservoir
The system is two dimensional with uniform properties.
There are no chemical reactions (mainly neglecting in-situ soap generation)
Darcy's law applies to the flow of each phase.
Simplified mass balance with Navier-Stroke equation (Keshtkar, 2015):
For oil component
𝜕(∅[𝑥𝑚 𝜀𝑜𝑆𝑜])
𝜕𝑡+ ∇. (𝑥𝑚𝜀𝑜𝑢𝑜) = 𝑞𝑜𝑖𝑙 (6)
For water component
𝜕(∅[𝑦𝑚 𝜀𝑤𝑆𝑤])
𝜕𝑡+ ∇. (𝑦𝑚𝜀𝑤𝑢𝑤) = 𝑞𝑤𝑎𝑡𝑒𝑟
(7)
Where, ∅ is porosity of the reservoir bed
𝜀 is density of oil and water as per subscript
S is saturation of oil and water as per subscript
9
xm is fractional composition of m specie in oil
ym is fractional composition of m specie in water
u is velocity of oil and water as per subscript
2.4.2 Volumetric Constrains
As all components are inside the core, total summation of volumes of each component should be
same as the pore volume (PV) of the system (Najafabadi, 2012).
PV =
∑ 𝑉𝑤
ξ 𝑤+
∑ 𝑉𝑜
ξ 𝑜+
∑ 𝑉𝑠𝑢𝑟𝑓
ξ 𝑠𝑢𝑟𝑓 (8)
Where, ξ is density of the component as per subscript
V is volume of the component as per subscript
2.4.3 Flow Modeling
Flow for each component can be modeled separately with Darcy’s equation (Veedu, 2013):
u∝ = −
𝐾 ∗ 𝑘𝑟∝
𝜇∝(∇𝑃∝ − 𝜌∝𝑔∇𝑍)
(9)
Where, K is total permeability of the system
u, μ and Kr are velocity, viscosity and relative permeability of α component
(𝛻𝑃∝ − 𝜌∝𝑔𝛻𝑍) is the pressure gradient for α component
All differential terms in above equations are approximated into linear equations using finite
difference method. These linear equations are solved with Newton-Raphson method.
2.4.4 Relative Permeability Curves: Corey Equation
Relative permeability strongly depends on saturation of wetting and non-wetting phase. A
commonly used approach is to express the relative permeability and capillary pressure as a
function of the normalized saturation. In 1964, Brooks and Corey proposed following equations
for relative permeabilities (Corey, et al., 1964):
Krw = Krw(Sorw)
[𝑆𝑤 − 𝑆𝑤𝑐𝑟
Sw,max − 𝑆𝑤𝑐𝑟 − 𝑆𝑜𝑟𝑤]
Nw
(10)
And relative permeability for oil phase is calculated as:
10
Kro = Kro(Sw,min) [
Sw,max − 𝑆𝑤 − 𝑆𝑜𝑟𝑤
Sw,max − 𝑆𝑤𝑖 − 𝑆𝑜𝑟𝑤]
No
(11)
Where, Sw,min is minimum water saturation
Swcr is critical water saturation
Swi is initial water saturation
Sorw residual oil saturation
No & Nw are Corey oil exponent
These saturation values are determined by core
analysis, and the curve in between is generally
interpolated with default values of No and Nw.
This results into uncertainty in simulations.
Figure 2 Standard Relative Permeability Curve
2.4.5 Interfacial Tension
Calculations of interfacial tensions (IFTs) for microemulsion-oil (σ23) and microemulsion-water
(σ13) systems are based on model of Healy and Reed along with Huh equation (Huh, 1979).
Simplified version of the Huh’s equation can be written as: (Farajzadeh, 2012)
𝜎 =
𝐶
𝑍2 (12)
Where, σ is interfacial tension between microemulsion phase and oil or water
C is empirical constant, with value approximated to 0.3
Z is a solubalization parameter of microemulsion in oil or water
Combining the above equation with model of Healy and Reed (UTCHEM Technical Guide 9.0),
we get:
𝜎 = 𝜎𝑜𝑖𝑙−𝑤𝑎𝑡𝑒𝑟e−10Z +
𝐶 ∗ 𝐹𝑙
𝑍2(1 − e−10Z3
) (13)
Where, σoil-water is interfacial tension between oil and water
Fl is Hirasaki’s correlation factor, which in is a turn function of concentrations
Note: ECLIPSE does not predict IFT values with above equations, but only interpolates from input
of correlation between concentration of alkali and concentration of surfactant.
11
2.4.6 Phase Behavior Formulation
Depending on the brine salinity, equilibrated environments are categorized into 3 types. Proper
understanding of these types is important aspect in choosing right surfactant (Najafabadi, 2012)
Figure 3 Idealized Type I ternary phase environment
Figure 4 Idealized Type II ternary phase environment
Figure 5 Idealized Type III ternary phase environment
These curves are formed according to
Hand’s rule. Hand's rule is based on the
empirical observation that equilibrium
phase concentration ratios are straight lines
on a log-log scale. (Hand, 1939)
In the Figure 3, Figure 4 and Figure 5, the
lines in two-phase system are called as “tie
lines” and “plait point” is a point where
these lines converge. These properties play
important role modeling of phase behavior.
At low salinities, the surfactant is more water soluble and stays in the aqueous phase. Due to head-
tail structure of the surfactants, surfactant molecules gather around oil molecules, forming small
droplets. This results in some insoluble oil into the aqueous phase. The resulting
thermodynamically stable phase is called microemulsion (ME) phase (oil in water).
12
The ME phase is in equilibrium with the oleic phase. As shown in Figure 3 (Type I), the area below
the binodal curve would result in two phases with their compositions given by the tie lines. Only
single phase ME is present above the binodal curve.
After certain salinity level, most of the surfactant migrates out of the aqueous phase generating a
ME phase in equilibrium with water and oil. This level of surfactant concentration is called the
lower critical salinity limit (CSEL). This creates a three-phase environment, known as Winsor
Type III. (Figure 5)
Above upper critical salinity limit (CSEU), some of the aqueous components are solubilized in the
oleic phase resulting in an oil-external ME phase in equilibrium with the aqueous phase. This phase
behavior is referred to as the Winsor Type II. (Figure 4)
(Due to high complexity and variability of modeling across different types of phase behavior,
further modeling equations have been omitted in this report.)
2.5 Digital Rock Physics
Digital Rock Physics (DRP) for core analysis is a breakthrough for oil and gas companies that
need large volumes of accurate results faster than the current SpeacSCAL labs can normally
deliver. Main objective of use of digital rock physics is to understand local heterogeneities in the
core. Due to these heterogeneities, cores can show deviating results from their average property
calculations. Without the understanding of local heterogeneities, the averaged properties
calculated from lab results can increase uncertainty in reservoir calculations.
Computerized Tomography (CT) scanning is an X-ray technology that produces an image of the
internal structure of a cross-sectional slice through an object by the reconstruction of a matrix of
X-ray attenuation coefficients (Hunt, 1988). Normally the plugs are scanned at a resolution of 500
microns (Kalam, 2012), and petro-physical models are developed with this resolution.
Results of CT scan are in form of local attenuations, as shown in Figure 15. The attenuations are
based on measurement of reduction of X-rays’ intensity, due to transmission through the object at
certain coordinates. As a result, this attenuations can be translated into local density distribution.
From density, other local petrophysical properties (like porosity, permeability) can be derived with
some uncertainty. Standard procedure followed by the industry is summarized in Figure 6.
13
Figure 6 Typical Digital Rock Physics Analysis Procedure (Kalam, 2012)
Till date, only few major companies are using this technology. The companies use this information
as input to numerical reservoir simulators, fracture design programs etc. which will improve
reserves’ forecasts, rate’s forecasts, well placement and completion designs. With potential to
improve efficiency of oil industry, this technology will surely have a bright future ahead.
14
3 Experimental Coreflooding
As described above, core analysis plays important role in understanding reservoir. Costs of each
core extraction can vary from hundreds to thousands of USD (Libecap, 1985), depending on
complexity of the reservoir. Despite developing robust extraction techniques, many cores or plugs
have to be discarded due to undesired shape, composition etc. These flaws can arise from core
origin, falling extraction, transportation or cutting methods. As a result, effective cost of each core
increases tremendously.
To utilize each core efficiently, there are many standardized methods set across the industry;
mainly categorized into ‘Routine Core Analysis’ and ‘Special Core Analysis’. Routine core
analysis characterizes porosity, permeability and saturation. Whereas, Special Core Analysis
centers around pore throat distribution, wettability, capillary pressure and other complex factors.
This chapter gives an overall idea of the coreflooding procedure and its experimental setup.
3.1 Coreflooding Procedure
Core undergoes Routine Core Analysis initially and later corefloodings are performed, as follows:
After mud-cleaning, the core is dried with prolonged N2 injection. The core is measured for
pore volume and dry weight. Core is installed into coreholder at moderate confining pressure.
The core is saturated with formation brine, by flooding brine until constant pressure drop is
observed. Permeability measurements and tracer analysis is performed on the core.
Crude oil flooding until saturation is achieved; followed by aging at the reservoir temperature.
Duration: At least 14 days (Varies according to core conditions)
This is followed by 2 to 4 weeks of oil flooding to ensure core at initial water saturation (Swi).
Now the core is ready for coreflooding. Following steps are used in Chemical EOR flooding:
Initial waterflooding is performed until steady state is achieved. Secondary oil recovery is
determined easily with gravity separation of the effluent.
ASP flooding performed with optimum salinity and planned batch size. Close monitoring of
concentrations in the effluent and pressure is performed.
Normally the ASP drive should be followed by polymer drive (AP drive).
Ultimately, the water flooding is performed till residual oil saturation (Sor) is attained.
15
3.2 Coreflooding Setup
Advanced coreflooding systems are made robust enough to handle pressure as high as 250 bars
along with temperature in the range of 100°C. Due to small volumes of cores, highly accurate
injection pumps and pressure transducers are needed for precise flooding and monitoring.
But along with the robustness, the unit needs to be flexible to accommodate wide range of flooding
schemes. The complexity of flooding schemes increases many folds with EOR techniques, like
surfactant-gas co-flooding. Due to high risk with hydrocarbon leak, thorough a hazard and
operability study (HAZOP) is mandatory for the coreflooding units.
So, the coreflooding setups are designed with minute details and long term planning. This section
glimpses at the coreflooding unit designed and fabricated at R&D Center of CEPSA (Figure 7).
Figure 7 Simplified Schematics of Coreflooding Setup (Courtesy: R&D Center, CEPSA)
Initial and final stage of the coreflooding can be schematically represented by Figre 8.
Figure 8 Simplified Stages of coreflooding (Courtesy: R&D Center, CEPSA)
BPR: Back Pressure Valve (Stabilizes pressure at outlet) | Aux. Pump: Auxiliary Pump (Injects secondary fluids)
P1 & P2 are pressure transducers, used to calculate pressure drop across the core
16
4 1D Coreflooding Simulation
This case study was performed at R&D center of Compañía Española de Petróleos, S.A.U.
(CEPSA). For coreflooding simulations over a core from Caracara Sur Field in Colombia,
ECLIPSE 2014.1 (black oil simulator) and PETREL 2013 (reservoir simulator) were used .
4.1 Caracara Oil Field
As show in Figure 9, Caracara Sur field (CCS) is located at the south west of Llanos Foreland
basin (Bozorgzadeh, et al., 2015). The producing formation in the CCS field is the early Oligocene
Carbonera-7. The CCS consists of multilayered compartmentalized fluviodeltaic reservoirs
(Cubillos, et al., 2013). The main characteristics of the field are shown in Table 1.
.
Figure 9 Location of Caracara Sur Field (Bozorgzadeh, et al., 2015)
Table 1 Caracara Sur Field Characteristics (Bozorgzadeh, et al., 2015)
Parameters Value Parameters Value
Average depth (ft. TVDSS) 4000 Temperature 86 C
Porosity % 25-30 Permeability (mD) 500-5000
Oil Properties Water Properties
- Gravity (API) 18-22 - pH 7.5-10.6
- Viscosity (cP) 6-14 - Chloride (ppm) 30-800
- Gas:Oil ratio (SCF/STB) 7-50 - Salinity total (ppm) 200-2100
17
4.2 1D Static Model
The 1D model is developed by approximating cylindrical plug into cuboidal rock sample. Then
the cuboid is divided into 100 layers, as shown Figure 10:
Real plug dimensions:
Diameter: 38.5 mm
Length: 112 mm
Cartesian Model (1D): 100 X 1 X 1
Dy = Dz = 38.5mm
Dx = 1.12mm
Figure 10 Scheme for approximating a cylindrical plug into cuboidal rock sample.
The volume of the simulation model exceeds real plug volume due to the approximation of the
shape. The extra amount of oil produced, corresponding to this extra volume, is compensated by
dividing with the ratio of volume of simulation model to volume of actual plug.
Each layer was assigned with average porosity and permeability values, obtained from Routine
Core Analysis. All other properties assigned are extracted from Caracara reservoir’s simulation
model developed by CEPSA’s Exploration and Production division. The model is maintained at
simplistic level to ensure small simulation time along with ease of modification and debugging.
4.3 Initial and boundary conditions of 1D Dynamic Model
Dynamic Simulation Constraints:
The dynamic model is bounded with following constraints, as per laboratory experiments:
Constant pressure at production face = 117.67psia = 8.1 bar
[This pressure is lower than the actual reservoir condition. But, due to absence of any gas in
the reservoir, this difference in pressure will not alter flooding to large extent. A backpressure
regulator (BRP) was used at the outlet of the coreholder to control the pressure in the system
during the displacement process.]
Constant inlet flow rate = 4ml / hour
[With the help of highly precise double-piston pump, constant flow rate is maintained.]
18
In the simulator all the grid blocks were set at initial saturations. The ASP process was simulated
to generate oil production curve and pressure drop curve, as described in Experimental
Coreflooding chapter. Dynamics of the floods are shown in Table 2.
Table 2 Dynamics of Flooding (1D Model)
Type of Slug and Chemical Components Concentration
(ppm)
Approximate Slug Size
(PV)
Initial Waterflood 10
ASP Flood
0.3 Alkali 5000
Surfactant 5520
Polymer 400
AP (Polymer drive)
2 Alkali 5000
Polymer 800
Final Waterflood 10
19
4.4 History Matching of 1D Dynamic Model
History Matching is a common reservoir engineering technique to update the geological model.
The reservoir model is modified to match the response of the field during production phase, and
further extrapolated to predict future response of the reservoir. This method is commonly used to
fit oil production trend and Bottom Hole Pressure (BHP). With advanced simulation power, most
of the reservoirs are frequently monitored with history match.
Similar to reservoir history matching, in coreflooding experiments, oil production and injection
pressure are used to update the model. In this 1D model, apart from relative permeability curve,
all other parameters are consider to have less uncertain experimental data.
As a result, Kr curves are modified to attain better history match, as show in Figure 10.
Figure 10 Comparison of Kr Curves: Lab and Modified (1D Model)
Note: The modified relative permeability curves deviate from field reality, as residual oil
saturation was altered from experimental value of 75% to only 45%. Due to oversimplification of
petrophysical model, largely modified Kr curve is needed to attain good history match. But the 1D
Model has been developed only to establish basis for simulation models ahead. All further analysis
on 1D model is done with these modified Kr curves only.
20
History Match results are shown in Figure 11.
Figure 11 Oil Recovery and Injection Pressure History Match (1D Model)
The results show that:
Close history match was obtained in both injection pressure and oil production
Dynamic results showed homogenous sweep throughout the core.
The rise in oil recovery is due to alterations of contact angle between oil-water-rock
equilibrium to mobilize more oil; due to presence of alkali and surfactant.
The sharp rise and drop in pressure profile can be attributed to high viscosity of polymer
21
4.5 Sensitivity Analysis of 1D Dynamic Model
In the sensitivity analysis study, effect of alterations in individual parameters of the system on final
outputs is analyzed. Trends of variations of output parameters with marginal change of an input
parameter are plotted. Also extreme cases are generated to rectify boundary assumptions.
Sensitivity analysis plays important role to understand systems with multiple variable parameters.
Similar to reservoir flooding, coreflooding is dependent on dozens of parameters. So sensitivity
analysis is often used to explore optimized flooding in reservoirs as well as plugs.
In this study, 3 parameters are varied to see effective change in oil production, as follows:
Table 3 Sensitivity Analysis Parameters Summary
Parameter Base Case Sensitivity Analysis Values / Multipliers
Injection Rate 4 ml/ h
Keeping injection time constant: 2ml/h
Keeping injected PV constant: 2ml/h, 8ml/h,
16ml/h, 32ml/h, 64ml/h
Interfacial Tension (IFT) ~ 0.001 mN/m
IFT (at each surfactant concentration node) is
multiplied with: 5, 10, 100, 500, 1000, 2000,
4000, 8000, 16530
Viscosity
(Polymer Concentration) 800 ppm
Viscosity variation with polymer concentration
variation: 0ppm, 100ppm, 200ppm, 400ppm,
1200ppm, 1600ppm, 2000ppm
4.5.1 Injection Rate
Initially models that were generated for sensitivity analysis of injection rate had equal pore volume
injected of each phase, as base case. This was achieved by adjusting injection time.
One model was developed with half of the volume injected at each stage of injection, without
altering total injection time. So total pore volume injected became half.
22
Results:
Figure 12 Results of sensitivity analysis for Injection Rate (1D Model)
The results show that:
As observed experimentally, increasing injection rate changes capillary pressure due to end
effect; as well as alters relative permeability curve (Arne Skauge, 2001). As these effects are
not incorporated by ECLIPSE, all injection rates showed similar oil production.
Similar recovery range was observed in half pore volume of injection too. This can be justified
because of elongated waterflooding near the saturation level.
23
4.5.2 Interfacial Tension
Interfacial Tension (IFT) variation is mainly caused by alkali and surfactant concentration. As the
surfactants are the costliest component of the Chemical EOR process, sensitivity analysis of IFT
can play important role in economic viability of the project.
ECLIPSE models need to be developed with experimental IFT values at multiple salinity
concentration for a particular surfactant concentration. ECLIPSE interpolates this three
dimensional IFT dependence with salinity concentration and surfactant concentration. In this case
study, the IFT scale is altered with following multipliers, keeping concentrations constant.
Results:
Figure 13 Result of sensitivity analysis for IFT Concentration (1D Model)
The results show that:
Decreasing oil recovery trend is clearly visible with increasing IFT value.
At multiplying factor 16530, effect of surfactant is negligible. As a result, given ASP flood
acts just as AP flood. This number was achieved by targeting IFT value at injection well in
ASP flood equal to IFT value of water-oil (without surfactant) for same salinity.
24
4.5.3 Viscosity (Polymer Concentration)
Viscosity variation is mainly caused by alterations in polymer concentration. Though injection of
higher polymer concentration can give a stable water front to improve sweep efficiency, it can
increase skin factor of the injection well or even block zones with small pore sizes.
This case study tries to understand effect of polymer concentration on sweep efficiency and
pressure gradient across the plug.
Results:
Figure 14 Results of sensitivity analysis for Polymer Concentration (1D Model)
Results show that:
With increasing polymer concentration, recovery factor increased. But in lower range of
polymer concentration, marginal increase in recovery factor is higher compared to marginal
increase in higher concentration of polymer. This can be attributed to stabilization of water
front. Due to stable water front above 800ppm, polymer concentrations above it resulted into
almost equal recovery factor.
25
5 3D Static Model
As the one dimensional model of the core will never be able to capture radial heterogeneity, the
further study is focused on three dimensional (3D) modeling. The complete 3D static model used
in this study was developed by Exploration and Production division of CEPSA. This study
analyses the development of the static model, and further integrates it into the dynamic model.
X-ray computed tomography (CT) scan is an X-ray technology that produces an image of the
internal structure of a cross-sectional slice through an object by the reconstruction of a matrix of
X-ray attenuation coefficients (Hunt, 1988). CT scanning is mainly used for core inspection at the
macro level, core-log correlation, and plug sample characterization.
Results of axial CT scans have similar data format as seismic survey results; so imported into
PETREL 2013. The resolution of CT scan are in the range of micrometers to millimeters. Each
node of the data is an attenuation corresponding to local reflection. As the dampening of X-rays
corresponds at certain coordinate corresponds to the local average density, attenuations can be
used to derive petrophysical model. All the above steps were performed by Exploration and
Production division of CEPSA. This chapter only analyses these static model development steps.
5.1 CT Scan Results
Results of the CT Scan for the given core
sample can be summarized as:
Model Geometry: Orthogonal Grid
Model dimensions: 35.4x35.4x50.6 mm
CT scan resolution: 500x500x625 μm
Total number of grid cells 408k
Active number of grid cells 316k
Z direction lies along the axis of the core
X and Y directions are arbitrary
Figure 15 Processed CT Scan Results (Attenuations)
Note: The model, as shown in Figure 15, is achieved after several processing of the raw data.
26
5.2 Attenuation Model to Density Model
Attenuations recorded from reflection of waves result from complex correlation between wave
frequency, wavelength, local density and source and/or receiver error. So it is impossible to
establish a direct theoretical correlation between attenuations and density.
Analytical correlation was established by E&P division of CEPSA with average attenuation of
complete plug and bulk density of the plug. Data of 10 plugs for average attenuation vs average
density showed highly linear trend (R2 = 0.96).
Plug under study, Plug 184, showed a close match to the trend line. So this trend line can be used
further for correlating local density.
Figure 16 Average Attenuation vs Average Density Correlation (Courtesy: E&P, CEPSA)
The plug model was transformed from attenuation distribution to density distribution with
following equation, as extracted from Figure 16.
𝐴𝑡𝑡𝑒𝑛𝑢𝑎𝑡𝑖𝑜𝑛 (𝑖, 𝑗, 𝑘) = 911.5706 ∗ 𝐷𝑒𝑛𝑠𝑖𝑡𝑦(𝑖, 𝑗, 𝑘) + 315.7657 (14)
Where i,j,k indexes refer to a certain grid cell.
27
5.3 Density Model to Porosity Model
Porosity model could have been estimated using data intensive complex correlations like Archie
Equation (Orsi, et al., 1994). But due to limitation of data and resolution of the model, more
simplistic correlation is established between density and porosity. The following assumptions were
made to establish the correlation:
Core is assumed to be made of ‘Grain’ particles & ‘Fluid’ particles.
Fluid is a mixture of oil, water and air.
From Routine Core Analysis, average density of the fluid was calculate [𝜌𝐹𝑙𝑢𝑖𝑑 = 0.84 gm/cc].
Grain mainly consists of Quartz [𝜌𝑄𝑢𝑎𝑟𝑡𝑧 = 2.65 gm/cc ] and minor quantities of other sand
and asphaltenes.
Density of Grains was calculated with weighted average of the constituents’ density. [𝜌𝐺𝑟𝑎𝑖𝑛 =
2.60 gm/cc]
Local porosity was determined with a simple assumption of all pore spaces are occupied by
fluids and rest of the plug volume is occupied by Grains.
Simplified correlation can be equated as:
Porosity [Φ (i, j, k)] = 1 −
ρ(𝑖, 𝑗, 𝑘) − ρFluid
ρGrain − ρFluid
… (15)
Figure 17 Porosity Model Generated & Corresponding Univariate Distribution
Mean porosity of the model generated closely matched with experimental porosity distribution.
This verifies calculations and assumptions made till this point.
28
5.4 Porosity Model to Permeability Model
As permeability does not follow simple arithmetic or geometric correlations, it can only be
modelled with data-backed correlations with other petrophysical properties. This section explains
the methodology used behind generating permeability model and corresponding uncertainties.
Mercury Injection Test is often used to characterize the pore (throat) size distribution of porous
material. Result of the test, a graph between injection pressure and pore volume saturation, gives
pore size distribution (Lenormand, 2003). Permeability can be directly determined with radius of
pore throats as per Hagen–Poiseuille equation for viscous flow in pipe.
Following methodology was implemented:
On the basis of pore throat distribution with mercury injection test, all the plugs from Caracara
field were divided into 4 ‘Rock Types’ (namely RT1, RT2, RT3 and RT4).
RT1 corresponds to the most permeable rocks, with permeability in range of 5 Darcy (D).
RT4 showed the lowest permeability, in the range 50 milliDarcy.
As shown in Figure 18, these rock types showed different polynomial trend lines between
permeability (log-scaled) and porosity.
Figure 18 Permeability vs Porosity Correlation with Rock Type Classification
29
Results of the permeability model generated show that:
The plug under study (Plug 184) was categorized into Rock Type 2 (RT2). Using the trend line
equation for RT2, following permeability distribution was generated.
Figure 19 Permeability Model Distribution Histogram
For above distribution, geometric mean is 2962 mD and arithmetic mean is 3598 mD.
Whereas, experimentally observed air permeability of the plug is 2790 mD (at 400psi)
As the permeability is a complex phenomenon, it is not easy to understand if arithmetic mean
is more representative or the geometric mean is more representative of average permeability.
Initial simulations showed much higher oil recovery from flooding compared to experimental
results. To lower the oil production, arithmetic mean of the permeability distribution was
assumed to be average permeability.
Uncertainties in generating permeability distribution were:
Key assumption of the modeling was the categorization of the core into one rock type. This
assumption indicated that there are no micro heterogeneities in the plug. But in reality, there
are different rock-types scattered across the plug.
Also, only averaged trend line for the rock-type was used to extrapolate the model. This
neglects extremities within a rock-type. (But RT1 and RT2 show less deviation form
corresponding average trend lines compared to RT3 & RT4. So uncertainty generated by
using averaged trend line are negligible within this model.)
30
6 3D Dynamic Model
The static model was developed in Petrel, and further imported in ECLIPSE-100 to simulate
dynamic corefloodings. Main steps in developing dynamic model and simulations are explained
in this chapter.
6.1 Initiation
6.1.1 Generating Well Geometry
Initial simulations were run with a single well connection at the center of each face of the plug.
Due to high flux through small cell at the center resulted into simulation failures. Injection with a
well per cell on injection face will impose forced injection of equal volume through every cell. To
generate more realistic simulation following methodology was followed:
To replicate experimental conditions, an injection well connected to upper face of the plug (k
= 81) and a production well connected to lower face of the plug (k = 1).
Wells are connected to each cell of corresponding face, in the form of zigzag connections,
using path generated in MATLAB.
Figure 20 Well Geometry 3D Model
Due to activation of cells in the cylindrical shape only, rest of the well connections became
inactive, as shown in Figure 20.
The model resulted into equal pressure distribution of injection fluid over the face of plug,
without forced injection through any of the cell.
31
6.1.2 Optimizing Convergence Error vs Simulation Time
At every step, ECLIPSE runs iterative loop of linear solver to solve complex polynomial equations
for each cell. These iterations continue till the error margin is negligible, or maximum number of
permitted iterations is reached. ‘Convergence Error’ was generated, if after maximum number of
iterations is reached and error margin is still above permitted level.
Using Tuning keyword in ECLIPSE, it is possible to alter default iteration parameters. Increasing
default number of iterations reduces convergence problems, but significantly increases simulation
time too. Several unsuccessful attempts, with alterations of Tuning inputs, were made to overcome
the convergence error. Ultimately timesteps were reduced to overcome the convergence error.
Similar to iteration number, decreasing timesteps results into higher simulation time. Following
algorithm was developed to find optimum timesteps scheme:
It was noticed that oil
saturation decreases
significantly (up to 40%)
during first pore volume of
water injection.
Due to high variations
during the initial period,
many convergence errors
were generated
Figure 21 Optimized Timestep Scheme
These errors were suppressed with small timesteps in the beginning (starting in the range of
0.001hr per step) and exponentially rose to longer timesteps (up to 0.1 hr).
Timestep scheme, as shown in Figure 21, was developed with few simulation errors and
practically acceptable simulation time.
Though the simulation generated few errors, the final results were almost similar to the
simulation with no convergence error.
32
6.1.3 Assigning Base Relative Permeability Curve
As explained in Relative Permeability Curves: Corey Equation, relative permeability (Kr) curves
are complex correlation between saturations and mobility of fluids in a given system. As a result,
relative permeability curve is specific to system of fluids, rock and their pressure-temperature
conditions.
Standard Kr curve was available for the given plug, according to its geological classification (Rock
Type 2). This Kr curve is also used on reservoir scale simulations. But due to different scale and
conditions of simulations, following two curves were tested for comparative study:
Kr_CEPSA: Kr curve used for reservoir simulations by CEPSA for Rock Type 2 (RT2)
Kr_Lab: Kr curve to justify experimental oil production, generated by SCAL provider
Kr_Plug126: Kr curve used for another plug from same reservoir (Plug Number 126)
Figure 22 Different Kr Curves Tested in Simulations
As evident from Figure 22, Kr_CEPSA predicts highest oil recovery while Kr_Lab predicts
the lowest oil recovery. Kr_Plug showed highest water mobility at complete water saturation.
Sensitivity analysis of the dynamic model with given set of Kr curves will give broad insight
into effect of range of residual oil saturation (Sro) and Corey Index (C).
33
Comparative Results
Figure 23 Comparative Results for Different Relative Permeability Curves
Inferences:
Kr_Lab generated closest history match with experimental production curve.
Experimental pressure gradient is following non-theoretical trend. Henceforth, in further study,
pressure gradient trend will not be attempted to reach perfect history match.
Kr_Lab was generated to fit results from SCAL analysis. But as SCAL results were anomalous,
further simulations were run with Kr_CEPSA or its variations with Corey exponent.
34
6.2 Goal, Methods & Constraints
The goal of the work is to generate a set of relative permeability curves representative of field
behavior; which can be further utilized in full scale field models. This can be achieved by history
matching global and local trends of dynamic simulation model with experimental findings.
The simulation methods used in work were:
History matching for oil production profile.
(As the end-effect generated in experimental coreflooding cannot be reproduced completely
in the ECLIPSE simulations, the exact history match cannot be achieved. But the profile trend
and approximate profile range should be achieved.)
Regenerating of pressure gradient range across the core.
(Pressure gradient trend generated in laboratory does not follow physical phenomenon. So
complete regeneration of this trend is impossible too.)
Apart from the above global history match, history matching is done to regenerate local trends.
(Local trends include oil un-swept zones and zonal water saturation. Oil un-swept zones, as
seen after coreflooding in lab, is generated in dynamic model. Zonal water saturation, as
measured with XRD, is reproduced by dynamic model too.)
6.2.1 Simulation Constraints
The constraints considered in the simulation were the following:
End points of Kr_CEPSA are obtained using multiple laboratory experiments on numerous
plugs from the reservoir. So, end points of the relative permeability curve should not be altered,
unless specified in the model.
Multiple relative permeability curves should be generated by adjusting corresponding Corey
Exponents. As the exponents lie in theoretical range of 1 to 5 (Corey, et al., 1956), all following
models are developed accordingly.
Apart from permeability distribution, other static models have high certainty. So other
parameters of static models should not be modified during the study.
All further simulations will follow above constrains to achieve the goal; unless and until
specifically mentioned.
35
6.3 Development
The Eclipse code for 1D model was further developed into 3D model. Most of the data used in
following models is either extracted from lab reports or generalized from reservoir scale models,
details mentioned at respective descriptions. Static model and initiation steps, as elaborated in
previous chapters, were integrated into the dynamic model too.
Among many simulation models generated over the span of this study, few important Steps are
listed as follows. Every step justifies the major changes and analyses final results.
6.3.1 Step 1: Manual Alteration of Permeability Distribution
Objective: Target of regenerating un-swept zones after flooding can be achieved with some
zones with larger permeability contrast. This step widens permeability distribution without
altering basics behind distribution development, as explained in 3D Static Model development.
Major Changes:
Following the algorithm was developed to generate lower permeability zones while
maintaining distribution mean roughly constant.
Condition on Permeability Value
(mD)
Multiplying
Factor
Less than 100 0.01
Less than 500 0.05
Less than 1000 0.1
Less than 1500 0.3
Less than 2000 0.5
Less than 2500 0.7
Less than 2800 0.9
Less than 3500 1
Above 3500 1.2
Finally arithmetic mean was adjusted to air permeability by multiplying complete permeability
model with 0.751
Original Distribution
(mD)
Step 1
(mD)
Min: 3.8 0.02
Max: 50521 45529
Mean: 3598 2791
Standard Deviation: 2445 2505
Results:
36
Figure 24 Results of Manual Permeability Distribution Alteration (Model 1)
Conclusions:
Production profile is showing lower production trend in the beginning, but eventually the final
oil production is on same level as original model by 10PV.
Higher permeability deviation is generating higher pressure difference.
In this manual alteration of the permeability distribution, generic trend was not maintained.
Further permeability alterations should be performed more mathematically.
37
6.3.2 Step 2: Co-kriging for Permeability Distribution Alteration 1
Objective: Similar to Step 1, Step 2 tries to regenerate larger permeability contrast across the plug
Major Changes:
Like other petrophysical properties, permeability follows log-normal distribution.
To maintain its natural distribution trend, and increase the standard deviation, the permeability
distribution was co-kriged with a reference lognormal distribution
Parameters of the reference lognormal distribution:
Mean = 2700 Std. Deviation = 3000
Minimum = 0.025 Maximum = 25000
The resulting distribution (K_V2):
Figure 25 Permeability Distribution Comparison (Step2)
Original Distribution
(mD)
Step 2 (K_V2)
(mD)
Min: 3 31
Max: 50521 24994
Mean: 3597 2741
Standard Deviation: 2445 2711
Original distribution: Dark blue
Model 2: Light blue
38
Results:
Figure 26 Results of Permeability Distribution Alteration with Co-kriging (Step 2)
Conclusion:
Similar to Step 1, increase in relative standard deviation has decreased production rate
initially, but final oil recovery was similar.
Slightly higher pressure gradient was observed throughout the production.
Further steps need to be developed with higher deviation in permeability distribution.
39
6.3.3 Step 3: Co-kriging for Permeability Distribution Alteration 2
Objective: Due to minute deviation in production profiles in previous models, this step tries to
reach extreme standard deviations in permeability distribution.
Major Changes:
Similar to Step 2, original permeability distribution was co-kriged with a reference
lognormal distribution.
The reference lognormal distribution can be described as:
Mean = 2700 Std. Deviation = 6000
Minimum = 0.025 Maximum = 25000
(Std. Deviation of reference distribution increased from 3000 in Step 2 to 6000 in Step 3)
The resulting distribution (K_V4):
Original Distribution
(mD)
Step 2 (K_V2)
(mD)
Step 3 (K_V4)
(mD)
Min: 4 32 3
Max: 50521 24995 24998
Mean: 3598 2742 2381
Standard Deviation: 2445 2711 3352
Figure 27 Permeability Distribution Comparisons (Step 3)
Original distribution: Blue
Step 3: Yellow
Step 2: Blue
Step 3: Yellow
40
Results:
Figure 28 Results of Permeability Distribution Alteration with Co-kriging (Step 3)
Conclusions:
Similar to Step 1 and Step 2, small variations in production was observed in the beginning of
the production curve. But final recovery is observed to be on similar level.
This certifies that only widening permeability distribution will not affect final oil recovery
significantly. Another approach is necessary for altering production curve.
Compared to original distribution, around 20% higher pressure gradient is observed.
41
6.3.4 Step 4: Kr Curve Alterations 1 using Corey Exponents
Objective: As increasing permeability distribution is not giving any significant change in
permeability curve, Step 4 targets for change in relative permeability curve.
Major Changes:
The original relative permeability curve used till now, was based on data from past experience
in Rock Type 2 of Caracara Sur field.
End points of the relative permeability curve were achieved from lab experiments, giving
reliable data points. But the curve in between was extrapolated with standard parameters.
“Corey Exponent” (n) of these curves altered as follows:
Original CEPSA
(kr Original)
Step 4
(Kr1 curve)
Swi 0.21 0.21
Sor 0.23 0.23
Nwater 2 1
Noil 1.3 5
krw,ro 0.24 0.24
Kro,wi 1 1
Figure 29 Comparison of Relative Permeability Curves (Step 4)
Results:
42
Figure 30 Results of Relative Permeability Curve with Corey Exponents (Model 4)
Conclusions:
Oil production has been reduced from 67% in base case to 47%, as the oil mobility has been
decreased significantly with the extreme Corey Exponent.
But the plug is almost homogeneously swept at the end of 11PV on injection
Pressure gradient across the plug increased from 0.009 bar in base case to 0.014 bar.
43
6.3.5 Step 5: Kr Curve Alterations 2 by Krw at Sor
Objective: Step 5 attempts to explore effect of water mobility on oil recovery.
Major Changes:
To generate more oil un-swept zones, water should have higher mobility at residual oil
saturation (Sor). This will make water a preferred fluid phase to flow.
Water mobility can be increased by increasing relative permeability of water (Krw) at the end
point. Keeping all other parameters constant as Step 4, only Krw is doubled at Sor.
Resulting permeability curve:
Original CEPSA
(kr Original)
Step 4
(Kr1 curve)
Step 5
(Kr3 Curve)
Swi 0.21 0.21 0.21
Sor 0.23 0.23 0.23
Nwater 2 1 1
Noil 1.3 5 5
krw,ro 0.24 0.24 0.48
Kro,wi 1 1 1
Figure 31 Comparison of Relative Permeability Curves (Step 5)
44
Results:
Figure 32 Results of Relative Permeability Curve with Higher Water Mobility (Step 5)
Conclusions:
Due to increased mobility of water, oil production is lowered by 4%.w.r.t. Step 4 results.
Results of Step 5 showed overlapping trend of pressure gradient as Step 4 results.
There are no un-swept zones distinctly visible in dynamic results of coreflooding in Petrel.
So the water mobility does not play dominating role in altering oil production.
45
6.3.6 Step 6: Permeability Distribution Alterations 3 for All Rock Types
Objective: Higher heterogeneity can be achieved by reevaluating averaging assumptions in the
static model development. All previous steps assumed that the core is made up of Rock Type 2,
(RT2) based on average pore size distribution. Step 6 assumes the plug contains all rock types.
Major Changes:
Classification of the plug into RT2 resulted into single porosity-permeability correlation. The
resultant was a relative homogenous plug as extreme correlations were neglected.
So in this step, different permeability-porosity trend lines were used for different ranges of
porosity distribution, as highlighted in Figure 33:
Figure 33 Permeability vs Porosity Correlation with Rock Type Classification
As explained in “Porosity Model to Permeability Model” section, the above correlation is
based in mercury injection. The categorization into RT is done based on porosity cutoffs.
Porosity limits in this step are calculated by equating percentile of cells with porosity
distribution with weight percentage of rock types in the reservoir.
46
The resulting permeability distribution (K_V5):
Figure 34 Permeability Distribution with all Rock Types (Step 6)
Due to dominant presence of higher porosity cells compared to lower porosity cells, the resulting
permeability distribution is shifted towards higher end.
Original
Distribution
(mD)
Step 2
(K_V2)
(mD)
Step 3
(K_V4)
(mD)
Step 6
(K_V5)
(mD)
Min: 4 32 3 0
Max: 50521 24995 24998 105408
Mean: 3598 2742 2381 5191
Standard Deviation: 2445 2711 3352 6096
For relative comparison of standard deviations along with means; all models are normalized in
scale of Step 6 parameters:
Original
Distribution
(mD)
Step 2
(K_V2)
(mD)
Step 3
(K_V4)
(mD)
Step 6
(K_V5)
(mD)
Mean: 0.69 0.53 0.46 1.00
Standard Deviation: 0.40 0.44 0.55 1.00
47
Results:
Figure 35 Results of Permeability Distribution Model with All Rock Types (Step 6)
Conclusion:
Oil production graph showed the lower recovery despite having much higher permeability
mean. This anomaly arises because of preferential flow path.
The step did create zones which were not swept out of oil after 11PV of water injection.
Pressure gradient curve showed marginally lower pressure difference trend across the plug,
supporting probable preferential path assumption.
48
6.3.7 Step 7: Permeability Distribution Alterations 4 for All Rock Types
Objective: As the mean of the permeability distribution in Step 6 was higher than air
permeability, comparison with other models is difficult to explain. Step 7 adjusts the mean of the
permeability distribution to experimental air permeability.
Major Changes:
The complete distribution was multiplied with a correction factor, calculated by dividing air
permeability (2790 mD) with mean of Step 6 permeability mean.
Also the permeability values generated by Rock Type 4 (lower than 100mD) were neglected.
The resulting model:
Figure 36 Permeability Distribution Comparison (Step 6 and Step 7)
Original
Distribution
(mD)
Step 6
(K_v5)
(mD)
Step 7
(K_v7)
(mD)
Min: 4 0 0
Max: 50521 105408 56710
Mean: 3598 5191 2793
Standard Deviation: 2445 6096 3280
Step 6 (K_v5): Dark blue
Step 7 (K_v7): Light blue
49
Results:
Figure 37 Results of Permeability Distribution Model with All Rock Types (Step 7)
Conclusion:
Similar to step 6, step 7 did generate un-swept zones after 11 PV of water injection.
Despite reducing permeability to 53%, almost insignificant change in oil recovery was
observed. This establishes an important aspect, that the permeability distribution trend plays
more significant role than average permeability with respect to oil recovery.
Both production profile as well as pressure profile did not show much deviation compared to
Step 6 (K_v5)
50
6.3.8 Step 8: Kr Curve Alterations 3 by Kr Curve Variations for Each Rock Type
Objective: Despite creating un-swept zones, the final oil recovery is not significantly lower than
the initial models. This range of recovery is attributed to residual oil saturation in relative
permeability curve. Step 4 and Step 5 have already showed effect of Kr curve on oil production,
but changing Kr curve to such extreme deviates the model from reality. Step 8 tries to alter Kr
curve in the boundaries of reality.
Major Changes:
In this step, different Kr curves were generated for each rock type. These curves are
generated assuming that Rock Type 1 is least oil wet; and Rock Type 4 is most oil wet.
Kr Curves generated based on:
Kr_RT1
(Original Curve) Kr_RT2 Kr_RT3 Kr_RT4
Swi 0.21 0.21 0.21 0.21
Sor 0.23 0.25 0.35 0.5
Nwater 2 2 2 2
Noil 1.3 1.3 1.3 1.3
krw,ro 0.24 0.3 0.4 0.6
Kro,wi 1 1 1 1
Figure 38 Different Kr curves for different Rock Types (Kr_Mix1 | Step 8)
51
Results:
Figure 39 Results of different Kr Curve for Different Rock Types (Kr_Mix1 | Step 8)
Conclusion:
For similar permeability distribution, oil recovery decreased by 3% from 63% to 60% by using
different Kr curves for different rock types.
Considering decrease in oil recovery in Step 4 and Step 5, this small decrease of 3% advocates
for oil production dominated from RT1 and RT2. (Kr curves for RT1 and RT2 haven’t been
changed significantly to adhere to laboratory results.)
52
6.3.9 Reference Model: Permeability Distribution of Step 7 & Kr Curves of Step 8
Reference Model is developed with combined results of alterations of permeability distribution
and relative permeability curves, as explained in Step 1 to Step 8 above. Following the ‘Simulation
Constrains’ defined earlier, the base model was generated with permeability distribution K_v7
(Figure 36) and set of relative permeability curve Kr_Mix1 (Figure 38).
Few stages of water saturation
distribution stages generated by
simulation are appended here:
[Note: All water saturation
distributions follow the same
color gradient scale as shown at
initial condition.]
Figure 40 Water Saturation Distribution Models (Reference Model)
Injection = 0.05PV Injection = 1 PV
Injection = 5 PV Injection = 11 PV
Initial Conditions (Swi)
53
Results of the Reference Model (ECLIPSE_PERM_Dist_K_v7_kr-Mix1_Reference_Model) are
compared with the initial base model (ECLIPSE_kr CEPSA_23hr) and experimental results.
Figure 41 Oil Production and Pressure Gradient History Match for Reference Model
After 11 pore volumes of water injection, base model of the study was giving oil recovery of 67%,
whereas experiments recorded almost 20% of oil recovery. The reference model is resulting with
60% of oil recovery.
Residual pressure gradient across the plug after 11 pore volume injection in reference case is
0.009 bar, close to initial base model of 0.008 bar. Experiments gave gradient of 0.031 bar.
54
The plug is further divided into 24 zones across the axis. Water saturation of the zones is calculated
experimentally with X-ray scanning of coreholder during flooding.
Zonal saturation profile comparison between lab data and simulation data is one of the most
important standard of representativeness of the simulation towards experimental conditions.
Comparative Results:
Figure 42 History Match of Zonal Water Saturation Profile (Reference Model)
Conclusion:
Initial water saturation (Swi) profile showed similar trend to Swi profile of lab results. But in
later timesteps, the saturation values have less deviations from the average at given timestep.
This advocates the inability of the model to recreate heterogeneity across the plug.
On an average, water saturation given by ECLIPSE is at higher level than the lab results.
This is reflected back in the oil recovery trend, as shown in Figure 41.
Trends of End Effects#, as visible in experimental data, are not regenerated by ECLIPSE.
(Refer to relatively lower water saturation for all time steps at the end of the core.)
# ’End Effect’ arises from pressure gradient across two phases in the plug; compensated with capillary forces to achieve equilibrium
at production outlet. Therefore it is also known as “Capillary End Effect” (Arne Skauge, 2001). Though it is a very important
phenomenon for understanding of corefloodings, due to high complexity, this study does not address the phenomenon.
Note: Each line / dot, represent corresponding saturation at given time (hrs), as represented in right hand side of the
chart. Though results from experiment as well as lab have more time steps, only few time steps are shown here.
55
Individual zonal saturation profile are as follows:
Figure 43 Experimental Zonal Water Saturation Profiles with X-Ray Diffraction
Figure 44 Simulation Generated Zonal Water Saturation Profile (Reference Model)
Though there is a clear distinct trend, complete reproduction of lab profile is impossible due to
End Effects. Parameters should not be varied vaguely to attain the perfect history match.
56
7 Sensitivity Analysis
The Reference Model developed in the previous chapter serves as a base case for further sensitivity
analysis. In this sensitivity analysis study, effects of alterations in individual parameters of the
system on final outputs are analyzed. But due to high simulation time of the 3D model, in most of
the parameters are tested with extremities to rectify boundaries.
7.1 Analysis 1: Wettability Variations of RT2 Mixed Wet & RT3, RT4 Oil Wet
Objective: More oil wet systems show lower oil mobility. As RT1 have experimentally shown
high oil mobility, making them less oil wet will deviate the case study from reality. Also, as RT2
occupies majority of the plug; altering wettability of RT2 to extremity will deviate average
wettability of the plug significantly. So Analysis 1 aims to understand effects of oil wetting
behavior, by making with RT3 & RT4 completely oil wet and RT2 mixed wet.
Methodology:
Increasing Corey Index for oil curve (Noil) decreases oil mobility; as observed in rocks with
high oil wet behavior. So this study uses Noil alterations as a proxy for oil wet behavior.
Kr_Mix5 is a set of Kr curves for all rock types, generated with:
Noil (RT1) = 1.3 (water wet) | Noil (RT2) = 2 (mixed wet) | Noil (RT3 and RT4) = 5 (oil wet)
Figure 45 Sets of Kr Curves for Varied Oil Wettability (Analysis 1)
57
Results:
2
Figure 46 Result of sensitivity analysis of wettability (Analysis 1)
Inferences:
Significant drop in oil production is observed in Kr_Mix5 compared to Kr_Mix1
Sor (Kr_Mix1) = 40% | Sor (Kr_Mix2) = 47%
Pressure gradient curve showed almost negligible variations
Un-swept oil zones are observed throughout the plug, with increasing contrast from kr_Mix1
to kr_Mix5.
58
7.2 Analysis 2: Water Injection Rate Variation
Objective: Analysis 2 tries to understand effect of injection rate variation on oil production.
Major Changes:
Keeping all parameters constant, injection rate increased to 160 ml/h (10 times of base case)
Results:
Figure 47 Results of Injection Rate Variation (Sensitivity Analysis 2)
Inference:
Due to no theoretical difference created by flow rates, ECLIPSE generated same trend in oil
production for 160 ml/hour as base case (16 ml/hour).
Due to complex permeability distribution, pressure difference curve was saturated at 0.047 bar
compared to 0.009 bar initially for 10 times higher injection rate.
59
7.3 Analysis 3: Injection Well Area Variation
Objective: As described in the chapter 3D Dynamic Model, well geometry is recreated by
connecting every cell on the faces of the plug. But realistic injection area is a thin grid, distributing
injection fluid symmetrically over plug face. So Analysis 3 tries to understand effect of varying
well injection area over plug face.
Methodology:
Injection area of the Reference Model
covering complete plug face is 984 mm2.
Following two new well geometries have
been created by restricting number of cells
from center:
Well1 (20*20 cells)
Injection area = 100 mm2
Well2 (10*10 cells)
Injection area = 25 mm2
Figure 48 Well Models Created for Injection Area Sensitivity Analysis
Reference Model – Complete Face Injection
Well1 Model – 20*20 Cells Injection Well2 Model – 10*10 Cells Injection
60
Results:
Figure 49 Injection Well Area Alteration Results (Analysis 3)
Inference:
Both well models showed similar production trend as base model. This can be attributed to
higher sweep efficiency near the face of the core with higher axial mobility for water.
Saturation pressure (Psat) values were smaller over larger injection area, as follows:
Psat (Base Model) = 0.009 bar | Psat (Well1) = 0.010 bar | Psat (Well2) = 0.012 bar
61
7.4 Analysis 4: Injection Geometry Variation using Experimental Shape
Objective: The coreholder’s injection area is a thin grid,
distributing injection fluid symmetrically over plug face; as
shown in Figure 50. Integrating this injection geometry is not
expected to affect the oil production significantly, it will be
interesting to understand effect on water saturation profile through
the plug.
Figure 50 Lab injection face in the
coreholder (Courtesy: E&P, CEPSA)
Methodology:
Several attempts were used to integrate the real well injection grid (Figure 51). But origin of
the errors was suspected to be high pressure gradient across few cells in the injection face.
Same simulation error was observed in one cell injection in early steps of model development.
To avoid the error, the injection geometry was shifted to the 2nd layer. This ensured smooth
injection in the first layer, and decreased high pressure gradient across any cell.
Figure 51 Experimental Well Geometry Integration (Analysis 4)
Injection well geometry at layer 2 Drainage effect on plug after 0.1 PV injection
62
Results:
Figure 52 Results of Inject Geometry Variations (Analysis 4)
Inference:
The production curve showed exactly same trend as base model with equal recovery. Also the
pressure gradient profile showed same trend as base model.
This ensures negligible effect of the injection pattern across the complete core in sweeping, as
can be justified with oil production curves obtained in Analysis 3: Injection Well Area.
63
Zonal Water Saturation Comparison:
This comparison will certify the assumption that injection through complete face creates same
coreflooding results as actual injection face geometry.
Comparitive Results:
Figure 53 Zonal Water Sat. for Real Injection Geometry & Reference Model (Analysis 4)
Inference:
There are some minor deviations from reference model results near the injection face. But
after mid of the plug, the saturation profiles have exactly same trends.
Also, along with time, the deviation from reference model results have decreased. In fact the
final timestep showed complete match with zonal saturation trend. This ensures the strong
similarity between results of base case and the model with realistic geometry.
64
8 Results and Discussion
The foundation of the research done for this thesis was to confront the uncertainty arising from
heterogeneities in the plugs used for coreflooding analysis. This thesis dealt primarily with
generation of three dimensional dynamic coreflooding model in a black oil simulator. The
development of the static representative model from digital rock physics data of the plug was the
most challenging part of this study. In the frame of realistic boundaries, the study gave good
results. Finally a series of sensitivity analysis studies have been performed to learn boundaries of
coreflooding results.
Literature Review:
The study was initiated with literature review chemical EOR corefloodings and their modeling.
Testing EOR methodologies on a core material helps to understand reservoir’s response at
miniature scale, but under controlled environment. It also helps to predict boundary conditions of
the reservoir response at economical investment. Literature review also established theoretical
background about coreflooding simulations in association with Digital Rock Physics (DRP).
Literature review showed relatively low use of the technology across the industry, but also has
high potential. This ensures steep growth of the technology in upcoming years across the industry.
On the basis of literature review, two simulators were shortlisted for further investigation, namely
UTCHEM 9.1 and ECLIPSE 100 (2014.1). It was noticed that UTCHEM 9.1 has better technical
accuracy for chemical EOR corefloodings; whereas ECLIPSE 100 has better computational power
and ease of handling even for complex models. Due to data limitation and ease of modeling,
ECLIPSE 100 was chosen for further study.
One Dimensional Model:
One dimensional (1D) coreflooding model was developed, as an initiating stage of development
of the full-fledged three dimensional (3D) coreflooding model. The 1D model was developed to
replicate chemical coreflooding experiments on a core from Caracara Sur field (CCS), Colombia.
A close history match was attained, but by hugely modifying experimental relative permeability
curve. This modification of relative permeability curve, until unrealistic range, showed inability
65
of the 1D model to represent the core. Still, due to simplicity of the model, the model was further
tested for sensitivity analysis.
The sensitivity analysis for injection rate showed inability of 1D model in ECLIPSE to reproduce
end effects. Whereas sensitivity analysis of viscosity showed expected trend of increasing viscosity
of injected flooding resulting in increased oil production. Similarly, sensitivity analysis of IFT
showed expected trend of decreasing IFT generating increased oil production. The results from
this sensitivity analysis can be further extended to optimization of chemical corefloodings, and
eventually optimizing reservoir floodings.
Three Dimensional Model:
Furthermore, 3D static model, for another core from CCS field, was built based on results of DRP
analysis. Computerized Tomography (CT) scan results, as a stack of local attenuations, were
transformed into density model, porosity model and finally into permeability model. Analysis of
the transformation stages showed the permeability model, unlike density and porosity model, has
high uncertainty involved.
Similar to permeability distribution generated, relative permeability curves have high uncertainty
involved. Though end points of the relative permeability curves are obtained from laboratory
experiments, rest of the curves are interpolated with standardized Corey Index numbers. So the 3D
dynamic model had uncertainties involved mainly in static permeability model and relative
permeability curve. A reference model was developed after multiple steps of alterations in the
permeability distribution and the relative permeability curve.
Altering global mean of the permeability distribution (by less than 10%) was not altering total oil
production significantly. Also, altering global standard deviation of the permeability distribution
(by less than 10%) could not alter the production profile to large extent. But increasing local
standard deviation of the permeability distribution generated few preferential paths for injected
water; resulting into lower oil production. Increasing standard deviation of local permeability
distribution was achieved with consideration of multiple rock types, instead of a single rock type
assumption, in the given plug.
66
Relative permeability curves also play important role in altering residual oil saturation level. The
system can be transformed into more oil wet, by increasing Corey Index for oil, to decrease oil
mobility. This study maintained average wettability of the plug by gradually altering the
wettability across different rock types. Results of these alterations of relative permeability curve
and permeability distribution, residual oil saturation was modified by around 10%, constraining
parameters within the boundaries of reality.
The reference model developed here showed locally un-swept oil zones; as observed
experimentally. Also the zonal water saturation profile predicted via simulations showed close
match with experimental observations near the injection face of the plug. So the reference dynamic
model developed here closely represents the experimental coreflooding conditions. But the plug
exhibited strong capillary end effect, as a larger margin is observed between zonal saturation
profiles near production face of the plug.
Similar to sensitivity analysis performed on 1D model with injection rate variations, sensitivity
analysis on 3D model could not show effect of injection rate variations on oil production.
Sensitivity analysis of the wettability predicted lower production by making core more oil wet.
Whereas, sensitivity analysis of the injection area showed marginal increment in oil production
with increasing injection area. Finally the reference model was tested by incorporating laboratory
injection geometry. The analysis verified the assumption of using complete face injection in place
of symmetric grid used in laboratory.
67
9 Future Work
Computational simulations of corefloodings, in association with DRP, have high potential to make
field oil production more efficient across the globe. With recent introduction of high definition
DRP in the oil industry, along with better computational power, the technology can give promising
results. So more research and development efforts are needed in future to explore potential of this
technology.
All models in this work, were simulated with a black oil simulator, ECLIPSE 100 (2014.1).
Though black oil simulators give reliable simulation results for coreflooding experiments, pore
scale simulators are ideal for coreflooding simulations. One of the prominent advantage of the pore
scale simulator is generating relative permeability curves for the given plug as an output, on the
basis of petro-physical properties of the rock-oil-water system. On contrary, black oil simulators
need relative permeability curve as an input for simulations. Developing the same dynamic model
in pore scale simulator will help to understand different aspects of the coreflooding.
Another black oil simulator, UTCHEM 9.1, has higher technical accuracy for chemical EOR in
comparison with ECLIPSE 100 (2014.1) (Goudarzi, et al., 2013). If the 3D model developed in
this study, is needed to be extended for chemical corefloodings, it should be redeveloped in
UTCHEM 9.1.
The complete work was aimed at generating the relative permeability curves and the permeability
distribution for better history matching with experimental response of the plug. Other parameters
were assumed to have higher certainty based on lab or field tests. Reassessment of other
parameters, and corresponding sensitivity analysis will give deeper insight into optimization for
future corefloodings.
Complete automation of history matching process will give fine-tuned results. This can be
achieved either with software like Raven 2.0 (by Heriot-Watt University) or developing
personalized program.
68
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Other References:
ECLIPSE 2014.1 Reference Manual
ECLIPSE 2014.1 Technical Description
UTCHEM 9.0 User’s Guide (Volume 1)
UTCHEM 9.0 Technical Documentation (Volume 2)
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