Module 3 - Phase Behavior and Fluid Properties

8/12/2019 Module 3 - Phase Behavior and Fluid Properties

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PETE 609 Module 3 Phase Behavior and Fluid Properties

Class Notes for PETE 609 Module 3 Page 1/74 Author: Dr. Maria Antonieta Barrufet - Fall, 2001

Instructional Objectives

After seeing this module the student should be able to: Understand pure component phase behavior as a function of Pressure, Temperature,

and molecular size.

Understand the behavior of binary and multicomponent mixtures.

Construct pressure-composition diagrams for a fixed temperature.

Construct temperature -composition diagrams for a fixed pressure.

Construct ternary phase diagrams.

Sketch a miscible gas injection using a ternary diagram.

Represent qualitatively phase behavior dependence on compositions using phasediagrams.

Represent miscible displacement processes using ternary diagrams.

Module 3 Phase Behavior and Fluid PropertiesEstimated Duration: 2 weeks

Phase Behavior Fundamentals from Pressure/Temperature and Pressure/CompositionDiagramsFluid Properties of Interest to EORQualitative Representation of Phase Equilibria Processes: Gas Injection andProductionQuantitative: Representation of Phase Equilibria Processes: Gas Injection andProductionTernary Diagrams to represent Gas Injection Processes: Miscible and ImmiscibleProcesses

Suggested reading: MAB, S


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Phase Behavior and Fluid Properties

Except polymer flooding, all of EOR methods rely on the phase behavior of reservoir fluidsand fluids injected into the reservoir. This behavior is used to classify the recovery method(i.e., thermal, miscible, chemical, etc.), and to design the recovery process.

This section reviews qualitative and quantitative aspects of phase behavior that will beused through the reminder of the course.

As oil and gas are produced from the reservoir, they are subjected to a series of pressureand temperature changes. Such changes affect the volumetric and transport behavior ofthese reservoir fluids and, consequently, the produced oil and gas volumes.

We need to quantify the real oil and gas volumes under various pressures andtemperatures. There are basically two models to do this.

Black Oil models describe volumetric properties using correlations in terms of measured

macroscopic properties such as API gravity, bubble point pressures, and gas gravities,pressure and temperature.

Compositional models require compositional information in addition to the primaryvariables: pressure and temperature.

Compositional Model

1. Oil and gas are mixtures of several components

2. All components may be present in both phases (liquid and gas)

3. Volumetric properties of the phases are determined as a function of pressure,temperature, and the phase compositions using the same model an Equation ofState (EOS) for all phases.


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Black Oil Model

The black oil model can be considered a special case of a compositional model with therestriction that:

1. Has only two components named as the phases: Gas (G) and Oil (O).

2. The G component may be dissolved in the oil phase and this is taken into accountthrough the solution gas oil ratio (Rs). However the oil component (O), cannot dissolvein the gas phase.

3. Volumetric properties are determined from separate correlations for gas and oil

phases.

Phase Behavior Diagrams

Pressure versus temperature diagrams can be used to visualize the fluids production pathfrom the reservoir to the surface, and to classify reservoir fluids according to the location ofits critical temperature with respect to the reservoir temperature.

The phase behavior of crude oil, water, and EOR fluids is a common ground forunderstanding the displacement mechanisms of EOR processes. This behavior includesthe two or more phases formed in crude oil miscible solvent injection processes, thegasoilwater phases of steam flooding, and the two and three phase behavior ofsurfactantbrineoil systems.

The main application of Phase Behavior Diagrams is to develop strategies for efficient oil(petroleum) and gas production.

Major Definitions

SYSTEM: A body of matter with finite boundaries (physical or virtual), which can beconsidered as isolated from surroundings if desired.


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CLOSED SYSTEM: Does not exchange matter with surroundings but may exchangeenergy (heat).

OPEN SYSTEM: Does exchange matter and energy with surroundings.ISOLATED (ADIABATIC) SYSTEM: Does not exchange matter or energy with

surroundings.

HOMOGENEOUS SYSTEM: Intensive properties change continuously and uniformly(smoothly)

HETEROGENEOUS SYSTEM: System made up of two or more phases in which theintensive properties change abruptly at phase-contact surfaces.

PHASE: A portion of the system which has homogeneous intensive properties and it isbounded by a physical surface. Homogeneous means that it is possible to movefrom one point to another within that region without detecting a discontinuouschange in a property. An abrupt change in a property is observed when aninterface is crossed. An interface separates two or more phases. These phasesare solid, liquid(s), and gas.

PROPERTIES: Characteristics of a system (phase) that may be evaluated quantitatively.These properties are

Phase density (liquid, gas, solid)

Compressibility

Surface tension

Viscosity (with help from Transport Models)

Heat capacity

Thermal conductivity

COMPONENT: A molecular species defined or hypothetical. Reservoir fluids contain

many components, and we are commonly forced to combine severalcomponents into hypothetical or pseudo-components, to simplify phase behaviorrepresentations and subsequent calculations.

Defined: C l, C 2 , H 2O

Hypothetical: C 7+


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STATE: Condition of a system at a particular time determined when all intensiveproperties are fixed

PHASE BEHAVIOR DIAGRAMS: These diagrams are called phase envelopes. The dewpoint curve and the bubble point curve converge at the mixture critical point.


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Characteristic Phase Envelopes (Phase Composition is Fixed)

Critical

Cricondenbar

Cricondentherm

BubblepointCurve

Dew Point Curve

QualityLines

Temperature

P r e s s u r e

75%

50%

25%

Figure 1- Characteristic phase envelope.

Bubble Point Curve: Boundary between liquid phase and 2-phase region

Dew Point Curve: Boundary between gas phase and 2-phase region.

Critical Point: Location where bubble point and dew-point curves meet.

Cricondentherm: Highest T in phase envelope

Cricondenbar: Highest P in phase envelope.

Quality Lines: Lines of constant volumetric or molar percentage of a phase.


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Classification of reservoirs based on phase diagram

1. Gas Reservoirs (Single Phase ): Dry Gas (see Figure 2), and

Wet Gas(see Figure 3).

2. Gas Condensate Reservoirs (Dew-Point Reservoirs):

Retrograde or Condensate Gases (see Figure 4).

3. Undersaturated Solution-Gas Reservoirs (Bubble-Point Reservoirs):

Volatile Oil (see Figure 5), and

Black Oil (see Figure 6).

Temperature

P r e s s u r e

Path of Production

Initial ReservoirConditions

Separator Conditions

CP

Figure 2 - Phase diagram of a dry gas reservoir.


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Temperature

P r e s s u r e

Path of Production



CP

Figure 3 - Phase diagram of a wet gas reservoir.

Separator conditions are within the phase envelope, therefore some liquid will beproduced at surface

Temperature

P r e s s u r e


CP

Path of Production


Temperature

P r e s s u r e


CP

Path of Production


Temperature

P r e s s u r e


CP

Path of Production



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Figure 4 - Phase diagram of a retrograde gas (condensate) reservoir.

Temperature

P r e s s u r e


CP

Path of Production


75%

50%25%

Figure 5 - Phase diagram of volatile oil reservoir.


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Temperature

P r e s s u r e


CPPath of Production


25%50%75%

Figure 6 - Phase diagram of a black oil reservoir.

If we overlap the phase envelopes for all fluid types in one diagram we will have a series ofphase envelopes in which the critical points of the mixtures have the following trend:

Critical Pressures increase from dry gas, to condensate and volatile where theyreach a maximum and drop again for black oils.

Critical Temperatures increase from dry gas to black oil systems.

The concentration of C 1 increases from Black Oil to Dry Gas.

The character of a fluid type is dictated by its composition.

The following plot contains calculated phase envelopes with hydrocarbon mixtures with thesame components but with different proportions.


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0

1000

2000

3000

4000

5000

6000

7000

P r e s s u r e

( p s

i a )

-200 -100 0 100 200 300 400 500 600 700 800

Temperatureo

F

Critical Points

Dry Gas

Wet Gas

Condensate

Volatile I

Black Oil

TR

Volatile I

Volatile II

Figure 7 - Calculated phase envelopes of different mixtures of the same hydrocarboncomponents at different proportions. (Barrufet, 1999b).

Typical compositions of reservoir fluids are given in the following table.

Com po nen t Black Oil Volatile Oil Gas Con dens ate Wet Gas Dry Gas

C 1 48.83 64.36 87.07 95.85 86.67

C 2 2.75 7.52 4.39 2.67 7.77

C 3 1.93 4.74 2.29 0.34 2.95

C 4 1.60 4.12 1.74 0.52 1.73

C 5 1.15 3.97 0.83 0.08 0.88


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C 6 1.59 3.38 0.60 0.12

C 7+ 42.15 11.91 3.80 0.42

M w C 7 + 225 181 112 157

GOR 625 2000 18,200 105,000 -

Tank o API 34.3 50.1 60.8 54.7 -

LiquidColor

GreenishBlack

MediumOrange

LightStraw

WaterWhite

-

Table 1 - Typical compositions mole % of single-phase reservoir fluids

The transition between a volatile and a condensate fluid in terms of characteristiccompositions is not well defined.

Reservoir fluids also contain other chemical species that may complicate the phasebehavior even further. Table 2 provides a general guideline of reservoir fluid compositions.


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Table 2 - Guideline of reservoir fluid compositions. (Table taken from Mc Cain TheProperties of Petroleum Fluids, Pennwell 1990)


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Classification of Reservoirs Based on

Production and PVT Data

Before we use a certain fluid model (compositional or black oil), we should have someguidelines about the type of reservoir fluid we are dealing with: volatile oil, black oil, gas-condensate, etc.

The (PT) envelope can be generated using any EOS graphics based package such asPVTSIM, PVTi, etc. once the composition of the fluid are provided.

Other guidelines in terms of Production and PVT Data are

BLACK OIL RESERVOIRS:

GOR less than 1,000 SCF/STB

Density less than 45 API

Reservoir temperatures less than 250 F

Oil FVF less than 2.00 (low shrinkage oils)

Dark green to black in color

C 7+ composition > 30%

VOLATILE OIL RESERVOIRS:

GOR between1,000-8,000 SCF/STB

Density between 45-60 API

Oil FVF greater than 2.00 (high shrinkage oils)

Light brown to green in color


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C 7+ composition > 12.5%

GAS CONDENSATE RESERVOIRS:

GOR between 70,000-100,000 SCF/STB

Density greater than 60 API

Light in color

C 7+ composition < 12.5%

WET GAS RESERVOIRS:

GOR > 100,000 SCF/STB

No liquid is formed in the reservoir

Separator conditions lie within phase envelope and liquid is produced at surface

DRY GAS RESERVOIRS:

GOR greater than 100,000 SCF/STB

No liquid produced at surface

Additional guidelines to classify reservoir fluid type:


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Reservoir Surface GOR range Gas specific API Typical composition, mole %fluid appearance gravity gravity C 1 C2 C 3 C 4 C 5 C6

Dry gas Colorless gas Essentially 0.60 - 0.65 96 2.7 0.3 0.5 0.1 0.4no liquids

Wet gas Colorless gas Greater than 0.65 - 0.85 60 o -70 owith small amount 100 MSCF/bblof clear or strawcolored liquid

Condensate Colorless gas 3 to 100 0.65 - 0.85 50 o -70 o 87 4.4 2.3 1.7 0.8 3.8with significant MSCF/bblamounts of light- (900-18000 m 3 /m 3)colored liquid

Volatile or Brown liquid About 0.65 - 0.85 40 o -50 o 64 7.5 4.7 4.1 3.0 16.7high shrinkage with various 3000 SCF/bbloil yellow, red, or (500m 3 /m 3 )

green hues

Black or low Dark brown 100-2500 SCF/bbl 30 o -40 o 49 2.8 1.9 1.6 1.2 43.5shrinkage oil to black (20-450 m 3 /m 3)

viscous liquid

Heavy oil Black, very Essentially no gas 10 o -25 o 20 3.0 2.0 2.0 2.0 71viscous liquid in solution

Tar Black substance Viscosity >10,000cp


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As the reservoir pressure decreases, the gas evolves from solution to form a two-phasesystem. The relative rates of the gas and oil being removed from the reservoir would affectthe oil volume behavior in the reservoir as well as at stock tank conditions.

Likewise, injection of gases, is the reverse process, gas is added in solution.

Some typical pressure, temperature ranges

Location Pressure (psia) Temperature ( oF)Reservoir 500-10,000 100-300 (500 + thermal)

Separator 100-600 75-150Stock tank 14.7 AmbientStandard Conditions 14.7 60

The oil and gas properties of interest to reservoir engineers and their typical units are:

oil formation volume factor (B o) = [res bbl/STB],

gas formation factor (B g) = [cu ft/SCF] or [res bbl/SCF],

total formation volume factor (B t) = [res bbl/STB], solution gas-oil ratio (R s) = [SCF/STB]

oil and gas viscosities (o , g) = [cp],

compressibility and thermal expansion coefficients.

The properties of reservoir fluids will change during production because of

Pressure and/or Temperature changes

Injections of recovery agents (miscible and chemical)

Adding fluids to the reservoir may change compositions and pressures and as a result thephysical properties will change. Additionally, rock-fluid interactions may be changed as willbe seen in future lectures.


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The fluid properties of interest for EOR processes are those that affect the mobility of fluids

within the reservoirs.These properties include:

Densities ( Bo , B g , Compressibility and thermal expansion coefficients)

Viscosities

Interfacial Tensions (more about this in future modules)

The following figures sketch the behavior of oil and gas properties as a function ofpressure, temperature, and composition.

Compressibility Factor Charts

The general shape of this chart is indicated in Figure 8.


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T r

P r

Z

1

Figure 8 - General shape of compressibility factor.

Only one compressibility factor chart can be used to determine volumetric properties forany pure hydrocarbon fluid and mixtures. That is accomplished by using the correspondingstates principle and reduced, or pseudoreduced, properties (P r & Tr ) , (P pr & Tpr )

The reduced properties are defined as

c

r

c

r P

P P

T

T T == and (Eq. 1)

The compositional dependence is seen through the evaluation of the critical, orpseudocritical properties of the mixture (subject from another course). These give rise toreduced, or pseudoreduced properties.


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Table 3 - Physical constants of pure hydrocarbons.

The following diagram illustrates changes in the phase envelope of a reservoir fluid duringproduction and/or injection.

Temperature

t1

Composition Changes Due to Production

and Gas Injection

P r e s s u r e

t3

t2

GasInjection

Production

Temperature

t1

Composition Changes Due to Production

and Gas Injection

P r e s s u r e

t3

t2

GasInjection

Production

Figure 9 - Composition changes due to production and gas injection. Review from McCain(Petroleum Fluids,1990).

The following sketches indicate the behavior of the main fluid properties with pressure andtemperature.


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Total Formation Volume Factor

B t o r

B o

PressureP b

B t

Bo

B t=B o

Figure 10 - Total formation volume factor.

The phase behavior of reservoir fluids (oil and gas) is determined from a laboratoryanalysis of a reservoir fluid sample. The pressure-volume-temperature relationship can beused to evaluate the reservoir oil behavior under different pressure and temperatureconditions.


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Gas Formation Volume Factor

B g

Pressure Figure 11 - Gas formation volume factor.


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Oil Viscosity

V i s c o s i

t y

Pressure

P b

Figure 12 - Oil viscosity.


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Gas Solubility

G a s

i n S o l u t

i o n

PressureP b

Figure 13 - Gas solubility.


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Isothermal Compressibility

S p e c

i f i c V o

l u m e

Pressure

T

V

P

Figure 14 - Isothermal compressibility.


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Flash Vaporization

The flash vaporization is a process of gas-oil separation in which the gas and oil are

always in contact throughout the entire life of the separation. It is conducted at the reservoirtemperature.

The following figure shows the flash separation process.

V t1 V t2 V

t 3 =

V b

V t5V t4oil oil oil oil

oil

gas gas

Hg Hg HgHg Hg

P 1 >> P b P 2 > P b P 3 = P b P 4 < P b P 5 < P 4

1 2 3 4 5

Flash Separation (Liberation)Flash Vaporization

Figure 16 - Flash vaporization process.

TEMPERATURE OF TEST = RESERVOIR TEMPERATURE

Differential Separation

The differential separation is a gas-oil separation process in which the gas separated atone stage is removed before the remaining oil is subjected to the next stage of separation.


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The separation process is conducted at the reservoir temperature and pressure except thelast stage which is conducted at standard conditions (P = 14.7 psia, T = 60 oF).

The following figure illustrates the differential liberation process.

gas

oil

oil oil oil

oil

gas

Hg

Hg

HgHg

Hg

P1 = P b P2 < P b P2 < P b P2 < P b P3 < P 2 < P b

1 2 3 4 5

Differential Separation (Liberation)

gasoil

Gas off

Figure 17 - Differential separation (liberation) process.

These oil properties can either be determined from laboratory tests or from available

correlations.

Water in Petroleum Engineering

Water plays a very important role in petroleum engineering. It exists in the reservoir as theconnate water. It is certainly present in the aquifer. It is more often than not comes out from


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the reservoir with the produced oil and gas. The resistivity of brines (water + dissolvedions) is used by the log analyst for saturation calculation. For a waterflood expert, it iscertainly an indispensable commodity.

The basic water properties of interest to reservoir engineers are compressibility, formationvolume factor, viscosity, chemical composition, and resistivity. The chemical compositionof the formation water is used to determine the source of reservoir water, the waterresistivity for well log analysis, and the compatibility of the injected water for waterflood.

Presence of Water

Connate Water

Aquifer

Production

Well Log Analysis

Injection

Water Treatment

Formation Water (Brine) Properties

The properties of interest for reservoir engineering are:

Solubility of Gas in Water

Water Compressibility

Water Formation Volume Factor

Water Viscosity Chemical Properties

Resistivity


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Chemical Analysis of Water

All formation water contains dissolved ions. The ions may be classified into two groups.

Positively charged, or cations, and negatively charged or anions, these ions proceed fromsalts in solution and conduct electricity offering more or less resistance depending uponthe salt concentration (property used in electric logs).

Formation waters are neutral, that is positive and negative charges balance. The followingtable shows typical ions in formation waters.

Cations AnionsNa + K+ Ca ++ Mg++ Fe ++

Cl - HCO 3

- SO 4

- - CO 3

- -

Table 4 - Typical ions in formation waters.

Stiff diagrams are used to indicate the (+) and (-) ion contents in water following specificpatterns (see McCain 1990).

Electrical Resistivity of Water

Electrical resistivity is property used in well-log analysis to determine rock properties suchas porosity, oil-water contacts etc.

Applications of Fluid Analysis Data

The use of these properties in Reservoir Engineering Calculations include:

Volumetric

Volume Balance - Black Oil


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Material Balance Equation Black Oils and Gases

Compositional Material Balance Equation - Volatile Oil & Gas Condensates.

Enhanced Oil Recovery

The use of these properties in Production Engineering Calculations include:

Surface Equipment Design

Wellbore Fluid Mechanics

Production Test

Pressure Transient Analysis

Well Completion

Phase Diagrams

To see the effect of compositions in the phase behavior we need to analyze single andbinary systems. The diagrams seen so far do not show any compositional dependence.

Equations of state models are calibrated with properties of pure components and latergeneralized to mixtures by using mixing rules and molar compositions.

The most common types of phase diagrams are:

Single: (PT), (PV), (TV)

Binary: (PT) zi , (PV) zi , (P,x,y) T , (T,x,y) P

The nomenclature (PT) zi means: Pressure vs Temperature diagram at a fixed mixturecomposition zi


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P r e s s u r e

Pc

TemperatureTc

Liquid (1 phase)

Vapor (1 phase)

Solid(1 phase)

Sublimation Curve (2 phases)

Triple Point (3 phases)

Vapor PressureCurve (2 phases)

Critical

Point

Fusion Curve2 phases

Figure 18 - Single component phase diagram.

The petroleum engineer is usually interested in a smaller region of this phase diagram: Theregion covering vapor-liquid-equilibrium (VLE).


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P r e s s u r e

Temperature

Vapor

Liquid

Critical Point l

v

Pc

Tc

Figure 19 - Vapor pressure curve (VLE).

This graph illustrates the vapor pressure curve for a pure component. As the temperatureincreases the vapor pressure increases until the critical point. At temperatures higher thanthe critical temperature there is no phase transition (from vapor to liquid and vice versa) atany pressure.

The state of the component (remember: single component) at a P or/and T greater than itscritical values is a fluid state and as pressure increases its density varies smoothly fromlow (gas-like) to high (liquid-like).

This graph also illustrates two lines of constant density (isochores) a vapor and a liquid

density. Notice that at a fixed temperature and pressure two densities coexist.

For a single component fluid the vapor pressure curve is a line with dew-point and bubble-point being identical.


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Vapor Pressure ModelsVapor pressures are well represented using the Antoine Model

T C

B Ap sat

+=)ln( (Eq. 3)

Where A, B, and C are constants specific for each component (i.e., propane, decane). Thismodel can be used in thermal simulations.

Density (mass/volume) is the inverse of specific volume (volume/mass). To see thevariation of density (or specific volume) with pressure and temperature another phasediagram must be used. This is the pressure-specific volume diagram. For a puresubstance this looks like:


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T c

2-phase

T

Specific Volume (ft 3/lbm)

P r e s s u r e

( p s i a

)

VvV L

CP

Figure 20 - Pressure vs. specific volume diagram for a pure substance.

The critical point (CP) is the highest temperature and pressure at which a vapor and aliquid phase can coexist

Gas and liquid volumes become identical at the critical point.

Isotherms are steeper in the liquid region than in the gas region to reflect lower liquidcompressibilities.

Phase Behavior of Single and Binary Systems

The following phase diagrams for single and binary mixtures serve to illustrate the behaviorof multicomponent fluids at different pressures, temperatures, and compositions.


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(Left) (Right)

Temperature x1, y 1

P r e s s u r e

P1v

P2vP2v

P1v

T = T a

Ta

CP1

CP2

B u b b l e

C u r v e

D e w C u

r v e2-phases

Liquid

Vapor

Figure 21 - Phase diagrams for single and binary mixture.

The left side of this Figure 21 illustrates two vapor pressure curves for component [1] and

[2]. At T a , the vapor pressures arevv P P 21 , and component [1] is the most volatile.

Heavier components, in general, exhibit high critical temperatures and lower critical

pressures than more volatile components. For example:

C 2 (ethane) T c = 89.92oF P c = 706.5 psia

C 10 (decane) T c = 652.0oF P c = 305.2 psia

The right hand side of Figure 21 illustrates the phase behavior of all possible mixturesbetween [1] and [2] at the selected temperature T a .

By convention the most volatile component is plotted in the x -axis. The two extremes

indicate the vapor pressures of the pure components.

The two lines enclosing the two-phase region indicate the bubble pressures (above), andthe dew pressures (below) as a function of composition at T = T a.

Note that bubble point pressures increase as the composition of the most volatilecomponent increases.


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Hydrocarbon Composition

The hydrocarbon composition may be expressed on a weight basis or on a molar basis.For compositional modeling we use a molar basis. The relationship between moles andmass is given through the molecular weight.

i""componentof weightMoleculari""componentof Mass

i""componentof Moles = (Eq. 4)

i

i i M w

M n =

(Eq. 5)

Molecular weights for pure components are tabulated, and for undefined chemicals are

determined from correlations.

By convention liquid compositions (mole fractions) are indicated with an x and gascompositions with a y .

Thus

liquid n n

n x

+= 211

1 (Eq. 6)


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Figure 22 - Phase diagrams of a binary mixture.

At a fixed pressure P a , the two vapor pressures are intersected at their correspondingsaturation temperatures vv T T 21 , .

The right side of this Figure shows a temperature composition projection at the selectedpressure P a . The state of all mixture combinations between [1] and [2] at P = P a aredepicted in this figure.

Supercritical Components

Up to this point, we selected pressures and temperatures such that we could intersect thevapor pressures of both components. However, there are temperatures and pressures atwhich one or both pure components are supercritical (single phase) while certain mixturesmay exhibit VLE.

Figure 23 shows three different temperature projections in the composition space.


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(Left) (Right)

Ta T b Tg

Temperature x1, y 1

Ta

T b

Tg

[1]

[2]

P1

P2v

Figure 23 - Phase diagram of a binary mixture, pressure vs. composition.

Note that at T g both components are supercritical. However, there may be a region of two-phase equilibria. Similarly, in Figure 24, we have three different pressure projections that

indicate the same features.

(Left) (Right)

Pa

P b

Pg

Temperature x1, y1

P r e s s u r e

Pa

P b

Pg

T2v

T1v

T1v

T2v

T e m p e r a t u r e


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Figure 24 - Phase diagram of a binary mixture, temperature vs. composition.

Depletion Path

All diagrams up to this point indicate the vapor and liquid composition in the same axis.Next, we will identify three different compositions, of the same component (please note; thedifference between composition and component!) in the same diagram.

z 1 = overall mole fraction of [1]y 1 = vapor mole fraction of [1]

x 1 = liquid mole fraction of [1]

Figure 25 illustrates an isothermal reservoir depletion process for a reservoir oil with twocomponents.

(Left) (Right)

Temperature

r e s s u r e

PD

PB

T = T a

Ta

CP Mz1 = fixed

z1

P r e s

s u r e

y1x1 10

AB

C


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Figure 25 - Isothermal reservoir depletion process for a reservoir oil with two components.

At pressure A, the reservoir fluid is undersaturated , at single phase above the BubblePoint pressure and has a composition z 1 . As production occurs, pressure drops to point B.

At this location, the fluid is at its bubble point, the reservoir fluid is said to be saturated . Aspressure continues to drop to point C, the original reservoir composition changes. Gasevolves from solution and this gas has a composition indicated by y 1 in the figure. The oilbecomes richer in heavy component and its composition is indicated by x 1.

The vapor mole fraction is read along the DEW curve, while the liquid mole fraction is readfrom the BUBBLE curve.

Relative amounts of [1] and [2] in the two-phase mixture are obtained from a mass balance.

Note that any overall mixture composition bounded by the horizontal line joining x 1 and y 1 has the SAME equilibrium compositions. What changes are the relative amounts of vaporand liquid.

This is indicated mathematically as:

v l f y f x z 111 += (Eq. 10)

v v f y f x z 111 )1( += (Eq. 11)

where f v is the molar fraction of vapor in the mixture. That is:

( ) ( )l v v

v n n n n

n n f

2121

21 )(+++

+= (Eq. 12)

Or


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11

1 1

x y

x z

f v

= (Eq. 13)

(Eq. 13) is valid for any number of components, and for all components. That is,

i i

i i v x y

x z f

= (i = 1, 2, 3, Nc) (Eq. 14)

Separator gas and separator oil are recombined to reconstruct the reservoir composition.When working in a recombination problem, the producing GOR is converted into a molarbasis and thus the reservoir composition can be found. This will be covered later.

Figure 26 shows VLE for a mixture using a temperature-composition projection. All theconcepts are equivalent to those indicated in Figure 25.

Any state in the two phase region requires pressure and temperature to be specified(Flash calculations). To obtain other physical properties such as: densities,compressibilities, and interfacial tensions the modeling equation used to predict VLE(usually a cubic EOS) is solved at the corresponding P , T and set of equilibrium vapor andliquid compositions. The flash type of calculations is the work-horse in any compositionalreservoir simulation package.

(Left) (Right)


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Temperature

P r e s s u r e TD

T B

P = P a

Pa

CPM

z1 = fixed

z1 y1x1 10

T B

TD

Ta

Ta

Figure 26 - Representation of a common distillation process (usually isobaric columns).

Figure 27 represents ALL possible states that a reservoir fluid with CONSTANT (or fixed)overall composition ( z i ) would exhibit at different pressures and temperatures. Asproduction takes place, when the average reservoir pressure is the bubble point pressurethere will be compositional changes.

Reservoirs with a gas-cap can be illustrated as. Intersecting two phase diagrams for fluidsof different composition, intersecting at a given T res , P res .


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Pressure-Temperature DiagramMulti-Component System

R e s e r v o

i r P r e s s u r e

Reservoir Temperature

B u b b l e -

P o i n t

D e w -

P o i n t

60%

20% 0%

2-Phase

1-Phase 1-PhaseCP

1-Phase

Figure 27 - Pressure -Temperature diagram for a multicomponet mixture.

Figure 28 illustrates how compositional changes occur during production shifting the phaseenvelope towards a heavier oil.


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P r e s s u r e

Temperature

t1t2

t3

Time increasing

Figure 28 - Dynamic phase envelope of a reservoir fluid as production takes place.

All diagrams seen up to this point are projections of a three-dimensional diagram as canbee seen in the following figure.

Phase Behavior of Ternary Systems

A general classification of Reservoir Fluids in terms of compositional distribution ispresented in a ternary diagram.


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Figure 29 - General classification of reservoir fluids in terms of compositional distribution.


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Qualitative Representation of Phase Equilibria

Figure 31 represents the evolution of a mixture of methane (C 1), propane (C 3) and n-pentane (C 5) at a specific temperature, 160

oF, and at various pressures (remember thatone ternary diagram represents the equilibrium of the mixture at one pressure and one temperature). This figure represents actual data, and it has been redrawn from McCainsbook.

Following these ternary phase diagrams at the same temperature (160 oF) and at differentpressures, you can visualize typical phase behavior changes in the mixture as the pressurechanges.


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nC 5 C 3

C1

Gas

p=14.7 psia nC 5 C3

C 1

G a s

2-phase

Liquid

p=200 psia

C3

C 1

nC5

G a s

2-phase

Liquid

p=380 psia nC 5

C 1

C3

G a s

2-phase

Liquid

p=500 psia

C1

G a s

2-phase

Liquid

C 3nC 5 p=1040 psia

C 1

G a s

2-phase

Liquid

C3nC5 p=1500 psia

G a s

2-phase

Liquid

C 1

C3nC5

G a s

p=2000 psianC5 C3

C 1

Liquid

p=2350 psia

Figure 31 - Evolution of a mixture of methane (C 1), propane (C 3) and n-pentane (C 5) at160 oF and at various pressures.


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Dilution lines

When representing phase behavior relations in a ternary diagram, the compositions of ALL

possible mixtures from mixing two fluids will fall in the straight line connecting the pointsindicating the compositions of the two source fluids. For example, ALL mixtures of n-C 4and bubble point fluid X in the figure are miscible in all proportions, while mixtures of X withC 1 are miscible at high concentrations of C 1 .

. 9

. 8

. 7

. 6

. 5

. 4

. 3

. 2

. 1

. 1

. 2

. 3

. 4

. 5

. 6

. 7

. 8

. 9

1 . 1 . 2 . 3 . 4 . 5 . 6 . 7 . 8 . 9 0

0 1

C 1

C 1 0 n - C 4

x

Figure 32 - Dilution lines example.

Quantitative Representation of Phase Equilibria

Tie (or equilibrium) lines

Tie lines join equilibrium conditions of the gas and liquid at a given pressure andtemperature.

Dew point curve gives the gas composition.


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Bubble point curve gives the liquid composition.

Hints: B.P. richer in the heavier component.

D.P. richer in the lighter component.

All mixtures whose overall composition (z i) is along a tie line have the SAME equilibriumgas (y i) and liquid composition (x i), but the relative amounts on a molar basis of gas andliquid (f v and f l) change linearly (0 vapor at B.P., 1 liquid at B.P.).

Relative amounts of gas are,

molesof numbertotalvaporof molesof number==

t

v v n

n f (Eq. 15)

in other words,

321

321

t t t

v v v v n n n

n n n f ++ ++=

(Eq. 16)

where,

vi l i ti n n n += with i=1, 2, 3 (Eq. 17)

v i l i i f y f x z += (Eq. 18)

or


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v i v i i f y f x z += )1( (Eq. 19)

thus,

linetieof lengthncompositiogastoncompositiooverallfromlength=

=

i i

i i v x y

y z f (Eq. 20)

This is also known as the Lever Rule , and f v can be determined graphically as well.

.9

.8

.7

.6

.5

.4

.3

.2

.1

.1

.2

.3

.4

.5

.6

.7

.8

.9

1.1 .2 .3 .4 .5 .6 .7 .8 .90

01

C1

C10 n-C 4

CP

Figure 33 - A ternary phase diagram illustrating the phase envelope and tie lines.


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Uses of Ternary Diagrams - Representation of Multi-Component Phase Behavior with a Pseudoternary Diagram

Ternary diagrams may approximate phase behavior of multi-component mixtures bygrouping them into 3 pseudocomponents . A frequent way of grouping differentcomponents of a mixture based on similarities of critical and other physical properties is,

light (C 1, CO 2, N2- C 1, CO 2-C2, ...)

heavy (C 7+)

intermediate (C2

-C6

)

The representation of the phase behavior of a solvent/reservoir fluid mixture bypseudocomponents is a highly useful tool for the conceptual understanding of miscibleprocesses where a solvent is injected in the reservoir and gets mixed with the reservoirfluid.

For computational purposes using EOS (Equation of States) a set of critical properties

must be assigned to pseudocomponents. These are usually characterized in terms of theirnormal boiling point, molecular weight and/ or density at standard conditions. Severalcorrelations are available to characterize these fractions.

The following pictures show the relationship among these properties according to Katz andFiroozabadi.


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Physical Properties of Alkanes

0

400

800

1200

1600

0 200 400 600 800 1000 1200 1400Tb (F)

T c ,

P c

0

0.5

1

1.5

2

2.5

A c e n

t r i c F a c

t o r

Tc /FPc (psia)w

Figure 35 - Katz and Firozaabadis relationship among normal boiling point, criticalpressure, critical temperature, and acentric factor for alkanes.

First Contact Miscible Recovery Processes (FCM)

The simplest and most direct method for achieving miscible displacement is to inject asolvent that mixes completely with the reservoir oil in all proportions, such that all mixturesare in single phase. Some examples are: intermediate molecular weight hydrocarbon C 3-

C4 or mixtures of LPG.


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.9

.8

.7

.6

.5

.4

.3

.2

.1

.1

.2

.3

.4

.5

.6

.7

.8

.9

1.1 .2 .3 .4 .5 .6 .7 .8 .90

01

C1

C2-C6C7+

A

O

Figure 36 - Example of a First Contact Miscible recovery process (FCM).

Reservoir oil with composition "O" could be diluted with methane up to concentration "A"and still achieve FCM.

Exercise

Find overall composition of mixture made with 100 moles oil "O" + 10 moles of mixture"A".

________________________________________________

________________________________________________

________________________________________________ ________________________________________________

________________________________________________


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.9

.8

.7

.6

.5

.4

.3

.2

.1

.1

.2

.3

.4

.5

.6

.7

.8

.9

1.1 .2 .3 .4 .5 .6 .7 .8 .90

01

C1

C2-C6C7+

A

O

Figure 37 - Ternary diagram for FCM exercise.

For first contact miscibility to be achieved between solvent and oil, the displacementpressure must be above the cricondenbar (CB) pressure of all possible combinationsbetween injected solvent and reservoir oil at the selected temperature. This guaranties thatall solvent/oil mixtures above this pressure are single phase.

As the concentration of methane in the injection fluid increases (moving above point A inFigure 36), the CB increases and will not have FCM. However, dynamic miscibility can beachieved by multiple-contact-mechanisms (MCM)

(1) condensing-gas drive

(2) or vaporizing gas drive(3) condensing-vaporizing gas drive (most likely)

Problems associated with FCM:


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Intermediate molecular weight hydrocarbon solvents for fixed contact FMC may precipitatesome of the asphalt from asphaltic crudes. Severe asphalt precipitation may reducepermeability and effect well injectivities and productivities. It may also cause plugging inproducing wells.

Pressure and temperature changes and/or the addition of intermediate molecular weighthydrocarbons or CO 2 to some reservoir fluids may cause multiple phases to form. Some

of these phases are,

Solid precipitation of asphaltenes and/or waxes (supersaturation achieved due to P,T, or composition changes).

Two or more liquid phases (i.e. Hydrocarbon-rich, CO 2-rich)

Gas-liquid -solid-liquid phases.

In the past, LPG solvents that are FCM have been too expensive to inject continuously.Instead solvent was injected in a limited volume, or slug, and the slug was displacedmiscible with a less expensive fluid such as natural gas or flue gas.

SolventSlug

FlueGas

Oil

Figure 38 - Compositional grading.

Ideally with such a process scheme, solvent miscible displaces oil while drive gas miscibledisplaces the solvent, propelling the small solvent slug through the reservoir.

Miscibility between solvent and driving gas normally determines the minimum pressurerequired for miscible displacement in the FCM slug process with LPG solvents.


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As solvent slug travels through the reservoir, at mixes with oil at the leading edge and withthe drive gas at the trailing edge.

When it reaches the two phases no further displacement miscibility is lost.


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Practice Ternary Diagrams

Exercises from this module will be based on these diagrams.

Pressure Effect

The following ternary diagrams illustrate the effect of pressure on the phase equilibria. Alldiagrams have been calculated using an EOS. The temperature is fixed in all of them(T=180 F), but p varies from 14.7 to 4000 psia.

T=180FP=14.7 psia

Pressure Effect

O

Figure 39 -


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T=180FP=200 psia

C1-C3-C10

Pressure Effect

O

Figure 40 -

T=180F

P=400 psia

Pressure Effect

O

Figure 41 -


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T=180FP=600 psia

Pressure Effect

O

Figure 42 -


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T=180FP=1000 psia

Pressure Effect

O

Figure 43 -

T=180FP=1500 psia

Pressure Effect

O

Figure 44 -


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T=180FP=2000 psia

Pressure Effect

O

Figure 45 -

T=180F

P=3000 psia

Pressure Effect

O

Figure 46 -


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T=180FP=4000 psia

Pressure Effect

O

Figure 47 -


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Temperature Effect

The following ternary diagrams illustrate the effect of temperature on the phase equilibria. All diagrams have been calculated using an EOS. The pressure is fixed in all of them(p=2000 psia), but T varies from 100 to 450 F.

T=100FP=2000 psia

Temperature Effect

O

Figure 48 -


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T=150FP=2000 psia

Temperature Effect

O

Figure 49 -

T=200FP=2000 psia

Temperature Effect

O

Figure 50 -


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T=300FP=2000 psia

Temperature Effect

O

Figure 51 -

T=350FP=2000 psia

Temperature Effect

O

Figure 52 -


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T=400FP=2000 psia

Temperature Effect

O

Figure 53 -

T=450FP=2000 psia

Temperature Effect

O

Documents

Module 3 - Phase Behavior and Fluid Properties