thermodynamics 1

Phase Behavior Fundamentals & Review of Thermodynamics - Colombia – Summer 2000

Author: Dr. Maria Barrufet - Summer, 2000 /69

Instructional Objectives After seeing this module the student should be able to:

• Classify reservoir fluid using PVT and production data.

• Understand the differences and limitations among standard PVT tests (CCE,DL, etc.)

• Establish the difference between a black oil and compositional model.

• Select the appropriate fluid model based upon fluid characteristics and production data.

• Represent quantitatively phase behavior dependence on compositions using phase diagrams.

• Understand pure component phase behavior as a function of Pressure, Temperature, and molecular size.

– Phase Behavior Fundamentals and Review of Thermodynamics Concepts and Definitions. Oil and Gas Properties. Hydrocarbon Phase Behavior. Classification of reservoir fluids based on phase diagrams and PVT and production data. Standard PVT tests: Differential Liberation, Constant Composition Expansion, Separator Tests. Volumetric and phase behavior of pure substances, binary and multicomponent systems. Phase diagrams (P-V, P-T, P-x, y-x). Ternary Diagrams. Phase Equilibria Representation. Suggested reading: MAB, McCain



• 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.

• Represent miscible displacement processes using ternary diagrams.

• Sketch a miscible gas injection using a ternary diagram.



Concepts & Definitions

Phase behavior is the study of changes of the intensive properties of fluids (either single component or mixtures) as a function of changes in pressure, temperature and compositions. These properties include:

• Phase density (liquid, gas, solid)

• Compressibility

• Surface tension

• Viscosity (with help from Transport Models)

• Heat capacity

We will concentrate in property and phase changes of Hydrocarbon Species and fluids used for EOR purposes.

The main applications of phase behavior studies include:

• To assist in strategies for efficient oil and gas production,

• To support enhanced oil recovery processes by miscible gas injection and by thermal processes, and

• To help in the design and operation of surface facilities, multiphase pumps, etc.

Definitions Before beginning this course we must become familiar with certain definitions.

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



• Closed System: Does not exchange matter with surroundings but may exchange energy (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). Examples:

Gas reservoir, oil above the saturation pressure (bubble point

pressure).

Density increases gradually as pressure increases and vice-versa.

• Heterogeneous System: System made up of two or more phases in which the intensive properties change abruptly at phase-contact surfaces. Examples:

System including oil and a gas cap.

Density changes abruptly at the interface (gas-oil contact).

Fluids within a separator (gas-liquid). Emulsions.

Phase: A portion of the system which has homogeneous intensive properties and it is bounded by a physical surface. Homogeneous means that it is possible to move from one point to another within that region without detecting a discontinuous change in a property. An abrupt change in a property is observed when an interface is crossed. An interface separates two or more phases. These phases are solid, liquid(s), and gas. A phase can be a system by itself since the selection of a system is arbitrary. Examples:

Reservoir brine, gas cap, oil reservoir above bubble point.

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

Extensive Properties: Depend upon system's mass. Additive. Examples:

Caloric content (BTU value), saturations (oil, gas, water).

Intensive Properties: Independent of system's mass. Cannot be added. Examples:

Caloric content per unit mass (BTU/lbm), density, compressibility,

viscosity, composition, pressure, temperature.

Component: A molecular species – defined or hypothetical. Reservoir fluids contain many components, and we are commonly forced to combine several components into hypothetical or pseudo-components, to simplify phase behavior representations and subsequent calculations.

Defined: Cl, C2, H2O

Hypothetical: C7+

State: Condition of a system at a particular time determined when all intensive properties are fixed.

Equilibrium State: When all intensive properties remain unchanged with time. In thermodynamics it is taken to mean not only the absence of change but the absence of any tendency toward change on a macroscopic scale. At equilibrium, there are not driving forces:

Mechanical driving force = 0 ! Pressure is constant

Thermal driving force = 0 ! Temperature is constant

Chemical driving force = 0 ! Chemical potential of each species ‘i’ is constant

Non-Equilibrium State: Properties change with time. Can be modeled as a sequence of equilibrium states.



Phase Behavior Diagrams: These diagrams are called phase envelopes. The dew point curve and the bubble point curve converge at the mixture critical point.

Process: Any change of a system is called a thermodynamic process which may occur with no restrictions or under arbitrarily prescribed conditions ( i.e. T constant, P constant, V constant)

Mathematical Concepts The following is a list of the mathematical concepts required for this course.

Variables: Understand the difference between dependent and independent variables. Many times these can be interchanged, and they are to facilitate computations.

“Space” Coordinates: Here we will not deal with space coordinates but the axes will be: P, V, T, and the composition of a selected component (pseudocomponent).

Graphical and Analytical Tools Required

• 3-D plots, 2-D projections i.e Pressure versus Tempearture at fixed composition.

• Slopes (analytical, numerical & graphical)

• Differentials (analytical & numerical)

• Partial Derivatives (numerical & analytical)

• Integration

• Solution of non linear equations

• Root finding routines

• A great deal of abstraction



Oil and Gas Properties Petroleum reservoir fluids are made up of mainly hydrocarbon components, and in lesser proportion some non-hydrocarbon components such as CO2, N2, and sulfur compounds. Water is also present in oil and gas reservoirs, although most of the time the effect of water upon the physical properties of the hydrocarbons can be neglected since water and oil may be considered nearly immiscible at the pressures and temperatures found normally in reservoirs. This is not the case at the high temperatures used in steam injection processes to recover heavy oil, therefore a small portion of this course will cover the concepts of water-hydrocarbon phase equilibrium.

The phase behavior of reservoir fluids at surface and at reservoir conditions is determined primarily by their chemical composition, pressure, and temperature. Phase behavior and phase properties are indispensable for the development and managing of any reservoir and affect all aspects of petroleum production, exploration, and of processing.

Although reservoir fluids are composed of many different compounds, sometimes impossible to determine quantitatively, the fundamentals of phase behavior can be explained by describing the behavior of single, binary and ternary systems.

To model the behavior of multicomponent hydrocarbon mixtures we need to characterize the oil using a limited number of components. The success of a phase behavior match depends on the characterization procedure used.

The overall objectives of this course are to understand and to be able to predict the phase behavior and fluid phase properties using a variety of methods, mainly equations of state (EOS). This requires a sequence of steps which will be covered along the



course, beginning with pure substances and extending to binary and multicomponent systems.

Crude oil is always associated with gas under any condition in the production system.

The pressure-volume behavior of oil is intimately affected by the type and amount of gas in solution.

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

Location Pressure (psia) Temperature (oF)

Reservoir 500-10,000 100-300

Separator 100-600 75-150

Stock tank 14.7 Ambient

Standard Conditions 14.7 60

Table 1 - Some pressure & temperature ranges.

The oil and gas properties of interest to reservoir engineers from a Black Oil model perspective are:

• oil formation volume factor (Bo),

• gas formation factor (Bg),

• total formation volume factor (Bt),

• solution gas-oil ratio (Rs)

• oil and gas viscosities (µo, µg)

• compressibility and thermal expansion coefficients.



From a compositional perspective these properties are replaced as shown in Figure 1.

Black Oil Model Compositional Model

BoBg,RsBtµo µg.....

ρρρρo, xi (i = 1, 2...Nc)ρρρρg, yi (i = 1, 2...Nc) ρρρρm, zi (i = 1, 2...Nc) µo µg...

Figure 1 - Properties in Black Oil and Compositional models.

Viscosities, compressibilities, and thermal expansions are also used in compositional formulations, but they are evaluated from a compositional model.

The sketch in Figure 2 indicates the behavior of volumetric properties, as expressed in a black oil formulation, with pressure and temperature.



Sepa

rato

r gas

gas gas

Decreasing Pressure

Sepa

rato

r gas

Sepa

rato

r gas

gas

StandardConditions Se

para

tor g

as

Sepa

rato

r gas

oiloil oiloil

oil

STB

STBSTB STB

StandardConditions

Bg =

Rv =

Bo= Rs=

P2 P1

P4 P3 Reservoir

Definition of Oil & Gas PVT Properties

Figure 2 - Definition of oil and gas PVT properties based on their volumetric behavior.

Classification of Reservoirs Based Upon Production and PVT Data Before we use a certain fluid model (compositional or black oil). We should have some guidelines about the type of reservoir fluid we are dealing with: volatile oil, black oil, gas-condensate etc. Some 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

C7+ 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

C7+ composition > 12.5%

GAS CONDENSATE RESERVOIRS:

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

Density greater than 60° API

Light in color

C7+ 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

PVT Properties for Reservoir Engineering

Gas Formation Volume Factor By definition the gas formation volume factor is the ratio of the volume of gas at reservoir conditions (Tres,Pres) required to produce one cubic feet at standard conditions.

The standard conditions are defined as,

T=520oR and P=14.65 psia.

Its main use is for converting reservoir gas volume to surface gas volume, and vice versa. The mathematical expression is:

Pressure & eTemperatur Standardat mass same by the Occupied VolumePressure & eTemperaturreservoir at gas of massgiven aby Occupied Volume=Bg

SC

Rg V

VB ==== (1)

… mathematically using the real gas EOS …



SC

SCSC

PnRTZP

ZnRT

Bg = (2)

Replacing values for the standard pressure and temperature and considering that the compressibility factor at standard conditions is essentially equal to one we have:

=

SCFRCF

7.380 PZRTBg (3)

This property is expressed in terms of the gas compressibility factor (Z) as follows

where SCF = standard cubic feet & RCF = reservoir cubic feet

Other common units for the gas formation volume factor are (reservoir barrels / standard cubic feet). In that case:

====

SCFRB00502.0

PZRTBg (4)

The key is how to determine the compressibility factor “Z” for the gas in question, at different pressures, & at different temperatures and gas compositions.

The general shape of a Z factor chart is



T r

P r

Z

1

Figure 3 - Compressibility factor shape.

Only one compressibility factor chart can be used to determine volumetric properties for any pure hydrocarbon fluid and mixtures. That is accomplished by using the corresponding states principle and reduced properties (Pr & Tr)

Isothermal Compressibility

dPdV

VC g

gg

1−−−−==== (5)

Numerically can be evaluated as …

(((( ))))(((( ))))211

21

PPBBB

Cg

ggg −−−−

−−−−−−−−==== (6)

The units for isothermal compressibility are: psia-1

The following figures show the typical behavior of reservoir engineering properties such as Bo, Rs, Bg, Co, etc. with pressure. The student should review these properties and their definitions from McCain book.



Oil Formation Volume Factor

Pressure

Pb

Bt

Bo

Bt=B

o

Bt,

Bo

Figure 4 - Oil formation volume factor.

The phase behavior of reservoir fluids (oil and gas) is determined from a laboratory analysis of a reservoir fluid sample. The pressure-volume-temperature relationship can be used to evaluate the reservoir oil behavior under different pressure and temperature conditions. It can also be used to classify the type of reservoir and the reservoir fluid.

Gas Formation Volume Factor

Bg

Pressure

Figure 5 - Gas formation volume factor.



Oil Viscosity

Vis

cosi

ty

Pressure

Pb

Figure 6 - Oil viscosity.

Gas Solubility

Gas

in S

olut

ion

PressurePb

Figure 7 - Gas solubility.



Isothermal CompressibilitySp

ecifi

c V

olum

e

Pressure

T

∆V

∆P

Phas

e Bou

ndary

Figure 8 - Isothermal compressibility.



Thermal ExpansionSp

ecifi

c V

olum

e

Temperature

DV

∆Τ

P

Figure 9 - Thermal expansion.

Laboratory PVT Experiments There are three gas-oil separation models used in measuring the oil and gas behavior under different pressures and temperatures. These are:

• flash vaporization or constant composition expansion tests

• differential separation (liberation) tests

• separator tests

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 reservoir temperature.



The following figure shows the flash separation process in which the temperature of the test equals the reservoir temperature.

Vt1 Vt2V

t3=V

bV t5

Vt4oil oil oil oil

oil

gas gas

Hg Hg Hg HgHg

P1 >> Pb P2 > Pb P3 = Pb P4 < Pb P5 < P4

1 2 3 4 5

Flash Separation (Liberation)Flash Vaporization

Figure 10 - Flash vaporization PVT analysis.

This test is used to determine bubble point pressures by intersecting the lines representing volume variations in the liquid and two phase regions.

This test is used to determine relative oil volumes as well.



Pres

sure

Pb

Volume

Vb

Figure 11 - Bubble point determination.

DIFFERENTIAL SEPARATION

The differential separation is a gas-oil separation process in which the gas separated at one stage is removed before the remaining oil is subjected to the next stage of separation. The separation process is conducted at the reservoir temperature and pressure except the last stage which is conducted at standard conditions (P = 14.7 psia, T = 60oF).

The following figure illustrates the differential liberation process:



gas

oil

oil oil oil

oil

gas

Hg

Hg

Hg Hg

Hg

P1 = Pb P2 < Pb P2 < Pb P2 < Pb P3 < P2 < Pb

1 2 3 4 5

Differential Separation (Liberation)

gasoil

Gas off

Figure 12 - Differential liberation process.

These tests are used to determine formation volume factors and solution gas oil ratios.

Equations of state are usually calibrated to these data.

SEPARATOR TESTS

The separator separation process is essentially a two-step gas-oil separation process. The bubble point oil is flashed through a separator and stored at the stock tank condition. The purpose of this separation test is to obtain data for converting the flash and differential separation data to stock tank oil basis.

The following figure illustrates the separator process:



OilGas

Separator-Separation

Oil

Reservoir

PbTres

Separator

Standard Conditions

VSTO

PseparatorTseparator

Stock tank oil

Figure 13 - Separator tests.

Other oil properties of interest are oil compressibility, thermal expansion, and viscosity. These oil properties can either be determined from laboratory tests or from available correlations.



Production System

WaterKnockout Separator

Gas Sales

Stock Tank

Oil Sales

Water

Well Head

ReservoirLab Tests

Figure 14 - Production system representation.

Applications of Fluid Analysis Data The use of these properties in Reservoir Engineering Calculations include:

• Volumetric

• Volume Balance - Black Oil

• 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



Hydrocarbon Phase Behavior Except polymer flooding, all of EOR methods rely on the phase behavior of reservoir fluids and 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 be used through the reminder of the course.

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

We need to quantify the real oil and gas volumes under various pressures and temperatures. 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 primary variables: pressure and temperature.

The major characteristics of each method are:

Compositional Model

• Oil and gas are mixtures of several components

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

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



Black Oil Model The black oil model can be considered a special case of a compositional model with the restriction that:

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

• The G component may be dissolved in the oil phase and this is taken into account through the solution gas oil ratio (Rs). However the oil component (O), cannot dissolve in the gas phase.

• 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 path from the reservoir to the surface, and to classify reservoir fluids according to the location of its critical temperature with respect to the reservoir temperature.

The phase behavior of crude oil, water, and EOR fluids is a common ground for understanding the displacement mechanisms of EOR processes. This behavior includes the two or more phases formed in crude oil – miscible solvent injection processes, the gas–oil–water phases of steam flooding, and the two – and three – phase behavior of surfactant–brine–oil systems.

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

Figure 15 is a sketch of a typical phase diagram for a reservoir fluid.



Critical

Cricondenbar

Cricondentherm

Bubblepoint Curve

Dew Point Curve

QualityLines

Temperature

Pres

sure 75%

50%

25%

Figure 15- Characteristic phase envelope.

The description of this diagram is indicated in Table 2.

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.

Table 2 - Description of a typical phase diagram.



Classification of reservoirs based on phase diagram 1. Gas Reservoirs (Single Phase):

• Dry Gas (see Figure 16), and

• Wet Gas (see Figure 17).

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

• Retrograde or Condensate Gases (see Figure 18).

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

• Volatile Oil (see Figure 19), and

• Black Oil (see Figure 20).

Temperature

Pres

sure

Path of Production

Initial Reservoir Conditions

Separator Conditions

CP

Figure 16 - Phase diagram of a dry gas reservoir.



Temperature

Pres

sure

Path of Production



CP

Figure 17 - Phase diagram of a wet gas reservoir.

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



Temperature

Pres

sure


CP

Path of Production


Temperature

Pres

sure


CP

Path of Production


Temperature

Pres

sure


CP

Path of Production


Figure 18 - Phase diagram of a retrograde gas (condensate) reservoir.

Temperature

Pres

sure


CP

Path of Production


75%

50%25%

Figure 19 - Phase diagram of volatile oil reservoir.



Temperature

Pres

sure


CPPath of Production


25%50%75%

Figure 20 - 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 of phase envelopes in which the critical points of the mixtures have the following trend:

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

• Critical Temperatures increase from dry gas to black oil systems.

The concentration of C1 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 the same components but with different proportions.



0

1000

2000

3000

4000

5000

6000

7000

Pres

sure

(psi

a)

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

Temperature o

F

Critical Points

Dry Gas

Wet Gas

Condensate

Volatile I

Black Oil

TR

Volatile I

Volatile II

Figure 21 - Calculated phase envelopes of different mixtures of the same hydrocarbon components at different proportions. (Barrufet, 1999b).

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



Component Black Oil Volatile Oil Gas Condensate Wet Gas Dry Gas

C1 48.83 64.36 87.07 95.85 86.67

C2 2.75 7.52 4.39 2.67 7.77

C3 1.93 4.74 2.29 0.34 2.95

C4 1.60 4.12 1.74 0.52 1.73

C5 1.15 3.97 0.83 0.08 0.88

C6 1.59 3.38 0.60 0.12

C7+ 42.15 11.91 3.80 0.42

MwC7+ 225 181 112 157

GOR 625 2000 18,200 105,000 -

Tank oAPI 34.3 50.1 60.8 54.7 -

Liquid

Color Greenish Black

Medium Orange

Light Straw

Water White

-

Table 3 - Typical compositions mole % of single-phase reservoir fluids

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

Reservoir fluids also contain other chemical species that may complicate the phase behavior even further. Table 3 provides a general guideline of reservoir fluid compositions, while Table 4 contains information about typical petroleum gases and heavy oil fractions.



Table 4 - Typical compositions of petroleum gases and heavy crude oil fractions.



Pressure versus temperature diagrams can be used to visualize the fluids production path from the reservoir to the surface, and to classify reservoir fluids according to the location of its critical temperature with respect to the reservoir temperature.

Based upon this classification one may decide to use a black oil model or a compositional model.

The following diagram indicates the region of applicability for a black oil model.

Figure 22 - Pressure Temperature diagram of a typical reservoir fluid and areas of application for a Black Oil model.



Pressure versus temperature diagrams are called phase envelopes. The dew point

curve and the bubble point curve converge at the mixture critical point.

The region of application for a compositional model is indicated in the following figure.

Compositional

Figure 23 - Pressure Temperature diagram of a typical reservoir fluid and areas of application for a Compositional model.



Compositional Effects on Phase Behavior To see the effect of compositions in the phase behavior we need to analyze single and binary systems. The diagrams seen so far do not show any compositional dependence.

Equations of state models are calibrated with properties of pure components and later generalized 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 mixture

composition ‘zi’.

Single Component

Pres

sure

Pc

Temperature Tc

Liquid (1 phase)

Vapor (1 phase)

Solid(1 phase)

Sublimation Curve (2 phases)

Triple Point (3 phases)

Vapor PressureCurve (2 phases)

CriticalPoint

Fusion Curve2 phases

Figure 24 - Pressure vs. Temperature diagram for a Single Component.



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

Vapor Pressure Curve

Pres

sure

Temperature

Vapor

Liquid

Critical Pointρl

ρv

Pc

Tc

Figure 25 - Vapor pressure curve for a single component.

Figure 25 illustrates the vapor pressure curve for a pure component. As the temperature increases the vapor pressure increases until the critical point. At temperatures higher than the critical temperature there is not a phase transition (from vapor to liquid and vice versa) at any pressure.

The state of the component at a P or/and T greater than its critical values is a “fluid” state and as pressure increases its density varies smoothly from low (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.

The phase envelope represents ALL possible states that a reservoir fluid with CONSTANT (or fixed) overall composition (zi) would exhibit at different pressures and temperatures. As production takes place, when the average reservoir pressure is the bubble point pressure there will be compositional changes.

Reservoirs with a gas-cap can be illustrated as. Intersecting two phase diagrams for fluids of different composition, intersecting at a given Tres,Pres.

The following diagram illustrates how compositional changes occur during production shifting the phase envelope towards a heavier oil, or gas injection shifting the envelope towards a lighter oil.



Temperature

t1

Composition Changes Due to Production

and Gas InjectionPr

essu

re

t3

t2

GasInjection

Production

Temperature

t1

Composition Changes Due to Production

and Gas InjectionPr

essu

re

t3

t2

GasInjection

Production

Figure 26 - Composition changes due to production and gas injection. Review from McCain (Petroleum Fluids,1990).

Some Characteristic Physical Properties for Pure Components The following graph indicates the behavior of the main fluid properties with pressure and temperature for hydrocarbon families such as alkanes (the main constituents of reservoir fluids.)



Figure 27 - Behavior of some molecules with temperature.

Typically gas and oil are both mixtures made up of alkanes which impart to them distinct physical properties (densities, viscosities, heat capacities, color, smell, etc.) Gases contain mainly C1 to C3, while oil includes higher hydrocarbon numbers, usually denoted as C7

+.

On a more elementary basis crude oils are made of … (Table from McCain)

Table 5 - Elemental analysis of typical crude oils.



Composition may be expressed on a weight basis and on a molar basis. The relationship between moles and mass is:

MwMn ==== (7)

where M is the mass expressed in grams or pounds and Mw is the molecular weight of the component which is tabulated.

For example one kilogram of water is equivalent to

=−

=mollblbm

lbmn/18

1 (8)

We cannot say that one pound of water contains the same amount of moles as a pound of gasoline (C8 mainly).

The following tables (taken from McCain book) contain physical property data for pure substances.



Heat Effects Accompanying Phase Changes of Pure Substances

When a pure substance is isobarically liquefied from the solid state or vaporized from the liquid state, there is no change in temperature but there is a definite transfer of heat from the surroundings to the substance. These heat effects are the latent heats of fusion for the solid-liquid transition and the latent heat of vaporization for the liquid-vapor transition.

The characteristic feature of such processes is the coexistence of two phases; therefore the state of the system is determined from the specification of just one intensive property. That is, if pressure is given and we know that 2 phases coexist there is a unique corresponding temperature at which this may happen. The (P, T) pair defines the saturation point and belong to the vapor pressure line.

The fundamental relationship between the latent heat accompanying the phase change and PVT data for the system is provided by the Clapeyron equation.

∆H vap = T∆V dPsat

dT (9)

Where

∆V = Vv - Vl at (Psat, Tsat) [=] ft3/lbmol or cm3/g-mol

∆Hvap = latent heat of vaporization [=] BTU/lbmol or cal/g-mol.

dP sat/dT = rate of change of the vapor pressure with temperature (slope).



Thus latent heats of vaporization can be calculated from vapor pressure and volumetric data.

For vaporization processes at low pressures one may introduce a reasonable approximation into the Clapeyron equation by assuming that the gas phase is an ideal gas and that the molar volume of the liquid phase is negligible compared to the vapor (or gas) volume. In that case:

∆V ≈ V v = RTP (10)

And the Clapeyron equation becomes:

dPsat

dT = ∆H vap

RT 2 Psat

(11)

This approximate equation is known as the Clausius-Clapeyron equation.

Integration of Equation (11) assuming that the heat of vaporization is temperature independent gives:

ln (Psat ) = A - B

T (12)

This equation is useful for many purposes, but not sufficiently precise. The Antoine equation, is more widely used and it has the form:



ln (Psat ) = A - BC + T (13)

Where A, B, and C are constants specific for each component (i.e propane, cycloheptane, benzene etc.)

An even more accurate equation is the Riedel equation (obviously, with more parameters):

6lnln FTTDTBAP sat ++−= (14)

Two-Phase Properties (Single Component) Properties of mixtures of the two phases are related to the property of each phase and the amount of that phase. Let f be the mole fraction of the gas phase (usually called quality).

f = ngng + nl (15)

Then for a given saturation point provided by the coordinate pair (P sat, T sat):

V = f Vg + (1 - f )Vl @ P sat, T sat (16)

Vapor pressures can also be read from the COX charts in the following figures.



Notice that the temperature scale in the horizontal coordinate in neither linear nor logarithmic. Made up such that, curves are essentially straight.



Figure 28 - Vapor pressures of normal paraffins. (From Handbook of Natural Gas Engineering by Katz et al.)



Figure 29 - Vapor pressures of isomeric paraffins. (From Handbook of Natural Gas Engineering by Katz et al.)



Density (mass/volume) is the inverse of specific volume (volume/mass). To see the variation of density (or specific volume) with pressure and temperature another phase diagram must be used. This is the pressure-specific volume diagram.

For a pure substance this looks like:

Tc

2-phase

T

Specific Volume (ft3/lbm)

Pres

sure

(psi

a)

VvVL

CP

Figure 30 - Pressure-specific volume diagram for a pure substance.

• The CP is the highest temperature and pressure at which a vapor an a liquid 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 liquid compressibilities.



Phase Behavior of Single and Binary Systems

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

Temperature x1, y1

Pres

sure

P1v

P2vP2v

P1v

T = Ta

Ta

CP1

CP2

Bubble Curve

Dew Curve2-phases

Liquid

Vapor

Left Right

Figure 31 - Vapor pressure curves (left) and (Px)T diagram (right).

The left side of Figure 31 illustrates two vapor pressure curves for component [1] and

[2]. At Ta, the vapor pressures are vv PP 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:

C2 (ethane) Tc = 89.92 oF Pc = 706.5 psia

C10 (decane) Tc = 652.0 oF Pc = 305.2 psia



The right hand side of Figure 31 illustrates the phase behavior of all possible mixtures between [1] and [2] at the selected temperature Ta.

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), and the dew pressures (below) as a function of composition at T = Ta..

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

Hydrocarbon Composition May be expressed on a weight basis and on a molar basis. For compositional modeling we use a molar basis. The relationship between moles and mass is given through the molecular weight.

i""component ofweight Molecular i""component of Mass i""component of Moles = (17)

i

ii Mw

Mn ==== (18)

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 gas compositions with a y.

Thus

liquidnnnx

++++

====21

11 (19)

gasnnny

++++

====21

11 (20)

And

121 ====++++ xx (21)

121 ====++++ yy (22)

The left side of Figure 32 illustrates the two vapor pressures of components [1] and [2] and two phase envelopes (shaded lines) that result from two different mixtures of components [1] and [2]. Each phase envelope has a constant overall composition. The envelope closer to component [1] represents a higher concentration of that component.



Temperature x1, y1

Pres

sure

T1v

T2v

T2vT1v

P = Pa

Pa

CP1

CP2

Bubble Curve

Dew Curve

2-phases

Liquid

Vapor

Left Right

Figure 32 - Vapor pressure curves (left) and (Tx)P diagram (right).

At a fixed pressure Pa, the two vapor pressures are intersected at their corresponding

saturation temperatures vv TT 21 , .

The right side of Figure 32 shows a temperature composition projection at the selected pressure Pa. The state of all mixture combinations between [1] and [2] at P = Pa are depicted in this figure.

Supercritical Components Up to this point we selected pressures and temperatures such that we could intersect the vapor pressures of both components. However, there are temperatures and pressures at which one or both pure components are supercritical (single phase) while certain mixtures may exhibit VLE.

Figure 33 shows three different temperature projections in the composition space.



Ta Tb Tg

Temperature x1, y1

Ta

Tb

Tg

[1]

[2]

P1

P2v

Left Right

Figure 33 - Vapor pressures (left) and (Px)T diagram (right) showing supercritical behavior.

Note that at Tg both components are supercritical. But there may be a region of two-phase equilibria.

Similarly, in the following figure, we have three different pressure projections that indicate the same features.



Pa

Pb

Pg

Temperature x1, y1

Pres

sur e

Pa

Pb

Pg

T2v

T1v

T1v

T2v

Tem

pera

ture

Left Right

Figure 34 - Vapor pressures (left) and (Tx)P diagram (right) showing supercritical behavior.

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 in the same diagram.

z1 = overall mole fraction of [1]

y1 = vapor mole fraction of [1]

x1 = liquid mole fraction of [1]

Figure 35 illustrates an isothermal reservoir depletion process for a reservoir oil with two components.

At pressure A, the reservoir fluid is undersaturated, at single phase above the Bubble Point pressure and has a composition z1. 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. As pressure continues to drop to point C, the original reservoir composition changes. Gas evolves from solution and this gas has a composition indicated by ‘y1’ in the figure. The oil becomes richer in heavy component and its composition is indicated by ‘x1’.

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

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

Temperature

Pres

sure

PD

PB

T = Ta

Ta

CPMz1 = fixed

z1

Pres

sure

y1x1 10

AB

C

Left Right

Figure 35 - Depletion path for a hypothetical 2 component reservoir fluid.

Note that any overall mixture composition bounded by the horizontal line joining x1 and y1 has the SAME equilibrium compositions. What changes are the relative amounts of vapor and liquid.

This is indicated mathematically as:



vl fyfxz 111 += (23)

vv fyfxz 111 )1( +−= (24)

where fv is the molar fraction of vapor in the mixture.

That is:

( ) ( )lv

vv nnnn

nnf

2121

21 )(+++

+= (25)

Or

11

1 1

xyxz

fv −−

= (26)

Equation (26) is valid for any number of components, and for all components. That is:

ii

iiv xy

xzf

−−

= (i = 1, 2, 3, … Nc) (27)

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 molar basis and thus the reservoir composition can be found. This will be covered later.



Figure 36 shows VLE for a mixture using a temperature-composition projection. All the concepts are equivalent to those indicated in the previous Figure.

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 and liquid compositions. The flash type of calculations is the work-horse in any compositional reservoir simulation package.

Temperature

Pres

sure TD

TB

P = Pa

Pa

CPM

z1 = fixed

z1 y1x1 10

TB

TD

Ta

Ta

Left Right

Figure 36 - Phase equilibrium compositions at Ta, Pc are x1 for the liquid and y1 for the gas.

This Figure represents a common distillation process (usually isobaric columns).



Ternary Diagrams

Review - Conventions

Each corner of a diagram represents 100% of a set component the opposite sites are 0% of that component.

Binary mixtures are represented on the sides of the triangular diagram, ternary mixtures (compositions) are represented within the triangle.

A 100% of the lightest component is drawn at the top, the intermediate is at the right, and the heavy is at the left

A ternary diagram has its pressure and temperature fixed (P,T).

.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

L

H I

Figure 37 - Ternary diagram of the H, I, and L components.



Qualitative Representation of Phase Equilibria

Figure 38 represents the evolution of a mixture of methane (C1), propane (C3) and n-pentane (C5) at a specific temperature, 160oF, and at various pressures (remember that one 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 McCain’s book.

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



nC5 C3

C1

Gas

p=14.7 psia nC5 C3

C1

Gas

2-phase

Liquid

p=200 psia

C3

C1

nC5

Gas

2-phase

Liquid

p=380 psia nC5

C1

C3

Gas

2-phase

Liquid

p=500 psia

C1

Gas

2-phase

LiquidC3nC5 p=1040 psia

C1

Gas

2-phase

LiquidC3nC5 p=1500 psia

Gas

2-phase

Liquid

C1

C3nC5

Gas

p=2000 psianC5 C3

C1

Liquid

p=2350 psia

Figure 38 - Evolution of a mixture of methane (C1), propane (C3) and n-pentane (C5) at 160oF and at various pressures.



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 points indicating the compositions of the two source fluids. For example, ALL mixtures of n-C4 and bubble point fluid X in the figure are miscible in all proportions, while mixtures of X with C1 are miscible at high concentrations of C1.

. 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 39 - 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 and temperature.

Dew point curve gives the gas composition.



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 (zi) is along a tie line have the SAME equilibrium gas (yi) and liquid composition (xi), but the relative amounts on a molar basis of gas and liquid (fv and fl) change linearly (0 – vapor at B.P., 1 – liquid at B.P.).

Relative amounts of gas are,

moles ofnumber totalvapor of moles ofnumber ========

t

vv n

nf (28)

in other words,

321

321

ttt

vvvv nnn

nnnf++++++++++++++++==== (29)

where,

viliti nnn ++++==== with i=1, 2, 3 (30)

vilii fyfxz ++++==== (31)



or

vivii fyfxz ++++−−−−==== )1( (32)

thus,

line tie of lengthncompositio gas to ncompositio overall from length====

−−−−−−−−====

ii

iiv xy

yzf (33)

This is also known as the Lever Rule, and fv 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-C4

CP

Figure 40 - A ternary phase diagram illustrating the phase envelope and tie lines.



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

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

• light (C1, CO2, N2- C1, CO2-C2, ...)

• heavy (C7+)

• intermediate (C2-C6)

The representation of the phase behavior of a solvent/reservoir fluid mixture by pseudocomponents is a highly useful tool for the conceptual understanding of miscible processes where a solvent is injected in the reservoir and gets mixed with the reservoir fluid.

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 their normal boiling point, molecular weight and/ or density at standard conditions. Several correlations are available to characterize these fractions.



Phase Behavior of Ternary Systems A general classification of Reservoir Fluids in terms of compositional distribution is presented in a ternary diagram.



Figure 41 - General classification of reservoir fluids in terms of compositional distribution.

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