Phase Behavior [Compatibility Mode]

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Properties of Reservoir FluidsPhase Behavior

Fall2010 Shahab Gerami1

Thermodynamic studies are generally focused on arbitrarily chosen systemswhile the restof theuniverse is assumedas surroundings.

System Boundary: the surface of the system - real or imaginary - is called aboundary.

A system is a region of space or quantity of matter we want to study.

System & Surrounding

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A systemis called a closed systemif it does not exchange matter with thesurroundings, in opposite to an open system which exchanges matter withthesurroundings. Both systems mayexchange energywith the surroundings.

Open system (or control volume)Closed system (or control mass)

Closed & Open Systems

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Closed System with Moving Boundary

Open System (Control Volume)Open System (Control Volume)

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The concept of a closed system is of major interest in applied hydrocarbonthermodynamics.

It is called a homogeneousclosed systemif it contains a single phase,e.g. a natural gas phase or anoil phase.A heterogeneousclosedsystemcontains more thanone phase.

Phase: a phase is defined as a physically homogeneous portion of matter.

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Phase

The phases of a heterogeneous system are separated by interfaces and areopticallydistinguishable.It is notobligatory thata phase is chemicallyhomogeneous. It mayconsists ofseveral compounds, e.g. ofa large number ofvarious hydrocarbons.

Property

A property is a characteristic of a system to which numerical values can beassigned to describe the system (Mass, Temperature, Pressure ,Density,...)

Property:

1. Extensive Property: Extensive properties are properties which can be

counted and their value for the whole system is the sum of the value forsubdivisions of the system.

They depend on the extentof the system. Examples: Volume, Mass

2. Intensive Property: Intensive properties are independent of the size (mass orvolume) of the system. Examples: Density, Temperature

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Property

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The state of a system is defined by the values of its properties.

A system is in equilibrium if its properties are not changing at any givenlocation in the system.

This is also known as thermodynamic equilibrium or total equilibrium.

Equilibrium implies balance--no unbalanced potentials (driving forces) in thesystem.

We will distinguish four different types of equilibrium

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State


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State and Equilibrium

Thermodynamics deals with equilibrium states

A system is in thermodynamic equilibrium if it maintains thermal, mechanical,phase, and chemical equilibrium.

1. Thermal equilibrium-- the temperature does notchangewith time2. Mechanical equilibrium-- Pressure does notchange with time3. Chemicalequilibrium-- molecularstructure does notchangewith time4. Phase equilibrium mass and composition of each phase is unchanging

with time (i.e., same liquid/gas or liquid/solidcomposition)

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State functions or state variables are those properties for which thechange instate onlydepends on the respective initial and final state.

It is this path-independent characteristic of the state functions that makes itpossibleto quantify any change ofa system.

P

V

1

2

Path 1

Path 2

Path 3

State Functions


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Equilibriumhas beendefined as a state of rest.

In an equilibrium state, no further change or - more precisely - no net-flux willtake place unless one ormore properties of thesystemare altered.

On theother side, a systemchanges until itreaches its equilibriumstate.

Any change of a system is called a thermodynamic interest in thethermodynamicstudyof the system:

adiabatic (no heataddedto or removedfromthesystem),isothermal (constanttemperature),isobaric (constantpressure),isochoric (constantvolume).

A process is called reversible if it proceeds through a series of equilibriumstates in such a way that the work done by forward change along the path isidentical to the work attained fromthe backward changealong the same path.

However, all real processes are irreversiblewith varyingdegrees of departurefroma reversibleone.

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Equilibrium

Temperature ScalesTemperature Scales


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Atmospheric, Absolute, Gage, and

Vacuum Pressures

Atmospheric, Absolute, Gage, and

Vacuum Pressures

Phase BehaviorHydrocarbon reservoirs = Rock + Fluids

Reservoir Fluid: Water in brine form and a gaseous and/or liquid hydrocarbonphaseare regardedas reservoir fluids.

The phase behavior of the actual hydrocarbon mixture in the reservoir can be

describedas a function of the state of the system.

A system in thermodynamic equilibrium possesses an accurately definedrelationship between the state variables. These are united in the so-calledequationof state:

By specification of two variables, the third will be stipulated.

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A phase diagram is a concise graphical method of representing phasebehavior of fluids. It provides an effective tool for communicating a largeamountof informationabouthow fluids behave atdifferentconditions.

Phase Diagram

Two Classes of Fluids

1. Pure-component systems: the composition is not a variable and thereforecannotinfluence behavior.

2. Mixtures: the behavior of a mixture is strongly controlled by composition. Infact, as the number of components in the system increases, the complexity ofthephase diagramincreases as well. Two components Multi components

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Single or Pure-Component System

The curve inFigure 1 is calledthe vapor pressure curve orboiling pointcurve.

The line also represents the dew point curve and the bubble point curve; one ontopof theother.This curve represents the transitionbetween the vaporand liquidstates.

Figure1

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Vapor Pressure: The pressure that the vapor phase of a fluid exerts over itsown liquid atequilibriumata given temperature.

Dew Point: The pressure and temperature condition at which an infinitesimal

quantity of liquid (a droplet) exists in equilibrium with vapor. It represents theconditionof incipient liquid formation in an initiallygaseous system. Notice that itcan be also visualized as a liquid systemwhere all butan infinitesimal quantityof liquid has beenvaporized.

Bubble Point: The pressure and temperature condition at which the system isall liquid, and in equilibrium with an infinitesimal quantity (a bubble) of gas. Thissituation is, inessence, the opposite of thatof the dewpoint.

Definition of Basic Terms

Figure1

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Definition of Basic TermsNOTE: For single-component systems, one single curve represents all three ofthese conditions (vapor pressure, dew point and bubble point conditions) simplybecauseVaporPressure =Dew Point=BubblePoint for unarysystems.

In Figure 1, once a saturation pressure has been selected, there is one (andonlyone) saturation temperature associatedwith it. This is only true for a singlecomponent system. In other words, this is the only temperature (at the givenpressure), at which liquid and gas phase will co-exist in equilibrium. The rulethat governs the uniqueness of this point, for a single-component system, iscalledthe Gibbs Phase Rule.

Figure1

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Complete P-T Diagram for Pure-component

Systems

Two very importantthermodynamicpoints bound the vaporpressure curve:the Critical Point atits upperend andthe Triple Point atits lowerend.

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Figure2

The Triple Point is the meeting point of the vapor pressure, solidificationand sublimation curves; hence, it represents the only condition at which allthree phases of a pure substance (solid, liquid and gas) can co-exist inequilibrium.

Figure2

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Triple Point

For water, the triple point is at 273.16 K (0.01 C or 32.018 F) and0.6113kPa (0.0887psia).


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At the Critical Point, gas and liquid are in equilibrium without any interface todifferentiate them; they are no longer distinguishable in terms of their properties.As we recall, the only location on the P-T diagram where liquid and gas can befound together in equilibriumis along the vapor pressure curve. Hence, the criticalpoint is clearly the maximum value of temperature and pressure at which liquid

and vapor can be at equilibrium. This maximum temperature is called the criticaltemperature (Tc); the corresponding maximum pressure is called the criticalpressure (Pc).

Figure3

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Crit ical Point

The critical point is the point atwhich all intensive properties of thegas and liquidphases are equal.

An intensive property is a property

independent of the quantity of thesystem. Pressure, temperature,density, composition, and viscosityare examples of intensiveproperties.

Properties Of The Critical Point (Tc,Pc)

(For Pure Substances)

Temperature and pressure for which liquid and vapor are no longerdistinguishable.ForT >Tc, liquidand vaporwill notco-exist, no matterwhatthe pressure is.For P >Pc, liquidand vaporwill notco-exist, nomatterwhat thetemperature is

The vaporliquid critical point in a pressure

temperature phase diagram is at the high

temperature extreme of the liquidgas phase

boundary. The dotted green line gives the

anomalous behavior of water.

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isobaricheating

Sensible Heat: Its main purpose is tocause an increase in temperature of the

system.

Latent Heat: It serves only one purpose:to convert the liquid into vapor. It doesnotcause a temperature increase.

thephaseboundaryiscrossed

Two Thermodynamic Path to Go from A to B

Path AD: Isothermal compressionPath DE: Isobaric heating

Path EB: Isothermal expansion

thephaseboundary isNOTcrossedatall

We went from an all-liquid condition(point A) to an all-vapor condition(point B) without any sharp phasetransition.

Thephaseboundaryrepresents

asharpdiscontinuityindensity

(andotherphysicalproperties)

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PV Diagram for Pure Systems

The temperature is being held constant; Isothermalcompressionprocesspath F-G: two-phase condition, the liquid (L) and vapor (V) co-exist inequilibriumE: all-vaporcondition

F: saturated vapor condition (vapor in equilibrium with an infinitesimal amountof liquid;dewpintG: saturated liquid condition (liquid in equilibriumwith an infinitesimal amountofvapor;bubble point

L+V

Where is path F-G in this figure?

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Family of P-V Isotherms for a Pure Component

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P-V Phase Diagram for a Pure Component

The critical point has a point of inflexion

(change of curvature).

The critical point also represents the

maximum point (apex) of the Pv envelope

The criticality conditions:

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Three-dimensional Diagram of

Single-Component System

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GIBBS Phase Rule

When referring to the number of phases coexisting in thethermodynamical equilibrium, the phase rule introduced byGIBBS (1928) is applied.

where P: number of phases, C: number of components, F: number of degrees of freedom.

C is defined as the smallest number of constituents by which the coexistingphases can be completely described. F is defined as the number of quantitiessuch as pressure, temperature, concentrations which can be varied within finiteboundaries without changing the number of phases in the system.

Equation describes the system in a qualitative and very general manner.However, no reference to the state variables (p,T), to the composition of theparticularphases or to theproportionsof thephases are given.

Gibbs, JosiahWillard(18391903)

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Waterphasediagram

a)Atthetriplepoint:

P=3(solid,liquid,andgas)

C=1(water)

P+F=C+2

F=0(nodegreeoffreedom)

b)liquidsolidcurve

P=2

2+F=1+2

F=1

Onevariable(TorP)canbechanged

c)Liquid

P=1

SoF=2

Twovariables(TandP)canbevariedindependentlyandthesystemwillremainsa

singlephase

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The real-life systems are never single-component; they are multicomponentsystems.The presence of one or more additional components bring the additionalcomplexity in descriptionof phase diagram.The good news: the behavior of multicomponent systems are quite similar to

thatof binarysystems.

BinarySystem

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Why is pressure increasing during the phase transition?

P-v Diagram for a Binary Mixture

P-v Diagram for a Pure Component

When a mixture exists in a two-phase condition, differentmolecules of different species arepresent and they can be either ina liquid or vapor state (two-phasecondition). Some of them would

prefer to be in the gas phasewhile the others would prefer tobe in the liquid phase. Thispreference is controlled by thevolatilityof the given component.

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Pressure/volume diagram for the n-C5 and n-C7

system containing 52.4 wt % n-C7.

Family of Isotherms on a P-V diagram Binary Mixture

Can we say now that the critical point is themaximum value of pressure and temperaturewhere liquidand gas cancoexist?

Critical Point (Pc,Tc): The temperatureand pressure for which liquid and vapor

are indistinguishable.

Cricondentherm(Tcc):1. The highest temperature in the two-

phase envelope.2. For T > Tcc, liquid and vapor cannot

co-exist at equilibrium, no matterwhat the pressure is.

Cricondenbar(Pcc):1. The highest pressure in the two-

phase envelope.2. For P > Pcc, liquid and vapor cannot

co-exist at equilibrium, no matterwhat the temperature is.

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P-V diagram of a Binary Mixture

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PT diagram for two pure components and PT diagram for a 50:50 mixture

of the same components

P-T diagram of a Binary Mixture

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Quality lines describe the pressure and temperature conditions of equal volumes ofliquid. Obviously, the bubble-point curve and the dew-point curve represent 100%and0% liquid, respectively.


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Retrograde Phenomenon

Regarding multi-component mixtures (where the binary system is the simplestcase), some interesting phenomenon profoundly differentiate their behaviorfrom the behavior of single-component systems. We are now talking aboutretrogradephenomena.

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Let us now consider the isothermal processes taking place at T = T1 and T = T2

Retrograde Phenomenon

Tc < T2 < TccT1 < Tc

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The curve is commonly called theliquid dropout curve. The maximum

liquid dropout (LDO) is 26.5%, whichoccurs when the reservoir pressuredrops from a dew-point pressure of5900 psi to 2800 psi. In most gas-condensate reservoirs, the condensedliquid volume seldom exceeds morethan 1519% of the pore volume. Thisliquid saturation is not large enough toallow any liquid flow through the bulkof reservoir.

A Typical Liquid Shrinkage Volume Curve for

a Relatively Rich Condensate System.

Effect of Composit ion on Phase Behavior

We would expect that the P-Tdiagramof each pure componentwill have some sort of influenceon the P-T diagram of anymixture inwhich it is found.

it would be reasonable to thinkthat as the presence of a givencomponent A dominates over B,the P-T graph of that mixture(A+B) should get closer andcloser to that of A as a purecomponent.

What this is telling us is that anew variable is coming into the

picture: composition.

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Phase Diagram of a Methane/Ethane Mixture

Lightest components Tc < Mixture components Tc < Heaviest components Tc

A mixtures Pc can be found to be higher than the critical pressures of both purecomponents hence, we see a concave shape for the critical locus.

In general, the more dissimilar the two substances, the farther the upward reachof the critical locus.

When the substances making up the mixture are similar in molecular complexity,the shape of the critical locus flattens down.

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P-x and T-x DiagramsInadditiontoconsideringvariationswithpressure,temperature,andvolume,aswehave

donesofar,itisalsoveryconstructivetoconsidervariationswithcomposition.Most

literatureonthesubjectcallsthesediagramsthePxandTxdiagramsrespectively

InaPxdiagram,thebubblepointanddewpoint

curvesboundthetwophaseregionatitstopand

itsbottom,respectively

In the Tx diagram, this happens in the reverse

order; vapor is found at high temperatures and

liquid at low temperatures

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TheLeverRule px&TxDiagrams For a binary system Px a n d Tx diagrams phase diagrams can give quantitative

information pertaining to the amounts of each phase present, as well as the composition

of each phase.

At a given temperature or pressure in a Tx or Px diagram (respectively), a horizontal

line may be drawn through the twophase region that will connect the composition of the

liquid (xA) and vapor (yA) in equilibrium at such condition that is, the bubble and dewpoints at the given temperature or pressure, respectively. If, at the given pressure and

temperature, the overall composition of the system (zA) is found within these values (xA

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Phase Behavior [Compatibility Mode]