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Phase Behaviour of Hydrocarbons

Unit II

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Unit Rationale• An equation of state (EOS) is an analytical expression

relating the pressure P to the temperature T and the volume V.

• A proper description of this PVT relationship for real hydrocarbon fluids is essential in determining the volumetric and phase behavior of petroleum reservoir fluids and predicting the performance of surface separation facilities; these can be described accurately by equations of state.

• This unit deals with the study of the various equations of state which will enable the learner to choose the proper form for a particular system.

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Unit Objectives

At the end of this unit, you will be able to:• Understand the behavior of fluids with the help of PV

and PT diagram• Describe the PVT behavior with the help of equation of

state• Calculate the heat and work effects involved in the

various processes with ideal gases• Choose the proper equation of state for real gases• Understand the utility of compressibility charts in the

absence of experimental data

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Classification of Reservoir Fluids

Reservoir Fluids

Dry Gas Wet Gas Gas Condensate Volatile oil Black Oil

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Classification of fluids

• Pure component systems• Multicomponent systems

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Vapor pressure curve (Pure substance)

• As pressure increases, boiling point increases

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Basic Terms• Vapor Pressure: The pressure that the vapor phase of a

fluid exerts over its own liquid at equilibrium at a given temperature.

• Dew Point: The pressure and temperature condition at which an infinitesimal quantity of liquid (a droplet) exists in equilibrium with vapor.

• Bubble Point: The pressure and temperature condition at which the system is all liquid, and in equilibrium with an infinitesimal quantity (a bubble) of gas.

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Unary systems

• For single-component systems,A single curve represents all three of these conditions

i.eFor unary systems,Vapor Pressure = Dew Point = Bubble Point

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Complete P-T diagram for pure-component systems

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Critical properties

• Critical point is defined as the point at which the saturated liquid and saturated vapor states are identical.

• Critical pressure Pc is the pressure of a substance at the critical point.

• Critical temperature Tc is the temperature of a substance at the critical point.

• Critical volume Vc is the volume of a substance at the critical point.

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Critical Properties

• Critical temp and pressure represent the highest temp at which a pure substance will exist in vapour liquid equilibrium

• If T<Tc then the substance to the right of the saturated vapour line is called vapour

• If T>Tc then the substance to the right of the saturated vapour line is called gas

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Critical Properties

• If the temperature and pressure are above TC and PC, the substance is in fluid region and it can neither be condensed nor be vaporised

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P-V Diagram for a Pure Component

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P-V isotherms for a pure component

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P-v Diagram and Phase Envelope of Pure Substance

P-T Phase Envelope for a Binary System

• Is the critical point is the maximum value of pressure and temperature where liquid and gas can coexist? 16

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Cricondentherm and Cricondenbar

• Cricondentherm (Tcc):– The highest temperature in the two-phase

envelope.– For T > Tcc, liquid and vapor cannot co-exist at

equilibrium, no matter what the pressure is.

• Cricondenbar (Pcc):– The highest pressure in the two-phase envelope.– For P > Pcc, liquid and vapor cannot co-exist at

equilibrium, no matter what the temperature is.

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Cricondentherm and Cricondenbar

For pure substances only: Cricondentherm = Cricondenbar = Critical Point

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P-T curves for different types of Hydrocarbon Reservoirs

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Equation of state

• It is a functional relationship between the properties like temperature, pressure and volume that define the thermodynamic state of a single homogeneous fluid.

f (P, V, T) = 0

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Ideal Gas

• Size of the molecule is very small compared to the distance between them

• Volume of the molecules is negligible in comparison with the total volume of the gas

• Intermolecular forces are negligible

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Properties applicable for an ideal gas

• For one mole of gas, the equation of state is PV = RT

where, R is the universal gas constant

• Internal energy depends only on temperature. It is independent of pressure and volume

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Properties applicable for an ideal gas

• The Joule Thomson coefficient is zero

• Joule Thomson coefficient is defined as the change in temperature resulting from the expansion of a gas between constant pressures under adiabatic condition and with no exchange of work with the surrounding.

0

HP

T

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Properties applicable for an ideal gas

• Real gases follow ideal behaviour at absolute zero temperature.

• At room temperature gases like hydrogen, helium, nitrogen and oxygen follow perfect gas law closely

• For engineering purposes all gases in the neighbourhood of atmospheric pressure are treated as ideal.

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Processes involving ideal gases

• Constant volume process (Isochoric)• Constant pressure process (Isobaric)• Constant temperature process (Isothermal)• Adiabatic process• Polytropic process

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Constant Volume Process (Isochoric)

• No work of expansion, hence dW = 0• Heat supplied is used to increase the internal

energy

dU = dQ = CvdT

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Constant Pressure Process (Isobaric)

• Work of expansion done = PdV• Internal energy rises = dU• Enthalpy = dU + PdV

dH = dQ = CPdT

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Constant Temp.Process (Isothermal)

• dH = 0 and dU = 0, dQ = dW

2

1

1

2 lnlnPPRT

VVRTWQ

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Adiabatic Process

• No heat interaction between the system and the surrounding

Where, = CP/CV

PV = constant

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Adiabatic Process

1

1

2

2

1

1

1

2

1

2

1

2

1

1

2

PP

VV

PP

TT

VV

TT

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Adiabatic Processes

1

1

211

21

2211

21V

11

1

1

)(C doneWork

PPVP

RTRT

VPVPTT

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Polytropic Process

PV n = constant

Process n

Isobaric n = 0

Isothermal n = 1

Isochoric n =

Adiabatic n =

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Equation of State for real gases

• At low molar volumes or high pressures, molecules come close to each other and molecular interactions cannot be neglected.

• The volume occupied by the gas molecules is appreciable as compared to the volume occupied by the gas

• Only when pressures are low ideal gas equation can be used to explain real gases.

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Equations of state for real gases

• Van der Waals equation• Redlich-Kwong equation• Redlich-Kwong-Soave equation (SRK)• Peng Robinson (PR)• Benedict –Webb-Rubin equation• Virial equation

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van der Waals Equation

RTbVVaP

)(2

C

C

C

C

PRTb

PTRa

8 ;

6427 22

Where,

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Redlich-Kwong Equation

)(5.0 bVVTa

bVRTP

C

C

C

C

PRTb

PTRa 0867.0 ; 4278.0 5.22

Where,

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Redlich-Kwong-Soave Equation

• a and b are constants similar to those for Redlich Kwong equation with the only change that the exponent of TC is 2 instead of 2.5

• depends on temperature and acentric factor

aTabVV

TabV

RTP

)(' where,

,)(

)('

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Acentric Factor ()

7.0

log0.1

RTC

S

PP

PS = Vapour PressurePC = Critical PressureTR = Reduced Temperature

For Simple fluids, acentric factor = 0 Complex fluids, acentric factor > 0

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Acentric Factor ()

• It is the measure of deviation of the intermolecular potential of the molecule from that of a spherical molecule (a-centric)

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Reduced Temperature and Pressure

• Gases behave differently at a given temperature and pressure, but they behave very much the same at temperatures and pressures normalized with respect to their critical temperatures and pressures.

CR

CR T

TTPPP and

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Peng Robinson Equation

• Where, a and b are constants = f(TR, )

)()( bVbbVVa

bVRTP

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Benedict-Webb-Rubin Equation

2223632

2000 exp1/

VVTVc

Va

VabRT

VTCARTB

VRTP

Where, A0, B0, C0, a, b, c, and are constants

This equation is widely used in petroleum and natural gas industry to determine the properties of light hydrocarbons and their mixtures

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Benedict-Webb-Rubin Equation

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Compressibility Factor

• The ratio of the volume of real gas (V) to the volume (RT/P) if the gas behaved ideally at a stated temperature and pressure is called compressibility factor

PRTV

VVZideal

actual

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Compressibility Factor

• It measures the deviation of real gas from ideal behaviour.

• For a perfect gas the value of Z is 1• For a real gas Z approaches 1 … as pressure

tends to zero

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Virial Equations

• Virial equations express the compressibility factor of a gas or a vapour as a power series expansion in P and 1/V

• ‘Virial’ in latin means ‘force’• The coefficients take into account the

interaction forces between the molecules

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Virial Equations

• B,C,D and B’,C’,D’.. are called virial coefficients• B and B’ are called second virial coefficients• C and C’ are called third virial coefficients and so on…..

Form)(Leiden ............1

Form)(Berlin ..........'''1

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VD

VC

VB

RTPVZ

PDPCPBRTPVZ

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Significance

• It can be made to represent experimental PVT data more accurately by increasing the number of terms in the power series depending on the complexity of the substance

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Principle of corresponding states

• All gases when compared at the same reduced temperature and the reduced pressure, have approximately the same compressibility factor.

Z = f (Tr , Pr)

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Compressibility Charts

• Provides the best means of expressing the deviation from ideal behaviour.

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Observations from compressibility charts

• At very low pressures (PR 1), gases behave as an ideal gas regardless of temperature

• At high temperatures (TR > 2), ideal-gas behaviour can be assumed with good accuracy regardless of pressure (except when PR >> 1).

• The deviation of a gas from ideal-gas behavior is greatest in the vicinity of the critical point

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Compressibility Chart

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Retrograde Phenomena• Bubble point curve:

Line of saturated liquid (100 % liquid with an infinitesimal amount of vapor)

• Dew point curve : Line of saturated vapor (100 % vapor with an infinitesimal amount of liquid).

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Isothermal Process T = T1 and T = T2

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Common Phenomena

At T = T1

• An isothermal compression (increasing pressure while temperature is held constant) causes the condensation of a vapor.

• More the compression, more liquid is obtained

• True for a pure-component system, such as water.

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Liquid Yield for the Isothermal Compression at T1

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At Tc < T2 < Tcc

• At point C: ALL VAPOR condition (0 % liquid)• By increasing pressure, the system enters the

two-phase region. Thus, some liquid has to drop out

• One expects that as the pressure keeps increasing, more and more liquid should be produced.

• This is true till point C’, after that it starts to vaporize and not condense

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Liquid Yield for the Isothermal Compression at T2

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Retrograde Condensation

• The increase in the liquid fraction with decreasing pressure between points C and D is exactly the opposite of the normal trend. Hence called Retrograde condensation

• This behavior is typical of gas condensate systems.

• Retrograde conditions may be encountered in deep-well gas production, as well as in reservoir conditions

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Applications

• For production operations, usually the objective is to maintain pressure so as to achieve maximum liquid dropout.

• The initial PVT conditions of the well may correspond to a point above point D.

• If the conditions at the wellhead are then maintained near point C’, liquid recovery is maximized at the surface.

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Dry Gas

• Methane, N2, CO2• Reservoir temp. well

above the critical• Gas remains single

phase from reservoir to separator conditions

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Wet Gas

• Methane, light HC• Phase envelope below

the temp. of reservoir• No liquid drop out in

reservoir• Condensation at

separator conditions

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Gas Condensate

• Heavy HC present• Reservoir temp is

between critical pt. and cricondentherm

• Retrograde condensation occurs

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Volatile Oil

• Heavier HC• Reservoir temp. near

critical• Small reduction in

pressure near bubble pt. vaporises the oil. Hence the name Volatile oil

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Black Oil (Ordinary Oil)

• 20 mole% heptanes and heavier HC

• Reservoir temp. well below the critical

Ref: Ali Danesh, ‘PVT and Phase Behaviour of Petroleum Reservoir Fluids’, Chapter 1, pp. 22-29

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Cox Charts

Vapour pressure of normal paraffins

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Cox ChartsVapour pressure of normal paraffins

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Problem

• Calculate the vapour pressure of normal– hexane – decane

at 355.15 K using Cox chart