Vapour Liquid Equilibrium

7/21/2019 Vapour Liquid Equilibrium

http://slidepdf.com/reader/full/vapour-liquid-equilibrium-56d8ad4479c42 1/32

Vapor

Liquid Equilibrium

Dr. Mohammed Abdalla Ayoub

Reservo ir Engineer ing I

PCB2023

1



Lesson outcomes

At the end of this class students should be ableto :

Identify the importance of VLE

Apply the Ideal and non- Ideal Solution

Determine Compositions & Quantities of theEquilibrium Gas & Liquid Phases.

Calculate the saturation pressure of themixture

2



Importance of Vapour Liquid Equilibrium

Multiphase aspects of hydrocarbon mixtures are important

part of reservoir management.

Reservoir flow & well productivity,

facility design

and pipeline transport.

Predicting relative amounts of phases and their physical

properties is an important part.

Behavior of multicomponent mixtures in reservoirs and their

production to surface is a serious challenge.3



VLE Data,…. Intro.

The most accurate and reliable source of obtaining data on

equilibrium conditions and the phases is laboratory studies,

including compositional analysis and reservoir fluid studies.

practical limitations: cost , time, and limited amount of sample

availability.

In the absence of such laboratory studies, calculation methods are

relied upon, and these methods are called phase equilibrium or

vapor –liquid equilibrium (VLE) calculations.

4



The input data for the VLE calculations consist of the overall

composition of the reservoir fluid, pressure and temperature

conditions, and the properties of the individual components (defined

as well as pseudo-components and plus fractions).

Based on such input data, VLE calculations typically involve the

determination of saturation pressures (bubble or dew points),

equilibrium phase compositions, volumes, compressibility factors

VLE Data,…. Intro.

5



TotalProduction

System

6



Complexity of allocationof produced oil to supplyfields

Main issues to reservoir

engineer.

Multiphase behavior –relative

permeability etc.

Volumes between reservoir

and surface.

Physical properties of gas and

oil in reservoir and at surface

7



Vapor-liquid equilibrium

Phase diagram defines area bounded by bubble point and dew point

curves where two phases exist.

Too simple to describe as in volatile oil and solution gas.

Quick definitions:

A mole is what

6.02x10 23 molecules

weigh.

MW=no. mass units

(1.6x10-24 g) a moleculeweighs

8




Throughout the production process from the reservoir

through the separator to the stock tank conditions, large

volumes of gas are generated from the reservoir oil.

The oil shrinks.

Oo

ST

GS

ST

VOil formation volume factor B

V

V Solution gas to oil ratio R V

Volume factors can be determined directly in the laboratory

or from equilibrium calculations 9



Besides separator calculations vapor

liquid equilibrium calculations used for.

Reservoir calculations

Two phase pipeline flow calculations

Process calculations


10



Vapor-liquid equilibrium calculations

The grid

block of asimulator

can be

considered

to be theseparator of

a process

unit.

11



Vapor-liquid equilibrium calculations

VLE calculations have been restricted to separate areas;

reservoirs and wells, surface operations, pipelines,

onshore treatment and refinery operations

Increasing trend is the integration of this to determine

for example impact of a change in a reservoir parameter

on refinery or pipeline outputs.

12



Ideal solutions

An ideal solution is a solution for which:

1. Mutual solubility results when components are mixed.

2. No chemical interaction occurs upon mixing, and

3. The intermolecular forces of attraction and repulsion are

the same between the unlike and like molecules.

13



Ideal Mixtures

Ideal mixtures of gases or liquids are those in which there is

insignificant interaction between various constituents, which is

generally the case at low pressures for simple mixtures.

Although, petroleum reservoir fluids are not ideal mixtures.

Equilibrium ratio is on the basis of two important laws, namely,

Raoult’s and Dalton’s law

14



Ideal solutions

Raoult’s Law

Partial pressure of a given component in a multicomponent system is theproduct of its mole fraction in the liquid phase and its vapor pressure.

Dalton’s Law

For an ideal gas mixture, the partial pressure of a component is the

product of its mole fraction and the total system pressure

P Y p ii

viii P X p

P i : The partial pressure of component i in the gas phase X i

: The mole fraction of componenti

in the liquid phase P v i : The vapor pressure of component i at the giventemperature

P : The total system pressureY i : The mole fraction of component i in the vapor phase

15



Ideal Equilibrium Ratio

Equilibrium ratio is the ratio of the composition in the vapor phase to

that of the liquid phase. Regardless of the overall composition of the

hydrocarbon mixture, the equilibrium ratio is only a function of the

system pressure and temperature.

The vapor pressure of a component is only a function of temperature

From Raoult’s and Dalton’s Laws

----------(1)

Ratio Eqilibrium K P

P

X

Y ivi

i

i

Although, on the basis of vapor pressures and the system pressure,

equilibrium ratios for various components can be determined.

16



Equilibrium Ratio

Ki is defined at a particular pressure and

temperature

Other names: K-factors, K values, equilibrium

vapor liquid distribution coefficients

17



Concept of PT Flash

Almost all petroleum reservoir fluids undergo this type of PT flash

process either in the reservoir, production tubing, or on the surface.

nv moles of vapor having

composition Y i and nL moles of

liquid having composition X i.

This particular process, resulting

in the splitting of the feed or a

hydrocarbon mixture into

equilibrium vapor and liquid

phases at a given pressure and

temperature, is called PT flash.

18



By definition, the overall material balance on the feed and the equilibrated

vapor and liquid phases lead to

n

=n

L +n

V A similar material balance equation can also be written in terms of the ith

component of the mixture:

Z in: moles of component i in the feed

X inL: moles of component i in the equilibrium liquid phase

Y inV : moles of component i in the equilibrium vapor phase

Z in = X

in

L+ Y

in

V

----------(3)

----------(2)

19

Concept of PT Flash, cont.

C iti & Q titi f th E ilib i



Compositions & Quantities of the EquilibriumGas & Liquid Phases of an Ideal Solution

So

---------(5)

Equations (2) and (3) can be further simplified by considering the basis of

1mol of feed, that is, n = 1:

n L + n V = 1

X i nL + Y i nV = Z i

---------(4)

Combining Equations 1, 4, and 5

X i (1− nV) + K i X i nV = Z i

11

iv

i

i K n

Z X

---------(6)

---------(7)

20





Also by definition of mole fraction

0.1

1111

n

i iv

in

ii K n

Z X

0.1

1111

n

i iv

iin

i

i K n

K Z Y

Similarly

---------(9)

---------(8)

21





On the basis of the given mole fraction of the feed Z i and the calculated

equilibrium ratio K i from Equation 1 (from vapor pressure at a given

temperature and the system pressure), the only unknown that remains in

Equation 8 or 9 is the moles of the equilibrium phase vapor nV.

However, considering the nature of these equations, a trial-and-errorsolution is required in either case.

Since the calculations are based on 1mol of feed, a trial value of nV between 0

and 1 is chosen.

If the selected value of nV results in the summation of 1 in Equation (8) or (9),

the moles of equilibrium liquid phase and the compositions of all the

components in the equilibrium vapor phase and the liquid phase can then be

calculated. If the summation does not equate 1, a new iteration cycle may be

needed.22



Flash Functions

Alternatively, Equations (8) and (9) can be written as follows (called the flash

functions):

01

11 or, ,01

11

n

i iv

i

n

i

i K n Z X

00.1

11 or, ,01

11

n

i iv

iin

i

i

K n

K Z Y ----(11)

----(10)

Those eqs. may result in unpredictable trends in the vicinity of nV = 0 and nV = 1.23



Rachford and Rice

Is considered as mathematically much more robust compared to

Equation (10) or (11) and is thus commonly used or preferred in

VLE calculations:

011

1 or, ,0

111

n

i iv

ii

n

i

i

n

i

i

K n

K Z X Y ----(12)

It needs to be solved iteratively in such a way that a certain value

of nV will satisfy the condition of the right-hand side resulting in a

value of zero.

24



25

Compositions & Quantities of the Equilibrium Gas &



---------(8)

Compositions & Quantities of the Equilibrium Gas &Liquid Phases of an Ideal Solution

Example:

Calculate the compositions and quantities of the gas and liquid when 1.0

lb. mole of the following mixture is brought to equilibrium at 150oF and

200 psia. Assume ideal-solution behavior.Component Composition, mole

fraction

Propane 0.610

n-Butane 0.280

n-Pentane 0.110

1.000

0.1

1111

n

i iv

iin

i

i K n K Z Y

By trial and error, determine the value of nv

which satisfies the equation26

Compositions & Quantities of the Equilibrium




component Composition ofmixture (molefraction), Zi

Vaporpressure@150oF, P vi

Composition ofthe gas, molefraction, Y i

Composition ofthe liquid, molefraction, Xi

Propane, c3 0.610 3500.76896 0.439406

n-Butane, nC4 0.280 1050.19493 0.371296

n-Pentane, nC5 0.110 370.035201 0.190274

≅1.000 ≅1.000 ≅1.000

The summation equals 1 for nv =0.517651; thus there are 0.482349 moles of liquid and 0.517651 moles of vapor for each mole of total mixture. The

compositions for vapor and liquid are given in the last two columns.

27



Calculation of the Bubble-Point Pressure of an IdealSolution

The bubble point is the point at which the first bubble of gas is formed.

For all practical purposes, the quantity of gas is negligible.

nv to be equal to zero and nL to be equal to the total moles of the

mixture.

Substituting of nv ≅ 0, nL ≅ 1 (assuming the basis to be 1 mole of feed)

and p=pb

into equation

---------(13)0.111

n

i

i

n

i

i X Z

28



Thus the equilibrium is established for the newly formed gasphase

by substituting the value of Ki from Equation (1)

Or

---------(14)

---------(15)

Calculation of the Bubble-Point Pressure of an IdealSolution

0.111

i

n

i

i

n

i

i K Z Y

0.1

1

b

vi

n

i

i

P

P Z

vi

n

i

ib P Z P

1

---------(16)

It’s a simple molar mixing rule that uses mole fractions and vapor

pressures of individual components. 29



At the dew-point pressure, the quantity of liquid essentially is negligible.

p=pd, nL≅0andnv≅ 1 (assuming the basis to be 1mol of feed)

and thus, the equilibrium is established for the newly formed liquid phase

by substituting the value of Ki from Equation (1)

Calculation of the Dew-Point Pressure of an IdealSolution

---------(17)

---------(18)

---------(19)

0.111

n

i

i

n

i

i Y Z

0.111

n

i i

in

i

i K

Z X

0.11

n

i d vi

i

P P

Z

n

i

vii

d

P Z

P

1

1

---------(20)



Summary

At the end of this class students managed to :

Identify the importance of VLE

Apply the concept of Ideal Solution

Determine Compositions & Quantities of the

Equilibrium Gas & Liquid Phases for ideal solutions.

Calculate the saturation pressure of the mixture.

31



End of Chapter 5

32

Documents

Vapour Liquid Equilibrium