vapour liquid equilibrium
DESCRIPTION
VLETRANSCRIPT
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Vapor
Liquid Equilibrium
Dr. Mohammed Abdalla Ayoub
Reservo ir Engineer ing I
PCB2023
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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
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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
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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.
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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.
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TotalProduction
System
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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
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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
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Vapor-liquid equilibrium
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
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Besides separator calculations vapor
liquid equilibrium calculations used for.
Reservoir calculations
Two phase pipeline flow calculations
Process calculations
Vapor-liquid equilibrium
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Vapor-liquid equilibrium calculations
The grid
block of asimulator
can be
considered
to be theseparator of
a process
unit.
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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.
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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.
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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
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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
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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.
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Equilibrium Ratio
Ki is defined at a particular pressure and
temperature
Other names: K-factors, K values, equilibrium
vapor liquid distribution coefficients
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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.
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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)
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Concept of PT Flash, cont.
C iti & Q titi f th E ilib i
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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)
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C iti & Q titi f th E ilib i
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Compositions & Quantities of the EquilibriumGas & Liquid Phases of an Ideal Solution
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)
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C iti & Q titi f th E ilib i
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Compositions & Quantities of the EquilibriumGas & Liquid Phases of an Ideal Solution
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
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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
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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.
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Compositions & Quantities of the Equilibrium Gas &
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---------(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
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Compositions & Quantities of the EquilibriumGas & Liquid Phases of an Ideal Solution
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.
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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
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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
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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)
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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.
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