Q913 rfp w3 lec 11

Reservoir Fluid Properties Course (1st Ed.)

1. Cubic EoS:
A. SRK EoS
B. PR EoS
C. Other Cubic EoS

2. Non Cubic EoS
3. EoS for Mixtures
4. Hydrocarbons
A. Components
B. Mixtures
C. Heavy Oil

2013 H. AlamiNia

Reservoir Fluid Properties Course: Flash and Equilibrium Ratios

2

1.
2.
3.
4.

PT-Flash Process
Equilibrium Ratios
PT-Flash Calculations
Mixture Saturation Points

2013 H. AlamiNia


3

Flash Calculations
Flash calculations are an integral part of all
reservoir and process engineering calculations.
They are required whenever it is desirable to know
the amounts (in moles) of hydrocarbon liquid and
gas coexisting in a reservoir or a vessel at a given
pressure and temperature.
These calculations are also performed to determine
the composition of the existing hydrocarbon
phases.

2013 H. AlamiNia


5

PT-Flash Process Procedure
A feed stream consisting of a mixture of N
components is led to a flash separator kept at a
constant temperature and pressure.
Two phases are present in the separator.
In a gas–oil separator, the gas is let out at the top
and the oil at the bottom.

2013 H. AlamiNia


6

PT-Flash Process Results
If P, T, and component mole fractions in the feed (z
1, z 2, …, z N) are known, a flash calculation will
provide the following results:
1. Number of phases.
2. Molar amounts of each phase (moles of Liquid and gas
phase).
3. Molar compositions of each phase.

2013 H. AlamiNia


7

Principle of PT-Flash Process for
a Hydrocarbon Reservoir Fluid Mixture

Figure illustrates a two-phase PTflash process
The term β for the vapor mole
fraction, (y 1, y 2, …, y N) for the
component mole fractions in the gas
phase, and the (x 1, x 2, …, x N) for
the component mole fractions in the
liquid phase

2013 H. AlamiNia


8

Phases Occurring in
Petroleum Production
A phase is defined as that part of a system which is
uniform in physical and chemical properties,
homogeneous in composition, and separated from
other coexisting phases by definite boundary
surfaces.
The most important phases occurring in petroleum
production are the hydrocarbon liquid phase and
the gas phase. Water is also commonly present as
an additional liquid phase.

2013 H. AlamiNia


9

Phases Coexistence
These can coexist in equilibrium when the variables
describing change in the entire system remain
constant with time and position.
The chief variables that determine the state of
equilibrium are system temperature, system
pressure, and composition.
These types of calculations are based on the
concept of equilibrium ratios.

2013 H. AlamiNia


10

K-Factors Expression
The following relations apply for two phases in
equilibrium:
𝒚𝒊
𝝓 𝒊𝑳
𝑲 𝒊 = = 𝑽 , 𝒊 = 1,2, … , 𝑵
𝒙𝒊
𝝓𝒊

The vapor and liquid phase fugacity coefficients of
component i, ϕ iV and ϕ iL
Ki is the equilibrium ratios or K-factors (for low pressures
and ideal gas and ideal solutions is equal to vapor
pressure of component i divided by total system
pressure Ki=Pvi/p)

2013 H. AlamiNia


12

Equilibrium Ratios Assumption
The equilibrium ratios, which indicate the
partitioning of each component between the liquid
phase and gas phase, as calculated by (ki=pvi/p) in
terms of vapor pressure and system pressure,
proved to be inadequate.
The basic assumptions behind Equation (ki=pvi/p)
are that:
The vapor phase is an ideal gas as described by Daltons
Law

The above combination of assumptions is
unrealistic and results in inaccurate predictions of
equilibrium ratios' at high pressures.
2013 H. AlamiNia


13

Equilibrium Ratios For Real Solutions
For a real solution, the equilibrium ratios are no
longer a function of the pressure and temperature
alone, but also a function of the composition of the
hydrocarbon mixture. This observation can be
stated mathematically as
Ki = K (p, T, Zi)
Numerous methods have been proposed for
predicting the equilibrium ratios of hydrocarbon
mixtures.
These correlations range from a simple mathematical
expression to a complicated expression containing
several compositional dependent variables.
2013 H. AlamiNia


14

K-Factor Determination: Correlations
Wilson's Correlation: A simplified thermodynamic
expression for estimating K-values.
Ki=Pci/p*EXP [5.37(1+ω i) (1-Tci/T)]
Where Pci & Tci= critical pressure & temperature of component
i
The above relationship generates reasonable value for the
equilibrium ratio when applied at low pressures.

2013 H. AlamiNia


15

K-Factor Determination:
Convergence Pressure Method
Early high pressure phase-equilibria studies
revealed that when a hydrocarbon mixture of a
fixed overall composition is held at a constant
temperature as the pressure increases, the
equilibrium values of all components converge
toward a common value of unity at certain
pressure.
This pressure is termed the convergence pressure
Pk of the hydrocarbon mixture

2013 H. AlamiNia


16

Equilibrium Ratios vs. P Relationship

A Schematic Diagram of
Equilibrium Ratios vs. P Relationship

2013 H. AlamiNia


17

K-Factor Determination:
Convergence Pressure Method (Cont.)
The convergence pressure is essentially used to
correlate the effect of the composition on
equilibrium ratios.
The illustration shows a tendency of the
equilibrium ratios to converge isothermally to a
value of Ki = 1 for all components at a specific
pressure, i.e., convergence pressure.
A different hydrocarbon mixture may exhibit a
different convergence pressure.

2013 H. AlamiNia


18

Component Material Balance
A material balance for each component yields
𝒛 𝒊 = 𝜷𝒚 𝒊 + 1 − 𝜷 𝒙 𝒊 , 𝒊 = 1,2, … , 𝑵

In addition, the component mole fractions must for
each phase sum to unity, yielding one additional
relation in the form suggested by Rachford and Rice
𝑵

𝒚𝒊 − 𝒙𝒊 = 0
𝒊=1

2013 H. AlamiNia


21

Component Mole Fractions in
the Liquid and Gas Phase
The liquid phase is an ideal solution as described by
Raoult's Law

Using the equations we have:
𝒚𝒊 =

𝒛𝒊 𝑲𝒊
, 𝒊 = 1,2, … , 𝑵
1 + 𝜷 𝑲𝒊 − 1

𝒛𝒊
𝒙𝒊 =
, 𝒊 = 1,2, … , 𝑵
1 + 𝜷 𝑲𝒊 − 1
𝑵

𝒂𝒏𝒅

𝒚𝒊 − 𝒙𝒊 =
𝒊=1

2013 H. AlamiNia

𝑵

𝒊=1

𝒛𝒊 𝑲𝒊 − 1
=0
1 + 𝜷 𝑲𝒊 − 1


22

Fugacity
In chemical thermodynamics, the fugacity (f) of a real
gas is an effective pressure which replaces the true
mechanical pressure in accurate chemical equilibrium
calculations. It is equal to the pressure of an ideal gas
which has the same chemical potential as the real gas.
The fugacity f is a measure of the molar Gibbs energy of
a real gas.
The fugacity has the units of pressure, in fact, the
fugacity may be looked upon as a vapor pressure
modified to represent correctly the escaping tendency
of the molecules from one phase into the other.
2013 H. AlamiNia


23

Fugacity Determination
Fugacities are determined experimentally or
estimated from various models such as a Van der
Waals gas that are closer to reality than an ideal
gas.
In a mathematical form, the fugacity of a
component is defined by the following expression:
𝒇 = 𝒑𝒆

𝒑
0

𝒁−1
𝒑 𝒅𝒑

Where f = fugacity, psia, p = ideal gas pressure,
psia, Z = compressibility factor
The ratio of the fugacity to the pressure, (f/p), is
called the fugacity coefficient ϕ.
2013 H. AlamiNia


24

Solving Equations
With T and P fixed, the number of variables is also (N +
1), these being (K 1, K 2, …, K N) and β.
 Before solving Equations, it is necessary to make sure
that there are really two phases present and not just a
single gas or a single liquid (oil) phase.
Solution of the two equations is further complicated by
the fact that the fugacity coefficients entering into kfactor Equation are functions of the phase compositions
resulting from the flash calculation, meaning that the
fugacity coefficients have to be determined in an
iterative manner.
 Before dealing with the flash problem in general, it
may be useful to first consider some simplified cases.
2013 H. AlamiNia


25

Flash Calculations Procedure
Step 1. Calculation of the total number of moles in
the vapor (gas) phase (β)
𝑵

𝒇(𝜷) =
𝒊=1

𝒛𝒊 𝑲𝒊 − 1
=0
1 + 𝜷 𝑲𝒊 − 1

Equation can be solved for β by using the NewtonRaphson iteration techniques.

Step 2. Calculation of total number of moles in the
liquid phase (1-β)
Step 3&4 Calculation of xi and yi
𝒛𝒊
𝒛𝒊 𝑲𝒊
, 𝒚𝒊 =
,𝒊
1 + 𝜷 𝑲𝒊 − 1
1 + 𝜷 𝑲𝒊 − 1
= 1,2, … , 𝑵
𝒙𝒊 =

2013 H. AlamiNia


26

Pure Component Vapor Pressures
from Cubic Equations of State
Neglecting solid states, a pure component will
either form a single-phase gas, a single-phase
liquid, or a gas and a liquid phase in equilibrium.
For a given temperature, two phases in equilibrium
can only exist at the pure component vapor
pressure.
Pure component vapor pressures may be
determined from a cubic equation of state, but in
an iterative manner.

2013 H. AlamiNia


27

Mixture Saturation Points from
Cubic Equations of State
If a single component is not at its vapor pressure,
only one phase exists at equilibrium.
With two or more components present, the
determination of the number of phases is less
trivial because the equilibrium phase compositions
are unknown.
Before considering the general PT-flash problem, it
may be useful to first consider the problem of
locating mixture saturation pressures.

2013 H. AlamiNia


29

Mixture Bubble and
Dew Point Pressure
Bubble point
For a mixture initially in liquid form, the saturation point
pressure is detected as the pressure at which the first
gas bubble is seen to form in the liquid.
A saturation point of a liquid is therefore also called a
bubble point.

Dew point
For a mixture initially in gaseous form, the saturation
point is the pressure at which the first liquid drop is
formed.
The saturation point of a gas is therefore also known as a
dew point.
2013 H. AlamiNia


30

Mixture Bubble Point Pressure from
Cubic EoS
As compared to the general PT-flash calculation,
bubble and dew point calculations are simpler, in
the sense that one of the equilibrium phases equals
the feed composition.
At the bubble point pressure, the vapor mole
fraction β equals zero, and
Equation Σ (zi (Ki-1))/ (1+β (Ki-1)) =0 can be
simplified to
𝑵

𝑭=

𝒛𝒊 𝑲𝒊 − 1 = 0
𝒊=1

2013 H. AlamiNia


31

Wilson K-Factor Approximation
For a given estimate of the bubble point pressure, a
K-factor estimate may be obtained from the Kfactor approximation (Wilson, 1969)
𝒍𝒏𝑲 𝒊 = 𝒍𝒏

𝑷 𝒄𝒊
+ 5.373 1 + 𝝎 𝒊
𝑷

𝑻 𝒄𝒊
1−
𝑻

The liquid phase equals the feed composition and
an initial estimate of the vapor phase composition
at the bubble point may be obtained from yi= (ziKi)/
(1+β (Ki-1)) with K-factors from above.
2013 H. AlamiNia


32

K-factor Methods
Explain different k-factor methods

2013 H. AlamiNia


33

Applications of the Equilibrium Ratio
Some of the practical applications are:
Determination of the Dew Point Pressure
Determination of the Bubble-Point Pressure
Separator Calculations

2013 H. AlamiNia


34

1.
2.
3.
4.

Mixture Saturation Points Calculation
Surface Separation
Phase Envelope
Phase Identification

2013 H. AlamiNia


35

1. Pedersen, K.S., Christensen, P.L., and Azeem,
S.J. (2006). Phase behavior of petroleum
reservoir fluids (CRC Press). Ch6.

2013 H. AlamiNia


36

Q913 rfp w3 lec 11

Recommended

Recommended

More Related Content

What's hot

What's hot (20)

Viewers also liked

Viewers also liked (20)

Similar to Q913 rfp w3 lec 11

Similar to Q913 rfp w3 lec 11 (20)

More from AFATous

More from AFATous (20)

Recently uploaded

Recently uploaded (20)

Q913 rfp w3 lec 11