PETE 310

Lecture # 29

Chapter 14

Equilibrium Ratio Correlations (K-values)

Gas-Liquid Equilibrium Non Ideal Behavior

When evaluating VLE we use models for the equilibrium ratios (Ki-values)

Simpler models Ki = f (P,T)

low pressure applications

explicit

More complex models Ki = f(P,T,xi,yi) use equations of state EOS (current), or convergence pressure methods (earlier)

apply lo low and high pressures

implicit, highly iterative

What’s a “low” or a “high” pressure?

Separator pressures for a black oil are usually considered low

Reservoir pressures considered high are > 1000 psia, but this limit depends upon type of fluid

For black oils simple K-value correlations do a good job

Volatile oils and gas condensates have a more complex behavior

K-values

Compositionally independent correlations assume that k-values depend upon pressure and temperature only

In fact Ki values depend upon the type and proportions of other molecules in the mixture

Example: Your behavior is different when you are surrounded by people of your same age than when you are surrounded by professors, or potential employers

Statement of Equilibrium

Only component 3 has a vapor pressure for the selected T – 2 & 1 are supercritical

iii Kxy

P

T

1

2 3

3P

Bubble Point & Dew Point Evaluations

The bubble point pressure at a given T is

The dew point pressure at a given T is

,...)T,pKzy bpiii,...T,pKz1 bpii

,...)T,p(Kxz

Kxy

dpiii

iii

Flash Calculations

Objective function (flash function) is

01fKf1

Kz)f(F

viv

iiv

One of the Models for Equilibrium Ratios

T

T1137.5exp

p

pK ci

ici

i

Requires critical properties & acentric factors

We need other models for higher pressures

For higher pressures and temperatures

Equilibrium ratio charts for different convergence pressures

Tedious but…

Illustrate fundamental concepts

Equations of State (mainly cubic)

Tedious by hand

Suitable for computers

More in later lectures

Convergence Pressure Equilibrium Ratio Charts

Plot Ki vs p in a log-log scale

K-values converge to a unique pressure called convergence pressure

But this ‘convergence pressure’ depends upon type of fluid

Black oils have convergence pressures of about 10000 psia

Observed experimental behavior (see Fig. 14-1 and 14-2) of text book

Convergence Pressure Highlights

Is a property that takes into account the compositional effect

When the mixture is a volatile oil the K-values of their components have convergence pressures of about 7000 psia

When the mixture is a gas condensate the K-values of their components have convergence pressures of about 5000 psia

Book contains only charts for convergence pressure (pk) of 5,000 psia

90 Convergence pressure charts are tabulated for pk’s of 800, 1000, 1500, 2000, 3000, 5000, and 10000

Convergence Pressure Highlights

Convergence pressure is found iteratively

Some interpolation may be needed among charts

Charts have not been digitized and no publicly available equations have been generated from these charts (GPSA have computer codes at a cost)

Procedure is lengthy and tedious

For repetitive computations (reservoir simulation), Equations of State (EOS) have replaced this methodology

Still a good approach for few calculations

Other Uses of Convergence Pressure Charts

To determine the pressure range of ideal behavior

To have a quick comparison among K-values of different components

To estimate vapor pressures

Convergence Pressure Equilibrium Ratio Charts

Note the slope for low pressures…

Errors: Black Oil at Surface Conditions

Errors: Black Oil at Surface Conditions

What would be the percent error in the evaluated liquid produced at 65 psia and 120 oF if the K-value for methane is

15% higher than the actual value

15% lower than the actual value

How about the effects of the other components in the mixture?

Errors: Retrograde Gas at Reservoir Conditions

Errors: Retrograde Gas at Reservoir Conditions

What would be the percent error in the evaluated liquid volume at 2650 psia and 195 oF if the K-value for C7

+ is

15% higher than the actual value

15% lower than the actual value

Which are the most ‘influential’ components

Equilibrium Ratios for Methane Convergence Pressure = 5000 psia

Note the slope and dotted lines

Equilibrium Ratios for Ethane Convergence Pressure = 5,000 psia

Given a temperature lower than the Tc

of C2, How can we estimate the vapor pressure of C2 from this chart?

Equilibrium Ratios for Octane Convergence Pressure = 5,000 psia

According to this chart, what is the pressure range for which we could have used the Raoult’s law model for KC8 as a very good approximation?

Standings K-value Correlation (SPE 7903)

Correlation good for Pressures up to 1000 psia

Observed behavior

F is a component characterization factor

Number in chart indicates compound

Standings K-value Correlation (SPE 7905, JPT - September 1979)

Correlation is

With

p

10K

cFa

i

T

1

T

1bF

bi

i

cibi

ci

i

T

1

T

1

7.14

plog

b

(T in oR and p in psia)

biTIs the normal boiling point temperature of the component

Standings K-value Correlation (SPE 7905, JPT - September 1979)

Correlation is (F already defined)

With

p

10K

cFa

i

284

284

p105.3p107.189.0c

p1015p105.42.1a

Values for bi and Tb (from SPE paper)

For heptanes and heavier we can use…

We will use the following approach

Other approaches include using an equivalent carbon number that determines a normal boiling point for the heavy fraction (paper)

77CC

K15.0K

Modified Homework

Use the data from problem 14-1 and determine the K-value for each component at T = 160oF and p = 1500 psia

Compare the K-values with the K-values provided in the book – Indicate the % differences

Calculate the initial oil composition if the fraction of gas produced with the ‘old K-values’ is 10%

Use the recently obtained reservoir composition with the new K-values, run a flash and determine the new gas fraction.

Compare with the previously reported one and discuss