effect of pseudo-component selection on the simulation of

Folake OgunbanwoMay 21st, 2014

Effect of Pseudo-Component

Selection on the Simulation of a CO2 Gas Injection Process

Outline

• Objective

• Introduction

• Literature Background

• 1-D Simulation results

• Conclusions

• Future work

221st May, 2014 SCCS Annual Meeting & Workshop

Objective


00.1

0.20.3

0.40.5

0.60.7

0.80.9

1

00.1

0.20.3

0.40.5

0.60.7

0.80.9

1

0

0.1

0.2

0.3

0.4

0.5

0.6

0.7

0.8

0.9

1

C2-9

C1

C10-29

CO2

MOVE FROM

A static approach of selecting

pseudo-components using phase

diagrams

TO

A dynamic selection based on the

path of the reference fluid in

compositional space

Capture the flow dynamics and phase behavior of multi-component fluids

undergoing CO2 EOR using pseudoized components.

-200 0 200 400 600 800 10000

500

1000

1500

2000

Temperature (degF)

Pre

ssu

re (

psia

)

Ref. fluid

Pseudo fluid

Critical pt

Critical pt

Typical CO2 injection process

4

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ccs-industry-sectoral-assessment- CO2 -enhanced-oil-recovery-3


Compositional Simulation Challenges

• Reservoir fluids contain a large number of components (C1------C30+)

• Mass conservation and phase equilibria calculations have to be solved at each time step

• Large number of iterative flash calculations required

• Increased computer storage and simulation run time


Solution –Pseudocomponents

Lumping :

• Where n is less than N.

• Each component has the following properties:

Pc, Tc, Vc, ω, Mw and δij

Two main issues arise :

• Grouping scheme: What components should be lumped together?

• Mixing rules: How do we assign properties to the pseudo -components?

6

C1, C2, C3,………...,CN

Ca, Cb, Cc,…,Cn


Literature Background

• Lumping schemes have been proposed based on the

– Mass fractions (Whitson, 1980)

– Boiling point range (Lee et al., 1981)

– Saturation pressure (Mehra, 1982)

– K-value similarity (Lee, 1985)

– Flow based lumping using K value variation (Rastegar, 2009)


Mixing Rules

• Weighted arithmetic averaging is the method generally used such that

• δij is calculated using

8

si tj

ji

si tj

ijji

sxx

xx

• EOS-Tcs[1]is calculated by

• Factors used as weights include

– Molar[2] and Mass[3]

fractions, Vc[4] and Pc

[5]

si

i

si

iis xx /PrPr

s ci

ciis

ijcj

j

ciji

i

cs

PTx

x

kTTxxT )1()( 2/1

[1] Reid (1977), [2] Kay (1938), [3] Pedersen et al.(1985), [4] Hong (1982), [5] Lee (1981)


Simulation Set up in CMG GEM

9

• Synthetic fluid containing C1-C29+ generated using WinProp

• 1-D Cartesian grid of 140*1*1 (0.05ft*2ft*1ft)

• K = 200 md, φ =30 %

• T = 90oF, P = 800 psi

• Gas injection rate = 500 scf/d


21st May, 2014 SCCS Annual Meeting & Workshop 10

Physical Properties of Reference Fluid

0 5 10 15 20 25 300

5

10

15

20

Carbon number, Cn

Co

mp

ositio

n

0 50 100 150 200 250 300 350 400 450 5000

10

20

30

40

50

Critical P

ressure

Pc (

psi)

0 50 100 150 200 250 300 350 400 450 5000

200

400

600

800

1000

Critical T

em

pera

ture

Tc (

K)

Molecular Weight (g/mol)

Lumping using Whitson’s rule

• The multi-component mixture was lumped gradually into a pseudo-component fluid

• By rule of thumb, C1 is not lumped

11

)(log3.3101 nNIntN g

I

nNgnI MMNMM /ln*/1exp

C1, C2, C3,………...,C29+

C1, C2-10, C11-29+

light, intermediate and heavy fractions


Results

12

0 1 2 3 4 5 6 70

0.1

0.2

0.3

0.4

0.5

0.6

0.7

distance (ft)

volu

me

fra

ctio

n (

CC

O2)

5 days

10 days

15 days

20 days

25 days

30 days


Molar Weighted Pseudocomponents

13

P-T diagram for Pseudoized Fluids CO2 front after 29 days of injection

• The phase diagram shrinks with lumping

and the errors introduced in the front

propagation increases.


-200 0 200 400 600 800 10000

200

400

600

800

1000

1200

1400

1600

1800

Temperature (degF)

Pre

ssu

re (

psia

)

3

4

5

6

7

8

9

10

11

12

13

29

ref. pt

op. pt

crit. pt

3.5 4 4.5 5 5.50

0.1

0.2

0.3

0.4

0.5

0.6

distance (ft)

vo

lum

e fra

ctio

n C

CO

2

29 comp

13 comp

12 comp

11 comp

10 comp

9 comp

8 comp

7 comp

6 comp

5 comp

4 comp

3 comp

Mass Weighted Pseudocomponents

14

P-T diagram for Pseudoized Fluids CO2 front after 29 days of injection

• The phase diagram shrinks with lumping.


-200 0 200 400 600 800 10000

200

400

600

800

1000

1200

1400

1600

1800

Temperature (degF)

Pre

ssu

re (

psia

)

3

4

5

6

7

8

9

10

11

12

13

29

ref. pt

op. pt

crit. pt

3.5 4 4.5 5 5.50

0.1

0.2

0.3

0.4

0.5

0.6

distance (ft)

volu

me

fra

ctio

n C

CO

2

29 comp

13 comp

12 comp

11 comp

10 comp

9 comp

8 comp

7 comp

6 comp

5 comp

4 comp

3 comp

Mixing rule effect

15

P-T diagram for a 3 – pseudocomponent mixture using different mixing

rules


-200 0 200 400 600 800 10000

200

400

600

800

1000

1200

1400

1600

1800

Temperature (degF)

Pre

ssu

re (

psia

)

Mass weighted

Mol weighted

Surface fraction

Pc weighted EOS Tc

Vc2/3

weighted EOS Tc

Vc weighted EOS Tc

Z weighted EOS Tc

True Mixture

True crit pt

critical points

Mixing rule effect

16

CO2 front after 29 days of injection using different mixing rules on a 3

pseudocomponent mixture


2 2.5 3 3.5 4 4.5 5 5.50

0.1

0.2

0.3

0.4

0.5

0.6

distance (ft)

volu

me fra

ction (

CC

O2)

Mass weighted

Mol weighted

Surface fraction

Pc weighted EOS Tc

Vc2/3

weighted EOS Tc

Vc weighted EOS Tc

Z weighted EOS Tc

True Mixture

Lines of Constant Volume fraction Vapor

17

Phase Diagrams for 70% Primary fluid and 30 % CO2 mixture

0 100 200 300 400 500 600 700 800 900 10000

500

1000

1500

2000

2500

3000

Temperature (degF)

Pre

ssu

re (

psia

)

P-T diagram70PRI

True boundary

30% CO2

critical pt

Mass av boundary

30% CO2

critical pt

Mol av boundary

30% CO2

critical pt

operating pt

80 85 90 95 100 105 110 115 120

720

740

760

780

800

820

840

860

880

Temperature (degF)

Pre

ssu

re (

psia

)

P-T diagram70PRI


Comparing Paths on Quaternary Plots

Path of Reference fluid

00.1

0.20.3

0.40.5

0.60.7

0.80.9

1

00.10.2

0.30.40.5

0.60.70.8

0.910

0.1

0.2

0.3

0.4

0.5

0.6

0.7

0.8

0.9

1

C2-10

CH4

C11-29

CO2

Path of Pseudoized fluid

00.1

0.20.3

0.40.5

0.60.7

0.80.9

1

00.10.20.30.4

0.50.60.70.80.91

0

0.1

0.2

0.3

0.4

0.5

0.6

0.7

0.8

0.9

1

C2-10

CH4

C11-29

CO2

18

Path in quaternary diagram after 29 days of CO2 injection into the

reservoir


Determining Best Lumping Scheme

• Run fully descriptive model and obtain Zref at alltime steps

• Run simulations using different groupingschemes

• Get composition of pseudoized fluid per timestep (Zps)

• Determine the error using L2 norm:

• Select group with the least error


2

2

22 )())(( PSrefPSref ZZZZnormLerror

Plot of Error vs Grouping Scheme


C1, C2-9, C10-29 and C1-2, C3-12, C13-29 have the lowest errors

8 10 12 14 16 18 20 220

0.5

1

1.5

2

2.5

3m

ea

su

rem

en

t o

f e

rro

r

carbon number (Cx)

C1, C

2-C

x, C

x+1 - C

29

C1-2

, C3-C

x, C

x+1 - C

29

C1-3

, C4-C

x, C

x+1 - C

29

Properties Plot of Pseudoized Fluids


0 100 200 300 400 5000

10

20

30

40

50

MW

Pc (

psi)

0 100 200 300 400 5000

0.2

0.4

0.6

0.8

1

1.2

1.4

MW

Ac

0 100 200 300 400 5000

200

400

600

800

1000

MW

Tc (

K)

Reference

C1-2

,C3-12

,C13-29

C1,C

2-9,C

10-29

Results


Fluid Simulation Time (S)

Reference 12165

C1, C2-9, C10-29 117.453

C1-2, C3-12, C13-29 234.53

0 20 40 60 800

0.05

0.1

0.15

0.2

0.25

0.3

0.35

time (days)

cu

mu

lative

liq

uid

(b

bl)

Reference

C1,C

2-9,C

10-29

C1-2

, C3-12

, C13-29

0 20 40 60 800

50

100

150

200

250

time (days)

cu

mu

lative

ga

s (

ft3)

Reference

C1,C

2-9,C

10-29

C1-2

, C3-12

, C13-29

Results


CO2 front after 29 days of injection P-T Diagram for pseudoized fluid

3.5 4 4.5 5 5.50

0.1

0.2

0.3

0.4

0.5

0.6

0.7

distance (ft)

vo

lum

e fra

ctio

n C

CO

2

Reference

C1,C

2-9,C

10-29

C1-2

, C3-12

, C13-29

-200 0 200 400 600 800 10000

200

400

600

800

1000

1200

1400

1600

1800

Temperature (degF)P

ress

ure

(psi

a)

C1, C

2-9, C

10-29

C1-2

,C3-12

,C13-29

Reference

Comparing Paths on Quaternary Plots

Path of Reference Fluid

00.1

0.20.3

0.40.5

0.60.7

0.80.9

1

00.1

0.20.3

0.40.5

0.60.7

0.80.9

1

0

0.1

0.2

0.3

0.4

0.5

0.6

0.7

0.8

0.9

1

C2-9

C1

C10-29

CO2

Path of Best Pseudoized Fluid

00.1

0.20.3

0.40.5

0.60.7

0.80.9

1

00.1

0.20.3

0.40.5

0.60.7

0.80.9

1

0

0.1

0.2

0.3

0.4

0.5

0.6

0.7

0.8

0.9

1

C2-9

C1

C10-29

CO2


Conclusion

• The grouping scheme and mixing rule used for assigning properties to the pseudo-components are important.

• Matching the path in compositional space can be used to group a large number of components into pseudo-components for faster simulations


Future Work

• Tune pseudoized fluid parameters by matching the path in compositional space.

• Run simulations at other operating conditions.

• Use a different fluid

• Check the effect on viscosity


effect of pseudo-component selection on the simulation of

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