Estimation of parameters for simulation of

steady state foam flow in porous media

Kun Ma, Jose L. Lopez-Salinas, Sibani Lisa Biswal and George J. Hirasaki

Department of Chemical & Biomolecular Engineering

Rice University, Houston, TX

07/02/2012

Outline

1. Foam simulators have many parameters. How do we

determine them?

2. Compare the experimental results with the foam models in

a commercially available reservoir simulator.

3. Develop methodology to describe foam mobility from

common foam experiments.

System A

System B

1-D foam experiments (System A)

Sandpack: silica sand 20/40

Length: 27.5 cm

Inner diameter: 2.58 cm

Permeability: 158.0 darcy

Porosity: 36.0%

Surfactant: IOS 1518 with 1.0% wt NaCl

R-CH(OH)-CH2-CH(SO3-)-R’ (~75%)

R-CH=CH-CH(SO3-)-R’ (~25%),

where R+R’ = C12-15

1-D foam experiments

Total superficial velocity: 20 ft/day

gw

appfoamuu

pk

,

1-D foam experiments

Total superficial velocity: 20 ft/day

Foam model

FMkk nfrgf

rg

surfwater FFfmmobFM

1

1

)( Dgpkk

u ggg

rg

g

Gas mobility is a function of both water saturation and surfactant

concentration.

1. Ashoori E, Heijden TLM, Rossen WR (2010) Fractional-Flow Theory of Foam Displacements With Oil. SPE Journal

15:pp. 260-273

2. Computer Modeling Group (2007) STARSTM User's Guide. Calgary, Alberta, Canada

gas m

obili

ty r

eduction (

1/F

M)

STARS Foam model (old)

surfwater FFfmmobFM

1

1

)](arctan[5.0

fmdrySepdryF wwater

1. Rossen, W. R. and Renkema, W. J. (2007). Success of Foam SAG Processes in Heterogeneous Reservoirs. SPE Annual

Technical Conference and Exhibition. Anaheim, California, U.S.A., Society of Petroleum Engineers.

( )

1

epsurfswsurf s

s

CF for C fmsurf

fmsurf

for C fmsurf

fmmob: the reference foam

mobility reduction factor;

fmdry: the critical water

saturation (volume fraction)

above which the maximum foam

strength is reached;

fmsurf: the critical surfactant

concentration above which gas

mobility is independent of

surfactant concentration.

High and low quality regime

1. Cheng, L., Reme, A. B., et al. (2000). Simulating Foam Processes at High and Low Foam Qualities. SPE/DOE Improved

Oil Recovery Symposium. Tulsa, Oklahoma.

2. Alvarez, J. M., Rivas, H. J., et al. (2001). Unified Model for Steady-State Foam Behavior at High and Low Foam

Qualities. SPE Journal 6(3).

1

( ) /

( ) / ( ) /

( ) /1 (1 )

( ) /

rg g

g

rw w rg g

rg g

rw w

k Sf

k S k S

k S

k S

fmdrySS ww *

1

*

**

* ))(

)()(1(1

g

w

wrw

ww

nf

rg

gSk

SFMSkf

?

Sw* and fmdry

An example using fmmob = 10000,

epdry=1000 and fmdry = 0.1:

1. Sw* is close but not equal to fmdry;

2 . Sw* can be calculated through

)()(max *,, wappfoamwappfoam SS

fmdry=0.1000

Sw*=0.1038

Sw* and fmdry

An example using fmmob = 10000,

epdry=1000 and fmdry = 0.1:

fg-Sw curve is very steep near Sw* and precise

calculation of Sw* is needed.

fg*

fmdry=0.1000

Sw*=0.1038

transition

foam quality

The problem to solve

g

w

f

rg

w

wrw

appfoamfmdryfmmobSkSk

measured

),,()(

1)(

**

*

,

),,(

)(1

1)(

*

*

*

fmdryfmmobSk

Skmeasuredf

w

f

rg

g

w

wrw

g

)()(max *,, wappfoamwappfoam SS

g

w

f

rg

w

wrw

wappfoamSkSk

S

)()(

1)(,

Solve fmmob, fmdry and Sw* through the following equations:

Using Equations (c) and (d) to determine a

contour plot 2 of μfoam,app as a function of fmmob and fmdry

Eqn (c)

Eqn (d)

Using Equations (a) and (b) to determine a

contour plot 1 of fg* as a function of fmmob and

fmdry

Eqn (a)

Perform superposition of contour plots 1 and 2 and indentify

the point (fmmob, fmdry) where fg*= fg,measured

* in contour plot

1 and μfoam,app= μfoam, measured* in contour plot 2 cross over

Eqn (b)

)(

)(1

1

*

*

*

w

f

rg

g

w

wrw

g

Sk

Skf

)(

)(1

1*,

w

f

rg

g

w

wrw

measuredg

Sk

Skf

g

w

f

rg

w

wrw

wappfoamSkSk

S

)()(

1)(,

)()(max *,, wappfoamwappfoam SS

Match experimental data

fg=0.5

Computed from:

)(

)(1

1

*

*

*

w

f

rg

g

w

wrw

g

Sk

Skf

Computed from:

g

w

f

rg

w

wrw

wappfoamSkSk

S

)()(

1)(,

Match experimental data

fmdry = 0.072

fmmob

= 44200

Match experimental data Total superficial velocity: 20 ft/day

fmmob=44200

fmdry=0.072

epdry=1000

Effect of epdry

fmmob = 44200, and fmdry = 0.072

Dependence on surfactant concentration

Revised Foam model (new)

surfwater FFfmmobFM

1

1

)])((arctan[

5.0

epfmdrysww

water

fmsurf

CfmdrySepdry

F

instead of

fmdry in the old

model

fmsurfC

fmsurfCfmsurf

C

F

sw

sw

epsurfsw

surf

for 1

for )(

Surface tension

fmsurf (hypothesized)

Match experimental data

Comparison of Sw

System A

System B

Foam apparatus for high temperature

(System B)

Experimental data

Surfactants: ZA blend

Temperature: 94℃

Match experimental data

38799fmmob

044.0fmdry

Match experimental data

Surfactants: ZA blend

Temperature: 94℃ Total superficial velocity: 31.0 ft/day

Experimental data (shear thinning)

Shear thinning effect in foam model

surfshearwater FFFfmmobFM

1

1

FMkk nfrgf

rg

)](arctan[5.0

fmdrySepdryF wwater

epv

refg

g

shearu

uF )(

,

1surfF (default value)

Shear thinning effect

g

gw

f

rg

w

wrw

wappfoamuSkSk

S

),()(

1)(,

),(

)(1

1)(

gw

f

rg

g

w

wrw

wg

uSk

SkSf

wn

wcgr

wcwrwrw

SS

SSkk )

1(0

FMSS

SSkk g

n

wcgr

wcwrg

f

rg

)

11(0

(next slide)

Shear thinning effect

1)1

1(

)()](arctan[

5.0

,

0

,

gn

wcgr

wcw

gg

appfoamrg

epv

refg

gw

SS

SS

f

k

u

ufmdrySepdryfmmob

wn

appfoamrw

gw

wcgrwcwk

fSSSS

1

,

0

)1()1(

(next slide)

Log-log fit to experimental data

)(log10 gux

})1(

)1({arctan

5.0

1)1(

1

log1

,

0

1

,

0

,

0

10

fmdryk

fSSSepdry

k

f

f

k

ywn

g

wn

appfoamrw

gw

wcgrwc

n

appfoamrw

gw

gg

appfoamrg

)(log,

10 epv

refgu

fmmobxepvy

Log-log fit to experimental data

(fg=0.7)

Match experimental data

8693.0epv

6883.5)(log,

10 epvrefgu

fmmob

dayftuif refg /7.21,

6883.58693.0

)(log,

10

xy

u

fmmobxepvy

epv

refg

33614fmmob

7.0gf for shear-thinning modeling

Parameters obtained

33614fmmob 044.0fmdry 8693.0epv

,

,

dayftu refg /7.217.00.31,

Shear-thinning modeling

Dry-out modeling

(assumed)

(assumed)

38799fmmob 044.0fmdry 0epv

arbitraryu refg ,

dayftutotal /0.31

7.0gf

Used in next slide

Slide 25

Match experimental data

Conclusions

1. A new method of fitting the parameters in the STARS foam

model is presented and a unique group of parameters is

found for modeling the foam property in silica sandpack with

the surfactant 0.02%-0.2% IOS 1518 in 1.0% NaCl solution.

2. A revised dry-out model for effect of surfactant

concentration is proposed.

3.The critical surfactant concentration (fmsurf) in the foam

model is at least one order of magnitude above the CMC.

4. The shear thinning effect is modeled using the STARS

foam model.

Thank you!

Parameters for foam simulation

Match experimental data (System B)

38799fmmob

044.0fmdry

Effect of epdry

An example using fmmob = 10000, and

fmdry = 0.1: