Estimation of parameters for simulation of steady state foam flow in porous media

Kun Ma, Sibani Lisa Biswal and George J. Hirasaki

Department of Chemical & Biomolecular Engineering

Rice University, Houston, TX

04/23/2012

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.

Foam in porous media ★ Foam in porous media is defined as a dispersion of gas in liquid such that the liquid phase is continuous and at least some part of the gas phase is made discontinuous by thin liquid films called lamellae1.

Pore-level schematic of fluid distribution for foam flow2

1. Hirasaki, G. J. (1989). Journal of Petroleum Technology 41(5): 449-456. 2. Radke, C. J. and J. V. Gillis (1990). SPE Annual Technical Conference and Exhibition, 23-26 September 1990, New

Orleans, Louisiana.

grains

1-D foam experimentsSandpack: 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 experimentsTotal superficial velocity: 20 ft/day

gwappfoam uu

pk

,

1-D foam experimentsTotal superficial velocity: 20 ft/day

Foam model

FMkk nfrg

frg

surfwater FFfmmobFM

1

1

)( Dgpkk

u ggg

rgg

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. 260-2732. Computer Modeling Group (2007) STARSTM User's Guide. Calgary, Alberta, Canada

gas

mob

ility

red

uctio

n (1

/FM

)

surfactant concentration (g/L)water saturation

STARS Foam model (old)

surfwater FFfmmobFM

1

1

)](arctan[

5.0fmdrySepdry

F 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 gg

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

wwnfrg

g Sk

SFMSkf

?

Sw* and fmdry

An example using fmmob = 12000 and fmdry = 0.34:

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

2 . Sw* can be calculated through

)()(max *,, wappfoamwappfoam SS

fmdry=0.3400

Sw*=0.3461

Sw* and fmdry

fmdry=0.3400

Sw*=0.3461

An example using fmmob = 12000 and fmdry = 0.34:

fg-Sw curve is very steep near Sw* and precise calculation of Sw* is needed.

fg*

The problem to solve

g

wfrg

w

wrw

appfoam fmdryfmmobSkSkmeasured

),,()(

1)(

**

*,

),,(

)(1

1)(

*

**

fmdryfmmobSk

Skmeasuredf

wfrg

g

w

wrwg

)()(max *,, wappfoamwappfoam SS

g

wfrg

w

wrw

wappfoam SkSkS

)()(

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

*

**

wfrg

g

w

wrwg

Sk

Skf

)(

)(1

1*,

wfrg

g

w

wrwmeasuredg

Sk

Skf

g

wfrg

w

wrw

wappfoam SkSkS

)()(

1)(,

)()(max *,, wappfoamwappfoam SS

Match experimental data

fg=0.5

Computed from:

)(

)(1

1

*

**

wfrg

g

w

wrwg

Sk

Skf

Computed from:

g

wfrg

w

wrw

wappfoam SkSkS

)()(

1)(,

Match experimental data

Match experimental dataTotal superficial velocity: 20 ft/dayfmmob=26800fmdry=0.311

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

CF

sw

swepsurfsw

surf

for 1

for )(

Surface tension

fmsurf (hypothesized)

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 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.

Acknowledgment

This work was financially supported by ADNOC, ADCO, ZADCO, ADMA-OPCO and PI, U.A.E.

Thank you!

Parameters for foam simulation