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.
grains
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.
1-D foam experiments
Sandpack: silica sand 20/40
Surfactant: IOS 1518 with 1.0% wt NaCl
Length: 27.5 cm
R-CH(OH)-CH2-CH(SO3-)-R’ (~75%)
R-CH=CH-CH(SO3-)-R’ (~25%),
where R+R’ = C12-15
Inner diameter: 2.58 cm
Permeability: 158.0 darcy
Porosity: 36.0%
1-D foam experiments
Total superficial velocity: 20 ft/day
 foam , app 
 k p
uw  ug
1-D foam experiments
Total superficial velocity: 20 ft/day

ug  
k rg
g


k  ( p g   g g  D )
k rg  k rg  FM
f
FM 
nf
1
1  fmmob  F water  F surf
gas mobility reduction (1/FM)
Foam model
Gas mobility is a function of both water saturation and surfactant
concentration.
1.
2.
Ashoori E, Heijden TLM, Rossen WR (2010) Fractional-Flow Theory of Foam Displacements With Oil. SPE Journal
15:pp. 260-273
Computer Modeling Group (2007) STARSTM User's Guide. Calgary, Alberta, Canada
STARS Foam model (old)
FM 
1
1  fmmob  F water  F surf
F water  0 . 5 
Fsurf  (

1.
arctan[ epdry ( S w  fmdry )]
C sw
fm surf
1

)
epsurf
for C s  fm surf
for C s  fm surf
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.
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.
High and low quality regime
fg 
k rg ( S ) /  g
k rw ( S ) /  w  k rg ( S ) /  g
 1  (1 
k rg ( S ) /  g
k rw ( S ) /  w
S w  S w  fmdry
*
f
1.
2.
 1  (1 
1
?
k rg ( S w )  FM ( S w )
nf
*
g
)
*
*
*
k rw ( S w )

w
g
)
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.
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).
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  foam , app ( S w )   foam , app ( S w )
*
Sw*=0.3461
fmdry=0.3400
Sw* and fmdry
An example using fmmob = 12000 and fmdry =
0.34:
fg-Sw curve is very steep near Sw* and precise
calculation of Sw* is needed.
Sw*=0.3461
fg*
fmdry=0.3400
The problem to solve
Solve fmmob, fmdry and Sw* through the following equations:

*
foam , app
1
( measured ) 
f
*
k rw ( S w )

w
g
1
f g ( measured ) 
*
g
*
1
k rw ( S w )
w

f
*
1
k rw ( S w )
w
f

*
k rg ( S w , fmmob , fmdry )
max  foam , app ( S w )   foam , app ( S w )
 foam , app ( S w ) 
*
k rg ( S w , fmmob , fmdry )
k rg ( S w )
g
Using Equations (a) and (b) to determine a
contour plot 1 of fg* as a function of fmmob and
fmdry
max  foam , app ( S w )   foam , app ( S w )
*
Eqn (a)
Using Equations (c) and (d) to determine a
contour plot 2 of μfoam,app as a function of
fmmob and fmdry
1
f g , measured 
*
1
1
fg 
*
1
*
w
k rw ( S )
w

Eqn (b)
g
f
rg
*
w
k (S )

foam , app
(S w ) 
k rw ( S w )
w
g

f
k rg ( S w )
1
k rw ( S w )
w
Eqn (c)
Eqn (d)
f

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
k rg ( S w )
g
Match experimental data
fg=0.5
Computed from:
Computed from:
1
fg 
*
g
*
1
k rw ( S w )
w


f
*
k rg ( S w )
foam , app
(S w ) 
1
k rw ( S w )
w
f

k rg ( S w )
g
Match experimental data
Match experimental data
Total superficial velocity: 20 ft/day
fmmob=26800
fmdry=0.311
Dependence on surfactant concentration
Revised Foam model (new)
FM 
1
1  fmmob  F water  F surf
arctan[ epdry ( S w  fmdry (
F water  0 . 5 
F surf
C sw

epsurf
)
 (
  fmsurf
1

C sw
fmsurf

for C sw  fmsurf
for C sw  fmsurf
instead of
fmdry in the old
model
)
epfmdry
)]
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