Upload
daniella-carroll
View
217
Download
0
Embed Size (px)
Citation preview
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