1. 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

2. 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.

3. 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 lamellae 1. Pore-level schematic of fluid distribution for foam flow 2 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

4. 1-D foam experiments 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)-CH 2 -CH(SO 3 -)-R’ (~75%) R-CH=CH-CH(SO 3 -)-R’ (~25%), where R+R’ = C12-15

5. 1-D foam experiments Total superficial velocity: 20 ft/day

6. 1-D foam experiments Total superficial velocity: 20 ft/day

7. Foam model 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) STARS TM User's Guide. Calgary, Alberta, Canada gas mobility reduction (1/FM) surfactant concentration (g/L) water saturation

8. STARS Foam model (old) 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. 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.

9. 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). ?

10. S w * and fmdry An example using fmmob = 12000 and fmdry = 0.34: 1. S w * is close but not equal to fmdry; 2. S w * can be calculated through fmdry=0.3400 S w * =0.3461

11. S w * and fmdry fmdry=0.3400 S w * =0.3461 An example using fmmob = 12000 and fmdry = 0.34: f g -S w curve is very steep near S w * and precise calculation of S w * is needed. fg*fg*

12. The problem to solve Solve fmmob, fmdry and S w * through the following equations:

13. Using Equations (c) and (d) to determine a contour plot 2 of μ foam,app as a function of fmmob and fmdry Eqn (c) Eqn (d) Using Equations (a) and (b) to determine a contour plot 1 of f g * as a function of fmmob and fmdry Eqn (a) Perform superposition of contour plots 1 and 2 and indentify the point (fmmob, fmdry) where f g * = f g,measured * in contour plot 1 and μ foam,app = μ foam, measured * in contour plot 2 cross over Eqn (b)

14. Match experimental data f g =0.5 Computed from:

15. Match experimental data

16. Total superficial velocity: 20 ft/day fmmob=26800 fmdry=0.311

17. Dependence on surfactant concentration

18. Revised Foam model (new) instead of fmdry in the old model

19. Surface tension fmsurf (hypothesized)

20. Match experimental data

21. 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.

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

23. Thank you!

24. Parameters for foam simulation