Fractal Prediction Model of Spontaneous Imbibition Rate

Transport in Porous Media

Volumn 91, Issue 2, 2012, Pages 363-376

  Li, Kewen ^a,b   Zhao, Haiyang ^c  

^a CHINA UNIVERSITY OF GEOSCIENCES   (China)

^b STANFORD UNIVERSITY   (United States)

^c SINOPEC   (China)

Author keywords

Fractal dimension; Production model; Spontaneous imbibition

Indexed keywords

BEREA SANDSTONE; EXPERIMENTAL DATA; POWER LAW RELATIONSHIP; PREDICTION MODEL; PRODUCTION MODEL; PRODUCTION MODELS; PRODUCTION RATES; SPONTANEOUS IMBIBITION; WATER IMBIBITION;

MATHEMATICAL MODELS; MERCURY (METAL); POROUS MATERIALS; PRODUCTION ENGINEERING; ROCKS; SANDSTONE;

FRACTAL DIMENSION;

BEREA SANDSTONE; CAPILLARY PRESSURE; EXPERIMENTAL STUDY; FRACTAL ANALYSIS; GRAYWACKE; IMBIBITION; NUMERICAL MODEL; PERMEABILITY; POROUS MEDIUM; PREDICTION;

EID: 83855165763     PISSN: 01693913     EISSN: None     Source Type: Journal    
DOI: 10.1007/s11242-011-9848-0     Document Type: Article

References (52)

1. Al-Lawati, S., Saleh, S.: Oil recovery in fractured oil reservoirs by low IFT imbibition process, paper SPE 36688, presented at the 1996 SPE Annual Technical Conference and Exhibition, Denver, 6-9 Oct 1996.
2. Angulo, R. F., Gonzalez, H.: Fractal dimensions from mercury intrusion capillary tests, SPE 23695. Presented at the 2nd Latin American petroleum engineering conference of SPE held in Caracas, Venezuela, 8-11 Mar (1992).
3. Aronofsky J. S., Masse L., Natanson S. G.: A model for the mechanism of oil recovery from the porous matrix due to water invasion in fractured reservoirs. Trans. AIME 213, 17-19 (1958).
4. Babadagli T.: Scaling of cocurrent and countercurrent capillary imbibition for surfactant and polymer injection in naturally fractured reservoirs. SPEJ 6(4), 465 (2001).
5. Barenblatt, G. I., Patzek, T. W., Silin, D. B.: The mathematical Model of non-equilibrium effects in water-oil displacement, SPE 75169. In: Proceedings of the SPE/DOE Thirteenth Symposium on Improved Oil Recovery held in Tulsa, Oklahoma, 13-17 Apr 2002.
6. Brooks R. H., Corey A. T.: Properties of porous media affecting fluid flow. J. Irrig. Drain. Div. 6, 61 (1966).
7. Cai J., Yu B., Zou M., Luo L.: Fractal characterization of spontaneous co-current imbibition in porous media. Energy and Fuels 24, 1860-1867 (2010).
8. Camacho-Velázquez, R, Fuentes-Cruz, G., Vásquez-Cruz, M.: Decline curve analysis of fractured reservoirs with fractal geometry, SPE 104009, presented at the first international oil conference and exhibition in Mexico held in Cancun, 31 Aug-2 Sept 2006.
9. Chandler R., Koplik J., Lerman K., Willemsen J. F.: Capillary displacement and percolation in porous media. J. Fluid Mech. 119, 249-267 (1982). doi: 10. 1017/S0022112082001335.
10. Cuiec L. E., Bourbiaux B. J., Kalaydjian F. J.: Oil recovery by imbibition in low-permeability chalk. SPEFE. 9(3), 200-208 (1994).
11. Darcel C., Bour O., Davy P., de Dreuzy J. R.: Connectivity properties of two-dimensional fracture networks with stochastic fractal correlation. Water Resour. Res. 39(10), 1272 (2003). doi: 10. 1029/2002WR001628.
12. Du Prey E. L.: Gravity and capillary effects on imbibition in porous media. SPEJ 18, 195-206 (1978).
13. Du C., Xu B., Yortsos Y. C., Chaouche M., Rakotomalala N., Salin D.: Correlation of occupation profiles in invasion percolation. Phy. Rev. Lett 74(5), 694-697 (1995).
14. Friesen W. I., Mikula R. J.: Fractal dimensions of coal particles. J. Colloid Interface Sci. 120(1), 263-271 (1987).
15. Gueguen Y., Dienes J.: Transport properties of rocks from statistics and percolation. Math. Geol. 21(1), 1-13 (1989).
16. Handy L. L.: Determination of effective capillary pressures for porous media from imbibition data. Pet. Trans. AIME 219, 75-80 (1960).
17. Hamon, G., Vidal, J.: Scaling-up the capillary imbibition process from laboratory experiments on homogeneous and heterogeneous samples, paper SPE 15852, presented at the SPE European Petroleum Conference, London, 20-22 Oct, 1986.
18. Hansen J. P., Skjeltorp A. T.: Fractal pore space and rock permeability implications. Phys. Rev. B 38(4), 2635-2638 (1988).
19. Hirsch L. M., Thompson A. H.: Size-dependent scaling of capillary invasion including buoyancy and pore size. Phys. Rev. E 50(3), 2069-2086 (1994).
20. Høgnesen E. J., Standnes D. C., Austad T.: Scaling spontaneous imbibition of aqueous surfactant solution into preferential oil-wet carbonates. Energy Fuels 18(6), 1665-1675 (2004).
21. Katz A. J., Thompson A. H.: Fractal sandstone pores: implications for conductivity and pore formation. Phys. Rev. Lett. 54, 1325-1328 (1985).
22. Katz A. J., Thompson A. H.: Quantitative prediction of permeability in porous rock. Phy. Rev. B 34(11), 8179-8181 (1986).
23. Krohn C. E.: Fractal measurements of sandstones, shales, and carbonates. J. Geophys. Res. 93(B4), 3297-3305 (1988).
24. Laughlin R. D., Davies J. E.: Some aspects of capillary absorption in fibrous textile wicking. Textile Res. U. 31, 39 (1961).
25. Lenormand, R.: Gravity-assisted inert gas injection: micromodel experiments and model based on fractal roughness. The European Oil and Gas Conference, Altavilla Milica, 9-12 Oct (1990).
26. Li K., Horne R. N.: Characterization of spontaneous water imbibition into gas-saturated rocks. SPEJ 6(4), 375 (2001).
27. Li K., Horne R. N.: An analytical scaling method for spontaneous imbibition in gas-water-rock systems. SPEJ 9(3), 322-329 (2004).
28. Li, K., Chow, K., Horne, R. N.: Influence of initial water saturation on recovery by spontaneous imbibition in gas-water-rock systems and the calculation of relative permeability. SPEREE (2006), 295-301.
29. Li K., Horne R. N.: Generalized scaling approach for spontaneous imbibition: an analytical model. SPEREE 9(3), 251-258 (2006).
30. Li K., Horne R. N.: Fractal modeling of capillary pressure curves for the Geysers rocks. Geothermics 35, 198-207 (2006b). doi: 10. 1016/j. geothermics. 2006. 2. 001.
31. Li K.: Scaling of spontaneous imbibition data with wettability included. J. Contam. Hydrol. 89, 218-230 (2006).
32. Li, K.: A new method for calculating two-phase relative permeability from resistivity data in porous media. Trans. Porous Med. (2007). doi: 10. 1007/s11242-007-9178-4.
33. Li, K.: More general capillary pressure and relative permeability models from fractal geometry. J. Contam. Hydrol. (2009). doi: 10. 1016/j. jconhyd. 2009. 10. 005.
34. Li, K.: Analytical derivation of Brooks-Corey capillary pressure model using fractal geometry and evaluation of rock heterogeneity. J. Pet. Sci. Eng. (2010). doi: 10. 1016/j. petrol. 2010. 05. 002.
35. Li K.: Interrelationship between resistivity index, capillary pressure and relative permeability. Trans. Porous Med. 88(3), 385 (2011). doi: 10. 1007/s11242-011-9745-6.
36. Li, K., Horne, R. N.: Experimental study and fractal analysis of heterogeneity in naturally fractured rocks. Trans. Porous Med. (2009). doi: 10. 1007/s11242-008-9295-8.
37. Li, K., Williams, W.: Determination of capillary pressure function from resistivity data. Trans. Porous Med. (2006). doi: 10. 1007/s11242-006-0009-9.
38. Ma, S., Morrow, N. R., Zhang, X.: Generalized scaling of spontaneous imbibition data for strongly water-wet systems, paper 95-138, presented at the 6th Petroleum Conference of the South Saskatchewan Section, the Petroleum Society of CIM, held in Regina, Saskatchewan, 16-18 Oct (1995).
39. Pérez Bernal J. L., Bello López M. A.: The fractal dimension of stone pore surface as weathering descriptor. Appl. Surf. Sci. 161, 47-53 (2000).
40. Perfect E., Kenst A. B., Díaz-Zorita M., Grove J. H.: Fractal analysis of soil water desorption data collected on disturbed samples with water activity meters. Soil Sci. Soc. Am. J. 68, 1177-1184 (2004).
41. Perrier E., Rieu M., Sposito G., de Marsily G.: Models of the water retention curve for soils with a fractal pore size distribution. Water Resour. Res. 32(10), 3025-3032 (1996). doi: 10. 1029/96WR01779.
42. Reis J. C., Cil M.: A model for oil expulsion by countercurrent water imbibition in rocks: one-dimensional geometry. J. Pet. Sci. Eng. 10, 97 (1993).
43. Rieu M., Sposito G.: Fractal fragmentation, soil porosity, and soil water properties: I. Theory. Soil Sci. Soc. Am. J. 55, 1231-1238 (1991a).
44. Rieu M., Sposito G.: Fractal fragmentation, soil porosity, and soil water properties: II. Applications. Soil Sci. Soc. Am. J. 55, 1239-1244 (1991b).
45. Sahimi M., Mukhopadhyay S.: Scaling properties of a percolation model with long-range correlations. Phys. Rev. E. 54(4), 3870-3880 (1996).
46. Tavassoli Z., Zimmerman R. W., Blunt M. J.: Analysis of counter-current imbibition with gravity in weakly water-wet systems. J. Pet. Sci. Eng. 48, 94-104 (2005).
47. Tyler S. W., Wheatcraft S. W.: Fractal processes in soil water retention. Water Resour. Res. 26, 1047-1054 (1990).
48. Wang, H.: Describing and predicting breakthrough curves for non-reactive solute transport in statistically homogeneous porous media, Ph. D. Dessertation, Virginia Polytechnic Institute and State University (2002).
49. Wong P., Howard J., Lin J. S.: Surface roughening and the fractal nature of rocks. Phys. Rev. Lett. 57, 637-640 (1986).
50. Washburn E. W.: The dynamics of capillary flow. Phys. Rev. 17(3), 273-283 (1921).
51. Zimmerman R. W., Bodvarsson G. S.: A simple approximate solution for horizontal infiltration in a Brooks-Corey medium. Trans. Porous Med. 6, 195-205 (1991).
52. Zhang X., Morrow N. R., Ma S.: Experimental verification of a modified scaling group for spontaneous imbibition. SPERE. 11, 280-285 (1996).