Empirical parameters for the model of countercurrent capillary imbibition in rocks
Category: 15-1
UDC 532.68
V.L. Barabanov
Institute of Oil and Gas Research RAS, Moscow, Russia
Abstract. The review was carried out of the theoretical models of countercurrent capillary flow of porous media and its experimental tests. The results of the new experiments are discussed. The permeability of test kerns ranges between several D to several hundreds D. The characteristic feature of our experiments was their relatively long duration with regard to traditional tests. It was shown that after rapid decrease of imbibition rate and reaching apparent constant saturation level, imbibition rate increased again and reached the second maximum. The curves of the saturations dependence on time were approximated by power and semi-logarithmic functions. The empirical parameters of these functions were obtained and compared to petrophysical properties of the rocks.
Keywords: rocks, countercurrent imbibitions, capillarity effects, permeability, porosity, laboratory experiments.
References
Akin S., Schembre J.M., Bhat S.K., and Kovscek A.R., Spontaneous imbibition characteristics of diatomite, J. Pet. Sci. Eng., 2000, vol. 25, No 1/2, pp. 149–165.
Alekseeva A.G., Numerous modeling of capillary imbibition of porous medium in nonisotermic conditions, II All-Russia Sci. Conf. “Mathematical modeling of development of northern territories of Russian Federation”, Yakutsk, 2009, pp. 23-25.
Babenko Yu.I. and Ivanov E.V., Extraction from a solid with bidisperse porous structure, Theoretical Foundations of Chemical Engineering, 2009, vol. 43, No. 4, pp. 388-394.
Baldwin B.A. and Spinler E.A., In situ saturation development during spontaneous imbibition, J. Pet. Sci. Eng,. 2002, vol. 35, No. 1/2, pp. 23–32.
Barabanov V. L. and Lyubushin A. A., Fractal properties of capillary imbibition of rocks, Journal of Engineering Physics and Thermophysics, 2013, vol. 86, no. 1, pp. 1-11.
Barenblatt G. I., Entov V. M., and Ryzhik V. M., Motion of Liquids and Gases in Natural Seams [in Russian], Moscow: Nedra, 1984.
Blair P.M., Calculation of oil displacement by countercurrent water imbibition, SPEG, 1964, No 9, pp. 95–202.
Blake T.D., Dynamics of contact line, Wettability / Ed. J. Berg. NY., 1993, pp. 251–310.
Blake T.D. and Haynes J.M. Kinetics of liquid/liquid displacement, J. Colloid Interface Sci., 1969, vol. 30. pp. 421.
Bourbiaux B.J. and Kalaydjian F.J., Experimental study of concurrent and countercurrent flows in natural porous media, SPERE, 1990, No. 8, pp. 361–368.
Brochard-Wyart F. and de Gennes P.-G., Dynamics of partial wetting, Adv. Colloid Interface Sci., 1992, vol. 29, pp. 1.
Camps-Roach G., O’Carroll D.M., Newson T.A., Sakaki T., and Illangasekare T.H., Experimental investigation of dynamic effects in capillary pressure: grain size dependency and upscaling, Water Resources Research, 2010, vol. 46. W08544, doi: 10.1029/2009WR008881.
Cox R.G., The dynamics of the spreading of a liquids on a solid surface. Pt. 1. Viscous flow, J. Fluid Mech., 1986, vol. 168, pp. 169.
Cuiec L.E., Bourbiaux B.J., and Kalaydjian F.J. Imbibition in low-permeability porous media: understanding and improvement of oil recovery, 7th Annual Symp. on Enhanced Oil Recovery. Tulsa, OK, April 1990. Paper SPE 20259.
Cuiec L.E., Bourbiaux B.J., and Kalaydjian F.J., Oil recovery by imbibition in low permeability chalk, Soc. Pet. Eng., Form. Eval., 1994, vol. 9, No. 9, pp. 200–208.
Doster F., Zegeling P.A., and Hilfer R., Numerical solutions of a generalized theory for macroscopic capillarity, Phys. Rev. E., 2010, vol. 81, pp. 036307-1-036307-13.
Dussan E.B., V. and Davis S.H., On the motion of a fluid-fluid interface along a solid surface, J. Fluid Mech., 1974, vol. 65, pp. 71.
Eliseenko E. D., Zemskikh V. I., Molchanova A. G., and Khromovichev M. N., Experimental study of oil displacement by means of concurrent capillary imbibition with water and water solutions of sodium metasilicate, in: Proc. 2nd All-Union School-Seminar "Development of Oil and Gas Fields: Current State, Problems, and Prospects," March 11–16, 1991, Zvenigorod, 1991, pp. 450–454.
Ershova A. A., Popov I. Yu., Chivilikhin S. A., and Gusarov V. V., Waveguide modes and adhesion conditions for flow in a nanochannel, Doklady Physics, 2010, vol. 55, No. 6, pp 271-273.
Gimatudinov Sh.K., Fizika neftyanogo i gazovogo plasta (Physics of oil and gas reservoir), Moscow: Nedra, 1971.
Grattoni C.A., Chiotis E.D., and Dawe R.A., Determination of relative wettability of porous sandstones by imbibition studies, J. Chemical Technology and Biotechnology, 1995, vol. 64, N 1, pp. 17–24.
Hocking L.M., A moving fluid interface, Pt. 2, The removal of the force singularity by a slip flow, J. Fluid Mech., 1977. vol. 79, pp. 209.
Hocking L.M., Rival contact-angle models and the spreading of droplet, J. Fluid Mech., 1992, vol. 239, pp. 671.
Huh C., Scriven L.E. Hydrodynamics model of steady movement of a solid/liquid/fluid contact line, J. Colloid Interface Sci., 1971, vol. 35, pp. 85.
Koplik J., Banavar J.R., Willemsen J.F. Molecular dynamics of Poiseuille flow and moving contact lines, Phys. Rev. Lett., 1988, vol. 60, pp. 1282.
Koplik J., Banavar J.R., and Willemsen J.F., Molecular dynamics of fluid flow at solid surfaces, Phys. Fluids A., 1989, vol. 1, pp. 781.
Korotaev Yu. P., Gerov L. G., Zakirov S. N., and Shcherbakov G. A., Filtration of Gases in Fissured Collectors [in Russian], Moscow: Nedra, 1979.
Li Y., Analytical solutions for linear counter-current spontaneous imbibition in the frontal flow period, Transport in Porous Media, 2011, vol. 86, pp. 827–850.
Li Y., Morrow N.R., and Ruth D.W., Capillary pressure at the imbibition front during water/oil counter-current spontaneous imbibition, Transport in Porous Media, 2008, doi: 10.1007/s 11242-008-9272-2.
Li Y., Mason G., Morrow N.R., and Ruth D.W., Capillary pressure at a saturation front during restricted counter-current spontaneous imbibition with liquid displacing air, Transport in Porous Media, 2011, vol. 87, pp. 275–289.
Lobanov E. M., Exact self-similar solution of countercurrent capillary imbibition, Journal of Engineering Physics and Thermophysics, 2011, vol. 84, No. 5, pp. 985-996.
Moshinskii A. I., Mathematical model of impregnation and extraction for a bidisperse porous material, Theoretical Foundations of Chemical Engineering, 2009, vol. 43, No 4, pp. 381-387.
Ma S.M., Morrow N.R., Zhang X., and Zhou X., Characterization of wettability from spontaneous imbibition measurements, J. Canadian Petroleum Technology, Special Edition, 1999, vol. 38, No. 13, pp. 94–47.
Mattax C.C. and Kyte J.R., Imbibition oil recovery from fracture, water-drive reservoirs, SPEJ, 1962, No. 6, pp. 177–184.
Morrow N.R., Fischer H., Li Y., Mason G., Ruth D., Yin P., and Wo S., Fundamental of reservoir surface energy as related to surface properties, wettability, capillary action, and oil recovery from fractured reservoirs by spontaneous imbibition, DE-FC26-03NT15408/Semi-Annual Report 07/01/2006 –12/31/2006/ University Ave Laramie, WY 82071.
Nizovtsev M. I., Stankus S. V., Sterlyagov A. N., Terekhov V. I., and Khairulin R. A., Experimental determination of the diffusivities of moisture in porous materials in capillary and sorption moistening, Journal of Engineering Physics and Thermophysics, 2005, vol. 78, No. 1, 68–74.
Patro D., Bhattacharyya S., and Jayaram V., Flow kinetics in porous ceramics: understanding with non-uniform capillary models, J. Amer. Ceram. Soc., 2007, vol. 90, No. 10, pp. 3040–3046.
Petrov P.G. and Petrov J.G., A combined molecular-hydrodynamic approach to wetting kinetics, Langmuir, 1992, vol. 8, pp. 1762.
Pezron I., Bourgain G., and Queret D., Imbibition of a fabric, J. Colloid and Interface Science, 1995, vol. 173, No. 2, pp. 319–327.
Reis J.C. and Cil M. A model for oil expulsion by countercurrent water imbibition in rocks: one-dimensional geometry, J. Petrol. Sci. Eng., 1993, No. 12, pp. 97–107.
Ren W. and Hu D., E W. Continuum models for the contact line problem, Phys. Fluids, 2010, vol. 22, No. 10, pp. 102103/1–13.
de Ruijter M.J., de Coninck J., and Oshanin G. Droplet streading: Partial wetting regime revisited, Langmuir, 1999, vol. 15, pp. 2209.
de Ruijter M.J., Charlot M., Voue M., and de Coninck J. Experimental evidence of several time scales in drop spreading, Langmuir, 2000, vol. 16, pp. 2363.
Shikhmurzaev Y.D. and Sprittles J.E. Wetting front dynamics in an isotropic porous medium, J. Fluids Mechanics, 2012, vol. 694, pp. 399–407.
Thompson P.A. and Robbins M.O. Simulation of contact-line motion: Slip and the dynamic contact angle, Phys. Rev. Lett., 1989, vol. 63, pp. 766.
Washburn E.W. The dynamics of capillary flow, Phys. Rev., 1921, vol. 17, pp. 273–283.
Yazzan S.K., Bentsen R.G., and Trivedi J.J. Theoretical development of a novel equation for dynamic spontaneous imbibition with variable inlet saturation and interfacial coupling effects, Transport in Porous Media, 2011, vol. 86, pp. 705–717.
Zakirov S. N. and Murtazaliev A. Sh., On the determination of displacement coefficients for terrigeneous and carbonate traps, Geolog., Geofiz., Razrab. Neft. Gaz. Mestorozhd., 2009, No. 9, pp. 45–48.
Zhilin A. A. and Fedorov A. V., Physicomathematical modeling of the processes of capillary impregnation of porous materials, Journal of Applied Mechanics and Technical Physics, 2009, vol. 50, No. 1, pp. 35-43.