In a series of laboratory experiments, the deterministic and fractal parameters of spontaneous capillary imbibition of rocks have been investigated. The capillary imbibition of higher-permeability samples was characterized by a sharp increase in the saturation at the initial stage and a further increase that is not described by the power law. Analysis of the parameters of the multifractal spectrum of water-saturation variations of the investigated samples in the process of capillary imbibition has shown that the generalized Hurst constant tends to decrease with time in the process of imbibition.
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References
E. W. Washburn, The dynamics of capillary flow, Phys. Rev., 17, 273–283 (1921).
Yu. P. Korotaev, L. G. Gerov, S. N. Zakirov, and G. A. Shcherbakov, Filtration of Gases in Fissured Collectors [in Russian], Nedra, Moscow (1979).
C. C. Mattax and J. R. Kyte, Imbibition oil recovery from fracture, water-drive reservoirs, SPEJ, No. 6, 177–184 (1962).
J. C. Reis and M. Cil, A model for oil expulsion by countercurrent water imbibition in rocks: one-dimensional geometry, J. Petrol. Sci. Eng., No. 12, 97–107 (1993).
P. M. Blair, Calculation of oil displacement by countercurrent water imbibitions, SPEG, No. 9, 195–202 (1964).
B. J. Bourbiaux and F. J. Kalaydjian, Experimental study of concurrent and countercurrent flows in natural porous media, SPERE, No. 8, 361–368 (1990).
E. D. Eliseenko, V. I. Zemskikh, A. G. Molchanova, and M. N. Khromovichev, 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.
L. E. Cuiec, B. J. Bourbiaux, and F. J. Kalaydjian, Imbibition in low-permeability porous media: understanding and improvement of oil recover, in: Proc. 7th Annual Symp. on Enhanced Oil Recovery, Tulsa, OK, April 1990, Paper SPE 20259.
L. E. Cuiec, B. J. Bourbiaux, and F. J. Kalaydjian, Oil recovery by imbibition in low permeability chalk, Soc. Pet. Eng., Form. Eval., 9, No 9, 200–208 (1994).
I. Pezron, G. Bourgain, and D. Queret, Imbibition of a fabric, J. Colloid Interface Sci., 173, No. 2, 319–327 (1995).
C. A. Grattoni, E. D. Chiotis, and R. A. Dawe, Determination of relative wettability of porous sandstones by imbibition studies, J. Chem. Technol. Biotechnol., 64, No 1, 17–24 (1995).
S. M. Ma, N. R. Morrow, X. Zhang, and X. Zhou, Characterization of wettability from spontaneous imbibition measurements, J. Can. Petrol. Technol. Spec. Ed., 38, No. 13, Paper 94–47 (1999).
S. Akin, J. M. Schembre, S. K. Bhat, and A. R. Kovscek, Spontaneous imbibition characteristics of diatomite, J. Petrol. Sci. Eng., 25, No. 1/2, 149–165 (2000).
B. A. Baldwin and E. A. Spinler, In situ saturation development during spontaneous imbibitions, J. Petrol. Sci. Eng., 35, No. 1/2, 23–32 (2002).
M. I. Nizovtsev, S. V. Stankus, A. N. Sterlyagov, et al., Experimental determination of the diffusivities of moisture in porous materials in capillary and sorption moistening, Inzh.-Fiz. Zh., 78, No. 1, 67–73 (2005).
D. Patro, S. Bhattacharyya, and V. Jayaram, Flow kinetics in porous ceramics: understanding with non-uniform capillary models, J. Amer. Ceram. Soc., 90, No. 10, 3040–3046 (2007).
S. N. Zakirov and A. Sh. Murtazaliev, On the determination of displacement coefficients for terrigeneous and carbonate traps, Geolog., Geofiz., Razrab. Neft. Gaz. Mestorozhd., No. 9, 45–48 (2009).
J. Feder, Fractals, Plenum Press, New York, London (1988).
J. W. Kantelhardt, S. A. Zschiegner, E. Konscienly-Bunde, et al., Multifractal detrended fluctuation analysis of nonstationary time series, Physica A. No. 316, 87–114 (2002).
A. A. Lyubushin, Analysis of the Data of Geophysical and Ecological Monitoring Systems [in Russian], Nauka, Moscow (2007).
A. A. Lyubushin, The seismic catastrophe in Japan on March 11, 2011. Long-term forecast by low-frequency microseisms, Geofiz. Prots. Biosfera, 10, No. 1, 9–35 (2011).
V. L. Barabanov and D. V. Barabanov, Influence of seismic effects on the fractal character of filtration processes and the increase in oil recovery, Tekhnol. TÉK, No. 4(35), 30–35 (2007).
V. L. Barabanov, Analysis of the mechanism of seismic action on oil pools from the viewpoint of the fractal character of filtration processes, Geolog., Geofiz., Razrab. Neft. Gaz. Mestorozhd., No. 3, 35–43 (2008).
N. A. Skibitskaya, D. V. Surnachev, M. N. Bol’shakov, and V. A. Kuz’min, Modeling of the porosity in carbonate strate using the Orenburg oil and gas condensate deposit as an example, Izv. Vyssh. Uchebn. Zaved.: Geol. Razved., No. 3, 72–74 (2007).
Yu. V. Vlasov, A. V. Frolov, and V. V. Yanyushkin, Simulation of the processes of pollution of porous surfaces by liquids on the basis of fractal representations, Bezop. Tekhnosf., No. 1, 33–35 (2007).
B. Yu, Analysis of flow in fractal porous media, Appl. Mech. Rev., 61, Nos. 1–6, 050801/1–19 (2008).
Yu. I. Babenko and E. V. Ivanov, Extraction from a fractal system of branching capillaries, Teor. Osn. Khim. Tekhnol., 43, No. 1, 99–104 (2009).
O. N. Soboleva and E. P. Kurochkina, Subgrid sumulation of the flow processes in an anisotropic fractal medium, Prikl. Mekh. Tekh. Fiz., 50, No. 5, 75–89 (2009).
B. A. Suleimanov, F. S. Ismailov, O. A. Dyshin, and N. I. Guseinova, Determination of the fractal dimensionality of the front of oil displacement by water on the basis of data of normal operation of wells, Neft. Khoz., No. 12, 111–115 (2011).
R. K. Khalkechev, A multifractal model with a scale of inhomogeneity of effective elastic properties of gas-containing rock masses, Izv. Vyssh. Uchebn. Zaved., Severo-Kavkaz. Reg.: Tekh. Nauki, No. 3, 68–70 (2012).
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Translated from Inzhenerno-Fizicheskii Zhurnal, Vol. 86, No. 1, pp. 3–13, January–February, 2013.
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Barabanov, V.L., Lyubushin, A.A. Fractal properties of capillary imbibition of rocks. J Eng Phys Thermophy 86, 1–11 (2013). https://doi.org/10.1007/s10891-013-0798-y
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DOI: https://doi.org/10.1007/s10891-013-0798-y