{"status":"ok","message-type":"work","message-version":"1.0.0","message":{"indexed":{"date-parts":[[2026,4,13]],"date-time":"2026-04-13T06:51:52Z","timestamp":1776063112142,"version":"3.50.1"},"reference-count":31,"publisher":"Cambridge University Press (CUP)","license":[{"start":{"date-parts":[[2006,4,21]],"date-time":"2006-04-21T00:00:00Z","timestamp":1145577600000},"content-version":"unspecified","delay-in-days":7356,"URL":"https:\/\/www.cambridge.org\/core\/terms"}],"content-domain":{"domain":[],"crossmark-restriction":false},"short-container-title":["J. Fluid Mech."],"published-print":{"date-parts":[[1986,3]]},"abstract":"<jats:p>A theoretical simulator of immiscible displacement of a non-wetting fluid by a wetting one in a random porous medium is developed. The porous medium is modelled as a network of randomly sized unit cells of the constricted-tube type. Under creeping-flow conditions the problem is reduced to a system of linear equations, the solution of which gives the instantaneous pressures at the nodes and the corresponding flowrates through the unit cells. The pattern and rate of the displacement are obtained by assuming quasi-static flow and taking small time increments. The porous medium adopted for the simulations is a sandpack with porosity 0.395 and grain sizes in the range from 74 to 148 \u03bcrn. The effects of the capillary number, <jats:italic>Ca<\/jats:italic>, and the viscosity ratio, \u03ba = \u03bc<jats:sub>o<\/jats:sub>\/\u03bc<jats:sub>w<\/jats:sub>, are studied. The results confirm the importance of the capillary number for displacement, but they also show that for moderate and high Ca values the role of \u03ba is pivotal. When the viscosity ratio is favourable (\u03ba &lt; 1), the microdisplacement efficiency begins to increase rapidly with increasing capillary number for <jats:italic>Ca<\/jats:italic> &gt; 10<jats:sup>\u22125<\/jats:sup>, and becomes excellent as <jats:italic>Ca<\/jats:italic> \u2192 10<jats:sup>\u22123<\/jats:sup>. On the other hand, when the viscosity ratio is unfavourable (\u03ba &gt; 1), the microdisplacement efficiency begins to improve only for Ca values larger than, say, 5 \u00d7 10<jats:sup>\u22124<\/jats:sup>, and is substantially inferior to that achieved with \u03ba &lt; 1 and the same <jats:italic>Ca<\/jats:italic> value. In addition to the residual saturation of the non-wetting fluid, the simulator predicts the time required for the displacement, the pattern of the transition zone, the size distribution of the entrapped ganglia, and the acceptance fraction as functions of <jats:italic>Ca<\/jats:italic>, \u03ba, and the porous-medium geometry.<\/jats:p>","DOI":"10.1017\/s0022112086002574","type":"journal-article","created":{"date-parts":[[2006,4,21]],"date-time":"2006-04-21T11:59:09Z","timestamp":1145620749000},"page":"305-336","source":"Crossref","is-referenced-by-count":180,"title":["Network models for two-phase flow in porous media Part 1. Immiscible microdisplacement of non-wetting fluids"],"prefix":"10.1017","volume":"164","author":[{"given":"Madalena M.","family":"Dias","sequence":"first","affiliation":[]},{"given":"Alkiviades C.","family":"Payatakes","sequence":"additional","affiliation":[]}],"member":"56","published-online":{"date-parts":[[2006,4,21]]},"reference":[{"key":"S0022112086002574_ref010","unstructured":"Hinkley, R. E. 1982 Oil ganglion motion. M.S. thesis,University of Houston,Houston, Texas."},{"key":"S0022112086002574_ref026","unstructured":"Rapin, S. 1980 Behaviour of non-wetting oil ganglia displaced by an aqueous phase. M.S. thesis,University of Houston,Houston, Texas."},{"key":"S0022112086002574_ref001","unstructured":"Chandler, R. , Koplik, J. , Lerman, K. & Willemsen, J. F. 1982 Capillary displacement and percolation in porous media.J. Fluid Mech. 119,249\u2013267."},{"key":"S0022112086002574_ref029","unstructured":"Tilton, J. N. & Payatakes, A. C. 1984 Collocation solution of creeping Newtonian flow through a sinusoidal tube: a correction.AIChE J. 30,1016\u20131021."},{"key":"S0022112086002574_ref023","unstructured":"Payatakes, A. C. , Tien, Chi & Turian, R. M. 1973 A new model for granular porous media\u2014Part I. Model formulation.AIChE J. 19,67\u201376."},{"key":"S0022112086002574_ref030","unstructured":"Washburn, E. W. 1921 The dynamics of capillary flow.Phys. Rev. 17,273\u2013283."},{"key":"S0022112086002574_ref006","unstructured":"Dias, M. M. 1984 Formation and dynamics of oil ganglia in porous media. Ph.D. dissertation, University of Houston, Houston, Texas."},{"key":"S0022112086002574_ref002","unstructured":"Chatzis, I. , Morrow, N. R. & Lim, H. T. 1983 Magnitude and detailed structure of residual oil saturation.Soc. Pet. Engng. J. 23,311\u2013326."},{"key":"S0022112086002574_ref014","unstructured":"Leverett, M. C. 1941 Capillary behavior in porous solids.AIME Trans. 142,152\u2013169."},{"key":"S0022112086002574_ref004","unstructured":"Deiber, J. A. & Schowalter, W. R. 1979 Flow through tubes with sinusoidal axial variations in diameter.AIChE J. 25,638\u2013644."},{"key":"S0022112086002574_ref015","unstructured":"Nelra, M. A. & Payatakes, A. C. 1978 Collocation solution of creeping Newtonian flow through periodically constricted tubes with piecewise continuous wall profile.AIChE J. 24,43\u201354."},{"key":"S0022112086002574_ref009","unstructured":"Fedkiw, P. & Newman, J. 1977 Mass transfer at high P\u00e9clet numbers for creeping flow in a packed bed reactor.AIChE J. 23,255\u2013263."},{"key":"S0022112086002574_ref028","unstructured":"Slattery, J. C. & Flumerfelt, R. W. 1978 Interfaeial phenomena. In Handbook of Multiphase Systems (ed. G. Hetsroni ), pp. 224\u2013241."},{"key":"S0022112086002574_ref008","unstructured":"Egbogah, E. O. & Dawe, A. 1981 A model of oil ganglion movement in porous media. SPE 10115, 56th Annual Fall Tech. Conf. and Exhib. of SPE , San Antonio, Texas, Oct. 5\u20137."},{"key":"S0022112086002574_ref017","unstructured":"Ng, K. M. & Payatakes, A. C. 1980 Stochastic simulation of the motion, break-up and stranding of oil ganglia in water-wet granular porous media during immiscible displacement.AIChE J. 26,419\u2013429."},{"key":"S0022112086002574_ref025","unstructured":"Peasad, S. 1978 Flow of Newtonian fluids through axisymmetric converging\u2014diverging channels. M.S. thesis,University of Houston,Houston, Texas."},{"key":"S0022112086002574_ref005","unstructured":"Desoer, C. A. & Kuh, E. S. 1969 Basic Circuit Theory. McGraw-Hill."},{"key":"S0022112086002574_ref016","unstructured":"Neira, M. A. & Payatakes, A. C. 1979 Collocation solution of creeping Newtonian flow through sinusoidal tubes.AIChE J. 25,725\u2013730."},{"key":"S0022112086002574_ref003","unstructured":"Chow, J. C. F. & Soda, K. 1972 Laminar flow in tubes with constriction.Phys. Fluids 15,1700\u20131706."},{"key":"S0022112086002574_ref012","unstructured":"Koplik, J. & Lasseter, T. J. 1982 Two-phase flow in random network models of porous media, SPE 11014, 57th Annual Fall Tech. Conf. and Exhib. of SPE , New Orleans, Louisiana, Sept. 26\u201329."},{"key":"S0022112086002574_ref007","unstructured":"Dias, M. M. & Payatakes, A. C. 1986 Network models for two-phase flow in porous media. Part 2: Motion of oil ganglia.J. Fluid Mech. 164,337\u2013358."},{"key":"S0022112086002574_ref011","unstructured":"Jacquin, C. & Legait, B. 1984 Influence of capillarity and viscosity during spontaneous imbibition in porous media and in capillaries.Phys. Chem. Hydrodyn. 5,307\u2013319."},{"key":"S0022112086002574_ref013","unstructured":"Legait, B. & Jacquin, C. 1982 Conditions n\u00e9cessaires au passage d'un col par une gouette en d\u00e9placement dans un capillaire de section carr\u00e9e, en r\u00e9gime de Stokes.C.R. Acad. Sci., Paris, S\u00e9r. II, 294, 487\u2013492."},{"key":"S0022112086002574_ref020","unstructured":"Payatakes, A. C. & Dias, M. M. 1984 Immiscible microdisplacement and ganglion dynamics in porous media.Rev. Chem. Eng. 2 (2), 85\u2013174."},{"key":"S0022112086002574_ref024","doi-asserted-by":"crossref","unstructured":"Payatakes, A. C. , Woodham, G. & Ng, K. M. 1981 On the fate of oil ganglia during immiscible displacement in water wet granular porous media. In Surface Phenomena in Enhanced Oil Recovery (ed. D. O. Shah ). Plenum Press, New York.","DOI":"10.1007\/978-1-4757-0337-5_29"},{"key":"S0022112086002574_ref018","unstructured":"Oh, S. C. & Slattery, J. C. 1979 Interfacial tension required for significant displacement of oil.Soc. Pet. Eng. J. 19,83\u201396."},{"key":"S0022112086002574_ref019","unstructured":"Payatakes, A. C. 1982 Dynamics of oil ganglion during immiscible displacement in water-wet porous media.Ann. Rev. Fluid Meeh. 14,365\u2013393."},{"key":"S0022112086002574_ref027","unstructured":"Sheffield, R. E. & Metzner, A. B. 1976 Flows of nonlinear fluids through porous media.AIChE J. 22,736\u2013744."},{"key":"S0022112086002574_ref031","unstructured":"Wilkinson, D. & Willemsen, J. 1983 Invasion percolation: a new form of percolation theory.J. Phys. A16,3365\u20133376."},{"key":"S0022112086002574_ref022","unstructured":"Payatakes, A. C. , Ng, K. M. & Flumerfelt, R. W. 1980 Oil ganglia dynamics during immiscible displacement. Model formulation.AIChE J. 20,430\u2013443."},{"key":"S0022112086002574_ref021","unstructured":"Payatakes, A. C. & Neira, M. A. 1977 Model of the constricted unit cell type for isotropic granular porous media.AIChE J. 23,922\u2013930."}],"container-title":["Journal of Fluid Mechanics"],"original-title":[],"language":"en","link":[{"URL":"https:\/\/www.cambridge.org\/core\/services\/aop-cambridge-core\/content\/view\/S0022112086002574","content-type":"unspecified","content-version":"vor","intended-application":"similarity-checking"}],"deposited":{"date-parts":[[2019,6,7]],"date-time":"2019-06-07T20:00:03Z","timestamp":1559937603000},"score":1,"resource":{"primary":{"URL":"https:\/\/www.cambridge.org\/core\/product\/identifier\/S0022112086002574\/type\/journal_article"}},"subtitle":[],"short-title":[],"issued":{"date-parts":[[1986,3]]},"references-count":31,"alternative-id":["S0022112086002574"],"URL":"https:\/\/doi.org\/10.1017\/s0022112086002574","relation":{},"ISSN":["0022-1120","1469-7645"],"issn-type":[{"value":"0022-1120","type":"print"},{"value":"1469-7645","type":"electronic"}],"subject":[],"published":{"date-parts":[[1986,3]]}}}