Physica A 200 (1993) 241-249 North-Holland zyxwvutsrqponmlkjihgfedcbaZYXWVUTSRQPONMLKJIHGFEDCBA SDI: 037%4371(93)E0116-V Simulations of migration, fragmentation and coalescence of non-wetting fluids in porous media Paul Meakin, Geri Wagner, Jens Feder and Torstein Jossang Department of Physics, University of Oslo, Box 1048, Blindern, Oslo 0316, Norway and Center for Advanced Study at The Norwegian Academy of Science and Letters, Box 7585, Skillebekk, Oslo 0205, Norway A model based on invasion percolation was used to simulate the migration of a non-wetting fluid through a porous medium filled with an immiscible wetting fluid under the influence of a gradient such as that provided by gravity. The migrating fluid clusters undergo both fragmentation and coalescence. The fragment size distribution obtained from two-dimensional simulations in which the gradient g is slowly increased from 0 can be represented by the scaling form N,(g) - s-‘f(s/lgl-‘) w h ere z = 1 + (D - I)v/(Y + 1). Here D is the fractal dimensionahty of invasion percolation, with trapping, and Y is the ordinary percolation correlation length exponent. zyxwvutsrqponmlkjihgfedcbaZYXWVUTSRQPONMLKJIHGFEDC 1. Introduction The study of two-phase flow in porous media has led to the observation of complex pattern formation processes [l-3]. Displacement of one fluid by another in a porous medium in the quasistatic limit, where capillary forces dominate viscous forces, is important in a large number of processes. Examples in nature include buoyancy-driven secondary oil migration from the source rocks to a reservoir, penetration of pollutants through soils and the drying of a wide variety of porous media. Previous investigations [4-71 of the effects of gravity on the slow displace- ment of a wetting fluid by a non-wetting fluid with a different density in two-dimensional and three-dimensional porous media indicate that the result- ing displacement patterns can be described in terms of a fractal blob model with a characteristic blob size or correlation length 5. On short length scales A (A < 5) capillary effects dominate and on long length scales the effects of the external field (gravity in most cases) are dominant. In the case of a stabilizing field the displacement pattern can be described as a dense packing of fractal blobs (fig. lb). The pattern formed in the presence of a destabilizing gradient 0378-4371/93/$06.00 0 1993 - Elsevier Science Publishers B.V. All rights reserved