Immiscible displacements in porous media with both capillary and viscous effects can be characterized by two dimensionless numbers, the capillary number C, which is the ratio of viscous forces to capillary forces, and the ratio M of the two viscosities. For certain values of these numbers, either viscous or capillary forces dominate and displacement takes one of the basic forms: (a) viscous fingering, ( b ) capillary fingering or (c) stable displacement. We present a study in the simple case of injection of a non-wetting fluid into a two-dimensional porous medium made of interconnected capillaries. The first part of this paper presents the results of network simulators (100 x 100 and 25 x 25 pores) based on the physical rules of the displacement a t the pore scale. The second part describes a series of experiments performed in transparent etched networks. Both the computer simulations and the experiments cover a range of several decades in C and M . They clearly show the existence of the three basic domains (capillary fingering, viscous fingering and stable displacement) within which the patterns remain unchanged. The domains of validity of the three different basic mechanisms are mapped onto the plane with axes C and M , and this mapping represents the 'phase-diagram ' for drainage. In the final section we present three statistical models (percolation, diffusion-limited aggregation (DLA) and anti-DLA) which can be used for describing the three 'basic' domains of the phase-diagram.
The mechanisms of displacement of one fluid by another are investigated in an etched network. Experiments show that both fluids are simultaneously present in a duct, the wetting fluid remaining in the extreme corners of the cross-section. Calculation of displacement pressures are in good agreement with experiments for drainage, imbibition and removal of blobs. The results may be related to some flow behaviour exhibited in porous media.
Dissolution of a porous medium creates, under certain conditions, some highly conductive
channels called wormholes. The mechanism of propagation is an unstable
phenomenon depending on the microscopic properties at the pore scale and is controlled
by the injection rate. The aim of this work is to test the ability of a Darcy-scale
model to describe the different dissolution regimes and to characterize the influence
of the flow parameters on the wormhole development. The numerical approach is
validated by model experiments reflecting dissolution processes occurring during acid
injection in limestone. Flow and transport macroscopic equations are written under
the assumption of local mass non-equilibrium. The coupled system of equations is
solved numerically in two dimensions using a finite volume method. Results are
discussed in terms of wormhole propagation rate and pore volume injected.
scite is a Brooklyn-based organization that helps researchers better discover and understand research articles through Smart Citations–citations that display the context of the citation and describe whether the article provides supporting or contrasting evidence. scite is used by students and researchers from around the world and is funded in part by the National Science Foundation and the National Institute on Drug Abuse of the National Institutes of Health.