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.

The basic mechanisms which take place during the displacement of immiscible fluids in porous media have been observed in micromodels and have been modelled. At the pore level, in drainage, the invading fluid chooses the largest throat. In imbibition, the displacement depends on the local geometry. For a large pore-to-throat ratio (aspect ratio), the main mechanism is the collapse of the invading fluid in the smallest channel, without entering the pore. For a small aspect ratio, the wetting fluid invades the pore first, and then the adjacent channels. From observations at the pore level, the author has modelled the displacement on a large scale in some extreme cases by using statistical theories. The different behaviours are then displayed as domains in three phase diagrams: one for drainage and two for imbibition (large and small aspect ratios). At a high rate, when viscous forces are dominant, all the diagrams show a stable domain (described by anti-DLA) and a viscous fingering domain (DLA). In drainage, low capillary numbers lead to capillary fingering represented by invasion percolation. In imbibition, the capillary domain is described either by a compact cluster growth (small aspect ratio) or percolation theory (large aspect ratio). In addition the possibility of flow by film along the roughness of the walls leads to disconnected structures.

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