We present a pore-network model, based on a pores-and-throats representation of the porous medium, to simulate the generation and mobilization of foams in porous media. The model allows for various parameters or processes empirically treated in current models, to be quantified and interpreted. Contrary to previous works, we also consider a dynamic (invasion) in addition to a static process. We focus on the properties of the displacement, the onset of foam flow and mobilization, the foam texture and the sweep efficiencies obtained.
The model simulates an invasion process, in which gas invades a porous medium occupied by a surfactant solution. The controlling parameter is the snap-off probability, which in turn determines the foam quality for various size distributions of pores and throats. For the front to advance, the applied pressure gradient needs to be sufficiently high to displace a series of lamellae along a minimum capillary resistance (threshold) path. We determine this path using a novel algorithm (Kharabaf and Yortsos, 1996). The fraction of the flowing lamellae, Xf (and, consequently, the fraction of the trapped lamellae, Xt) which are currently empirical, are also calculated.
The model allows the delineation of conditions under which high-quality (strong) or low-quality (weak) foams form. In either case, the sweep efficiencies in displacements in various media are calculated. In particular, the invasion by foam of low permeability layers during injection in a heterogeneous system is demonstrated.
Foams are used in the oil industry in a variety of applications, to improve sweep efficiency, block swept channels, and in gas storage and acidizing operations. These applications rely on the substantial reduction of the gas mobility in rocks in the presence of foams. During foam injection in oil reservoirs, the transient behavior is an important stage of the process. Experimental data and foam flow models on this particular stage are therefore useful.
As in many other processes in porous media, foam flow and displacement can benefit from studies at the pore and pore-network scales. Currently, because of the complexity of the problem, foam injection is modeled by various effective continuum models (for example, Patzek, 1988, Kovscek et al., 1995), which can adequately simulate various aspects of the process, given the value or functional relations of various parameters. The information needed on these empirical parameters can be provided by pore-network models. At present, pore-network models of foam generation and propagation are rare. The existing models are concerned mostly with static properties of foams, using concepts of ordinary percolation (for example, Chou, 1990, Rossen and Gauglitz, 1990, Laidlaw et al., 1993, Rossen and Mamun, 1993, Miller and Fogler, 1995), which as we will show below may not necessarily apply in modeling foam flow.
Using a network model based on ordinary percolation theory, Chou (1990) related foam generation to the pore size distribution. In his model, there is no minimum pressure gradient requirement to generate or propagate foam.