Capillary Effects in Heterogeneous Porous Media: Experiments, Pore Network Simulations, and Continuum Modeling

Abstract We investigate effects of capillary heterogeneity induced by variations in permeability in the direction of displacement in heterogeneous porous media. The investigation is three-pronged and uses macroscopic simulation, based on the standard continuum equations, experiments with the use of an acoustic technique and pore network numerical models. It is found that heterogeneity affects significantly the saturation profiles, the effect being stronger at lower rates. For drainage, a good agreement is found between continuum model predictions, experimental results and the pore network numerical models based on which it can be concluded that capillary heterogeneity effects in the direction of displacement act much like a body force (e.g. gravity). The results are interpreted with the use of invasion percolation concepts. For secondary imbibition, a poorer agreement exists between continuum model and experimental results at low capillary numbers, which requires the use of a pore network simulator involving film flow. Numerical simulation results are discussed for 2-D geometries. INTRODUCTION In displacement processes in porous media, such as oil reservoirs, of particular significance is the inherent heterogeneity of medium properties. While recognized in early studies, a systematic investigation of the effects of heterogeneity has been undertaken mostly during the last decade [1]. In immiscible displacement, pore-scale studies led to statistical tools such as Invasion Percolation (IP) and Diffusion-Limited-Aggregation (DLA) [2]. In miscible displacement, large-scale investigations led to classifications of flow regimes in terms of correlation length, degree of heterogeneity and mobility ratio [3], [4]. The emphasis on miscible displacement (for an exception, see [5]) reflects the premise that on a large scale, differences between immiscible and miscible displacements are minimal. However, this depends on geometric and flow properties. In immiscible displacement at sufficiently low capillary numbers, for example, permeability gradients have effects similar to gravity, leading to gradient percolation patterns (both stable and unstable) [6]; sharp changes in permeability in the direction of flow significantly change steady-state saturation profiles [7]; random distribution of permeabilities attributes large-scale percolation features (such as large-scale trapping) to displacements [8]; while correlated fields drastically alter the percolation aspects of the displacement [9]. All these capillary effects are driven by permeability heterogeneity and they are absent in miscible displacement.