Pore-Scale Modeling: Stochastic Network Generation and Modeling of Rate Effects in Waterflooding

Abstract

Pore scale network modeling has been used to predict transport flow properties for multiphase flow successfully. The prediction is based on having geologically realistic networks that are computationally expensive to generate and normally represent only a very small section of the rock sample. We present a new method to generate stochastic random networks representing the pore space of different rocks with given input pore and throat size distributions and connectivity – these distributions can be obtained from an analysis of pore-space images. The stochastic networks can be arbitrarily large and hence are not limited by the size of the original image. The basic assumption made in the prediction of transport flow properties using most pore-scale models is that the flow is capillary dominated. This implies that the viscous pressure drop is insignificant compared to the capillary pressure. However, at the field scale, gravity and viscous forces dominate displacement processes. We develop a rate-dependent network model that accounts for viscous forces by solving for the wetting and non-wetting phase pressure and which allows wetting layer swelling near an advancing flood front. We propose a new time-dependent algorithm by accounting for partial filling of elements. We use the model to study the effects of capillary number and mobility ratio on imbibition displacement patterns, saturation and velocity profiles. We also investigate the effects of capillary number and mobility ratio on the water fractional flow curve, cumulative oil production and residual oil saturation for water-wet and mixed-wet systems. By using large networks we reproduce Buckley-Leverett profiles directly from pore-scale modeling thereby providing a bridge between pore-scale and macroscale transport