Modeling bimodal capillary bundle two-phase flow in the shale matrix for predicting water saturation distribution

Abstract

In gas field development, the distribution of water saturation is one of the most effective estimated two-phase flow law methods for the shale matrix. Water saturation has been widely studied; however, few studies exist to show that water saturation distribution is related to pore diameter distribution of shale matrix. Furthermore, based on experimental observations, imbibition and gas-driven water flow nuclear magnetic resonance experiments also show the phenomenon. Therefore, the objective of this work is to build a bimodal capillary bundle two-phase flow model to investigate the relation of water saturation with pore diameter distribution of shale matrix. Firstly, this work combines the bimodal pore size distribution with the truncated Gaussian distribution theory to present the shale matrix pore. Moreover, we develope a shale core imbibition model and a gas-driven water flow model to predict the distribution of the water saturation distribution during the two-phase flow, by using the gas-water two-phase seepage theory. Shale imbibition and gas-driven water flow experiments are carried out on shale samples from the underground Longmaxi Formation. The relative error of distribution curve of water saturation predicted by model and experiments has been calculated. At the initial stage of imbibition the shale matrix core is not completely dried model values do not match the measured values, but, the relative error is stable at 1–2% at the late stage of imbibition. The average relative error is 2.13% in gas-driven water flow process. As a result, the shale imbibition model and the displacement model can accurately characterize the two-phase (gas-water) flow process, providing a theoretical support to study the two-phase flow in the shale matrix.