A New Non-Darcy Flow Model for Low Velocity Multiphase Flow in Tight Reservoirs

Abstract

Abstract This paper is to present a new non-linear flow model for low-velocity multiphase flow in tight petroleum reservoirs as well as its analytical and numerical solutions. The pore and pore-throat sizes of shale and tight-rock formations are on the order of tens of nanometers. The fluid flow in such small pores is significantly affected by walls of pores and pore-throats. This boundary-layer effect on fluid flow in tight rocks has been investigated through laboratory work. In analogue to flow through capillary tubes, it is found that the ratio of the thickness of boundary layer over the size of capillary tube is a function of pressure gradient; and the non-linear relationship between flow rate and pressure gradient is pronounced under the drive of small pressure gradient or low flow velocity. It is also observed that low permeability is associated with large boundary layer effect on fluid flow. Based on the studies of single-phase and multiphase flow though capillary tubes, the new non-Darcy flow model is proposed for describing multiphase flow in tight rock. The experimental results from a single capillary tube are extended to a bundle of tubes and finally to porous media of tight formations. A physics-based, non-Darcy low-velocity flow equation is derived to account for the boundary layer effect of tight reservoirs by adding a non-Darcy coefficient term, which is function of dimensionless thickness of boundary layer and pressure gradient. This non-Darcy equation describes the fluid flow more accurately for tight oil reservoir with low production rate and low pressure gradient as compared to laboratory observation. Both analytical and numerical solutions are obtained for the new non-Darcy flow model. First, a Buckley-Leverett type analytical solution is derived including gravity effect with this non-Darcy flow equation. Then, a numerical model has been developed for implementing this non-Darcy flow model for accurate simulation of multi-dimensional porous and fractured tight oil reservoirs. The sensitivity studies based on numerical simulations demonstrate the non-negligible effect of boundary layer on fluid flow in tight formations using an actual field example. Eventually, the experiment-based non-Darcy flow model could improve the forecast accuracy for long-term production rate and recovery factors of tight oil reservoirs. A new, physics-based low-velocity non-Darcy flow model is developed for description of single-phase and multiphase flow in tight reservoirs. In addition, both analytical and numerical solutions are provided for application of the new non-Darcy flow model for field studies. The results and knowledge obtained in this study may be applicable to both oil and gas flow in unconventional reservoirs.