A nonlinear mathematical model for fluid flow in low-permeability reservoirs and its effect on well production performance

Fluid flow in low-permeability reservoirs exhibits nonlinear behavior owing to the presence of nano-sized pores and strong fluid-solid interactions. The percolation velocity significantly deviates from that estimated by Darcy's law, particularly in regions with low-pressure gradients. Several modified Darcy's equations have been proposed to describe these nonlinear phenomena. However, existing flow models often suffer from practical limitations, such as complex formulations or challenging determination of parameters. To address this, non-Darcy flow behavior was investigated and a novel low-velocity-nonlinear flow equation that accounts for the boundary layer effect is presented. The curves with different coefficients are plotted and the sensitivity of the corresponding parameters are discussed. Moreover, considering that core flooding experiments fail to accurately reflect actual flow behavior in reservoirs, an inversion method based on genetic algorithm (GA) that utilizes bottomhole pressure (BHP) testing data to estimate the pending coefficients is introduced. Finally, the proposed nonlinear flow equation is applied, using the finite difference method (FDM), to simulate the production performance, including pressure distribution, production rate, and recovery factor of vertical and multi-fractured horizontal wells in low-permeability reservoirs. The results demonstrated significant deviations in reservoir pressure distribution from those estimated using Darcy's law, and the production rate and recovery factor of nonlinear flow were notably lower than those predicted by Darcy's flow law, albeit to varying degrees.