Comparison of Different Permeability Models for Production-induced Compaction in Sandstone Reservoirs

We investigate pore pressure conditions and reservoir compaction associated with oil and gas production using 3 different permeability models, which are all based on one-dimensional radial flow diffusion model, but differ in considering permeability evolution during production. Model 1 assumes the most simplistic constant and invariable permeability regardless of production; Model 2 considers permeability reduction associated with reservoir compaction only due to pore pressure drawdown during production; Model 3 also considers permeability reduction but due to the effects of both pore pressure drawdown and coupled pore pressure-stress process. We first derive a unified stress-permeability relation that can be used for various sandstones. We then apply this equation to calculate pore pressure and permeability changes in the reservoir due to fluid extraction using the three permeability models. All the three models yield pore pressure profiles in the form of pressure funnel with different amounts of drawdown. Model 1, assuming constant permeability, obviously predicts the least amount of drawdown with pore pressure condition highest among the three models investigated. Model 2 estimates the largest amount of drawdown and lowest pore pressure condition. Model 3 shows slightly higher pore pressure condition than Model 2 because stress-pore pressure coupling process reduces the effective stress increase due to pore pressure depletion. We compare field data of production rate with the results of the three models. While models 1 and 2 respectively overestimates and underestimates the production rate, Model 3 estimates the field data fairly well. Our result affirms that coupling process between stress and pore pressure occurs during production, and that it is important to incorporate the coupling process in the permeability modeling, especially for tight reservoir having low permeability.