Transient Pressure Behavior for Low Permeability Oil Reservoir Based on New Darcy's Equation

Abstract With further progress of oilfields development in China, more and more ultra-low permeability oil reservoirs are being put into production. However, in ultra-low permeability oil reservoirs, pore throats are small and the specific surface area is big. Fluid always has a slow seepage velocity and the relationship between the seepage velocity and driving pressure is a curve, not a straight line. Fluid flow in low permeability porous media does not obeys Darcy's law any more, so traditional well testing interpretation methods may cause error in estimation of ultra-low permeability oil reservoir parameters. This paper describes problems encountered when analyzing transient pressure tests in ultra-low permeability oil reservoir. The equation to describe the non-Darcy's flow was given according to theoretical derivation and experimental method, and three factors were introduced into the equation to improve the Darcy's law. Based on the new model, the theoretical well test model for dual-porosity media in ultra-low permeability oil reservoirs with complex fractures was derived which allows for the influence analysis of non-Darcy's effect. By using Laplace transform and Fourier transform, the model was solved by analytical solution and numerical method. The analytical solution obtained is accurate and simple by contrast numerical method results. Besides, the curves for the pressure responses were plotted. The effects of parameters including fracture width, fracture length and the position of the fracture on the pressure were fully investigated in detail. The advantage of the solution is easy to incorporate storativity ratio and skin factor. It can also reduce the amount of computation and compute efficiently and quickly. Sensitivity analysis shows that non-Darcy flow mainly affects the transition section between the pure wellbore storage and radial flow region, and the pressure derivative curves exhibit a gentle transition region compared with the Darcy's flow. These type curves give a better interpretation of well testing pressure response in ultra-low permeability oil reservoir.