Nonlinear seepage flow of ultralow permeability reservoirs

Nonlinear seepage flow is chiefly caused by medium deformation and threshold pressure gradient (TPG) in low and ultralow permeability reservoirs. According to laboratory experiment on medium deformation and TPG, a novel stress sensitive coefficient is defined, and the variation rules of the coefficient and TPG (including single phase and oil-water two phases) are analyzed. The nonlinear seepage models of single phase and oil-water two phases are set up with consideration of medium deformation and TPG. The single-phase model is solved based on the condition of constant flow rate, changing production rate, and constant bottom-hole pressure respectively. For oil-water non-piston displacement flow, the fractional flow equation, oil/water front equation, pressure equation and production equation are put forward with solutions. The reservoir engineering application shows that the decline of production rate in low permeability formations is more serious than that in medium-high permeability formations, and nonlinear factors exert serious influence on the flow of oil-water two phases when the velocity is low. Moreover, reasonable injector–producer distance can be determined by the models. Key words: low-permeability reservoir, nonlinear flow, threshold pressure gradient, medium deformation, stress sensitive coefficient, mathematical mode