Solution of Nonlinear Seepage Model for Fracture Well Groupin Low Permeability Reservoirs

Having a closely detailed description of the nonlinear relationship between flow velocity and pressure gradient in low permeability reservoir is necessary for accurately developing the frac design, and calculating the production of a group (or unit) of wells that have been hydraulically fractured. Therefore, based on the description of the nonlinear seepage characteristics of low permeability reservoir, a nonlinear mathematical model of coupling low permeability reservoir and hydraulic fractures was established, which divided the seepage process into the nonlinear seepage stage and quasi-linearity stage according to the seepage characteristics. The Taylor expansion was used to linearize the nonlinear mathematical model, and established the finite difference equations, and then formed the computer solving model. The results of example analysis showed that the distributions of formation pressure and saturation calculated by the nonlinear mathematical model were in line with the actual situations of the stratum; the fracture flow conductivity of injection well in the fractured five-spot well pattern decreased with the formation closure, which led to poor water injection effect and low oil well production. Thus, the fracture design should be modified in accordance with the study’s results. The study results indicated that the nonlinear mathematical model and hydraulic fracture coupling could accurately describe the nonlinear relationship between flow velocity and pressure gradient in low-permeability reservoir. This breakthrough establishes a foundation to calculate the production of fractured well group in low-permeability reservoir accurately, and provides a guidance for water flooding development of low permeability reservoir.