Dynamical Analysis of Composite Reservoirs Considering Quadratic Gradient Term Based on Douglas-Jones Predictor-Corrector Method

Traditional well test models are not consistent with the material balance condition because of neglecting the quadratic gradient term in the nonlinear partial differential equation, which results in errors for long time well test. A well test model of composite reservoirs considering the effects of well bore storage and skin is established in this paper. The quadratic gradient term in the flow equation of composite reservoirs is retained. The numerical solution of the composite reservoir model is obtained by the Douglas-Jones predictor-corrector method at a constant rate production for an infinitely large system. The flow mechanism of composite reservoirs considering the quadratic gradient term is analyzed. The change rule of pressure is addressed when the parameters change. The plots of typical dimensionless pressure curves are drawn. The results can be applied to the flow mechanism research for composite reservoirs and the well test analysis.