A nonlinear mathematical model for low-permeability reservoirs and well-testing analysis

Abstract

Based on a capillary model and integrated with the boundary layer theory,we proposed a new mathematical model for seepage in low-permeability reservoirs by introducing two parameters c1 and c2 that could characterize seepage of low-permeability reservoirs.This model well explained origins of a start-up pressure gradient and nonlinear seepage.According to the new model,a well-testing model considering the influence of moving boundaries was established and solved with the finite difference method,an impact of dimensionless characteristic c1D and c2D parameters on well-testing curves was investigated as well.The results show that pressure and pressure derivative curves for both the new model and a pseudo pressure gradient model are upward compared with the Darcy model though the upward degree for the new model is gentle.And c1D and c2D are characteristic parameters that determine the shape of well-testing curves.The upward degree increases with an increase of c1D or c2D when the sum of c1D and c2D is not a constant,while the upward degree increases with an increase of c1D but a decease of c2D when the sum of c1D and c2D is a constant.On well-testing curves,a pressure response to the new model is in agreement with that to the Darcy model both for closed boundaries and for constant pressure boundaries.