Study on Seepage Model of the Dual-Permeability Quadruple-Media Homogeneous Reservoirs

According to the complex reservoir characteristics of carbonate reservoir, this paper will consider seepage relations of the quadruple medium-bedrock, dissolution hole, micro fracture and large fracture. The equation of motion and state of reservoir fluid are substituted into the equation of conservation of mass to obtain the differential equation of seepage flow in quadruple medium. By properly defining dimensionless parameters, the seepage differential equation and its definite solution conditions are reduced to dimensionless form. The dimensionless seepage differential equation can be reduced to algebraic equation by Laplace transformation. In the algebraic equation, the dimensionless pressure in Laplace space of large fracture and micro fracture is used to express the pressure in bedrock and dissolution cavity respectively. The general solution of the differential equation of seepage under different conditions is substituted into the differential equation of seepage with large and micro cracks to obtain the solution of Bessel function with undetermined coefficients. According to the uniqueness of the solution and the properties of Bessel function, the special solutions of different seepage differential equations in Laplace space are obtained by linear analysis.