Triple Porosity Model-Dual Permeability with Transient Diffusivity Hydraulic in Naturally Fractured Reservoirs

Abstract

Constant flow rate solutions are presented for a triple porosity model-dual permeability using the transient interporosity flow and a skin between two media in mention for to generate a pseudosteady interporosity flow. Transient interporosity flow is modeled in a convolution form, considering matrix, microfractures, vugs and fractures flow. New solutions are presented for two cases, where there is no primary flow through the microfractures and where the compressive and distensive strength process has created an interconnected system of microfractures. In both cases there is an interaction between matrix, microfractures, and fracture systems.

Due to the total diffusivity hydraulic depends on fracture pressure is modeled in a convolution form in combination with a partial derivative of fracture pressure with respect to dimensionless time for to incorporate the geometry changes in fractures during the production and depletion.
The numerical inversion was carried out with Stehfestís algorithm. In addition, approximate analytical solution for short and long dimensionless time are obtained and compared with the solution calculated by numerical inversion, providing satisfactory results. The values of the numerical inversion were used to generate the results, presented in terms of the dimensionless groups derived from the approximate analytical solution.