Modeling interporosity flow functions and shape factors in low-permeability naturally fractured reservoir

A new method is proposed to derive interporosity flow functions (also called transfer functions) and shape factors between the fracture and low-permeability matrix in naturally fractured reservoirs with dual porosity model. The differential form of single-phase seepage equation and the analytical solution for pressure diffusion equation are adopted to deduce the analytical solution for shape factors in transient pressure diffusion equation. By employing this approach, the limitations resulting from the process of deducing interporosity flow function and shape factors under many assumptions are avoided, and the no-linear pressure gradients in the matrix can be well explained. The defects of the interporosity flow function and shape factors mostly are generated under the pseudo-steady state hypothesis, in which no-linear pressure gradients in the matrix cannot be accurately captured. The interporosity flow function, constant shape factors and time-varying shape factors considering threshold pressure in one, two and three dimensional fractures are derived for low permeability fractured reservoirs under no pseudo-steady state hypothesis. The newly developed analytical solution is useful in compressible fluid productivity prediction and transient well testing application. The field case study shows that those shape factors are able to provide more accurate parameters for compressible fluid productivity prediction and more reasonable theoretical basis for the correct interpretation of well testing.