Poroelastic dual-porosity/dual-permeability after-closure pressure-curves analysis in hydraulic fracturing

The dual-porosity and dual-permeability theory of poroelasticity is used to analyze the wellbore dual-pressure responses of dual-porosity or naturally fractured formations. The pressure decline is analyzed by modeling the dual-pressure regimes of the dual-porosity/dual-permeability medium during the after-closure phase of hydraulic fracturing. The analysis shows that both the matrix and natural-fracture permeability, as well as the developed-frac-ture length, can be estimated on the basis of the obtained pseudo-linear and pseudoradial dual-pressure and dual-flow regimes. The estimations are made by use of the corresponding one-half and -1 slopes in the time-history plots of the wellbore-pressure derivative. The transition period between pseudolinear and pseudoradial regimes is also analyzed. The solution involves three time scales related to the rate of fluid flow through and in between the matrix and fractures network. Findings indicate the possible emergence of an additional -^1/2 slope in the log-log pressure-derivative plot of low-permeability shale formations. It is further shown that the transient-pressure response of the formation could be calibrated by incorporating an appropriate interporosity flow coefficient as a measure of the linear-fluid-exchange capacity between the matrix and fracture porosities. The analytical expressions for the time markers of the upper limit for the pseudolinear regime, lower limit for the pseudoradial regime, and the time at which the dip bases occur in pressure-derivative curves are given to estimate this parameter. The solution is successfully applied to and matched with a published set of field data to provide estimations for the associated reservoir properties. The field-data analysis is elaborated by a corresponding sensitivity analysis, through which the prominent poroelastic parameters of the solution are determined. Last, the definitions of conventional key parameters attributed to solutions of this type, such as formation total compressibility, storage coefficients, and hydraulic diffusivity, are reformulated by use of the presented dual-porosity poroelastic approach to the problem.