Poroelastic After-Closure Pressure Decline Analysis In Dual-Porosity Dual-Permeability Formations

Abstract

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 and dual-permeability medium during the after-closure phase of hydraulic fracturing. The analysis shows that both the matrix and natural fractures permeability, as well as the developed fracture length, can be estimated based on the obtained pseudo-linear and pseudo-radial dual-pressure and dual-flow regimes. The estimations are made by use of the corresponding 1/2 and -1 slopes in the time-history plots of the wellbore pressure derivative. The transition period between pseudo-linear and pseudo-radial 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 inter-porosity 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 pseudo-linear regime, lower limit for the pseudo-radial 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 upon by a corresponding sensitivity analysis, through which the prominent poroelastic parameters of the solution are determined. Lastly, the definition of conventional key parameters attributed to solutions of this type, such as formation total compressibility, storage coefficients and hydraulic diffusivity, are reformulated using the presented dual-porosity poroelastic approach to the problem.