| Popis: |
In this study, an extended version of the fractional decline model is analytically developed for gas flow in fracture reservoir using the anomalous diffusion equation incorporated with the fractional calculus and equation of state. The model can represent the heterogeneity of complex fracture networks and can further be used to interpret reservoir properties by performing type-curve matching of flow rate and cumulative production from multi-fractured horizontal wells in unconventional reservoirs. To address the limitations of conventional planar fracture idealization, the hydraulic fractures in this present study are integrated with the fracture network, and the fractional diffusivity is solved for a horizontal wellbore. Upon establishing and solving the governing equation in the Laplace domain, the solutions are converted back to the real-time and space domain by performing numerical Laplace inversion. A set of distinctive type curves is generated on the basis of an infinite conductivity horizontal well model, considering early and middle times, in order to capture the heterogeneity of the fractal network in the reservoir model. Application of this new model is demonstrated through type-curve matching of two synthetic cases of simulation data obtained from commercial software; the cases cover orthogonal evenly and unevenly distributed networks. Results from these examples show an acceptable match between the fractional decline model and synthetic data and, hence, showcase the applicability of this model to capture the transient flow in heterogeneous fractured reservoirs. |
