Transient pressure behavior for a horizontal well with multiple finite-conductivity fractures in tight reservoirs

Horizontal drilling and multi-stage hydraulic fracturing have been common and efficient practices in exploitation of tight reservoirs. Establishing corresponding mathematical models and analyzing transient pressure behaviors of this type of well-reservoir configuration can provide a better understanding of fluid flow patterns in formation as well as estimations of important parameters. Most current models proposed for fractured horizontal wells in tight reservoirs do not incorporate either reservoir permeability loss during the production, which is believed to be non-ignorable or finite conductivity of hydraulic fractures. A coupling model for a multi-fractured horizontal well (MFHW) in tight reservoirs is presented in this article, in which finite conductivity of hydraulic fractures and stress-dependant reservoir permeability are taken into account simultaneously. A semi-analytical solution is obtained in the Laplace domain by using source function theory, Laplace transformation, perturbation technique, discretization of fractures, and superposition principle. Analysis of transient pressure responses indicates that several characteristic flow periods of fractured horizontal wells in tight reservoirs can be identified, including linear flow in fracture, bi-linear flow, linear flow in reservoir, pseudo-radial flow around fractures, and pseudo-radial flow around the horizontal wellbore and fractures. Parametric analysis shows that fracture conductivity, fracture spacing, fracture length, permeability modulus, and skin effect can significantly influence the transient pressure responses of fractured horizontal wells in tight reservoirs. The model presented in this article can be applied to obtain important parameters pertinent to reservoir or fractures by type curve matching, and it can also provide useful information for optimizing fracture parameters. Finally, the model presented in this article can also be easily extended to dual-porosity cases.