Semianalytical Solution for Modeling the Performance of Complex Multifractured Horizontal Wells in Unconventional Reservoirs

Abstract

Summary Analytical models have evolved in their capacity to represent the transient response of multifractured horizontal wells producing from unconventional reservoirs. However, as is common with analytical solutions, they are based on simplified reservoir/well geometries and flow-pattern assumptions that inherently restrict their scope of application. Their use for analyzing flow scenarios that transcend their scope is thus prone to errors. This paper documents a semianalytical model that overcomes the aforementioned limitations, and thereby expands analysis to the realm of reservoir/well architectures that are inaccessible to analytical models. Our solution is based on the Laplace-transform boundary-element-method (BEM) implementation of the Green's function solution of the diffusivity equation. We represent the reservoir as a 2D composite system, with the outer boundaries and the interface between reservoir regions discretized appropriately. With the collocation procedure, the solution is distilled to a system of algebraic equations that is solved for the reservoir's transient response. The hydraulic fractures need not be regular (equidistant and/or isometric), as is required by most analytical models; instead, they can traverse arbitrary spatial orientations and dimensions with respect to the horizontal well. We demonstrate the application of our solution by modeling multifractured-horizontal-well performance with two verification cases and three synthetic examples. The first example showcases a multifractured horizontal well traversed by identical, evenly spaced, fully penetrating, vertical hydraulic fractures within a stimulated reservoir volume (SRV). The second example models an enhanced-permeability region local to each hydraulic fracture as opposed to a single SRV housing all the fractures. The last example typifies complex fracture geometries, where the fractures have different half-lengths, spacings, and orientations. Besides showing that all the verification and example cases are in excellent agreement with numerical solution, we demonstrate the utility of our solution for modeling variable-rate flow commonly observed in practical field-production scenarios, showing its potential for history matching and forecasting the performance of multifractured horizontal wells.