Transient Performance Behaviors of a Well Intercepting a Uniform-Flux Hydraulic Fracture within a Shale Reservoir A Fractional Integration Approach
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AbstractThe standard modeling techniques for fractured wells were developed for conventional (higher permeability) reservoirs. The application of these techniques in fractal (shale) reservoirs often yield physically-inconsistent results which can cause over/mis-interpretation of the transient data. The purpose of this work is to provide a new modeling scheme using the "fractional integration" solution for hydraulically fractured wells producing from a fractal reservoir. This methodology takes into account the reservoir heterogeneity in the modeling of the fluid flow towards the hydraulic fracture and provides physically consistent diagnostic interpretations and parameters.We have used the "fractional integration" approach to "couple" the fluid flow from a fractal (reservoir) to a Euclidean object (i.e., the hydraulic fracture). This approach requires rescaling the coordinate axes for the fractal reservoir using power-law relations.In this work we derive generalized models that can reproduce the classic Euclidean hydraulic fracture scenarios. We studied the constant-rate and constant-pressure cases and found that our proposed models yield the following three flow periods: Period 1: Early Fractal-Formation (EFF) flow. This flow period is analogous to the formation-linear flow for conventional reservoirs. The transient signature of this flow period is only influenced by the conductivity index (reservoir heterogeneity fractal parameter).Period 2: Late Fractal-Formation (LFF) flow. This flow period can also be observed in conventional reservoirs, although its characteristics are not extensively documented in the existing literature. This period is influenced by the fracture length and the reservoir fractal parameters, i.e., the fractal dimension and the conductivity index.Period 3: Pseudo-Fractal (PF) Flow. This is analogous to the pseudo-radial flow regime for conventional reservoirs. The transient performance behavior of this flow period depends on the two reservoir fractal parameters defined in this work.In performing this work, we provide the following technical contributions: We introduce a physically-consistent modeling scheme for a well with uniform-flux vertical fracture producing from a fractal (shale) reservoir.We show that the transient flow behavior for a well intercepting a uniform-flux vertical fracture can exhibit three distinct flow periods.We provide field demonstration cases which are analyzed and interpreted using the new solutions presented in this work.
