Production-Decline Models Using Anomalous Diffusion Stemming From a Complex Fracture Network

In this work, we develop a well-based fractional-production-decline model, which resorts to anomalous diffusion to characterize the heterogeneity of complex fracture networks and can be conveniently used to interpret the rate and cumulative data in the early and middle times of production from multifractured horizontal wells in unconventional reservoirs. We first develop a model (the fracture-based model) to be used in inverse problems by simplifying the fractional-time-derivative model using the traditional multiple-planar-fracture framework to essentially contain three parameters (a, Ar, and Ix). After performing tests with elaborate synthetic cases, the trace of anomalous diffusion is captured but the drawbacks of this model are also detected and analyzed. Then, by focusing on improving the fracture-based model, we consider an infinite-conductivity horizontal well draining a complex fracture network through a fractional-flux-related skin. The improved model (the well-based model) is bolstered with the corresponding type curves regarding production rate and cumulative production, which can be applied to interpret the single-phase production in the early and middle times and to mainly characterize the fracture-network-related heterogeneity reflected in the production data during this early-to-middle period. The well-based model is applied to two synthetic cases with explicitly modeled complex fracture networks and to the cases of multifracture horizontal wells in the Permian Basin. The results of all case studies display good matches between our model and the production data, which indicates the model's capability to accurately describe the transient regime of the flow in the extremely heterogeneous fracture networks on the basis of average values of the formation properties.