Nonlinear Flow Model for Calculating Maximum Fracture Spacing in Horizontal Wells Considering Gaussian Distribution of Reservoir Heterogeneity

In order to improve production rate, multi-stage fractured horizontal wells are often used to develop tight reservoirs. The fracture spacing has an impact on production. How to determine the optimal fracture spacing (shot spacing) is very important. Firstly, a nonlinear one-dimensional steady non-Darcy flow model in a stimulated reservoir volume (SRV) area around the main fracture in a tight reservoir is established by introducing the moving boundary theory of low-velocity non-Darcy flow. The model comprehensively considers the heterogeneity of reservoir permeability and porosity, the stress sensitivity of permeability and the low-velocity non-Darcy flow with threshold pressure gradient. In particular, Gaussian distribution function is used to accurately characterize the reservoir heterogeneity. An analytical solution without considering the stress sensitivity is also derived by using L’Hospital’s rule. Secondly, the limit utilization boundary is determined, and then a novel method for calculating the maximum fracture spacing is proposed. The method is effectively applied to an actual well, and the necessity of considering permeability stress sensitivity is verified. Finally, the effects of different fracturing modes (slow descent type, transitional type and rapid descent type) and some characteristic parameters of the Gaussian distribution function on permeability and pressure distribution are analyzed. This presented work provides some theoretical basis and technical guidance for optimizing the fracture spacing of multi-stage fractured horizontal wells in tight reservoirs. In addition, the optimization of fracture spacing needs to consider both the impact on production capacity and the impact of fracturing costs on profits. The optimization of fracture spacing considering economic profits is the direction of future research.