Analyzing the production data of fractured horizontal wells by a linear triple porosity model: Development of analysis equations

Tight reservoirs stimulated by multistage hydraulic fracturing are commonly described by a dual porosity model. This model consists of homogeneous matrix blocks separated by vertical hydraulic fractures. This work hypothesizes that the production data of some fractured horizontal wells may also be described by a triple porosity model. The third medium can be either reactivated natural fractures or thin horizontal beds of higher permeability. We test this hypothesis by extending the existing triple porosity models to develop an analytical procedure to determine the reservoir parameters. We derive simplified equations for different regions of the rate-time plot including linear and bilinear flow regions. These equations can be used to calculate the effective fracture half-length, matrix permeability and length of micro-fractures. We use the proposed model to analyze the production data of two wells drilled in Barnett shale. The results show that a dual porosity model is more appropriate for describing Barnett shale data. Even if the micro-fractures are present they are not inter-connected and the length scale is much smaller than the hydraulic fracture spacing.