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 paper 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 with a higher permeability. We test this hypothesis by extending the existing triple porosity models to develop an analytical procedure for determining the reservoir parameters. We derive the 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.
The second part of this paper focuses on analyzing production data of tight oil reservoirs. We plot rate-normalized pressure (RNP) versus material balance time (MBT) of two wells drilled in Cardium and Bakken formations. We observe a half-slope followed by a unit-slope in both cases. This paper hypothesizes that the half slope reflects the linear transient flow regime, and the unit slope reflects the linear pseudosteady state (PSS) flow. We test this hypothesis by developing a new model for pseudo steady state flow when pressure interference occurs between two adjacent hydraulic fractures. We determine the reservoir properties by both PSS and transient analysis methods. For Cardium well, both methods give very close results. For Bakken well, both methods give relatively close results. We conclude that analyzing the late time production data of tight oil wells complement the linear transient analysis and can be used to calculate the stimulated reservoir volume, which can eventually help the industry to optimize the fracturing operation.