Pressure transient analysis of a fractured well in multi-region linear composite reservoirs

Linear composite reservoirs, which can be represented as linear assemblies of distinct homogeneous regions, are among the most common types of ideal heterogeneous reservoirs. Many types of heterogeneous reservoirs, such as conventional and unconventional (tight) fluvio-deltaic reservoirs, meandering stream reservoirs, and fault reservoirs, can be approximated as linear composite systems. However, few studies have focused on the analysis and modeling of fractured wells, which are commonly used to produce tight oil/gas in such systems. In this paper, we present an analytical solution for fluid flows in a vertical finite-conductivity fractured well at an arbitrary position with arbitrary azimuth of fracture plane and in rectangular bounded anisotropic multi-region linear composite reservoirs considering finite-conductivity (partially communicating) faults. The solution is obtained by applying the methods of equivalent transformation, Green's function, and Laplace-finite Fourier cosine transformation. The standard log-log type curves, the dimensionless pressure, and its derivative with respect to t(D)/C-D, of the transient pressure response are plotted. Then, the behavior of two well-known linear composite systems (multi-region composite reservoirs and fault reservoirs) and a general linear composite system are examined. The effects of the relevant parameters were analyzed. It is shown that each main characteristic pressure behavior of wellbore storage and the skin, fractured well, linear composite structure, and finite-conductivity (partially communicating) faults can be identified on the type curves by their characteristic flow regimes. However, the characteristic behavior of each region may be masked by others in the complex multi-region case. It is also shown that the behavior of a fractured well in a general linear reservoir can be considered as a combinational behavior of the fault and multi-region composite reservoir. The presented solution can also be used in well testing to obtain reservoir and well parameters.