Performance analysis for a model of a multi-wing hydraulically fractured vertical well in a coalbed methane gas reservoir

This paper proposes a composite model to investigate the pressure behavior and production performance of a multi-wing hydraulically fractured multiple fractured vertical well (MFVW) in a coalbed gas reservoir with a stimulated reservoir volume (SRV). The model simultaneously considers adsorption-desorption, diffusion, and viscosity flow. The MFVW model combines line-source method with Laplace transformation and discretization method. Then, the Stehfest numerical inversion and the Gauss elimination are utilized to obtain the transient pressure responses and production dynamics. The results show that the main flow regimes for an MFVW in a coal seam gas reservoir are linear flow between hydraulic fractures, pseudo radial flow in the SRV, transition flow from the inner to the outer region, and radial flow in the outer region. Further, a slight hump is observed during the linear flow period, which could not be observed in the curves of MFVWs with two-wing hydraulic fractures. The effects on MFVW performance of permeability and size of the SRV, properties of hydraulic fractures (fracture angle asymmetry, different fracture angle, and fracture number), Langmuir volume, and Knudsen diffusion coefficient are discussed. The conclusions obtained in this paper will be helpful to understand the transient performance of MFVWs in coalbed gas reservoirs.