A semi-analytical model for the transient pressure behaviors of a multiple fractured well in a coal seam gas reservoir

Abstract

Multiple radial fractures can be generated in unconventional gas reservoirs after stimulation treatments such as hydraulic refracturing, high-energy gas fracturing, and explosive fracturing. This study presents a semi-analytical model to simulate the bottom-hole pressure (BHP) performances of a fractured well with multiple radial hydraulic fractures (MRHF) in a stress-sensitive coal seam gas reservoir. The adsorption–desorption and diffusion for fluid in reservoirs are considered. The continuous line-source function associated with discretization method in a composite coalbed gas reservoir is applied in Laplace domain. By means of Stehfest numerical inversion algorithm and Gauss elimination, the transient pressure responses in the well bottom are obtained and discussed.The results demonstrate that, from type curves, the main flow regimes for the proposed model in the coalbed gas reservoir are bilinear flow between adjacent radial hydraulic fractures, linear flow between adjacent radial hydraulic fractures, pseudo radial flow in stimulated region, and radial flow in un-stimulated region. Moreover, an obvious “hump” appears between the bilinear flow regime and the linear flow regime in stimulated region, which represents the interference between adjacent radial hydraulic fractures. The impacts of the ratio of permeability in stimulated region to that in un-stimulated region, the radius of stimulated reservoir volume (SRV), the permeability modulus, and the properties of hydraulic fractures on the transient pressure responses in well bottom are analyzed. The findings obtained in this study can pave the way for the quantitative understanding of the transient performances of multiple fractured vertical wells in unconventional reservoirs.