Pressure transient analysis for multi-wing fractured vertical well in coalbed methane reservoir based on fractal geometry and fractional calculus

Abstract

In this paper, a semi-analytical mathematical model of pressure transient analysis (PTA) for multi-wing fractured vertical well (MWFV) in coalbed methane (CBM) reservoir is proposed, which considers the complexity of porous media by fractal geometry, the anomalous diffusion based on fractional calculus and the stress sensitivity represented by the exponential expression. Then through line source theory, dimensionless transformation, Pedrosa transformation, and other methods, the solution of the bottom hole pressure is obtained. At last, the PTA curve is presented by the Stehfest inversion method, and seven flowing regimes are identified. It can be observed that after introducing fractal geometry and fractional calculus, the PTA curve is quite different from the traditional curve in the slope of the derivative curve. The influences of related parameters are discussed, including mass fractal dimension, anomalous diffusion coefficient, number of hydraulic fractures, fracture angle, and stress sensitivity factor. Relevant results can provide better guidance to understand the CBM production performance in MWFV.

The inflow performance relationship in fractured, vertical, and dewatered coalbed-methane wells

“…The hydraulic fractures of a horizontal well are much more complicated than those of a vertical well and are difficult to depict (Ren et al, 2019). Hydraulic fractures can improve CBM production dramatically (Jiang et al, 2017), and there are multiwing fractures controlling production in fractured vertical CBM wells (Zhang et al, 2018;Xu et al, 2021;Li et al, 2022). Due to the complications of hydraulic fracturing, two-wing fractures were considered simple solutions in previous productivity models (Xu et al, 2013;Zhang, 2014).…”