A Semi-Analytical Mathematical Model for Off-Center Fractured Vertical Wells With Asymmetrical Fractures in Columnar Coalbed Methane

Coalbed methane (CBM) is one of the important unconventional oil and gas resources. Since the permeability of the CBM reservoir is very low, CBM is usually developed by hydraulic fracturing technology to enhance gas productivity. In fact, most of the wells are not at the center of the columnar CBM reservoirs, which leads to different wellbore pressure responses. It is meaningful to analyze the wellbore pressure response of the off-center fractured vertical wells with asymmetrical fracture. The adsorption-desorption, fracture asymmetry are considered and a semi-analytical mathematical model is established. The pressure wellbore solution of the Laplace domain can be obtained by Laplace transformation, model coupling, and Gauss elimination. Then, the Stehfest numerical inversion is employed to obtain the pressure solution and rate distribution in the real-time domain. This semi-analytical solution is verified; the results show that the wellbore pressure includes six flow regimes, which include bilinear flow, linear flow, elliptic flow, radial flow, arc boundary reflection, and boundary dominated flow regime. The influence of fracture angle, dimensionless conductivity, and off-center distance on wellbore pressure and rate distribution are discussed in detail.