Productivity estimations for vertically fractured wells with asymmetrical multiple fractures

Abstract Through hydraulically fracturing, vertical wells can also create a region of stimulated reservoir volume (SRV) to enhance ultimate recovery. Thus, implementing SRV measures on old vertical wells is being common practices in Chinese oilfield, Ordos Basin. It is a significant problem that should be solved urgently about how to estimate productivities of vertical wells with SRV. Microseismic fracture imaging strongly shows multiple fractures (MF) can develop during SRV treatments. However, most of the published works on the productivities of vertically fractured wells assumed the wells contained a single and symmetrical fracture, and little work in literature has focused on asymmetrical MF. To study this problem thoroughly, the paper proposed an approximate analytical productivity equation for fractured wells with asymmetrical MF in low-permeability and anisotropic cylinder-shaped formations, using conformal mapping and mirror reflection. Based on analytical and numerical methods, equation validations are conducted by comparing the results of proposed solutions with analytical/numerical solutions. In addition, the effects of some critical parameters on productivity have been investigated: average MF conductivity, average MF penetration ratio, fracture asymmetry, and MF number. Results show that there is a good consistence between the results of proposed solutions and analytical/numerical solutions for fractured wells. The fractured well productivity is a weak function of average MF penetration ratio; it is a stronger function of average MF conductivity, and MF number. The fractured well productivity increases as: average MF penetration ratio increases, average MF conductivity increases, and MF number increases. The effect on fractured well productivity appears to be weaker as: average MF conductivity increases, and average MF number increases. Additionally, for a single-fracture well, the productivity can decrease by about 8%, when asymmetry ratio increases from 0 to 0.8.