A pressure transient analysis model of multi-fractured horizontal well in consideration of unequal production of each fracture

Key words:  horizontal well  unequal production of fractures  pressure transient analysis  Green 's function  Newman 's product method  type curves

Abstract:

In this study, the effect of unequal production of each fracture (UPEF) on well testing behavior was considered in order to develop a pressure transient analysis (PTA) model for multi-fractured horizontal wells (MFHW), and semi-analytical solutions were given based on the Green 's function, the Newman 's product method and superposition principles. The flow in a hydraulic fracture is divided into two flow regimes (i.e. a variable-mass linear flow far from the horizontal wellbore and a radial flow near the horizontal wellbore) to characterize the finite conductivity flow within the fractures. Then, characteristic pressure curves were obtained using a numerical Stehfest inversion algorithm, and sensitivity analysis (e.g. UPEF, fracture and parameters) was further conducted. The analysis results indicate that there are obvious differences among the type curves obtained via assuming an equal production of each fracture (EPEF) and the UPEF. The early-radial flow behaves as a horizontal line in the pressure derivative curves when the fractures located at the ends of wellbore contribute much more to total oil production than those at the middle section, or when the fractures are wide-spaced and short, or when the fractures behave as spindle shape. In comparison with the classic PTA model of the MFHW in Saphir software, the accuracy and reliability of the newly proposed model has been proven.