A Simple and Accurate Mathematical Model for Predicting Productivity of Multifractured Horizontal Wells

Abstract

Abstract Horizontal wells drilled in the direction of the minimum horizontal stress allow for multiple transverse fractures be hydraulically created for enhancing well productivity in low-permeability oil and gas reservoirs. Dominating factors affecting the productivity of the multi-fractured horizontal wells vary with reservoir and fracture properties, as well as well trajectories. A simple and accurate mathematical model for evaluating and optimizing productivity of this type of wells is not available and is highly desirable to reservoir engineers. This paper fills the gap. After a case study with existing analytical models that were derived for multi-fractured wells we found that these models cannot describe the performance of oil wells with acceptable accuracy. We then formulated a simple analytical model that better describes the productivity of multi-fractured horizontal wells. The new model couples the radial flow in the non-fractured region of reservoir, the linear flow toward the fractures in the fractured region, the linear flow in the fracture, and the radial flow in the fracture toward the horizontal wellbore. It can model pseudo-steady state flow of reservoir fluids in sections reservoir of any shape with the fractured region being located at any area in the reservoir. The difference between the production rate given by the new model and the actual production rates was found to be less than 5% in the two cases studied. This paper provides reservoir engineers a simple and accurate tool for predicting, evaluating, and optimizing the performance of multi-fractured horizontal oil and gas wells.