Effects of Non-Darcy Flow and Penetrating Ratio on Performance of Horizontal Wells With Multiple Fractures in a Tight Formation

Abstract

A novel slab source function has been formulated and successfully applied to examine effects of non-Darcy flow and penetrating ratio on performance of a horizontal well with multiple fractures in a tight formation. The Barree–Conway model is incorporated in the mathematical model to analyze non-Darcy flow behavior in the hydraulic fractures, while the pressure response under non-Darcy flow is determined by two dimensionless numbers (i.e., relative minimum permeability (kmr) and non-Darcy number (FND)). A semi-analytical method is then applied to solve the newly formulated mathematical model by discretizing the fracture into small segments. The newly developed function has been validated with numerical solution obtained from a reservoir simulator. Non-Darcy effect becomes more evident at a smaller relative minimum permeability (kmr < 0.05) and a larger non-Darcy number (FND > 10). The non-Darcy number is found to be more sensitive than the relative minimum permeability, resulting in a larger pressure drop even at a larger kmr. In addition, the non-Darcy flow is found to impose a significant impact on the early-stage bilinear/linear flow regime, resulting in an additional pressure drop that is similar to lowering the fracture conductivity. The pressure response can be classified into two categories by a penetrating ratio of 0.5. When the penetrating ratio is decreased, the early bilinear/linear flow regime occurs, followed by an early radial flow regime.