Hydraulic fracturing is a technique that increases the efficiency of a production well for a wide range of low to high permeability reservoirs. Many analytical and semianalytical solutions have been presented to model the performance of hydraulic fractured wells. Most models that are developed to investigate the effect of hydraulic fractures on the performance of a well only consider flow from the fracture to wellbore and neglect the direct flow through the matrix to the wellbore. These models consider the linear flow around the fracture, and ignore the radial flow and pressure drop due to interaction between different flow regimes. Neglect of this pressure drop due to flow convergence, is satisfactory only for low permeability formations, such as shale gas and tight oil reservoirs. This pressure drop between the linear and radial flow regimes around the wellbore and hydraulic fracture can contribute to significant inaccuracy in the existing models, particularly in the case of the medium to high reservoir permeability (10 mD and above).
This paper presents a new semianalytical approach to determine the simultaneous fluid flow from the matrix and fracture to the wellbore. The concept of the electrical resistance based on the conservation of electrical current and Ohm's law are applied to use the superposition of rate from the fracture and the matrix to the wellbore. Although this method can be applied to transient flow, this paper focuses on the single phase pseudo steady state flow of a vertical well intersecting a vertical fracture with the finite conductivity. This work models the flow convergence pressure drop due to the interaction between linear flow that occurs around the fracture and radial flow in the matrix around the wellbore. Further, a solution for partially communicating fracture with the wellbore is presented as well. In the literature, this form of partial completion pressure drop or skin has been solved for radial flow through the matrix to the wellbore, but this paper presents the pressure drop due to partial completion that opens to a narrow rectangular communication to wellbore which would control the well performance and the contribution of fracture rate.
The results clearly demonstrate that the radial flow contributes significantly when reservoir permeability is medium to high. In low permeability reservoirs, linear flow is substantially larger than radial flow and interaction between flow regimes that causes flow convergence pressure drop is negligible. Another important conclusion is the contribution of the hydraulic fracture can be substantially restricted by different flow resistances inside the fracture and the matrix. This paper estimates properly the performance of a hydraulic fractured well and predicts the relative contribution of the fracture and the matrix to the total flow rate in the presence of the additional pressure drops due to different skins as flow resistances around or inside of the fracture, the matrix, and the wellbore.