Inflow performance of wells intersecting long fractures with transient pressure and variable flow-rate behavior

• A simple mathematical model for predicting the performance of vertical and horizontal wells intersecting fractures in the transient and steady-state stages.
• This model predicts the transient pressure behavior during the increasing pressure and declining pressure stages.
• Useful tool for productivity analyses of hydraulically fractured wells during the rapid decline stage.
• The model is compared with real well data.
• The model generalizes previous mathematical models and it is consistent with transient flow analyses of bilinear flow.

A mathematical model which predicts the performance of vertical and horizontal wells intersecting fractures is presented. Based on the formulation originally proposed by Guo and Schechter (1997), this model predicts the transient pressure behavior with variable flow-rate both during the increasing pressure stage and in the declining pressure and flow-rate situation. The flow in the matrix and that in the fracture are coupled to allow the calculation of the pressure distribution in the matrix and in the fracture, as functions of space and time. The model is consistent with transient pressure analyses in finite-conductivity vertical fractures (Cinco-Ley and Samaniego, 1981), and presents a useful tool for productivity analyses of hydraulically fractured wells during the rapid decline stage. Comparisons with real well data are analyzed and discussed.