The transient pressure behavior of a vertically fractured reservoir has been solved successfully based on numerical solutions.1,2 These solutions enhance the understanding of early time portion during the drawdown or the build-up test conducted in a vertically fractured reservoir. To completely understand the performance of a gas reservoir, solutions for later time are also necessary. However, stability considerations always complicate the design of the model. The main objective of this work is to develop a numerical model which could be stable for all times.
The model is formulated for a fracture of limited and radial extent completely penetrating the producing formation vertically. The model equations are transformed using conformal mapping. Appropriate stability criteria are developed and the resulting finite difference equations are solved using the Iterative ADIP method. The boundary conditions are handled using a special numerical approach resulting in stable solutions for all times. Another feature of the developed procedure is the ability to handle finite fracture conductivity and stress sensitivity.