Pressure transient analysis for off-centered fractured vertical wells in arbitrarily shaped gas reservoirs with the BEM

Because transient pressure analysis is important for postfracture evaluation and reservoir characteristic assessment, and hydraulic fracturing has been widely applied in recent oil/gas development, physical and mathematical models are important for petroleum engineers. Although there numerous reports relate to fractured wells in the centers of reservoirs, research on off-centered fractured wells is rare, and it is difficult to obtain a semianalytical solution with conventional methods. In this paper, a mathematical model of an off-centered, infinite-conductivity fractured well in an arbitrarily shaped gas reservoir is established. The boundary element method (BEM) is implemented to analyze the well transient pressure response. Two validation cases of center wells with circular and rectangular outer boundaries are used to verify the correctness of our method. The pressure response of an off-centered fractured well differs from that of the conventional case at the early stage of the boundary reflection flow period. Furthermore, if the well is close enough to the boundary, the pressure derivative curves will show another step before the boundary-dominated flow period. In the end, the model is extended to dual- and triple-porosity reservoirs. The pressure type curves and their sensitivity analyses are also determined. From this study, it is clear that the BEM can be an effective and precise method to cope with the fluid flow problems in such a complex situation.