Abstract
Calculation of inflow to a well and hydraulic fracture in the reservoir simulation is presented in this paper. An algorithm of well index (WI) calculation based on a new numerical-analytical solution is proposed. In simple cases, the proposed method is identical to the classic Peaceman's formula, and surpasses it in accuracy in more complicated cases, taking into account different properties of the perforated grid block and its neighbors, imperfect perforation, location of a well in a grid block, impermeable boundaries next to a well.
Acquired WI coefficients were compared with analytical solutions for imperfect well, five-spot pattern, inflow to infinite and semi-infinite hydraulic fractures and also for the problem presented in [1], in which production rates before and after fracturing are compared. It is shown, that in these cases presented algorithm provides a lesser deviation from the analytical results than Peaceman's formula. Therefore developed algorithm is proved to be more accurate and applicable in more general cases.
Additionally, to demonstrate the effect of using the WI coefficients acquired with different formulas in reservoir simulation both methods were applied to comparison project SPE1 [2], in which it is necessary to account for impermeable boundaries and imperfect perforation. A significant difference of simulation results can be seen in the oil rate of the producing well, gas oil ratio, and pressures.
