Simulation of a Finite-Capacity Vertical Fracture in a Gas Reservoir

One- and two-dimensional gas reservoir simulators were combined in such a manner that pressure distributions, both in an induced vertical fracture and in the surrounding formation, could be determined as a function of time for any specified well production rate. Basic assumptions regarding the fracture were as follows: (1) the fracture completely penetrates the formation, (2) all flow into the wellbore enters via the fracture, and (3) flow in the fracture is described by Darcy's law. The technique used consisted basically of the alternate use of one- and two-dimensional algorithms for obtaining new pressure distributions in the fracture and the reservoir, respectively. The finite-difference grid penetrates the fracture in the direction normal to the fracture axis so that corresponding to each fracture node, there is an adjacent reservoir node. The pressures at these adjacent nodes were used to calculate flow rates from the formation into the fracture, which provided source terms for both algorithms. By alternately using large and small time-steps, stabilized distributions were obtained after a few days production for several different fracture permeabilities. All other reservoir and fracture parameters were fixed so that the effect of fracture permeability on fracture pressure drop and well pressure decline could bemore » determined. Results are presented for a production rate of 1MMscf/day from a 40-acre square of 2 md-ft flow capacity. The combination model developed provides the only known means of simulating a vertical fracture of given characteristics in a gas reservoir under transient conditions. Thus, the technique developed would be useful in locating wells in a storage field in that the effects of both fracture length and conductivity could be considered prior to drilling and fracturing operations.« less