Simulation of a Finite-Capacity Vertical Fracture in a Gas Reservoir
Authors: Sawyer W.K. , Locke C.D. , Overbey W.K. 
Published: December 2007

This paper was prepared for the 48th Annual Fall Meeting of the Society of Petroleum Engineers of AIME, to be held in Las Vegas, Nev., Sept. 30-Oct. 3, 1973. Permission to copy is restricted to an abstract of not more than 300 words. Illustrations may not be copied. The abstract should contain conspicuous acknowledgment of where and by whom the paper is presented. Publication elsewhere after publication in the JOURNAL OF PETROLEUM TECHNOLOGY or the SOCIETY OF PETROLEUM ENGINEERS JOURNAL is usually granted upon request to the Editor of the appropriate journal provided agreement to give proper credit is made.
Discussion of this paper is invited. Three copies of any discussion should be sent to the Society of Petroleum Engineers office. Such discussion may be presented at the above meeting and, with the paper, may be considered for publication in one of the two SPE magazines.

Abstract
One- and two-dimensional gas reservoir simulators were combined in such a manner that pressure distributions, both in an induced 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:the fracture completely penetrates the formation,all flow into the wellbore enters via the fracture, andflow 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 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 timesteps, 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 pressure drop and well pressure decline could be determined. Results are presented for a production rate of 1 MMscf/day from a 40-acre production rate of 1 MMscf/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.

Introduction
The American Gas Association Pipeline Research Committee and the U.S. Bureau of Mines are involved in a cooperative study of methods for increasing the capacity and operating efficiency of gas-storage reservoirs. The expansion of an existing storage field to achieve increased capacity frequently requires that new wells be drilled and fractured. The question thus arises: With regard to the area's preferred direction of fracture and the preferred direction of fracture and the existing formation permeability, what is the minimum number and location of new, fractured wells required to achieve the desired increase in capacity?