The Optimization Of Well Spacing And Fracture Length In Low Permeability Gas Reservoirs
Authors: Holditch Stephen A. , Jennings James W. , Neuse Stephen H. , Wyman Richard E. 
Published: December 2007

Introduction
Low permeability gas reservoirs are currently being developed in numerous basins in the United States and Canada. Typical reservoirs contain 25 to 100 net feet of gas pay, gas porosities ranging from 3 to 8 percent, original reservoir pressures from 1500 to 15,000 psi and formation gas permeabilities that range from .001 to 1.0 md. Considering these wide ranges in formation properties, it is of primary concern to determine the properties, it is of primary concern to determine the economic optimum well spacing and fracture length for a particular formation.
Numerous publications in recent years have proposed and documented the use of massive hydraulic fracturing techniques for stimulating tight gas reservoirs. As a result of the success of massive hydraulic fracturing, the average size of a typical treatment has been increasing. As the propped fractured length is increased, the initial flow rate and the ultimate recovery from a well are usually increased. This does not mean, however, that the bigger the fracture treatment the better. For any given set of reservoir parameters, an economic optimum fracture length can be parameters, an economic optimum fracture length can be calculated. If the induced fracture actually created in a well is greater than the economic optimum length, the well performance may be better but the profit from the well can be reduced. To determine the optimum fracture length and well spacing in a given reservoir, it is necessary to (1) predict propped fracture length as a function of fracturing costs, (2) predict well performance as a function of fracture length and (3) performance as a function of fracture length and (3) to perform present value economic calculations considering well costs, operating costs, fracturing costs and well performance. After these calculations are made, graphs of present value profit versus fracture length for various well spacings can be constructed. Such graphs can be used to determine the optimum economic values of well spacing and fracture length for a given reservoir.
The objectives of this paper are to present a simple technique for optimizing profit from a tight gas reservoir and to present several examples which illustrate the utility of the proposed method.

THE OPTIMIZATION MODEL
A computer model, FRACOP, was written to solve this problem. The model combines the fracture length problem. The model combines the fracture length calculations of Geertsma and de Klerk, reservoir performance calculations using the analytical solutions of performance calculations using the analytical solutions of Gringarten et al. and a present value economic analysis. The computer model requires minimum storage, minimum computing time and is well suited for use on a time-share computing system.

Fracture Length Calculations
The equations of Geertsma and de Klerk, for vertical fractures, were used to calculate the created fracture dimensions. The fracture length calculations in FRACOP are very similar to a model built for designing stable foam fracturing treatments. Non-Newtonian fracturing fluids can be simulated by inputting values of n' and K' for the specified fluid. The program uses the following equation to calculate the apparent viscosity of the fluid in the fracture.
(1)
Then using Eq. 1 and Eqs. 7a and 21a in ref. 4, the model simultaneously solves for width, length and viscosity.
Sand transport is not included in FRACOP. The total volume of the fracturing treatment is, however, corrected for the volume of sand. The propped fracture length is determined by first calculating the volume of pad that is still in the fracture at the end of the pad that is still in the fracture at the end of the treatment. This volume represents the initial pad volume minus the volume lost to the formation due to spurt and fluid loss. By assuming the remaining pad volume occupies the far end of the fracture, the propped fracture length is the distance from the wellbore to the pad remaining in the fracture.