Optimal Fracture Design For Tight Gas Reservoirs
Authors: Payne David A. , Cormack Donald E. 
Published: March 2010

Abstract
Type curves for the production of gas from artificially fractured reservoirs have been used to determine the fracture characteristics that maximize the expected economic return. It is shown that if possible fractures should be propped to yield a dimensionless conductivity of 4.2. The volume of the fracture and, hence, its length are established based on an economic analysis such that the incremental cost a/increasing the fracture volumeis equal to the incremental increase in revenue generated by alarger fracture.
In a particular case study examined, the present value revenue for a tight gas reservoir could be increased by 8.75% (i.e. $0.35 million) by decreasing the conductivity from 10 to the optimal value of 4.2.

Introduction
Hydraulic fracturing has become a standard treatment procedure for stimulating production from gas reservoirs. Particularly significant are the improvements in production which accompany massive fracturing in tight gas reservoirs. The design of hydraulic fractures is often undertaken in a rather casual manner. Treatment procedures are frequently chosen based on previous success in similar formations(1). Alternatively, several possible fracture designs are selected and compared for performance using standard performance curves, or using numerical simulators(2, 3). Although such fractures invariably improve the production performance of a well, such approaches will not likely yield the best performance that could potentially be achieved.
The cost of a fracture treatment can represent a significant fraction of the total cost of drilling and completing a well. Hence, the design of the fracture deserves a great deal of ttention. A fracture which is too small will result in an unnecessarily low rate of gas production, whereas one which is too large will result in excessive completion costs. Both undersized and oversized fractures will compromise the economic viability of a well.
In this paper, a systematic approach is presented for the design of fractures in unbounded gas reservoirs. We consider only the case of vertical fractures because these are most requently encountered in deep formations which are characteristic of tight gas deposits.

Analysis
To begin the analysis, we will consider a well in an unbounded reservoir, that is to be produced at a constant rate, qp until some maximum desired drawdown, ΔPmax is reached. The lime 'It which ΔPmax is reached is referred to as the time until production drop-off, t'. After this time, the production rate will be assumed to decline, with drawdown held constant.
For an infinite reservoir, if one considers several possible fracture treatments, the treatment which maximizes the timentil production drop-off will in general also maximize the present value revenue generated from the well. This point will be discussed in more detail later in the paper. This is an important observation, because it means that to a large extent, optimal fracture characteristics can be established based on the constant rate period. However, efforts to maximize t', without some additional constraint are not particularly productive because t ' an always be increased by making the fracture a little larger.