Fracture Length Optimization as a Function of Discount Revenue and Gas Reservoir Permeability
Authors: Khan M. , Klyza S. , Ochs D.E. , Hareland G. 
Published: December 2007

Abstract
This paper shows how a fracture generation, cost and fractured well production model can be used to optimize the fracture length of a reservoir as a function of discount revenue and gas reservoir permeability. The hydraulic fracturing model gives the fracture dimensions, fracture leakoff and the estimated fracture proppant volume for any pump time during fracture generation. For any generated fracture length, the total cost of the fracture job can be estimated based on fracture fluid, proppant and equipment costs. The fracture dimensions for any fracture length is used in a production model which is linked with the reservoir material balance. This gives the capability to predict the production rate at different times for any fracture length. A field study gives a clear illustration of the effectiveness of this study. By simulating different fracture lengths, gas reservoir permeabilities, and discount rates the optimum fracture length for maximum net revenue returned is estimated.

Introduction
Advances in fracturing technology have shifted low permeability gas reservoirs which had been of subeconomic potential to profitability. High porosity and low permeability gas reservoirs found in the Rocky Mountain region of the United States which were originally completed thirty to forty years ago are being recompleted with significant production improvements. Without stimulation after completion, the typical tight gas well will not produce at an economic rate. Prior to initiating any type of stimulation treatment, some cost benefit analysis must be done to determine if the expense is justified. For operators, the tools and personnel to conduct an economic study are generally available.
During the past not enough attention has been given into the economic analysis of the hydraulic fracturing. Several models have been developed to predict the fracture geometry but little attention was given to determine the exact cost of fracture operations and the relation between fracture dimensions, and the ultimate return of the stimulation job. The relationship between fracture dimensions, well production, and the overall fracturing cost are the import parameters to consider for any fracture job. These factors combined can ensure an economically viable fracture treatment. A successful hydraulic fracture job still requires much experience and keen judgment, as well as extensive prior analysis, studies, and tests. Herein, this problem is investigated through the use of an integrated fracture propagation, reservoir production, and economic computer simulation based on published analytical models. Generally, it is assumed that the larger fracture creates more profit. However, as the size of the treatment increases, the cost of the stimulation rises faster than the incremental profit gained by the increased well productivity over the planned producing life of the well. In this work the optimum fracture dimensions are determined based on maximum net present value (NPV).

The Fracture Propagation Model
The PKN fracture model approximates propagated fracture dimensions assuming the fracture height is fixed, the pressure is constant along a vertical cross section perpendicular to the direction of propagation and formation yield strength is constant along a vertical plane. The fracture predicted by the PKN model is a narrow ellipse. The PKN model is more appropriate for simulations of fractures at depths where pressures would be high enough so there would be no slipping of adjacent rock layers. The dimensions calculated by the PKN algorithm approximate the real fracture only to the extent that input variables represent the formation properties. P. 399