Fracture Design and Validation With Uncertainty and Model Limitations
Authors: Nolte K.G. , Economides M.J. 
Published: December 2007

Summary.
Standard methods fracture design and evaluation us idealized assumptions that result differences between the design length and the apparent length during production. These limitations provide economic risks, which can be reduced by quantifying the limitation, and including their effects in an economic analysis before selecting the optimal design length.

Introduction
The basic elements of fracture design were developed between 1955 and 1961. These developments include fracture-geometry models, in-situ stress and fracture orientation, characterization of fluid loss, coupling of geometry, fluid loss, and material balance for predicting penetration; and fractured-reservoir response. These contributions provided an adequate foundation for the relatively small treatments (e.g., average of 25,000 lbm sand in 1971**) performed before the advent of massive performed before the advent of massive hydraulic fracturing in the late 1970's. These larger treatments were more costly and had an increased likelihood of disappointing results. Consequently, a period of significant R and D began. This led to improved descriptive models, diagnostic methods for deviations from the idealized models used in standard practice, and analysis procedure for parameter definition. Economic analyses. Coupling treatment costs with posttreatment production performance were also introduced to the design performance were also introduced to the design process. These advances provided a basis process. These advances provided a basis process. These advances provided a basis process. These advances provided a basis for the evolution of improved fracturing practices. Applications of this advanced practices. Applications of this advanced technology have been limited, however, because of the additional cost necessary to obtain and interpret the required data. The reluctance to make this investment is fostered by the failure to quantify and consider the economic risks inherent in standard practice. The advanced methods and practice. The advanced methods and economic risk are discussed in this paper. Engineering by nature is a compromise between reduction of the sources of risk, control of the additional costs and resources associated with the application of advanced analysis, and the use of relatively simple models within standard practice. The compromise is generally achieved in the design process through safety factors. Effective process through safety factors. Effective application of safety factors requires identifying and quantifying the effects of uncertainties and other limitations on the total design process through a risk analysis. These requirements are also essential to validate the design process. Fracture design and evaluation have not achieved a universal standard of validation, nor has general practice reached a level of maturity that practice reached a level of maturity that rationally includes its basic uncertainties and limitations. A framework to begin this task is provided here and more comprehensively in Ref. 9. A basic analysis of risk, using probability distributions to describe parameter uncertainity, does not provide the primary feature for fracture design and evaluation. Instead, the primary feature is that most of the limitations for standard practice provide bias and accumulating effects. These effects separate the design length and the length inferred from the production responsethe quantities that the validation process seeks to reconcile. Although fracture design and reservoir performance are integral parts of this process, validation has suffered because these parts are often developed and applied independently, reported separately, and hence do not benefit from their natural synergy and related constraints. These constraints are discussed in this paper. To account for the limitations, the analog of safety factors is introduced to the design process. These factors multiply nominal process. These factors multiply nominal values to achieve the design factors. Outside the scope of these factors is reservoir permeability, the most important parameter for permeability, the most important parameter for reservoir performance and thus for an economics-based fracture design procedure. Because permeability generality is poorly defined for most fracturing applications, some uncertainty distribution about its estimated value is expected. For a complete procedure, this uncertainty must be included, perhaps with a Monte Carlo approach coupled with the proposed design factors. However, we assume here that the initial permeability from a pretreatment well test. In addition to introducing the concept of design factors, this paper reviews the design process, identifies the related model process, identifies the related model limitations and their diagnostics for the design/ placement and production-response phases, placement and production-response phases, and quantifies these limitations as required for defining the design factors.
JPT
P. 1147