The Mechanics of Design and Interpretation of Hydraulic Fracture Treatments

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Abstract
Introduction Since formal introduction of hydraulic fracturing to the petroleum industry in 1948, the technique has increased in prominence each year until in many areas it is now the most popular method of well stimulation. In some areas it is the only technique which will effect commercial production; even some limestone formations which refuse to respond to multiple-stage acid treatments will, subsequent to hydraulic fracture treatments, make commercial wells. Many theories have been expounded to define conditions associated with hydraulic fracturing - some based on unrealistic prototypes and others on mathematical analyses substantiated as far as practical with laboratory experimentation. However, progress made has been mainly not the result of any mathematical or physical definition of the process, but industry's willingness to spend more for larger and higher rate treatments. Service companies have met the demands of the industry for treatments of greater magnitude until in some areas, treatments of from 100,000 to 200,000 gal injected at rates approaching 100 bbl/min are not only common but are performed with minimum difficulty. The cost of such treatments is of necessity great, and it is imperative that the manpower, equipment and materials be as effectively utilized as is technically possible. The purpose of this paper is not to clarify the turbid waters of fracturing theory, but to present the tools which we had used to make the technique more effective. Some equating will be necessary; however, development and discussion of theories will be largely confined to that necessary to justify the method of analysis. Basic Assumptions The following assumptions have been allowed as a basic definition of conditions:The pressure required to maintain fracture parting can be determined with fair reliability from either theoretical or empirical methods.The pressure required to maintain fracture parting is independent of fluid injection rate.For any one plane of parting, the functional variation in surface injection pressure with injection rate is the result of increased or decreased friction drop in conductor pipe and perforations.Functional variation in bottom-hole casing injection pressure with rate is the result of friction drop through perforations and is generally assumed, depending on number of perforations open, to be negligible for most wells below 3,000 ft in which ball sealers are not employed.

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