Horizontal Fracture Design Based on Propped Fracture Area
Authors: Wahl Harry A. 
Published: December 2007

Abstract
Present fracture design procedures are based on the total fracture area created. A method to distinguish between total area and the propped or effective fracture area has not been available. This paper presents a solution to this problem, applicable to horizontal fractures. The differences between effective fracture area and total area are demonstrated in example calculations. This work is based on experimentally determined transport efficiencies of solids in sand-liquid slurries. Newtonian and non-Newtonian systems are considered.
Introduction
Fifteen years after commercial introduction, hydraulic fracturing remains the most successful stimulation technique in the oil field. This success is primarily due to ability of induced fractures to penetrate and alter permeabilities deep within formations. Many fields producing today could not have been developed without the hydraulic fracturing process. Because of wide usage, fracture-treatment design has received a great deal of engineering and research effort. This work, resulting in improved equipment and materials, has increased the benefits from fracture treatments as well as the applicability of the process. A major contribution was the development of fluid-loss additives. Necessarily, the number of parameters to be considered in treatment design has steadily increased, resulting in more complicated design techniques. Almost all present design procedures are based on the precepts set forth by Howard and Fast. Relating the fluid volume lost into the formation, the volume required in extending the fracture, and the total slurry volume injected. They developed an expression for the total fracture area created in terms of pertinent treatment parameters. Fluid loss during treatment was expressed as a function of time for three flow mechanisms. Although modifications of fluid loss equations have been made, the total fracture area concept has remained unaltered. A vast amount of field data indicate that induced fractures must be propped and held open to be effective. A notable exception is the Mesa Verde formation in the San Juan basin. However, analysis of these treatments shows that improved well productivities are obtained when propping agents are incorporated in the treating fluid. Although propped fracture area has been recognized as an important design parameter, a method to distinguish between total area and effective fracture area has not been available. The necessary information on slurry-sand transport in fractures has been lacking. Interest in the propped region of induced fractures is not restricted to areal extent alone. The distribution of sand within fractures is important from the standpoint of fracture flow capacities. Flow capacity affects the increase in well productivity after stimulation. The work of Huitt and Darin shows that partial monolayers of sand have large flow capacities compared to thick, dense sand packs. It has been postulated that gelled fluids have the ability to transport sand within the fractures at the desired low concentrations. An early contribution in the area of sand placement in fractures was made by Kern et al. They studied sand movement in a transparent vertical fracture model. It was observed that the sand tended to settle out in the bottom of the model before moving very far. When the fluid velocity exceeded a certain critical value, all of the sand injected began moving through the crack even though it settled to the bottom. This critical velocity was determined under several flow conditions. Some work on sand movement in horizontal fractures has been reported in Russian publications. Sand movement was studied by Izyumova and Shan'gin using a transparent "pie-shaped" flow model to simulate a horizontal radial flow system. However, the data were limited, especially in a quantitative sense. Dorozhkin, Zheltov and Zheltov studied the behavior of sand-liquid slurries in a horizontal linear flow model. The quantitative data were restricted primarily to the thickness of sand deposits formed at the bottom of the fracture. An earlier paper provided basic data on the flow of sand in horizontal fractures. This study was designed to yield specific quantitative information on rate of advance of sand particles and pressure behavior under various flow conditions. A comprehensive photographic study was undertaken in a 10-ft windowed flow cell to provide the necessary qualitative and quantitative data. Since the number of potential variables far exceeded the capacity of the initial study, emphasis was placed on the effects of sand concentration, oil viscosity and oil flow rate. A detailed description of these experiments and the results are described in Ref. 9. However, the implications of this work on the fracture design calculations were not discussed. An analysis of these data as well as new data is provided in the following sections.
EXPERIMENTAL RESULTS
The primary objective of the experimental investigation was to provide information on the rate of advance of the solids in sand-liquid slurries.
JPT
P. 723ˆ