This paper reviews the procedures for interpreting, modeling, and predicting fracturing pressure. This review shows that excessive pressure resulting from fluid flow in the fracture can cause such problems as excessive height growth and screenouts, which reduce the potential fracture penetration. As a result, an important design consideration is to limit the pressure by controlling the fluid viscosity.


In 1978, Amoco Production Co. initiated a coordinated program of field data collection1 and analysis to improve the understanding of the mechanics of the hydraulic fracturing process. Much of this understanding had not changed since the early 1960's and was being severely tested by larger and more expensive treatments. In 1979, a series of papers presented results from this program dealing with fracture-height determination,2 fracture confinement by in-situ stresses,3 application of fracture azimuth measurements,4 and the interpretation of fracturing pressure during5 and after6 a treatment. In 1981, another group of papers was presented related to massive hydraulic fracturing (MHF) in the east Texas Cotton Valley7 and the Mesaverde of southwestern Wyoming,8 and the design of precise-length treatments for a pilot flood in the Salt Creekfield of Wyoming.9 Most of these papers were based on the use of the pressure response during and after fracturing to interpret the fracturing process and to change the design of subsequent treatments or a treatment in progress.9

The potential importance of pressure in the understanding and improving of the fracturing process was realized in 1958.10 Analysis of the fracturing pressure response is analogous to pressure-transient analysis in reservoir engineering. In both cases, the pressure response resulting from fluid flow in rock can be interpreted with the same basic principles to provide insights into a complicated physical process and ultimately a basis for rational decisions. These basic principles are continuity of flow, flow resistance (fracture width squared is equivalent to permeability in porous media), and system compressibility. Another important parallel is that although the principles remain the same for all applications, each successtul application for a new area starts with the collection of new data and the participation of experienced personnel. While pressure analysis of reservoirs is a maturing discipline, however, the application to fracturing is still in its infancy.

The purpose of this paper is to outline the basis for fracturing-pressure analysis and interpretation. Field examples and special considerations for the successful application of this technology are given in a companion paper.11

Fracturing-Pressure Analysis

This section provides a review of fracturing pressures during and after a treatment and the basis of a computer program used for the analysis and design of fracture treatments.

The interpretations and expressions presented are based on the analysis of pressure during fracturing, as given by Nolte and Smith,5 and after fracturing, as given by Nolte,6 and apply only for fractures in the vertical plane with horizontal extension exceeding vertical height and no slip on horizontal bedding planes. For these assumptions, the fracture model of Perkins and Kern12 is most applicable. This model requires the pressure needed to extend a fracture of constant height under constant injection to increase with time. This is in contrast to another model13–15 that is consistent with the assumption that the fractured zone slips relative to the adjacent zones and results in a constant vertical width and a decreasing pressure to extend constant-height fracture. This second model is also applicable in the absence of slip for vertical fractures with horizontal extensions less than the vertical height.14,16

The Perkins and Kern model is used in this paper because it is consistent with my review of the generally increasing pressure response of more than 60 treatments in about 20 different formations at depths greater than 4,000 ft [1200 m] and with the field measurements of pressure and width by Smith et al.17 and Warpinski.18 The applicability of this model (i.e., no slip) for these cases was clarified by the work of Teufel.19 His experimental study indicated that a fracture can propagate across a rock interface without slip because of function. This condition occurs if the pressure between the rocks exceeds a value approximately equal to the tensile strength of the rock. In terms of a vertical fracture, this implies that slip will not occur at the fracture's top or bottom, even for perfectly flat nonbounded beds, if the effective vertical pressure (overburden minus pore) exceeds the tensile strength of the rock. Therefore, for normal gradients, slip would not be expected to occur in competent rock (e.g., 1,000-psi [7-MPa] tensile strength) for depths below about 1,750 ft [550 m], or more generally. if the overburden pressure exceeds the pore pressure by more than the tensile strength (e.g., 1,000 psi [7 MPa]). Conversely, for shallower depths, slip may occur and result in a decreasing pressure to extend a fracture.

Fig. 1 shows an example that highlights the aspects of the pressure analyses for the bottomhole pressure (BHP) during and after a fracture treatment of a tight-gas sand. The analogy to transient pressures in reservoirs can be seen with increasing pressure during injection and the pressure falloff or decline after shut-in. Fig. 1 also shows that during the first half of the treatment, the pressure increased, while during the last half of the treatment, the pressure remained essentially constant. The increasing pressure indicates5 extension at essentially constant height, while the constant-pressure period indicates increasing fracture height. During the treatment, the rock confined fluid at a pressure up to 1,400 psi [10 MPa] above the in-situ rock stress of the formation. During the initial portion of the decline (clock time of 41 to 44 hours), the fracture closes because of fluid loss to the formation, with the rate of loss proportional to the rate of pressure decline.6 The increased rate of pressure decline at 44 hours was caused by the increasing stiffness of the fracture closing on the proppant at the wellbore. This time is significant for two reasons: the propped width can be inferred from the net pressure divided by the stiffness defined in Eq. 1, and the well can be backflowed with minimum proppant production. Beyond 44 hours, the fracture is essentially closed on the proppant, and the pressure decline reflects the reservoir pressure decline resulting from fluid loss during the treatment. At 56 hours, the pressure has essentially decayed back to the initial pressure of the reservoir. This example indicates the information that can be obtained by recording the fracturing and decline pressures.

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