Fracture-Width Estimation for an Arbitrary Pressure Distribution in Porous Media

Abstract

Accurate estimation of fracture width is necessary for successful hydraulic fracturing or FracPac treatments. This information becomes even more critical when most of the fluid leakoff is forced through the proppant pack and out through the tip of the fracture during hydraulic fracturing or FracPac treatments. With the development of new, low-leakoff fluid systems, the coupling of fluid flow through porous media and subsequent pressure responses must be incorporated in predicting fracture-width profile. The generalized width equations, although well-known, are seldom solved for cases other than constant pressure throughout the fracture or for simple pressure distributions. This paper demonstrates how these complex fracture-width equations can be solved for an arbitrary pressure distribution in a simplified approach. The generalized width equations for fracturing calculate a fracture’s width along its length or radius, w(x) or w(r), given a pressure profile, p(x) or p(r). Two main width techniques are discussed, one based on a modified Perkins-Krech approach and the other on a corrected Valko-Economides approach. A comparison to the Jaeger-Cook deflection equation is made. In the Perkins-Krech and the Jaeger-Cook cases, the method of superposition is used. In the Valko-Economides case, the pressure is fit with a polynomial equation, and the integration is carried out term by term. The results are comparable with a finite element analysis (FEA) model, and good agreement has been observed. Examples are presented on how these techniques can be set up in spreadsheets, allowing the engineer to investigate concepts like "dry tip" and stresses around a fracture perimeter.

Quantitative Investigation of Fracture Apertures during Temporary Plugging and Diverting Fracturing

“…Todd et al estimated the fracture aperture for arbitrary pressure distribution in porous media. They pointed out that the fluid leak-off, the fluid flow in porous media, and the pressure response should be considered [10]. Guo et al investigated the aperture of two fractures symmetrically located at the edge of a wellbore subjected to a uniform wellbore pressure.…”

Effects of Thermally-Induced Secondary Cracks on Hydraulic Fracture Geometry

“…The design process of hydraulic fracturing stimulation involves many factors such as fracture geometry, material properties, frac fluid type as well as the initial effective stress in the formation. In hydraulic fracturing stimulation, the fracture aperture is considered an important factor; therefore, fracture aperture should be estimated as accurately as possible (Todd et al, 2011). The analytical solutions of fracture width were been developed by many authors for stationary as well as propagating fractures (Sneddon and Lowengrub, 1961;Perkins and Kern, 1961;Geertsma and de Klerk, 1969).…”