This paper describes approximate models which yield credible descriptions of hydraulic fracturing processes and are amenable to calculations on microcomputers. These models provide the basis for both analysis of conventional fracturing treatments and for proposing/designing new procedures suitable to varied reservoir conditions. Satisfying a shortterm need for realistic analysis that offer improved fracture designs, the models also admit considerable upgrading as more detail/realism is described by more complex simulators. The two levels of analysis presented are:

  1. Lumped models, in which the spatial variation is represented by integral coefficients. Although simple enough for use on a microcomputer or programmable calculator, the models are detailed enough to describe geometries varying from long Perkins & Kern-type, through circular shapes, to high CGD (Christianovich et al.)-type fractures.

  2. More complex pseudo-three-dimensional (P3DH) models (which require at least a small microcomputer for proper implementation); these divide the 3D problem into coupled sets of equations governing one-dimensional lateral fluid flow and two-dimensional growth of vertical cross sections. A major feature is a refined mesh that moves with the fracture, rather than one fixed to the reservoir; the result is detailed tracing of evolving geometry, pressure distribution and flow throughout the job and after shut-in.

Although not as complex as our full 3D simulations under development, these approximate models contain most important elements governing fracture evolution. They compute such significant design evaluation quantities as length, height, width and pressure variation with specified injection rate (or vica versa). To date, the models have produced many significant results that aid in explaining observed pressure profiles and may, in the future, be used at the wellhead for real-time control of fracturing operations.

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