This paper provides a number of comprehensive algebraic formulae, with readily determinable coefficients, which can be used to predict the extent and width of fractures produced by fluid injection at specified rates or borehole pressures, when these are reasonably well-behaved functions of time. The fracture geometries described include as special cases the models currently in use for industrial design of hydraulic fractures, but extensions to allow variable fracture height are readily achieved. The formulae serve both to simplify the implementation of conventional models and to allow development of more realistic simulations which contain the rather idealised concepts of those models in their rightful place as components of a more general three-dimensional description. One such pseudo-3-D model is described in its simplest form; it allows physically credible tracing of length, height and width distributions under conditions of slow vertical spreading which a desirable stimulation treatment would achieve. All of the models admit quite general reservoir properties and frac-fluid behavior. A few popular applications are used to illustrate their power and simplicity.

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