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By substituting net pressure values for the fluid mechanics of typical fracture growth calculations, numerical models for calculating fracture growth from these pressures, using any of three popular fracture width equations, have been developed. One model uses expected net pressure behavior, ideally obtained from a similar treatment in an offset well, to predict fracture growth for design calculations. A second model uses collected pressures and injection or flowback rates to pressures and injection or flowback rates to calculate fracture dimensions over time, allowing fracture, behavior to be monitored during a treatment or analyzed afterward.
The governing equations for these models were examined under specific conditions, leading to guidelines for interpretating fracturing pressures under a variety of conditions.
And, by considering fluid mechanics, as well as fracture mechanics and a volume balance, expected pressure behaviors for power-law fluids in all three fractures geometries have been determined.
Normal hydraulic fracturing treatment design calculations combine fracture mechanics, fluid mechanics, and a volume balance to predict fracture growth with time. Fracture mechanics relate fracture width to pressure and fracture length, height, or radius; fluid mechanics relate pressure to injection rate, width, and length or radius and the volume balance relates fracture volume to injection and fluid-loss rates.
As pointed out by Shlypaborsky et al. pressures obtained during fracturing treatments do pressures obtained during fracturing treatments do not always agree with pressures predicted by fracture design models. They listed five factors that had the potential for causing this disagreement:
high perforation friction pressure,
high friction pressure in the pressure,
high friction pressure in the fracture
the generation of multiple parallel fractures
higher actual fracture toughness values than measured in the lab, and
a nonpenetrating region near the fracture tip.
To isolate the cause of the disagreement, they measured overpressure, the difference between downhole instantaneous shut-in pressure and the least principal stress, and thus eliminated the three principal stress, and thus eliminated the three friction-related effects. The overpressure, the result of one or both of the remaining two factors, was then used to determine an apparent fracture toughness.
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