Flow of truncated power-law fluid between parallel walls for hydraulic fracturing applications

An essential closure of hydraulic fracturing models is the solution of the momentum equation for flow between plane parallel walls. Newtonian or simple power-law rheology is usually assumed. In real treatments, fracturing fluid often has more complicated rheology, such as Carreau. An earlier introduced modification to the power-law model enables a fair approximation to Carreau rheology. Unlike Carreau, it also enables a closed-form solution for the flow rate between plane parallel walls. The computational cost is, however, considerably smaller than with Carreau. Closed-form solution for the flow rate versus pressure gradient is obtained which is useful in hydraulic fracturing simulations. Compared to simple power-law model, the truncated power-law model improves accuracy of flow computations in small-aperture and large-aperture parts of the fracture, thereby improving the overall accuracy of hydraulic fracturing simulation.