On comparison of thinning fluids used for hydraulic fracturing

The paper aims to answer the question: if and how non-Newtonian fluids may be compared in their mechanical action when used for hydraulic fracturing? We give an answer for thinning fluids by (i) suggesting an appropriate definition of fluid equivalence, and (ii) employing this definition in the analysis of the solution for a fracturing fluid with the power rheological law. The definition accepted in the paper is: two fluids are equivalent in their hydrofracturing action if they produce fractures of the same length at a given reference (treatment) time under the same pumping rate. The solution in self-similar variables, serving for the comparison, is actually independent on fluid behavior index. It implies that for thinning fluids, equivalent in the sense of the definition accepted, the differences in the evolution of main quantities (fracture length, speed, opening, net pressure) are insignificant within the range of time from 10 s to 27 h. It is shown that, at most, the differences may serve to have some quantity greater (less) at time notably less or greater than the reference time. Neglecting the differences, we obtain the equation, which translates the equivalence of thinning fluids in terms of their fracturing action into the equivalence in terms of their rheology. The equation defines the reference strain rate and, consequently, the apparent viscosity, which is the basic value used for fracture design. We conclude that when compared fluids are equivalent in accordance with the equation obtained, the further choice between them is to be made primarily from economic, technological, safety and environmental considerations.