  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? By
employing the modified formulation of the PKN problem we obtain its simple
analytical solutions in the cases of perfectly plastic and Newtonian fluids.
Since the results for shear thinning fluids are intermediate between those for
these cases, the obtained equation for the fracture length suggests a criterion
of the equivalence of various shear thinning fluids for the problem of
hydraulic fractures. We assume fluids equivalent in their hydrofracturing
action, when at a reference time they produce fractures of the same length. The
equation for the fracture length translates the equivalence in terms of the
hydraulic fracture length and treatment time into the equivalence in terms of
the properties of a fracturing fluid (behavior and consistency indices).
Analysis shows that the influence of the consistency and behavior indices on
the fracture length, particle velocity and propagation speed is quite similar
when considering the PKN and KGD models despite the models refer to different
plain-strain states. It appears that from the mechanical point of view, the
differences between thinning fluids are not significant; they may be taken into
account when wishing to have some quantity to be greater (less) at small
(large) time. We conclude that a choice of a fracturing fluid is to be made
mostly from technological and/or economic considerations under the condition
that the compared fluids are equivalent in their mechanical effect according to
the suggested criterion.
