The prediction of friction pressures for proppant-laden fracturing fluids requires estimations of both the base-gel friction factor and the effect of proppant on fluid rheology. This paper introduces two new expressions, each theoretically based with constants determined from data, that address these two issues for hydroxypropyl guar (HPG)-based fracturing fluids in laminar and turbulent flow.
The paper first introduces a new expression for the turbulent friction factor of HPG base gels. This implicit expression for the friction factor is more theoretically correct and requires one less empirical constant than explicit forms currently used. The effect of proppant on the effective viscosity of non-Newtonian fluids is then discussed and a new expression, which includes shear rate, temperature, gel concentration, and proppant volume fraction as parameters, is derived. Developed from laboratory data and existing slurry rheology theories, this expression is shown to provide excellent predictions of laboratory and field data for both tubing and annulus injection.