A New Method for Predicting Friction Pressures and Rheology of Proppant-Laden Fracturing Fluids

Abstract

Summary The prediction of friction pressures for proppant-laden fracturing fluidsrequires estimations of both the base-gel friction factor and the effect ofproppant on fluid rheology. This paper introduces two new expressions, eachtheoretically based with constants determined from data, that address these twoissues for hydroxypropyl guar (HPG)-based fracturing fluids in laminar andturbulent flow. The paper first introduces a new expression for the turbulent frictionfactor of HPG base gels. This implicit expression for the friction factor ismore theoretically correct and requires one less empirical constant thanexplicit forms currently used. The effect of proppant on the effectiveviscosity of non-Newtonian fluids is then discussed and a new expression, whichincludes shear rate, temperature, gel concentration, and proppant volumefraction as parameters, is derived. Developed from laboratory data and existingslurry rheology theories, this expression is shown to provide excellentpredictions of laboratory and field data for both tubing and annulusinjection. Introduction Real-time diagnosis and redesign of hydraulic fracture operations requireaccurate knowledge of the bottomhole treating pressure. Because real-timebottomhole gauges are not routinely used during fracturing, the bottomholepressure (BHP) is estimated from known wellbore information and parameterspressure (BHP) is estimated from known wellbore information and parametersmeasured at the surface. For incompressible fluids, the difference between thesurface pressure and the BHP results from the hydrostatic head and thefrictional losses in the tubular goods. While the hydrostatic head can easilybe calculated accurately, estimation of friction losses for fracturing-fluidslurries is considerably more complex. This complexity is a result of the nature of the fluid systems and theconditions under which the fluids are pumped. Water-based fracturing fluids aregenerally a two-phase slurry consisting of a base gel and proppant. They oftenare pumped in turbulent flow in tubing and proppant. They often are pumped inturbulent flow in tubing and casing/tubing annuli. The base gels, such as the HPG systems considered here, are highly non-Newtonian viscoelastic fluids thatdisplay drag reduction when pumped in turbulent flow. The addition of proppantto these base gels increases the non-Newtonian character of the fluid system. Predicting the friction pressures for these complicated slurry systems is Predicting the friction pressures for these complicated slurry systems ishindered by the lack of general theories for either part of the problem. Unlikepredictions of the friction pressure for Newtonian or power-law fluids inturbulent flow, there is no general theory for predictions of turbulentfriction pressures for viscoelastic fluids. Likewise, several expressions areavailable for predicting friction pressures for slurries composed of Newtonianfluids and proppant particles, but no general theories describe how particlesaffect the friction pressure of highly non-Newtonian fluids. This paper presents two new correlations for predicting friction pressuresfor proppant-laden linear and delayed crosslinked HPG pressures forproppant-laden linear and delayed crosslinked HPG fracturing-fluid systems. Equally valid in tubing and annulus injection, as well as in the fracture, these correlations can be used in real-time wellsite computers and inoffice-based fracture design programs. The first correlation calculates thefriction pressure for the base gel in laminar and turbulent flow. Thisexpression, developed from field-sized yard tests with Prandtl's law offriction for turbulent Newtonian flow, avoids problems of diameter scale-up andexplicit equation approximations present problems of diameter scale-up andexplicit equation approximations present in other prediction methods. Thesecond correlation predicts the increased friction loss caused by proppant. This expression is an extension of an existing slurry viscosity relation, modified with laboratory data to include shear rate and non-Newtonian effectsexplicitly. This laboratory-based equation provides reasonable predictions ofpublished field data for flow in tubing and annuli. Theory Review Despite the absence of sufficient theoretical understanding of theseproblems, numerous predictive schemes are available to estimate problems, numerous predictive schemes are available to estimate fracturing-fluid frictionpressures by empirical or semianalytical methods. For example, the most commonsource of base-gel friction pressures is the empirical friction curves suppliedby service companies. In addition, a number of authors have dealt directly withsome or all portions of this problem, as summarized below. problem, assummarized below. For all types of fluids and flows, from laminar Newtonian tomultiphase highly non-Newtonian, the prediction of friction pressure in pipesrequires estimation of the nondimensional friction factor.