Rheological Modeling and Scale-Up of a Delayed-Crosslinked Gel in Nonhomogeneous Flow

Abstract

Summary Previous work has shown that delayed-crosslinked fracturing fluids can flow as nonhomogeneous fluids in Couette and tubular geometries and therefore may exhibit nonhomogeneous flow in fractures. In this case, laboratory-measured power-law parameters no longer can be used for design without proper scale-up. Methods were evaluated for scaling data among Couette, tubular, and fracture (slot) geometries with a nonhomogeneous slip-flow model that avoids the limitations of a zero-thickness slip layer. The best scaling method uses a variable wall-fluid thickness that scales the apparent consistency index on the basis of equal wall-fluid volume per surface area at the same apparent shear rate. Data for an organometallic gel crosslinked at 400 seconds-1 and 70 seconds-1 were scaled successfully between Couette and tubular geometries. Wall-fluid thicknesses of the gel crosslinked at 400 seconds-1 were about 0.015 cm and more shear-rate dependent than those for the gel crosslinked at 70 seconds-1, which were about 0.003 cm thick and nearly constant. Introduction Previous flow-visualization studies have shown that organometallic crosslinked hydroxypropyl guar (HPG) gels can flow at low stresses in apparent slip flow with a gelled (solid) central region. This would be a nonhomogeneous flow if one assumes that the nonslip boundary condition applies. The nonhomogeneous flow in this case would comprise a gelled solid region and a wall fluid. At moderate stresses, however, the bulk gel breaks up with a corresponding pronounced buildup in apparent viscosity as the flow transforms to a dispersed, although usually still nonhomogeneous, flow. Other studies have indicated similar slip flow with a viscosity transformation for crosslinked water gels and suspensions of cellulose powder in glycerol. Apparent slip flow is modeled conventionally with slip velocities (often functions of shear stress), assuming a zero-thickness slip layer. These models neglect the presence of a wall fluid and therefore are homogeneous flow models. They sometimes yield erroneous slip velocities (e.g., greater than the average bulk flow). It can be shown, however, that very small slip layers can dramatically affect apparent viscosity. A general theory for nonhomogeneous flow composed of theologically distinct regions has been developed for Couette, tubular, and slot flows that extends modeling capabilities from two-layer models based on Newtonian wall fluids. Recent studies have indicated close correspondence of apparent viscosities for an organometallic crosslinked HPG gel when flowing in tubing with those of the same gel when in apparent slip flow in a Couette viscometer. This indicates that slip flow may be occurring in tubular flow, where it may persist to higher apparent shear rates. Hydrodynamic analysis predicts the stability of this type of tubular slip flow. 10 In this work, a procedure is developed for scaling nonhomogeneous slip-flow data that is based on testing of a delayed organometallic crosslinked gel crosslinked in tubular flow and retested in Couette flow.