Rheology of Hydraulic Fracturing Fluids: Wall Slip During Viscosity Measurement
Authors: Pilehvari Ali , Clark P.E. 
Published: December 2007

Summary
Two slot-flow rheometers, one with a rough and one with a smooth surface, have been constructed to study slip flow in hydraulic fracturing fluids. Each slot has been equipped with a set of flush-mount pressure transducers to measure pressure drop and a thin-film anemometer probe to measure pressure drop and a thin-film anemometer probe to measure heat transfer at the wall. Experiments with crosslinked gels show that rough surfaces inhibit wall slippage while smooth surfaces promote it. Both batch and continuous crosslinked gels show significantly different shear stress measured with the two rheometers for the same shear rates, a clear indication of wall slip. For batch crosslinked gels, this is confirmed with the results of hot-film anemometry.

Introduction
The determination of crosslinked fluid rheology is an important aspect in fracturing fluid development, proppant transport prediction, and treatment design. A concentric cylinder device traditionally has been used to measure the fluid flow properties of fracturing fluids. The suitability of this type of device for rheological characterization of fluids is questionable when fluids that have an inherent structure are examined. Structure in a fluid may be induced by crosslinking, adding suspended solids, or, in some cases, shearing the fluid. One of the primary problems associated with the rheological measurement of problems associated with the rheological measurement of crosslinked gels is a general lack of reproducibility in the measurements caused primarily by slip at the wall of the measuring device, which is the result of structure in the fluid. The no-slip condition (zero fluid velocity at the wall) is a basic tenet of fluid mechanics; all the commonly used data analysis techniques are based on the concept of zero fluid velocity at the wall.
The momentum and continuity equations and a suitable constitutive relation are necessary, but not sufficient, to solve isothermal flow problems. In addition, suitable boundary conditions must be prescribed. No-slip is frequently the most physically realistic and mathematically simple boundary condition. The assumption that there is no relative velocity between a fluid and a solid boundary in contact with the fluid is one of the cornerstones of classic continuum fluid mechanics. Wall slip, however, has been observed in elastomers, suspensions (cement and drilling muds), non-Newtonian fluids, and polymer solutions.
Most of the effort expended in the study of crosslinked gel systems has been directed toward finding reproducible techniques for measuring the rheological properties of these systems. Clark and Cloud and Clark have discussed some of the problems. Conway et al. have shown that these systems are shear-history dependent, a result confirmed by the Gardner and Eikerts recirculating loop study. Little study, however, has been done on the nature of the flow near boundaries. Crosslinked gels have been suspected of having wall slip under certain conditions. To our knowledge, no direct attempt has been made to evaluate the validity of the no-slip condition for these fluids. No wall-slip boundary condition has been assumed in all the experimental work on crosslinked gels. If some indication of slippage did appear in other works, the effect was attributed to other factors to explain the anomaly. In a recent work, crosslinked gels showed much less shear stress in a 1/8-in. [0.33-cm] -nominal-diameter (0.06-in. [0.152-cm] -ID) tube than in a 1/4-in. [0.64-cm] -nominal-diameter (0.18-in. [0.457-cm] -ID) tube for moderate shear rates, a finding easily explained by wall slip. In their study with crosslinked fluids, Buechley and Lord observed higher pressure drop in lower flow rates in their closed-loop apparatus and confirmed their observation with field application. Such findings have made these fluids suspects of wall slippage.
Almost any device that can measure rheological properties of fluids can be used to detect slippage. One method is to obtain flow curves with different tube sizes and to show that smaller sizes of tubes give lower shear stress for the same shear rate. Inclined-plane studies have also been used for detecting the effects of wall slip because it causes the laminar gravitational flow along inclined-plane surfaces to increase significantly. Another more recent approach is based on a comparison of measurements in two devices with the same overall dimensions but with a variation of surface roughness. If these differences affect the wall slip, flow response in each apparatus will differ. Although this approach has been used successfully with crosslinked polymer solutions. However, there is still no single convincing explanation for the molecular-level details of slip phenomena in the vicinity of a solid wall.
For suspensions and polymer solutions, it has been suggested that a very thin layer of much less viscous fluid separates the bulk fluid from the solid wall. This less viscous layer could be formed by particle migration from the vicinity of the wall or by degradation of the fluid under
JPT
P. 1840