Proppant Settling Correlations for Non-Newtonian Fluids Under Static and Dynamic Conditions

This paper presents a new approach for analysis of proppant sealing data in non-Newtonian pseudoplastic fracturing fluids and develops drag coefficient correlations as a function of fluid model parameter n', Results of experiments with these fluids under static as well as dynamic conditions are discussed. A wide range of n' and particle Reynolds number is investigated. It is shown that at low-particle Reynolds numbers the fluid model parameter n' has a significant effect on proppant settling velocity. This effect diminishes at higher particle Reynolds numbers. The dynamic settling velocity data agree reasonably well with the correlations developed from static velocity data. Further, experimental results of earlier investigations agree well with the correlations of this study. Introduction Many examples of flow around submerged objects appear in engineering work. In the oilfield industry, one example is particle or proppant transport in a fracture during hydraulic fracturing. Hydraulic fracturing has been in use commercially for 30 years. The formations are fractured hydraulically by pumping a slurry of viscous fracturing fluid and proppant at high pressures. The purpose of the proppant is to hold the fracture open at the end of the treatment. The production increase resulting from the treatment depends on fracture conductivity and final proppant distribution. Knowledge of settling velocity of a single particle in the fracture and streamlines around the particle is of great value in understanding the complex transport process leading to a particular proppant distribution in the fracture. A thorough understanding of proppant transpose would help design better fracturing treatments. The purpose of this investigation is two fold:to gather experimental data of proppant settling velocity in several non-Newtonian fracturing fluids, andto develop correlations between drag coefficient and particle Reynolds number. These correlations later can be used to predict the settling velocity of a particular particle in a non-Newtonian fracturing fluid of known rheological properties. Experience has shown that most fracturing fluids exhibit highly non-Newtonian fluid characteristics. They may possess completely different properties under shear than when at rest. For simplicity, most of the studies reported in the literature are undertaken by dropping proppant in a stagnant fluid. In the actual fracturing process, however, the proppant is settling while fluid is moving in the fracture. Thus, to validate the correlations derived from the settling velocity data in a stagnant fluid, some dynamic experiments also are conducted. Literature Review The subject of particle motion in Newtonian fluids has been studied extensively by many investigators. In contrast, very little has been accomplished in the case of particle motion in non-Newtonian fluids, particularly on proppant transport in the fracture. Most recently, a preliminary work on dynamic proppant transport in fracturing gels has been reported by Hannah and Harrington. Experiments were conducted with a concentric cylinder tester to measure the fall rate of proppant in non-Newtonian fracturing gels. The test device used was similar to one reported previously by Novotny. Their experimental data did not agree with the theoretical predictions, and no explanation has been given for the discrepancy. Later, using a similar tester, Harrington et al. measured the settling rate of proppant in cross-linked fracturing gels. SPEJ P. 164^