New Empirical Correlation To Predict Apparent Viscosity of Borate-Crosslinked Guar Gel in Fractures

Abstract

Summary Successful design and completion of hydraulic fracturing treatments depend on accurate estimation of fracturing fluid viscosity. This requires better knowledge of the fluid viscosity under in situ conditions. The viscosity estimation is even more important for borate-crosslinked guar gel because the gel behavior depends on temperature, wellbore shear pre-conditioning, fracture shear rate, and fluid pH. These factors require that the fluid characterization be performed under representative field conditions. Borate-crosslinked gel rheology is currently characterized in the laboratory and there is no theoretical correlation available to describe the gel rheology as a function of its dependent properties. The present study describes a correlation that is developed from data gathered by utilizing a field-scale fracture simulator and is based on the method of reduced variables. The study also extends the method to include the effect of shear history on the rheology of guar crosslinked with borate ions. The correlation relates the apparent viscosity of the crosslinked guar to the fluid temperature, shear history, and shear rate. It is presented in a simple equation, which can be incorporated into fracturing software. The present study also provides master curves of the reduced apparent viscosity-shear rate for the borate-crosslinked guar at three pH values. Introduction Estimation of fluid viscosity is crucial for the success of a hydraulic fracturing treatment. A successful treatment means a wide fracture and proper distribution of proppant in complete length of the fracture; it can be realized with a high-viscosity fracturing fluid. This fact is supported by several case histories which have shown that the viscous fluid system improves the treatment results.1 Prior to a treatment, knowledge of the viscosity is important for proper fracture design. Moreover, the information on the viscosity is necessary for estimation of friction pressure losses down tubular and for prediction of proppant transport in the fracture. Also, reliable predictive viscosity correlations can be integrated into hydraulic fracturing computer simulators. Furthermore, the usefulness of correlations is considerably increased when it is developed from the results of experiments performed using a field-scale fracture simulator. The Fracturing Fluid Characterization Facility (FFCF) has been established to study fluid behavior under representative surface and downhole conditions. The facility characterizes the fluid using field-scale mixing and pumping equipment. The fluid viscosity is measured in a parallel-plate-type device, which has provisions to dynamically vary the fracture gap width. Prior to the viscosity measurements, the fluid is subjected to shear pre-conditioning through various lengths of coiled tubing. This pre-conditioning provides a shear history simulation for the fluid and brings the viscosity measurements under conditions that are closer to the fluid flow in an actual downhole situation. The Importance of Shear History. Shear pre-conditioning of a fluid is important in hydraulic fracturing. This importance arises from the highly sensitive characteristics of crosslinked-based fracturing fluids. Several researchers have shown the effect of pre-shearing on the viscosity of guar crosslinked with different crosslinkers like titanium, zirconium, and borate.2–5 The shear history effects are also well known for other fluid systems;6–10 these effects, however, are not included into the viscosity models used to describe the various systems. The present work is part of a study conducted to include the effect of shear history on the rheological properties of fracturing fluids. The results from experiments performed on the rheology of borate-crosslinked guar-based fracturing fluids were presented earlier.5 In the present paper, these results are utilized to develop an empirical relationship between the fluid viscosity and its controlling parameters. The empirical relationship is based on the method of reduced variables.11 This method is widely used to correlate the rheology of a polymer at different temperatures,12,13 and is also known as the time-temperature superposition.14 The method of reduced variables has been used earlier by other researchers to relate the viscoelastic properties of guar and hydroxypropyl guar (HPG) crosslinked with borate ions.15,16 These studies, however, did not consider the effect of shear history in their measurements. In the present work, the effect of shear history is included in the method of reduced variables and a correlation is developed to relate the nominal shear rate with the borate-crosslinked guar viscosity measured at different temperatures and shear histories. The present study also provides viscosity-shear rate master curves at different fluid pH values. Experimental Procedure A schematic of the experimental setup is shown in Fig. 1. A brief description of the setup is given below; a detailed description of the instruments used in the setup is presented elsewhere.17 A batch of 100 bbl of 35 lbm/Mgal guar polymer solution was prepared in mixing and storage tanks. Upon hydration, the fluid pH was adjusted to a desired level. The adjustment in pH was necessary to initiate a reaction between the borax crosslinker and the polymer. The guar solution was fed to a triplex pump by a centrifugal pump, which was also used to mix the crosslinking agent into the base polymer. The fluid was then pumped through different lengths of coiled tubing. These lengths were varied from 0 to 5,000 ft. The tubings have an internal diameter of 1.188 in. A constant flow rate of 60 gal/min was maintained through the coiled tubing and the pressure drop was measured. A single flow rate was used to maintain uniform shearing prior to characterizing the fluid in the slot flow apparatus. 18,19 The flow through the coiled tubing helped to simulate pre-conditioning of the fluid, and to introduce the effect of shear history into the rheological properties. For the case where fluid viscosity was measured without shearing in coiled tubing, the measurement was termed as "no pre-shear" characterization.

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