Zero Shear Viscosity Determination of Fracturing Fluids: An Essential Parameter In Proppant Transport Characterizations

Abstract

Abstract This paper details the importance of zero shear viscosity in proppant transport evaluation and presents a methodology to obtain zero shear viscosity of fracturing fluids. Knowledge of zero shear viscosity is a major factor in modeling and predicting proppant transport in hydraulic fractures. The importance of this factor arises from the fact that shear rate in the fracture decreases from its highest value at fracture walls to zero value at the center of the fracture. And since proppants are mostly concentrated at the center of the fracture, it is therefore, essential to know the viscosity of a fluid at that shear rate so that proppant transport capability of a fluid can be realistically evaluated. The developed methodology to measure zero shear viscosity of a fluid involves measurements of viscoelastic parameters such as viscosity and elasticity as a function of oscillatory frequency. A non-linear regression model based on Maxwell's model is then used to calculate fluid's viscosity at various relaxation times and hence zero shear viscosity. Detailed explanations and examples are also presented on the measurements of viscosity, elasticity, and relaxation time as well as the process at which zero shear viscosity is obtained. Introduction Behavior of the fracturing fluids can be characterized by their rheological properties either quantitatively or qualitatively. The qualification is usually based on terms such as viscoelastic, Newtonian, non-Newtonian, thixotropic (a fluid which exhibits a time dependent response to change in shear rate), and dilatant or shear thickening. Quantification of a fluid is based on the measurements of viscosity, elasticity, shear rate, shear strain, shear stress, and relaxation time which all affect proppant transport. From these quantities viscosity and elasticity, loss and storage moduli, are calculated. Before qualitatively and quantitatively characterization of fracturing fluids, one needs to understand the structure of fluid rheology in terms of its molecules behavior. Structure of Rheology. Molecules in a fluid are under isotropic conditions, that is, they are relaxed in their natural form and collectively these molecules form a large isotropic group. That is, each molecule in its relaxed mode, is tangled to another relaxed molecule to produce a mass of tangled molecules which would be in isotropic form, Fig. 1. As fluid starts to flow under a shear flow, molecules of fluid orient to the direction of the imposed shear force and therefore, fluid becomes anisotropic, Fig. 2. The change in the structure of fluid made by this work is of two types:a recoverable energy which is associated with elasticity of the fluid or store energy anddissipated energy which is associated with the viscosity of fluid. Finally, as fluid stops, the anisotropy decays to the original isotropic condition with time. Development or loss of anisotropy within a fluid structure needs time. The relaxation time is a measure of the rate at which fluid structure changes from anisotropy to isotropy.1 A fluids behavior may be characterized by numerous relaxation times depending on the available stored energy at each time it is sheared under flow and stopped. The summation of all viscosities measured at each is the zero shear viscosity of the fluid. Zero Shear Viscosity A central question in the industry today is "what viscosity is required for proppant transport"? A definite answer to this question may be difficult if not impossible. Nevertheless, according to literature2,3,4 and work conducted at Stim Lab over the past 10 years, it is concluded that proppant transport is mainly governed by zero shear viscosity of the fluid.