Stimulation Fluid Rheology - A New Approach
Authors: Clark P.E. 
Published: December 2007

Clark, P.E., Dowell Division of Dow Chemical U.S.A.

Abstract
This paper describes a new approach to the rheological characteristics of fracturing fluids. The new approach uses an oscillating or dynamic shear rate rather than a steady shear rate which allows the determination of the rheology of highly viscous, cross-linked gels accurately with a variation between measurements of less than 5 percent. An accurate and reproducible method of determining fluid properties is necessary for both fracturing treatment design in the field and fluid development and optimization in the laboratory. The coaxial cylinder and capillary-type viscometers in general use throughout the industry are adequate for uncross-linked fluids but are less than adequate for cross-linked, high viscosity fluids.
Fracturing fluids of all types can be measured using a dynamic viscometer. There is a wealth of information available from dynamic measurements that cannot be derived from steady shear measurements. As an example, both the elastic storage modulus and the viscous-loss modulus can be measured. These parameters are related to the amount of energy stored parameters are related to the amount of energy stored elastically and lost through viscous heating, respectively, both are related to the pumping pressure. The instrument that will be described is also capable of accurately determining yield stresses, normal forces and viscosities of prop laden fluids.
In this paper, the relationship between steady shear and dynamic viscosity data for several common fracturing fluids will be established. Data for cross-linked fluids will be presented as well as data for sand laden fluids.

Introduction
The rheology of well stimulation fluids play a commanding role in the results of hydraulic fracturing treatments. Fracture width, height and length, as well as prop-pack height and penetration, are determined in part by the rheological properties of the treating fluid. The standard method for determining the rheology of fracturing fluids specifies the use of a rotational viscometer with a couette fixture, such as a Fann Model 35, Model 50 or an equivalent instrument. This type of viscometer is well suited for measuring the properties of Newtonian or non-Newtonian fluids that exhibit only weak viscoelastic properties. Non-Newtonian fluids that exhibit strong properties. Non-Newtonian fluids that exhibit strong viscoelastic properties are difficult or impossible to study using a rotational viscometer.
The need for a different measurement technique has been brought about by the advent of cross-linked gels that exhibit strong viscoelastic properties. This paper will describe a technique that can be used to paper will describe a technique that can be used to successfully study the rheology of cross-linked fluids, as well as noncross-linked fluids. Dynamic mechanical testing, which has been used to characterize a wide variety of materials used in other industries, can be used to study fracturing fluids over a wide range of conditions. It will be shown that even fluids containing proppants can be tested.

FUNDAMENTALS
The concept of fluids exhibiting a resistance to flow or viscosity originated with Newton. For simple fluids, the laminar flow behavior can be completely described by viscosity. In this case, the viscosity is given by:
............(1)
This relationship hold for a number of materials including most low molecular weight fluids. Fluids that obey Equation 1 are termed of interest in well stimulation do not exhibit a linear relationship between shear rate and shear stress. Fluids that exhibit a complex relationship between shear rate and shear stress are called non-Newtonian fluids.
The plot in Figure 1 illustrates the various types of non-Newtonian fluids. For the most part pseudoplastic, viscoelastic, Bingham plastic and yield pseudoplastic-type fluids are the most important in well stimulation. Measurements of the fluid properties for most of these fluids are relatively straight forward, although accurately determining the yield point for Bingham or yield type materials is difficult.