Rheological classification

Rheological Classification of Drilling Fluids 829. Flow Regimes 830. Principle of Additive Pressures 834. Friction Pressure Loss Calculations 836. Pressure Loss Through Bit Nozzles 839. 

DRILLING MUD HYDRAULICS Rheological Classification of Drilling Fluids... 

The manner in which the shear strain responds to the shear stress (or vice versa) in this situation defines the mechanical or rheological classification of the material. The parameters in any quantitative functional relation between the stress and strain are the rheological properties of the material. It is noted that the shear stress has dimensions of force per unit area (with units of, e.g., Pa, dyn/cm2, lbf/ft2) and that shear strain is dimensionless (it has no units). 

There are numerous ways in which viscosities are expressed in the literature. Some of the most common are defined Table 6.8. There is an entire lexicon of terms used to describe the different rheological classifications of colloidal dispersions [9-11,353,355]. 

This chapter presents a brief review of the rheological classification of fluids and instruments used for viscosity measurements. A discussion of the rheology of suspensions and how it relates to that of emulsions is given. Predictive correlations for emulsion viscosity are discussed in detail. The effect of added solids to an emulsion is fully treated, and its relation to a bimodel system is discussed. 

The manner by which a fluid obeys a given shear-stress-shear-rate relationship determines its class within the rheological classification of a fluid. 

The key point in the rheological classification of substances is the question as to whether the substance has a preferred shape or a natural state or not [19]. If the answer is yes, then this substance is said to be solid-shaped otherwise it is referred to as fluid-shaped [508]. The simplest model of a viscoelastic solid-shaped substance is the Kelvin body [396] or the Voigt body [508], which consists of a Hooke and a Newton body connected in parallel. This model describes deformations with time-lag and elastic aftereffects. A classical model of viscoplastic fluid-shaped substance is the Maxwell body [396], which consists of a Hooke and a Newton body connected in series and describes stress relaxation. 

A convenient way to summarize the flow properties of fluids is by plotting flow curves of shear stress versus shear rate (r versus 7). These curves can be categorized into several rheological classifications. Foams are frequently pseudoplastic that is, as shear rate increases, viscosity decreases. This is also termed shear-thinning. Persistent foams (polyeder-schaum) usually exhibit a yield stress (rY), that is, the shear rate (flow) remains zero until a threshold shear stress is reached, then pseudoplastic or Newtonian flow begins. An example would be a foam for which the stress due to gravity is insufficient to cause the foam to flow, but the application of additional mechanical shear does cause flow (Figure 17). 

Pseudoplastic flow that is time dependent is termed thixotropic. That is, viscosity decreases at constant applied shear rate, and in a flow curve, hysteresis occurs. Several other rheological classifications are covered in the Glossary of this book. Even viscosity itself is represented in many ways, as shown in Table IV. 

The rheological classification of liquids is normally given by a general expression, where the shear stress applied t [force length" ] and the resulting shear rate y [time" ] are correlated as follows (e.g., Metz et al, 1979) ... 

FIGU RE 17.6 Rheological classification of fluids showing (a) Newtonian, (b) non-Newtonian,... 

FIGURE 17.7 Rheological classification of solids (a) linear elastic, (b) nonlinear elastic, and (c) viscoelastic behavior. 

A kinematic flow classification can be based on Q. If the flow is extensional Ck = 0, for viscometric flow = 1 and for flow which is rigid rotational - oo similarly, a rheological flow classification based on can be formulated. When the flow is viscometric = 0, if the flow has extensional characteristics > 0, and for a flow which has rigid rotational characteristics < 0. This seems to be the most satisfactory flow classification yet devised the distinction between a kinematic and a rheological classification is particularly useful and significant. The criticism of this classification made by Huilgol is false, as Astarita has shown. 

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