Most fluids are non-Newtonian. For these fluids, no constant of proportionality exists between shear stress and shear rate; their viscosity varies with changing shear rate.
Non-Newtonian fluids are separated further into subcategories defined by various models. The models of most interest in drilling fluid technology are the Bingham plastic, power-law and Herschel-Bulkley models. Most fluids do not conform precisely to a single model but rather to a combination of models.
The behavior of many drilling fluids, and most water-base cement slurries, can be described by the two-parameter Bingham plastic model, which assumes a linear relationship between the shear stress and the shear rate. Fluids that exhibit Bingham plastic behavior do not flow until the shear stress exceeds a critical value known as the yield point. Once the yield point is reached, changes in shear stress and shear rate are proportional. This constant of proportionality, or the slope of the curve, is termed the plastic viscosity. The Bingham plastic model does not accurately predict fluid flow behavior at low shear rates but is useful for continuous monitoring and treating of drilling fluids.
Unlike the Bingham plastic model, the power-law model assumes a non-linear relationship between the shear stress and the shear rate. For power-law fluids, the shear stress increases as a function of the shear rate raised to a constant exponent. This model is a good fit for fluids when measured at low shear rates. Power-law fluids do not have a yield point and do not develop gel strengths—in which they maintain suspensions—when left undisturbed. Polymeric solutions and melts are examples of fluids that exhibit power-law behavior.
The Herschel-Bulkley model combines the effects of Bingham and power-law behavior in a fluid; the model is applied to fluids that have a yield stress and a nonlinear relationship between the shear stress and the shear rate.
Most non-Newtonian fluids are sensitive to shear rate. Some non- Newtonian fluids are useful in the oil industry because their viscosities decrease with increasing shear rate but then increase, or gel, when shear ceases. The ongoing increase in gel strength, which depends on how long the fluid has been at rest, is an indication of thixotropy. These fluids are termed thixotropic fluids and exhibit time-dependent changes in viscosity; the longer the duration of shear, the lower the fluid’s viscosity until it eventually reaches a constant value. Some cements, such as gypsum and port-land and clay-based cement formulations, are thixotropic. Thixotropic cement is commonly used in wells in which fractures and lost circulation are concerns. When sheared, these cements exhibit low viscosities, but if they enter a fracture in a formation and are no longer subjected to shear, they immediately start to gel and become self-supporting.
To maintain control of hole cleaning, mud engineers measure the suspension and filtration properties of a drilling fluid at the rig site on a daily basis. The mud engineer conducts these tests following procedures in API RP 13-B1, Recommended Practice for Field Testing Water-Based Drilling Fluids, and API RP 13-B2, Recommended Practice Standard Procedure for Field Testing Oil-Based Drilling Fluids.
Drilling fluid density, often referred to as mud weight, is expressed as kilograms per cubic meter (kg/m3), pounds per gallon (lbm/galUS) or specific gravity (SG). Mud weight is typically measured by using a mud balance, which is a balance-beam scale (Figure 2). A cup of known volume and mass is attached to one end of the beam. Engineers fill the cup with drilling mud. The mass of the filled cup is balanced on the other end of the beam by a fixed countermass and a rider that can move freely along the graduated scale. The density of the fluid is read directly from the scales located on both sides of the mud balance.