API RP 13D-2006 pdf download.Rheology and Hydraulics of Oil-well Drilling Fluids.
4.2.2 Viscosity is not a constant value for most drilling fluids. It varies with shear rate. To check for rate dependent effects, shear stress measurements are made at a number of shear rates. From these measured data, rheological parameters can be calculated or can be plotted as viscosity versus shear rate. 4.2.3 The term effective viscosity is used to describe the viscosity either measured or calculated at the shear rate corresponding to existing flow conditions in the wellbore or drillpipe. This special term is used to differentiate the viscosity as discussed in this clause from other viscosity terms. To be meaningful, a viscosity measurement must always specify the shear rate. 4.3 Shear stress 4.3.1 Shear stress is the force required to sustain a particular rate of fluid flow and is measured as a force per unit area. Suppose, in the parallel-plate example (see Figure 1 ), that a force of 1 .0 dyne is applied to each square centimeter of the top plate to keep it moving. Then the shear stress would be 1 .0 dyne/cm 2 . The same force in the opposite direction is needed on the bottom plate to keep it from moving. The same shear stress of 1 .0 dyne/cm 2 is found at any level in the fluid.
4.4 Shear rate 4.4.1 Shear rate is a velocity gradient measured across the diameter of a pipe or annulus. It is the rate at which one layer of fluid is moving past another layer. As an example, consider two large flat plates parallel to each other and one centimeter (cm) apart. The space between the plates is filled with fluid. If the bottom plate is fixed while the top plate slides parallel to it at a constant velocity of 1 cm/s, the velocities indicated in Figure 1 are found within the fluid. The fluid layer near the bottom plate is motionless while the fluid layer near the top plate is moving at almost 1 cm/s. Halfway between the plates the fluid velocity is the average 0.5 cm/s. 4.4.2 The velocity gradient is the rate of change of velocity ∆ V with distance from the wall h . For the simple case of Figure 1 , the shear rate is dV/h and will have units of 1 /time. The reciprocal second, or often called the inverse second, (1 /s or s -1 ) is the standard unit of shear rate. 4.4.3 This reference example is unusual in that the shear rate is constant throughout the fluid. This situation is not the case with a circulating fluid. In laminar flow inside a pipe, for example, the shear rate is highest next to the pipe wall. An average shear rate may be used for calculations, but the shear rate itself is not constant across the flow channel.
4.6 Fluid characterization 4.6.1 Fluids can be classified by their rheological behavior. Fluids whose viscosity remains constant with changing shear rate are known as Newtonian fluids. Non-Newtonian fluids are those fluids whose viscosity varies with changing shear rate. 4.6.2 Temperature and pressure affect the viscosity of a fluid. Therefore, to properly describe the drilling fluid flow, the test temperature and pressure must be specified. 4.6.3 Some mathematical models used for hydraulic calculations are shown in this subclause. 4.7 Newtonian fluids 4.7.1 Fluids for which shear stress is directly proportional to shear rate are called Newtonian. Water, glycerin, and light oil are examples of Newtonian fluids. 4.7.2 A single viscosity measurement characterizes a Newtonian fluid at a specified temperature and pressure. 4.8 Non-Newtonian fluids 4.8.1 Fluids for which shear stress is not directly proportional to shear rate are called non-Newtonian. Most drilling fluids are non Newtonian. 18.104.22.168 Drilling fluids are shear thinning when they exhibit less viscosity at higher shear rates than at lower shear rates. 22.214.171.124 There are some non-Newtonian fluids which exhibit dilatant behavior. The viscosity of these fluids increases with increasing shear rate. Dilatant behavior rarely occurs in drilling fluids. 4.8.2 The distinction between Newtonian and non-Newtonian fluids can be illustrated by using the API standard concentric-cylinder viscometer. If the 600-rpm dial reading is twice the 300-rpm reading, the fluid exhibits Newtonian flow behavior. If the 600-rpm reading is less than twice the 300-rpm reading, the fluid is non-Newtonian and shear thinning.