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 welibore 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/cm2. 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/cm2 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 51) 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.
4.4.4 It is important to express the above concept mathematically so that models and calculations can be developed. Shear rate (y) is defined as.
API RP 13D:2006 pdf download
