Hydraulics - Deformation of a Fluid by Simple Shear

Deformation of a Fluid by Simple Shear

The magnitude of shear between the layers is represented by the shear-rate, which is defined as the difference in the velocities between the layers, divided by the distance of separation. It is this relationship between the shear-stress and shear-rate that defines the behavior of the fluid.

For some fluids the relationship is linear (i.e., if the shear-stress is doubled then the shear-rate will also double, or if the circulation rate is doubled then the pressure required to pump the fluid will double). Fluids such as this are known as “Newtonian fluids”. Examples of Newtonian fluids are water, glycerine and diesel. The Newtonian fluid model is defined by the following relationship:

Shear-Stress = Absolute Viscosity x Shear-Rate

The slope of the flow curve in the diagram is given by the absolute viscosity, this is the shear stress divided by the shear rate. A typical flow profile for a Newtonian fluid in a cylindrical pipe is a parabola, with a maximum shear-rate at the wall and a minimum (0) at the center.

Drilling fluids are generally Non-Newtonian in behavior, and are defined by more complex relationships between shear-stress and shear-rate. When fluids contains colloidal particles (or clays), these particles tend to increase the shear-stress or force necessary to maintain a given flow rate. This is due to electrical attraction between particles and to them physically “bumping” into each other. Long particles, randomly oriented in a flow stream, will display high interparticle interference. However, as shear-rate is increased, the particles will tend to develop an orderly orientation and this interaction will decrease.

In the center of a pipe, the shear-rate will be low and hence particle interaction high, giving it a flattened flow profile. This profile has an improved sweep efficiency and an increased carrying capacity for larger particles.

As can be seen from the previous examples, the ratio of shear-stress to shear-rate is not constant but will vary with each shear-rate. Various “oilfield” models have been proposed to describe this non-

Newtonian shear-rate/shear-stress curve. In order to arrived at “standard” variables, these models require the measurement of shear-stress at two or more shear-rates to define the curve.

The two most common models used at the wellsite are the Bingham Plastic Model and the Power Law Model.