The torque is represented by a “dial unit” or “degree” on the read-out display for a given shear rate. The indicated read-out multiplied by 1.067 is equivalent to shear stress in lb/100 sq ft i.e. one dial unit equals 1.067 lb/100 sq ft. A direct reading rotational viscometer, FANN viscometer or V-G Meter is used daily when drilling to determine the shear stress at different shear rates (3, 6, 100, 200, 300 and 600 RPM). These shear rates are selected to correspond approximately to shear rates at different points in the circulating system, with the annular shear rates corresponding to the lower shear rates. The 6 RPM reading is typically considered the shear rate most relevant for hole cleaning (viscous coupling) and the rule of thumb for effective hole cleaning is to maintain a 6 RPM value between 1.1 and 1.5 x the hole size in inches. The Shear Rate to Rpm at the other end of the rheology scale is >>600 RPM for the shear rates at the bit nozzles. Figure 3 below shows the approximate relationship between desired fluid viscosity (y-axis) and downhole shear rates (x-axis).

Rheology is a branch of physics related to the study of the deformation and flow of materials, both solids and liquids. The term rheology was coined by Eugene C. Bingham, a professor at Lafayette College, in 1920.

In drilling we use the term to describe how fluid viscosity changes under different conditions. If the shear stress is known at all shear rates, the complete flow behaviour of the fluid can be described. For simple Newtonian fluids such as water or oil, the ratio of shear stress to shear rate is a constant and the measurement of shear stress at one shear rate is sufficient to predict flow behaviour at all shear rates.

The ratio of shear stress to shear rate is the viscosity. The viscosity is a constant number and characterizes the flow behaviour of a Newtonian fluid.  When polymers are added to a Newtonian fluid, the irregular and entangled polymer chains resist flow in a manner not directly proportional to rate of shear as shear rate increases, the polymer chains start to stretch out and align. Consequently, the ratio of shear stress to shear rate, or the viscosity is high at low shear rates and decreases with increasing shear rate.  This is known as “shear thinning, non-Newtonian, or Power law” behaviour.  In other words, the increase in effective viscosity over that of water decreases with increasing shear rate. The shear stress is directly proportional to the pressure required to produce the flow. In Newtonian and non-Newtonian fluids, the smallest possible amount of pressure will cause the fluid to flow.

When a fluid is in laminar flow, it exerts a frictional drag called “shear stress” on the surface of the conduit it is flowing through. The magnitude of the shear stress depends on the frictional drag between adjacent “layers” of fluid traveling at different velocities, and the difference in velocities of adjacent layers next to the wall of the conduit.  The difference in velocities between adjacent layers is called the shear rate.  A point of special interest is at the wall where both shear rate and shear stress are a maximum (see Figure 4 below).

The bentonite in bentonite-based drilling fluids has unique properties because of its surface charges. These electrically charged solids link together to form a structure, flow will stop when the pressure or shear stress is reduced to a point that is less than the shear strength of the structure. This point is called the yield stress of the fluid. These non-Newtonian fluids, such as Bingham Plastic and Herschel Bulkley fluids, when allowed to remain still for a period, continue to develop this semi rigid structure and the shear stress required to initiate flow increases. This shear stress is called gel strength. The structure becomes more rigid with time, causing the gel strength to increase with time, this time dependent behaviour is called thixotropy.

Various models are used to represent the behaviour of drilling fluids as shown in Figure 5 below.

Understanding and being able to model the flow behaviour at different points of the circulating system is important.

• The shear rates inside the drill pipe, drill collars and BHA, are towards the higher end of the scale (see Figure 3) in the circulating system. This is where most of the pressure loss is produced and therefore has a major influence on circulating pressures and consequently the ability to deliver flow rates for hole cleaning.
• The shear rates in the annulus are at the other end of the scale, which is why the lower end rheology measurements are of more interest with respect to hole cleaning and ECD management.

Plastic viscosity (PV) and yield point of Drilling Mud (YP) are two coefficients used to monitor the non-Newtonian properties of drilling fluid. There are many different models and manufacturers of viscometers, however they all share the same geometry and measure shear stress at the standard six speed (RPM) settings. The difference between the dial readings produced when the viscometer is set at the 600 and 300 RPM speeds is the PV and the PV subtracted from the 300 RPM dial reading is the YP. Historically, the higher end rheology readings (600 and 300) could be more accurately measured than the lower end readings, therefore the 600 and 300 RPM were used to define the Bingham Plastic straight line (see Figure 6 below). PV is calculated in centipoise (cps) and the YP is calculated in lb/100 sq ft, as shown below:

                                                                              PV (cps) = ϴ₆₀₀ –  ϴ₃₀₀

                                                                        YP (lb/100 sq ft) = ϴ₃₀₀ – PV

Viscosities should be measured and reported at standard temperatures, which are usually 120°F for most wells or 150°F for high-temperatures wells. Typically six speed shear rates are taken at 600, 300, 200, 100, 6 and 3 RPM.

PV depends mainly on the concentration of solids and the viscosity of the base liquid and is more representative of the high shear rate viscosity inside the drill string. YP is a measure of the degree of non-Newtonian shear thinning behaviour (higher YP implies increased thickening at low shear rates). The YP is driven by the attractive forces between particles in the fluid at lower shear rates.

No. Traditionally, rheology data has been used to calculate the YP and PV in the Bingham Plastic model (the straight line on chart below – Figure 6), which does not actually represent the shear rate / shear stress behaviour of most fluids. YP is supposed to represent the shear stress at zero shear rate (the y-intercept on the chart), so it should be lower than the 3 RPM reading. In reality, it is normally much high because the YP recorded in the mud report by the mud engineer is not actually the shear stress at zero shear rate, it is the y-intercept of the extrapolated straight line derived from the 300 and 600 dial readings (PV and YP). YP₁ shown on Figure 6 below is the value reported on the mud report and YP₂ is the actual yield point.

If a drilling fluid has an ability to build gel strength when stationary, it will require additional shear stress or pressure, above what would be required to overcome the yield stress (actual YP), to break the gels before the fluid can move freely into laminar flow. The charts below show the relationship between pump pressure and time for a drilling fluid with no gel strength (Figure 7) and a drilling fluid with gel strength (Figure Y). The pressure effect of the gel strength can be seen to disappear after breaking the gels, whereas the effect of the YP remains.