Hydraulic Calculations
In the “Advanced Logging Procedures Workbook” (P/N 80269H), an introduction to hydraulics illustrates the Bingham method for hydraulic optimization. The second, and more commonly used method is the Power Law Model.
This model fits the actual flow properties more closely, although at low shear rates, it will predict slightly low shear stresses. The model describes a fluid in which the shear stress increases as a function of shear rate, raised to some power. As mentioned earlier, the equation for the Power Law model is:
Shear Stress = k x Shear raten
“k” is known as the “consistency index”, and is indicative of the pumpability of the fluid. “n” is the power index, denoting the degree of how “non-Newtonian” the fluid is.
Both parameters can be determined from the Fann VG meter. “k” is defined as the viscosity of a fluid at a shear rate of 1 sec-1. When “n” equals 1, the fluid is Newtonian. As the fluid becomes more shear thinning, the “n” value decreases.
where: 300rpm = Fann VG meter dial reading at 300 rpm's
600rpm = Fann VG meter dial reading at 600 rpm's
If the Fann VG meter dial readings are not available, both “k” and “n” can be determined using the Plastic Viscosity and Yield Point.
where: PV = Plastic Viscosity (cps)
YP = Yield Point (lb/100ft2)
Once these values have been determined, they are used in calculating the pressure losses throughout the circulating system. This section will describe the pressure losses, using the Power Law Model, in the surface system, the drillstring, and the annulus.
