Stories from the Field,Fundamental Questions and Solutions - Measurement While Drilling Signal Analysis, Optimization and Design - page 8

not - the case. In “Flow Distribution in a Tricone Jet Bit Determined from Hot-
Wire Anemometry Measurements,” SPE Paper No. 14216, by A.A. Gavignet,
L.J. Bradbury and F.P. Quetier, presented at the 1985 SPE Annual Technical
Conference and Exhibition in Las Vegas, and in “Flow Distribution in a Roller
Jet Bit Determined from Hot-Wire Anemometry Measurements,” by A.A.
Gavignet, L.J. Bradbury and F.P. Quetier, SPE Drilling Engineering, March
1987, pp. 19-26, the investigators, following ideas suggested by the lead author,
who had by then routinely used wind tunnels to study sirens and turbines,
showed how more detailed flow properties can be obtained using aerospace
measurement methods in air . The scientific justification offered was the “highly
turbulent nature of the flow.” This counter-intuitive (but correct) approach to
modeling mud provides a strategically important alternative to traditional testing
that can reduce the cost of developing new MWD systems. Wind tunnel use in
the petroleum industry was, by no means, new at the time. For instance, Norton,
Heideman and Mallard (1983), with Exxon Production Research Company, and
others, had published studies employing wind tunnel use in offshore platform
design, extrapolating air-based results dimensionlessly to water flows using
standard Strouhal and Reynolds number normalizations.
Additional reasons for wind tunnel usage are suggested by some simpler,
but deeper arguments, than those in Gavignet et al . For static measurements
(e.g., those for stall torque, power determination, erosion trends and streamline
pattern) wind tunnels apply also to laminar flows. From basic fluid mechanics,
for two flows to be alike dynamically, their Reynolds numbers need to be
similar. This dimensionless parameter is given by Re = UUL/P = UL/Q where U
and P are density and viscosity, U is the speed of the oncoming flow, and L is a
characteristic length (Qis the kinematic viscosity P/U). It can be shown that if
both U's and both L's are identical in an experiment (which is actually ideal and
doable since full-scale testing of plastic or wood mockups at full speed is
inexpensive and straightforward for downhole tools) then dynamic similarity is
achieved when both kinematic viscosities match. In fluid-dynamics, even a ten-
fold difference is “close” for modeling purposes. Reference to physical tables
shows that this is remarkably the case - the kinematic viscosities for mud and air
are very close and justify wind tunnel usage!
Additionally, a common normalization given in turbomachinery topics can
be used to reduce static and dynamic torque properties for various flow rates and
densities to a single dimensionless performance curve - simply plot torque
(normalized by a dynamic head) against the velocity swirl or “tip speed” ratio.
This also motivates intelligent test matrix design: by judiciously choosing
widely separated test points, everything there is to know about torque can be
inferred - there is no need to perform hundreds of tests for different flow rates,
rotation speeds and mud weights. Taken together, the two recipes just discussed
allow simple and rigorous characterization of siren and turbine properties over
the entire operating envelope with a minimum of labor, time and expense !