The Prediction of Pressure Gradients for a non-Newtonian Crude Oil Flowing in a Pipeline
- W.N. McKay (Imperial Oil Ltd.) | W.W. Boucher (Imperial Pipeline Ltd.) | J. Milne (Imperial Oil Ltd.)
- Document ID
- Petroleum Society of Canada
- Journal of Canadian Petroleum Technology
- Publication Date
- March 1964
- Document Type
- Journal Paper
- 1 - 7
- 1964. Petroleum Society of Canada
- 4.2 Pipelines, Flowlines and Risers, 4.3.4 Scale
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Several Western Canada crudes exhibit non-Newtonian flow characteristics.Thus, the use of the standard definition of viscosity is unreliable in pipelinesizing formulae.
A "model pipeline" viscometer was constructed, adapted from an instrumentdesigned by Coe, and based upon the theoretical aspects of the scale-up problemfor non-Newtonian flow. Using this instrument, laboratory pressure gradientswere determined and compared directly to the pressure gradients measured in atest section of pipeline carrying the crude oil. The field tests were for ayear's operation, and covered the full range of probable temperatures and flowvolumes. Laboratory pressure gradients agreed with the field values with anaverage error of less than 5 per cent.
Fluids are classified into two main categories - Newtonian or non-Newtonian- according to their behaviour at constant temperature under various steadyshearing forces. A Newtonian fluid obeys the equation:
in the laminar flow regime. Here, T is the shear stress, du/dr the shearrate, and ? the viscosity of the fluid in question. For laminar flow ina round tube, a double integration yields the classic Hagen-Poisseuilleequation
where R is the radius, P/L is the pressure gradient and Q is the throughputor rated volume flow.
Because of the identity of equation (i) with equation (ii), it has become anaccepted procedure to call RP/2L the shear stress at the wall of a tube ofradius R, and 4Q/pR3 the resultant shear rate. For reasons that willbe explained later, it is more rigorous to define these terms, in equation(ii), as the "apparent" shear stress and the "apparent" shear rate. The "real"or "true" terms should be only identified with equation (i).
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