The Interpretation of Data On the Rheological BehavioLlr Of Thixotropic Crude Oils
Authors: Govier G.W. , Fogarasi Maria 
Published: March 2010

Abstract
Two correlations for the prediction of the rheological behaviour of thixotropic crude oils are described and tested on a set of data. A comparison shows that the Perkins-Turner correlation, which Is simpler to use, n-ill give adequate predictions over the range of their data, whereas the more complex correlation of Ritter and Govier reproduces the shear stress - shear rate - shear duration relationships for shear rates greater than 0.1 sec−1 for all values of shear durations with good accuracy.

Introduction
THE LAST FEW YEARS have seen the publication of a number of papers on various aspects of the rheological behaviour of thixotropic materials including crude oils. Several of these deal with the general nature of thixotropic behaviour(1–6). The thixotropic behaviour is usually described by a "model" or a set of constitutive equations in-volving several material constants which may be evaluated from rheological measurements. A successful model permits the construction of the shear stress shear rate shear duration (T - S - U) relationships from the material constants. Several models are reviewed by Govier and Aziz.(7).
Another group of papers(6–10) deals with practical aspects of pipeline flow characteristics of thixotropic crude oils, including the starting behaviour after the oil has gelled in the pipeline. The pressure drop required to start flow is related to the yield value or "gel strength" of the crude oil
Some actual data on the rheological behaviour of specific crude oils, or their pressure drop - flow rate relationship in pipelines, are included in both groups of papers.

The Data And Correlation Of Perkins And Turner
Recently, Perkins and Turner (10) presented data on the flow behaviour of crude oil from the Prudhoe Bay field. Their data were carefully taken in precision rotational viscometers over an exceptionally wide range of shear rates. For the Prudhoe Bay crude oil the observed the same general features, some in accentuated form, observed by Govier and Ritter(11) for the Pembina crude oil, i.e.: sensitivity to previous thermal history shear history and aging: sensitivity to temperature; existence of yield value; decay of shear stress with time at constant shear rate; pseudoplastic behaviour of the zero-time shear stress.
Perkins and Turner correlated their data covering a range of temperatures and a variety of previous thermal and shear treatments in terms of
(Equation Available In Full Paper)
Equation (1) may therefore be considered an interpolation formula for the evaluation of τ at any value of θ based on the above limiting values. Equation (2) is of reasonable form to describe a yield-pseudoplastic fluid. Equation (3) is the Newtonian equation; its applicability even to the infinite-time behaviour of a thixotropic yield - pseudoplastic crude oil is questionable in principle. Its suitability for the Prudboe Bay crude oil is not supported by the trend of the data. This is discussed further later.
The correlation also presupposes that the effect on the rheological behaviour of shear rate, γ and shear duration, θ, is expressible through γ itself and the product E = γ θ, i.e., that the effect of shear duration, θ, is fully expressible through.