Investigation of methods for direct rheological model parameter estimation

Abstract A number of rheological models are examined to establish how well they can characterise a data set of different, pseudoplastic, non-Newtonian fluids used in North Sea operations when their parameters are evaluated using the `direct' parameter calculation procedure. The study considers how modelling accuracy is affected by the choice of rotational viscometer readings used to calculate these parameters and provides the necessary expressions for direct parameter solution. Conventional measurement combinations of rotational viscometer readings fail to deliver the accuracy provided when non-conventional reading combinations are employed. As such, recommendations for suitable `default' rotational viscometer measurement combinations are given for each rheological model. It is also concluded that the three-parameter model of Sisko [Sisko, A.W., 1958. Flow of lubricating greases. Ind. Eng. Chem. 50 (12) 1789–1792] delivers the most accurate pseudoplastic characterisation of all the models examined (as illustrated in box-plot representations).

[1]  Saeed M. Al-Zahrani,et al.  A generalized rheological model for shear thinning fluids , 1997 .

[2]  S C Ellis,et al.  A rotational viscometer for surface films , 1955 .

[3]  L. Prandtl,et al.  Ein Gedankenmodell zur kinetischen Theorie der festen Körper , 1928 .

[4]  B. V. Randall,et al.  Flow of Mud During Drilling Operations , 1982 .

[5]  I. M. Krieger,et al.  Comparison of Methods for Calculating Shear Rates in Coaxial Viscometers , 1978 .

[6]  Wolfgang Ostwald,et al.  Ueber die Geschwindigkeitsfunktion der Viskosität disperser Systeme. IV , 1925 .

[7]  Markus Reiner,et al.  In Search for a General Law of the Flow of Matter , 1930 .

[8]  Bernt S. Aadnøy,et al.  Improved pressure drop/flow rate equation for non-Newtonian fluids in laminar flow , 1994 .

[9]  Frederick Denny Farrow,et al.  XXIII.—THE FLOW OF STARCH PASTE THROUGH CAPILLARY TUBES , 1923 .

[10]  J. D. Raal,et al.  Rates of shear in coaxial cylinder viscometers , 1973 .

[11]  W. Philippoff,et al.  Zur Theorie der Strukturviskosität. I , 1935 .

[12]  Ray Taylor,et al.  A New and Practical Application of Annular Hydraulics , 1973 .

[13]  N. Casson,et al.  A flow equation for pigment-oil suspensions of the printing ink type , 1959 .

[14]  Keith K. Millheim,et al.  Applied Drilling Engineering , 1986 .

[15]  Alun Whittaker,et al.  Theory and application of drilling fluid hydraulics , 1985 .

[16]  M. M. Cross.  Rheology of non-Newtonian fluids: A new flow equation for pseudoplastic systems , 1965 .

[17]  A. A. Gavignet,et al.  Computer processing improves hydraulics optimization with new methods , 1987 .

[18]  R. E. Robertson,et al.  An Improved Mathematical Model for Relating Shear Stress to Shear Rate in Drilling Fluids and Cement Slurries , 1976 .

[19]  H. Elrod,et al.  Direct Determination of the Flow Curves of Non‐Newtonian Fluids. II. Shearing Rate in the Concentric Cylinder Viscometer , 1953 .

[20]  H. Eyring.  Viscosity, Plasticity, and Diffusion as Examples of Absolute Reaction Rates , 1936 .

[21]  J. G. Savins,et al.  A Practical Utilization of the Theory of Bingham Plastic Flow in Stationary Pipes and Annuli , 1958 .

[22]  R. M. Beirute,et al.  An Evaluation of the Robertson-Stiff Model Describing Rheological Properties of Drilling Fluids and Cement Slurries , 1977 .

[23]  Iain Weir,et al.  A Statistical Study of Rheological Models for Drilling Fluids , 1996 .

[24]  T. Hemphill,et al.  Yield-power law model more accurately predicts mud rheology , 1993 .

[25]  J. Sutterby,et al.  Laminar converging flow of dilute polymer solutions in conical sections: Part I. Viscosity data, new viscosity model, tube flow solution , 1966 .

[26]  A. W. Sisko.  The Flow of Lubricating Greases , 1958 .

[27]  R. Monicard,et al.  Drilling Mud and Cement Slurry Rheology Manual , 1982 .

[28]  Inge S. Helland,et al.  On the Interpretation and Use of R 2 in Regression Analysis , 1987 .