Brine Viscosity Correlation with Temperature Using the Vogel-Tammann-Fulcher (VTF) Equation
- Faruk Civan (U. of Oklahoma)
- Document ID
- Society of Petroleum Engineers
- SPE Drilling & Completion
- Publication Date
- December 2007
- Document Type
- Journal Paper
- 341 - 355
- 2007. Society of Petroleum Engineers
- 4.3.1 Hydrates, 1.6 Drilling Operations, 2 Well Completion, 1.8 Formation Damage, 4.3.3 Aspaltenes, 2.7.1 Completion Fluids
- 4 in the last 30 days
- 851 since 2007
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Theoretically meaningful correlation of the viscosity of typical brines with temperature and dissolved salt concentration is presented. The temperature dependence of the brine viscosity is described using the VTF equation type asymptotic exponential function. The parameters of this equation are correlated with the brine concentration. This approach for developing accurate empirical correlations is verified by means of experimental data. The present approach is proven to lead to accurate correlations of the brine viscosity using a mathematically simple, but theoretically-meaningful equation, when reliable experimental data is available.
Accurate correlation of the brine-viscosity data is of utmost practical importance when seeking optimal conditions of completion fluids for particular applications. Although the best correlations of experimental data for temperature dependency can be accomplished by taking advantage of the VTF equation (Vogel 1921; Tammann and Hesse 1926; Fulcher 1925) and avoiding the use of temperature-dependent variables, correlations are still being attempted by the mixed use of both the temperature-dependent and independent variables in many studies. For example, Ortego and Vollmer (2006) developed several empirical correlations in this manner for the viscosity of the single-salt and mixed-salt brines using the experimental data obtained at temperatures below 200oF. Their correlations are unnecessarily complicated and therefore of low accuracy because the brine viscosities were expressed as functions of both the temperature and density. However, density is dependent upon temperature and therefore should not be included in the correlation of viscosity when only the temperature effect is considered. Including the density as a variable is not only unnecessary, but also reduces the accuracy of the correlations. The experimental measurement errors associated with both the viscosity and density, produce a compound affect in reducing the accuracy of the resulting correlations. Such exercises should be avoided in correlation of any experimental data. It is important to distinguish between the true independent and dependent variables and the data should be correlated using only the truly independent variables. The accuracy of their correlations also suffers from being solely empirical, thus, not taking advantage of a relevant theory.
The objective of this paper is to correlate the data of Ortego and Vollmer (2006) in a theoretically rigorous manner to achieve the maximum possible accuracy in the correlation of the brine viscosity. This paper attempts at a practical but theoretically, meaningful correlation of the experimental measurements of the viscosity of typical brines with temperature and concentration. The temperature dependence of the brine viscosity is described using the VTF equation type asymptotic exponential function. The parameters of this equation are correlated with the brine concentration. The present approach yields a mathematically simple but theoretically rigorous correlation of the brine viscosity, providing better accuracy than the correlations given by Ortego and Vollmer (2006) when the experimental data is accurate.
The author has chosen to provide supplemental information for this paper. This supplemental information is freely available at http://www.spe.org/files/spedc/108463/
|File Size||4 MB||Number of Pages||15|
Arrhenius, S. 1889. Uber die reaktionsgeschwindigkeit der inversion vonrohrzucker durch saeuren. Z. Physik. Chem. 4: 226-248.
Beggs, H.D. and Robinson, J.R. 1975. Estimating the Viscosity of Crude OilSystems. JPT 27 (9):1140-1141. SPE-5434-PA. DOI:10.2118/5434-PA
Civan, F. 2004. Temperature Dependence of Wettability Related RockProperties Correlated by the Arrhenius Equation. Petrophysics 45(4): 350-362.
Civan, F. 2005. Applicability of the VTF Type Asymptotic ExponentialFunctions for Ice, Hydrates, and Polystyrene Latex. J. of Colloid andInterface Science 285: 429-432.
Civan, F., 2006a. Viscosity-Temperature Correlation for Crude Oils Using anArrhenius-Type Asymptotic Exponential Function. Petroleum Science andTechnology 24 (6): 699-706.
Civan, F., 2006b. Discussionof A Practical Method for Anticipating Asphaltene Problems. SPEPO21 (3): 411. SPE-104235-PA. DOI: 10.2118/104235-PA.
Civan, F., 2007a. Temperature Effect on Power for Particle Detachment fromPore Wall Described by an Arrhenius-Type Equation. Transport in PorousMedia 67 (2): 329-334.
Civan, F., 2007b. Critical Modification to the Vogel-Tammann-FulcherEquation for Temperature Effect on the Density of Water. IndustrialEngineering & Chemistry Research Journal 46 (17):5810-5814.
Fulcher, G.S. 1925. Analysis of Recent Measurements of the Viscosity ofGlasses. J. Am. Ceram. Soc. 8: 339-355.
García-Colín, L. S., del Castillo, L. F., and Goldstein, P. 1989.Theoretical Basis for the Vogel-Fulcher-Tammann Equation, Physical Review B(Condensed Matter) 40 (10): 7040-7044.
García-Colín, L. S., del Castillo, L. F.; Goldstein, P. 1990. Erratum:Theoretical Basis for the Vogel-Fulcher-Tammann equation. Phys. Rev. B.(Condensed Matter) 41 (7): 4785.
Glasø, Ø. 1980. GeneralizedPressure-Volume-Temperature Correlations. JPT 32 (5) 785-795.SPE-8016-PA. DOI: 10.2118/8016-PA.
Hashim, E.T. and Hassaballah, A.A. 2003. An Improved Viscosity-TemperatureCorrelation for Crude Oils. Petroleum Science and Technology 21(11-12): 1625-1630.
Monkos, K., 2003. A Method of Calculations of the Parameters in the VTFsEquation: An Application to the Porcine Serum Albumin Aqueous Solutions.Current Topics in Biophysics 27 (1-2): 17-21.
Ortego, A.M. and Vollmer, D.P. 2006. Viscosities for Completion Fluids atTemperature and Density. SPEDC 21 (2): 81-89. SPE-86506-PA.DOI:10.2118/86506-PA.
Tammann, G. and Hesse, W. 1926. Die abhängigkeit der viskosität von dertemperature bei unterkühlten flüssigkeiten. Z. Anorg. Allg. Chem.156: 245-257.
Vogel, H. 1921. Das temperature-abhängigketsgesetz der viskosität vonflüssigkeiten. Phys. Zeit. 22: 645-646.