Hostname: page-component-cd9895bd7-lnqnp Total loading time: 0 Render date: 2024-12-27T13:28:34.507Z Has data issue: false hasContentIssue false
  • English
  • Français

A Survey on Mathematical Modelling of Deposition in Waxy CrudeOils

Published online by Cambridge University Press:  10 August 2011

A. Fasano ,
L. Fusi ,
S. Correra  and
M. Margarone
A. Fasano
Affiliation:
Dipartimento di Matematica “U.Dini”- Viale Morgagni 67/a -50134 Firenze
L. Fusi*
Affiliation:
Dipartimento di Matematica “U.Dini”- Viale Morgagni 67/a -50134 Firenze
S. Correra
Affiliation:
eni exploration & production - Via Emilia 1 - 20097 S. Donato Milanese, Milano
M. Margarone
Affiliation:
eni exploration & production - Via Emilia 1 - 20097 S. Donato Milanese, Milano
*
⋆ Corresponding author. E-mail: fusi@math.unifi.it
Get access

Abstract

Waxy Crude Oils (WCO’s) are characterized by the presence of heavy paraffins insufficiently large concentrations. They exhibit quite complex thermodynamical andrheological behaviour and present the peculiar property of giving rise to the formation ofsegregated wax deposits, when temperature falls down the so called WAT, or Wax AppearanceTemperature. In extreme cases, segregated waxes may lead to pipeline occlusion due todeposition on cold walls. In this paper we review the mathematical models formulated todescribe: (i) wax cystallization or thawing in cooling/heating cycles; (ii) the mechanismsof mass transport in saturated non-isothermal solutions; (iii) the experimental deviceused to measure wax solubility and wax diffusivity; (iv) wax deposition in pipelinescarrying a warm, wax-saturated WCO through cold regions; (v) wax deposition accompanied bygelification during the cooling of a WCO under a thermal gradient.

Keywords

waxy crude oilsmolecular diffusionmathematical modelsfree boundary problems
Type
Research Article
Information
Mathematical Modelling of Natural Phenomena , Volume 6 , Issue 5: Complex Fluids , 2011 , pp. 157 - 183
Copyright
© EDP Sciences, 2011

Access options

Get access to the full version of this content by using one of the access options below. (Log in options will check for institutional or personal access. Content may require purchase if you do not have access.)

References

Avrami, M.. Kinetics of Phase Change. I. General Theory. J. Chem. Phys., 7 (1939), No. 12, 1103–1112. CrossRefGoogle Scholar
Avrami, M.. Kinetics of Phase Change. II. Transformation-Time Relations for Random Distribution of Nuclei. J. Chem. Phys., 8 (1940), No. 2, 212–224. CrossRefGoogle Scholar
Avrami, M.. Kinetics of Phase Change. III. Granulation, Phase Change, and Microstructure. J. Chem. Phys., 9 (1941), No. 2, 177–184. CrossRefGoogle Scholar
Azevedo, L.F.A., Texeira, A.M.. A critical review of the modeling of wax deposition mechanisms. Pet. Sci. Technol., 21 (2003), No. 3& 4, 393–408. CrossRefGoogle Scholar
Burger, E.D., Perkins, T.K., Striegler, J.H.J.. Studies of wax deposition in the trans Alaska pipeline. J. Pet. Technol., June (1981), 1075–1086.. CrossRefGoogle Scholar
E. Comparini, F. Talamucci. A general model for wax diffusion in crude oils under thermal gradient, in Applied and Industrial Mathematics in Italy, (v. Cutello et al. eds.), World Scientific (2007), 259–270.
Correra, S., Fasano, A., Fusi, L., Primicerio, M., Rosso, F.. Wax diffusivity under given thermal gradient: a mathematical model, ZAMM Z. Angew. Math. Mech., 87 (2007), No. 1, 24–36. CrossRefGoogle Scholar
Correra, S., Fasano, A., Fusi, L., Primicerio, M.. Modelling of wax diffusion in crude oils: the cold finger device, Appl. Math. Modl., 31 (2007), No. 10, 2286–2298. CrossRefGoogle Scholar
Correra, S., Fasano, A., Fusi L. , L., Merino–Garcia D., D.. Calculating deposit formation in the pipelining of waxy crude oils. Meccanica, 42 (2007), No. 2, 149–165. CrossRefGoogle Scholar
Coto, B., Martos, C., Espada, J.J., Robustillo, M.D., Peña, J.L.. Analysis of paraffin precipitation from petroleum mixtures by means of DSC: iterative procedure considering solid-liquid equilibrium equations. Fuel, 89 (2010), 1087–1094. CrossRefGoogle Scholar
Coutinho, J.A.P., Knudsen, K., Andersen, S.I.. A local composition model for paraffinic solis solution. Chem. Eng. Science, 51 (1996), No. 12, 3273–3282. CrossRefGoogle Scholar
Coutinho, J.A.P., Ruffier-Meary, V.. The use of differential scanning calorimetry in studies of wax deposition: measuring the solid formation and binary solid-liquid equilibrium phase diagrams. Oil Gas Sci. Technol., 54 (1999), No. 5, 641–648. CrossRefGoogle Scholar
Coutinho, J.A.P., Edmonds, B., Moorwood, T., Szczepanski, R., Zhang, X.. Reliable wax predictions for flow assurance. Energ. Fuel, 20 (2006), 1081–1088. CrossRefGoogle Scholar
Escobar-Remolina, J.C.. Prediction of characteristics of wax precipitation in synthetic mixtures and fluids of petroleum: a new model. Fluid Phase Equilibr., 240 (2006), 197–203. CrossRefGoogle Scholar
L. Faienza. Mathematical models for wax deposition in crude oils. PhD Thesis, Dept. of Math., University of Florence (2010).
A. Fasano, M. Primicerio. Heat and mass transfer in non-isothermal partially saturated solutions. New Trends in Mathematical Physics,(P. Fergola et al. eds.), World Scientific (2003), 33–44.
Fasano, A., Primicerio, M.. Temperature driven mass transport in concentrated saturated solutions. Prog. nonlin., 61 (2005), 91-108. Google Scholar
Fasano, A., Primicerio, M.. Wax deposition in crude oil: a new approach. Rend. Mat. Acc. Lincei, 9 (2005), 251-263. Google Scholar
Fasano, A., Fusi, L., Ockendon, J.R., Primicerio, M.. Gelification and mass transport in a static non-isothermal waxy solution. Euro. J. of Appl. Math., 20 (2009), No. 1, 93–122. CrossRefGoogle Scholar
Gianni, R., Petrova, A.G.. One-dimensional problem for heat and mass transport in oil-wax solution. Rend. Mat. Acc. Lincei, 9 (2005), 181–196. Google Scholar
Hammami, A., Mehrotra, A.K.. Non-isothermal crystallization kinetics of n-paraffins with chain lenght between thirty and fifty. Thermochim. Acta, 211 (1992), 137–153. CrossRefGoogle Scholar
Hammami, A., Mehrotra, A.K.. Non-isothermal crystallization kinetics of even-numbered and odd-numbered normal alkanes. Thermochim. Acta, 215 (1993), 197–209. CrossRefGoogle Scholar
Kolmogorov, A.N.. In Russian. Bull. Acad. Sci. USSR. Ser. Math., 3 (1937), 355–359. Google Scholar
M. Margarone, R. Bagatin, C. Busto, P. D’Olimpio, L. Fusi, L. Faienza, A. Fasano, M. Primicerio. A wax crystallization model from DSC experiments. 11th International Conference on Petroleum Phase Behavior and Fouling, 13 - 17 June 2010, Jersey City, NJ, US.
Merino-Garcia, D., Margarone, M., Correra, S.. Kinetics of waxy gel formation from batch experiments. Energ. Fuel, 21 (2007), 1287–1295. CrossRefGoogle Scholar
Ozawa, T.. Kinetics of non-isothermal crystallization. Polymer, 12 (1971), 150–158. CrossRefGoogle Scholar
Pedersen, S.K., Skovborg, P., Hans, P.D.. Wax Precipitation from North Sea Crude Oils: Thermodyamic Modeling. Energ. Fuel, 5 (1991), 924–932. CrossRefGoogle Scholar
M. Primicerio. Wax Segregation in Oils: A Multiscale Problem. in Progress in Industrial Mathematics at ECMI 2008 (A.D.Fitt et al. eds.), Springer 2010, pp 43-68.
Ramirez-Jaramillo, E., Lira-Galeana, C., Manero, O.. Modeling wax deposition in pipelines. Petrol. Sci. Technol., 22 (2004), 821–861. CrossRefGoogle Scholar
Sajkiewicz, P., Carpaneto, L., Wasiak, A.. Application of the Ozawa model to non-isothermal crystallization of poly(ethylene terephthalete). Polymer, 42 (2001), 5365–5370. CrossRefGoogle Scholar
Singh, P., Venkatesan, R., Fogler, H.S., Nagarajan, N.. Formation and aging of incipient thin film wax-oil gels. AIChE J., 46 (2000), No. 5, 1059–1074 CrossRefGoogle Scholar
Won, K.W.. Thermodynamics for Solid Solution-Liquid-Vapor-Equilibria: Wax Phase Formation from Heavy Hydrocarbon Mixtures. Fluid Phase Equilibr., 30 (1986), 265–279. CrossRefGoogle Scholar
Zhang, Z., Xiao, C., Dong, Z.. Comparison of the Ozawa and modified Avrami models of polymer crystallization under non-isothermal conditions using a commputer simulation method. Thermochim. Acta, 466 (2007), 22–28. CrossRefGoogle Scholar
Zougari, M.I., Sopkow, T.. Introduction to Crude Oil Wax Crystallization Kinetics: Process Modeling. Ind. Eng. Chem. Res., 46 (2007), 1360–1368. CrossRefGoogle Scholar