This paper presents a model for predicting the contaminated mixing volume arising in pipeline batch transfers without physical separators. The proposed technique represents an improvement over the existing methods since it takes into account time-dependent flow rates and accurate concentration-varying axial dispersion coefficients. The governing equation of the model forms a nonlinear boundary-value problem that is solved by a finite element method coupled to the Newton’s method. A comparison among the theoretical predictions of this method, a field test, and other classical procedures show that the proposed method exhibits the best estimate over the whole range of admissible concentrations investigated.
Issue Section:
Additional Technical Papers
1.
Hara
, A.
, Hayashi
, H.
, and Tsuchiya
, M.
, 1979
, “Sphere separation system aids long-haul oil-product transport
,” Oil & Gas Journal
, 22
, pp. 47
–51
.2.
Benke
, H.
, and Gravert
, W.
, 1989
, “Process analysers for optimisation of reinjection of contaminated product in product pipelines
,” Oil Gas European Magazine
, 1
, pp. 42
–44
.3.
Aunicky
, Z.
, 1970
, “The longitudinal mixing of liquids flowing successively in pipelines
,” Can. J. Chem. Eng.
, 48
, pp. 12
–16
.4.
Austin
, J. E.
, and Palfrey
, J. R.
, 1964
, “Mixing of miscible but dissimilar liquids in a serial flow in a pipeline
,” Proc. Inst. Mech. Eng.
, 178
, Part 1, No. 15
, pp. 377
–395
.5.
Levenspiel, O., 1958, “How much mixing occurs between batches?,” Pipe Line Industry, May, pp. 51–54.
6.
Ova´di
, Z.
, and To¨ro¨k
, E.
, 1977
, “Examination of pipeline transport from the viewpoint of goods quality
,” Ko¨olaj e´s Fo¨ldga´z
, 10
, No. 4
, pp. 121
–123
. In Hungarian.7.
Sjenitzer
, F.
, 1958, “How much do products mix in a pipeline?,” The Pipeline Engineer, Dec., pp. D31–D34.8.
Smith
, S. S.
, and Schulze
, R. K.
, 1948
, “Interfacial mixing characteristics of products in products pipe line—Part 1
,” The Petroleum Engineer
, 20
, pp. 94
–104
.9.
Maron
, V. I.
, and Galianov
, A. I.
, 1970
, “Mixture coefficients for liquid flows in pipes
,” Izsvesta Vischikh Utchebnuikh Zavedenii Neft’i Gaz
, 2
, pp. 74
–78
. In Russian.10.
Botros
, K. K.
, 1984
, “Estimating contamination between batches in products lines
,” The Oil and Gas Journal
, 13
, pp. 112
–114
.11.
Netchval
, M. V.
, Tugunov
, P. I.
, and Slesa´reva
, V. G.
, 1972
, “Mixture formation during the process of sequential pumping of petroleum products of varying viscosities
,” Neftyanoy Khozyaistvo
, 50
, No. 8
, pp. 57
–59
. In Russian.12.
Smith
, S. S.
, and Schulze
, R. K.
, 1948
, “Interfacial mixing characteristics of products in products pipe line - Part 2
,” The Petroleum Engineer
, 20
, pp. 7
–12
.13.
Taylor
, G. I.
, 1954
, “The dispersion of matter in turbulent flow through a pipe
,” Proc. R. Soc. London, Ser. A
, 223
, pp. 446
–468
.14.
Tichacek
, L. J.
, Barkelew
, C. H.
, and Baron
, T.
, 1957
, “Axial mixing in pipes
,” American Institute of Chemical Engineering Journal
, 3
, No. 4
, pp. 439
–442
.15.
Atesmen
, K. M.
, Baldwin
, L. V.
, and Haberstroh
, R. D.
, 1971, “The dispersion of matter in turbulent pipe flows,” ASME J. Basic Eng., Dec., pp. 161–477.16.
Bischoff
, K. B.
, and Levenspiel
, O.
, 1962
, “Fluid dispersion-generalization and comparison of mathematical models-II Comparison of models
,” Chem. Eng. Sci.
, 17
, pp. 257
–264
.17.
Yablonski
, V. S.
, Asaturyan
, A. S.
, and Khizgilov
, I. H.
, 1960
, “Turbulent Diffusion in Pipes
,” Inzh.-Fiz. Zh.
, 3
, No. 3
, pp. 117
–122
. In Russian.18.
Wasan
, D. T.
, and Dayan
, J.
, 1970
, “The dispersion of solute in turbulent pipe flow of non-Newtonian fluids
,” Can. J. Chem. Eng.
48
, pp. 129
–131
.19.
Krantz
, W. B.
, and Wasan
, D. T.
, 1974
, “Axial dispersion in turbulent flow of power-law fluids in straight tubes
,” Industrial Chemical Fundamentals
, 13
, No. 1
, pp. 56
–61
.20.
Gambill
, W. R.
, 1959
, “How to estimate mixtures viscosities
,” Chem. Eng.
, 66
, pp. 151
–152
.21.
Haisan
, Q.
, 1997
, “Contamination due to intermixing in pipelines
,” Journal of Petrochemical Universities
, 10
, No. 2
, pp. 68
–70
. In Chinese.22.
Adams, R. A., 1968, Sobolev Spaces, The Academic Press, New York.
23.
Couto
, N. C.
, 1998, “Products separation in pipeline by using low-density foam pigs (Final Report),” Internal Report Petrobras-Petro´leo Brasileiro S. A., CENPES/SUPEP/DIPLOT/SEPROT, Project 02.05.07. In Portuguese.24.
Freitas Rachid
, F. B.
, Carneiro de Araujo
, J. H.
, Martins-Costa
, M. L.
, and Costa Mattos
, H. S.
, 1999a, “Development of models and operational procedures aiming to minimize the interfacial volume-Second Report,” Internal Report, Project Petrobras-UFF. In Portuguese.25.
Baptista, R. M., Freitas Rachid, F. B., and Carneiro Araujo, J. H., 2000, “Mixing volume determination in batch transfers through sonic detectors,” Proceedings of the 8th Brazilian Congress of Thermal Engineering and Sciences, Paper S22P1, Porto Alegre, October 3–6.
26.
Freitas Rachid
, F. B.
, Carneiro de Araujo
, J. H.
, Martins-Costa
, M. L.
, and Costa Mattos
, H. S.
, 1999b, “Development of models and operational procedures aiming to minimize the interfacial volume-Third Report,” Internal Report, Project Petrobras-UFF. In Portuguese.Copyright © 2002
by ASME
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