Effect of initial-interfacial mixing on the amount of contamination in multiproduct pipelines

References

• Ahmed, S. 2012. A numerical algorithm for solving advection-diffusion equation with constant and variable coefficients. Open Numerical Methods 4:1–7. doi:10.2174/1876389801204010001.
   Google Scholar
• Al-Jawad, M. S, and F. H. Omar. 2012. Comprehensive model for flash calculations of heavy oils using the Soave-Redlich-Kwong equation of state. North Africal Technical Conference Exhibition. Cairo, Egypt, February 20. doi:10.2118/150083-MS.
   Google Scholar
• API. 2018. Design, construction, operation, maintenance, and inspection of terminal and tank facilities (API STD 2610). Washington: American Petroleum Institute. https://standards.globalspec.com/std/13051821/api-std-2610.
   Google Scholar
• Aris, R. 1956. On the dispersion of a solute in a fluid flowing through a tube. Mathematical, Physical and Engineering Science 235:1200. doi:10.1098/rspa.1956.0065.
   Google Scholar
• ASME. 2006. Pipeline transportation systems for liquid hydrocarbons and other liquids (ASME B31.4). New York: American Society of Mechanical Engineering. Google Books
   Google Scholar
• Aunicky, Z. 1970. The longitudinal mixing of liquids flowing successively in pipelines. The Canadian Journal of Chemical Engineering 48 (1):12–6. doi:10.1002/cjce.5450480103.
   Web of Science ®Google Scholar
• Austin, E, and R. Palfrey. 1963. Mixing of miscible but dissimilar liquids in a serial flow in a pipeline. Proceedings of the Institution of Mechanical Engineers 178 (1):377–89. doi:10.1177/002034836317800160.
   Google Scholar
• Bahar, E, and G. Gurarslan. 2017. Numerical solution of advection-diffusion equation using operator splitting method. International Journal of Engineering & Applied Sciences 9 (4):76–88. doi:10.24107/ijeas.357237.
   Google Scholar
• Cafaro, D. C, and J. Cerdá. 2008. An efficient tool for the scheduling of multiproduct pipelines and terminal operations. Industrial & Engineering Chemistry Research 47 (24):9941–56. doi:10.1021/ie071630d.
   Web of Science ®Google Scholar
• Cafaro, D. C, and J. Cerdá. 2009. Optimal scheduling of refined products pipelines with multiple sources. Industrial & Engineering Chemistry Research 48 (14):6675–89. doi:10.1021/ie900015b.
   Web of Science ®Google Scholar
• Chen, L., Z. Yuan, J. Gao, J. Xu, Y. Zhang, and G. Liu. 2021. A novel predictive model of mixed oil length of products pipeline driven by traditional model and data. Journal of Petroleum Science and Engineering 205:108787. doi:10.1016/j.petrol.2021.108787.
   Web of Science ®Google Scholar
• Ekambara, K, and J. B. Joshi. 2003. Axial mixing in pipe flows: Turbulent and transition regions. Chemical Engineering Science 58 (12):2715–24. doi:10.1016/S0009-2509(03)00102-7.
   Web of Science ®Google Scholar
• Goldschmidt, V. W, and M. K. Householder. 1969. Longitudinal dispersion for turbulent flow in pipes. Industrial & Engineering Chemistry Fundamentals 8 (1):172–3. doi:10.1021/i160029a030.
   Google Scholar
• Gong, J., Q. Wang, W. Wang, and Y. Guo. 2010. The calculation method of mixing volume in a products pipeline. 8th International Pipeline Conference. Alberta, Canada, September 27. doi:10.1115/IPC2010-31462.
   Google Scholar
• Greenwood, M. S, and J. A. Bamberger. 2004. Self-Calibrating sensor for measuring density through stainless steel pipeline wall. Journal of Fluids Engineering 126 (2):189–92. doi:10.1016/S0041-624X(02)00153-1.
   Web of Science ®Google Scholar
• Greenwood, M. S, and J. Bamberger. 2002. Ultrasonic sensor to measure the density of a liquid or slurry during pipeline transport. Ultrasonics 40 (1-8):413–7. doi:10.1115/1.1677462
   PubMed Web of Science ®Google Scholar
• Greenwood, M. S., D. J. Adamson, and L. J. Bond. 2006. Measurement of the viscosity density product using multiple reflections of ultrasonic shear horizontal waves. Ultrasonics 44: E 1031–e1036. doi:10.1016/j.ultras.2006.05.093.
   Web of Science ®Google Scholar
• Hawkins, C., L. Angheluta, M. Krotkiewski, and B. Jamtveit. 2016. Reynolds number dependence of the longitudinal dispersion in turbulent pipe flow. Physical Review. E 93:043119. doi:10.1103/PhysRevE.93.043119.
   PubMed Web of Science ®Google Scholar
• Helge, H., L. Christian, and R. Henrik. 2011. Operator splitting for partial differential equations with burgers nonlinearity. Mathematics of Computation 82:281. doi:10.1090/S0025-5718-2012-02624-X.
   Web of Science ®Google Scholar
• Holman, J. P. 2012. Experimental methods for engineers. Singapore: McGraw-Hill. Google Books.
   Google Scholar
• Horner, J. W. 2008. Modeling multi-product pipeline hydraulics with a spreadsheet. 7th International Pipeline Conference. Alberta, Canada, September 29. doi:10.1115/IPC2008-64106.
   Google Scholar
• Hsu, C. S, and P. R. Robinson. 2017. Springer handbook of petroleum technology. Cham: Springer. doi:10.1007/978-3-319-49347-3.
   Google Scholar
• Hull, D. E, and J. W. Kent. 1952. Radioactive tracers to mark interfaces and measure intermixing in pipelines. Industrial & Engineering Chemistry 44 (11):2745–50. doi:10.1021/ie50515a066.
   Google Scholar
• Jones, G. M., R. L. Sanks, G. Tchobanoglous, and B. E. Bosserman. 2008. Pumping station design. California: Butterworth-Heinemann. doi:10.1016/B978-1-85617-513-5.X5001-X.
   Google Scholar
• Kazys, R., R. Sliteris, R. Rekuviene, E. Zukauskas, and L. Mazeika. 2015. Ultrasonic technique for density measurement of liquids in extreme conditions. Sensors (Basel, Switzerland) 15 (8):19393–415. doi:10.3390/s150819393.
   PubMed Web of Science ®Google Scholar
• Kirschstein, T. 2018. Planning of multi-product pipelines by economic lot scheduling models. European Journal of Operational Research 264 (1):327–39. doi:10.1016/j.ejor.2017.06.014.
   Web of Science ®Google Scholar
• Levenspiel, O. 1958. Longitudinal mixing of fluids flowing in circular pipes. Industrial & Engineering Chemistry 50 (3):343–6. doi:10.1021/ie50579a034.
   Web of Science ®Google Scholar
• Liang, Y., M. Li, and J. Li. 2012. Hydraulic model optimization of a multi-product pipeline. Petroleum Science 9 (4):521–6. doi:10.1007/s12182-012-0237-2.
   Web of Science ®Google Scholar
• Luo, H., Y. Li, and H. Wang. 2014. A universal semi-analytic model for axial mixing in a straight pipe. International Mechanical Engineering Congress. Quebec, Canada, November 14. doi:10.1115/IMECE2014-37351.
   Google Scholar
• Martins, N., N. Carrico, H. Ramos, and D. Covas. 2014. Velocity distribution in pressurized pipe flow using CFD: Accuracy and mesh analysis. Computers & Fluids 105:218–30. doi:10.1016/j.compfluid.2014.09.031.
   Web of Science ®Google Scholar
• Menon, E. S. 2004. Liquid pipeline hydraulics. Boca Raton: CRC Press. doi:10.1201/9780203021385.
   Google Scholar
• Menon, E. S., H. Ozanne, B. Bubar, W. Bauer, and G. Wininger. 2011. Pipeline planning and construction field manual. Houston: Gulf Professional. doi:10.1016/C2009-0-63837-X.
   Google Scholar
• Mikhail, V. L. 2008. Modeling of oil product and gas pipeline transportation. Berlin: Wiley-VCH. doi:10.1002/9783527626199.
   Google Scholar
• Mohitpour, M., M. S. Yoon, and J. H. Russell. 2012. Hydrocarbon liquid transmission pipeline and storage systems: Design and operation. New York: ASME Press. doi:10.1115/1.860007.
   Google Scholar
• Moradi, S., S. A. MirHassani, and F. Hooshmand. 2019. Efficient decomposition-based algorithm to solve long-term pipeline scheduling problem. Petroleum Science 16 (5):1159–75. doi:10.1007/s12182-019-00359-3.
   Web of Science ®Google Scholar
• Omer, R. B., E. Bashier, and I. Arbab. 2017. Numerical solutions of a system of ODEs based on lie-trotter and strange operator-splitting methods. Universal Journal of Computational Mathematics 5 (2):20–4. doi:10.13189/ujcmj.2017.050202.
   Google Scholar
• Patrachari, R, and A. Johannes. 2012. A conceptual framework to model interfacial contamination in multiproduct petroleum pipelines. International Journal of Heat and Mass Transfer 55 (17-18):4613–20. doi:10.1016/j.ijheatmasstransfer.2012.04.017.
   Web of Science ®Google Scholar
• Pharris, T. C, and R. L. Kopla. 2008. Overview of the design, construction, and operation of interstate liquid petroleum pipelines. Technical Report, USA: Argonne National Lab. doi:10.2172/925387.
   Google Scholar
• Pienaar, W. J. 2010. Logistics aspects of petroleum pipeline operations. Transport and Supply Chain Managment 4 (1):69. doi:10.4102/jtscm.v4i1.69.
   Google Scholar
• Puri, A. N., C. Y. Kuo, and R. S. Chapman. 1983. Turbulent diffusion of mass in circular pipe flow. Applied Mathematical Modelling 7 (2):135–8. doi:10.1016/0307-904X(83)90125-7.
   Web of Science ®Google Scholar
• Rachid, B., H. Carneiro, and R. Baptista. 2002. Prediction mixing volumes in serial transport in pipelines. Journal of Fluids Engineering 124 (2):528–34. doi:10.1115/1.1459078.
   Web of Science ®Google Scholar
• Reichardt, H. 1951. Complete representation of the turbulent velocity distribution in smooth pipes. Journal of Applied Mathematics and Mechanics 31 (7):208–19. doi:10.1002/zamm.19510310704.[Mismatch
   Google Scholar
• Rudraiah, C, and N. Ng. 2008. Convective diffusion in steady flow through a tube with a retentive and absorptive wall. Physics of Fluids 20 (7):073604–31. doi:10.1063/1.2958322.
   Web of Science ®Google Scholar
• Sadaf, M. 2019. Interface management during transportation of products through multi-product petroleum pipelines without kerosene plug. Journal of the Institution of Engineers (India): Series C 100 (3):587–90. doi:10.1007/s40032-018-0479-x.
   Google Scholar
• Sepehr, H., P. Nikrityuk, D. Breakey, and R. Sanders. 2019. Numerical study of crude oil batch mixing in a long channel. Petroleum Science 16 (1):187–98. doi:10.1007/s12182-018-0276-4.
   PubMed Web of Science ®Google Scholar
• Sheldon, J. W., K. A. Hardy, and P. Kehler. 1991. Convective diffusion of a solute in pipe flow. International Journal of Multiphase Flow 17 (3):415–20. doi:10.1016/0301-9322(91)90008-Q.
   Web of Science ®Google Scholar
• Shen, Y, and D. Mu. 2018. Evaluation and optimization of operation efficiency of oil transfer depot. AIP Conference Proceeding, 20009. doi:10.1063/1.5075649.
   Google Scholar
• Shongsheng, D, and P. Jianing. 1998. Application of convection-diffusion equation to the analyses of contamination between batches in multi-products pipeline transport. Applied Mathematics and Mechanics 19 (8):757–64. doi:10.1007/BF02457750.
   Google Scholar
• Sjenitzer, F. 1958. How much do products mix in a pipeline? Petroleum Engineering 30: 31–34.
   Google Scholar
• Sorg, L. V, and R. E. Dickey. 1948. Color contamination of petroleum products transported by pipeline. Industrial & Engineering Chemistry 40 (11):2163–6. doi:10.1021/ie50467a031.
   Google Scholar
• Szymczak, P, and A. J. Ladd. 2003. Boundary conditions for stochastic solutions of the convection-diffusion equation. Physical Review. E, Statistical, Nonlinear, and Soft Matter Physics 68 (3 Pt 2):036704–7. doi:10.1103/PhysRevE.68.036704
   PubMed Web of Science ®Google Scholar
• Taylor, G. 1954. The dispersion of matter in turbulent flow through a pipe. Proceedings of the Royal Society 223:446–68. doi:10.1098/rspa.1954.0130.
   Web of Science ®Google Scholar
• Tichacek, L. J., C. H. Barkelew, and T. Baron. 1957. Axial mixing in pipes. AIChE Journal 3 (4):439–42. doi:10.1002/aic.690030404.
   Web of Science ®Google Scholar
• Truong, Y. K, and M. Sarfraz. 2018. Topics in splines and applications. London: IntechOpen. doi:10.5772/intechopen.68737.
   Google Scholar
• Udoetok, E. S, and A. N. Nguyen. 2009. A disc pig model for estimating the mixing volumes between the product batches in multi-product pipelines. Pipeline Engineering 8 (3):195–204.
   Google Scholar
• Wang, W. 2003. The alternating segment Crank-Nicolson method for solving convection-diffusion equation with variable coefficient. Applied Mathematics and Mechanics 24: 32–34. doi:10.1007/BF02439375.
   Google Scholar
• Widiatmojo, A., K. Sasaki, N. Widodo, and Y. Sugai. 2013. Discrete tracer point method to evaluate turbulent diffusion in circular pipe flow. Journal of Flow Control, Measurement & Visualization 01 (02):57–68. doi:10.4236/jfcmv.2013.12008.
   Google Scholar
• Zhao, L., J. Derksen, and R. Gupta. 2010. Simulations of axial mixing of liquids in a long horizontal pipe for industrial applications. Energy & Fuels 24 (11):5844–50. doi:10.1021/ef100846r.
   Web of Science ®Google Scholar
• Zhou, F., G. Sun, X. Han, Y. Zhang, and W. Bi. 2018. Experimental and CFD study on effects of spiral guidevanes on cyclone performance. Advanced Powder Technology 29 (12):3394–403. doi:10.1016/j.apt.2018.09.022.
   Web of Science ®Google Scholar