References

  1. J. Makinia, S.A. Wells, Evaluation of empirical formulae for estimation of the longitudinal dispersion in activated sludge reactors, Water Res., 39 (2005) 1533–1542.
  2. B. De Clercq, F. Coen, B. Vanderhaegen, P.A. Vanrolleghem, Calibrating simple models for mixing and flow propagation in waste water treatment plants, Water Sci. Technol., 39 (4) (1999) 61–69.
  3. Y. Gao, F.J. Muzzio, M.G. Ierapetritou, A review of the residence time distribution (RTD) applications in solid unit operations, Powder Technol., 228 (2012) 416–423.
  4. D.C. de Freitas, F.H. Passig, C. Kreutz, K.Q. de Carvalho, E. J. Arantes, S.D. Gomes, Effect of hydraulic retention time on hydrodynamic behavior of anaerobic-aerobic fixed bed reactor treating cattle slaughterhouse effluent, Acta Sci. Techol., 39 (4) (2017) 469–476.
  5. O.N. Manjrekar, Y. Sun, L. He, Y.J. Tang, M.P. Dudukovic, Hydrodynamics and mass transfer coefficients in a bubble column photo-bioreactor, Chem. Eng. Sci., 168 (2017) 55–66.
  6. J.A. Jáuregui-Jáuregui, H.O. Méndez-Acosta, V. González-Álvarez, R. Snell-Castro, V. Alcaraz-González, J.J. Godon, Anaerobic treatment of tequila vinasses under seasonal operating conditions: Start-up, normal operation and restart-up after a long stop and starvation period, Bioresour. Technol., 168 (2014) 33–40.
  7. M. Mulas, S. Tronci, F. Corona, H. Haimi, P. Lindell, M. Heinonen, R. Vahala, R. Baratti, Predictive control of an activated sludge process: An application to the Viikinmäki wastewater treatment plant, J. Process Control, 35 (2015) 89–100.
  8. M. Rajasimman, S.V. Babu, N. Rajamohan, Biodegradation of textile dyeing industry wastewater using modified anaerobic sequential batch reactor – Start-up, parameter optimization and performance analysis, J. Tai. Inst. Chem. Eng., 72 (2017) 171–181.
  9. X. Tang, Y. Guo, B. Jiang, S. Liu, Metagenomic approaches to understanding bacterial communication during the anammox reactor start-up, Water Res., 136 (2018) 95–103.
  10. P.V. Danckwerts, Continuous flow systems. Distribution of residence times, Chem. Eng. Sci., 2 (1) (1953) 1–13.
  11. R.B. MacMullin, M. Weber, The theory of short-circuiting in continuous-flow mixing vessels in series and kinetics of chemical reactions in such systems. Trans. AIChE, 31 (2) (1935) 409–458.
  12. O. Levenspiel, Chemical reaction engineering, 3rd ed., Wiley & Sons Inc., New York, 1999.
  13. G.F. Froment, K.B. Bischoff, Non-steady state behavior of fixed bed catalytic reactors due to catalyst fouling, Chem. Eng. Sci., 16 (1961) 189–201.
  14. P.A.G. Encina, F. Fernández-Polanco, Behaviour of an anaerobic expanded bed reactor in non-steady state conditions, Wat. Res., 21 (11) (1987) 1329–1334.
  15. S. Claudel, J.P. Leclerc, L. Tétar, H.G. Lintz, A. Bernard, Recent extensions of the residence time distribution concept: unsteady state conditions and hydrodynamic model developments, Braz. J. Chem. Eng., 17 (4–7) (2000) 947–954.
  16. J.G. Boelhouwer, H.W. Piepers, A.A.H. Drinkenburg, Nonsteady state operation of trickle-bed reactors, Stud. Surf. Sci. Catal., 133 (2001) 231–238.
  17. S. Yang, X. Li, Influences of extracellular polymeric substances (EPS) on the characteristics of activated sludge under nonsteady- state conditions, Proc. Biochem., 44 (2009) 91–96.
  18. E.B. Nauman, Residence time distribution theory for unsteady stirred tank reactors, Chem. Eng. Sci., 24 (1969) 1461–1470.
  19. A. J. Niemi, Residence time distributions of variable flow process, Int. J. Ap. Rad. Iso., 28 (1977) 855–860.
  20. A.J. Niemi, Z. Kai, T. Jovan, M.J. Griffith, Tracer testing of processes under variable flow and volume, Nukleonika 43 (1) (1998) 73–94.
  21. J. Fernández-Sempere, R. Font-Montesinos, O. Espejo-Alcaraz, Residence time distribution for unsteady-state systems, Chem. Eng. Sci., 50 (1995) 223–230.
  22. L. Furman, J.P. Leclerc, Z. Stegowski, Tracer investigation of a packed column under variable flow. Chem. Eng. Sci., 60 (2005) 3043–3048.
  23. E. Domínguez, F. Ardila, S. Bustamante, System Solver: an open source tool for mathematically modelling dynamical systems, Ing. Inv., 30 (3) (2010) 157–164.
  24. Isee systems, Inc. 2018. STELLA: System Thinking for Education and Research. Availabe at: https://www.iseesystems.com/.
  25. The Math Works, Inc. 2018. SIMULINK: Simulation and Model Based Design. Available at: https://www.mathworks.com/products/simulink.html.
  26. Ventana Systems, Inc. 2018. Vensim industrial simulation software. Available at: http://vensim.com/.
  27. R.B. Chowdhury, G.A. Moore, A.J. Weatherley, M. Arora, A novel substance flow analysis model for analysing multi-year phosphorus flow at the regional scale, Sci. Total Environ., 572 (2016) 1269–1280.
  28. U.S. McKnight, S.G. Funder, J.J. Rasmussen, M. Finkel, P.J. Binning, P.L. Bjerg, An integrated model for assessing the risk of TCE groundwater contamination to human receptors and surface water ecosystems, Ecol. Eng., 36 (2010) 1126–1137.
  29. J.C.S.I. Gonçalves, M.F. Giorgetti, Mathematical model for the simulation of water quality in rivers using the Vensim PLE® software, J. Urb. Environ. Eng., 7 (1) (2013) 48–63.
  30. R. Chaves, D. López, F. Macías, J. Casares, C. Monterroso, Application of system dynamics technique to simulate the fate of persistent organic pollutants in soils, Chemosphere, 90 (2013) 2428–2434.
  31. H. Ibrahim, M. Pansu, D. Blavet, A. Hatira, P. McDonald, M. Bernoux, J. Drevon, Modelling the continuous exchange of carbon between living organisms, the soil and the atmosphere, Plant Soil, 398 (2016) 381–397.
  32. J. Álvarez, M. Roca, C. Valderrama, J.L. Cortina, A phosphorous flow analysis in spain, Sci. Total Environ., 612 (2018) 995– 1006.
  33. F.R.A. Nascimento, A. Kiperstok, J. Martín, J. Morató, E. Cohim, Decision support system for management of reactive nitrogen flows in wastewater system, Environ. Sci. Pollut. Res., 25 (2018) 8644–8653.
  34. P. Fleury, V. Plagnes, M. Bakalowicz, Modelling of the functioning of karst aquifers with a reservoir model: Application to Fontaine de Vaucluse (South of France), J. Hydrol., 345 (2007) 38–49.
  35. A. Hartmann, M. Kralik, F. Humer, J. Lange, M. Weiler, Identification of a karst system’s intrinsic hydrodynamic parameters: upscaling from single springs to the whole aquifer, Environ. Earth Sci., 65 (2012) 2377–2389.
  36. Y. Chang, J. Wu, G. Jiang, Modeling the hydrological behavior of a karst spring using a nonlinear reservoir-pipe model, Hidrog. J., 23 (2015) 901–914.
  37. G.M. von Medeazza, V. Moreau, Modelling of water–energy systems. The case of desalination, Energy, 32 (2007) 1024–1031.
  38. O. Sahin, R. Siems, R.G. Richards, F. Helfer, R.A. Stewart, Examining the potential for energy-positive bulk-water infrastructure to provide long-term urban water security: A systems approach, J. Clean. Prod., 143 (2017) 557–566.
  39. A. Ghasemi, B. Saghafian, S. Golian, System dynamics approach for simulating water resources of an urban water system with emphasis on sustainability of groundwater, Environ. Earth Sci., 76 (637) (2017) 1–15.
  40. R. Li, P. Guo, J. Li, Regional water use structure optimization under multiple uncertainties based on water resources vulnerability analysis, Water Resour. Manage., 32 (2018) 1827–1847.
  41. K. Kontomaris, T.J. Hanratty, Effect of molecular diffusivity on turbulent diffusion in isotropic turbulence, Int. J. Heat Mass Transfer, 36 (5) (1993) 1403–1412.
  42. O. Levenspiel, W.K. Smith, Notes on the diffusion-type model for the longitudinal mixing of fluids in flow, Chem. Eng. Sci., 50 (24) (1995) 3891–3896.
  43. M.F. Edwards, J.F. Richardson, Gas dispersion in packed beds, Chem. Eng. Sci., 23 (2) (1968) 109–123.
  44. Z. Dou, Z. Zhou, J. Wang, Y. Huang, Roughness scale dependence of the relationship between tracer longitudinal dispersion and Peclet number in variable-aperture fractures, Hydrol. Processes, 32 (2018) 1461–1475.
  45. D. Dochain, Analysis of the multiplicity of steady-state profiles of two tubular reactor models, Comput. Chem. Eng., 114 (2018) 318–324.
  46. V.V. Oliveira, M.V. Mateus, J.C.S.I. Gonçalves, A.G. Utsumi, M. F. Giorgetti, Prediction of the longitudinal dispersion coefficient for small watercourses, Acta Sci. Techol., 39 (3) (2017) 291–299.
  47. S.C. Chapra, R.P. Canale, Numerical Methods for Engineers, McGrawHill, 6th ed, 2008.
  48. Metcalf, Eddy, Wastewater Engineering: Treatment and Reuse, McGrawHill, 4th ed, 2002.
  49. D.J.L. Costa, Mathematical model for hydrodynamic evaluation in non-steady state reactors. (in Portuguese). DSc. Thesis. EESC – USP, São Carlos, SP, Brazil, 2015. Available at: http://www.teses.usp.br/.
  50. M. Flury, T. Gimmi, Solute diffusion, in Methods of Soil Analysis, Part 4, Physical Methods, J.H. Dane, G.C. Topp, eds., 1323–1351, SSSA, Madison, WI, 2002.
  51. R.B. Bird, W.E. Stewart, E.N. Lightfoot, Thermal conductivity and the mechanisms of energy transport. In: Transport Phenomena (Chapter 9), 2nd ed, 2002.
  52. E. Bianchi, G. Groppi, W. Schwieger, E. Tronconi, H. Freund, Numerical simulation of heat transfer in the near-wall region of tubular reactors packed with metal open-cell foams, Chem. Eng. J., 264 (2015) 268–279.
  53. N. Amini, Y.A. Hassan, Experimental study of bypass flow in near wall gaps of a pebble bed reactor using hot wire anemometry technique, Ann. Nuc. Ener., 65 (2014) 60–71.