The Modelling of the Urea Fertilizer Dissolution Process in Finite/Infinite Volumes of Water

Document Type : Research Article


1 Department of Chemical Engineering, Faculty of Engineering, University of Mohaghegh Ardabili, Ardabil, I.R. IRAN

2 Department of Chemical Engineering, Faculty of Engineering, RMIT University, Melbourne, AUSTRALIA


This research aims to provide a model to investigate the impact of some parameters such as impeller speed, temperature, and solid concentration on mass transfer coefficient and the dissolution rate of urea fertilizer in the water. To study the effect of solid concentration two models are presented for finite and infinite-volume fluids using mass balance. Then the urea-water mass transfer coefficient was calculated at various impeller speeds and temperatures by measuring the time to complete dissolution. To investigate the effect of impeller speed and turbulence on the mass transfer coefficient, the impeller speed and Reynolds number were set in a range of 10-50 rpm and 300-3000, respectively. The Schmidt number also was used to study the effect of temperature on the mass transfer coefficient in the range of 5-25 °C. The results show that in both finite and infinite fluid volumes, at a constant impeller speed with decreasing Schmidt number, and at a constant temperature with increasing Reynolds number, the mass transfer coefficient, and mass transfer rate increase. Furthermore, four models are presented for mass transfer coefficient in finite and infinite volume, which that shows the mass transfer coefficient and release rate in finite volume were lower than that of infinite volume at a constant impeller speed and temperature.


Main Subjects

[1] Zych D., Stańczyk Ł., Kalisz I., Żak K., Pankalla E., New Methods for Determination of Composition of Urea-Ammonium Nitrate Solution-Control of the Final Product, Int. J. Res.  Chem. Environ. (IJRCE), 7(4): 23-27 (2017).
[2] Trenkel M.E., "Slow-and Controlled-Release and Stabilized Fertilizers: An Option for Enhancing Nutrient Use Efficiency in Agriculture", IFA, International Fertilizer Industry Association (2010).
[3] Cortese-Krott M.M., Fernandez B.O., Kelm M., Butler A.R., Feelisch M., On the Chemical Biology of the Nitrite/Sulfide Interaction, Nitric Oxide, 46: 14-24 (2015).
[4] Costa P., Lobo J.M.S., Modeling and Comparison of Dissolution Profiles, Eur. J.  Pharm. Sci., 13(2): 123-133 (2001).
[5] Varadachari C., "Slow-release and Controlled-release Nitrogen Fertilizers", (Introduction): Indian Nitrogen Group, Society (2010).
[6] Butler A., Nitrites and Nitrates In The Human Diet: Carcinogens or Beneficial Hypotensive Agents,
J. Ethnopharmacol.
, 167: 105-107 (2015).
[7] Sayadi M., Farasati M., G Mahmoodlu M., Rostami F., Removal of Nitrate, Ammonium, and Phosphate from Water Using Conocarpus and Paulownia Plant Biochar, Iran. J. Chem. Chem. Eng. (IJCCE), 39(4): 205-222 (2020).
[8] Darvish M., Moradi Dehaghi S., Taghavi L., Karbassi A.R., Removal of Nitrate Using Synthetic Nano Composite ZnO/Organoclay: Kinetic and Isotherm Studies, Iran. J. Chem. Chem. Eng. (IJCCE), 39(1): 105-118 (2020).
[9] Zare L., Ghasemi-Fasaei R., Investigation of Equilibrium Isotherm and Kinetic Modeling to Asses Sorption Characteristics of Nitrate onto Palm Leaf Biochar, Iran. J. Chem. Chem. Eng. (IJCCE), 38(5): 143-153 (2019).
[10] Shaviv A., Advances in Controlled-Release Fertilizers, Adv. Agron., 71: 1-49 (2001).
[12] Trinh T.H., Kushaari K., Shuib A.S., Ismail L., Azeem B., Modelling the Release of Nitrogen from Controlled-Release Fertilizer: Constant and Decay Release, Biosyst. Eng., 130: 34-42 (2015).
[13] Basu S., Kumar N., Srivastava J., Modeling NPK Release From Spherically Coated Fertilizer Granules, Simul. Model. Pract. Theory., 18(6): 820-835 (2010).
[14] Du C., Zhou J., Shaviv A., Wang H., Mathematical Model for Potassium Release from Polymer- Coated Fertilizer, Biosyst. Eng., 88(3): 395-400 (2004).
[15] Shaviv A., Raban S., Zaidel E., Modeling Controlled Nutrient Release from a Population of Polymer-Coated Fertilizers: Statistically Based Model for Diffusion Release, Environ. Sci. Technol., 37(10): 2257-2261 (2003).
[16] Basu S., Kumar N., Mathematical Model and Computer Simulation for Release of Nutrients from Coated Fertilizer Granules, Math. Comput. Simul., 79(3): 634-646 (2008).
[17] Moradi S., Shayesteh K., Behboodi., G Preparation and Characterization of Biodegradable Lignin-Sulfonate Nanoparticles Using the Microemulsion Method to Enhance the Acetylation Effi Ciency of Lignin-Sulfonate, Int. J. Biol. Macromol., 160(2020): 632-641 (2020).
[18] Rice R., Jones P., Complete Dissolution of Spherical Particles in Free-Fall, Chem. Eng. Sci., 34(6): 847-852 (1979).
[19] Rice R.G., Transpiration Effects in Solids Dissolution, Chem. Eng. Sci., 37(10): 1465-1469 (1982).
[20] Rice R., Do D., Dissolution of a Solid Sphere in an Unbounded, Stagnant Liquid, Chem. Eng. Sci., 61(2): 775-778 (2006).
[21] Petrescu S., Petrescu J., Lisa C., Mass Transfer at Solid Dissolution, Chem. Eng. J., 66(1): 57-63 (1997).
[22] Paul D.R., Harris F.W., “Controlled Release Polymeric Formulations", American Chemical Society, (Chapter1) (1976).
[23] Fernández‐Pérez M., Garrido‐Herrera F., González‐Pradas E., Villafranca‐Sánchez M., Flores‐Céspedes F., Lignin and Ethylcellulose as Polymers in Controlled Release Formulations of Urea, J. Appl. Polym. Sci., 108(6): 3796-3803 (2008).
[24] Doan H.D., Trass O., Fayed M.E., Mass Transfer from Spherical Particles and Reservoirs into Quiescent Liquids, Can. J. Chem. Eng., 76(5): 893-901 (1998).
[25] Laycock A., "Irrigation Systems: Design, Planning and Construction", Wallingford, UK, Cabi, (Chapter10) (2010).
[26] Gosting L.J., Akeley D.F., A Study of the Diffusion of Urea in Water At 25° with the Gouy Interference Method1, J. Am. Chem. Soc., 74(8): 2058-2060 (1952).
[27] Wagenet R., Biggar J., Nielsen D., Tracing the Transformations of Urea Fertilizer During Leaching, Soil. Sci. Soc. Am. J., 41(5): 896-902 (1977).
[28] Bong E.Y., Eshtiaghi N., Wu J., Parthasarathy R., Optimum Solids Concentration for Solids Suspension and Solid-Liquid Mass Transfer in Agitated Vessels, Chem. Eng. Res. Des., 100: 148-156 (2015).
[29] Shiba R., Uddin M.A., Kato Y., Kitamura S.-y., Solid/Liquid Mass Transfer Correlated to Mixing Pattern in a Mechanically-Stirred Vessel, ISIJ. Int., 54(12): 2754-2760 (2014).
[30] Sykes P., Gomezplata A., Particle Liquid Mass Transfer in Stirred Tanks, Can. J. Chem. Eng., 45(4): 189-196 (1967).
[31] Yu C., Parthasarathy R., Wu J., Eshtiaghi N., "Effect of Solids Concentration on Solid-Liquid Mass Transfer in an Agitated Dissolution System", in Chemeca, Quality of Life Through Chemical Engineering: 23-26 September 2012, Wellington New Zealand (2012).
[32] Sensel M.E., Myers K.J., Add Some Flavor to Your Agitation Experiment, Chem. Eng. Educ., 26(3): 156-159 (1992).
[33] Miller D.N., Scale-up of Agitated Vessels, Mass Transfer from Suspended Solute Particles, Ind. Eng. Chem. Process. Des. Dev., 10(3): 365-375 (1971).
[34] Boon-Long S., Laguerie C., Couderc J., Mass Transfer from Suspended Solids to a Liquid in Agitated Vessels, Chem. Eng. Sci., 33(7): 813-819 (1978).
[35] Kalaga D.V., Dhar A., Dalvi S.V., Joshi J.B., Particle-Liquid Mass Transfer in Solid–Liquid Fluidized Beds, Chem. Eng. J., 245: 323-341 (2014).
[36] Bong E., "Solid-Liquid Mass Transfer in Agitated Vessels with High Solids Concentration", School of Civil, Environmental and Chemical Engineering, RMIT University (2013).
[37] Bilbao L., Ortueta M., Mijangos F., Effect of Concentration and Temperature on Mass Transfer in Metal Ion Exchange, Ind. Eng. Chem. Res., 55(27): 7287-7295 (2016).
[39] Pinck L., Kelly M.A., The Solubility of Urea in Water, J. Am. Chem. Soc., 47(8): 2170-2172 (1925).
[40] Fedors R., Relationships between Viscosity and Concentration for Newtonian Suspensions, J. Colloid. Interface. Sci., 46: 545-547 (1974).
[43] Rakymkul Y., "Solubilities and Mass Transfer Coefficients of Gases, i. Heavy Synthetic Hydrocarbon Liquids", University of Pittsburgh: Pittsburgh, USA (2012).
[44] Treybal R.E., "Mass Transfer Operations".  McGraw Hil, New York (1980).
[45] Hassanvand A., Hashemabadi S.H., Direct Numerical Simulation of Mass Transfer from Taylor Bubble Flow Through a Circular Capillary, Int. J. Heat. Mass. trans., 55(21-22): 5959-5971 (2012).
[46] Doran P.M., "Bioprocess Engineering Principles", Elsevier: Academic press (1995).
[47] Nienow A., Dissolution Mass Transfer in a Turbine Agitated Baffled Vessel, Can. J. Chem. Eng., 47(3): 248-258 (1969).
[48] Harriott P., Mass Transfer to Particles: Part I. Suspended in Agitated Tanks, AIChE. J., 8(1): 93-101 (1962).
[49 Barker J.J., Treybal R.E., Mass Transfer Coefficients For Solids Suspended in Agitated Liquids, AIChE. J., 6(2): 289-295 (1960).
[50] Lal P., Kumar S., Upadhyay S.N., Upadhya Y.D., Solid-Liquid Mass Transfer in Agitated Newtonian and Non-Newtonian Fluids, Ind. Eng. Chem. Res., 27(7): 1246-1259 (1988).
[51] Livingston A.., Chase H., Liquid-Solid Mass Transfer in a Three-Phase Draft Tube Fluidized Bed Reactor, Chem. Eng. Commun., 92(1): 225-244 (1990).
[52] Pangarkar V., Yawalkar A., Sharma M., Beenackers A., Particle-Liquid Mass Transfer Coefficient in Two-/Three-Phase Stirred Tank Reactors, Ind. Eng. Chem. Res., 41(17): 4141-4167 (2002).
[53] Kasat G.R.., Pandit A.B., Review on Mixing Characteristics in Solid‐Liquid and Solid‐Liquid‐Gas Reactor Vessels, Can. J. Chem. Eng., 83(4): 618-643 (2005).
[54] Kato Y., Hiraoka S., Tada Y., Nomura T., Solid-Liquid Mass Transfer in a Shaking Vessel for a Bioreactor with “Current Pole”, Can. J. Chem. Eng., 76(3): 441-445 (1998).