Mathematical model for the particle size distribution of a kieselguhr filter granulation
Abstract
Diatomaceous Earth, also known as diatomite, diatomaceous silica, or kieselguhr is the material of natural origin which is composed of the skeletons of diatoms, single-celled algae, which are accumulated in huge beds. Some diatomite's are industrially processed and used for different applications most frequently as filter aid. Particle size distribution of any filter granulation, composed of these materials, has to be appropriately prepared. A mathematical model of particle size distribution of a kieselguhr granulation is presented in this paper and experimentally verified. Particle sizes of a kieselguhr granulation are measured by the microscopic morphometric method, ordinarily used in the experimental microbiology, and the empirical probability density function (pdf) of particle sizes is formulated Experimental pdf data are fitted according to the exponential function, which represents a solution of a developed model of differential equation. The fitting procedure followed the iterat...ive algorithm of Levenberg-Marquardt to adjust the parameter values. This way, an experimentally determined pdf can be approximated with an analytic function with a small number of constants in the adopted model of fit function. This approach facilitates further modeling and analysis of filtering mediums. Based on the particle sizes, pdf's of different kieselguhr, and perlite granulations, it is possible to determine an optimal medium mixture (containing different filtration granulations), depending of the filtration requirements.
Keywords:
Kieselguhr / probability density function / partial differential equation / fitting / exponential functionSource:
Metalurgia International, 2012, 17, 10, 192-197Publisher:
- Editura Stiintifica Fmr, Bucharest
Funding / projects:
- The Improvement and Preservation of Biotechnology Procedures for Rational Energy Use and Improvement of Agricultural Production Quality (RS-MESTD-Technological Development (TD or TR)-31051)
- Dynamic stability and instability of mechanical systems subjected to stochastic excitations (RS-MESTD-Basic Research (BR or ON)-174011)
- Pressure equipment integrity under simultaneous effect of fatigue loading and temperature (RS-MESTD-Technological Development (TD or TR)-35011)
- Development of methods and techniques for early diagnostic of cervical, colon, oral cavity cancer and melanoma based on a digital image and excitation-emission spectrum in visible and infrared domain (RS-MESTD-Integrated and Interdisciplinary Research (IIR or III)-41006)
- Functionalization of Nanomaterials for obtaining new contact lenses, and early diagnostics of diabetes (RS-MESTD-Integrated and Interdisciplinary Research (IIR or III)-45009)
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Institution/Community
Poljoprivredni fakultetTY - JOUR AU - Tomantschger, Kurt AU - Petrović, Dragan AU - Golubović, Zorana AU - Trisović, Nataša PY - 2012 UR - http://aspace.agrif.bg.ac.rs/handle/123456789/2944 AB - Diatomaceous Earth, also known as diatomite, diatomaceous silica, or kieselguhr is the material of natural origin which is composed of the skeletons of diatoms, single-celled algae, which are accumulated in huge beds. Some diatomite's are industrially processed and used for different applications most frequently as filter aid. Particle size distribution of any filter granulation, composed of these materials, has to be appropriately prepared. A mathematical model of particle size distribution of a kieselguhr granulation is presented in this paper and experimentally verified. Particle sizes of a kieselguhr granulation are measured by the microscopic morphometric method, ordinarily used in the experimental microbiology, and the empirical probability density function (pdf) of particle sizes is formulated Experimental pdf data are fitted according to the exponential function, which represents a solution of a developed model of differential equation. The fitting procedure followed the iterative algorithm of Levenberg-Marquardt to adjust the parameter values. This way, an experimentally determined pdf can be approximated with an analytic function with a small number of constants in the adopted model of fit function. This approach facilitates further modeling and analysis of filtering mediums. Based on the particle sizes, pdf's of different kieselguhr, and perlite granulations, it is possible to determine an optimal medium mixture (containing different filtration granulations), depending of the filtration requirements. PB - Editura Stiintifica Fmr, Bucharest T2 - Metalurgia International T1 - Mathematical model for the particle size distribution of a kieselguhr filter granulation EP - 197 IS - 10 SP - 192 VL - 17 UR - https://hdl.handle.net/21.15107/rcub_agrospace_2944 ER -
@article{ author = "Tomantschger, Kurt and Petrović, Dragan and Golubović, Zorana and Trisović, Nataša", year = "2012", abstract = "Diatomaceous Earth, also known as diatomite, diatomaceous silica, or kieselguhr is the material of natural origin which is composed of the skeletons of diatoms, single-celled algae, which are accumulated in huge beds. Some diatomite's are industrially processed and used for different applications most frequently as filter aid. Particle size distribution of any filter granulation, composed of these materials, has to be appropriately prepared. A mathematical model of particle size distribution of a kieselguhr granulation is presented in this paper and experimentally verified. Particle sizes of a kieselguhr granulation are measured by the microscopic morphometric method, ordinarily used in the experimental microbiology, and the empirical probability density function (pdf) of particle sizes is formulated Experimental pdf data are fitted according to the exponential function, which represents a solution of a developed model of differential equation. The fitting procedure followed the iterative algorithm of Levenberg-Marquardt to adjust the parameter values. This way, an experimentally determined pdf can be approximated with an analytic function with a small number of constants in the adopted model of fit function. This approach facilitates further modeling and analysis of filtering mediums. Based on the particle sizes, pdf's of different kieselguhr, and perlite granulations, it is possible to determine an optimal medium mixture (containing different filtration granulations), depending of the filtration requirements.", publisher = "Editura Stiintifica Fmr, Bucharest", journal = "Metalurgia International", title = "Mathematical model for the particle size distribution of a kieselguhr filter granulation", pages = "197-192", number = "10", volume = "17", url = "https://hdl.handle.net/21.15107/rcub_agrospace_2944" }
Tomantschger, K., Petrović, D., Golubović, Z.,& Trisović, N.. (2012). Mathematical model for the particle size distribution of a kieselguhr filter granulation. in Metalurgia International Editura Stiintifica Fmr, Bucharest., 17(10), 192-197. https://hdl.handle.net/21.15107/rcub_agrospace_2944
Tomantschger K, Petrović D, Golubović Z, Trisović N. Mathematical model for the particle size distribution of a kieselguhr filter granulation. in Metalurgia International. 2012;17(10):192-197. https://hdl.handle.net/21.15107/rcub_agrospace_2944 .
Tomantschger, Kurt, Petrović, Dragan, Golubović, Zorana, Trisović, Nataša, "Mathematical model for the particle size distribution of a kieselguhr filter granulation" in Metalurgia International, 17, no. 10 (2012):192-197, https://hdl.handle.net/21.15107/rcub_agrospace_2944 .