DOI: https://doi.org/10.15587/1729-4061.2018.145232

### Construction of a mathematical model of extraction process in the system "solid body ‒ liquid" in a microwave field

Boris Kotov, Valentina Bandura

#### Abstract

We have analyzed the extraction process in the technology of oilseed processing. This paper describes the original provisions, specificity, modern scientific schools, and the level of representation of the classic extraction process. The specificity of mathematical modeling of the extraction process, given the introduction of an additional driving force that significantly affects the kinetics of extraction in an electromagnetic field of ultra-high frequency, is considered from the classical theory of the process.

We have constructed the extraction kinetics calculation formulae, in microwave field, which develop the theory of extraction kinetics in an electromagnetic field. The paper gives an analysis of variants for the representation of a mathematical notation of the extraction process of disperse materials in an electromagnetic field of ultra-high frequency. A complete model of the mass exchange processes during extraction in a microwave field in the differential form will make it possible to generate conditions for conducting comprehensive experimental studies, which would fully define the extraction process of oilseeds.

We have theoretically substantiated the process of heat and mass exchange between the all defining objects inside an extraction unit with an electromagnetic field of ultra-high frequency. Based on material balances, we derived equations describing the basic dynamic characteristics of oil extraction mode in an extraction unit. Since the precise analytical solution to the presented mathematical model in the form of a system of differential equations in particular derivatives does not exist, the approximate solution has been proposed. It makes it possible to identify the distribution of an extractant depending on the size of fractions of raw materials, the existence and magnitude of power of the pulsed electromagnetic field of ultra-high frequency, the extractant's hydro-module, temperature, solvents, for any point in time.

Based on the experimental research into extraction of oilseed material, it was established that under the action of microwave radiation a value for the mass release coefficient during extraction of oilseed raw materials grows by an order of magnitude (β=1·10-5) compared to extraction without the effect of MW field (β=1·10-6). Oil extraction under the action of a microwave field increases to 30 %, while electricity consumption decreases by 93‒97 %. The application of a microwave field would not only improve production efficiency, but reduce energy costs during process by an order of magnitude

#### Keywords

extraction; microwave field; heat and mass exchange; material balance; differential equations

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#### References

Romankov, P. G., Frolov, V. F. (1990). Teploobmennye processy himicheskoy tekhnologii. Leningrad: Himiya, 384.

Aksel'rud, G. A., Lysyanskiy, V. M. (1974). Ekstragirovanie (sistema tverdoe telo – zhidkost'). Leningrad: Himiya, 256.

Beloborodov, V. V. (1999). Ekstragirovanie iz tverdyh materialov v elektromagnitnom pole sverhvysokih chastot. Inzhenerno-fizicheskiy zhurnal, 72 (1), 141–146.

Burdo, O. G. (2013). Pishchevye nanoenergotekhnologii. Herson: Izd. Grin' D.S., 304.

Burdo, O. G. (2007). Ekstragirovanie v sisteme «kofe – voda». Odessa: «TES», 176.

Toda, T. A., Sawada, M. M., Rodrigues, C. E. C. (2016). Kinetics of soybean oil extraction using ethanol as solvent: Experimental data and modeling. Food and Bioproducts Processing, 98, 1–10. doi: https://doi.org/10.1016/j.fbp.2015.12.003

So, G. C., Macdonald, D. G. (1986). Kinetics of oil extraction from canola (rapeseed). The Canadian Journal of Chemical Engineering, 64 (1), 80–86. doi: https://doi.org/10.1002/cjce.5450640112

Perez, E. E., Carelli, A. A., Crapiste, G. H. (2011). Temperature-dependent diffusion coefficient of oil from different sunflower seeds during extraction with hexane. Journal of Food Engineering, 105 (1), 180–185. doi: https://doi.org/10.1016/j.jfoodeng.2011.02.025

Rakotondramasy-Rabesiaka, L., Havet, J.-L., Porte, C., Fauduet, H. (2010). Estimation of effective diffusion and transfer rate during the protopine extraction process from Fumaria officinalis L. Separation and Purification Technology, 76 (2), 126–131. doi: https://doi.org/10.1016/j.seppur.2010.09.030

Seikova, I., Simeonov, E., Ivanova, E. (2004). Protein leaching from tomato seed–experimental kinetics and prediction of effective diffusivity. Journal of Food Engineering, 61 (2), 165–171. doi: https://doi.org/10.1016/s0260-8774(03)00083-9

Chan, C.-H., Yusoff, R., Ngoh, G.-C. (2014). Modeling and kinetics study of conventional and assisted batch solvent extraction. Chemical Engineering Research and Design, 92 (6), 1169–1186. doi: https://doi.org/10.1016/j.cherd.2013.10.001

Rogov, I. A., Nekrutman, C. B. (1986). Sverhchastotnyy nagrev pishchevyh produktov. Moscow: Agropromizdat, 350.

Burdo, O., Bandura, V., Kolianovska, L., Dukulis, I. (2017). Experimental research of oil extraction from canola by using microwave technology. Engineering for rural development, 296–302. doi: https://doi.org/10.22616/erdev2017.16.n056

Burdo, O., Bandura, V., Zykov, A., Zozulyak, I., Levtrinskaya, J., Marenchenko, E. (2017). Development of wave technologies to intensify heat and mass transfer processes. Eastern-European Journal of Enterprise Technologies, 4 (11 (88)), 34–42. doi: https://doi.org/10.15587/1729-4061.2017.108843

Burdo, O. G. (2005). Nanomasshtabnye effekty v pishchevyh tekhnologiyah. Inzhenerno-fizicheskiy zhurnal, 78 (1), 88–93.

Bandura, V. M., Kolyanovs'ka, L. M. (2013). Obrobka eksperimental'nih danih procesu ekstraguvannya roslinnih olіy mіkrohvil'ovim polem. Zbirnyk naukovykh prats Odeskoi natsionalnoi akademiyi kharchovykh tekhnolohiy, 43 (2), 66–69.

Lykov, A. V. (1967). Teoriya teploprovodnosti. Moscow: Vysshaya shkola, 590.

Lykov, A. V. (1971). Teplomassoobmen: spravochnik. Moscow: Energiya, 560.

Romanovskiy, S. G. (1969). Processy termicheskoy obrabotki i sushki v elektromagnitnyh ustanovkah. Minsk: Nauka i tekhnika, 348.

Rogov, I. A., Nekrutman, C. B., Lysov, G. V. (1981). Tekhnika sverhvysokochastotnogo nagreva pishchevyh produktov. Moscow: Leg. i pishch. prom-t', 199.

#### GOST Style Citations

Romankov P. G., Frolov V. F. Teploobmennye processy himicheskoy tekhnologii. Leningrad: Himiya, 1990. 384 p.

Aksel'rud G. A., Lysyanskiy V. M. Ekstragirovanie (sistema tverdoe telo – zhidkost'). Leningrad: Himiya, 1974. 256 p.

Beloborodov V. V. Ekstragirovanie iz tverdyh materialov v elektromagnitnom pole sverhvysokih chastot // Inzhenerno-fizicheskiy zhurnal. 1999. Vol. 72, Issue 1. P. 141–146.

Burdo O. G. Pishchevye nanoenergotekhnologii. Herson: Izd. Grin' D.S., 2013. 304 p.

Burdo O. G. Ekstragirovanie v sisteme «kofe – voda». Odessa: «TES», 2007. 176 p.

Toda T. A., Sawada M. M., Rodrigues C. E. C. Kinetics of soybean oil extraction using ethanol as solvent: Experimental data and modeling // Food and Bioproducts Processing. 2016. Vol. 98. P. 1–10. doi: https://doi.org/10.1016/j.fbp.2015.12.003

So G. C., Macdonald D. G. Kinetics of oil extraction from canola (rapeseed) // The Canadian Journal of Chemical Engineering. 1986. Vol. 64, Issue 1. P. 80–86. doi: https://doi.org/10.1002/cjce.5450640112

Perez E. E., Carelli A. A., Crapiste G. H. Temperature-dependent diffusion coefficient of oil from different sunflower seeds during extraction with hexane // Journal of Food Engineering. 2011. Vol. 105, Issue 1. P. 180–185. doi: https://doi.org/10.1016/j.jfoodeng.2011.02.025

Estimation of effective diffusion and transfer rate during the protopine extraction process from Fumaria officinalis L. / Rakotondramasy-Rabesiaka L., Havet J.-L., Porte C., Fauduet H. // Separation and Purification Technology. 2010. Vol. 76, Issue 2. P. 126–131. doi: https://doi.org/10.1016/j.seppur.2010.09.030

Seikova I., Simeonov E., Ivanova E. Protein leaching from tomato seed–experimental kinetics and prediction of effective diffusivity // Journal of Food Engineering. 2004. Vol. 61, Issue 2. P. 165–171. doi: https://doi.org/10.1016/s0260-8774(03)00083-9

Chan C.-H., Yusoff R., Ngoh G.-C. Modeling and kinetics study of conventional and assisted batch solvent extraction // Chemical Engineering Research and Design. 2014. Vol. 92, Issue 6. P. 1169–1186. doi: https://doi.org/10.1016/j.cherd.2013.10.001

Rogov I. A., Nekrutman C. B. Sverhchastotnyy nagrev pishchevyh produktov: ucheb. pos. Moscow: Agropromizdat, 1986. 350 p.

Experimental research of oil extraction from canola by using microwave technology / Burdo O., Bandura V., Kolianovska L., Dukulis I. // Engineering for rural development. 2017. P. 296–302. doi: https://doi.org/10.22616/erdev2017.16.n056

Development of wave technologies to intensify heat and mass transfer processes / Burdo O., Bandura V., Zykov A., Zozulyak I., Levtrinskaya J., Marenchenko E. // Eastern-European Journal of Enterprise Technologies. 2017. Vol. 4, Issue 11 (88). P. 34–42. doi: https://doi.org/10.15587/1729-4061.2017.108843

Burdo O. G. Nanomasshtabnye effekty v pishchevyh tekhnologiyah // Inzhenerno-fizicheskiy zhurnal. 2005. Vol. 78, Issue 1. P. 88–93.

Bandura V. M., Kolyanovs'ka L. M. Obrobka eksperimental'nih danih procesu ekstraguvannya roslinnih olіy mіkrohvil'ovim polem // Zbirnyk naukovykh prats Odeskoi natsionalnoi akademiyi kharchovykh tekhnolohiy. 2013. Issue 43 (2). P. 66–69.

Lykov A. V. Teoriya teploprovodnosti. Moscow: Vysshaya shkola, 1967. 590 p.

Lykov A. V. Teplomassoobmen: spravochnik. Moscow: Energiya, 1971. 560 p.

Romanovskiy S. G. Processy termicheskoy obrabotki i sushki v elektromagnitnyh ustanovkah. Minsk: Nauka i tekhnika, 1969. 348 p.

Rogov I. A., Nekrutman C. B., Lysov G. V. Tekhnika sverhvysokochastotnogo nagreva pishchevyh produktov: ucheb. pos. Moscow: Leg. i pishch. prom-t', 1981. 199 p.

Copyright (c) 2018 Boris Kotov, Valentina Bandura