Modeling of temperature profile in semi-permeable membrane channel at non-isothermal conditions
We present a model for thermo- and pressure-driven membrane processes accompanied by transmembrane water and heat fluxes combined in a single unit. High-pressure channel (high-pressure control volume) is characterized by low operating temperature and vice versa. A symmetric plate-and-frame membrane...
| Main Authors: | , |
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| Format: | Article |
| Language: | English |
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Elsevier
2023-06-01
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| Series: | Results in Engineering |
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| Online Access: | http://www.sciencedirect.com/science/article/pii/S2590123023003067 |
| _version_ | 1797802712011636736 |
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| author | Daniel Oganesian Sergey Agashichev |
| author_facet | Daniel Oganesian Sergey Agashichev |
| author_sort | Daniel Oganesian |
| collection | DOAJ |
| description | We present a model for thermo- and pressure-driven membrane processes accompanied by transmembrane water and heat fluxes combined in a single unit. High-pressure channel (high-pressure control volume) is characterized by low operating temperature and vice versa. A symmetric plate-and-frame membrane channel was considered in this study. An elementary parallelepiped was selected as a control volume. Balance equations were written over the control volume. A membrane element was represented as a set of conjugate semipermeable volumes. The model is based on the following assumptions: (1) incompressible fluid under steady-state conditions; (2) trans-membrane water flux is opposed to transmembrane heat flux. Transverse velocity profile is approximated by Berman distribution; (3) the mechanisms of transverse transport include: convection resulting from pressure differences and conduction resulting from temperature gradients; (4) the thickness of thermal layer is equal to half height of the channel (δt=H). The temperature polarization (TP) module reveals high sensitivity to thermo-physical properties and hydrodynamics such as to the coefficient of thermal diffusivity a=λ/cρ and to the transverse velocity, V(z). We find that (a) variation of the coefficient of thermal diffusivity in liquid phase from a= 2.0 10−7 m2/s to a= 1.0 10−7 m2/s will reduce TP module from 0.96 to 0.91; (b) variation of transverse velocity at the membrane surface from 5.5 10−5 to 1.5 10−5 m/s can decrease of TP module from 0.95 to 0.79. The developed solution can be used as a sub-model for quantitative estimation of TP phenomena in thermo-driven membrane operations. It can be applied for analysis of pressure-driven processes at non-isothermal conditions and be used as a mathematical algorithm for process analysis and optimization. |
| first_indexed | 2024-03-13T05:10:50Z |
| format | Article |
| id | doaj.art-558e1c2e3beb4e51baf09a5f9fed602b |
| institution | Directory Open Access Journal |
| issn | 2590-1230 |
| language | English |
| last_indexed | 2024-03-13T05:10:50Z |
| publishDate | 2023-06-01 |
| publisher | Elsevier |
| record_format | Article |
| series | Results in Engineering |
| spelling | doaj.art-558e1c2e3beb4e51baf09a5f9fed602b2023-06-16T05:11:12ZengElsevierResults in Engineering2590-12302023-06-0118101179Modeling of temperature profile in semi-permeable membrane channel at non-isothermal conditionsDaniel Oganesian0Sergey Agashichev1Corresponding author.; R&D Center DEWA, PO Box 564, Dubai, United Arab EmiratesR&D Center DEWA, PO Box 564, Dubai, United Arab EmiratesWe present a model for thermo- and pressure-driven membrane processes accompanied by transmembrane water and heat fluxes combined in a single unit. High-pressure channel (high-pressure control volume) is characterized by low operating temperature and vice versa. A symmetric plate-and-frame membrane channel was considered in this study. An elementary parallelepiped was selected as a control volume. Balance equations were written over the control volume. A membrane element was represented as a set of conjugate semipermeable volumes. The model is based on the following assumptions: (1) incompressible fluid under steady-state conditions; (2) trans-membrane water flux is opposed to transmembrane heat flux. Transverse velocity profile is approximated by Berman distribution; (3) the mechanisms of transverse transport include: convection resulting from pressure differences and conduction resulting from temperature gradients; (4) the thickness of thermal layer is equal to half height of the channel (δt=H). The temperature polarization (TP) module reveals high sensitivity to thermo-physical properties and hydrodynamics such as to the coefficient of thermal diffusivity a=λ/cρ and to the transverse velocity, V(z). We find that (a) variation of the coefficient of thermal diffusivity in liquid phase from a= 2.0 10−7 m2/s to a= 1.0 10−7 m2/s will reduce TP module from 0.96 to 0.91; (b) variation of transverse velocity at the membrane surface from 5.5 10−5 to 1.5 10−5 m/s can decrease of TP module from 0.95 to 0.79. The developed solution can be used as a sub-model for quantitative estimation of TP phenomena in thermo-driven membrane operations. It can be applied for analysis of pressure-driven processes at non-isothermal conditions and be used as a mathematical algorithm for process analysis and optimization.http://www.sciencedirect.com/science/article/pii/S2590123023003067Temperature polarizationModelingPressure-driven membrane processesNon-isothermal conditionsSemi-permeable channel |
| spellingShingle | Daniel Oganesian Sergey Agashichev Modeling of temperature profile in semi-permeable membrane channel at non-isothermal conditions Results in Engineering Temperature polarization Modeling Pressure-driven membrane processes Non-isothermal conditions Semi-permeable channel |
| title | Modeling of temperature profile in semi-permeable membrane channel at non-isothermal conditions |
| title_full | Modeling of temperature profile in semi-permeable membrane channel at non-isothermal conditions |
| title_fullStr | Modeling of temperature profile in semi-permeable membrane channel at non-isothermal conditions |
| title_full_unstemmed | Modeling of temperature profile in semi-permeable membrane channel at non-isothermal conditions |
| title_short | Modeling of temperature profile in semi-permeable membrane channel at non-isothermal conditions |
| title_sort | modeling of temperature profile in semi permeable membrane channel at non isothermal conditions |
| topic | Temperature polarization Modeling Pressure-driven membrane processes Non-isothermal conditions Semi-permeable channel |
| url | http://www.sciencedirect.com/science/article/pii/S2590123023003067 |
| work_keys_str_mv | AT danieloganesian modelingoftemperatureprofileinsemipermeablemembranechannelatnonisothermalconditions AT sergeyagashichev modelingoftemperatureprofileinsemipermeablemembranechannelatnonisothermalconditions |