Expanding the Controllable Range of the Mean Residence Time Ratio of Polydisperse Particles in Multiple-Chamber Fluidized Beds: A Coarse-Grained CFD-DEM Study

IF 3.8 3区 工程技术 Q2 ENGINEERING, CHEMICAL
Shuai Lu, Dandan Li, Bin Lan, Chuanlin Fan, Fan Xu, Ji Xu, Bidan Zhao, Zheng Zou, Hongzhong Li, Junwu Wang, Qingshan Zhu
{"title":"Expanding the Controllable Range of the Mean Residence Time Ratio of Polydisperse Particles in Multiple-Chamber Fluidized Beds: A Coarse-Grained CFD-DEM Study","authors":"Shuai Lu, Dandan Li, Bin Lan, Chuanlin Fan, Fan Xu, Ji Xu, Bidan Zhao, Zheng Zou, Hongzhong Li, Junwu Wang, Qingshan Zhu","doi":"10.1021/acs.iecr.4c02112","DOIUrl":null,"url":null,"abstract":"The residence time of polydisperse particles is crucial for their simultaneous conversion in a fluidized bed. This study focuses on regulating the residence time of polydisperse particles to expand their controllable range by optimizing the reactor design and operation step-by-step. The mean residence time (MRT) ratio of coarse and fine particles (<i></i><span style=\"color: inherit;\"></span><span data-mathml='&lt;math xmlns=\"http://www.w3.org/1998/Math/MathML\" display=\"inline\"&gt;&lt;msubsup&gt;&lt;mrow&gt;&lt;mi&gt;t&lt;/mi&gt;&lt;/mrow&gt;&lt;mrow&gt;&lt;mi&gt;p&lt;/mi&gt;&lt;/mrow&gt;&lt;mrow&gt;&lt;mi&gt;c&lt;/mi&gt;&lt;/mrow&gt;&lt;/msubsup&gt;&lt;mo&gt;/&lt;/mo&gt;&lt;msubsup&gt;&lt;mrow&gt;&lt;mi&gt;t&lt;/mi&gt;&lt;/mrow&gt;&lt;mrow&gt;&lt;mi&gt;p&lt;/mi&gt;&lt;/mrow&gt;&lt;mrow&gt;&lt;mi&gt;f&lt;/mi&gt;&lt;/mrow&gt;&lt;/msubsup&gt;&lt;/math&gt;' role=\"presentation\" style=\"position: relative;\" tabindex=\"0\"><nobr aria-hidden=\"true\"><span style=\"width: 2.564em; display: inline-block;\"><span style=\"display: inline-block; position: relative; width: 2.103em; height: 0px; font-size: 122%;\"><span style=\"position: absolute; clip: rect(1.078em, 1002.1em, 2.769em, -999.997em); top: -2.2em; left: 0em;\"><span><span><span style=\"display: inline-block; position: relative; width: 0.771em; height: 0px;\"><span style=\"position: absolute; clip: rect(3.23em, 1000.31em, 4.152em, -999.997em); top: -3.993em; left: 0em;\"><span><span style=\"font-family: MathJax_Math-italic;\">t</span></span><span style=\"display: inline-block; width: 0px; height: 3.998em;\"></span></span><span style=\"position: absolute; clip: rect(3.537em, 1000.36em, 4.152em, -999.997em); top: -4.352em; left: 0.361em;\"><span><span style=\"font-size: 70.7%; font-family: MathJax_Math-italic;\">c</span></span><span style=\"display: inline-block; width: 0px; height: 3.998em;\"></span></span><span style=\"position: absolute; clip: rect(3.537em, 1000.41em, 4.306em, -999.997em); top: -3.737em; left: 0.361em;\"><span><span style=\"font-size: 70.7%; font-family: MathJax_Math-italic;\">p</span></span><span style=\"display: inline-block; width: 0px; height: 3.998em;\"></span></span></span></span><span style=\"font-family: MathJax_Main;\">/</span><span><span style=\"display: inline-block; position: relative; width: 0.822em; height: 0px;\"><span style=\"position: absolute; clip: rect(3.23em, 1000.31em, 4.152em, -999.997em); top: -3.993em; left: 0em;\"><span><span style=\"font-family: MathJax_Math-italic;\">t</span></span><span style=\"display: inline-block; width: 0px; height: 3.998em;\"></span></span><span style=\"position: absolute; clip: rect(3.332em, 1000.46em, 4.306em, -999.997em); top: -4.506em; left: 0.361em;\"><span><span style=\"font-size: 70.7%; font-family: MathJax_Math-italic;\">f<span style=\"display: inline-block; overflow: hidden; height: 1px; width: 0.054em;\"></span></span></span><span style=\"display: inline-block; width: 0px; height: 3.998em;\"></span></span><span style=\"position: absolute; clip: rect(3.537em, 1000.41em, 4.306em, -999.997em); top: -3.84em; left: 0.361em;\"><span><span style=\"font-size: 70.7%; font-family: MathJax_Math-italic;\">p</span></span><span style=\"display: inline-block; width: 0px; height: 3.998em;\"></span></span></span></span></span><span style=\"display: inline-block; width: 0px; height: 2.205em;\"></span></span></span><span style=\"display: inline-block; overflow: hidden; vertical-align: -0.559em; border-left: 0px solid; width: 0px; height: 1.816em;\"></span></span></nobr><span role=\"presentation\"><math display=\"inline\" xmlns=\"http://www.w3.org/1998/Math/MathML\"><msubsup><mrow><mi>t</mi></mrow><mrow><mi>p</mi></mrow><mrow><mi>c</mi></mrow></msubsup><mo>/</mo><msubsup><mrow><mi>t</mi></mrow><mrow><mi>p</mi></mrow><mrow><mi>f</mi></mrow></msubsup></math></span></span><script type=\"math/mml\"><math display=\"inline\"><msubsup><mrow><mi>t</mi></mrow><mrow><mi>p</mi></mrow><mrow><mi>c</mi></mrow></msubsup><mo>/</mo><msubsup><mrow><mi>t</mi></mrow><mrow><mi>p</mi></mrow><mrow><mi>f</mi></mrow></msubsup></math></script>) increased significantly with increasing elutriation pipe width of the multiple-chamber fluidized bed, thus enabling the MRT ratio to exceed <i></i><span style=\"color: inherit;\"></span><span data-mathml='&lt;math xmlns=\"http://www.w3.org/1998/Math/MathML\" display=\"inline\"&gt;&lt;msup&gt;&lt;mrow&gt;&lt;mrow&gt;&lt;mo stretchy=\"false\"&gt;(&lt;/mo&gt;&lt;/mrow&gt;&lt;mrow&gt;&lt;mrow&gt;&lt;msubsup&gt;&lt;mrow&gt;&lt;mi&gt;d&lt;/mi&gt;&lt;/mrow&gt;&lt;mrow&gt;&lt;mi&gt;p&lt;/mi&gt;&lt;/mrow&gt;&lt;mrow&gt;&lt;mi&gt;c&lt;/mi&gt;&lt;/mrow&gt;&lt;/msubsup&gt;&lt;/mrow&gt;&lt;mrow&gt;&lt;mo&gt;/&lt;/mo&gt;&lt;/mrow&gt;&lt;mrow&gt;&lt;msubsup&gt;&lt;mrow&gt;&lt;mi&gt;d&lt;/mi&gt;&lt;/mrow&gt;&lt;mrow&gt;&lt;mi&gt;p&lt;/mi&gt;&lt;/mrow&gt;&lt;mrow&gt;&lt;mi&gt;f&lt;/mi&gt;&lt;/mrow&gt;&lt;/msubsup&gt;&lt;/mrow&gt;&lt;/mrow&gt;&lt;mrow&gt;&lt;mo stretchy=\"false\"&gt;)&lt;/mo&gt;&lt;/mrow&gt;&lt;/mrow&gt;&lt;mrow&gt;&lt;mn&gt;2&lt;/mn&gt;&lt;/mrow&gt;&lt;/msup&gt;&lt;/math&gt;' role=\"presentation\" style=\"position: relative;\" tabindex=\"0\"><nobr aria-hidden=\"true\"><span style=\"width: 4.511em; display: inline-block;\"><span style=\"display: inline-block; position: relative; width: 3.691em; height: 0px; font-size: 122%;\"><span style=\"position: absolute; clip: rect(0.925em, 1003.69em, 2.769em, -999.997em); top: -2.2em; left: 0em;\"><span><span><span style=\"display: inline-block; position: relative; width: 3.691em; height: 0px;\"><span style=\"position: absolute; clip: rect(2.923em, 1003.18em, 4.562em, -999.997em); top: -3.993em; left: 0em;\"><span><span><span style=\"font-family: MathJax_Main;\">(</span></span><span><span><span><span style=\"display: inline-block; position: relative; width: 0.976em; height: 0px;\"><span style=\"position: absolute; clip: rect(3.128em, 1000.51em, 4.152em, -999.997em); top: -3.993em; left: 0em;\"><span><span style=\"font-family: MathJax_Math-italic;\">d<span style=\"display: inline-block; overflow: hidden; height: 1px; width: 0.003em;\"></span></span></span><span style=\"display: inline-block; width: 0px; height: 3.998em;\"></span></span><span style=\"position: absolute; clip: rect(3.537em, 1000.36em, 4.152em, -999.997em); top: -4.403em; left: 0.566em;\"><span><span style=\"font-size: 70.7%; font-family: MathJax_Math-italic;\">c</span></span><span style=\"display: inline-block; width: 0px; height: 3.998em;\"></span></span><span style=\"position: absolute; clip: rect(3.537em, 1000.41em, 4.306em, -999.997em); top: -3.737em; left: 0.515em;\"><span><span style=\"font-size: 70.7%; font-family: MathJax_Math-italic;\">p</span></span><span style=\"display: inline-block; width: 0px; height: 3.998em;\"></span></span></span></span></span><span><span style=\"font-family: MathJax_Main;\">/</span></span><span><span><span style=\"display: inline-block; position: relative; width: 1.027em; height: 0px;\"><span style=\"position: absolute; clip: rect(3.128em, 1000.51em, 4.152em, -999.997em); top: -3.993em; left: 0em;\"><span><span style=\"font-family: MathJax_Math-italic;\">d<span style=\"display: inline-block; overflow: hidden; height: 1px; width: 0.003em;\"></span></span></span><span style=\"display: inline-block; width: 0px; height: 3.998em;\"></span></span><span style=\"position: absolute; clip: rect(3.332em, 1000.46em, 4.306em, -999.997em); top: -4.403em; left: 0.566em;\"><span><span style=\"font-size: 70.7%; font-family: MathJax_Math-italic;\">f<span style=\"display: inline-block; overflow: hidden; height: 1px; width: 0.054em;\"></span></span></span><span style=\"display: inline-block; width: 0px; height: 3.998em;\"></span></span><span style=\"position: absolute; clip: rect(3.537em, 1000.41em, 4.306em, -999.997em); top: -3.737em; left: 0.515em;\"><span><span style=\"font-size: 70.7%; font-family: MathJax_Math-italic;\">p</span></span><span style=\"display: inline-block; width: 0px; height: 3.998em;\"></span></span></span></span></span></span><span><span style=\"font-family: MathJax_Main;\">)</span></span></span><span style=\"display: inline-block; width: 0px; height: 3.998em;\"></span></span><span style=\"position: absolute; top: -4.659em; left: 3.281em;\"><span><span style=\"font-size: 70.7%; font-family: MathJax_Main;\">2</span></span><span style=\"display: inline-block; width: 0px; height: 3.998em;\"></span></span></span></span></span><span style=\"display: inline-block; width: 0px; height: 2.205em;\"></span></span></span><span style=\"display: inline-block; overflow: hidden; vertical-align: -0.559em; border-left: 0px solid; width: 0px; height: 1.941em;\"></span></span></nobr><span role=\"presentation\"><math display=\"inline\" xmlns=\"http://www.w3.org/1998/Math/MathML\"><msup><mrow><mrow><mo stretchy=\"false\">(</mo></mrow><mrow><mrow><msubsup><mrow><mi>d</mi></mrow><mrow><mi>p</mi></mrow><mrow><mi>c</mi></mrow></msubsup></mrow><mrow><mo>/</mo></mrow><mrow><msubsup><mrow><mi>d</mi></mrow><mrow><mi>p</mi></mrow><mrow><mi>f</mi></mrow></msubsup></mrow></mrow><mrow><mo stretchy=\"false\">)</mo></mrow></mrow><mrow><mn>2</mn></mrow></msup></math></span></span><script type=\"math/mml\"><math display=\"inline\"><msup><mrow><mrow><mo stretchy=\"false\">(</mo></mrow><mrow><mrow><msubsup><mrow><mi>d</mi></mrow><mrow><mi>p</mi></mrow><mrow><mi>c</mi></mrow></msubsup></mrow><mrow><mo>/</mo></mrow><mrow><msubsup><mrow><mi>d</mi></mrow><mrow><mi>p</mi></mrow><mrow><mi>f</mi></mrow></msubsup></mrow></mrow><mrow><mo stretchy=\"false\">)</mo></mrow></mrow><mrow><mn>2</mn></mrow></msup></math></script>; however, the MRT ratio of medium and fine particles (<i></i><span style=\"color: inherit;\"></span><span data-mathml='&lt;math xmlns=\"http://www.w3.org/1998/Math/MathML\" display=\"inline\"&gt;&lt;msubsup&gt;&lt;mrow&gt;&lt;mi&gt;t&lt;/mi&gt;&lt;/mrow&gt;&lt;mrow&gt;&lt;mi&gt;p&lt;/mi&gt;&lt;/mrow&gt;&lt;mrow&gt;&lt;mi&gt;m&lt;/mi&gt;&lt;/mrow&gt;&lt;/msubsup&gt;&lt;mo&gt;/&lt;/mo&gt;&lt;msubsup&gt;&lt;mrow&gt;&lt;mi&gt;t&lt;/mi&gt;&lt;/mrow&gt;&lt;mrow&gt;&lt;mi&gt;p&lt;/mi&gt;&lt;/mrow&gt;&lt;mrow&gt;&lt;mi&gt;f&lt;/mi&gt;&lt;/mrow&gt;&lt;/msubsup&gt;&lt;/math&gt;' role=\"presentation\" style=\"position: relative;\" tabindex=\"0\"><nobr aria-hidden=\"true\"><span style=\"width: 2.974em; display: inline-block;\"><span style=\"display: inline-block; position: relative; width: 2.41em; height: 0px; font-size: 122%;\"><span style=\"position: absolute; clip: rect(1.078em, 1002.41em, 2.769em, -999.997em); top: -2.2em; left: 0em;\"><span><span><span style=\"display: inline-block; position: relative; width: 1.078em; height: 0px;\"><span style=\"position: absolute; clip: rect(3.23em, 1000.31em, 4.152em, -999.997em); top: -3.993em; left: 0em;\"><span><span style=\"font-family: MathJax_Math-italic;\">t</span></span><span style=\"display: inline-block; width: 0px; height: 3.998em;\"></span></span><span style=\"position: absolute; clip: rect(3.537em, 1000.72em, 4.152em, -999.997em); top: -4.352em; left: 0.361em;\"><span><span style=\"font-size: 70.7%; font-family: MathJax_Math-italic;\">m</span></span><span style=\"display: inline-block; width: 0px; height: 3.998em;\"></span></span><span style=\"position: absolute; clip: rect(3.537em, 1000.41em, 4.306em, -999.997em); top: -3.737em; left: 0.361em;\"><span><span style=\"font-size: 70.7%; font-family: MathJax_Math-italic;\">p</span></span><span style=\"display: inline-block; width: 0px; height: 3.998em;\"></span></span></span></span><span style=\"font-family: MathJax_Main;\">/</span><span><span style=\"display: inline-block; position: relative; width: 0.822em; height: 0px;\"><span style=\"position: absolute; clip: rect(3.23em, 1000.31em, 4.152em, -999.997em); top: -3.993em; left: 0em;\"><span><span style=\"font-family: MathJax_Math-italic;\">t</span></span><span style=\"display: inline-block; width: 0px; height: 3.998em;\"></span></span><span style=\"position: absolute; clip: rect(3.332em, 1000.46em, 4.306em, -999.997em); top: -4.506em; left: 0.361em;\"><span><span style=\"font-size: 70.7%; font-family: MathJax_Math-italic;\">f<span style=\"display: inline-block; overflow: hidden; height: 1px; width: 0.054em;\"></span></span></span><span style=\"display: inline-block; width: 0px; height: 3.998em;\"></span></span><span style=\"position: absolute; clip: rect(3.537em, 1000.41em, 4.306em, -999.997em); top: -3.84em; left: 0.361em;\"><span><span style=\"font-size: 70.7%; font-family: MathJax_Math-italic;\">p</span></span><span style=\"display: inline-block; width: 0px; height: 3.998em;\"></span></span></span></span></span><span style=\"display: inline-block; width: 0px; height: 2.205em;\"></span></span></span><span style=\"display: inline-block; overflow: hidden; vertical-align: -0.559em; border-left: 0px solid; width: 0px; height: 1.816em;\"></span></span></nobr><span role=\"presentation\"><math display=\"inline\" xmlns=\"http://www.w3.org/1998/Math/MathML\"><msubsup><mrow><mi>t</mi></mrow><mrow><mi>p</mi></mrow><mrow><mi>m</mi></mrow></msubsup><mo>/</mo><msubsup><mrow><mi>t</mi></mrow><mrow><mi>p</mi></mrow><mrow><mi>f</mi></mrow></msubsup></math></span></span><script type=\"math/mml\"><math display=\"inline\"><msubsup><mrow><mi>t</mi></mrow><mrow><mi>p</mi></mrow><mrow><mi>m</mi></mrow></msubsup><mo>/</mo><msubsup><mrow><mi>t</mi></mrow><mrow><mi>p</mi></mrow><mrow><mi>f</mi></mrow></msubsup></math></script>) is only slightly exceeded <i></i><span style=\"color: inherit;\"></span><span data-mathml='&lt;math xmlns=\"http://www.w3.org/1998/Math/MathML\" display=\"inline\"&gt;&lt;msubsup&gt;&lt;mrow&gt;&lt;mi&gt;d&lt;/mi&gt;&lt;/mrow&gt;&lt;mrow&gt;&lt;mi&gt;p&lt;/mi&gt;&lt;/mrow&gt;&lt;mrow&gt;&lt;mi&gt;m&lt;/mi&gt;&lt;/mrow&gt;&lt;/msubsup&gt;&lt;mo&gt;/&lt;/mo&gt;&lt;msubsup&gt;&lt;mrow&gt;&lt;mi&gt;d&lt;/mi&gt;&lt;/mrow&gt;&lt;mrow&gt;&lt;mi&gt;p&lt;/mi&gt;&lt;/mrow&gt;&lt;mrow&gt;&lt;mi&gt;f&lt;/mi&gt;&lt;/mrow&gt;&lt;/msubsup&gt;&lt;/math&gt;' role=\"presentation\" style=\"position: relative;\" tabindex=\"0\"><nobr aria-hidden=\"true\"><span style=\"width: 3.435em; display: inline-block;\"><span style=\"display: inline-block; position: relative; width: 2.82em; height: 0px; font-size: 122%;\"><span style=\"position: absolute; clip: rect(1.13em, 1002.82em, 2.769em, -999.997em); top: -2.2em; left: 0em;\"><span><span><span style=\"display: inline-block; position: relative; width: 1.283em; height: 0px;\"><span style=\"position: absolute; clip: rect(3.128em, 1000.51em, 4.152em, -999.997em); top: -3.993em; left: 0em;\"><span><span style=\"font-family: MathJax_Math-italic;\">d<span style=\"display: inline-block; overflow: hidden; height: 1px; width: 0.003em;\"></span></span></span><span style=\"display: inline-block; width: 0px; height: 3.998em;\"></span></span><span style=\"position: absolute; clip: rect(3.537em, 1000.72em, 4.152em, -999.997em); top: -4.403em; left: 0.566em;\"><span><span style=\"font-size: 70.7%; font-family: MathJax_Math-italic;\">m</span></span><span style=\"display: inline-block; width: 0px; height: 3.998em;\"></span></span><span style=\"position: absolute; clip: rect(3.537em, 1000.41em, 4.306em, -999.997em); top: -3.737em; left: 0.515em;\"><span><span style=\"font-size: 70.7%; font-family: MathJax_Math-italic;\">p</span></span><span style=\"display: inline-block; width: 0px; height: 3.998em;\"></span></span></span></span><span style=\"font-family: MathJax_Main;\">/</span><span><span style=\"display: inline-block; position: relative; width: 1.027em; height: 0px;\"><span style=\"position: absolute; clip: rect(3.128em, 1000.51em, 4.152em, -999.997em); top: -3.993em; left: 0em;\"><span><span style=\"font-family: MathJax_Math-italic;\">d<span style=\"display: inline-block; overflow: hidden; height: 1px; width: 0.003em;\"></span></span></span><span style=\"display: inline-block; width: 0px; height: 3.998em;\"></span></span><span style=\"position: absolute; clip: rect(3.332em, 1000.46em, 4.306em, -999.997em); top: -4.403em; left: 0.566em;\"><span><span style=\"font-size: 70.7%; font-family: MathJax_Math-italic;\">f<span style=\"display: inline-block; overflow: hidden; height: 1px; width: 0.054em;\"></span></span></span><span style=\"display: inline-block; width: 0px; height: 3.998em;\"></span></span><span style=\"position: absolute; clip: rect(3.537em, 1000.41em, 4.306em, -999.997em); top: -3.737em; left: 0.515em;\"><span><span style=\"font-size: 70.7%; font-family: MathJax_Math-italic;\">p</span></span><span style=\"display: inline-block; width: 0px; height: 3.998em;\"></span></span></span></span></span><span style=\"display: inline-block; width: 0px; height: 2.205em;\"></span></span></span><span style=\"display: inline-block; overflow: hidden; vertical-align: -0.559em; border-left: 0px solid; width: 0px; height: 1.691em;\"></span></span></nobr><span role=\"presentation\"><math display=\"inline\" xmlns=\"http://www.w3.org/1998/Math/MathML\"><msubsup><mrow><mi>d</mi></mrow><mrow><mi>p</mi></mrow><mrow><mi>m</mi></mrow></msubsup><mo>/</mo><msubsup><mrow><mi>d</mi></mrow><mrow><mi>p</mi></mrow><mrow><mi>f</mi></mrow></msubsup></math></span></span><script type=\"math/mml\"><math display=\"inline\"><msubsup><mrow><mi>d</mi></mrow><mrow><mi>p</mi></mrow><mrow><mi>m</mi></mrow></msubsup><mo>/</mo><msubsup><mrow><mi>d</mi></mrow><mrow><mi>p</mi></mrow><mrow><mi>f</mi></mrow></msubsup></math></script>. Moreover, by further optimizing the elutriation pipe gas velocity, the latter can be adjusted to be exceed <i></i><span style=\"color: inherit;\"></span><span data-mathml='&lt;math xmlns=\"http://www.w3.org/1998/Math/MathML\" display=\"inline\"&gt;&lt;msup&gt;&lt;mrow&gt;&lt;mrow&gt;&lt;mo stretchy=\"false\"&gt;(&lt;/mo&gt;&lt;/mrow&gt;&lt;mrow&gt;&lt;mrow&gt;&lt;msubsup&gt;&lt;mrow&gt;&lt;mi&gt;d&lt;/mi&gt;&lt;/mrow&gt;&lt;mrow&gt;&lt;mi&gt;p&lt;/mi&gt;&lt;/mrow&gt;&lt;mrow&gt;&lt;mi&gt;m&lt;/mi&gt;&lt;/mrow&gt;&lt;/msubsup&gt;&lt;/mrow&gt;&lt;mrow&gt;&lt;mo&gt;/&lt;/mo&gt;&lt;/mrow&gt;&lt;mrow&gt;&lt;msubsup&gt;&lt;mrow&gt;&lt;mi&gt;d&lt;/mi&gt;&lt;/mrow&gt;&lt;mrow&gt;&lt;mi&gt;p&lt;/mi&gt;&lt;/mrow&gt;&lt;mrow&gt;&lt;mi&gt;f&lt;/mi&gt;&lt;/mrow&gt;&lt;/msubsup&gt;&lt;/mrow&gt;&lt;/mrow&gt;&lt;mrow&gt;&lt;mo stretchy=\"false\"&gt;)&lt;/mo&gt;&lt;/mrow&gt;&lt;/mrow&gt;&lt;mrow&gt;&lt;mn&gt;1.5&lt;/mn&gt;&lt;/mrow&gt;&lt;/msup&gt;&lt;/math&gt;' role=\"presentation\" style=\"position: relative;\" tabindex=\"0\"><nobr aria-hidden=\"true\"><span style=\"width: 5.587em; display: inline-block;\"><span style=\"display: inline-block; position: relative; width: 4.562em; height: 0px; font-size: 122%;\"><span style=\"position: absolute; clip: rect(0.925em, 1004.56em, 2.769em, -999.997em); top: -2.2em; left: 0em;\"><span><span><span style=\"display: inline-block; position: relative; width: 4.562em; height: 0px;\"><span style=\"position: absolute; clip: rect(2.923em, 1003.49em, 4.562em, -999.997em); top: -3.993em; left: 0em;\"><span><span><span style=\"font-family: MathJax_Main;\">(</span></span><span><span><span><span style=\"display: inline-block; position: relative; width: 1.283em; height: 0px;\"><span style=\"position: absolute; clip: rect(3.128em, 1000.51em, 4.152em, -999.997em); top: -3.993em; left: 0em;\"><span><span style=\"font-family: MathJax_Math-italic;\">d<span style=\"display: inline-block; overflow: hidden; height: 1px; width: 0.003em;\"></span></span></span><span style=\"display: inline-block; width: 0px; height: 3.998em;\"></span></span><span style=\"position: absolute; clip: rect(3.537em, 1000.72em, 4.152em, -999.997em); top: -4.403em; left: 0.566em;\"><span><span style=\"font-size: 70.7%; font-family: MathJax_Math-italic;\">m</span></span><span style=\"display: inline-block; width: 0px; height: 3.998em;\"></span></span><span style=\"position: absolute; clip: rect(3.537em, 1000.41em, 4.306em, -999.997em); top: -3.737em; left: 0.515em;\"><span><span style=\"font-size: 70.7%; font-family: MathJax_Math-italic;\">p</span></span><span style=\"display: inline-block; width: 0px; height: 3.998em;\"></span></span></span></span></span><span><span style=\"font-family: MathJax_Main;\">/</span></span><span><span><span style=\"display: inline-block; position: relative; width: 1.027em; height: 0px;\"><span style=\"position: absolute; clip: rect(3.128em, 1000.51em, 4.152em, -999.997em); top: -3.993em; left: 0em;\"><span><span style=\"font-family: MathJax_Math-italic;\">d<span style=\"display: inline-block; overflow: hidden; height: 1px; width: 0.003em;\"></span></span></span><span style=\"display: inline-block; width: 0px; height: 3.998em;\"></span></span><span style=\"position: absolute; clip: rect(3.332em, 1000.46em, 4.306em, -999.997em); top: -4.403em; left: 0.566em;\"><span><span style=\"font-size: 70.7%; font-family: MathJax_Math-italic;\">f<span style=\"display: inline-block; overflow: hidden; height: 1px; width: 0.054em;\"></span></span></span><span style=\"display: inline-block; width: 0px; height: 3.998em;\"></span></span><span style=\"position: absolute; clip: rect(3.537em, 1000.41em, 4.306em, -999.997em); top: -3.737em; left: 0.515em;\"><span><span style=\"font-size: 70.7%; font-family: MathJax_Math-italic;\">p</span></span><span style=\"display: inline-block; width: 0px; height: 3.998em;\"></span></span></span></span></span></span><span><span style=\"font-family: MathJax_Main;\">)</span></span></span><span style=\"display: inline-block; width: 0px; height: 3.998em;\"></span></span><span style=\"position: absolute; top: -4.659em; left: 3.589em;\"><span><span style=\"font-size: 70.7%; font-family: MathJax_Main;\">1.5</span></span><span style=\"display: inline-block; width: 0px; height: 3.998em;\"></span></span></span></span></span><span style=\"display: inline-block; width: 0px; height: 2.205em;\"></span></span></span><span style=\"display: inline-block; overflow: hidden; vertical-align: -0.559em; border-left: 0px solid; width: 0px; height: 1.941em;\"></span></span></nobr><span role=\"presentation\"><math display=\"inline\" xmlns=\"http://www.w3.org/1998/Math/MathML\"><msup><mrow><mrow><mo stretchy=\"false\">(</mo></mrow><mrow><mrow><msubsup><mrow><mi>d</mi></mrow><mrow><mi>p</mi></mrow><mrow><mi>m</mi></mrow></msubsup></mrow><mrow><mo>/</mo></mrow><mrow><msubsup><mrow><mi>d</mi></mrow><mrow><mi>p</mi></mrow><mrow><mi>f</mi></mrow></msubsup></mrow></mrow><mrow><mo stretchy=\"false\">)</mo></mrow></mrow><mrow><mn>1.5</mn></mrow></msup></math></span></span><script type=\"math/mml\"><math display=\"inline\"><msup><mrow><mrow><mo stretchy=\"false\">(</mo></mrow><mrow><mrow><msubsup><mrow><mi>d</mi></mrow><mrow><mi>p</mi></mrow><mrow><mi>m</mi></mrow></msubsup></mrow><mrow><mo>/</mo></mrow><mrow><msubsup><mrow><mi>d</mi></mrow><mrow><mi>p</mi></mrow><mrow><mi>f</mi></mrow></msubsup></mrow></mrow><mrow><mo stretchy=\"false\">)</mo></mrow></mrow><mrow><mn>1.5</mn></mrow></msup></math></script>. Finally, <i></i><span style=\"color: inherit;\"></span><span data-mathml='&lt;math xmlns=\"http://www.w3.org/1998/Math/MathML\" display=\"inline\"&gt;&lt;msubsup&gt;&lt;mrow&gt;&lt;mi&gt;t&lt;/mi&gt;&lt;/mrow&gt;&lt;mrow&gt;&lt;mi&gt;p&lt;/mi&gt;&lt;/mrow&gt;&lt;mrow&gt;&lt;mi&gt;c&lt;/mi&gt;&lt;/mrow&gt;&lt;/msubsup&gt;&lt;mo&gt;/&lt;/mo&gt;&lt;msubsup&gt;&lt;mrow&gt;&lt;mi&gt;t&lt;/mi&gt;&lt;/mrow&gt;&lt;mrow&gt;&lt;mi&gt;p&lt;/mi&gt;&lt;/mrow&gt;&lt;mrow&gt;&lt;mi&gt;f&lt;/mi&gt;&lt;/mrow&gt;&lt;/msubsup&gt;&lt;/math&gt;' role=\"presentation\" style=\"position: relative;\" tabindex=\"0\"><nobr aria-hidden=\"true\"><span style=\"width: 2.564em; display: inline-block;\"><span style=\"display: inline-block; position: relative; width: 2.103em; height: 0px; font-size: 122%;\"><span style=\"position: absolute; clip: rect(1.078em, 1002.1em, 2.769em, -999.997em); top: -2.2em; left: 0em;\"><span><span><span style=\"display: inline-block; position: relative; width: 0.771em; height: 0px;\"><span style=\"position: absolute; clip: rect(3.23em, 1000.31em, 4.152em, -999.997em); top: -3.993em; left: 0em;\"><span><span style=\"font-family: MathJax_Math-italic;\">t</span></span><span style=\"display: inline-block; width: 0px; height: 3.998em;\"></span></span><span style=\"position: absolute; clip: rect(3.537em, 1000.36em, 4.152em, -999.997em); top: -4.352em; left: 0.361em;\"><span><span style=\"font-size: 70.7%; font-family: MathJax_Math-italic;\">c</span></span><span style=\"display: inline-block; width: 0px; height: 3.998em;\"></span></span><span style=\"position: absolute; clip: rect(3.537em, 1000.41em, 4.306em, -999.997em); top: -3.737em; left: 0.361em;\"><span><span style=\"font-size: 70.7%; font-family: MathJax_Math-italic;\">p</span></span><span style=\"display: inline-block; width: 0px; height: 3.998em;\"></span></span></span></span><span style=\"font-family: MathJax_Main;\">/</span><span><span style=\"display: inline-block; position: relative; width: 0.822em; height: 0px;\"><span style=\"position: absolute; clip: rect(3.23em, 1000.31em, 4.152em, -999.997em); top: -3.993em; left: 0em;\"><span><span style=\"font-family: MathJax_Math-italic;\">t</span></span><span style=\"display: inline-block; width: 0px; height: 3.998em;\"></span></span><span style=\"position: absolute; clip: rect(3.332em, 1000.46em, 4.306em, -999.997em); top: -4.506em; left: 0.361em;\"><span><span style=\"font-size: 70.7%; font-family: MathJax_Math-italic;\">f<span style=\"display: inline-block; overflow: hidden; height: 1px; width: 0.054em;\"></span></span></span><span style=\"display: inline-block; width: 0px; height: 3.998em;\"></span></span><span style=\"position: absolute; clip: rect(3.537em, 1000.41em, 4.306em, -999.997em); top: -3.84em; left: 0.361em;\"><span><span style=\"font-size: 70.7%; font-family: MathJax_Math-italic;\">p</span></span><span style=\"display: inline-block; width: 0px; height: 3.998em;\"></span></span></span></span></span><span style=\"display: inline-block; width: 0px; height: 2.205em;\"></span></span></span><span style=\"display: inline-block; overflow: hidden; vertical-align: -0.559em; border-left: 0px solid; width: 0px; height: 1.816em;\"></span></span></nobr><span role=\"presentation\"><math display=\"inline\" xmlns=\"http://www.w3.org/1998/Math/MathML\"><msubsup><mrow><mi>t</mi></mrow><mrow><mi>p</mi></mrow><mrow><mi>c</mi></mrow></msubsup><mo>/</mo><msubsup><mrow><mi>t</mi></mrow><mrow><mi>p</mi></mrow><mrow><mi>f</mi></mrow></msubsup></math></span></span><script type=\"math/mml\"><math display=\"inline\"><msubsup><mrow><mi>t</mi></mrow><mrow><mi>p</mi></mrow><mrow><mi>c</mi></mrow></msubsup><mo>/</mo><msubsup><mrow><mi>t</mi></mrow><mrow><mi>p</mi></mrow><mrow><mi>f</mi></mrow></msubsup></math></script> and <i></i><span style=\"color: inherit;\"></span><span data-mathml='&lt;math xmlns=\"http://www.w3.org/1998/Math/MathML\" display=\"inline\"&gt;&lt;msubsup&gt;&lt;mrow&gt;&lt;mi&gt;t&lt;/mi&gt;&lt;/mrow&gt;&lt;mrow&gt;&lt;mi&gt;p&lt;/mi&gt;&lt;/mrow&gt;&lt;mrow&gt;&lt;mi&gt;m&lt;/mi&gt;&lt;/mrow&gt;&lt;/msubsup&gt;&lt;mo&gt;/&lt;/mo&gt;&lt;msubsup&gt;&lt;mrow&gt;&lt;mi&gt;t&lt;/mi&gt;&lt;/mrow&gt;&lt;mrow&gt;&lt;mi&gt;p&lt;/mi&gt;&lt;/mrow&gt;&lt;mrow&gt;&lt;mi&gt;f&lt;/mi&gt;&lt;/mrow&gt;&lt;/msubsup&gt;&lt;/math&gt;' role=\"presentation\" style=\"position: relative;\" tabindex=\"0\"><nobr aria-hidden=\"true\"><span style=\"width: 2.974em; display: inline-block;\"><span style=\"display: inline-block; position: relative; width: 2.41em; height: 0px; font-size: 122%;\"><span style=\"position: absolute; clip: rect(1.078em, 1002.41em, 2.769em, -999.997em); top: -2.2em; left: 0em;\"><span><span><span style=\"display: inline-block; position: relative; width: 1.078em; height: 0px;\"><span style=\"position: absolute; clip: rect(3.23em, 1000.31em, 4.152em, -999.997em); top: -3.993em; left: 0em;\"><span><span style=\"font-family: MathJax_Math-italic;\">t</span></span><span style=\"display: inline-block; width: 0px; height: 3.998em;\"></span></span><span style=\"position: absolute; clip: rect(3.537em, 1000.72em, 4.152em, -999.997em); top: -4.352em; left: 0.361em;\"><span><span style=\"font-size: 70.7%; font-family: MathJax_Math-italic;\">m</span></span><span style=\"display: inline-block; width: 0px; height: 3.998em;\"></span></span><span style=\"position: absolute; clip: rect(3.537em, 1000.41em, 4.306em, -999.997em); top: -3.737em; left: 0.361em;\"><span><span style=\"font-size: 70.7%; font-family: MathJax_Math-italic;\">p</span></span><span style=\"display: inline-block; width: 0px; height: 3.998em;\"></span></span></span></span><span style=\"font-family: MathJax_Main;\">/</span><span><span style=\"display: inline-block; position: relative; width: 0.822em; height: 0px;\"><span style=\"position: absolute; clip: rect(3.23em, 1000.31em, 4.152em, -999.997em); top: -3.993em; left: 0em;\"><span><span style=\"font-family: MathJax_Math-italic;\">t</span></span><span style=\"display: inline-block; width: 0px; height: 3.998em;\"></span></span><span style=\"position: absolute; clip: rect(3.332em, 1000.46em, 4.306em, -999.997em); top: -4.506em; left: 0.361em;\"><span><span style=\"font-size: 70.7%; font-family: MathJax_Math-italic;\">f<span style=\"display: inline-block; overflow: hidden; height: 1px; width: 0.054em;\"></span></span></span><span style=\"display: inline-block; width: 0px; height: 3.998em;\"></span></span><span style=\"position: absolute; clip: rect(3.537em, 1000.41em, 4.306em, -999.997em); top: -3.84em; left: 0.361em;\"><span><span style=\"font-size: 70.7%; font-family: MathJax_Math-italic;\">p</span></span><span style=\"display: inline-block; width: 0px; height: 3.998em;\"></span></span></span></span></span><span style=\"display: inline-block; width: 0px; height: 2.205em;\"></span></span></span><span style=\"display: inline-block; overflow: hidden; vertical-align: -0.559em; border-left: 0px solid; width: 0px; height: 1.816em;\"></span></span></nobr><span role=\"presentation\"><math display=\"inline\" xmlns=\"http://www.w3.org/1998/Math/MathML\"><msubsup><mrow><mi>t</mi></mrow><mrow><mi>p</mi></mrow><mrow><mi>m</mi></mrow></msubsup><mo>/</mo><msubsup><mrow><mi>t</mi></mrow><mrow><mi>p</mi></mrow><mrow><mi>f</mi></mrow></msubsup></math></span></span><script type=\"math/mml\"><math display=\"inline\"><msubsup><mrow><mi>t</mi></mrow><mrow><mi>p</mi></mrow><mrow><mi>m</mi></mrow></msubsup><mo>/</mo><msubsup><mrow><mi>t</mi></mrow><mrow><mi>p</mi></mrow><mrow><mi>f</mi></mrow></msubsup></math></script> can be simultaneously adjusted to exceed <i></i><span style=\"color: inherit;\"></span><span data-mathml='&lt;math xmlns=\"http://www.w3.org/1998/Math/MathML\" display=\"inline\"&gt;&lt;msup&gt;&lt;mrow&gt;&lt;mrow&gt;&lt;mo stretchy=\"false\"&gt;(&lt;/mo&gt;&lt;/mrow&gt;&lt;mrow&gt;&lt;mrow&gt;&lt;msub&gt;&lt;mrow&gt;&lt;mi&gt;d&lt;/mi&gt;&lt;/mrow&gt;&lt;mrow&gt;&lt;mi&gt;p&lt;/mi&gt;&lt;/mrow&gt;&lt;/msub&gt;&lt;/mrow&gt;&lt;mrow&gt;&lt;mo&gt;/&lt;/mo&gt;&lt;/mrow&gt;&lt;mrow&gt;&lt;msubsup&gt;&lt;mrow&gt;&lt;mi&gt;d&lt;/mi&gt;&lt;/mrow&gt;&lt;mrow&gt;&lt;mi&gt;p&lt;/mi&gt;&lt;/mrow&gt;&lt;mrow&gt;&lt;mi&gt;f&lt;/mi&gt;&lt;/mrow&gt;&lt;/msubsup&gt;&lt;/mrow&gt;&lt;/mrow&gt;&lt;mrow&gt;&lt;mo stretchy=\"false\"&gt;)&lt;/mo&gt;&lt;/mrow&gt;&lt;/mrow&gt;&lt;mrow&gt;&lt;mn&gt;2&lt;/mn&gt;&lt;/mrow&gt;&lt;/msup&gt;&lt;/math&gt;' role=\"presentation\" style=\"position: relative;\" tabindex=\"0\"><nobr aria-hidden=\"true\"><span style=\"width: 4.511em; display: inline-block;\"><span style=\"display: inline-block; position: relative; width: 3.691em; height: 0px; font-size: 122%;\"><span style=\"position: absolute; clip: rect(0.925em, 1003.69em, 2.769em, -999.997em); top: -2.2em; left: 0em;\"><span><span><span style=\"display: inline-block; position: relative; width: 3.691em; height: 0px;\"><span style=\"position: absolute; clip: rect(2.923em, 1003.18em, 4.562em, -999.997em); top: -3.993em; left: 0em;\"><span><span><span style=\"font-family: MathJax_Main;\">(</span></span><span><span><span><span style=\"display: inline-block; position: relative; width: 0.976em; height: 0px;\"><span style=\"position: absolute; clip: rect(3.128em, 1000.51em, 4.152em, -999.997em); top: -3.993em; left: 0em;\"><span><span style=\"font-family: MathJax_Math-italic;\">d<span style=\"display: inline-block; overflow: hidden; height: 1px; width: 0.003em;\"></span></span></span><span style=\"display: inline-block; width: 0px; height: 3.998em;\"></span></span><span style=\"position: absolute; top: -3.84em; left: 0.515em;\"><span><span style=\"font-size: 70.7%; font-family: MathJax_Math-italic;\">p</span></span><span style=\"display: inline-block; width: 0px; height: 3.998em;\"></span></span></span></span></span><span><span style=\"font-family: MathJax_Main;\">/</span></span><span><span><span style=\"display: inline-block; position: relative; width: 1.027em; height: 0px;\"><span style=\"position: absolute; clip: rect(3.128em, 1000.51em, 4.152em, -999.997em); top: -3.993em; left: 0em;\"><span><span style=\"font-family: MathJax_Math-italic;\">d<span style=\"display: inline-block; overflow: hidden; height: 1px; width: 0.003em;\"></span></span></span><span style=\"display: inline-block; width: 0px; height: 3.998em;\"></span></span><span style=\"position: absolute; clip: rect(3.332em, 1000.46em, 4.306em, -999.997em); top: -4.403em; left: 0.566em;\"><span><span style=\"font-size: 70.7%; font-family: MathJax_Math-italic;\">f<span style=\"display: inline-block; overflow: hidden; height: 1px; width: 0.054em;\"></span></span></span><span style=\"display: inline-block; width: 0px; height: 3.998em;\"></span></span><span style=\"position: absolute; clip: rect(3.537em, 1000.41em, 4.306em, -999.997em); top: -3.737em; left: 0.515em;\"><span><span style=\"font-size: 70.7%; font-family: MathJax_Math-italic;\">p</span></span><span style=\"display: inline-block; width: 0px; height: 3.998em;\"></span></span></span></span></span></span><span><span style=\"font-family: MathJax_Main;\">)</span></span></span><span style=\"display: inline-block; width: 0px; height: 3.998em;\"></span></span><span style=\"position: absolute; top: -4.659em; left: 3.281em;\"><span><span style=\"font-size: 70.7%; font-family: MathJax_Main;\">2</span></span><span style=\"display: inline-block; width: 0px; height: 3.998em;\"></span></span></span></span></span><span style=\"display: inline-block; width: 0px; height: 2.205em;\"></span></span></span><span style=\"display: inline-block; overflow: hidden; vertical-align: -0.559em; border-left: 0px solid; width: 0px; height: 1.941em;\"></span></span></nobr><span role=\"presentation\"><math display=\"inline\" xmlns=\"http://www.w3.org/1998/Math/MathML\"><msup><mrow><mrow><mo stretchy=\"false\">(</mo></mrow><mrow><mrow><msub><mrow><mi>d</mi></mrow><mrow><mi>p</mi></mrow></msub></mrow><mrow><mo>/</mo></mrow><mrow><msubsup><mrow><mi>d</mi></mrow><mrow><mi>p</mi></mrow><mrow><mi>f</mi></mrow></msubsup></mrow></mrow><mrow><mo stretchy=\"false\">)</mo></mrow></mrow><mrow><mn>2</mn></mrow></msup></math></span></span><script type=\"math/mml\"><math display=\"inline\"><msup><mrow><mrow><mo stretchy=\"false\">(</mo></mrow><mrow><mrow><msub><mrow><mi>d</mi></mrow><mrow><mi>p</mi></mrow></msub></mrow><mrow><mo>/</mo></mrow><mrow><msubsup><mrow><mi>d</mi></mrow><mrow><mi>p</mi></mrow><mrow><mi>f</mi></mrow></msubsup></mrow></mrow><mrow><mo stretchy=\"false\">)</mo></mrow></mrow><mrow><mn>2</mn></mrow></msup></math></script> by increasing the number of elutriation pipes. Therefore, present study enables the controllable range of the MRT ratio of polydisperse particles covering from <i></i><span style=\"color: inherit;\"></span><span data-mathml='&lt;math xmlns=\"http://www.w3.org/1998/Math/MathML\" display=\"inline\"&gt;&lt;msup&gt;&lt;mrow&gt;&lt;mrow&gt;&lt;mrow&gt;&lt;msub&gt;&lt;mrow&gt;&lt;mi&gt;d&lt;/mi&gt;&lt;/mrow&gt;&lt;mrow&gt;&lt;mi&gt;p&lt;/mi&gt;&lt;/mrow&gt;&lt;/msub&gt;&lt;/mrow&gt;&lt;mrow&gt;&lt;mo&gt;/&lt;/mo&gt;&lt;/mrow&gt;&lt;mrow&gt;&lt;msubsup&gt;&lt;mrow&gt;&lt;mi&gt;d&lt;/mi&gt;&lt;/mrow&gt;&lt;mrow&gt;&lt;mi&gt;p&lt;/mi&gt;&lt;/mrow&gt;&lt;mrow&gt;&lt;mi&gt;f&lt;/mi&gt;&lt;/mrow&gt;&lt;/msubsup&gt;&lt;/mrow&gt;&lt;/mrow&gt;&lt;/mrow&gt;&lt;mrow&gt;&lt;mn&gt;2&lt;/mn&gt;&lt;/mrow&gt;&lt;/msup&gt;&lt;/math&gt;' role=\"presentation\" style=\"position: relative;\" tabindex=\"0\"><nobr aria-hidden=\"true\"><span style=\"width: 3.589em; display: inline-block;\"><span style=\"display: inline-block; position: relative; width: 2.923em; height: 0px; font-size: 122%;\"><span style=\"position: absolute; clip: rect(0.925em, 1002.92em, 2.769em, -999.997em); top: -2.2em; left: 0em;\"><span><span><span style=\"display: inline-block; position: relative; width: 2.923em; height: 0px;\"><span style=\"position: absolute; clip: rect(2.923em, 1002.51em, 4.562em, -999.997em); top: -3.993em; left: 0em;\"><span><span><span><span><span style=\"display: inline-block; position: relative; width: 0.976em; height: 0px;\"><span style=\"position: absolute; clip: rect(3.128em, 1000.51em, 4.152em, -999.997em); top: -3.993em; left: 0em;\"><span><span style=\"font-family: MathJax_Math-italic;\">d<span style=\"display: inline-block; overflow: hidden; height: 1px; width: 0.003em;\"></span></span></span><span style=\"display: inline-block; width: 0px; height: 3.998em;\"></span></span><span style=\"position: absolute; top: -3.84em; left: 0.515em;\"><span><span style=\"font-size: 70.7%; font-family: MathJax_Math-italic;\">p</span></span><span style=\"display: inline-block; width: 0px; height: 3.998em;\"></span></span></span></span></span><span><span style=\"font-family: MathJax_Main;\">/</span></span><span><span><span style=\"display: inline-block; position: relative; width: 1.027em; height: 0px;\"><span style=\"position: absolute; clip: rect(3.128em, 1000.51em, 4.152em, -999.997em); top: -3.993em; left: 0em;\"><span><span style=\"font-family: MathJax_Math-italic;\">d<span style=\"display: inline-block; overflow: hidden; height: 1px; width: 0.003em;\"></span></span></span><span style=\"display: inline-block; width: 0px; height: 3.998em;\"></span></span><span style=\"position: absolute; clip: rect(3.332em, 1000.46em, 4.306em, -999.997em); top: -4.403em; left: 0.566em;\"><span><span style=\"font-size: 70.7%; font-family: MathJax_Math-italic;\">f<span style=\"display: inline-block; overflow: hidden; height: 1px; width: 0.054em;\"></span></span></span><span style=\"display: inline-block; width: 0px; height: 3.998em;\"></span></span><span style=\"position: absolute; 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border-left: 0px solid; width: 0px; height: 1.941em;\"></span></span></nobr><span role=\"presentation\"><math display=\"inline\" xmlns=\"http://www.w3.org/1998/Math/MathML\"><msup><mrow><mrow><mo stretchy=\"false\">(</mo></mrow><mrow><mrow><msub><mrow><mi>d</mi></mrow><mrow><mi>p</mi></mrow></msub></mrow><mrow><mo>/</mo></mrow><mrow><msubsup><mrow><mi>d</mi></mrow><mrow><mi>p</mi></mrow><mrow><mi>f</mi></mrow></msubsup></mrow></mrow><mrow><mo stretchy=\"false\">)</mo></mrow></mrow><mrow><mn>2</mn></mrow></msup></math></span></span><script type=\"math/mml\"><math display=\"inline\"><msup><mrow><mrow><mo stretchy=\"false\">(</mo></mrow><mrow><mrow><msub><mrow><mi>d</mi></mrow><mrow><mi>p</mi></mrow></msub></mrow><mrow><mo>/</mo></mrow><mrow><msubsup><mrow><mi>d</mi></mrow><mrow><mi>p</mi></mrow><mrow><mi>f</mi></mrow></msubsup></mrow></mrow><mrow><mo stretchy=\"false\">)</mo></mrow></mrow><mrow><mn>2</mn></mrow></msup></math></script> that meets the required reaction time ratio of different particle sizes, which is of great interest for realizing the synchronous conversion of polydisperse particles.","PeriodicalId":39,"journal":{"name":"Industrial & Engineering Chemistry Research","volume":null,"pages":null},"PeriodicalIF":3.8000,"publicationDate":"2024-09-20","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":"0","resultStr":null,"platform":"Semanticscholar","paperid":null,"PeriodicalName":"Industrial & Engineering Chemistry Research","FirstCategoryId":"5","ListUrlMain":"https://doi.org/10.1021/acs.iecr.4c02112","RegionNum":3,"RegionCategory":"工程技术","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":null,"EPubDate":"","PubModel":"","JCR":"Q2","JCRName":"ENGINEERING, CHEMICAL","Score":null,"Total":0}
引用次数: 0

Abstract

The residence time of polydisperse particles is crucial for their simultaneous conversion in a fluidized bed. This study focuses on regulating the residence time of polydisperse particles to expand their controllable range by optimizing the reactor design and operation step-by-step. The mean residence time (MRT) ratio of coarse and fine particles (tpc/tpf) increased significantly with increasing elutriation pipe width of the multiple-chamber fluidized bed, thus enabling the MRT ratio to exceed (dpc/dpf)2; however, the MRT ratio of medium and fine particles (tpm/tpf) is only slightly exceeded dpm/dpf. Moreover, by further optimizing the elutriation pipe gas velocity, the latter can be adjusted to be exceed (dpm/dpf)1.5. Finally, tpc/tpf and tpm/tpf can be simultaneously adjusted to exceed (dp/dpf)2 by increasing the number of elutriation pipes. Therefore, present study enables the controllable range of the MRT ratio of polydisperse particles covering from dp/dpf2 to (dp/dpf)2 that meets the required reaction time ratio of different particle sizes, which is of great interest for realizing the synchronous conversion of polydisperse particles.

Abstract Image

扩大多室流化床中多分散颗粒平均停留时间比的可控范围:粗粒度 CFD-DEM 研究
多分散颗粒的停留时间对于它们在流化床中的同步转化至关重要。本研究的重点是通过逐步优化反应器的设计和操作,调节多分散颗粒的停留时间,以扩大其可控范围。随着多室流化床洗脱管宽度的增加,粗颗粒和细颗粒(tcp/tfptpc/tpftpc/tpf)的平均停留时间(MRT)比显著增加,从而使MRT比超过了(dcp/dfp)2(dpc/dpf)2(dpc/dpf)2;然而,中颗粒和细颗粒(tmp/tfptpm/tpftpm/tpf)的MRT比仅略微超过了dmp/dfpdpm/dpfdpm/dpf。此外,通过进一步优化洗脱管道的气速,后者可以调整到超过 (dmp/dfp)1.5(dpm/dpf)1.5(dpm/dpf)1.5 的水平。最后,通过增加洗脱管道的数量,tcp/tfptpc/tpftpc/tpf 和 tmp/tfptpm/tpftpm/tpf 可同时调节到超过 (dp/dfp)2(dp/dpf)2(dp/dpf)2 的水平。因此,本研究实现了多分散颗粒 MRT 比率的可控范围,从 dp/dfp2dp/dpf2dp/dpf2 到 (dp/dfp)2(dp/dpf)2(dp/dpf)2,满足了不同粒度所需的反应时间比率,这对于实现多分散颗粒的同步转化具有重大意义。
本文章由计算机程序翻译,如有差异,请以英文原文为准。
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来源期刊
Industrial & Engineering Chemistry Research
Industrial & Engineering Chemistry Research 工程技术-工程:化工
CiteScore
7.40
自引率
7.10%
发文量
1467
审稿时长
2.8 months
期刊介绍: ndustrial & Engineering Chemistry, with variations in title and format, has been published since 1909 by the American Chemical Society. Industrial & Engineering Chemistry Research is a weekly publication that reports industrial and academic research in the broad fields of applied chemistry and chemical engineering with special focus on fundamentals, processes, and products.
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