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<front>
<journal-meta>
<journal-id journal-id-type="publisher-id">Front. Chem. Eng.</journal-id>
<journal-title>Frontiers in Chemical Engineering</journal-title>
<abbrev-journal-title abbrev-type="pubmed">Front. Chem. Eng.</abbrev-journal-title>
<issn pub-type="epub">2673-2718</issn>
<publisher>
<publisher-name>Frontiers Media S.A.</publisher-name>
</publisher>
</journal-meta>
<article-meta>
<article-id pub-id-type="publisher-id">742963</article-id>
<article-id pub-id-type="doi">10.3389/fceng.2021.742963</article-id>
<article-categories>
<subj-group subj-group-type="heading">
<subject>Chemical Engineering</subject>
<subj-group>
<subject>Original Research</subject>
</subj-group>
</subj-group>
</article-categories>
<title-group>
<article-title>Feasibility Study of Vacuum Pressure Swing Adsorption for CO<sub>2</sub> Capture From an SMR Hydrogen Plant: Comparison Between Synthesis Gas Capture and Tail Gas Capture</article-title>
<alt-title alt-title-type="left-running-head">Chen and Ahn</alt-title>
<alt-title alt-title-type="right-running-head">CO2 VPSA for H2 Plant</alt-title>
</title-group>
<contrib-group>
<contrib contrib-type="author">
<name>
<surname>Chen</surname>
<given-names>Yan</given-names>
</name>
<uri xlink:href="https://loop.frontiersin.org/people/1562447/overview"/>
</contrib>
<contrib contrib-type="author" corresp="yes">
<name>
<surname>Ahn</surname>
<given-names>Hyungwoong</given-names>
</name>
<xref ref-type="corresp" rid="c001">&#x2a;</xref>
<uri xlink:href="https://loop.frontiersin.org/people/158932/overview"/>
</contrib>
</contrib-group>
<aff>Institute for Materials and Processes, School of Engineering, The University of Edinburgh, <addr-line>Edinburgh</addr-line>, <country>United&#x20;Kingdom</country>
</aff>
<author-notes>
<fn fn-type="edited-by">
<p>
<bold>Edited by:</bold> <ext-link ext-link-type="uri" xlink:href="https://loop.frontiersin.org/people/767214/overview">Moises Bastos-Neto</ext-link>, Federal University of Ceara, Brazil</p>
</fn>
<fn fn-type="edited-by">
<p>
<bold>Reviewed by:</bold> <ext-link ext-link-type="uri" xlink:href="https://loop.frontiersin.org/people/903955/overview">Rui P.P.L. Ribeiro</ext-link>, New University of Lisbon, Portugal</p>
<p>
<ext-link ext-link-type="uri" xlink:href="https://loop.frontiersin.org/people/1079076/overview">Luca Riboldi</ext-link>, Norwegian University of Science and Technology, Norway</p>
<p>
<ext-link ext-link-type="uri" xlink:href="https://loop.frontiersin.org/people/987694/overview">Giorgia Mondino</ext-link>, SINTEF Industry, Norway</p>
</fn>
<corresp id="c001">&#x2a;Correspondence: Hyungwoong Ahn, <email>H.Ahn@ed.ac.uk</email>
</corresp>
<fn fn-type="other">
<p>This article was submitted to Chemical Reaction Engineering, a section of the journal Frontiers in Chemical Engineering</p>
</fn>
</author-notes>
<pub-date pub-type="epub">
<day>01</day>
<month>12</month>
<year>2021</year>
</pub-date>
<pub-date pub-type="collection">
<year>2021</year>
</pub-date>
<volume>3</volume>
<elocation-id>742963</elocation-id>
<history>
<date date-type="received">
<day>17</day>
<month>07</month>
<year>2021</year>
</date>
<date date-type="accepted">
<day>04</day>
<month>11</month>
<year>2021</year>
</date>
</history>
<permissions>
<copyright-statement>Copyright &#xa9; 2021 Chen and Ahn.</copyright-statement>
<copyright-year>2021</copyright-year>
<copyright-holder>Chen and Ahn</copyright-holder>
<license xlink:href="http://creativecommons.org/licenses/by/4.0/">
<p>This is an open-access article distributed under the terms of the Creative Commons Attribution License (CC BY). The use, distribution or reproduction in other forums is permitted, provided the original author(s) and the copyright owner(s) are credited and that the original publication in this journal is cited, in accordance with accepted academic practice. No use, distribution or reproduction is permitted which does not comply with these&#x20;terms.</p>
</license>
</permissions>
<abstract>
<p>In this paper, a feasibility study was carried out to evaluate cyclic adsorption processes for capturing CO<sub>2</sub> from either shifted synthesis gas or H<sub>2</sub> PSA tail gas of an industrial-scale SMR-based hydrogen plant. It is expected that hydrogen is to be widely used in place of natural gas in various industrial sectors where electrification would be rather challenging. A SMR-based hydrogen plant is currently dominant in the market, as it can produce hydrogen at scale in the most economical way. Its CO<sub>2</sub> emission must be curtailed significantly by its integration with CCUS. Two Vacuum Pressure Swing Adsorption (VPSA) systems including a rinse step were designed to capture CO<sub>2</sub> from an industrial-scale SMR-based hydrogen plant: one for the shifted synthesis gas and the other for the H<sub>2</sub> PSA tail gas. Given the shapes of adsorption isotherms, zeolite 13X and activated carbon were selected for tail gas and syngas capture options, respectively. A simple Equilibrium Theory model developed for the limiting case of complete regeneration was taken to analyse the VPSA systems in this feasibility study. The process performances were compared to each other with respect to product recovery, bed productivity and power consumption. It was found that CO<sub>2</sub> could be captured more cost-effectively from the syngas than the tail gas, unless the desorption pressure was too low. The energy consumption of the VPSA was comparable to those of the conventional MDEA processes.</p>
</abstract>
<kwd-group>
<kwd>CO<sup>2</sup> capture</kwd>
<kwd>equilibrium theory</kwd>
<kwd>hydrogen plant</kwd>
<kwd>pressure swing adsorption</kwd>
<kwd>synthesis gas</kwd>
<kwd>PSA tail gas</kwd>
<kwd>energy consumption</kwd>
<kwd>MDEA process</kwd>
</kwd-group>
<contract-sponsor id="cn001">Engineering and Physical Sciences Research Council<named-content content-type="fundref-id">10.13039/501100000266</named-content>
</contract-sponsor>
</article-meta>
</front>
<body>
<sec id="s1">
<title>Introduction</title>
<p>UK has set a legally binding target to achieve net zero GHG emission by 2050 by revising the Climate Change Act 2008 in 2019. Similarly, Scottish Government has published its Hydrogen Policy Statement in which it is aimed to achieve net zero greenhouse gas emissions by 2045 and a 75% reduction by 2030 against the 1990 baseline (<xref ref-type="bibr" rid="B16">Scottish Government, 2020a</xref>). There is no doubts that both low-carbon hydrogen and renewable energy will play a pivotal role in the net zero GHG emission economy. Hydrogen will be taken as a fuel in the sectors where full electrification is challenging, such as furnace, long haul transport, etc., Also, hydrogen is considered as a good energy carrier, as it can be generated by electrolysis using the extra renewable electricity that would otherwise be wasted. For a net zero GHG emission, it is crucial capturing CO<sub>2</sub> from the air, in other words, negative emission. The biomass-derived hydrogen integrated with CCUS (Carbon Capture, Utilisation and Storage) as well as direct air capture are identified as promising negative emission routes.</p>
<p>Accordingly, each country has announced a roadmap to expand drastically the hydrogen supply capacity for the next 30&#xa0;years. UK plans to install 5&#xa0;GW of green and blue H<sub>2</sub> production by 2030 and estimates the H<sub>2</sub> demand in 2050 will reach 250&#x20;&#x2013; 460&#xa0;TWh, equivalent to 20&#x20;&#x2013; 35% of UK energy consumption (<xref ref-type="bibr" rid="B21">UK BEIS, 2021</xref>).</p>
<p>Up to now, hydrogen is produced at scale by reforming fossil fuels, mainly natural gas and coal. However, a chemical process producing grey hydrogen by reforming a natural gas using steam involves enormous CO<sub>2</sub> emission at a rate of 10 ton CO<sub>2</sub> per 1 ton&#x20;H<sub>2</sub>.</p>
<p>In principle, such an enormous CO<sub>2</sub> emission involved in grey H<sub>2</sub> production can be reduced greatly by its integration with CCUS. The hydrogen that is produced by reforming reactions of fossil fuels with its CO2 emission curtailed by CCUS is referred to as blue hydrogen.</p>
<p>Green hydrogen is defined as the hydrogen produced by splitting water (H<sub>2</sub>O) in an electrolyser powered by electricity. The electricity that an electrolyser consumes must not involve CO2 emission over the process of its production to claim its &#x201c;green&#x201d; credit. Green hydrogen is obviously more promising than blue hydrogen in terms of sustainability, but the hydrogen demand that is expected to grow rapidly for achieving the net zero GHG emission target can be met only by producing both green and blue hydrogens. As pointed out by the latest Hydrogen Assessment report (<xref ref-type="bibr" rid="B17">Scottish Government, 2020b</xref>), green hydrogen is currently economically unfeasible, as its production cost is almost three times that of blue hydrogen. According to the study, it is not until 2050 that green hydrogen&#x2019;s levelised cost will be reduced to an extent that it becomes comparable to the blue hydrogen&#x2019;s levelised cost. Constructing an infrastructure for supplying a huge amount of renewable electricity to electrolysis plants must take precedence in order to produce green hydrogen at&#x20;scale.</p>
<p>Hence, blue hydrogen production is essential for propping up the hydrogen economy for the next decades to come before green hydrogen technologies mature. In this respect, we must endeavour to develop the most cost-effective way of capturing CO<sub>2</sub> from a reforming-based H<sub>2</sub>&#x20;plant.</p>
<p>Currently, a majority of hydrogen production plants are based on steam methane reforming (SMR) of hydrocarbon gases. The SMR H<sub>2</sub> plant mainly comprises reforming reactors followed by a hydrogen purification Pressure Swing Adsorption (PSA) as shown in <xref ref-type="fig" rid="F1">Figure&#x20;1</xref>. In principle, the highly endothermic SMR reaction is favoured by low pressure and high temperature conditions, whilst the subsequent PSA unit needs a feed at high pressure and low temperature conditions for a decent working capacity of adsorbents. It is not advisable compressing the synthesis gas between the reforming and purification sections, as it would incur a huge energy penalty. A SMR H<sub>2</sub> plant is normally designed to operate at around 20 bara, to reconcile the conflicting desired operating conditions of the two main&#x20;units.</p>
<fig id="F1" position="float">
<label>FIGURE 1</label>
<caption>
<p>Process flow of a SMR hydrogen production plant and three process streams where CO<sub>2</sub> can be captured.</p>
</caption>
<graphic xlink:href="fceng-03-742963-g001.tif"/>
</fig>
<p>As shown in <xref ref-type="fig" rid="F1">Figure&#x20;1</xref>, CO<sub>2</sub> can be captured from shifted synthesis gas (syngas), H<sub>2</sub> PSA tail gas (tail gas) or flue gas (<xref ref-type="bibr" rid="B19">Soltani et&#x20;al., 2014</xref>; <xref ref-type="bibr" rid="B22">Voss, 2014</xref>). To identify the stream conditions of the three process streams, a 6.8 ton H<sub>2</sub>/hr-scale H<sub>2</sub> production plant was simulated using Honeywell UniSim. <xref ref-type="table" rid="T1">Table&#x20;1</xref> shows stream conditions of the synthesis gas and the PSA tail gas that were estimated in the H<sub>2</sub> plant UniSim simulation. A typical SMR H<sub>2</sub> plant exhibits the following performances: 1) CH<sub>4</sub> feed consumption (2.5&#x2013;3.5 Gcal/1,000&#xa0;Nm<sup>3</sup> H<sub>2</sub>), 2) CH<sub>4</sub> fuel consumption (0.5&#x2013;1.5 Gcal/1,000&#xa0;Nm<sup>3</sup> H<sub>2</sub>), 3) Steam export (0.3&#x2013;0.8 Gcal/1,000&#xa0;Nm<sup>3</sup> H<sub>2</sub>), and 4) CO<sub>2</sub> emission rate (around 800&#xa0;kg CO<sub>2</sub>/1,000&#xa0;Nm<sup>3</sup> H<sub>2</sub>). The extra steam available in a SMR H<sub>2</sub> plant is so useful as it can be utilised to run a carbon capture plant that often requires heat or electricity for sorbent regeneration.</p>
<table-wrap id="T1" position="float">
<label>TABLE 1</label>
<caption>
<p>Stream conditions of two VPSA feed gases in the SMR hydrogen plant at the production capacity of 6.8 ton H<sub>2</sub>/hr.</p>
</caption>
<table>
<thead valign="top">
<tr>
<th align="left">Process stream</th>
<th align="center">Shifted synthesis gas</th>
<th align="center">H<sub>2</sub> PSA tail gas</th>
</tr>
</thead>
<tbody valign="top">
<tr>
<td align="left">Molar flowrate [kmol&#xa0;hr<sup>&#x2212;1</sup>]</td>
<td align="center">5,099</td>
<td align="center">1,626</td>
</tr>
<tr>
<td align="left">Actual volumetric flowrate [m<sup>3</sup>&#xa0;s<sup>&#x2212;1</sup>]</td>
<td align="center">1.73</td>
<td align="center">7.59</td>
</tr>
<tr>
<td align="left">Gas composition of the actual feed gas [mol %]</td>
<td align="center">75% H<sub>2</sub>, 18% CO<sub>2</sub>, 4% CH<sub>4</sub>, 2% CO, &#x3c;1% H<sub>2</sub>O</td>
<td align="center">24% H<sub>2</sub>, 57% CO<sub>2</sub>, 11% CH<sub>4</sub>, 7% CO, 1% H<sub>2</sub>O</td>
</tr>
<tr>
<td align="left">Gas composition of the simulated feed approximated by binary mixture [mol %]</td>
<td align="center">82% H<sub>2</sub>, 18% CO<sub>2</sub>
</td>
<td align="center">43% H<sub>2</sub>, 57% CO<sub>2</sub>
</td>
</tr>
<tr>
<td align="left">Temperature [K]</td>
<td align="center">308</td>
<td align="center">308</td>
</tr>
<tr>
<td align="left">Feed pressure [bar]</td>
<td align="center">21</td>
<td align="center">1.5</td>
</tr>
</tbody>
</table>
</table-wrap>
<p>Among the three stream candidates, the flue gas has been ruled out on the grounds that its CO<sub>2</sub> partial pressure is the lowest of three. Both syngas and tail gas are worth investigation as each of two has some distinctive features that make the gas favourable for CO<sub>2</sub> capture. The syngas has the highest CO<sub>2</sub> partial pressure of around 3 bara and the lowest actual gas volumetric flowrate. In contrast, the tail gas has the highest CO<sub>2</sub> mole fraction of 0.57 and the lowest molar flowrate. It should be noted that the overall CO<sub>2</sub> capture rate could increase from 59% to 90&#x2b;% in case of the syngas capture case, as the decarbonised syngas can also be used as fuel in place of natural gas fuel (<xref ref-type="bibr" rid="B7">Ieaghg, 2017</xref>).</p>
<p>Several blue hydrogen projects have been commercialised successfully. The most eminent ones are Air Products&#x2019; Port Arthur project and Shell&#x2019;s Quest CCS project, both of which capture CO<sub>2</sub> from syngas. The Port Arthur project has captured 7 million tonnes of CO<sub>2</sub> with a Vacuum Swing Adsorption process and used the CO<sub>2</sub> for EOR since 2013. Quest CCS Project has captured over 5 million tonnes of CO<sub>2</sub> with an amine process using ADIP-X solvent, a mixture of MDEA and piperazine, since 2015. CO<sub>2</sub> capture from tail gas has also been developed at scales close to commercialisation. Japan&#x2019;s Tomakomai project features a MDEA process with a capacity of 0.1&#xa0;Mt CO<sub>2</sub> per year. Air Liquide&#x2019;s Port Jerome Project has developed a hybrid process comprising a cold box for CO<sub>2</sub> liquefaction and a membrane unit for H<sub>2</sub> recovery.</p>
<p>Among various CO<sub>2</sub> capture processes considered for blue hydrogen production, it appears that adsorptive capture processes are the most harmonious with a hydrogen production plant in a sense that they may be able to produce pure hydrogen as well as pure CO<sub>2</sub>. Adsorption processes, once applied to syngas for CO2 capture, can be configured so as to produce a high purity of hydrogen as well as a high purity of CO<sub>2</sub> (<xref ref-type="bibr" rid="B18">Sircar and Kratz, 1988</xref>; <xref ref-type="bibr" rid="B20">Streb and Mazzotti, 2020</xref>). Accordingly, a CO<sub>2</sub> capture adsorption unit may be able to replace the existing H<sub>2</sub> purification PSA in case of syngas capture, and it can also produce additional hydrogen product in case of tail gas capture as shown in <xref ref-type="fig" rid="F2">Figure&#x20;2</xref>.</p>
<fig id="F2" position="float">
<label>FIGURE 2</label>
<caption>
<p>Block flow diagram of an SMR hydrogen plant integrated with a 5-step VPSA for CO<sub>2</sub> capture: <bold>(A)</bold> syngas capture and <bold>(B)</bold> tail gas capture.</p>
</caption>
<graphic xlink:href="fceng-03-742963-g002.tif"/>
</fig>
<p>In this study it was aimed to carry out a feasibility study of cyclic adsorption processes for CO<sub>2</sub> capture from the syngas and the tail gas. For the sake of simplicity, the process streams were approximated by a binary mixture of H<sub>2</sub> and CO<sub>2</sub> in which the other gases were replaced by hydrogen. The CO<sub>2</sub> capture PSA design was based on a simple five-step VPSA cycle as shown in <xref ref-type="fig" rid="F3">Figure&#x20;3</xref>. The CO<sub>2</sub> capture PSA was analysed by Equilibrium Theory method, the mathematical model of which is delineated in the reference (<xref ref-type="bibr" rid="B15">Ruthven et&#x20;al., 1994</xref>) and presented in <italic>Equilibrium Theory Model for PSA Analysis</italic> Section. As depicted in <xref ref-type="fig" rid="F3">Figure&#x20;3</xref>, the five-step PSA unit has four effluents: pure H<sub>2</sub>, pure CO<sub>2</sub>, rinse step effluent and mixed gas. Accordingly, <xref ref-type="fig" rid="F3">Figure&#x20;3</xref> shows clearly where the four outlet streams are directed to. The two capture systems are to be designed by Equilibrium Theory and evaluated in terms of various performance indices for comparison.</p>
<fig id="F3" position="float">
<label>FIGURE 3</label>
<caption>
<p>Step sequence of a five-step VPSA cycle for CO<sub>2</sub> capture.</p>
</caption>
<graphic xlink:href="fceng-03-742963-g003.tif"/>
</fig>
</sec>
<sec id="s2">
<title>Mathematical Model</title>
<sec id="s2-1">
<title>Adsorption Isotherm</title>
<p>In this study, activated carbon and zeolite 13X were chosen for selective adsorption of CO<sub>2</sub> from the syngas and the tail gas, respectively. In designing a hydrogen purification PSA system of a SMR hydrogen plant (see <xref ref-type="fig" rid="F1">Figure&#x20;1</xref>), activated carbons are often taken for the bottom layer near the column end that the feed gas is admitted to. This is because activated carbons own excellent CO<sub>2</sub> adsorption capacities at the CO<sub>2</sub> partial pressure in the feed (<xref ref-type="bibr" rid="B2">Ahn et&#x20;al., 1999</xref>; <xref ref-type="bibr" rid="B10">Lee et&#x20;al., 1999</xref>; <xref ref-type="bibr" rid="B5">Ahn et&#x20;al., 2001</xref>). In contrast, zeolite 13X is deemed a benchmark adsorbent for capturing CO<sub>2</sub> from a gas mixture around atmospheric pressure, for example, a flue gas composed mainly of N<sub>2</sub> and CO<sub>2</sub> (<xref ref-type="bibr" rid="B9">Krishnamurthy et&#x20;al., 2014</xref>; <xref ref-type="bibr" rid="B11">Luberti et&#x20;al., 2017</xref>; <xref ref-type="bibr" rid="B1">Ahn et&#x20;al., 2020</xref>) and a synthesis gas generated by biomass gasification (<xref ref-type="bibr" rid="B12">Oreggioni et&#x20;al., 2015</xref>). The CO<sub>2</sub> isotherms of the two adsorbents are compared in <xref ref-type="fig" rid="F4">Figure&#x20;4A</xref>. The CO<sub>2</sub> isotherm on 13X is so close to an irreversible isotherm that it can capture large CO<sub>2</sub> even at a very low CO<sub>2</sub> partial pressure and the CO<sub>2</sub> consumption for the rinse step would be very low. However, the 13X column is hard to regenerate unless it is evacuated to a very low pressure. The CO<sub>2</sub> isotherm on the activated carbon is still favourable but way less irreversible than that on 13X, which imparts an excellent working capacity of CO<sub>2</sub> without having to reduce the pressure so low for desorption.</p>
<fig id="F4" position="float">
<label>FIGURE 4</label>
<caption>
<p>Equilibrium adsorption isotherms of <bold>(A)</bold> CO<sub>2</sub> and <bold>(B)</bold> H<sub>2</sub> on zeolite 13X and activated carbon at 308&#xa0;K.</p>
</caption>
<graphic xlink:href="fceng-03-742963-g004.tif"/>
</fig>
<p>The dual-site Langmuir isotherm was taken to estimate the non-linear adsorption isotherm of CO<sub>2</sub> on the activated carbon.<disp-formula id="e1">
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<label>(1)</label>
</disp-formula>in which <italic>q</italic>
<sub>
<italic>As1</italic>
</sub> &#x3d; 6.611&#xa0;mol&#xa0;kg<sup>&#x2212;1</sup>, <italic>q</italic>
<sub>
<italic>As2</italic>
</sub> &#x3d; 0.011&#xa0;mol&#xa0;kg<sup>&#x2212;1</sup>, <italic>b</italic>
<sub>
<italic>A1</italic>
</sub> &#x3d;&#x20;0.4762&#x20;bar<sup>&#x2212;1</sup>, <italic>b</italic>
<sub>
<italic>A2</italic>
</sub> &#x3d; 3.492&#xa0;bar<sup>&#x2212;1</sup>&#xa0;at 308&#xa0;K (<xref ref-type="bibr" rid="B14">Park et&#x20;al., 2021</xref>).</p>
<p>The CO<sub>2</sub> adsorption on the 13X was estimated by single-site Langmuir isotherm.<disp-formula id="e2">
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<mml:mi>A</mml:mi>
</mml:msub>
</mml:mrow>
<mml:mrow>
<mml:mn>1</mml:mn>
<mml:mo>&#x2b;</mml:mo>
<mml:msub>
<mml:mi>b</mml:mi>
<mml:mi>A</mml:mi>
</mml:msub>
<mml:msub>
<mml:mi>P</mml:mi>
<mml:mi>A</mml:mi>
</mml:msub>
</mml:mrow>
</mml:mfrac>
</mml:mrow>
</mml:math>
<label>(2)</label>
</disp-formula>in which <italic>q</italic>
<sub>
<italic>As</italic>
</sub> &#x3d; 5.145&#xa0;mol&#xa0;kg<sup>&#x2212;1</sup>, <italic>b</italic>
<sub>
<italic>A</italic>
</sub> &#x3d; 9.007&#xa0;bar<sup>&#x2212;1</sup>&#xa0;at 308&#xa0;K (<xref ref-type="bibr" rid="B13">Park et&#x20;al., 2016</xref>).</p>
<p>In stark contrast, the equilibrium isotherms of hydrogen on both adsorbents are so close to linearity as shown in <xref ref-type="fig" rid="F4">Figure&#x20;4B</xref> (<xref ref-type="bibr" rid="B13">Park et&#x20;al., 2016</xref>; <xref ref-type="bibr" rid="B14">Park et&#x20;al., 2021</xref>). In this study, the two hydrogen isotherms were approximated by linear isotherms by regressing the data over the range of measurement. The slopes of the fitted linear isotherms are 0.0421&#xa0;mol&#xa0;kg<sup>&#x2212;1</sup> bar<sup>&#x2212;1</sup> and 0.0175&#xa0;mol&#xa0;kg<sup>&#x2212;1</sup> bar<sup>&#x2212;1</sup> for activated carbon and 13X, respectively.</p>
</sec>
<sec id="s2-2">
<title>Equilibrium Theory Model for PSA Analysis</title>
<p>The PSA system with a rinse step shown in <xref ref-type="fig" rid="F3">Figure&#x20;3</xref> is the simplest step sequence for producing the heavy component at a very high purity during the blowdown step and the 5-step PSA system was analysed by Equilibrium Theory. The performance of a 5-step PSA working to separate a binary gas mixture can be estimated by <xref ref-type="disp-formula" rid="e3a">Eqs 3a</xref>&#x2013;<xref ref-type="disp-formula" rid="e9">9</xref> that are derived and presented in the reference (<xref ref-type="bibr" rid="B15">Ruthven et&#x20;al., 1994</xref>). In the mathematical expression, the strongly adsorbing component A&#x2019;s adsorption equilibrium is allowed to be nonlinear while the weakly adsorbing component B&#x2019;s adsorption isotherm must be linear with pressure or concentration. In addition to the general assumptions required for Equilibrium Theory, it was also assumed that the two adsorption isotherms are uncoupled. This model was developed under the limiting condition that a column is fully regenerated during the purge step for the sake of simplicity.</p>
<p>In order to estimate the product recovery, bed productivity and power consumption, it is crucial to estimate the total number of moles of the influent and effluent during each step. The equations for the quantities were all derived using Equilibrium Theory and they are listed below. Subscript I and O indicate influent and effluent, respectively.<list list-type="simple">
<list-item>
<p>&#x2022; Feed&#x20;step.</p>
</list-item>
</list>
<disp-formula id="e3a">
<mml:math id="m3">
<mml:mrow>
<mml:msub>
<mml:mi>N</mml:mi>
<mml:mrow>
<mml:mi>F</mml:mi>
<mml:mi>I</mml:mi>
</mml:mrow>
</mml:msub>
<mml:mo>&#x3d;</mml:mo>
<mml:mfrac>
<mml:mrow>
<mml:msub>
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<mml:mi>H</mml:mi>
</mml:msub>
<mml:mi>L</mml:mi>
<mml:mi>&#x3b5;</mml:mi>
<mml:msub>
<mml:mi>A</mml:mi>
<mml:mi>c</mml:mi>
</mml:msub>
</mml:mrow>
<mml:mrow>
<mml:msub>
<mml:mi>&#x3b8;</mml:mi>
<mml:mi>A</mml:mi>
</mml:msub>
<mml:mrow>
<mml:mo>(</mml:mo>
<mml:mrow>
<mml:msub>
<mml:mi>P</mml:mi>
<mml:mi>H</mml:mi>
</mml:msub>
<mml:mo>,</mml:mo>
<mml:msub>
<mml:mi>y</mml:mi>
<mml:mi>f</mml:mi>
</mml:msub>
<mml:mo>,</mml:mo>
<mml:mn>0</mml:mn>
</mml:mrow>
<mml:mo>)</mml:mo>
</mml:mrow>
<mml:mi>R</mml:mi>
<mml:mi>T</mml:mi>
</mml:mrow>
</mml:mfrac>
</mml:mrow>
</mml:math>
<label>(3a)</label>
</disp-formula>
<disp-formula id="e3b">
<mml:math id="m4">
<mml:mrow>
<mml:msub>
<mml:mi>N</mml:mi>
<mml:mrow>
<mml:mi>F</mml:mi>
<mml:mi>O</mml:mi>
</mml:mrow>
</mml:msub>
<mml:mo>&#x3d;</mml:mo>
<mml:msub>
<mml:mi>N</mml:mi>
<mml:mrow>
<mml:mi>F</mml:mi>
<mml:mi>I</mml:mi>
</mml:mrow>
</mml:msub>
<mml:mrow>
<mml:mo>[</mml:mo>
<mml:mrow>
<mml:mn>1</mml:mn>
<mml:mo>&#x2b;</mml:mo>
<mml:mrow>
<mml:mo>[</mml:mo>
<mml:mrow>
<mml:mi>&#x3b8;</mml:mi>
<mml:mrow>
<mml:mo>(</mml:mo>
<mml:mrow>
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<mml:mi>H</mml:mi>
</mml:msub>
<mml:mo>,</mml:mo>
<mml:msub>
<mml:mi>y</mml:mi>
<mml:mi>f</mml:mi>
</mml:msub>
<mml:mo>,</mml:mo>
<mml:mn>0</mml:mn>
</mml:mrow>
<mml:mo>)</mml:mo>
</mml:mrow>
<mml:mo>&#x2212;</mml:mo>
<mml:mn>1</mml:mn>
</mml:mrow>
<mml:mo>]</mml:mo>
</mml:mrow>
<mml:msub>
<mml:mi>y</mml:mi>
<mml:mi>f</mml:mi>
</mml:msub>
</mml:mrow>
<mml:mo>]</mml:mo>
</mml:mrow>
</mml:mrow>
</mml:math>
<label>(3b)</label>
</disp-formula>
<list list-type="simple">
<list-item>
<p>&#x2022; Rinse&#x20;step.</p>
</list-item>
</list>
<disp-formula id="e4a">
<mml:math id="m5">
<mml:mrow>
<mml:msub>
<mml:mi>N</mml:mi>
<mml:mrow>
<mml:mi>R</mml:mi>
<mml:mi>I</mml:mi>
</mml:mrow>
</mml:msub>
<mml:mo>&#x3d;</mml:mo>
<mml:msub>
<mml:mi>N</mml:mi>
<mml:mrow>
<mml:mi>R</mml:mi>
<mml:mi>O</mml:mi>
</mml:mrow>
</mml:msub>
<mml:mfrac>
<mml:mrow>
<mml:mn>1</mml:mn>
<mml:mo>&#x2b;</mml:mo>
<mml:mrow>
<mml:mo>[</mml:mo>
<mml:mrow>
<mml:mi>&#x3b8;</mml:mi>
<mml:mrow>
<mml:mo>(</mml:mo>
<mml:mrow>
<mml:msub>
<mml:mi>P</mml:mi>
<mml:mi>H</mml:mi>
</mml:msub>
<mml:mo>,</mml:mo>
<mml:mn>1</mml:mn>
<mml:mo>,</mml:mo>
<mml:msub>
<mml:mi>y</mml:mi>
<mml:mi>f</mml:mi>
</mml:msub>
</mml:mrow>
<mml:mo>)</mml:mo>
</mml:mrow>
<mml:mo>&#x2212;</mml:mo>
<mml:mn>1</mml:mn>
</mml:mrow>
<mml:mo>]</mml:mo>
</mml:mrow>
<mml:msub>
<mml:mi>y</mml:mi>
<mml:mi>f</mml:mi>
</mml:msub>
</mml:mrow>
<mml:mrow>
<mml:mi>&#x3b8;</mml:mi>
<mml:mrow>
<mml:mo>(</mml:mo>
<mml:mrow>
<mml:msub>
<mml:mi>P</mml:mi>
<mml:mi>H</mml:mi>
</mml:msub>
<mml:mo>,</mml:mo>
<mml:mn>1</mml:mn>
<mml:mo>,</mml:mo>
<mml:msub>
<mml:mi>y</mml:mi>
<mml:mi>f</mml:mi>
</mml:msub>
</mml:mrow>
<mml:mo>)</mml:mo>
</mml:mrow>
</mml:mrow>
</mml:mfrac>
</mml:mrow>
</mml:math>
<label>(4a)</label>
</disp-formula>
<disp-formula id="e4b">
<mml:math id="m6">
<mml:mrow>
<mml:msub>
<mml:mi>N</mml:mi>
<mml:mrow>
<mml:mi>R</mml:mi>
<mml:mi>O</mml:mi>
</mml:mrow>
</mml:msub>
<mml:mo>&#x3d;</mml:mo>
<mml:mfrac>
<mml:mrow>
<mml:msub>
<mml:mi>P</mml:mi>
<mml:mi>H</mml:mi>
</mml:msub>
<mml:mi>L</mml:mi>
<mml:mi>&#x3b5;</mml:mi>
<mml:msub>
<mml:mi>A</mml:mi>
<mml:mi>c</mml:mi>
</mml:msub>
</mml:mrow>
<mml:mrow>
<mml:msub>
<mml:mi>&#x3b2;</mml:mi>
<mml:mi>B</mml:mi>
</mml:msub>
<mml:mi>R</mml:mi>
<mml:mi>T</mml:mi>
</mml:mrow>
</mml:mfrac>
</mml:mrow>
</mml:math>
<label>(4b)</label>
</disp-formula>
<list list-type="simple">
<list-item>
<p>&#x2022; Blowdown&#x20;step.</p>
</list-item>
</list>
<disp-formula id="e5">
<mml:math id="m7">
<mml:mrow>
<mml:msub>
<mml:mi>N</mml:mi>
<mml:mrow>
<mml:mi>B</mml:mi>
<mml:mi>O</mml:mi>
</mml:mrow>
</mml:msub>
<mml:mo>&#x3d;</mml:mo>
<mml:mfrac>
<mml:mrow>
<mml:msub>
<mml:mi>P</mml:mi>
<mml:mi>H</mml:mi>
</mml:msub>
<mml:mi>L</mml:mi>
<mml:mi>&#x3b5;</mml:mi>
<mml:msub>
<mml:mi>A</mml:mi>
<mml:mi>c</mml:mi>
</mml:msub>
</mml:mrow>
<mml:mrow>
<mml:msub>
<mml:mi>&#x3b8;</mml:mi>
<mml:mi>A</mml:mi>
</mml:msub>
<mml:mrow>
<mml:mo>(</mml:mo>
<mml:mrow>
<mml:msub>
<mml:mi>P</mml:mi>
<mml:mi>H</mml:mi>
</mml:msub>
<mml:mo>,</mml:mo>
<mml:mn>1,0</mml:mn>
</mml:mrow>
<mml:mo>)</mml:mo>
</mml:mrow>
<mml:mi>R</mml:mi>
<mml:mi>T</mml:mi>
</mml:mrow>
</mml:mfrac>
<mml:mo>&#x2212;</mml:mo>
<mml:mfrac>
<mml:mrow>
<mml:msub>
<mml:mi>P</mml:mi>
<mml:mi>L</mml:mi>
</mml:msub>
<mml:mi>L</mml:mi>
<mml:mi>&#x3b5;</mml:mi>
<mml:msub>
<mml:mi>A</mml:mi>
<mml:mi>c</mml:mi>
</mml:msub>
</mml:mrow>
<mml:mrow>
<mml:msub>
<mml:mi>&#x3b8;</mml:mi>
<mml:mi>A</mml:mi>
</mml:msub>
<mml:mrow>
<mml:mo>(</mml:mo>
<mml:mrow>
<mml:msub>
<mml:mi>P</mml:mi>
<mml:mi>L</mml:mi>
</mml:msub>
<mml:mo>,</mml:mo>
<mml:mn>1,0</mml:mn>
</mml:mrow>
<mml:mo>)</mml:mo>
</mml:mrow>
<mml:mi>R</mml:mi>
<mml:mi>T</mml:mi>
</mml:mrow>
</mml:mfrac>
</mml:mrow>
</mml:math>
<label>(5)</label>
</disp-formula>
<list list-type="simple">
<list-item>
<p>&#x2022; Purge&#x20;step</p>
</list-item>
</list>
<disp-formula id="e6a">
<mml:math id="m8">
<mml:mrow>
<mml:msub>
<mml:mi>N</mml:mi>
<mml:mrow>
<mml:mi>P</mml:mi>
<mml:mi>I</mml:mi>
</mml:mrow>
</mml:msub>
<mml:mo>&#x3d;</mml:mo>
<mml:mfrac>
<mml:mrow>
<mml:msub>
<mml:mi>P</mml:mi>
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<mml:mi>&#x3b5;</mml:mi>
<mml:msub>
<mml:mi>A</mml:mi>
<mml:mi>c</mml:mi>
</mml:msub>
</mml:mrow>
<mml:mrow>
<mml:msub>
<mml:mi>&#x3b2;</mml:mi>
<mml:mrow>
<mml:mi>A</mml:mi>
<mml:mn>0</mml:mn>
</mml:mrow>
</mml:msub>
<mml:mi>R</mml:mi>
<mml:mi>T</mml:mi>
</mml:mrow>
</mml:mfrac>
</mml:mrow>
</mml:math>
<label>(6a)</label>
</disp-formula>
<disp-formula id="e6b">
<mml:math id="m9">
<mml:mrow>
<mml:msub>
<mml:mi>N</mml:mi>
<mml:mrow>
<mml:mi>P</mml:mi>
<mml:mi>O</mml:mi>
</mml:mrow>
</mml:msub>
<mml:mo>&#x3d;</mml:mo>
<mml:mfrac>
<mml:mrow>
<mml:msub>
<mml:mi>P</mml:mi>
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</mml:msub>
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<mml:mi>&#x3b5;</mml:mi>
<mml:msub>
<mml:mi>A</mml:mi>
<mml:mi>c</mml:mi>
</mml:msub>
</mml:mrow>
<mml:mrow>
<mml:msub>
<mml:mi>&#x3b8;</mml:mi>
<mml:mi>A</mml:mi>
</mml:msub>
<mml:mrow>
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<mml:msub>
<mml:mi>P</mml:mi>
<mml:mi>L</mml:mi>
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<mml:mo>,</mml:mo>
<mml:mn>1,0</mml:mn>
</mml:mrow>
<mml:mo>)</mml:mo>
</mml:mrow>
<mml:mi>R</mml:mi>
<mml:mi>T</mml:mi>
</mml:mrow>
</mml:mfrac>
<mml:mo>&#x2b;</mml:mo>
<mml:msub>
<mml:mi>N</mml:mi>
<mml:mrow>
<mml:mi>P</mml:mi>
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</mml:mrow>
</mml:msub>
<mml:mo>&#x2212;</mml:mo>
<mml:mfrac>
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<mml:mi>L</mml:mi>
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<mml:msub>
<mml:mi>A</mml:mi>
<mml:mi>c</mml:mi>
</mml:msub>
</mml:mrow>
<mml:mrow>
<mml:msub>
<mml:mi>&#x3b2;</mml:mi>
<mml:mi>B</mml:mi>
</mml:msub>
<mml:mi>R</mml:mi>
<mml:mi>T</mml:mi>
</mml:mrow>
</mml:mfrac>
</mml:mrow>
</mml:math>
<label>(6b)</label>
</disp-formula>
<list list-type="simple">
<list-item>
<p>&#x2022; Light Product Pressurisation.</p>
</list-item>
</list>
<disp-formula id="e7">
<mml:math id="m10">
<mml:mrow>
<mml:msub>
<mml:mi>N</mml:mi>
<mml:mrow>
<mml:mi>L</mml:mi>
<mml:mi>I</mml:mi>
</mml:mrow>
</mml:msub>
<mml:mo>&#x3d;</mml:mo>
<mml:mfrac>
<mml:mrow>
<mml:mi>L</mml:mi>
<mml:mi>&#x3b5;</mml:mi>
<mml:msub>
<mml:mi>A</mml:mi>
<mml:mi>c</mml:mi>
</mml:msub>
</mml:mrow>
<mml:mrow>
<mml:msub>
<mml:mi>&#x3b2;</mml:mi>
<mml:mi>B</mml:mi>
</mml:msub>
<mml:mi>R</mml:mi>
<mml:mi>T</mml:mi>
</mml:mrow>
</mml:mfrac>
<mml:mrow>
<mml:mo>(</mml:mo>
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<mml:msub>
<mml:mi>P</mml:mi>
<mml:mi>H</mml:mi>
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<mml:mo>&#x2212;</mml:mo>
<mml:msub>
<mml:mi>P</mml:mi>
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</mml:msub>
</mml:mrow>
<mml:mo>)</mml:mo>
</mml:mrow>
</mml:mrow>
</mml:math>
<label>(7)</label>
</disp-formula>The product recoveries of H<sub>2</sub> and CO<sub>2</sub> are estimated by simply taking the mass balance around the column as follows:<disp-formula id="e8">
<mml:math id="m11">
<mml:mrow>
<mml:msub>
<mml:mi>R</mml:mi>
<mml:mi>B</mml:mi>
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<mml:mfrac>
<mml:mrow>
<mml:msub>
<mml:mi>N</mml:mi>
<mml:mrow>
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</mml:mrow>
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<mml:mo>&#x2212;</mml:mo>
<mml:msub>
<mml:mi>N</mml:mi>
<mml:mrow>
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</mml:mrow>
</mml:msub>
<mml:mo>&#x2212;</mml:mo>
<mml:msub>
<mml:mi>N</mml:mi>
<mml:mrow>
<mml:mi>L</mml:mi>
<mml:mi>I</mml:mi>
</mml:mrow>
</mml:msub>
</mml:mrow>
<mml:mrow>
<mml:mrow>
<mml:mo>(</mml:mo>
<mml:mrow>
<mml:mn>1</mml:mn>
<mml:mo>&#x2212;</mml:mo>
<mml:msub>
<mml:mi>y</mml:mi>
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</mml:msub>
</mml:mrow>
<mml:mo>)</mml:mo>
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<mml:mrow>
<mml:mo>(</mml:mo>
<mml:mrow>
<mml:msub>
<mml:mi>N</mml:mi>
<mml:mrow>
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<mml:mi>I</mml:mi>
</mml:mrow>
</mml:msub>
<mml:mo>&#x2212;</mml:mo>
<mml:msub>
<mml:mi>N</mml:mi>
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<mml:mi>R</mml:mi>
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</mml:mrow>
</mml:msub>
</mml:mrow>
<mml:mo>)</mml:mo>
</mml:mrow>
</mml:mrow>
</mml:mfrac>
<mml:mo>&#x3d;</mml:mo>
<mml:mn>1</mml:mn>
<mml:mo>&#x2212;</mml:mo>
<mml:mfrac>
<mml:mrow>
<mml:mfrac>
<mml:mrow>
<mml:msub>
<mml:mi>&#x3b8;</mml:mi>
<mml:mi>A</mml:mi>
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<mml:mrow>
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<mml:mn>0</mml:mn>
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<mml:mo>)</mml:mo>
</mml:mrow>
</mml:mrow>
<mml:mrow>
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<label>(9)</label>
</disp-formula>The PSA system consumes power for evacuation of the column during the blowdown and purge steps and pressurisation of the rinse step&#x2019;s effluent for its recycle to the feed. The power consumption for evacuation or compression was estimated by <xref ref-type="disp-formula" rid="e10">Eq. 10</xref>.<disp-formula id="e10">
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<label>(10)</label>
</disp-formula>where F is gas flowrate (mol/s), R is gas constant (J/mol/K), T<sub>1</sub> is inlet temperature (K), &#x3b3; is volume exponent, P<sub>1</sub> and P<sub>2</sub> are inlet and outlet pressure of a vacuum pump or a compressor, and <italic>&#x3b7;</italic>
<sub>ad</sub> is the adiabatic efficiency.</p>
</sec>
</sec>
<sec sec-type="results|discussion" id="s3">
<title>Results and Discussion</title>
<sec id="s3-1">
<title>Process Design and Operation</title>
<p>The column diameter and length were estimated based on the same actual interstitial velocity of the feed gas and feed step time, 1&#xa0;m/s and 600&#xa0;s, respectively. Accordingly, it was also assumed that the cycle times of the two adsorption systems would be identical. The column diameter was found so as to meet the gas velocity condition, given the sum of the fresh and recycled gas feed flowrates. The column length was determined as the distance that the shock wave travels along the column during the feed step time. The pressure drop along the column at the feed step was estimated by Ergun equation. The calculation results for the two cases are juxtaposed in <xref ref-type="table" rid="T2">Table&#x20;2</xref>. The required column volume of the syngas case was around 1.5&#x20;times larger than that of the tail gas case, but the difference was mainly down to the difference of the adsorbent densities. The masses of adsorbents in a column are very similar to each other. The ratios of the pressure drop to the feed inlet pressure are 8 and 7% for the syngas and tail gas cases, respectively.</p>
<table-wrap id="T2" position="float">
<label>TABLE 2</label>
<caption>
<p>Physical properties of the adsorbents and adsorption column design data (<xref ref-type="bibr" rid="B13">Park et&#x20;al., 2016</xref>; <xref ref-type="bibr" rid="B14">Park et&#x20;al., 2021</xref>).</p>
</caption>
<table>
<thead valign="top">
<tr>
<th align="left">case</th>
<th align="center">Syngas capture</th>
<th align="center">Tail gas capture</th>
</tr>
</thead>
<tbody valign="top">
<tr>
<td align="left">Adsorbent</td>
<td align="center">Activated carbon (Kuraray Chemical Co. 2GA-H2)</td>
<td align="center">Zeolite 13X (13X-APG MOLSIV)</td>
</tr>
<tr>
<td align="left">Interparticle void fraction [-]</td>
<td align="center">0.256</td>
<td align="center">0.284</td>
</tr>
<tr>
<td align="left">Adsorbent particle density, <inline-formula id="inf1">
<mml:math id="m14">
<mml:mrow>
<mml:msub>
<mml:mi>&#x3c1;</mml:mi>
<mml:mi>p</mml:mi>
</mml:msub>
</mml:mrow>
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</inline-formula> [kg&#xa0;m<sup>&#x2212;1</sup>]</td>
<td align="center">750</td>
<td align="center">1,050</td>
</tr>
<tr>
<td align="left">Adsorbent particle diameter [mm]</td>
<td align="center">1.7 - 2.4</td>
<td align="center">2.0 &#x2013; 2.2</td>
</tr>
<tr>
<td align="left">Column length, L [m]</td>
<td align="center">9.39</td>
<td align="center">1.66</td>
</tr>
<tr>
<td align="left">Column diameter [m]</td>
<td align="center">3.01</td>
<td align="center">5.90</td>
</tr>
<tr>
<td align="left">Column volume [m<sup>3</sup>]</td>
<td align="center">66.8</td>
<td align="center">45.3</td>
</tr>
<tr>
<td align="left">Adsorption time [s]</td>
<td align="center">600</td>
<td align="center">600</td>
</tr>
<tr>
<td align="left">Actual interstitial gas velocity at the feed step [m&#xa0;s<sup>&#x2212;1</sup>]</td>
<td align="center">1</td>
<td align="center">1</td>
</tr>
<tr>
<td align="left">Pressure drop along the column at the feed step [bar]</td>
<td align="center">1.77</td>
<td align="center">0.109</td>
</tr>
</tbody>
</table>
</table-wrap>
<p>
<xref ref-type="fig" rid="F5">Figure&#x20;5</xref> shows a z-t diagram to depict clearly how the simple and shock waves move around the column during each step of the 5-step VPSA, and this diagram is valid for both capture cases. As expected, the characteristic lines are straight during the constant-pressure steps while they are curved during the pressure-varying steps. During the feed and rinse steps, shock waves propagate along the column from one end to the other end of the column. The simple wave at y &#x3d; 0 reaches the column end during the purge step for complete regeneration. The gas leaving the column during the purge step is initially a pure heavy component, and the gas mole fraction decreases gradually to zero in case of complete regeneration. The performance may be improved by regenerating the column incompletely so that some of the heavy components still remain in the column at the end of the purge step. In <xref ref-type="fig" rid="F5">Figure&#x20;5</xref>, X indicates the extent of purging, e.g., X &#x3d; 1 for complete regeneration (<xref ref-type="bibr" rid="B6">Chiang, 1996</xref>; <xref ref-type="bibr" rid="B3">Ahn and Lee, 2020</xref>).</p>
<fig id="F5" position="float">
<label>FIGURE 5</label>
<caption>
<p>z-t diagram of a five-step VPSA process for syngas capture case. Lines represent the characteristics. The light grey area and the dark grey area indicate penetration of CO<sub>2</sub> (0 &#x3c; <italic>y</italic>&#x20;&#x3c; 1) and pure CO<sub>2</sub> (y &#x3d; 1), respectively.</p>
</caption>
<graphic xlink:href="fceng-03-742963-g005.tif"/>
</fig>
</sec>
<sec id="s3-2">
<title>Comparison of the Syngas and Tail Gas Capture Cases</title>
<sec id="s3-2-1">
<title>Product Recovery and Bed Productivity: Effect of Desorption Pressure</title>
<p>It is desorption pressure that is the only operating variable considered in this study, with the other operating variables fixed at constant values. <xref ref-type="fig" rid="F6">Figure&#x20;6</xref> shows the effect of desorption pressure on the product recovery and bed productivity in the two capture cases. The H<sub>2</sub> product recovery varies linearly with desorption pressure in both cases as shown in <xref ref-type="fig" rid="F6">Figure&#x20;6A</xref>. The H<sub>2</sub> recovery is estimated by <xref ref-type="disp-formula" rid="e8">Eq. 8</xref> that is derived from the H<sub>2</sub> mass balance around the column in a cycle. Among the terms in <xref ref-type="disp-formula" rid="e8">Eq. 8</xref>, only the moles of light product consumed for purging and pressurisation, <italic>N</italic>
<sub>
<italic>PI</italic>
</sub> and <italic>N</italic>
<sub>
<italic>LI</italic>
</sub>, are affected by desorption pressure. By rearranging <xref ref-type="disp-formula" rid="e8">Eq. 8</xref>, it turns out that only the pressure ratio, &#x3a8;, is varied by changing the desorption pressure while the other terms&#x2019; values remain constant, which leads to the linear changes of H<sub>2</sub> recovery with desorption pressure as shown in <xref ref-type="fig" rid="F6">Figure&#x20;6A</xref>. The H<sub>2</sub> recovery of the tail gas case is way too low, as the gas consumption for complete regeneration is so gigantic. The huge consumption of the purge gas is attributed to the CO<sub>2</sub> isotherm on the 13X being nearly irreversible (<xref ref-type="fig" rid="F4">Figure&#x20;4A</xref>). The desorption pressure has to be at least 0.07 bar, to have the H<sub>2</sub> recovery positive. It may not be practical operating the process at such a low pressure from the industrial perspective. The tail gas contains much less hydrogen than the syngas, as around 90% of the hydrogen contained in the syngas is recovered as a high purity of hydrogen product at a hydrogen purification PSA (see <xref ref-type="table" rid="T1">Table&#x20;1</xref>). The adjusted H<sub>2</sub> product recovery was also plotted in <xref ref-type="fig" rid="F6">Figure&#x20;6A</xref> for the tail gas case, based on the total hydrogen product recovered by H<sub>2</sub> PSA as well as CO<sub>2</sub>&#x20;VSA.</p>
<fig id="F6" position="float">
<label>FIGURE 6</label>
<caption>
<p>Effect of desorption pressure on <bold>(A)</bold> product recovery and <bold>(B)</bold> bed productivity.</p>
</caption>
<graphic xlink:href="fceng-03-742963-g006.tif"/>
</fig>
<p>As for CO<sub>2</sub> product recovery, <xref ref-type="disp-formula" rid="e9">Eq. 9</xref>, the desorption pressure affects the amount of CO<sub>2</sub> produced during the blowdown step, while the other quantities remain constant. The CO<sub>2</sub> recovery relies on the amount of the CO<sub>2</sub> being desorbed by depressurisation only, without using a purge gas. In this respect, the highly irreversible isotherm of CO<sub>2</sub> on the 13X must be so disadvantageous, as it is very hard to desorb CO<sub>2</sub> by reducing the pressure. The desorption pressure has to be decreased down to 0.01&#xa0;bar to achieve 90% CO<sub>2</sub> capture. In contrast, 92% CO<sub>2</sub> capture is achievable at the desorption pressure of 0.1&#xa0;bar in case of syngas capture.</p>
<p>The effect of desorption pressure on the bed productivity (<xref ref-type="fig" rid="F6">Figure&#x20;6B</xref>) is by and large similar to its effect on the product recovery (<xref ref-type="fig" rid="F6">Figure&#x20;6A</xref>). It should be noted that the CO<sub>2</sub> molar flowrates in the two feeds are almost the same as each other, whilst the H<sub>2</sub> molar flowrate of the syngas is six times larger than that of the tail gas. Such a high bed productivity with respect to hydrogen in the syngas case can be explained by the very large difference of H<sub>2</sub> flowrate. At very low desorption pressures up to 0.05 bara, the bed productivity with respect to CO<sub>2</sub> in the tail gas case is superior to that in the syngas case. But this is merely down to the difference of two bed volumes, and the two CO<sub>2</sub>-based bed productivities must be comparable to each other if they were expressed with respect to adsorbent mass instead of volume. At the desorption pressures being greater than 0.05 bara, the syngas case exhibits far greater bed productivity with respect to&#x20;CO<sub>2</sub>.</p>
</sec>
<sec id="s3-2-2">
<title>Energy Consumption</title>
<p>
<xref ref-type="fig" rid="F7">Figure&#x20;7</xref> shows the specific power consumptions of the 5-step VPSA with the desorption pressure ranging from 0.01 to 0.6 bara. The power consumption for pressurising the CO<sub>2</sub> gas needed for the rinse step remains constant regardless of desorption pressure. However, the power consumptions for pulling a vacuum during the blowdown and purge steps vary greatly with the desorption pressure. The adiabatic efficiencies for gas compression and evacuation were fixed at 0.8, while they may need to be adjusted to different values that the manufacturers provide for specific machines, particularly in case of a vacuum pump running at a very low vacuum pressure. The total specific power consumption of the syngas case is relatively low, decreasing monotonously from 1.1 to 0.4&#xa0;MJ/kg CO<sub>2</sub> with the desorption pressure. In stark contrast, the total specific power consumption of the tail gas case reaches its minimum value of 0.7&#xa0;MJ/kg CO<sub>2</sub> at 0.02 bara, and it increases rapidly with desorption pressure, mainly due to the drastic decrease of the CO<sub>2</sub> recovery. In general, the syngas case is superior to the tail gas case in terms of specific power consumption except for the very low desorption pressures below 0.05&#xa0;bar.</p>
<fig id="F7" position="float">
<label>FIGURE 7</label>
<caption>
<p>Effect of desorption pressure on specific power consumption.</p>
</caption>
<graphic xlink:href="fceng-03-742963-g007.tif"/>
</fig>
<p>It is interesting to compare the energy consumption between the CO<sub>2</sub> capture VPSA and an MDEA absorption process, as MDEA is one of the most conventional solvents taken for selective CO<sub>2</sub> removal from a feed gas with a relatively high CO<sub>2</sub> partial pressure. MDEA is one of the components of the ADIP solvent taken for Shell&#x2019;s Quest CCS project where CO<sub>2</sub> is captured from a high pressure syngas, and the amine solvent was also chosen in the Japan&#x2019;s Tomakomai project where CO<sub>2</sub> is captured from the PSA tail gas. The process configuration of a MDEA capture plant is similar to those of physical solvent capture plants, such as Selexol process (<xref ref-type="bibr" rid="B8">Kapetaki et&#x20;al., 2015</xref>). The rich solvent leaving the absorber is regenerated by two different mechanisms: depressurisation and steam stripping. In case of the absorber working at a high pressure, the entire rich solvent is admitted to flash drums where CO<sub>2</sub> is partially desorbed. The liquid stream leaving the flash drum is the semi-lean amine. The semi-lean solvent is split into two sub-streams. One is returned to the absorber in the middle, while the rest is regenerated more thoroughly by steam stripping. The lean amine leaving the stripper is fed to the absorber on the top. Therefore, a MDEA process spends both electricity and heat, and the total energy consumption varies with the semi-lean amine recycle ratio, i.e.,&#x20;the ratio of the semi-lean amine being recycled back to the absorber to the total semi-lean amine leaving the flash&#x20;drum.</p>
<p>In this study, an amine process using 40wt% aqueous MDEA solvent was simulated to estimate its energy consumption for two cases where CO<sub>2</sub> is captured from either the syngas or the tail gas at their actual compositions listed in <xref ref-type="table" rid="T1">Table&#x20;1</xref>. The process simulations were carried out with Honeywell UniSim R461.1 and its associated DBRamine package. In this simulation, the absorber and stripper were designed to have sufficient numbers of stages and large diameters so that the rich and lean loading could not be enhanced notably by increasing the number of stages further. In other words, the absorption system designed in this study can be considered as a limiting case where its performance is controlled by vapour-liquid equilibrium only, similarly to those of the adsorptive capture systems designed by Equilibrium Theory in this&#x20;study.</p>
<p>
<xref ref-type="fig" rid="F8">Figure&#x20;8</xref> shows the energy consumption of the two MDEA processes working to capture CO<sub>2</sub> from either syngas or tail gas. The energy consumption in terms of specific work consumption is affected greatly by the split ratio of the semi-lean amine between recycle to the absorber and steam stripping. It was found that the optimal ratio of the semi-lean recycle to the total semi-lean would be around 0.92, in other words, only 8% of the semi-lean solvent being directed to the stripper. The optimal semi-lean amine recycle ratio may vary slightly depending on what heat-to-work conversion factor to use. In this study, the reboiler heat of low pressure steam was converted to the equivalent work with the conversion factor of 0.3 (<xref ref-type="bibr" rid="B4">Ahn et&#x20;al., 2013</xref>). At the optimal recycle ratio, the specific work consumption was as low as 0.35&#xa0;MJ/kg CO<sub>2</sub>. Therefore the two capture processes are expected to incur the energy consumptions similar to each other in case of syngas capture.</p>
<fig id="F8" position="float">
<label>FIGURE 8</label>
<caption>
<p>Energy consumption of a 40wt% aqueous MDEA process in case of CO<sub>2</sub> capture from the syngas or tail gas under equilibrium-controlled condition.</p>
</caption>
<graphic xlink:href="fceng-03-742963-g008.tif"/>
</fig>
<p>For the low pressure tail gas, the absorption process was designed so that the rich amine was regenerated by steam stripping only. The specific reboiler duty of the tail gas capture was estimated around 3.3&#x20;MJ<sub>th</sub>/kg CO<sub>2</sub>, greater than 2.2&#x20;MJ<sub>th</sub>/kg CO<sub>2</sub> of the syngas capture case at the semi-lean recycle ratio set to zero. The difference of the reboiler duties is mainly down to the difference of the CO<sub>2</sub> partial pressure in the feed that results in different rich loading. In case of the tail gas feed, the VPSA may be competitive over the MDEA unit if the desorption pressure is set as low as less than 0.05 bara.</p>
</sec>
</sec>
</sec>
<sec id="s4">
<title>Conclusions and Future Work</title>
<p>A Pressure Swing Adsorption process incorporating a rinse step has been studied to decarbonise a conventional SMR H<sub>2</sub> plant by capturing CO<sub>2</sub> from either the synthesis gas or the H<sub>2</sub> PSA tail gas. For the sake of quick feasibility study, the 5-step VPSA system was analysed by Equilibrium Theory without conducting complex numerical simulation. As a result of the analysis, it was found out that the shifted synthesis gas would be by and large more advantageous than the tail gas with respect to product recovery, bed productivity and power consumption, unless the VPSAs would be operated at an impractically low desorption pressure, i.e.,&#x20;less than 0.05 bara. The energy consumption of the VPSA was estimated as low as those of the MDEA units with the CO<sub>2</sub> recovery greater than&#x20;90%.</p>
<p>The VPSA designed for syngas capture is similar to the Gemini process&#x2019;s A beds in that they work for CO<sub>2</sub> capture, while the two systems are different in terms of regeneration and repressurisation methods (<xref ref-type="bibr" rid="B18">Sircar and Kratz, 1988</xref>). The 5-step VPSA can be easily expanded to function to produce pure hydrogen as well as pure CO<sub>2</sub> by its integration with another adsorption cycle for hydrogen purification. In this respect, the existing H<sub>2</sub> PSA can be repurposed so that it can perform CO<sub>2</sub> capture as well as H<sub>2</sub> purification.</p>
<p>The theoretical model taken for PSA analysis in this study was so simple to use and the PSA performance was estimated effortlessly. But the PSA design/operation and adsorption dynamics that the model considered may not reflect the actual situation exactly. The Equilibrium Theory model will be developed further so as to enhance its accuracy and reliability, by considering incomplete regeneration, coupled isotherm, pressure equalisation steps,&#x20;etc.</p>
</sec>
</body>
<back>
<sec id="s5">
<title>Data Availability Statement</title>
<p>The raw data supporting the conclusions of this article will be made available by the authors, without undue reservation.</p>
</sec>
<sec id="s6">
<title>Author Contributions</title>
<p>YC: Equilibrium Theory calculation, wrote the mathematical model section, collected the data HA: Conceived and designed the analysis, wrote the paper, collected the data, performed the analysis, MDEA simulation.</p>
</sec>
<sec id="s7">
<title>Funding</title>
<p>This work was supported by the United&#x20;Kingdom Engineering and Physical Sciences Research Council (EPSRC) grant EP/J018198/1. HA and YC. are grateful for funding from Birse Trustees to support the PhD study at the University of Edinburgh.</p>
</sec>
<sec sec-type="COI-statement" id="s8">
<title>Conflict of Interest</title>
<p>The authors declare that the research was conducted in the absence of any commercial or financial relationships that could be construed as a potential conflict of interest.</p>
</sec>
<sec sec-type="disclaimer" id="s9">
<title>Publisher&#x2019;s Note</title>
<p>All claims expressed in this article are solely those of the authors and do not necessarily represent those of their affiliated organizations, or those of the publisher, the editors and the reviewers. Any product that may be evaluated in this article, orclaim that may be made by its manufacturer, is not guaranteed or endorsed by the publisher.</p>
</sec>
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</person-group> (<year>2014</year>). <article-title>Assessment of CO<sub>2</sub> Capture Options from Various Points in Steam Methane Reforming for Hydrogen Production</article-title>. <source>Int. J.&#x20;Hydrogen Energ.</source> <volume>39</volume>, <fpage>20266</fpage>&#x2013;<lpage>20275</lpage>. <pub-id pub-id-type="doi">10.1016/j.ijhydene.2014.09.161</pub-id> </citation>
</ref>
<ref id="B20">
<citation citation-type="journal">
<person-group person-group-type="author">
<name>
<surname>Streb</surname>
<given-names>A.</given-names>
</name>
<name>
<surname>Mazzotti</surname>
<given-names>M.</given-names>
</name>
</person-group> (<year>2020</year>). <article-title>Novel Adsorption Process for Co-production of Hydrogen and CO2 from a Multicomponent Stream-Part 2: Application to Steam Methane Reforming and Autothermal Reforming Gases</article-title>. <source>Ind. Eng. Chem. Res.</source> <volume>59</volume>, <fpage>10093</fpage>&#x2013;<lpage>10109</lpage>. <pub-id pub-id-type="doi">10.1021/acs.iecr.9b06953</pub-id> </citation>
</ref>
<ref id="B21">
<citation citation-type="book">
<collab>UK BEIS</collab> (<year>2021</year>). <source>UK Hydrogen Strategy</source>. <publisher-loc>London</publisher-loc>: <publisher-name>HM Government</publisher-name>. </citation>
</ref>
<ref id="B22">
<citation citation-type="journal">
<person-group person-group-type="author">
<name>
<surname>Voss</surname>
<given-names>C.</given-names>
</name>
</person-group> (<year>2014</year>). <article-title>CO<sub>2</sub> Removal by PSA: an Industrial View on Opportunities and Challenges</article-title>. <source>Adsorption</source> <volume>20</volume>, <fpage>295</fpage>&#x2013;<lpage>299</lpage>. <pub-id pub-id-type="doi">10.1007/s10450-013-9574-8</pub-id> </citation>
</ref>
</ref-list>
<sec id="s10">
<title>Nomenclature</title>
<def-list>
<def-item>
<term id="G15-fceng.2021.742963">
<inline-formula id="inf12">
<mml:math id="m25">
<mml:mrow>
<mml:msub>
<mml:mi>A</mml:mi>
<mml:mtext>c</mml:mtext>
</mml:msub>
</mml:mrow>
</mml:math>
</inline-formula>
</term>
<def>
<p>Cross section area of adsorption column,&#x20;m<sup>2</sup>
</p>
</def>
</def-item>
<def-item>
<term id="G16-fceng.2021.742963">
<bold>
<italic>b</italic>
</bold>
</term>
<def>
<p>Langmuir isotherm parameter, bar<sup>&#x2212;1</sup>
</p>
</def>
</def-item>
<def-item>
<term id="G17-fceng.2021.742963">
<inline-formula id="inf13">
<mml:math id="m26">
<mml:mi>L</mml:mi>
</mml:math>
</inline-formula>
</term>
<def>
<p>Column length, m</p>
</def>
<def>
<p>Light product pressurisation&#x20;step</p>
</def>
</def-item>
<def-item>
<term id="G18-fceng.2021.742963">
<bold>
<italic>N</italic>
</bold>
</term>
<def>
<p>Total moles of either influent or effluent during a step,&#x20;mol</p>
</def>
</def-item>
<def-item>
<term id="G19-fceng.2021.742963">
<bold>
<italic>P</italic>
</bold>
</term>
<def>
<p>Pressure,&#x20;bar</p>
</def>
<def>
<p>Purge&#x20;step</p>
</def>
</def-item>
<def-item>
<term id="G20-fceng.2021.742963">
<inline-formula id="inf14">
<mml:math id="m27">
<mml:mrow>
<mml:msub>
<mml:mi>P</mml:mi>
<mml:mtext>H</mml:mtext>
</mml:msub>
</mml:mrow>
</mml:math>
</inline-formula>
</term>
<def>
<p>Adsorption pressure,&#x20;bar</p>
</def>
</def-item>
<def-item>
<term id="G21-fceng.2021.742963">
<inline-formula id="inf15">
<mml:math id="m28">
<mml:mrow>
<mml:msub>
<mml:mi>P</mml:mi>
<mml:mtext>L</mml:mtext>
</mml:msub>
</mml:mrow>
</mml:math>
</inline-formula>
</term>
<def>
<p>Desorption pressure,&#x20;bar</p>
</def>
</def-item>
<def-item>
<term id="G22-fceng.2021.742963">
<inline-formula id="inf16">
<mml:math id="m29">
<mml:mi>R</mml:mi>
</mml:math>
</inline-formula>
</term>
<def>
<p>universal gas constant, bar m<sup>3</sup> mol<sup>&#x2212;1</sup>&#xa0;K<sup>&#x2212;1</sup>
</p>
</def>
</def-item>
<def-item>
<term id="G23-fceng.2021.742963">
<bold>q</bold>
</term>
<def>
<p>Adsorbed amount, mol kg<sup>&#x2212;1</sup>
</p>
</def>
</def-item>
<def-item>
<term id="G24-fceng.2021.742963">
<bold>q<sub>s</sub>
</bold>
</term>
<def>
<p>Saturation adsorption amount, mol&#xa0;kg<sup>&#x2212;1</sup>
</p>
</def>
</def-item>
<def-item>
<term id="G25-fceng.2021.742963">
<inline-formula id="inf17">
<mml:math id="m30">
<mml:mi>T</mml:mi>
</mml:math>
</inline-formula>
</term>
<def>
<p>Temperature, K</p>
</def>
</def-item>
<def-item>
<term id="G26-fceng.2021.742963">
<italic>t</italic>
</term>
<def>
<p>Time, s</p>
</def>
</def-item>
<def-item>
<term id="G27-fceng.2021.742963">
<inline-formula id="inf18">
<mml:math id="m31">
<mml:mi>y</mml:mi>
</mml:math>
</inline-formula>
</term>
<def>
<p>Mole fraction of heavy component, &#x2212;</p>
</def>
</def-item>
<def-item>
<term id="G28-fceng.2021.742963">
<inline-formula id="inf19">
<mml:math id="m32">
<mml:mrow>
<mml:msub>
<mml:mi>y</mml:mi>
<mml:mi>f</mml:mi>
</mml:msub>
</mml:mrow>
</mml:math>
</inline-formula>
</term>
<def>
<p>Mole fraction of heavy component in the feed, &#x2212;</p>
</def>
</def-item>
<def-item>
<term id="G29-fceng.2021.742963">
<bold>
<italic>z</italic>
</bold>
</term>
<def>
<p>Axial position, m</p>
</def>
</def-item>
</def-list>
</sec>
<sec id="s11">
<title>Greek Symbols</title>
<def-list>
<def-item>
<term id="G1-fceng.2021.742963">
<inline-formula id="inf2">
<mml:math id="m15">
<mml:mrow>
<mml:msub>
<mml:mi>&#x3b2;</mml:mi>
<mml:mi>B</mml:mi>
</mml:msub>
</mml:mrow>
</mml:math>
</inline-formula>
</term>
<def>
<p>
<inline-formula id="inf3">
<mml:math id="m16">
<mml:mrow>
<mml:mfrac>
<mml:mn>1</mml:mn>
<mml:mrow>
<mml:mn>1</mml:mn>
<mml:mo>&#x2b;</mml:mo>
<mml:mfrac>
<mml:mrow>
<mml:mn>1</mml:mn>
<mml:mo>&#x2212;</mml:mo>
<mml:mi>&#x3b5;</mml:mi>
</mml:mrow>
<mml:mi>&#x3b5;</mml:mi>
</mml:mfrac>
<mml:msub>
<mml:mi>&#x3c1;</mml:mi>
<mml:mi>p</mml:mi>
</mml:msub>
<mml:mi>R</mml:mi>
<mml:mi>T</mml:mi>
<mml:mfrac>
<mml:mrow>
<mml:mo>&#x2202;</mml:mo>
<mml:msub>
<mml:mi>q</mml:mi>
<mml:mi>B</mml:mi>
</mml:msub>
</mml:mrow>
<mml:mrow>
<mml:mo>&#x2202;</mml:mo>
<mml:msub>
<mml:mi>P</mml:mi>
<mml:mi>B</mml:mi>
</mml:msub>
</mml:mrow>
</mml:mfrac>
</mml:mrow>
</mml:mfrac>
</mml:mrow>
</mml:math>
</inline-formula>, &#x2212;</p>
</def>
</def-item>
<def-item>
<term id="G2-fceng.2021.742963">
<inline-formula id="inf4">
<mml:math id="m17">
<mml:mrow>
<mml:mi>&#x3b8;</mml:mi>
<mml:mrow>
<mml:mo>(</mml:mo>
<mml:mrow>
<mml:mi>P</mml:mi>
<mml:mo>,</mml:mo>
<mml:msub>
<mml:mi>y</mml:mi>
<mml:mn>1</mml:mn>
</mml:msub>
<mml:mo>,</mml:mo>
<mml:msub>
<mml:mi>y</mml:mi>
<mml:mn>2</mml:mn>
</mml:msub>
</mml:mrow>
<mml:mo>)</mml:mo>
</mml:mrow>
</mml:mrow>
</mml:math>
</inline-formula>
</term>
<def>
<p>
<inline-formula id="inf5">
<mml:math id="m18">
<mml:mrow>
<mml:mfrac>
<mml:mrow>
<mml:msub>
<mml:mi>&#x3b8;</mml:mi>
<mml:mi>A</mml:mi>
</mml:msub>
<mml:mrow>
<mml:mo>(</mml:mo>
<mml:mrow>
<mml:mi>P</mml:mi>
<mml:mo>,</mml:mo>
<mml:msub>
<mml:mi>y</mml:mi>
<mml:mn>1</mml:mn>
</mml:msub>
<mml:mo>,</mml:mo>
<mml:msub>
<mml:mi>y</mml:mi>
<mml:mn>2</mml:mn>
</mml:msub>
</mml:mrow>
<mml:mo>)</mml:mo>
</mml:mrow>
</mml:mrow>
<mml:mrow>
<mml:msub>
<mml:mi>&#x3b2;</mml:mi>
<mml:mi>B</mml:mi>
</mml:msub>
</mml:mrow>
</mml:mfrac>
</mml:mrow>
</mml:math>
</inline-formula>, &#x2212;</p>
</def>
</def-item>
<def-item>
<term id="G3-fceng.2021.742963">
<inline-formula id="inf6">
<mml:math id="m19">
<mml:mrow>
<mml:msub>
<mml:mi>&#x3b8;</mml:mi>
<mml:mi>A</mml:mi>
</mml:msub>
<mml:mrow>
<mml:mo>(</mml:mo>
<mml:mrow>
<mml:mi>P</mml:mi>
<mml:mo>,</mml:mo>
<mml:msub>
<mml:mi>y</mml:mi>
<mml:mn>1</mml:mn>
</mml:msub>
<mml:mo>,</mml:mo>
<mml:msub>
<mml:mi>y</mml:mi>
<mml:mn>2</mml:mn>
</mml:msub>
</mml:mrow>
<mml:mo>)</mml:mo>
</mml:mrow>
</mml:mrow>
</mml:math>
</inline-formula>
</term>
<def>
<p>
<inline-formula id="inf7">
<mml:math id="m20">
<mml:mrow>
<mml:mfrac>
<mml:mn>1</mml:mn>
<mml:mrow>
<mml:mn>1</mml:mn>
<mml:mo>&#x2b;</mml:mo>
<mml:mfrac>
<mml:mrow>
<mml:mn>1</mml:mn>
<mml:mo>&#x2212;</mml:mo>
<mml:mi>&#x3b5;</mml:mi>
</mml:mrow>
<mml:mi>&#x3b5;</mml:mi>
</mml:mfrac>
<mml:msub>
<mml:mi>&#x3c1;</mml:mi>
<mml:mi>p</mml:mi>
</mml:msub>
<mml:mi>R</mml:mi>
<mml:mi>T</mml:mi>
<mml:mfrac>
<mml:mrow>
<mml:msub>
<mml:mi>q</mml:mi>
<mml:mrow>
<mml:mi>A</mml:mi>
<mml:mn>1</mml:mn>
</mml:mrow>
</mml:msub>
<mml:mo>&#x2212;</mml:mo>
<mml:msub>
<mml:mi>q</mml:mi>
<mml:mrow>
<mml:mi>A</mml:mi>
<mml:mn>2</mml:mn>
</mml:mrow>
</mml:msub>
</mml:mrow>
<mml:mrow>
<mml:mi>P</mml:mi>
<mml:msub>
<mml:mi>y</mml:mi>
<mml:mn>1</mml:mn>
</mml:msub>
<mml:mo>&#x2212;</mml:mo>
<mml:mi>P</mml:mi>
<mml:msub>
<mml:mi>y</mml:mi>
<mml:mn>2</mml:mn>
</mml:msub>
</mml:mrow>
</mml:mfrac>
</mml:mrow>
</mml:mfrac>
</mml:mrow>
</mml:math>
</inline-formula>, &#x2212;</p>
</def>
</def-item>
<def-item>
<term id="G4-fceng.2021.742963">
<inline-formula id="inf8">
<mml:math id="m21">
<mml:mi>&#x3b5;</mml:mi>
</mml:math>
</inline-formula>
</term>
<def>
<p>Bed void fraction, &#x2212;</p>
</def>
</def-item>
<def-item>
<term id="G5-fceng.2021.742963">
<inline-formula id="inf9">
<mml:math id="m22">
<mml:mrow>
<mml:msub>
<mml:mi>&#x3c1;</mml:mi>
<mml:mi>P</mml:mi>
</mml:msub>
</mml:mrow>
</mml:math>
</inline-formula>
</term>
<def>
<p>Adsorbent particle density, kg&#xa0;m<sup>&#x2212;3</sup>
</p>
</def>
</def-item>
<def-item>
<term id="G6-fceng.2021.742963">
<inline-formula id="inf10">
<mml:math id="m23">
<mml:mi>&#x3c8;</mml:mi>
</mml:math>
</inline-formula>
</term>
<def>
<p>
<inline-formula id="inf11">
<mml:math id="m24">
<mml:mrow>
<mml:msub>
<mml:mi>P</mml:mi>
<mml:mi>H</mml:mi>
</mml:msub>
<mml:mo>/</mml:mo>
<mml:msub>
<mml:mi>P</mml:mi>
<mml:mi>L</mml:mi>
</mml:msub>
</mml:mrow>
</mml:math>
</inline-formula>, &#x2212;</p>
</def>
</def-item>
</def-list>
</sec>
<sec id="s12">
<title>Subscripts</title>
<def-list>
<def-item>
<term id="G7-fceng.2021.742963">
<bold>
<italic>A</italic>
</bold>
</term>
<def>
<p>Heavy component, CO<sub>2</sub>
</p>
</def>
</def-item>
<def-item>
<term id="G8-fceng.2021.742963">
<bold>
<italic>B</italic>
</bold>
</term>
<def>
<p>Light component, H<sub>2</sub> or Blowdown&#x20;step</p>
</def>
</def-item>
<def-item>
<term id="G9-fceng.2021.742963">
<bold>
<italic>F</italic>
</bold>
</term>
<def>
<p>Feed&#x20;step</p>
</def>
</def-item>
<def-item>
<term id="G10-fceng.2021.742963">
<bold>
<italic>I</italic>
</bold>
</term>
<def>
<p>Influent</p>
</def>
</def-item>
<def-item>
<term id="G11-fceng.2021.742963">
<bold>
<italic>L</italic>
</bold>
</term>
<def>
<p>Column length, m</p>
</def>
<def>
<p>Light product pressurisation&#x20;step</p>
</def>
</def-item>
<def-item>
<term id="G12-fceng.2021.742963">
<bold>
<italic>O</italic>
</bold>
</term>
<def>
<p>Effluent</p>
</def>
</def-item>
<def-item>
<term id="G13-fceng.2021.742963">
<bold>
<italic>P</italic>
</bold>
</term>
<def>
<p>Pressure,&#x20;bar</p>
</def>
<def>
<p>Purge&#x20;step</p>
</def>
</def-item>
<def-item>
<term id="G14-fceng.2021.742963">
<bold>
<italic>R</italic>
</bold>
</term>
<def>
<p>Rinse&#x20;step</p>
</def>
</def-item>
</def-list>
</sec>
</back>
</article>