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ance βπ‘ π βπ‘ βπ§τ° βπ§ 2.5. One-Dimensional Process Model Processes 2022, 10, 812 Usually, there are five basic cycle steps associated with any PSA process: adsorption, pressure equalization, purge/rinse, co-current or counter-current depressurization (blow- down) and re-pressurization steps, which can be scheduled in many different ways for a typical PSA process with multiple beds [48]. Many previous works reported approaches their sequence, and the number of beds, and then following a systematic procedure based on a few simple rules, some heuristics, and some experience [49β51]. Switching between onadfieifwferseinmntpolpeperruraltetiso,nsosmtepepshieisuereixsptircess,saenddnsuomerieicxaplleyriaeasnscaec[h4a9anβn5g1e].inSwboiotucnhndidnagrybectownedeitntions. diffeTrehnetgoepneerraratilobnosutnenpdsariysyecxopnrdeisitsieodnsnfufomreraichalslsyteapsarecehlaisntegededinbToaubnled1a1r.yAcsopnednitAiodnso.rTphtieionTM geneisrsaalnbioinudnudsatriyialclyoynadccictliaoinmsefdorsoefatwcwharsreteefporamrmeulilstitisetdepincoTuapbpled1.prAroscpesessns dAedsisgonrpatnidodnaTMsseissing an infedaussibtrililiaitlyly-maocodcdlealimdevdelslopftmweanrtet afnonrdmsiumltuislataetipionco[u47p7]l.eCdCopnrsosicdesrsindgesthihgencaunrrdrenantstsceosmsinpguting feasibility-model development and simulation [47]. Considering the current computing feasipboilwiteyer-mcondsetlradaienvtses,lompomosetnptraoncedessimdeusliagtniosnb[a4s7e]d. CoonnAsisdspeerningAdtdhseorcputriroenTMt coadmdoputeteidnga 1D power constraints, most process designs based on Aspen AdsorptionTM adopted a 1D powmeratcthoenmstartaticnmtms,omdeolswt ipithrhoacaenssadseosripgtniosnb-abseedmoonodAelspanend Aaudxsioliraprtyi-omnoTModualdeomptoedelals,1wDhich mathematic model with an adsorption-bed model and auxiliary-module models, which mathaerme sautimc moadriezlewditnhTaanbaleds2oarnpdtioTna-bled3m, roedspelecatnivdealyux[i5l2iaβr5y7-]m. Hodouwlevmeor,dtehles,1wDhmichodaerlecan- are summarized in Table 2 and Table 3, respectively [52β57]. However, the 1D model can- summnoatridzesdcirnibTeabthles f2inaendch3a, reascptercitsitviceslyd[5ir2eβc5tl7y]., Hsuocwheavsert,htheea1dDsomrboedrelstcrauncntuotred,eascdrsiboerbent not describe the fine characteristics directly, such as the adsorber structure, adsorbent the fipnaeckchedarfaocrtmeriastnicdssdinirgelcetlpy,asrutichleaisntheernaadlsmorobreprhsotrlougctyu,rneo, ardthsoerirbeinftlupeanckcedonfotrhmeanddsorp- packed form and single particle internal morphology, nor their influence on the adsorp- Purge | τ±±z==0 =00 τ°τ°τ°τ° τ±± βz πππππ§π§π§π§ τ°‘τ°‘τ°‘τ°‘τ°’τ°’τ°’τ°’τ²Ύτ²Ύτ²Ύτ²Ύ τ±± τ°τ°τ°τ° Purge πππππΆπΆπΆπΆ πππππ§π§π§π§βz τ±±z=0 = 0 πππππ¦π¦π¦π¦ πππππ§π§π§π§8 of 19 Equalization pressuriza- tion 0 τ°τ°τ°τ°p gτ°τ°τ°τ° τ°τ°τ°τ° g for a complex PSA-cycle scheduling, involving a priori specification of the cycle steps, single particle internal morphology, nor their influence on the adsorption-mass transfer, tion-mass transfer, resulting in the inability to accurately predict the local component con- resulting in the inability to accurately predict the local component concentration and other centration and other information in the adsorption process. More personalized program- information in the adsorption process. More personalized programming software, such as 0|z=0 τ°τ°τ°τ°βT τ±± |z=L outlet ππππππππ ππππππππ πππππ§π§π§π§βz βT τ±± τ°τ°τ°τ° gτ±±τ±± |=0=0 τ°τ°τ°τ° = 0 |gτ±±τ±± ==00 τ°‘τ°‘τ°‘τ°‘τ°’τ°’τ°’τ°’zτ°τ°τ°τ°= 0 z = L τ°‘τ°‘τ°‘τ°‘τ°’τ°’τ°’τ°’τ²Ύτ²Ύτ²Ύτ²Ύ βz πππππ§π§π§π§ 7 of 19 ming software, such as gPROMS, as well as the computational-flow-dynamics method for gPROMS, as well as the computational-flow-dynamics method for the in-depth study of the in-depth study of mass transfer between gasβsolid phases, can be used to assist the mass transfer between gasβsolid phases, can be used to assist the process design. process design. Step Adsorption Table 1. Boundary conditions for each step. Table 1. Boundary conditions for each step. Z =Z= 0= 0 0,inlet inlet,i z=0 0 i b τ±± Z =ZL= L Adsorption πππ¦π¦ ππ π¦π¦ τ° τ° π | = π πππ|τ°‘τ°’τ²Ύ =πππτ²Ώτ³τ²»τ²Ήτ²Ίτ²» τ±± τ±± P| βCi τ±± |τ°‘τ°‘τ°’τ°’τ²Ύτ²Ύ = 0 βyi =π’π’π’π’ πΆπΆπΆπΆ βππππ π·π·π·π· πΆπΆπΆπΆ τ°τ° π’π’π’π’ πΆπΆπΆπΆ | τ°τ°τ°τ°,τ²·τ²·τ²·τ²·τ²Έτ²Έτ²Έτ²Έuτ²Ήτ²Ήτ²Ήτ²Ήτ²Ίτ²Ίτ²Ίτ²Ίτ²»τ²»τ²»τ²» τ²·τ²·τ²·τ²·τ²Έτ²Έτ²Έτ²Έτ²Ήτ²ΉCτ²Ήτ²Ήτ²Ίτ²Ίτ²Ίτ²Ίτ²»τ²»τ²»τ²»,τ²·τ²·τ²·τ²· τ°‘τ°‘τ°‘τ°‘τ°’τ°’τ°’τ°’τ±±τ°τ°τ°τ° =τ°τ°τ°τ°uτ²·τ²·τ²·τ²·C βτ²Ότ²Ότ²Ότ²ΌΞ΅ τ°¬τ°¬τ°¬τ°¬Dτ°τ°τ°τ°axC τ°‘τ°‘τ°‘τ°’τ°’τ°’τ²Ύτ²Ύτ²Ύ τ²Ώτ²Ώτ²Ώτ³τ³τ³τ²»τ²»τ²»τ²Ήτ²Ήτ²Ήτ²Ίτ²Ίτ²Ίτ²»τ²»τ²» πππππ§π§βπ§π§z ππππ ππππ β T πππππ§π§π§π§ τ°τ° P π’π’π’π’ πΆπΆπΆπΆ | τ±± = π’π’π’π’ πΆπΆπΆπΆ τ°τ°τ°τ°,τ²·τ²·uτ²·τ²·τ²Έτ²Έτ²Έτ²Έ0τ²Ήτ²Ήτ²Ήτ²Ήτ²Ί,τ²Ίτ²Ίτ²Ίiτ²»nτ²»τ²»τ²»leτ²·τ²·τ²·τ²·tτ²Έτ²Έτ²Έτ²ΈCτ²Ήτ²Ήτ²Ήτ²Ήτ²Ίτ²Ίiτ²Ίτ²Ίnτ²»τ²»τ²»τ²»leτ°‘τ°‘τ°‘τ°‘tτ°’τ°’τ°’τ°’zτ°τ°τ°τ°=0 =τ°τ°τ°τ°u0C ππΆ ππππΆπΆπΆ τ±± τ°τ°τ°τ° τ±±τ±± u0πΆπΆπΆπΆ,inletCπΆπΆπΆπΆinlππππetCpT|inertτ±±=z=0π’π’π’π’=πΆπΆπΆπΆuπΆπΆπΆπΆ0CππππCpβTgππππβkgτ° π’π’π’π’ τ°τ°τ°τ°,τ²·τ²·τ²·τ²·τ²Έτ²Έτ²Έτ²Έτ²Ήτ²Ήτ²Ήτ²Ήτ²Ίτ²Ίτ²Ίτ²Ίτ²»τ²»τ²»τ²» τ²·τ²·τ²·τ²·τ²Έτ²Έτ²Έτ²Έτ²Ήτ²Ήτ²Ήτ²Ήτ²Ίτ²Ίτ²Ίτ²Ίτ²»τ²»τ²»τ²» τ°τ°τ°τ° τ²·τ²·τ²·τ²·τ²Έτ²Έτ²Έτ²Έτ²Ίτ²Ίτ²Ίτ²Ίτ²½τ²½τ²½τ²½τ²»τ²»τ²»τ²» τ°‘τ°‘τ°‘τ°‘τ°’τ°’τ°’τ°’τ°τ°τ°τ° τ°τ°τ°τ° τ°τ°τ°τ° τ°τ°τ°τ° Processes 2022, 10, x FOR PEER REVIEW ππ§βz τ±±z=0 = 0 Table 2. Mathematical model of 1D non-isothermal adsorption bed. Equation βπΆτ° +τ²΄1βπτ²΅π βπ€τ° βπ· βτ°πΆτ° +βτ²΄π’πΆτ°τ²΅=0 τ³ τ°¬τ° Equalization and co-cur- rent depressurization depressurization β|C|τ°‘τ°‘τ°‘iτ°’τ°’τ°’τ±±τ°τ°τ° =0 τ°‘τ°’τ° βCi τ±± |τ°‘τ°‘τ°‘τ°’τ°’τ°’τ²Ύτ²Ύτ²Ύ =0 τ°‘τ°’τ²Ύ π π π π π§ π§ π§ π§ β z τ±± z = 0 = 0 β z τ±± π π π π z π§ =π§ π§ π§ L = 0 τ°τ°τ° g τ°τ°τ°τ° βz ππππτ±± ππππ τ°τ°τ° = P z=L outlet τ°‘τ°‘=τ°’τ°’τ²Ύτ²Ύ0 βTg τ±± τ°|=0=0 τ±±πππzπ§=π§π§L βz ππ§ τ±±z=L τ°‘τ°‘τ°‘τ°‘τ°’τ°’τ°’τ°’τ²Ύτ²Ύτ²Ύτ²Ύ βz πππππ§π§π§π§ Equalization and co-current πππππΆπΆπΆπΆ τ°τ°τ° τ±± πππππΆπΆπΆπΆ τ±± τ°τ°τ° π’π’π’π’ | = 0 τ°τ°τ°τ°uτ°‘τ°‘τ°‘τ°‘τ°’τ°’τ°’τ°’τ°τ°τ°τ° = 0 ππππ| = ππππ τ°‘τ°‘τ°‘τ°‘=τ°’τ°’τ°’τ°’τ²Ύτ²Ύτ²Ύτ²ΎP τ²Ώτ²Ώτ²Ώτ²Ώτ³τ³τ³τ³τ²»τ²»τ²»τ²»τ²Ήτ²Ήτ²Ήτ²Ήτ²Ίτ²Ίτ²Ίτ²Ίτ²»τ²»τ²»τ²» Blolowdown πππππΆπΆπΆπΆ τ±± ππππτ±± πΆπΆπΆπΆ τ°τ°τ°τ° β|C| i τ±± = 0 βCi τ±± | τ°‘τ°‘τ°‘τ°‘τ°’τ°’τ°’τ°’τ°τ°τ°τ° τ°‘τ°‘τ°‘τ°‘τ°’τ°’τ°’τ°’τ²Ύτ²Ύτ²Ύτ²Ύ τ±±=0 τ±±=0 πππππ§π§π§π§βz z=0 βz ππππzπ§=π§π§π§L ππππ| = ππππ τ°‘τ°‘τ°‘τ°‘Pτ°’τ°’τ°’τ°’|τ°τ°τ°τ° =τ²Ώτ²Ώτ²Ώτ²Ώτ³Pτ³τ³τ³τ²»τ²»τ²»τ²»τ²Ήτ²Ήτ²Ήτ²Ήτ²Ίτ²Ίτ²Ίτ²Ίτ²»τ²»τ²»τ²» π’π’π’π’ | = 0 u | τ°τ°τ°τ° τ°‘τ°‘τ°‘τ°‘=τ°’τ°’τ°’τ°’τ²Ύτ²Ύτ²Ύτ²Ύ0 z=0 outlet τ°τ°τ°τ°βTg τ±±τ±± 0 z=L ππππππππ ππππππππ πππππ§π§π§π§βzτ°‘τ°‘τ°‘τ°‘τ°’τ°’τ°’τ°’τ°τ°τ°τ° βTg τ±±τ±± τ°τ°τ°τ° τ±±z=L|= 0= 0 β|C|τ°‘i τ°’τ±± τ° = 0 τ°‘τ°‘τ°‘τ°’τ°’τ°’τ°τ°τ° πΆπΆπΆ ππππ| =ππππ τ°‘τ°‘τ°‘τ°‘Pτ°’τ°’τ°’τ°’|τ°τ°τ°τ° =τ²Ώτ²Ώτ²Ώτ²Ώτ³Pτ³τ³τ³τ²»τ²»τ²»τ²»τ²Ήτ²Ήτ²Ήτ²Ήτ²Ίτ²Ίτ²Ίτ²Ίτ²»τ²»τ²»τ²» τ±± π’π’π’π’τ°,τ²·τ²Έτ²Ήτ²Ίτ²»πΆπΆπΆπΆτ²·τ±±τ²Έτ²Ήτ²Ίτ²»|τ°‘τ°’τ²Ύ =π’π’π’π’τ°πΆπΆπΆπΆ z=0 outlet τ°τ°τ°τ°βTg τ±±τ±± u C πΆπΆπΆπΆ C TπΆπΆπΆπΆ ππππ τ±± ππππππππ ππππππππ πππππ§π§π§π§ βzτ°‘τ°‘τ°‘τ°‘τ°’τ°’τ°’τ°’zτ°τ°τ°τ°=0 u π’π’π’π’ 0,inτ°τ°τ°τ°l,eτ²·τ²·τ²·τ²·τ²Έτ²Έτ²Έtτ²Έτ²Ήτ²Ήτ²Ήτ²Ήτ²Ίτ²Ίτ²Ίτ²Ίiτ²»τ²»τ²»τ²»nleτ²·τ²·τ²·τ²·tτ²Έτ²Έτ²Έτ²Έτ²Ήτ²Ήτ²Ήτ²Ήτ²Ίτ²Ίτ²Ίτ²Ίpτ²»τ²»τ²»τ²» iτ°τ°τ°τ°nerτ²·τ²·τ²·τ²·tτ²Έτ²Έτ²Έτ²Έτ±±τ²Ίτ²Ίτ²Ίzτ²Ίτ²½=τ²½τ²½τ²½τ²»τ²»τ²»τ²»Lτ°‘τ°‘τ°‘τ°‘τ°’τ°’τ°’τ°’τ²Ύτ²Ύτ²Ύτ²Ύ τ°τ°τ°τ° βz τ°τ°τ°τ° πππππ§π§π§π§ ππ¦τ° ππ§ | τ±± ==00 τ±± βTg | = u=Cπ’π’π’π’CπΆπΆπΆπΆTπΆπΆπΆπΆβππππkβππππ i π’π’π’π’τ°,τ²·τ²Έτ²Ήτ²Ίτ²»πΆπΆπΆπΆτ²·τ²Έτ²Ήτ±±τ²Ίτ²»,τ²·|τ°‘τ°’τ²Ύ = π’π’π’π’τ°πΆπΆπΆπΆτ²· β ππππτ²Όπ·π·π·π·τ°¬βτ°yπΆ τ°τ°τ°,,τ²·τ²·τ²·τ²Έτ²Έτ²Έτ²Ήτ²Ήτ²Ήτ²Ίτ²Ίτ²Ίτ²»τ²»τ²» τ²·τ²·τ²·τ²Έτ²Έτ²Έτ²Ήτ²Ήτ²Ήτ²Ίτ²Ίτ²Ίτ²»τ²»τ²»,,τ²·τ²·τ²· τ°‘τ°‘τ°‘τ°’τ°’τ°’τ²Ύτ²Ύτ²Ύ τ°τ°τ° τ²·τ²·τ²· τ²Ότ²Ότ²Ό τ°¬τ°¬τ°¬τ°τ°τ° u0,inletCinlet,iτ±±z=L = u0Ci β Ξ΅bDaxC βz τ°τ°τ°,,τ²·τ²·τ²·τ²ΈCτ²Έτ²Έτ²Ήτ²Ήτ²Ήτ²Ίτ²Ίτ²Ίτ²»τ²»τ²» τ²·τ²·τ²·τ²Έτ²Έτ²Έτ²Ήτ²Ήτ²Ήτ²Ίτ²Ίτ²Ίτ²»τ²»τ²» τ°‘τ°‘τ°‘=τ°’τ°’τ°’τ²Ύτ²Ύτ²Ύu C τ°τ°τ° 0,inlet inlet z=L 0 Equalization pressurizationand ππΆτ° ππ§βCi τ±±τ±±z=0 = 0 and Pressurization |τ±± =0 τ°‘τ°’τ° π’ πΆτ±± | =π’πΆβππ· πΆ τ°,τ²·τ²Έτ²Ήτ²Ίτ²» τ²·τ²Έτ²Ήτ²Ίτ²»,τ²· τ°‘τ°’τ²Ύ τ° τ²· τ²Ό τ°¬τ° Pressurization u0,inletCinlet,iτ±±τ±±z=L = u0Ci βΞ΅bDaxCβyi βz π’|=0 π’πΆ|=π’πΆ βz τ° τ°‘τ°’τ° τ°,τ²·τ²Έτ²Ήτ²Ίτ²» τ±±τ²·τ²Έτ²Ήτ²Ίτ²» τ°‘τ°’τ²Ύ τ° ππu0|z=0 = 0 u0,inletCinletτ±±z=L = u0C ππ τ°τ±±τ° gτ±±=0 βT|τ°‘τ°’τ° π’ πΆπΆπ|=π’πΆπΆπβπ τ°,τ²·τ²Έτ²Ήτ²Ίτ²» τ²·τ²Έτ²Ήτ²Ίτ²» τ° τ²·τ²Έτ±±τ²Ίτ²½τ²» τ°‘τ°’τ²Ύ τ° u0,inletCinletCpTinertτ±±z=L = u0CCpTg β kg βz ππ§ τ±± τ° τ° βTgτ° Category Componentmassbal-PDF Image | Numerical Research on the Pressure Swing Adsorption Process
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