1 Model equations and parameters

Transcription

1 Supporing Informaion: Pre-combusion capure by PSA: Comparison of laboraory PSA Experimens and Simulaions (Indusrial Engineering Chemisry Research) J. Schell, N. Casas, D. Marx and M. Mazzoi ETH Zurich, Insiue of Process Engineering, Swizerland Tel.: Model equaions and parameers The se of parial differenial equaions resuling from he mass, energy and momenum balances is summarized in Table and he addiional algebraic equaions are provided in Table. The parameers used o describe he adsorpion equilibrium by an empirical compeiive Sips isoherm are summarized in Table 3 (Schell e al., ).

2 Table : Mahemaical model: parial differenial equaions describing mass, energy and momenum balances. Componen and oal mass balances: c i ε + (uc i) x + ρ n i b = i =,..., I c ε + (uc) x + ρ b I j= n j = Mass ransfer (linear driving force (LDF) model): n i = κ i(n i n i) i =,..., I Energy balance for he fluid and solid phase: (ε C g + ρ b C s + ρ b C ads ) T ε p + uc T g x ρ b Energy balance for he wall: I ( H j ) n j + h L (T T w ) = R i j= T w = C w (R R i ) (h LR i (T T w ) h w R (T w T amb )) Momenum balance (Ergun equaion): p x = 5µ( ε b) u.75( ε b)ρ m ε 3 b d u u p ε 3 b d p

3 Table : Mahemaical model: addiional algebraic equaions. Compeiive adsorpion isoherm (Sips): n i = n i (k iy i p) s i + I (k j y j p) s j j= i =,..., I Temperaure dependence of isoherm parameers: n i = a i exp ( b i ) RT k i = A i exp ( B i ) RT i =,..., I i =,..., I s i = α i aan (β i (T T ref,i )) + s ref,i i =,..., I Hea capaciies (lumped expressions for he fluid and adsorbed phase): C g = I j= c j C g,j C ads = I n j C g,j EOS (ideal gas law): j= c i = y ip RT i =,..., I Porosiies: ε = ρ b ρ M ε b = ρ b ρ p Nussel correlaion for he hea ransfer from he column inside o he wall (Leva, 97; Ruhven, 98; Casas e al., ): Nu = h LR i = η Re η exp( d p /(R i )) wih Re = d puρ m K L µ 3

4 Table 3: Equilibrium adsorpion parameers: Sips isoherms and isoseric heas of adsorpion (Schell e al., ). n i k i s i [-] [mol/kg] [/Pa] a i [mol/kg].38. b i [J/mol] -5,8 A i [/Pa] B i [J/mol] -9,59-9,8 α i [-].7 β i [/K]. s ref,i [-].83.9 T ref,i [K] H i [J/mol] -, -9,8

5 Inernal concenraion profiles during a PSA cycle In he following, profiles of he gas phase mole fracion (Figures o ) and he amoun adsorbed (Figures 7 o ) in he adsorpion column a differen specified imes during he seps of a PSA cycle are illusraed. These daa are obained from he simulaion a cyclic seady sae using he condiions of he experimen a bar and can help o undersand he processes during he cycle in more deail. For he pressure changing seps, i.e. pressure equalizaion, pressurizaion and blowdown, addiionally he pressure profiles are shown in Figures 3 o. In Figure 3 of he manuscrip he flow direcion in he differen seps is indicaed and he open and closed ends of he column can be easily idenified. The profiles in Figures o are ploed in a way ha he righ side always corresponds o he upper column end ha Figure. mole fracion [ ].8... Adsorpion Figure : Gas phase mole fracion during he adsorpion sep as obained by he simulaion afer,,, 3 and s (ligher grey color shows laer imes during he sep). 5

6 mole fracion [ ].8... Peq Blow Figure : Gas phase mole fracion during he depressurizaion via pressure equalizaion (Peq Blow) sep as obained by he simulaion afer,, and 3 s (ligher grey color shows laer imes during he sep). mole fracion [ ].8... Blowdown Figure 3: Gas phase mole fracion during he blowdown sep as obained by he simulaion afer,.5, 5, 37.5 and 5 s (ligher grey color shows laer imes during he sep). mole fracion [ ].8... Purge Figure : Gas phase mole fracion during he purge sep as obained by he simulaion afer, 5, and 5 s (ligher grey color shows laer imes during he sep).

7 mole fracion [ ].8.. Peq Press... CO..8. Figure 5: Gas phase mole fracion during he pressurizaion via pressure equalizaion (Peq Press) sep as obained by he simulaion afer,.,, and 3 s (ligher grey color shows laer imes during he sep). mole fracion [ ].8... Pressurizaion Figure : Gas phase mole fracion during he pressurizaion sep as obained by he simulaion afer,, 8 and s (ligher grey color shows laer imes during he sep). adsorbed amoun [mmol/g] Adsorpion Figure 7: Adsorbed amoun during he adsorpion sep as obained by he simulaion afer,,, 3 and s (ligher grey color shows laer imes during he sep). 7

8 adsorbed amoun [mmol/g] Peq Blow Figure 8: Adsorbed amoun during he depressurizaion via pressure equalizaion (Peq Blow) sep as obained by he simulaion afer,, and 3 s (ligher grey color shows laer imes during he sep). adsorbed amoun [mmol/g] Blowdown Figure 9: Adsorbed amoun during he blowdown sep as obained by he simulaion afer,.5, 5, 37.5 and 5 s (ligher grey color shows laer imes during he sep). adsorbed amoun [mmol/g] Purge Figure : Adsorbed amoun during he purge sep as obained by he simulaion afer, 5, and 5 s (ligher grey color shows laer imes during he sep). 8

9 adsorbed amoun [mmol/g] Peq Press Figure : Adsorbed amoun during he pressurizaion via pressure equalizaion (Peq Press) sep as obained by he simulaion afer,.,, and 3 s (ligher grey color shows laer imes during he sep). adsorbed amoun [mmol/g] Pressurizaion Figure : Adsorbed amoun during he pressurizaion sep as obained by he simulaion afer,, 8 and s (ligher grey color shows laer imes during he sep). pressure [bar] 5 5 Peq Blow Figure 3: Pressure during he depressurizaion via pressure equalizaion (Peq Blow) sep as obained by he simulaion afer,.,, and 3 s (ligher grey color shows laer imes during he sep). 9

10 pressure [bar] 8 Blowdown Figure : Pressure during he blowdown sep as obained by he simulaion afer,.5, 5, 37.5 and 5 s (ligher grey color shows laer imes during he sep). pressure [bar] 8 Peq Press Figure 5: Pressure during he pressurizaion via pressure equalizaion (Peq Press) sep as obained by he simulaion afer,.,, and 3 s (ligher grey color shows laer imes during he sep). pressure [bar] 5 5 Pressurizaion Figure : Pressure during he pressurizaion sep as obained by he simulaion afer,, 8 and s (ligher grey color shows laer imes during he sep).

11 3 Process performance evaluaion 3. Calibraion of he roameer The roameer used o measure he flow rae is a Messglas V- (Vöglin insrumens, Swizerland). As he ubing beween he BPR and he roameer is no heaed, he gas is a ambien emperaure. Furhermore, as he roameer is insalled afer he BPR, he gas is no longer a high pressure. However, as here are sill hree manual valves and a check valve before he gas reaches he ven, he flowing gas is slighly above ambien pressure. A manomeer aached direcly a he enrance of he roameer was used o deermine he pressure dela o he ambien for a range of flow raes. This pressure drop was considered when deermining he densiy of he flowing gas. For he calibraion, hree known binary mixures of / were used, wih y H =.5,.75, and. The MFC used for he experimens was used o conrol he flowrae of each of he gases hrough he roameer, and he reading was noed. The resuling daa is shown in Figure 7, where he symbols show he recorded calibraion daa, and he lines are flow raes calculaed based on a calibraion using four parameers. 3. Calculaion of produc puriy and recovery In he following, he evaluaion of he experimenal process performance is described. The flow rae measured by each MFC during he corresponding seps is inegraed over he duraion of he sep, and muliplied wih he mole fracion of each componen in he feed o obain he amoun of each componen enering he column: press,end Ni in = VMFC d + ads,end VMFC d + purge,end VMFC d () press,sar ads,sar purge,sar Noe ha here each of he columns is considered separaely. The amoun of each componen in he -rich produc is calculaed by noing he roameer reading regularly during he adsorpion sep. The roameer was read a leas once every five seconds, more frequenly when needed. Using he composiion of he produc as measured by he MS, he densiy of he produc gas is calculaed. Wih he densiy and he calibraion of he roameer, he volumeric and molar flow raes of he produc are calculaed a each poin in ime when he roameer was read. Along wih he composiion measured by he MS, his is used o find he componen specific molar flow raes, which are inegraed over he duraion of he adsorpion sep using he rapezoidal rule o find he oal amoun of each componen in he produc: ρ f = pro M RT amb V = f cal (ρ f, z ro ) () N prod i = ads,end ads,sar V yi d (3) where p ro is he pressure in he roameer, M is he average molar weigh of he gas deermined from he measured composiion, ρ f is he fluid densiy,

12 V s % 75% 3 ( cm 3 ) 5% roameer reading [ ] Figure 7: Calibraion of he roameer using hree differen mixures of known composiion. and N prod i is he amoun of each componen in he produc. The amoun of each componen in he -rich sream is hen found by subracion: N cap i = N in i N prod i () From his resul, he puriy and capure rae are calculaed as follows: ȳ CO = N cap N cap i i =, CR = N cap N in (5) This is done for each column separaely, and over hree process loops. This resuls in six values, for which a mean is aken. The resuls for he experimen wih an adsorpion sep ime of seconds can be seen in Figure 8. The flow raes in (a) are inegraed o calculae he oal amoun fed. The informaion in (b) is used o deermine he flow rae of he produc, which is seen in (c). For his experimen, he calculaed puriy is 78.7 %, and he capure rae is 9.8 %.

13 MFC feed rae [mmol/s] 5 5 (a) roameer reading [mm] 5 5 ime [s] 8 (b) 5 5 ime [s] produc mole fracion [ ] molar flow rae [mmol/s] 5 5 (c) 5 5 ime [s] Figure 8: Bold lines refer o column, dashed lines o column. (a) molar feed rae as measured by MFC. circles are a high pressure, diamonds a low pressure. (b) roameer reading (riangle) and composiion (diamond) of he hydrogen produc. (c) Calculaed molar flow rae of he hydrogen produc. 3

14 References Leva, M. Hea Transfer o Gases hrough Packed Tubes. Indusrial & Engineering Chemisry 97, 39, 857. Ruhven, D. Principles of Adsorpion and Adsorpion Processes; John Wiley & Sons, Inc., 98. Casas, N.; Schell, J.; Pini, R.; Mazzoi, M. Fixed bed adsorpion of / mixures on acivaed carbon: experimens and modeling. Adsorpion, 8, 3. Schell, J.; Casas, N.; Pini, R.; Mazzoi, M. Pure and binary adsorpion of,, and N on acivaed carbon. Adsorpion, 8, 9.