ie502928y_si_001

S1
Table S1. Model equations for the batch experiment1, 2 The overall mass balance equation:
Vc dC ms d Q + =0 dt ρ p dt (S1)
with
Q=
(Sa + 1) Rp ∫ QR Sa dR = ε p C p + ρ p q ( Sa +1) 0 Rp (Sa + 1) Rp p Sa ∫ C R dR ( Sa +1) 0 Rp
S5
Table S4. Experimental Data of Nitrogen Adsorption Equilibrium on Carbon Molecular Sieves
at 303 K, 323 K, and 343 K T=303K P [kpa] 1.04 4.69 10.76 19.41 38.90 60.52 80.07 100.00 194.19 295.91 398.76 499.08 603.90 701.65 q [mol/kg] 0.0052 0.0187 0.0388 0.0678 0.1264 0.1844 0.2384 0.2847 0.4687 0.6225 0.7447 0.8475 0.9469 1.0145 T=323K P [kpa] 1.07 4.81 10.43 19.56 39.52 59.30 80.18 98.94 194.96 295.80 401.74 498.89 598.60 699.10 q [mol/kg] 0.0046 0.0143 0.0269 0.0465 0.0903 0.1295 0.1682 0.2029 0.3471 0.4756 0.5844 0.6728 0.7501 0.8257 T=343K P [kpa] 1.98 5.86 10.96 20.63 45.22 60.69 80.60 100.47 194.70 301.81 399.77 510.64 598.14 702.69 q [mol/kg] 0.0050 0.0105 0.0210 0.0370 0.0728 0.0958 0.1203 0.1461 0.2612 0.3713 0.4418 0.5225 0.5652 0.6569
where C p is the gas phase concentration in macropores, D p is the macropore diffusivity, ε p is the porosity of the particle, Si is the shape factor of the micropore, rµ is the micropore radius, q is the average adsorbed phase concentration in the micropores, and Q concentration of adsorbate in particle.
(S2)
Cp =
(S3)
q =
(Sa + 1) Rp Sa ∫ qR dR ( Sa +1) 0 Rp
(S4)
where C is the gas phase concentration in the microbalance cell, Vc is the entire closed volume of the microbalance cell , ms is the adsorbent mass used (kg), ρ p is the density of the particle ,
p = CRg T
(S9)
where p is the pressure, T is the temperature (K), and Rg is the ideal gas constant.
Knudsen diffusivity
Kauzmann correlation3
Dk = 9.7 × 10−8 rp
Macropore mass balance equation:
p ∂Q ∂C p ∂q 1 ∂ S a ∂C =εp + ρp = Sa ε D R p p ∂t ∂t ∂t R ∂R ∂R
(S5)
with
Q = ε pC p + ρ p q
(S6) (S7)
q=
(Si + 1) rµ Si ∫ 0 qr dr rµ( Si +1)
Macropore:
∂C p ∂R Cp
=0
R =0
(S15) (S16)
R = Rp
=C
Initial conditions Micropore:
q = qeq 0
(S17)
Macropore:
Cp = peq Rg T
(S18)
Microbalance cell:
C = C0 = p feed Rg T
(S19)
S4
Table S3. Experimental Data of Methane Adsorption Equilibrium on Carbon Molecular Sieve at
303 K, 323 K, and 343K T=303K P [kpa] 0.89 4.15 8.77 16.23 39.31 57.84 79.32 103.26 195.40 306.10 403.40 509.68 610.40 706.67 q [mol/kg] 0.0319 0.0511 0.0866 0.2242 0.3960 0.6076 0.7489 0.8667 1.1721 1.3996 1.5746 1.7066 1.8212 1.9082 T=323K P [kpa] 10.18 20.17 38.72 64.27 79.60 106.98 197.40 302.85 386.16 501.96 578.70 707.29 q [mol/kg] 0.0966 0.1815 0.3208 0.5170 0.5380 0.6583 0.9437 1.1369 1.2879 1.4217 1.5101 1.6153 T=343K P [kpa] 10.84 21.58 40.00 62.76 81.27 102.20 150.66 218.15 318.51 437.40 518.70 594.17 716.44 q [mol/kg] 0.0694 0.1328 0.2219 0.3243 0.4026 0.4810 0.6438 0.7933 0.9567 1.1178 1.2097 1.2903 1.3903
(S11)
where pc and Tc are critical pressure (atm) and temperature (K), respectively. Daa is the selfdiffusivity (m2/s), and C is the gas phase concentration in microbalance cell (mol/m3)
NOMENCLATURE
C = gas phase concentration, mol/ m3
C 0 = initial gas phase concentration, mol/ m3 C p = gas phase concentration in macropores, mol/ m3
S6
C p = average gas phase concentration in the macropores of the particle, mol/ m3
Supporting Information: Adsorption equilibrium and kinetics of methane and nitrogen on carbon molecular sieve
Ying Yang†‡, Ana M. Ribeiro‡, Ping Li†, Jian-Guo Yu†, Alirio E. Rodrigues*,‡
S2
Micropore mass balance equation:
∂q 1 ∂ ∂q = Si Dµ r Si ∂t r ∂r ∂r (S8)
where q is the adsorbed phase concentration, t is the time and Dµ is the micropores diffusivity. The ideal gas behavior:
R p is the particle radius, C p
is the average gas phase concentration in the macropores of the
particle, q is the average adsorbed phase concentration of the particle, Q is the total average concentration of is the shape factor of the particle
‡
Laboratory of Separation and Reaction Engineering (LSRE), Associated Laboratory
LSRE/LCM, Department of Chemical Engineering, Faculty of Engineering, University of Porto, Rua Dr. Roberto Frias s/n, 4200-465 Porto, Portugal Corresponding Author: Alirio E. Rodrigues, E-mail: arodrig@fe.up.pt.