Supporting information Efficient Simulation and Acceleration of Convergence for a Dual Piston Pressure Swing Adsorption System Daniel Friedrich, Maria-Chiara Ferrari, Stefano Brandani* Scottish Carbon Capture and Storage Centre, School of Engineering The University of Edinburgh, The King’s Buildings, Mayfield Road Edinburgh EH9 3JL. UK
[email protected]
Time integration
Figure S1: Change in the total mass in the DP-PSA system, i.e. mass in the pistons, dead volume and column gas phase plus the mass adsorbed, compared to the initial mass in the system.
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Experimental validation Table S1: Parameters for the simulation. All temperature dependent parameters are calculated at the simulation temperature of T=308 K. Parameter description Cycle time Piston length Piston radius Piston 1
Piston 2
Column length Column radius Bed voidage Total pellet voidage Pellet radius Initial mole fraction CO 2 Initial mole fraction N 2 Langmuir constant CO 2 Saturation capacity CO 2 Langmuir constant N 2 Saturation capacity N 2 Pore diffusivity CO 2 Pore diffusivity N 2 LDF coefficient CO 2 LDF coefficient N 2 Temperature Axial dispersion Relative tolerance Absolute tolerance
Parameter tc Lp Rp S 0,1 S 1,1 Φ1 S 0,2 S 1,2 Φ2 L R ε εp rp y1 y2 b1 q s,1 b2 q s,2 D p,1 D p,2 k1 k2 T Di rtol atol
Value 10 0.107 0.025 0.05 0.1 0 0 0.1 90 0.13 0.0076 0.4 0.625 0.002 0.2 0.8 4.6147 3974.9 0.0263 3974.9 1.405*10-6 1.350*10-6 0.0144 2.1 308 1.39*10-3 10-7 10-7
Unit s m m m m º m m º m m
m bar-1 mol m-3 bar-1 mol m-3 m2s-1 m2s-1 s-1 s-1 K m2s-1
The axial dispersion coefficient was calculated by the Wakao correlation.1 The axial dispersion coefficient is assumed to be constant and equal for both gas phase components. It was calculated at the average pressure and flow conditions in the column.
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Acceleration from the ε algorithm Table S2: Comparison of the number of cycles to CSS for several configurations of the ε algorithm Algorithm
q
m
Successive substitution ε algorithm ε algorithm ε algorithm ε algorithm ε algorithm ε algorithm ε algorithm ε algorithm ε algorithm ε algorithm ε algorithm ε algorithm
1 1 1 1 2 2 2 2 3 3 3 3
1 2 3 4 1 2 3 4 1 2 3 4
# cycles Scalar Vector 97 64 55 64 49 74 46 58 58 44 36 46 40 60 52 54 74 49 24 60 67 49 49 48 70
Derivation of the effective pore diffusivity The derivation follows the derivation given by Ruthven.2 In the case of macropore diffusion control the governing equation is
εp
∂c ∂q 1 ∂ 2 ∂c + (1 − ε p ) + 2 − Dpr =0 ∂r ∂t ∂t r ∂r
(S1)
where r is the pellet radius and D p is the macropore diffusivity. Since the system is macropore diffusion controlled it is assumed that q = q * (c ) and thus ∂c ∂q ∂c , = ∂r ∂r ∂q * ∂c ∂c ∂q . = ∂t ∂q * ∂t
(S2)
Substituting eq S2 and assuming D p is constant, eq S1 becomes
∂q ∂c D p ∂ 2 ∂q ∂c ε p ∂q * + (1 − ε p ) ∂t − ∂q * r 2 ∂r r ∂r = 0
(S3)
which can be simplified to ∂q = ∂t
1 ∂ 2 ∂q . r ∂q r 2 ∂r ∂r ε p + (1 − ε p ) ∂c Dp
*
(S4)
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References. (1)
Wakao, N.; Funazkri, T. Effect of fluid dispersion coefficients on particle-to-fluid mass transfer
coefficients in packed beds: Correlation of Sherwood numbers. Chem. Eng. Sci. 1978, 33, 1375. (2)
Ruthven, D. M. Principles of adsorption and adsorption processes; Wiley-Interscience, 1984
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