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Development of an Equilibrium Theory Solver
for CO2 Capture Pressure Swing Adsorption
cycles
Gabriel David OreggioniUniversity of Edinburgh , School of Engineering, Edinburgh
SCCS – Scottish Carbon Capture and Storage Centre
UKCSS Winter School
Adsorption separation processes• Adsorption phenomena can be used as an unit operation
aimed to separate a gaseous mixtures due to a selective
retention of the gases in the surface of a porous solid
• The amount of mass adsorbed by the solid will depend on:
� Material : Activated carbon and zeolite 13X
�Operating conditions: Pressure, temperature and the
number and kind of components of the mixture
•Adsorption Equilibrium curve relates the specie adsorbed
mass and the concentration of the specie at a constant
temperature. Curve concavity is a key parameter for the
process design
•In Post combustion capture, Langmuir model is the most
used to describe the equilibrium for CO2, N2 and other
exhaust gas components
CO2 at 303 K
0
0.5
1
1.5
2
2.5
3
3.5
4
4.5
0 1 2 3 4 5 6 7 8
P [bar]
q [
mo
l/kg
]
Experimental data AC
Dual-site Langmuir AC
Experimental data ZE
Dual-site Langmuir ZE
08/01/2013 UKCCS Winter School
Pressure Swing Adsorption(PSA) cycles
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• PSA/VPSA cycles consist of a cyclic adsorption and desorption step process due to pressure swing in the
bed
• The first industrial application for gaseous mixture separation was developed by Skastrom in the late 60s
•Skastrom cycle is made up by 4 steps
� Adsorption
� Blowdown
� Purge
� Pressurization
•Efforts in cycle design as far as operation condition as well as time duration of each step are aimed to
maximize the CO2 recovery, purity ,bed productivity and minimize energy consumption
• The addition of pressure equalization steps enables a reduction in energy consumption
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Material balances in adsorption columns
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• Concentration is function of position and time in adsorption columns
• Material balances in adsorption column lead to systems of Partial Differential Equations
Mass transfer and fluidodynamics assumptions will determine the sort of PDE that must
be solved!
Equilibrium Theory
UKCCS Winter School 5
Equilibrium theory model for adsorption dynamic is based in two key premises
• Axial dispersion is neglected The system becomes HYPERBOLIC!No second derivative
• Diffusion inside the solid is neglected so that a fast equilibrium between the solid and the
fluid phase is reached We do not have to solve differential equations for the solid phase
!
•The second premise can be considered a simplification however in term of numerical
implementation makes the problem more complicated than a parabolic system due to the
shock tracking associated to the pure hyperbolic system
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Riemann and Cauchy problem
•A system of hyperbolic differential equation is classified as a Riemann problem when the
boundary conditions of the system are a piecewise function.
•The solution of the system will be a wave which amplitude will depend on the absolute value
of the piecewise function and the propagation speed will be the characteristic one.
•Wave can deform as it propagates producing smooth curves or shocks (discontinuities)
UKCCS Winter School 08/01/2013
Numerical methods and shock capture
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Characteristic method is a very time consuming tool to solve the systems of PDES involved in adsorption
dynamics Need of faster numerical schemes that must identify and predict the proper position
for discontinuity
Commercial or available software Simulator under construction
•Solve the hyperbolic system as a limit
case in which the dispersive term tend to
zero
•Solves the exact hyperbolic case as a
Cauchy-Riemann problem
•Smoothing of the discontinuity.
Smoothing can be reduced with
increasing the number of cells but it is still
important
• Smoothing of the curve will produce
difference of the adsorbed mass in the
column for a fixed feed/adsorption time
•Discontinuity can be observed as a sharp
jump
• A large number of grids is required in
order to get the proper position of the
shock since the systems are in non
conservative form or come from a non
conservative hyperbolic equation
•Increase in the number of cells reduce
the effect of the non conservative
intrinsic viscous profiles
UKCCS Winter School
Numerical implementation
8
ESIM (Equilibrium Theory simulator) consists on an unibed upwind finite volume solver for the mass
balances associated to adsorption dynamics
Upwind finite volume methods calculate the change in the average concentration in one of the cells of
the column as the difference between the fluxes entering and leaving the cell at the current time step.
Godunov scheme
Upwind method
We transform the differential equations into algebraic equations that are solved
using Not Linear Finding Root algorithms
UKCCS Winter School 08/01/2013
Shock capture results
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100 105 110 115 120 125 130 135 140 145 1500
0.02
0.04
0.06
0.08
0.1
0.12
0.14
0.16
Time (seconds)
Mol
ar F
ract
ion
125 126 127 128 129 130 131 132 133 134 135 136 137 138 139 1400
0.02
0.04
0.06
0.08
0.1
0.12
0.14
0.16
Time (seconds)
Mol
ar F
ract
ion
•ESIM shock capture performance has been
compared with Cysim and G-Proms for the non
trace system adsorption(for which an analytical
solution can be also calculated)
•ESIM presents the sharpest profile for the same
amount of grids
Example: Adsorption breakthrough curve for a CO2 non trace system
Pfeed=1.5; feed flow =0.0051mol/s; yCO2f=0.15; yN2f=0.85; Lbed=0.5m ;qs = 2233 mol/s;
bCO2=0.0476502 m3/mol
• We can zoom and see that the numerical dispersion
in ESIM is the smallest one and that is the closest to
the analytical solution. if we use ESIM to select the
feed time in the VPSA cycle, we will not be over or
underestimate it as the other softwares do.
UKCCS Winter School
Parametric analysis(I)
1008/01/2013
qs = 2233 mol/m3, bCO2=0.0476502 mol/m3 , Pfeed=1.5 bar, feedflow=0.0051 mol/s, L=0.5 m
Saturation time =130s
Influence of the duration of blowdown step
•Feed time=100s, purge/feed ratio =0.1, using linear valve and vacuum fixed pressure of 0.10
UKCCS Winter School
Parametric Analysis (II)
UKCCS Winter School 1108/01/2013
Influence of the duration of feed step
Influence of the duration of purge and feed ratio Feed time =120 s; Blowdown=90s
Purge /feed ratio =0.1, blowdown=0.75*tfeed
Conclusions and further work
• Adsorption technologies (VPSA cycles)can be a competitive post combustion capture technology
•Cycle performance depends on operation conditions as well as cycle configuration
• Cycle simulation involves solving PDES . The assumption of equilibrium driven separation leads to a
system of hyperbolic equations which solution can be a shock or discontinuity.
•Commercial or available software solves the hyperbolic system as a limiting case of a parabolic system,
causing inaccuracy in the calculations.
• An Equilibrium driven solver using pure hyperbolic problem is under development
• Comparisons on the influence of different parameters in cycle performance has been obtained using the
above mentioned software
• Extension to N adsorbing components and non isothermal operation is planned to take place in the
future
UKCCS Winter School 08/01/2013
Acknowledgments
To EPSRC for its funding contribution
To all those special people that are constantly supporting me through this challenging life
experience
To all of you for your kind attention
UKCCS Winter School 08/01/2013