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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

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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

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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)

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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

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Numerical implementation

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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

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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.

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Parametric analysis(I)

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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

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Parametric Analysis (II)

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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

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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

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