Ward 2022: CO₂ breakthrough curves
In Ward & Pini’s study, they analyzed dynamic breakthrough experiments of pure CO₂ displacing helium from a bed of activated carbon by fitting a 1D transient breakthrough model to experimental data. In this tutorial we explain how the deck that replicates the paper is built in the Skarstrom workspace, run it, and compare it with the measured breakthrough curve.
1. Load the simulation data
In the menu bar, open Examples and, under Ward (2022), select Ward2022_Q100ccm. The link /workspace?example=Ward2022_Q100ccm.json opens it directly.
This loads the experiment with an inlet volumetric flow rate of 100 ccm. The paper fits a different internal heat transfer coefficient for each experiment, so there is one deck per flow rate (50, 100 and 200 ccm).
2. Components
Under Fluid Package, CO₂ (Carbon Dioxide) and Helium are ticked: the experiment fed pure CO₂ into a bed full of helium. The thermophysical properties of each component are calculated using CoolProp.
Ward models the heat capacity of the adsorbed phase. It is set per component on the Energy Balance tab of Column Properties, under Adsorbed-phase heat capacity: 36.96 J/(mol·K) for CO₂ and 0 for helium.
3. Column properties
The Geometry tab of Column Properties holds the column diameter (18.9 mm) and the ambient temperature (291.4 K), and the Wall tab the wall thickness and its material properties. The wall is aluminium, so its density, heat capacity and thermal conductivity are aluminium's.
Click the Activated Carbon layer (in the Navigator under Column Properties, or on the bed diagram) to open its Layer Properties on the right. Multi-layered beds can be created in Skarstrom, but this experiment has a single layer. Its length, bed voidage, particle diameter and number of cells are on the Layer tab, the pressure-drop model on the Momentum model tab, and the Transport model tab selects the correlations:
- Axial dispersion: a constant coefficient per flow rate, the paper's own value: its correlation D_L = 0.7 D_m + v r_p with D_m = 0.605 × 10⁻⁵ m²/s, multiplied by the factor 4 the paper fitted to the outlet composition.
- Heat dispersion (axial thermal conductivity): Yagi and Kunii (1957).
- Internal HTC: a constant coefficient, the value fitted in the paper for this flow rate.
- External HTC: Holman (2008), with an external air velocity of 0.5 m/s.
4. Adsorbent properties
The layer's adsorbent is the Activated Carbon entry under Adsorbents; click it to open Adsorbent Properties. Each component needs an isotherm model, which gives its equilibrium adsorbed-phase concentration, and a rate model, which gives the rate at which the adsorbed-phase concentration changes, i.e. the mass transfer rate between the gas and the solid.
- Isotherms: Ward uses the dual-site Langmuir isotherm on a concentration basis (Dual Site Langmuir (Concentration)). The tab plots the isotherm below its parameters, at the temperature and up to the pressure you choose.
- Rate Models: the linear driving force model (Linear Driving Force (1st Order)), with the mass transfer coefficient from the correlation of Haynes (1973).
5. Cycle design
A breakthrough simulation has a very simple cycle: one step, run for one cycle. Under Cycle Design, the Cycle Data tab sets one cycle with a 3000 s Feed step.
The Initial Conditions tab sets the state of the bed at t = 0: 1 bar and 291.4 K, at rest, full of helium. The initial mole fractions must sum to 1.
Click the Feed step (in the Navigator under Cycle Design, or its card) to open its Step Properties. In Skarstrom the Bottom boundary condition is at and the Top at . In a flow-through step the inlet sets the flow and the outlet the pressure: here the bottom is a Flow inlet, the CO2 Inlet stream of pure CO₂ at 293 K with a constant volumetric flow rate of 100 ccm, and the top is a Pressure outlet at a constant 1 bar.
6. Run the solver
With the model set up, click Solver in the Navigator, then Run. The Solver Log tab reports progress, and you can plot results while the run is still going. This deck takes a few seconds in a browser.
7. Plot the breakthrough curve
When the status reads Completed, the Results plot docks on the right. On the Plotter Options tab, variables are classified as Bulk or Component: bulk variables describe the fluid as a whole, such as pressure and temperature, whereas component variables are specific to a component within the fluid, such as its mole fraction. To plot the outlet CO₂ concentration against time, choose:
- Plot type: Boundary conditions
- Step: Feed, Stream: Feed Pressure Boundary Top (the column outlet)
- Variable group: Component, Variable: Mole Fraction, component CarbonDioxide
Plotting Results describes the other plots, such as profiles along the column.
8. Compare with the experiment
The deck carries the paper's measured data. Open the Experimental Data tab of the Solver panel and tick Overlay experimental data on the breakthrough plot. The overlay draws every dataset in the deck, and this one has three: the outlet CO₂ mole fraction, the outlet flow and a temperature inside the bed. The temperature (in K) sets the scale of the plot, so to compare the CO₂ curve on its own remove the other two series with their × (an ordinary edit: Edit → Undo brings them back, and nothing changes in a saved file unless you save). Upload CSV adds your own data; see Experimental Data.
The model breaks through slightly earlier than the measurement. The Validation page compares the three flow rates.