Workspace Tutorial: CO₂ VPSA with light-product pressurisation (Perez 2019)

Reference: Estupiñan Perez, L., Sarkar, P., Rajendran, A. Experimental validation of multi-objective optimization techniques for design of vacuum swing adsorption processes. Separation and Purification Technology 224, 553–563 (2019).

Goal. Run a five-step vacuum swing adsorption (VPSA) cycle that captures CO₂ from a 15 % CO₂ / 85 % N₂ flue gas on zeolite 13X, see how light-product pressurisation (LPP) is wired with a step connection, run it to cyclic steady state, and compare purity and recovery with the experiment. The deck is experiment D1 of Table 3 in the paper.

What you will get. Cyclic steady state, and CO₂ purity and recovery to compare with the measured values. The current numbers for this deck are on the engine's tutorial and the Validation page, which covers all six Perez experiments.

1. Load the deck

Open Examples → Perez (2019) → Perez2019_D1, or go to /workspace?example=Perez2019_D1.json. Perez2019_E and Perez2019_F use the same LPP cycle with other step times and pressures; A, B and C1 are the basic four-step cycle without LPP.

2. Walk through the setup

Fluid Package. CarbonDioxide and Nitrogen.

Adsorbents. 13X: the paper's competitive (extended) dual-site Langmuir isotherm in concentration form, a macropore-controlled linear driving force with the capacity factor $c/(\rho_p q^*)$ of the paper's model (Macropore Diffusion (capacity factor), tortuosity 3, particle voidage 0.35) and heats of adsorption of 30.85 kJ/mol (CO₂) and 15.93 kJ/mol (N₂). The same parameters are in the library as Zeolite 13X (Perez 2019).

Column Properties. The laboratory column: 0.30 m long, 0.032 m diameter, a 3.1 mm steel wall whose ends are held at the ambient temperature of 293 K (the Wall tab's Fixed wall temperature boundary condition, the paper's choice). The layer 13X has 30 cells, a bed voidage of 0.41, 1.5 mm particles and the Darcy (Kozeny–Carman) momentum model. Dispersion uses the Ruthven correlation; heat transfer uses constant coefficients of 8.6 W m⁻² K⁻¹ (bed to wall) and 10 W m⁻² K⁻¹ (wall to ambient) with an axial thermal conductivity of 0.0903 W m⁻¹ K⁻¹.

Initial Conditions. Pure N₂ at 1 bar and 298 K.

Cycle Design → Cycle Data. Five steps, 360 s per cycle:

Blowdown removes N₂ from the light end at an intermediate vacuum, so the evacuation product is rich in CO₂. The CO₂ product is drawn from the feed end, where the bed is most saturated.

Cycle Design → Interacting Steps. One connection, between the LPP Stream on the top of Feed 1 and the top pressure boundary of Pressurisation. This is the light-product pressurisation:

• the Pressurisation inlet takes its composition and temperature from the gas leaving the top of the bed during Feed 1, so the bed is re-pressurised with N₂-rich product, not with the placeholder composition typed into the step;
• the LPP Stream on Feed 1 withdraws, instant by instant, the molar flow that the Pressurisation step drew, so the gas used for pressurisation is taken out of the product.

The two steps represent two beds working at the same time, which is why they have the same duration, 27.5 s. The coupling lags by one cycle: each side uses what its partner did in the previous cycle, and on the first cycle the typed-in values (pure N₂, zero LPP flow) stand in. See Connecting Beds and Light Product Pressurisation.

Cycle Design → Cyclic Steady State. Mass Balance (Per-Component) with a tolerance of 0.005: the run stops once, for every component, the moles entering the column over a cycle match the moles leaving to within 0.5 %. Minimum cycles is 100 and the cycle limit is 250.

Cycle Design → KPI Configuration. CO₂ is tracked. Feed: Feed 1 inlet and Feed 2 inlet. Product: Evacuation Pressure Boundary Bottom.

3. Run

Click Solver → Run. The status becomes Cyclic steady state reached at cycle N when the mass-balance test passes.

4. Interpret the results

KPIs. The Solver's Performance Indicators tab shows the last logged cycle (cycles are numbered from 0). Compare CO₂ purity and recovery with the measured and paper-model values on the engine's tutorial and Validation pages. The Energy KPI is 0 because no pump has power calculation switched on (see below).

The deck uses the paper's model forms; the engine's test README traces every value to the paper and attributes the remaining error. The remaining LPP excess is the composition-coupled light-product connection, an open item (see Validation).

Approach to CSS. Plot Plot type → KPIs, KPI → Purity to see how the purity settles. With Max cycles to keep at 10 (Solver Settings) only the last ten cycles are logged.

Pressure history. Set Plot type to Column, Variable group Bulk, Variable Pressure, X-axis Position, and step through the steps of the last cycle. Look at the bed pressure at the end of each step: it should sit near 1 bar through the feed steps, fall towards vacuum during Blowdown and Evacuation (the exponential ramps approach, but do not quite reach, their end values), and return to 1 bar after Pressurisation.

Fronts. With X-axis Position, Variable group Component, Variable Mole Fraction and CarbonDioxide selected, drag the Time slider through Feed 2 to see how far the CO₂ front advances towards the top of the bed, then through Evacuation to see the bed being emptied through the feed end.

5. What to try next

• Add the vacuum pump energy. On the Evacuation bottom boundary and the Blowdown top boundary, tick Calculate pump power (the pump becomes a vacuum pump because the boundaries are outlets) and set the Discharge Pressure to 1 bar. The Energy KPI then reports a specific energy; purity and recovery do not change, because power calculation is post-processing only.
• Accelerate CSS. Set Cyclic Steady State → CSS acceleration method to Aitken (Graves-Morris) and compare the cycle at which CSS is reached. The 100-cycle minimum limits the gain; lower Minimum cycles to let the test stop sooner. See Numerics.
• Switch off LPP by disconnecting the pair on Interacting Steps, and compare with the four-step decks Perez2019_A to C1.
• Map the trade-off. Sweep the Feed 2 time or the evacuation end pressure with a Parametric Study, or optimise recovery subject to purity ≥ 0.95, as the paper does with its multi-objective optimiser.
• Overlay data. The paper reports purity and recovery only, but if you have measured outlet histories, load them on the Experimental Data tab (Experimental Data).