Wet flue gas: dual-adsorbent, two-bed VSA

This example sets up the process proposed in section 4 of Krishnamurthy et al. (2014) for CO₂ capture from a wet flue gas of 15% CO₂, 82% N₂ and 3% H₂O. A silica gel bed takes up the water, and the dried gas passes to a zeolite 13X bed that concentrates the CO₂. Keeping the adsorbents in separate beds, rather than layering them in one, lets each be evacuated on its own, so the CO₂ product comes out practically dry.

feed ──V_feed──┐                      ┌──V_link──┐                   ┌──V_product── raffinate
               bottom  SilicaGel  top ┘          bottom  Zeolite  top┤
H2O ◄─V_waste──┘                                 │                   └──V_lpp────── light product
                                      CO2 ◄─V_vacuum┘

Both beds run a four-step cycle, coupled only during adsorption:

Step	Silica gel bed	13X bed
pressurisation	with feed, from the bottom	with light product, from the top
adsorption	feed in; effluent to the 13X bed	silica gel effluent in; nitrogen out
blowdown	out of the bottom (counter-current)	out of the top (co-current)
evacuation	out of the bottom: the water	out of the bottom: the CO₂ product

The blowdown and evacuation times and pressures differ between the beds. The silica gel bed finishes first and stays closed until the 13X bed completes its cycle.

The model uses the paper's data: the isotherms (its Table 1, case 1, for both adsorbents), the column, particle and gas properties (Table S2 of its Supporting Information), the feed and the operating conditions for minimum energy (section 4.3). The particle size is not given there and is taken from Haghpanah et al. (2013). Two simplifications: the 13X light product pressurisation lasts a fixed 20 s, like the silica gel pressurisation, and uses pure nitrogen rather than the stored effluent of the previous adsorption step.

import Mocca
using Mocca.Units

1. Adsorbents

Both adsorbents are in Mocca's library. Silica gel adsorbs little CO₂ and N₂ but a great deal of water; 13X adsorbs both CO₂ and water strongly. Loadings in equilibrium with the feed:

gas = Mocca.krishnamurthy_2014_gas()
feed_composition = (CO2 = 0.15, N2 = 0.82, H2O = 0.03)
for name in ("silica_gel_krishnamurthy_2014", "zeolite_13x_krishnamurthy_2014")
    q = Mocca.equilibrium_loading(Mocca.load_adsorbent(name), gas; pressure = 1atm, temperature = 298.15, composition = feed_composition)
    println(rpad(name, 32), join(["$n $(round(qi, digits = 2))" for (n, qi) in zip(gas.names, q)], ", "), " mol/kg")
end

silica_gel_krishnamurthy_2014   CO2 0.0, N2 0.0, H2O 21.35 mol/kg
zeolite_13x_krishnamurthy_2014  CO2 0.1, N2 0.0, H2O 14.17 mol/kg

2. Process

dual_adsorbent_vsa_process builds the two beds, six devices and the cycle. Its defaults are the operating conditions for minimum energy in section 4.3 of the paper:

	Silica gel bed	13X bed
length	0.41 m	1 m
pressurisation	20 s	20 s
adsorption	46.2 s	46.2 s
blowdown	42.21 s to 0.48 bar	56.3 s to 0.07 bar
evacuation	46.02 s to 0.3 bar	101.2 s to 0.03 bar

with a feed interstitial velocity of 0.7 m/s. Each bed has 30 cells, as in the paper. The cycle has one sequence of steps per bed, run side by side and split into stages wherever either bed changes step. The time steps start at 0.01 s in every stage and double up to 1 s, which carries the solver through the abrupt start of a stage, such as the feed switching on at the start of adsorption.

As in the paper, the silica gel bed starts at its low pressure (the default: the lowest pressure of its cycle) and the 13X bed at the high pressure, both full of nitrogen.

process = Mocca.dual_adsorbent_vsa_process(timestepping = Mocca.TimeStepping(max_dt = 1.0, first_dt = 0.01),
    initial_state = Dict(:Zeolite => (pressure = 1atm,)))

Process dual-adsorbent VSA, wet flue gas: CO2/N2/H2O feed at 1.013 bar, 298.15 K, capturing CO2
  SilicaGel: fixed bed of silica gel, 30 cells
    bottom V_feed (feed), from boundary at 1.013 bar; V_waste (waste), to boundary at 0.3 bar
    top    V_link (link) to Zeolite bottom
  Zeolite: fixed bed of zeolite 13X, 30 cells
    bottom V_link (link) to SilicaGel top; V_vacuum (extract), to boundary at 0.03 bar
    top    V_product (product), to boundary at 1.013 bar; V_lpp (light_inlet), from boundary at 1.013 bar
  cycle of 6 stages, 223.7 s:
    silica gel pressurisation, 13X LPP    20.0 s   V_feed, V_lpp
    silica gel adsorption, 13X adsorption    46.2 s   V_feed, V_link, V_product
    silica gel blowdown, 13X blowdown    42.21 s   V_waste, V_product
    silica gel evacuation, 13X blowdown   14.09 s   V_waste, V_product
    silica gel evacuation, 13X evacuation   31.93 s   V_waste, V_vacuum
    silica gel idle, 13X evacuation      69.27 s   V_vacuum

3. Cycling to the paper's steady state

The paper judges cyclic steady state by the CO₂ balance: the CO₂ fed and the CO₂ leaving must agree within 0.5% for five consecutive cycles, after at least 50 cycles (its eq. S19).

result = Mocca.cyclic_steady_state(process; method = :mass_balance, max_cycles = 300)
println("Cycles: $(result.iterations), CO₂ balance met: $(result.converged), last error: $(round(100 * result.history[end], digits = 2))%")

Cycles: 131, CO₂ balance met: true, last error: 0.48%

The criterion only checks CO₂, and the water is far from steady when it is met. The silica gel keeps about 98% of the water fed each cycle and removes little of it in blowdown and evacuation, so it fills over the cycles. In this model the water starts to break through to the 13X bed after about 100 cycles, close to when the CO₂ balance closes, and rises from about 20 ppm at cycle 100 to over 1% by cycle 300. method = :anderson or :newton requires every variable, including the water loading, to settle; for this process it reaches a state in which the silica gel is saturated and much of the water passes into the 13X bed.

4. Process performance

performance measures the process from its devices' roles over the last cycle: the extract (13X evacuation) is the CO₂ product, recovery is relative to the CO₂ fed, and the energy counts the vacuum pumps on every outlet below atmospheric pressure (the silica gel waste line, the 13X blowdown and evacuation) and the feed compressor.

perf = Mocca.performance(result)

(purity = 0.9563784606815549, recovery = 0.8557833101552855, specific_energy = 194.65400484849138, productivity = 0.32483872119666807, energy = 140715.85760271622, cycle_time = 223.7000000000001, feed = [5.3316547214483165, 29.14653801787474, 1.0663198301473913], extract = [4.562741126126097, 0.20782674353623468, 0.0002852117365305823], product = [0.684421790534575, 35.35502620175978, 2.916603576772216e-8], adsorbent_volume = 0.0627902269691358, adsorbent_mass = 72.59619007452851)

The paper's productivity is per m³ of 13X per day, and its energy counts the vacuum pumps only. The water entering the 13X bed comes from the link between the beds.

states, ts = result.states, result.timesteps
n_product = perf.extract
n_to_zeolite = Mocca.stream_totals(states, ts, :V_link)
pumps = sum(Mocca.vacuum_pump_energy(states, ts, d) for d in (:V_waste, :V_product, :V_vacuum))
zeolite_volume = sum(process.parameters[:Zeolite][:SolidVolume])
M_CO2 = gas.molar_masses[1]
summary = (
    purity = perf.purity,
    recovery = perf.recovery,
    pump_energy_kWh_per_t = Mocca.specific_energy_kwh_per_tonne(pumps, n_product, M_CO2),
    energy_with_feed_compressor_kWh_per_t = perf.specific_energy,
    productivity_t_per_m3_13X_day = n_product[1] * M_CO2 / 1000 / zeolite_volume / (perf.cycle_time / 86400),
    water_to_13X_fraction_of_feed = n_to_zeolite[3] / perf.feed[3],
    water_to_13X_max_ppm = 1e6 * maximum(s[:V_link][:InletComposition][3, 1] for s in states if s[:V_link][:MolarFlow][1] > 0),
)
for (k, v) in pairs(summary)
    println(rpad(k, 40), round(v, sigdigits = 3))
end

purity                                  0.956
recovery                                0.856
pump_energy_kWh_per_t                   192.0
energy_with_feed_compressor_kWh_per_t   195.0
productivity_t_per_m3_13X_day           1.74
water_to_13X_fraction_of_feed           0.0236
water_to_13X_max_ppm                    775.0

For these conditions the paper reports 95% purity, 90% recovery, 177 kWh per tonne of CO₂ and 1.82 t of CO₂ per m³ of 13X per day, with 20 ppm of water in the gas entering the 13X bed. When the CO₂ balance closes, this model gives about 95.6% purity, 86% recovery, 190 kWh/t and 1.75 t/m³/day, with a few hundred ppm of water entering the 13X bed.

5. Bed profiles

Profiles at the end of each bed's steps in the last cycle, as in Figures 10 and 11 of the paper.

fs = process.flowsheet
sg_ends = cumsum([20.0, 46.20, 42.21, 46.02])
x_ends = cumsum([20.0, 46.20, 56.30, 101.20])
step_names = ["pressurisation", "adsorption", "blowdown", "evacuation"]
f_silica_gel = Mocca.plot_profiles(states, ts, fs[:SilicaGel], sg_ends;
    labels = step_names, unit = :SilicaGel, components = [1, 3])

The 13X bed. The silica gel keeps it almost free of water: the gas entering it holds less than 0.02% water, and only the first tenth of the bed takes up any. So the 13X holds CO₂ along its whole length, and at the end of evacuation the gas near its feed end is almost pure CO₂.

f_zeolite = Mocca.plot_profiles(states, ts, fs[:Zeolite], x_ends;
    labels = step_names, unit = :Zeolite, components = [1, 3])

The streams through the devices over the cycle:

f_streams = Mocca.plot_flowsheet_streams(states, process.model, ts; stages = Mocca.stages(process))

Example on GitHub

If you would like to run this example yourself, it can be downloaded from the Mocca.jl GitHub repository.

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