Carbon Capture Unit Operations

Carbon Capture Unit Operations#

This document provides comprehensive documentation for the difflow_cc plugin, which provides specialized tools for modeling and optimizing carbon capture processes.

Overview#

The difflow_cc plugin provides:

Amine-based absorption: MEA, DEA, MDEA, piperazine, amino acids
Membrane separation: Polymeric, mixed-matrix, facilitated transport
Adsorption systems: PSA, TSA, VSA, TVSA with various adsorbents
Direct Air Capture (DAC): Solid sorbent and liquid solvent systems
Economic analysis: CAPEX, OPEX, levelized cost of capture
Degradation models: Amine, adsorbent, and membrane aging

All models are fully differentiable using JAX, enabling gradient-based optimization, sensitivity analysis, and integration with machine learning.

Installation#

The carbon capture plugin is included as an optional dependency:

pip install difflow[cc]

Or install with all extras:

pip install difflow[all]

Database and Properties#

Amine Solvents#

Access amine solvent properties using the database functions:

from difflow_cc import get_solvent, list_solvents

# List available solvents
print(list_solvents())

# Get solvent properties
mea = get_solvent("MEA")
print(f"Heat of absorption: {mea.heat_of_absorption} kJ/mol")
print(f"Molecular weight: {mea.MW} g/mol")

Available Solvent Properties#

Property	Description	Units
`MW`	Molecular mass	g/mol
`density`	Solution density	kg/m^3
`heat_of_absorption`	Heat released on CO2 absorption	kJ/mol CO2
`loading_capacity`	Maximum CO2 loading	mol CO2/mol amine
`kinetics`	Rate-constant data (see `reaction_rate_constant`)	varies
`regen_temperature`, `regen_energy`	Typical regeneration conditions	K, GJ/t

Solvent Comparison#

Solvent	Full Name	Heat (kJ/mol)	Primary Use
MEA	Monoethanolamine	82	Post-combustion (benchmark)
DEA	Diethanolamine	68	Natural gas sweetening
MDEA	Methyldiethanolamine	55	Selective H2S removal
PZ	Piperazine	70	Fast kinetics, blends
AMP	2-amino-2-methyl-1-propanol	65	Sterically hindered

Adsorbent Materials#

from difflow_cc import get_adsorbent, list_adsorbents

print(list_adsorbents())
# ['Zeolite_13X', 'Zeolite_5A', 'Mg_MOF_74', 'CALF_20', 'ZIF_8',
#  'AC_Coconut', 'AC_Nitrogen_Doped', 'PEI_Silica', 'TEPA_Alumina']

zeolite = get_adsorbent("Zeolite_13X")
print(f"CO2 capacity: {zeolite.CO2_capacity} mol/kg")
print(f"Heat of adsorption: {zeolite.heat_of_adsorption} kJ/mol")

Adsorbent Comparison#

Adsorbent	Capacity (mol/kg)	Heat (kJ/mol)	Primary Use
Zeolite 13X	5.0	36	PSA, industrial benchmark
Mg-MOF-74	8.0	47	High capacity, lab scale
SIFSIX-3-Ni	2.5	45	High selectivity
Amine-silica	2.0	60	TSA, DAC
Activated Carbon	3.0	25	Pre-treatment, low cost

Membrane Materials#

from difflow_cc import get_membrane, list_membranes

print(list_membranes())
# ['Matrimid', 'PDMS', 'Cellulose_Acetate', 'PIM_1', 'ZIF8_Matrimid',
#  'MOF74_Polymer', 'PVAm_Carrier', 'IL_SIL_Membrane', 'CMS', 'Zeolite_DDR']

pim1 = get_membrane("PIM_1")
print(f"CO2 permeability: {pim1.permeability['CO2']} Barrer")
print(f"CO2/N2 selectivity: {pim1.selectivity['CO2_N2']}")

Membrane Comparison#

Membrane	CO2 Perm. (Barrer)	CO2/N2 Select.	Type
Polyimide	10	30	Glassy polymer
PIM-1	3000	20	Polymer of intrinsic microporosity
Pebax	150	50	Block copolymer
MMM-ZIF8	50	40	Mixed-matrix membrane
FTM-Glycine	1000	100+	Facilitated transport

Equilibrium Models#

Vapor-Liquid Equilibrium#

Model CO2-amine vapor-liquid equilibrium:

from difflow_cc import AmineVLE, co2_loading, co2_equilibrium_pressure

from difflow_cc.equilibrium.vle import equilibrium_loading

# VLE model for MEA (C_amine in mol/m^3, ~30 wt%)
vle = AmineVLE("MEA", C_amine=5000.0)

# Equilibrium CO2 pressure at a given loading
P_eq = vle.equilibrium_pressure(loading=0.4, T=393.15)
print(f"Equilibrium CO2 pressure: {float(P_eq):.0f} Pa")

# Loading in equilibrium with a CO2 partial pressure (robust inversion,
# used by the stripper's reboiler model)
loading = equilibrium_loading(10000.0, 313.15, "MEA")  # 10 kPa CO2
print(f"CO2 loading: {float(loading):.3f} mol/mol")

Equilibrium Model#

The CO2 partial pressure over loaded amine follows a Kent-Eisenberg type correlation:

\[P_{CO_2} = K_0 \exp\left(\frac{-\Delta H_{abs}}{RT}\right) \frac{\alpha^2}{(1 - \alpha/\alpha_{max})^{1.5}}\]

Where:

\(\alpha\): CO2 loading (mol CO2/mol amine), \(\alpha_{max}\) the solvent’s capacity
\(\Delta H_{abs}\): Heat of absorption
\(K_0\): calibrated to 1 kPa at \(\alpha = 0.4\), 313 K for 30 wt% MEA

Adsorption Isotherms#

Multiple isotherm models are available:

from difflow_cc import langmuir, sips, toth, dual_site_langmuir

# Langmuir isotherm (q_sat in mol/kg, b in 1/Pa)
q = langmuir(P=100000.0, q_sat=5.0, b=0.001)

# Sips isotherm (Freundlich-Langmuir)
q = sips(P=100000.0, q_sat=5.0, b=0.001, n=0.8)

# Toth isotherm
q = toth(P=100000.0, q_sat=5.0, b=0.001, t=0.7)

# Dual-site Langmuir
q = dual_site_langmuir(P=100000.0, q1=3.0, b1=0.01, q2=2.0, b2=0.0001)

Temperature-Dependent Isotherms#

from difflow_cc import langmuir_T, get_isotherm

# Temperature-dependent Langmuir: b = b0 exp(Q / (R T)), Q the heat of
# adsorption (J/mol, positive)
q = langmuir_T(P=100000.0, T=298.15, q_sat=5.0, b0=1e-9, Q=36000.0)

# Fitted isotherm for a database adsorbent (CO2 by default)
isotherm = get_isotherm("Zeolite_13X")
q = isotherm(100000.0, 298.15)   # (P, T)

Working Capacity#

from difflow_cc import working_capacity_PSA, working_capacity_TSA, get_isotherm

isotherm = get_isotherm("Zeolite_13X")

# PSA working capacity: q(P_ads, T) - q(P_des, T)
wc_psa = working_capacity_PSA(isotherm, P_ads=500000.0, P_des=100000.0, T=298.15)

# TSA working capacity: q(P, T_ads) - q(P, T_des)
wc_tsa = working_capacity_TSA(isotherm, P=15000.0, T_ads=298.15, T_des=423.15)
print(f"PSA {float(wc_psa):.2f}, TSA {float(wc_tsa):.2f} mol/kg")

Solubility Models#

from difflow_cc import co2_physical_solubility, diffusivity_co2_amine

# CO2 physical solubility in water
H = co2_physical_solubility(T=298.15)

# CO2 diffusivity in amine solution (C_amine in mol/m^3)
D = diffusivity_co2_amine(T=313.15, solvent="MEA", C_amine=5000.0)  # m²/s

Kinetics Models#

Reaction Kinetics#

Model CO2-amine reaction rates:

from difflow_cc import reaction_rate_constant, enhancement_factor, hatta_number

# Second-order rate constant for MEA
k2 = reaction_rate_constant(T=313.15, solvent="MEA")
print(f"Rate constant: {float(k2):.0f} L/(mol·s)")

# Hatta number (reaction vs. diffusion); C_amine in mol/m^3, kL in m/s
Ha = hatta_number(T=313.15, solvent="MEA", C_amine=5000.0, kL=1e-4)
print(f"Hatta number: {float(Ha):.1f}")

# Enhancement factor (regime chosen automatically)
E = enhancement_factor(T=313.15, solvent="MEA", C_amine=5000.0, kL=1e-4)
print(f"Enhancement factor: {float(E):.1f}")

Governing Equations#

Reaction Rate (second-order):

\[r = k_2 \cdot C_{CO_2} \cdot C_{amine}\]

Arrhenius Temperature Dependence:

\[k_2 = A \cdot \exp\left(-\frac{E_a}{RT}\right)\]

Hatta Number:

\[Ha = \frac{\sqrt{k_2 \cdot C_{amine} \cdot D_{CO_2}}}{k_L}\]

Mass Transfer#

from difflow_cc import gas_film_coefficient, liquid_film_coefficient, overall_mass_transfer

from difflow_cc import henry_constant

# Gas-side mass transfer coefficient (Onda)
k_G = gas_film_coefficient(
    u_G=1.0,          # m/s superficial gas velocity
    d_p=0.05,         # m packing nominal diameter
    mu_G=1.8e-5,      # Pa·s
    rho_G=1.1,        # kg/m^3
    D_G=1.5e-5,       # m²/s
    a_p=250.0,        # m²/m³ packing specific area
)

# Liquid-side coefficient
k_L = liquid_film_coefficient(
    u_L=0.01,         # m/s superficial liquid velocity
    d_p=0.05,
    mu_L=2e-3,        # Pa·s
    rho_L=1010.0,     # kg/m^3
    D_L=1.5e-9,       # m²/s
    a_p=250.0,
)

# Overall gas-side coefficient (H: Henry's constant, P: total pressure)
H_CO2 = henry_constant(313.15, "MEA")
K_G = overall_mass_transfer(k_G=k_G, k_L=k_L, E=E, H=H_CO2, P=101325.0)

Unit Operations#

AmineAbsorber#

Location: difflow_cc/units/absorber.py

Class: AmineAbsorber

Description: Equilibrium-stage model for amine absorption columns.

Parameters#

@dataclass
class AbsorberParams:
    solvent: str                   # Solvent name, e.g. "MEA"
    n_stages: int = 10             # Number of theoretical stages
    solvent_conc: float = 30.0     # Amine concentration (wt%)
    L_G_ratio: float = 3.0         # Liquid-to-gas molar ratio
    T_gas_in: float = 313.15       # K
    T_liquid_in: float = 313.15    # K (operating temperature)
    P_absorber: float = 101325.0   # Pa
    stage_efficiency: float = 0.25 # Murphree efficiency
    lean_loading: float = 0.2      # Lean loading (mol CO2/mol amine)
    model_water_transfer: bool = False

L_G_ratio, solvent_conc and lean_loading build the lean solvent when none is passed. A solvent_in stream (species Amine, H2O, CO2_absorbed), such as the stripper’s lean outlet, overrides them: its flows set the amine and water rates, the lean loading and therefore L/G.

Inputs#

Parameter	Type	Units	Description
`gas_in`	Stream	-	Inlet flue gas
`solvent_in`	Stream, optional	-	Lean solvent (`Amine`, `H2O`, `CO2_absorbed`)
`T_op`	float, optional	K	Operating temperature (default `T_liquid_in`)

Outputs#

Parameter	Type	Units	Description
`gas_out`	Stream	-	Treated gas
`solvent_out`	Stream	-	Rich solvent; `CO2_absorbed` is the TOTAL CO2 it holds (lean + captured)
`info['capture_efficiency']`	float	-	CO2 capture fraction
`info['CO2_captured']`	float	mol/s	CO2 moved from gas to liquid
`info['rich_loading']`, `info['lean_loading']`	float	mol/mol	Solvent loadings
`info['absorption_factor']`	float	-	Kremser \(A = L/(mG)\)
`info['n_stages_effective']`	float	-	Equilibrium stages after Murphree efficiency

The Kremser form holds for every absorption factor: when \(A < 1\) the column cannot capture more than the fraction \(A\) however many stages it has, which is what slow, low-capacity solvents such as MDEA show at flue-gas conditions.

Example Usage#

from difflow_cc import AmineAbsorber, AbsorberParams
from difflow import make_stream

params = AbsorberParams(
    solvent="MEA",
    solvent_conc=30.0,
    n_stages=15,
    stage_efficiency=0.25,
    lean_loading=0.2,
    L_G_ratio=3.0,
)
absorber = AmineAbsorber(params)

flue_gas = make_stream(
    {'N2': 75.0, 'CO2': 12.0, 'H2O': 8.0, 'O2': 5.0},
    T=313.15, P=101325.0
)

gas_out, rich_solvent, info = absorber(flue_gas)

print(f"CO2 capture: {float(info['capture_efficiency']):.1%}")
print(f"Rich loading: {float(info['rich_loading']):.3f} mol/mol")

AmineStripper#

Location: difflow_cc/units/stripper.py

Class: AmineStripper

Description: Equilibrium-stage stripper for solvent regeneration.

Parameters#

@dataclass
class StripperParams:
    solvent: str                         # Solvent name
    n_stages: int = 8
    T_reboiler: float = 393.15           # K
    P_stripper: float = 200000.0         # Pa
    steam_ratio: float = 2.0             # mol H2O stripped per mol CO2
    T_condenser: float = 313.15          # K, overhead condenser outlet
    target_lean_loading: float = 0.2     # mol CO2/mol amine
    reboiler_duty: float = None          # W; if set, limits stripping
    cross_exchanger_approach: float = 10.0  # K

The lean loading cannot go below the loading in equilibrium with the reboiler vapour: the CO2 partial pressure there is the column pressure less the water vapour pressure over the solution, \(P_{CO_2} = P - x_w P^{sat}_w(T_{reb})\), inverted through the solvent’s VLE. A hotter reboiler or a lower column pressure therefore strips deeper; a reboiler colder than the rich solvent is rejected. A specified reboiler_duty caps the CO2 that can be released after the sensible heat is paid.

The overhead condenser returns the steam it condenses to the column as reflux. The CO2 product leaves saturated with water at T_condenser and the column pressure (about 96 % CO2 at 2 bar and 40 C) and the solvent keeps its water, so an absorber-stripper loop needs no make-up water for the stripping steam. The achieved reflux (mol condensate per mol CO2) is info["reflux_ratio"]; the old reflux_ratio input is ignored.

Key Outputs#

Parameter	Description	Units
`lean_solvent`	Regenerated solvent (`CO2_absorbed` = CO2 left in it)	Stream
`co2_product`	CO2 product stream	Stream
`info['specific_energy']`	Specific regeneration energy	GJ/t CO2
`info['lean_loading']`	Achieved lean loading	mol/mol
`info['equilibrium_lean_loading']`	Reboiler equilibrium floor	mol/mol

Example Usage#

from difflow_cc import AmineStripper, StripperParams

params = StripperParams(solvent="MEA", n_stages=10, T_reboiler=393.15)
stripper = AmineStripper(params)

# rich_solvent from the absorber example above
lean_solvent, co2_product, info = stripper(rich_solvent)

print(f"Regen. energy: {float(info['specific_energy']):.2f} GJ/t CO2")
print(f"Lean loading: {float(info['lean_loading']):.3f} mol/mol")

Feeding lean_solvent back to absorber(flue_gas, lean_solvent) closes the solvent loop: the absorber then uses the stripper’s amine, water and lean loading, and at steady state the CO2 captured equals the CO2 stripped (water lost with the product needs make-up).

MembraneSeparator#

Location: difflow_cc/units/membrane.py

Class: MembraneSeparator

Description: Single-stage membrane gas separator using solution-diffusion model.

Parameters#

@dataclass
class MembraneParams:
    membrane_type: str                  # Name from list_membranes()
    area: float = 1000.0                # m^2
    thickness: float = None             # micrometres; None uses the database default
    pressure_ratio: float = 10.0        # Feed/permeate pressure
    T_operation: float = 298.15         # K
    feed_pressure: float = None         # Pa; None uses the feed stream's P
    permeate_pressure: float = None     # Pa; from the ratio if None
    stage_cut_target: float = None      # If set, the area is solved to hit it

pressure_ratio must exceed 1 (and an explicit permeate pressure must be below the feed pressure); otherwise nothing can permeate and the parameters are rejected.

Governing Equations#

Permeate Flux (solution-diffusion):

\[J_i = \frac{P_i}{\delta} (p_{i,feed} - p_{i,perm})\]

Where:

\(P_i\): Permeability of species i (Barrer)
\(\delta\): Membrane thickness (m)
\(p\): Partial pressures

Selectivity:

\[\alpha_{ij} = \frac{P_i}{P_j}\]

Stage Cut:

\[\theta = \frac{F_{permeate}}{F_{feed}}\]

Complete mixing. Both sides are taken as well mixed, so the retentate composition \(x_i\) is the one the membrane sees and every species obeys

\[F_{perm,i} = A\,Q_i\,(x_i P_{feed} - y_i P_{perm})\]

with \(y_i\) the permeate composition. The closure \(\sum_i y_i = 1\) is solved exactly for the stage cut (or, with stage_cut_target, for the area), so no species ever permeates against its partial-pressure gradient and every retentate flow stays non-negative. With enough area everything permeates and the permeate tends to the feed composition.

Example Usage#

from difflow import make_stream
from difflow_cc import MembraneSeparator, MembraneParams

params = MembraneParams(
    membrane_type="PIM_1",     # a name from list_membranes()
    area=200.0,
    thickness=1.0,             # micrometres
    pressure_ratio=10.0,
)
membrane = MembraneSeparator(params)

# Feed at 10 bar; the feed side runs at the stream's pressure
flue_gas = make_stream({'N2': 85.0, 'CO2': 15.0}, T=298.15, P=1000000.0)

retentate, permeate, info = membrane(flue_gas)

print(f"Stage cut: {float(info['stage_cut']):.2%}")       # 11.74%
print(f"CO2 purity: {float(info['CO2_purity']):.1%}")     # 55.0%
print(f"CO2 recovery: {float(info['CO2_recovery']):.1%}") # 43.0%

# Or fix the stage cut and let the unit solve for the area
_, _, cut = MembraneSeparator(MembraneParams(
    membrane_type="PIM_1", thickness=1.0, stage_cut_target=0.2))(flue_gas)
print(f"Area for a 20% cut: {float(cut['area_used']):.0f} m^2")

MultistageMembrane#

Location: difflow_cc/units/membrane.py

Class: MultistageMembrane

Description: A cascade of MembraneSeparator stages, in series or as a two-stage enriching cascade with recycle.

Process Role#

One membrane stage cannot be both selective and complete. Its purity is set by the selectivity and the pressure ratio, its recovery by the area, and pushing the area up to capture the last of the CO2 drags the permeate composition back towards the feed: the single PIM-1 stage of the previous section gives 55% purity at 43% recovery over 200 m^2, 31% purity at 81% recovery over 1000 m^2, and over 5000 m^2 it permeates essentially the whole feed (15% CO2) — no separation at all. Staging is the way out, and which way you stage depends on which of the two you need:

series — each stage treats the previous retentate, and the permeates are pooled. Recovery rises (every stage gets another chance at the CO2 the last one missed) and the pooled purity falls, because the later stages are working on an increasingly CO2-lean gas.
permeate_recycle — the stage-1 permeate is recompressed to the feed pressure and enriched in stage 2, whose permeate is the product; the stage-2 retentate is recycled to the stage-1 inlet and the loop is converged (info['recycle_residual']). Purity rises (the CO2 is enriched twice) and recovery falls. This layout is two stages by definition; other n_stages are rejected.

Parameters#

The constructor takes a MembraneParams (the same one MembraneSeparator takes, with area read per stage) plus the cascade’s own arguments:

MultistageMembrane(params, n_stages=2, configuration="series",
                   recycle_iterations=100, stage_params=None)
#  stage_params: optional list of MembraneParams, one per stage

Stage 2 of permeate_recycle sees only the stage-1 permeate, a small fraction of the feed, so on the same area it permeates nearly all of it and enriches nothing; give it its own, smaller area through stage_params.

Inputs and Outputs#

Parameter	Type	Units	Description
`feed`	Stream	-	Feed gas
`retentate`	Stream	-	Final treated gas
`permeate`	Stream	-	Final CO2 product
`info['overall_CO2_recovery']`	float	-	CO2 to the product, as a fraction of the feed’s
`info['overall_CO2_purity']`	float	-	CO2 mole fraction of the product
`info['stage_info']`	list	-	Each stage’s own `MembraneSeparator` info dict
`info['recycle_residual']`	float	-	`permeate_recycle` only: final relative change of the recycle

Governing Equations#

There is no new physics here — each stage is the complete-mixing solution-diffusion model of MembraneSeparator. What the cascade adds is the composition of stage cuts, which for stages in series is

\[\theta_{overall} = 1 - \prod_k (1 - \theta_k)\]

and a pooled product purity

\[y_{CO_2} = \frac{\sum_k \dot{n}_{CO_2,k}^{perm}}{\sum_k \dot{n}_k^{perm}}\]

Example Usage#

from difflow import make_stream
from difflow_cc import MembraneSeparator, MultistageMembrane, MembraneParams

params = MembraneParams(membrane_type="Matrimid", area=2000.0, pressure_ratio=10.0)
stage2 = MembraneParams(membrane_type="Matrimid", area=200.0, pressure_ratio=10.0)
flue_gas = make_stream({'N2': 85.0, 'CO2': 15.0}, T=298.15, P=10e5)

_, _, one = MembraneSeparator(params)(flue_gas)
_, _, ser = MultistageMembrane(params, 2, "series")(flue_gas)
_, _, rec = MultistageMembrane(params, 2, "permeate_recycle",
                               stage_params=[params, stage2])(flue_gas)

#                  purity   recovery
# single stage      0.666     0.241
# series            0.629     0.414   <- recovery bought with purity
# permeate_recycle  0.957     0.167   <- purity bought with recovery

Design Considerations#

Compression is not included in the duty. pressure_ratio is a membrane parameter, not a compressor; the duty that sustains it belongs to a CompressionTrain (CO2 Compression). permeate_recycle reports the interstage recompression it assumes in info['interstage_compression'].

Adsorption Units#

Location: difflow_cc/units/adsorption.py

Four swing adsorption variants, one per regeneration route. They share AdsorptionParams and the same Langmuir working-capacity calculation; what differs is which variable swings, and therefore which energy term the cycle pays for.

Class	Swing	Regeneration	Energy reported
`PSAUnit`	Pressure, above ambient	Blowdown to a lower pressure	`compression_power`
`VSAUnit`	Pressure, below ambient	Vacuum	`vacuum_power`
`TSAUnit`	Temperature	Heating	`heating_power`
`TVSAUnit`	Both	Warm and evacuated	`thermal_power` + `vacuum_power`

Parameters#

@dataclass
class AdsorptionParams:
    adsorbent: str                   # Name from list_adsorbents()
    cycle_type: str = 'PSA'          # 'PSA' | 'TSA' | 'VSA' | 'TVSA'
    bed_mass: float = 1000.0         # kg adsorbent per bed
    n_beds: int = 2                  # Beds, for continuous operation
    void_fraction: float = 0.4
    # Pressure swing
    P_adsorption: float = 101325.0   # Pa
    P_desorption: float = 10000.0    # Pa
    # Temperature swing
    T_adsorption: float = 298.15     # K
    T_desorption: float = 393.15     # K
    # Cycle timing (s): the four steps whose sum is the cycle time
    t_adsorption: float = 300.0
    t_blowdown: float = 60.0
    t_purge: float = 120.0
    t_repressure: float = 60.0
    # Declared targets. Carried for sizing and costing; the performance
    # the unit reports is computed, not clipped to these.
    CO2_purity_target: float = 0.95
    CO2_recovery_target: float = 0.90

The quantity all four compute#

Every variant reduces to a working capacity — the difference between what the adsorbent holds at adsorption conditions and what it still holds at regeneration conditions:

\[q(P, T) = \frac{q_{max} b(T) P}{1 + b(T) P}, \qquad b(T) = b_0 \exp\left(\frac{-\Delta H_{ads}}{RT}\right)\]

\[\Delta q_{working} = q(P_{ads}, T_{ads}) - q(P_{des}, T_{des})\]

with recovery following from the ratio of what the beds can take to what the feed brings, through an unused-bed (mass-transfer-zone) saturation:

\[\phi = \frac{\Delta q_{working}\, m_{bed}\, n_{beds}} {\dot{n}_{CO_2,feed}\, t_{cycle}}, \qquad \text{recovery} = R_{max}\left(1 - e^{-\phi/R_{max}}\right), \quad R_{max} = 0.95\]

A small bed is capacity-limited (recovery \(\approx \phi\)); an oversized one approaches \(R_{max}\), so bed mass, number of beds and step times always move the answer.

This is an equilibrium, lumped-capacity model: no intra-particle diffusion, no breakthrough profile, no bed dynamics. It sizes beds and compares technologies; it does not replace a cycle simulation. Two consequences worth knowing before reading its numbers:

Recovery saturates towards 95% of the feed CO2 (blowdown and breakthrough losses); info['capacity_ratio'] is \(\phi\), and values well above 1 mean the bed is oversized.
Every species is conserved. The co-adsorbed impurity implied by the purity correlation is drawn from all non-CO2 species in proportion to their feed; the offgas is the rest. info['purity'] is the product stream’s actual CO2 fraction.
Infeasible points are flagged, not hidden. With no working capacity (a TSA with T_desorption <= T_adsorption, or a dilute feed against too shallow a vacuum) the product is empty, info['purity'] is 0 and info['feasible'] is False.
Purity comes from the adsorbent’s selectivity and the swing, not from a breakthrough calculation: it is s' / (s' + 1) with s' the selectivity scaled by the swing ratio. That is a reasonable ranking of adsorbents and a poor prediction of a real product stream.

PSAUnit#

Adsorption at elevated pressure, regeneration by blowdown to a lower one. The swing is in \(P\) at constant \(T\), so the working capacity is the gap between two points on one isotherm — which is why PSA wants a steep isotherm at the feed partial pressure and an already-compressed feed. Its natural home is pre-combustion capture and hydrogen purification, where the gas arrives at pressure and the compression is paid for anyway. info['compression_power'] is what it costs to hold P_adsorption.

VSAUnit#

The same pressure swing, moved below atmospheric: adsorb near ambient, desorb under vacuum. Post-combustion flue gas is at ambient pressure and there is no compressing 100 times the flow of the CO2 in it, so the cheaper move is to pull vacuum on the bed instead. The working capacity is larger than PSA’s for the same ratio — the Langmuir isotherm is steepest near the origin — and the price is info['vacuum_power'], which dominates the energy balance.

TSAUnit#

Temperature swings instead of pressure: \(b(T)\) collapses with heating, so the bed gives up its CO2 at constant pressure. That makes TSA the variant that works on dilute feeds — direct air capture at 400 ppm, where no pressure ratio buys a useful working capacity — and the variant with the worst energy penalty, because the regeneration duty includes the sensible heat of the whole bed:

\[Q_{regen} = \left(m_{bed} C_p + m_{CO_2} \Delta H_{ads}\right) (T_{des} - T_{ads})\]

info['Q_sensible'] and info['Q_desorption'] report the two halves. The thermal mass also sets the cycle time: beds have to be heated and cooled, which is slow.

TVSAUnit#

Both at once — mildly warm and evacuated. The point is not to add the two working capacities but to reach a given one at a lower desorption temperature than TSA needs, which cuts the sensible-heat penalty and lets amine-functionalised sorbents regenerate below the temperature at which they degrade (see Adsorbent Degradation). It is the usual choice for solid-sorbent DAC, and it pays both info['thermal_power'] and info['vacuum_power'].

Example Usage#

from difflow import make_stream
from difflow_cc import PSAUnit, VSAUnit, AdsorptionParams

flue_gas = make_stream({'N2': 85.0, 'CO2': 15.0}, T=298.15, P=500000.0)

psa = PSAUnit(AdsorptionParams(
    adsorbent="Zeolite_13X",     # a name from list_adsorbents()
    cycle_type="PSA",
    bed_mass=5000.0,
    n_beds=4,
    P_adsorption=500000.0,
    P_desorption=100000.0,
))

product, offgas, info = psa(flue_gas)

print(f"CO2 purity:   {float(info['purity']):.1%}")          # 99.3%
print(f"CO2 recovery: {float(info['recovery']):.1%}")        # 44.8%
print(f"Productivity: {float(info['productivity']):.2f} "    # 1.64
      f"mol CO2/(kg.h)")
print(f"Working cap.: {float(info['working_capacity']):.3f} mol/kg")

The same feed at ambient pressure through a VSAUnit (P_adsorption=101325, P_desorption=10000) reaches 84% recovery with a 3.4x larger working capacity — the comparison the four classes exist to make, and the reason cycle_type is a parameter rather than the class name doing the work.

Heat Integration#

Location: difflow_cc/units/heat_integration.py

Efficient heat recovery is critical for minimizing energy penalty:

from difflow import make_stream
from difflow_cc import LeanRichExchanger, LeanRichExchangerParams

params = LeanRichExchangerParams(
    min_approach=10.0,      # K minimum approach
    effectiveness=0.85,
)
exchanger = LeanRichExchanger(params)

lean_hot = make_stream({"H2O": 200.0}, T=393.15, P=2e5)    # from stripper
rich_cold = make_stream({"H2O": 100.0}, T=313.15, P=2e5)   # from absorber

lean_cold, rich_hot, info = exchanger(lean_hot, rich_cold)

print(f"Duty: {float(info['Q'])/1e6:.3f} MW")
print(f"Effectiveness achieved: {float(info['effectiveness']):.2f}")
print(f"Heat recovery fraction: {float(info['heat_recovery_fraction']):.1%}")

One duty serves both sides: the minimum approach caps it at \(C_{min}(\Delta T_{in} - \Delta T_{min})\), both outlet temperatures follow from it, and info['effectiveness'] reports what was achieved (below the requested value when the approach binds).

CO2 Compression#

Location: difflow_cc/units/compression.py

CO2 must be compressed to pipeline or sequestration pressure:

from difflow_cc import CompressionTrain, CompressionTrainParams

from difflow import make_stream

params = CompressionTrainParams(
    n_stages=4,
    P_outlet=15000000.0,      # 150 bar (supercritical)
    eta_isentropic=0.80,
    T_intercool=313.15,       # 40°C
)
compressor = CompressionTrain(params)

# The train compresses from the inlet stream's pressure (here 1 atm).
co2_stream = make_stream({'CO2': 100.0}, T=313.15, P=101325.0)

compressed, info = compressor(co2_stream)

print(f"Outlet: {float(compressed['P'])/1e5:.0f} bar")
print(f"Total power: {float(info['total_power'])/1e6:.2f} MW")
print(f"Specific power: {float(info['specific_power']):.0f} kJ/kg CO2")

Direct Air Capture#

Location: difflow_cc/units/dac.py

Model direct air capture systems:

from difflow import make_stream
from difflow_cc import SolidSorbentDAC, DACParams, LiquidSolventDAC, LiquidDACParams

params = DACParams(
    sorbent="PEI_Silica",
    cross_section=100.0,       # m² face area per contactor
    n_units=4,
    T_adsorption=298.15,
    T_desorption=373.15,
    cycle_time_ads=1800.0,     # s
    cycle_time_des=900.0,      # s
)
dac = SolidSorbentDAC(params)

# Time-averaged air feed to the plant (mol/s); capture can never exceed
# the CO2 it carries.
air = make_stream({'N2': 12800.0, 'O2': 3440.0, 'CO2': 6.9}, T=298.15, P=101325.0)

co2_product, info = dac(air)

print(f"Captured: {float(info['CO2_captured_tonne_yr']):.0f} t CO2/yr")
print(f"Capture efficiency: {float(info['capture_efficiency']):.1%}")
print(f"Sorbent utilization: {float(info['sorbent_utilization']):.1%}")
print(f"Thermal: {float(info['specific_thermal_GJ_tonne']):.1f} GJ/t CO2")

# Liquid (KOH) DAC: capture from transfer units over the packing depth
_, liq = LiquidSolventDAC(LiquidDACParams(contactor_height=8.0, L_G_ratio=2.0))()
print(f"Liquid DAC capture: {float(liq['capture_efficiency']):.1%}")

Solid-sorbent capture is the smaller of what the beds can take (sorbent mass x working capacity / cycle time) and 95% of the CO2 in the processed air; without an ambient_air stream the air flow is air_velocity x cross_section per unit at 420 ppm. Liquid-solvent capture is \(1 - e^{-NTU}\) with NTU from the packing depth (contactor_height), the air velocity and the liquid wetting (L_G_ratio), calibrated to 75% at the default 8 m, 1.5 m/s, L/G = 2 design point; with no liquid nothing is captured.

Economics#

Location: difflow_cc/economics/

Comprehensive economic analysis:

from difflow_cc import (
    absorber_cost, stripper_cost, installed_cost,
    total_operating_cost, levelized_cost_capture, cost_of_co2_avoided,
    EconomicParams,
)

params = EconomicParams(
    capacity_factor=0.85,
    lifetime=25,               # years
    discount_rate=0.08,
)
CO2_rate = 1.0e6 * 1e6 / 44.01 / (8760 * 3600 * 0.85)   # mol/s for ~1 Mt/yr

# Capital costs (USD)
equipment = (absorber_cost(diameter=10.0, height=30.0)
             + stripper_cost(diameter=8.0, height=25.0,
                             reboiler_duty=150e6, condenser_duty=60e6))
capex = installed_cost(equipment)["total_overnight_cost"]

# Operating costs (USD/yr); duties in W, CO2 in mol/s
opex = total_operating_cost(
    steam_duty=150e6,
    electricity=20e6,
    cooling_duty=120e6,
    CO2_captured=CO2_rate,
    capital_cost=capex,
)["total_opex"]

# Levelized cost ($/t CO2)
lcoc = levelized_cost_capture(capex, opex, CO2_rate, params)
print(f"Levelized cost: ${float(lcoc['total_cost_per_tonne']):.1f}/tonne CO2")

# Cost of CO2 avoided
cca = cost_of_co2_avoided(
    capture_cost_per_tonne=lcoc["total_cost_per_tonne"],
    reference_emissions=0.80,     # t CO2/MWh without capture
    capture_emissions=0.10,       # t CO2/MWh with capture
    reference_energy=4.0e6,       # MWh/yr without capture
    capture_energy=3.0e6,         # MWh/yr after the energy penalty
)
print(f"Cost avoided: ${float(cca):.1f}/tonne CO2")

Degradation Models#

Location: difflow_cc/degradation/

Amine Degradation#

Each model takes a parameter set describing the solvent and its service conditions:

from difflow_cc import (
    AmineDegradationParams,
    oxidative_degradation_rate,
    thermal_degradation_rate,
    total_amine_loss,
    solvent_lifetime,
)

deg = AmineDegradationParams(
    solvent="MEA",
    O2_concentration=0.05,     # 5% O2 in the flue gas
    T_absorber=313.15,
    T_stripper=393.15,         # reboiler temperature
    CO2_loading=0.4,
)

r_ox = oxidative_degradation_rate(313.15, deg)   # absorber conditions
r_th = thermal_degradation_rate(393.15, deg)     # stripper conditions

loss = total_amine_loss(deg)
print(f"Amine loss: {float(loss['total_kg_m3_yr']):.1f} kg/m^3/yr")
print(f"Solvent lifetime: {float(solvent_lifetime(deg)):.1f} years")

Adsorbent Degradation#

from difflow_cc import AdsorbentDegradationParams, capacity_fade, adsorbent_lifetime

ads = AdsorbentDegradationParams(
    material_type="amine_silica",
    T_desorption=373.15,
    humidity=0.1,
    cycles_per_day=48.0,
)

fade = capacity_fade(8760.0, ads)            # after one year of operation
print(f"Capacity fade: {float(fade['capacity_loss_percent']):.1f}%")

lifetime_h = adsorbent_lifetime(ads, min_capacity_fraction=0.8)
print(f"Adsorbent lifetime: {float(lifetime_h) / 24:.0f} days")

Membrane Aging#

from difflow_cc import (
    MembraneAgingParams, physical_aging, plasticization, membrane_lifetime,
)

mem = MembraneAgingParams(membrane_type="glassy", T_operating=298.15)

# Physical aging (glassy polymers): permeance fraction after one year
remaining = physical_aging(1.0, mem)

# Plasticization from CO2 partial pressure
plast = plasticization(500000.0, mem)       # 5 bar CO2
print(f"Plasticized: {bool(plast['is_plasticized'])}")

lifetime = membrane_lifetime(mem, min_permeance_fraction=0.7)
print(f"Membrane lifetime: {float(lifetime):.1f} years")

Examples#

Example 1: Complete Amine Capture Plant#

The absorber, stripper and lean/rich exchanger close on the solvent: the stripper’s lean outlet is the absorber’s solvent_in. A few successive-substitution passes (or a Flowsheet recycle) converge the loop, after which CO2 captured equals CO2 stripped.

import jax
jax.config.update("jax_enable_x64", True)
from difflow import make_stream
from difflow.streams import get_flows
from difflow_cc import (
    AmineAbsorber, AbsorberParams,
    AmineStripper, StripperParams,
    LeanRichExchanger, LeanRichExchangerParams,
    CompressionTrain, CompressionTrainParams,
)

flue_gas = make_stream({"CO2": 13.0, "N2": 87.0}, T=313.15, P=101325.0)
absorber = AmineAbsorber(AbsorberParams(solvent="MEA", n_stages=15,
                                        L_G_ratio=3.5, lean_loading=0.25))
stripper = AmineStripper(StripperParams(solvent="MEA", n_stages=10))
exchanger = LeanRichExchanger(LeanRichExchangerParams())
compressor = CompressionTrain(CompressionTrainParams(n_stages=4))

@jax.jit
def loop_pass(rich):
    _, rich_hot, _ = exchanger(make_stream(get_flows(rich), 393.15, 2e5), rich)
    lean, co2, s_info = stripper(rich_hot)
    lean_flows = dict(get_flows(lean))
    lean_flows["H2O"] = lean_flows["H2O"] + get_flows(co2)["H2O"]  # make-up water
    lean = make_stream(lean_flows, T=313.15, P=101325.0)
    gas_out, rich, a_info = absorber(flue_gas, lean)
    return rich, (co2, s_info, a_info)

_, rich, _ = absorber(flue_gas)
for _ in range(200):
    rich, (co2, s_info, a_info) = loop_pass(rich)

compressed, c_info = compressor(co2)
print(f"Capture: {float(a_info['capture_efficiency']):.1%}")
print(f"Captured {float(a_info['CO2_captured']):.3f} = stripped "
      f"{float(s_info['CO2_stripped']):.3f} mol/s")
print(f"Regeneration: {float(s_info['specific_energy']):.2f} GJ/t CO2")
print(f"Compression: {float(c_info['total_power'])/1e3:.0f} kW")

Example 2: Gradient-Based Optimization#

import jax
import jax.numpy as jnp
from difflow import make_stream
from difflow_cc import AmineAbsorber, AbsorberParams

flue_gas = make_stream({"CO2": 13.0, "N2": 87.0}, T=313.15, P=101325.0)

def capture_cost(x):
    """Cost per mol CO2 captured (illustrative weights)."""
    n_stages, L_G_ratio = x
    absorber = AmineAbsorber(AbsorberParams(
        solvent="MEA", n_stages=n_stages, L_G_ratio=L_G_ratio))
    _, _, info = absorber(flue_gas)

    capex = n_stages * 1.0      # per stage
    opex = L_G_ratio * 2.0      # per unit solvent circulation
    return (capex + opex) / info["CO2_captured"]

gradients = jax.grad(capture_cost)(jnp.array([10.0, 3.0]))
print(f"d/d(n_stages)={float(gradients[0]):.4f}, d/d(L_G)={float(gradients[1]):.4f}")

Example 3: Technology Comparison#

from difflow import make_stream
from difflow_cc import (
    AmineAbsorber, AbsorberParams,
    MembraneSeparator, MembraneParams,
    VSAUnit, AdsorptionParams,
)

flue_gas = make_stream({"CO2": 15.0, "N2": 85.0}, T=313.15, P=101325.0)
compressed_gas = make_stream({"CO2": 15.0, "N2": 85.0}, T=313.15, P=10e5)

_, _, amine = AmineAbsorber(AbsorberParams(solvent="MEA"))(flue_gas)
_, _, mem = MembraneSeparator(MembraneParams(membrane_type="PIM_1", area=200.0,
                                             thickness=1.0))(compressed_gas)
_, _, vsa = VSAUnit(AdsorptionParams(adsorbent="Zeolite_13X", cycle_type="VSA",
                                     bed_mass=5000.0, n_beds=4))(flue_gas)

print(f"Amine (MEA):      capture {float(amine['capture_efficiency']):.1%}")
print(f"Membrane (PIM-1): recovery {float(mem['CO2_recovery']):.1%}, "
      f"purity {float(mem['CO2_purity']):.1%}")
print(f"VSA (13X):        recovery {float(vsa['recovery']):.1%}, "
      f"purity {float(vsa['purity']):.1%}")

Carbon Capture Unit Operations

Contents

Carbon Capture Unit Operations#

Overview#

Installation#

Database and Properties#

Amine Solvents#

Available Solvent Properties#

Solvent Comparison#

Adsorbent Materials#

Adsorbent Comparison#

Membrane Materials#

Membrane Comparison#

Equilibrium Models#

Vapor-Liquid Equilibrium#

Equilibrium Model#

Adsorption Isotherms#

Temperature-Dependent Isotherms#

Working Capacity#

Solubility Models#

Kinetics Models#

Reaction Kinetics#

Governing Equations#

Mass Transfer#

Unit Operations#

AmineAbsorber#

Parameters#

Inputs#

Outputs#

Example Usage#

AmineStripper#

Parameters#

Key Outputs#

Example Usage#

MembraneSeparator#

Parameters#

Governing Equations#

Example Usage#

MultistageMembrane#

Process Role#

Parameters#

Inputs and Outputs#

Governing Equations#

Example Usage#

Design Considerations#

Adsorption Units#

Parameters#

The quantity all four compute#

PSAUnit#

VSAUnit#

TSAUnit#

TVSAUnit#

Example Usage#

Heat Integration#

CO2 Compression#

Direct Air Capture#

Economics#

Degradation Models#

Amine Degradation#

Adsorbent Degradation#

Membrane Aging#

Examples#

Example 1: Complete Amine Capture Plant#

Example 2: Gradient-Based Optimization#

Example 3: Technology Comparison#

See Also#