Adsorbent Capillary Condensation Screening

Use this skill to turn a sorbent pore size into a contaminant concentration limit for the gas entering a fixed bed. It answers the question "how much methanol / water / heavy hydrocarbon can this feed carry before the bed stops working", which is a different and much tighter question than "when does a bulk liquid drop out".

When to Use

• A mercury guard bed, molecular sieve, or catalyst guard bed is degrading and there is no free liquid at the inlet.
• A feed specification has to be written for a condensable polar contaminant (methanol, water, glycol, heavy ends) upstream of an adsorbent.
• An agent needs to explain why a "no free liquids" clause is not a sufficient specification.

The physics in one line

A concave meniscus in a pore condenses vapour below bulk saturation:

$$\ln a_c = -\frac{G,\gamma V_m\cos\theta}{r R T}$$

with $G = 2$ for cylindrical pores and $G = 1$ for slit pores. The bed limit is then $y_{max} = a_c \cdot y_{sat}$, where $y_{sat}$ is the bulk saturation mole fraction of the contaminant in the gas.

For methanol at 20 °C, $2\gamma V_m/RT = 0.75$ nm, so a 1.5 nm pore floods at 60 % of bulk saturation and a 6 nm pore at 88 %.

Inputs

• temperature: gas temperature in kelvin.
• surface_tension: contaminant liquid surface tension in N/m.
• molar_volume: contaminant liquid molar volume in m³/mol.
• pore_radius_nm: representative sorbent pore radius in nm.
• saturation_mole_fraction: bulk saturation mole fraction $y_{sat}$ of the contaminant in the gas at bed T and P. Obtain this from a real equation of state, not from $P^{sat}/P$ — see the coupling note below.
• contaminant_mole_fraction: optional current concentration, for a margin check.
• contact_angle_deg: default 0 (perfect wetting, conservative).
• geometry_factor: 2.0 cylindrical (default), 1.0 slit.

Outputs

• kelvin_length_nm: $G\gamma V_m\cos\theta / RT$ in nm.
• onset_relative_saturation: $a_c$.
• max_mole_fraction / max_ppmv: the contaminant limit.
• relative_saturation, margin_ratio: only when a current concentration is given.
• kelvin_valid: false below ~2 nm radius, where Kelvin is non-conservative.
• warning: ok, watch, or condensation-expected.
• assumptions: the public assumptions applied.

Engineering Method

CapillaryCondensationScreeningModel.evaluate() applies the open Kelvin equation only, in four steps:

1. Kelvin length L = G * gamma * Vm * cos(theta) / (R T), reported in nm.
2. Onset relative saturation a_c = exp(-L / r) for pore radius r.
3. Contaminant limit y_max = a_c * y_sat, also reported as ppmv. y_sat is supplied by the caller and is never derived inside the model.
4. If a current concentration is given, relative_saturation = y / y_sat and margin_ratio = y / y_max set the warning: ok, watch above watch_margin (default 0.5), condensation-expected at or above 1.0.

kelvin_valid is false below KELVIN_VALIDITY_RADIUS_NM (2 nm), where the continuum meniscus breaks down and the Kelvin limit is an upper bound only; use micropore_filling_fraction() (Dubinin-Radushkevich volume filling) there.

This is educational, screening-only logic for a single condensable. It does not flash the mixture, does not model pore size distribution, and is not a substitute for the validated NeqSim route described below.

Critical coupling — get y_sat from an EOS, on a fugacity basis

The screening result is only as good as y_sat. Two traps:

1. Do not use $y_{sat} = P^{sat}/P$. At elevated pressure a real gas dissolves considerably more polar contaminant than the ideal ratio suggests. For methanol in rich natural gas the enhancement factor is about 1.5 at 40 bara, 1.9 at 70 bara and 2.9 at 100 bara. Using the ideal ratio makes the limit roughly two to three times tighter than it needs to be.
2. Use an associating EOS for associating contaminants. Methanol, water and glycols need CPA (SystemSrkCPAstatoil, setMixingRule(10)). Corresponding- states vapour-pressure correlations such as Lee-Kesler are unusable for these components — for methanol at 5–35 °C Lee-Kesler over-predicts $P^{sat}$ by roughly an order of magnitude.

Get y_sat by flashing the gas against an excess of the pure contaminant liquid and reading the gas-phase mole fraction:

sys = SystemSrkCPAstatoil(273.15 + 20.0, 70.0)
for name, frac in rich_gas.items():
    sys.addComponent(name, frac)
sys.addComponent("methanol", 5.0)          # excess liquid
sys.setMixingRule(10)
sys.setMultiPhaseCheck(True)
ThermodynamicOperations(sys).TPflash()
sys.initProperties()
y_sat = sys.getPhase("gas").getComponent("methanol").getx()

Python Usage Pattern

from adsorbent_capillary_condensation_screening import CapillaryCondensationScreeningModel

model = CapillaryCondensationScreeningModel()
result = model.evaluate(
    temperature=293.15,
    surface_tension=0.0225,        # methanol
    molar_volume=40.7e-6,
    pore_radius_nm=6.0,            # mesoporous alumina-supported sorbent
    saturation_mole_fraction=3.55e-3,   # from CPA, not Psat/P
    contaminant_mole_fraction=500e-6,
)

print(result.max_ppmv, result.warning)

Micropores — where this screening stops

Below about 2 nm radius the meniscus is only a few molecules across and the continuum Kelvin equation over-predicts the onset. Real micropores fill progressively from $a \sim 0.01$–0.1 by volume filling (Dubinin–Radushkevich):

$$W = W_0\exp\left[-\left(\frac{RT\ln(1/a)}{\beta E_0}\right)^2\right]$$

micropore_filling_fraction() provides this estimate. For a microporous sorbent (activated carbon, molecular sieve) treat the Kelvin number as an upper bound and expect the true tolerance to be lower.

Never specify two condensables independently

Methanol and water are fully miscible and co-condense. A pore fills when their combined activity reaches the Kelvin onset, so a gas that is individually below saturation in both can still flood the sorbent. Screening them separately is the most common way to get this wrong.

Use the activity sum:

$$\sum_i \frac{y_i}{y_{sat,i}} \geq a_c(r) \quad\Rightarrow\quad \text{pore fills}$$

so the allowance for the second contaminant is what the first leaves behind:

a_water = y_water / y_sat_water
a_methanol_allowed = onset - a_water          # onset from the Kelvin equation
methanol_limit = max(0.0, a_methanol_allowed) * y_sat_methanol

A worked case at 115 bara and 1 °C over a 6 nm sorbent, where the gas holds only 110 ppmv water in total:

Cross-check the result with ThermodynamicOperations.capillaryDewPointTemperatureFlash(poreRadiusM) on the real multicomponent mixture: condensation is expected when the capillary dew point rises above the bed temperature. In the case above the two methods agree, and the capillary dew point sits 1.2–1.4 °C above the bulk dew point — which is precisely the margin a "no free liquids" specification fails to capture.

Rigorous route in NeqSim

For a multicomponent gas where several contaminants can co-condense (methanol and water is the usual case), do not add limits component by component. Use:

• neqsim.physicalproperties.interfaceproperties.solidadsorption.CapillaryCondensationModel with setSaturationMoleFraction(component, ySat) and setRelativeSaturationBasis(SATURATION_MOLE_FRACTION) — the exact, flash-grounded basis — then getMaxAllowableMoleFraction(component, poreRadiusNm, phase). The FUGACITY basis is also available but references a hypothetical pure liquid, so it carries a bias of about 14 % at 70 bara and can report a limit above bulk saturation unless the saturation mole fraction is supplied to cap it;
• CapillaryCondensationModel.microporeFillingFraction(a, T, betaE0, beta) for the micropore regime, and the constant KELVIN_VALIDITY_RADIUS_NM;
• neqsim.process.equipment.adsorber.MercuryRemovalBed.assessContaminant(name, ySat) to screen a contaminant against a guard bed directly. It picks Kelvin or micropore filling from the sorbent pore radius, returns the relative saturation, the Kelvin onset, the ppmv limit and the blocked pore fraction, and applyContaminantDegradation(...) folds that blocked fraction into the bed's capacity instead of a hand-picked degradation factor;
• ThermodynamicOperations.capillaryDewPointTemperatureFlash(poreRadiusM) to get the pore dew-point temperature of the real mixture directly.

Validation Checklist

• y_sat came from an EOS flash against excess contaminant liquid, not from P_sat / P, and CPA was used for an associating contaminant.
• Temperature, surface tension, molar volume and pore radius are positive and 0 < y_sat <= 1.
• The pore radius is at or above 2 nm, or kelvin_valid being false is reported and the micropore route is used.
• Every condensable that can co-condense is included through the activity sum, not screened component by component.
• The result is described as an educational screening indicator, with real assessment redirected to the NeqSim classes above.

Common Mistakes

Limitations

• Screening only. Contact angle, pore geometry and the pore size distribution are assumptions unless a vendor BJH/DFT distribution is supplied.
• Perfect wetting ($\cos\theta = 1$) is assumed by default; a partially wetted or hydrophobised surface tolerates more.
• Single-contaminant. Mixed condensates (methanol + water) condense earlier than either component alone.
• Says nothing about chemical degradation routes (support hydration, sulphur mobilisation, pellet attrition from slugs).

References

• Thomson, W. (Lord Kelvin), On the Equilibrium of Vapour at a Curved Surface of Liquid, Philosophical Magazine, 42 (1871) 448-452.
• Gregg, S. J., and Sing, K. S. W., Adsorption, Surface Area and Porosity, 2nd Edition, Academic Press, 1982 — Kelvin equation validity and the micropore limit.
• Dubinin, M. M., and Radushkevich, L. V., Equation of the Characteristic Curve of Activated Charcoal, Proc. Acad. Sci. USSR, 55 (1947) 331-333.
• Kontogeorgis, G. M., et al., An Equation of State for Associating Fluids (CPA), Ind. Eng. Chem. Res., 35 (1996) 4310-4318.
• NeqSim repository: https://github.com/equinor/neqsim

Related skills

• neqsim-water-dewpoint-dehydration-screening — sets the water content that feeds the co-condensation case.
• neqsim-teg-dehydration-modeling — upstream dehydration performance.
• neqsim-flow-assurance — methanol injection and inhibitor carry-over sources.