Adsorption Modeling Review and Enhancement Proposal

Executive Summary

This document reviews NeqSim’s current adsorption modeling capabilities and proposes enhancements including additional isotherm models, capillary condensation, and improved database support for multiple adsorbent materials.

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Current Implementation Review

Architecture Overview

The adsorption functionality in NeqSim is located in:

• Interface: neqsim.physicalproperties.interfaceproperties.solidadsorption.AdsorptionInterface
• Implementation: neqsim.physicalproperties.interfaceproperties.solidadsorption.PotentialTheoryAdsorption
• Database: src/main/resources/data/AdsorptionParameters.csv

Current Model: Potential Theory (Polanyi/DRA)

The existing implementation uses the Dubinin-Radushkevich-Astakhov (DRA) potential theory with the following key equations:

Adsorption Potential: \(\epsilon = \epsilon_0 \cdot \left( \ln\frac{z_0}{z} \right)^{1/\beta}\)

Surface Excess Integration: The model integrates from the bulk phase to the surface using fugacity equilibrium.

Strengths of Current Implementation

1. Thermodynamically rigorous - Uses fugacity-based calculations
2. Multi-component capable - Handles mixtures
3. EoS integration - Uses NeqSim’s thermodynamic models for real gas behavior
4. Database-driven parameters - Parameters stored in CSV for easy extension

Limitations Identified

Issue	Description	Impact
Single isotherm model	Only DRA potential theory available	Limited applicability
Limited database entries	Only 9 component/solid combinations	Many systems unsupported
No capillary condensation	Critical for mesoporous materials	Incomplete physics
No temperature dependence	Parameters assumed constant	Poor extrapolation
Missing getSurfaceExcess(int)	Throws UnsupportedOperationException	Incomplete API
No BET surface area	Common characterization missing	No standardization
No pore size distribution	Required for accurate modeling	Oversimplified

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Proposed Enhancements

1. Additional Isotherm Models

1.1 Langmuir Isotherm (Single Component)

For monolayer adsorption on homogeneous surfaces:

\[q = q_{max} \cdot \frac{K \cdot P}{1 + K \cdot P}\]

Where:

• $q$ = amount adsorbed (mol/kg)
• $q_{max}$ = maximum adsorption capacity
• $K$ = Langmuir constant (1/bar)
• $P$ = partial pressure (bar)

1.2 Freundlich Isotherm

For heterogeneous surfaces:

\[q = K_F \cdot P^{1/n}\]

Where:

• $K_F$ = Freundlich capacity constant
• $n$ = heterogeneity parameter (n > 1 for favorable adsorption)

1.3 BET Isotherm (Brunauer-Emmett-Teller)

For multilayer adsorption:

\[\frac{P}{q(P_0 - P)} = \frac{1}{q_m \cdot C} + \frac{C - 1}{q_m \cdot C} \cdot \frac{P}{P_0}\]

Where:

• $P_0$ = saturation pressure
• $q_m$ = monolayer capacity
• $C$ = BET constant (related to heat of adsorption)

1.4 Sips Isotherm (Langmuir-Freundlich)

Combines Langmuir and Freundlich for heterogeneous surfaces:

\[q = q_{max} \cdot \frac{(K \cdot P)^{1/n}}{1 + (K \cdot P)^{1/n}}\]

1.5 Extended Langmuir (Multi-Component)

For competitive adsorption:

\[q_i = q_{max,i} \cdot \frac{K_i \cdot P_i}{1 + \sum_j K_j \cdot P_j}\]

2. Capillary Condensation Model

2.1 Theoretical Background

Capillary condensation occurs in mesopores (2-50 nm) when vapor condenses at pressures below saturation due to curved meniscus effects.

Kelvin Equation: \(\ln\frac{P}{P_0} = -\frac{2 \gamma V_m \cos\theta}{r \cdot R \cdot T}\)

Where:

• $\gamma$ = surface tension (N/m)
• $V_m$ = molar volume of liquid (m³/mol)
• $\theta$ = contact angle
• $r$ = pore radius (m)
• $R$ = gas constant
• $T$ = temperature (K)

Kelvin Radius: \(r_K = -\frac{2 \gamma V_m \cos\theta}{R T \ln(P/P_0)}\)

2.2 Pore Size Distribution

Implement support for common PSD models:

1. Cylindrical pores (BJH method)
2. Slit pores (for activated carbons)
3. User-defined distribution

2.3 Combined Adsorption + Capillary Condensation

Total uptake = Multilayer adsorption + Capillary condensate:

\[q_{total} = q_{BET} + \int_{r_{min}}^{r_K} \rho_L \cdot V(r) \cdot f(r) \, dr\]

3. Database Enhancement

New Database Table Structure

AdsorptionParameters.csv - Extended:

ID,Name,Solid,IsothermModel,eps,z0,beta,qmax,K_langmuir,K_freundlich,n_freundlich,C_BET,TempRef,dH_ads
1,methane,AC Calgon F400,DRA,7.458,0.298,2.0,,,,,298.15,-20000
2,CO2,AC Calgon F400,DRA,7.76,0.298,2.0,,,,,298.15,-25000

AdsorbentProperties.csv - New:

ID,SolidName,BETSurfaceArea_m2g,PoreVolume_cm3g,MeanPoreRadius_nm,PoreType,MinPoreRadius_nm,MaxPoreRadius_nm
1,AC Calgon F400,1100,0.45,1.2,cylindrical,0.3,5.0
2,AC Norit R1,950,0.42,1.5,slit,0.4,6.0
3,Zeolite 13X,540,0.28,0.4,cylindrical,0.3,0.7
4,Silica Gel,650,0.38,3.0,cylindrical,1.0,10.0

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Proposed Class Architecture

New Interface Hierarchy

AdsorptionInterface (existing)
├── calcAdsorption(int phaseNum)
├── getSurfaceExcess(int component)
├── getSurfaceExcess(String componentName)
├── setSolidMaterial(String solidM)
│
├── NEW: setIsothermModel(IsothermType type)
├── NEW: getIsothermModel()
├── NEW: calcCapillaryCondensation()
├── NEW: getCapillaryCondensateAmount(String component)
├── NEW: getTotalUptake(String component)
├── NEW: getKelvinRadius()
├── NEW: setPoreDistribution(PoreDistribution psd)

New Enums

public enum IsothermType {
    DRA,           // Dubinin-Radushkevich-Astakhov
    LANGMUIR,      // Single-site Langmuir
    FREUNDLICH,    // Freundlich
    BET,           // BET multilayer
    SIPS,          // Langmuir-Freundlich
    EXTENDED_LANGMUIR  // Multi-component Langmuir
}

public enum PoreType {
    CYLINDRICAL,   // e.g., MCM-41, zeolites
    SLIT,          // e.g., activated carbons
    SPHERICAL,     // e.g., cage-type zeolites
    INK_BOTTLE     // Constrained pores
}

New Classes

1. AbstractAdsorptionModel - Base class with common functionality
2. LangmuirAdsorption - Langmuir isotherm implementation
3. FreundlichAdsorption - Freundlich isotherm implementation
4. BETAdsorption - BET multilayer model
5. SipsAdsorption - Sips isotherm implementation
6. ExtendedLangmuirAdsorption - Multi-component competitive adsorption
7. CapillaryCondensationModel - Kelvin equation + PSD
8. PoreDistribution - Pore size distribution handling
9. AdsorbentMaterial - Adsorbent properties container

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Implementation Priority

Priority	Feature	Effort	Impact
1	Fix getSurfaceExcess(int)	Low	High
2	Langmuir isotherm	Medium	High
3	BET isotherm	Medium	High
4	Capillary condensation	High	High
5	Extended database	Medium	Medium
6	Freundlich/Sips	Low	Medium
7	Pore size distribution	High	Medium

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Test Cases Required

Unit Tests

1. LangmuirAdsorptionTest
   • Single component at various pressures
   • Verify saturation behavior
   • Check against published data
2. BETAdsorptionTest
   • Multilayer coverage calculation
   • BET plot linearity
   • Surface area determination
3. CapillaryCondensationTest
   • Kelvin radius calculation
   • Hysteresis handling (adsorption vs desorption)
   • Integration with BET model
4. MultiComponentAdsorptionTest
   • Competitive adsorption
   • Selectivity calculations
   • Mixture isotherms

Integration Tests

1. Adsorption + Flash calculations
2. Column breakthrough simulation
3. Temperature swing adsorption cycles

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Example Usage (Proposed API)

// Create fluid system
SystemInterface gas = new SystemSrkEos(298.15, 10.0);
gas.addComponent("CO2", 0.5);
gas.addComponent("methane", 0.5);
gas.setMixingRule("classic");

ThermodynamicOperations ops = new ThermodynamicOperations(gas);
ops.TPflash();
gas.initProperties();

// Initialize adsorption with specific model
gas.getInterphaseProperties().initAdsorption();
AdsorptionInterface ads = gas.getInterphaseProperties().getAdsorptionCalc("gas");
ads.setSolidMaterial("Zeolite 13X");
ads.setIsothermModel(IsothermType.EXTENDED_LANGMUIR);

// Calculate adsorption
ads.calcAdsorption(0);

// Get component uptakes
double co2Uptake = ads.getSurfaceExcess("CO2");  // mol/kg
double ch4Uptake = ads.getSurfaceExcess("methane");

// Calculate selectivity
double selectivity = (co2Uptake / ch4Uptake) /
    (gas.getPhase(0).getComponent("CO2").getx() /
     gas.getPhase(0).getComponent("methane").getx());

// With capillary condensation (for mesoporous materials)
ads.calcCapillaryCondensation();
double kelvinRadius = ads.getKelvinRadius();  // nm
double condensate = ads.getCapillaryCondensateAmount("CO2");
double totalUptake = ads.getTotalUptake("CO2");

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References

1. Dubinin, M.M., “The Potential Theory of Adsorption of Gases and Vapors for Adsorbents with Energetically Nonuniform Surfaces”, Chem. Rev. 1960, 60(2), 235-241
2. Langmuir, I., “The Constitution and Fundamental Properties of Solids and Liquids”, J. Am. Chem. Soc. 1916, 38(11), 2221-2295
3. Brunauer, Emmett, Teller, “Adsorption of Gases in Multimolecular Layers”, J. Am. Chem. Soc. 1938, 60(2), 309-319
4. Barrett, Joyner, Halenda, “The Determination of Pore Volume and Area Distributions in Porous Substances”, J. Am. Chem. Soc. 1951, 73(1), 373-380
5. Do, D.D., “Adsorption Analysis: Equilibria and Kinetics”, Imperial College Press, 1998

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Related Documentation

• Interfacial Properties
• Thermodynamic Models
• Component Database Guide