AIM: A User-friendly GUI Workflow program for Isotherm Fitting, Mixture Prediction, Isosteric Heat of Adsorption Estimation, and Breakthrough Simulation

This paper introduces AIM, a user-friendly MATLAB-based GUI that streamlines fixed-bed adsorption modeling by integrating isotherm fitting, mixture prediction, isosteric heat estimation, and breakthrough simulations, which were validated against experimental data for a ternary gas mixture.

The Gist

Imagine you are a chef trying to perfect a recipe for a very specific dish: capturing gases (like carbon dioxide) using a special sponge (an adsorbent material).

In the past, if you wanted to figure out how well this sponge works, you'd need to be a master chef and a computer wizard. You'd have to write complex code, juggle spreadsheets, and use expensive, locked-down software just to see if your sponge could actually clean the air or separate gases. It was like trying to bake a cake using a manual written in a foreign language with no pictures.

Enter AIM (Adsorption Isotherm Modeling). Think of AIM as a smart, all-in-one kitchen appliance that does the heavy lifting for you. It's a free, user-friendly computer program that lets anyone—from students to seasoned scientists—simulate how gases behave on these special sponges without needing to know how to code.

Here is how AIM works, broken down into four simple "stations" in your kitchen:

1. The Taste-Test Station (IsoFit)

The Problem: Before you can cook, you need to know how your ingredients behave. How much gas does the sponge hold at different pressures?
The AIM Solution: You upload your raw data (like a list of numbers showing how much gas the sponge grabbed). AIM acts like a super-smart taste-tester. It tries on 13 different "mathematical outfits" (models) to see which one fits your data perfectly.

• Analogy: Imagine trying to find the perfect pair of shoes. You try on sneakers, boots, and sandals. AIM tries on all the mathematical models and tells you, "Hey, the 'Dual-Site Langmuir' shoe fits your data perfectly!" It even tells you how good the fit is.

2. The Heat-Check Station (HeatFit)

The Problem: Sponges behave differently when it's hot versus when it's cold. You need to know how much heat is released when the gas sticks to the sponge (like how a hand warmer gets hot when you use it).
The AIM Solution: This station takes your data from different temperatures and calculates the heat of adsorption.

• Analogy: Think of this like checking how much energy a battery holds at different temperatures. AIM figures out exactly how "sticky" the sponge is at various temperatures, which is crucial for designing real-world machines that might get hot or cold during operation.

3. The Mixing Bowl (MixPred)

The Problem: In the real world, you rarely deal with just one gas. You usually have a messy mix (like air, which is mostly nitrogen and oxygen, plus some CO2). How does the sponge handle a cocktail of gases?
The AIM Solution: This is the mixing station. You tell AIM, "I have 50% Gas A and 50% Gas B." AIM uses the rules it learned in the first two stations to predict how the sponge will sort them out. It calculates who gets grabbed first and who gets left behind.

• Analogy: Imagine a bouncer at a club. If the bouncer (the sponge) likes Rock stars (Gas A) more than Pop stars (Gas B), who gets in first? AIM predicts exactly how the bouncer will handle a crowd of mixed celebrities.

4. The Simulation Track (BreakLab)

The Problem: Now you want to see what happens in a real factory. You pump gas through a long tube filled with the sponge. How long until the sponge gets full? Does the temperature spike?
The AIM Solution: This is the race track. You set up a virtual column (a pipe), fill it with your sponge, and hit "Go." AIM simulates the gas flowing through, showing you a live video of the "breakthrough curve"—the moment the gas finally leaks out the other end because the sponge is full.

• Analogy: It's like a video game simulation of a traffic jam. You can see exactly when the cars (gas molecules) start backing up and spilling out the exit. You can even turn on "heat mode" to see how the friction of the traffic heats up the road (the column).

Why is this a big deal?

• No Coding Required: Before AIM, you needed to be a programmer to run these simulations. Now, you just click buttons and drag-and-drop files. It's like switching from building a car engine by hand to driving a Tesla with an autopilot.
• Free and Open: It's free software (open-source), meaning anyone can look under the hood to see how it works. No more "black box" software where you don't know how the results were calculated.
• Proven to Work: The authors tested AIM against real-world experiments and other expensive software. The results were a perfect match, proving that this free tool is just as powerful as the expensive ones.

In summary: AIM takes the complex, scary math of gas separation and turns it into a simple, visual, and free workflow. It allows scientists and engineers to design better air filters, cleaner fuel, and more efficient industrial processes without needing a PhD in computer science. It's the ultimate "plug-and-play" tool for cleaning up our atmosphere.

Technical Summary

1. Problem Statement

Adsorption-based separation processes (e.g., gas purification, air separation) are critical for industrial applications. Evaluating adsorbent performance typically requires a multi-step workflow: fitting single-component isotherm data, estimating isosteric heat of adsorption, predicting mixture adsorption (often using Ideal Adsorbed Solution Theory, IAST), and simulating dynamic breakthrough curves in fixed-bed columns.

Current challenges in this field include:

• Accessibility: Many existing tools (e.g., Aspen Adsorption, gPROMS) are commercial, expensive, and lack transparency in their underlying algorithms.
• Usability: Open-source alternatives (e.g., pyIAST, RUPTURA, pyGAPS) often require scripting expertise or command-line inputs, creating a barrier for experimentalists and practitioners.
• Fragmentation: Existing GUI tools often lack integrated workflows. For instance, some tools fit isotherms but cannot perform breakthrough simulations, while others require pre-fitted parameters without built-in fitting capabilities.
• Reproducibility: The lack of standardized, open-source workflows hampers the sharing of raw data and simulation parameters, making it difficult to reproduce results across different research groups.

2. Methodology

The authors developed AIM, a MATLAB-based Graphical User Interface (GUI) application designed to provide an integrated, end-to-end workflow for adsorption modeling. The software is open-source (GPL-2.0) and runs on Windows, Mac, and Linux.

The workflow is divided into four interconnected modules:

A. IsoFit (Single-Temperature Isotherm Fitting)

• Function: Fits experimental or simulation (GCMC) isotherm data to mathematical models.
• Models: Supports 13 isotherm models, including Langmuir, Dual-site Langmuir, Langmuir-Freundlich, BET, Sips, Toth, Structural-Transition-Adsorption (STA), Dubinin-Astakhov, Klotz, and Do-Do.
• Features: Uses non-linear least squares regression (lsqnonlin) with a "Multistart" feature to avoid local minima. It supports various file formats (CSV, TXT, XLSX, AIF) and allows user-defined initial guesses and bounds.

B. HeatFit (Multi-Temperature Fitting & Enthalpy Estimation)

• Function: Fits isotherm data across multiple temperatures to estimate the isosteric enthalpy of adsorption ($\Delta H_{ads}$).
• Methods:
  1. Clausius-Clapeyron: Assumes constant $\Delta H_{ads}$ over the loading range. It fits a reference isotherm and then determines $\Delta H_{ads}$ by correlating pressure shifts at constant loading across temperatures.
  2. Virial Equation: Fits the natural log of pressure as a function of loading and temperature using Virial coefficients. This allows for the calculation of $\Delta H_{ads}$ as a function of loading.
• Output: Generates parameters for non-isothermal simulations.

C. MixPred (Mixture Adsorption Prediction)

• Function: Predicts mixture adsorption loadings based on single-component isotherm parameters.
• Models:
  1. IAST (Ideal Adsorbed Solution Theory): Solves non-linear equations for reduced grand potential equality using a modified FastIAS algorithm (Newton-Raphson method) for robustness and speed.
  2. Extended Dual-Site Langmuir (EDSL): A thermodynamically consistent extension of the Langmuir model for mixtures (requires equal saturation capacities for components).

D. BreakLab (Breakthrough Simulation)

• Function: Simulates dynamic, multicomponent breakthrough curves in fixed-bed columns.
• Governing Equations: Solves coupled partial differential equations (PDEs) for:
  • Mass Balance: Includes axial dispersion, convection, and adsorption terms.
  • Energy Balance: Accounts for heat of adsorption, conduction, convection, and wall heat transfer (non-isothermal capability).
  • Momentum Balance: Uses the Ergun equation for pressure drop.
  • Mass Transfer: Uses the Linear Driving Force (LDF) model.
• Numerical Solution: The PDEs are non-dimensionalized and discretized using the Finite Volume Method (FVM) with a Weighted Essentially Non-Oscillatory (WENO) scheme. The resulting system of ODEs is solved using MATLAB's ode15s (stiff solver).
• Capacity: Supports up to 5 components (1 non-adsorbing carrier gas + 4 adsorbing species).

3. Key Contributions

• Integrated GUI Workflow: AIM is the first tool to seamlessly connect isotherm fitting, enthalpy estimation, mixture prediction, and dynamic breakthrough simulation in a single, user-friendly interface without requiring coding.
• Algorithmic Robustness:
  • Implementation of the FastIAS algorithm with specific convergence criteria (standard deviation of reduced grand potential) to handle low-pressure breakthrough scenarios where standard IAST solvers often fail.
  • Use of Multistart optimization for isotherm fitting to ensure global minima are found.
• Advanced Simulation Capabilities: Supports non-isothermal and non-adiabatic simulations, including wall heat transfer effects, which are crucial for accurate temperature profile prediction in real-world adsorption columns.
• Open Science: The software, source code, and case study data are publicly available on GitHub, promoting reproducibility and transparency.

4. Results and Validation

The authors validated AIM through several case studies:

• Isotherm Fitting (IsoFit):

  • Fitted CO$_2$ adsorption in CALF-20 using GCMC data.
  • Results (Dual-site Langmuir model) showed excellent agreement ($R^2 = 0.9990$) with other tools like RUPTURA and pyIAST.
  • Uncertainty Quantification: Used Bayesian inference to demonstrate that the fitted parameters have low uncertainty relative to their mean values.

• Breakthrough Simulation (BreakLab - Isothermal):

  • Simulated Xe/Kr separation in SBMOF-1 and CO$_2$/CH$_4$ in CALF-20.
  • Results matched experimental trends (e.g., "roll-up" phenomenon for weakly adsorbing species) and showed excellent agreement with the open-source tool RUPTURA.
  • Demonstrated that IAST and EDSL models yield nearly identical breakthrough curves for these systems.

• Enthalpy Estimation (HeatFit):

  • Fitted CO$_2$ in CALF-20 using the Virial equation across 273–323 K.
  • Demonstrated the trade-off between the number of Virial parameters and fitting reliability (overfitting vs. underfitting) and validated the predicted isosteric heat of adsorption against GCMC data.

• Non-Isothermal Validation (BreakLab):

  • Validated against experimental ternary mixture (CO$_2$/N$_2$/H$_2$) breakthrough data from Marx et al.
  • Achieved excellent agreement for outlet composition profiles.
  • Temperature profiles showed good trend agreement, with a maximum deviation of ~10°C, attributed to assumptions of constant transport properties and radial temperature gradients.

5. Significance

AIM addresses a critical gap in adsorption research by democratizing access to high-fidelity simulation tools. By removing the barrier of programming expertise, it allows experimentalists to directly utilize their data for complex process modeling. The software's ability to handle non-isothermal conditions and its rigorous numerical implementation make it a valuable tool for designing and optimizing industrial adsorption processes (e.g., Carbon Capture, Hydrogen Purification). Furthermore, its open-source nature fosters collaboration and reproducibility, aligning with modern scientific standards. Future work aims to incorporate dynamic mass transfer models and expand physical property libraries.