Dynamic Diafiltration Model in Pyomo

Characterizing Transport Properties of Nanofiltration Membranes

This repository contains a Pyomo-based dynamic diafiltration model used to analyze the transport properties of nanofiltration (NF) membranes. It supports robust parameter estimation and data analytics workflows based on dynamic experiments.

---

Environment Setup

This project is developed with the following dependencies:

• Python: Version 3.11.6
• Pyomo: Version 6.8.0
• MATLAB: Implemented with R2020a and R2022a (for additional MATLAB analysis in DATA1-matlab)

Suggested Conda Configuration

To set up the Python environment, recommend the following Conda configuration:

conda create -n dynamic-diafiltration -c anaconda -c conda-forge -c IDAES-PSE python=3.11 numpy matplotlib pandas scipy idaes-pse scikit-learn

Activate the environment:

conda activate dynamic-diafiltration

In case CasADi is not installed (needed for model initialization)

pip install casadi

---

Repository Organization

Root Directory

1. data_library/
   Contains formatted experimental data (nested .mat files) used for the model and analysis.

2. DATA1-matlab/ Original MATLAB scripts and supporting functions for analyzing diafiltration and filtration experiments, performing parameter estimation, and generating heatmaps for Model-Based Design of Experiments (MBDoE) in DATA1 and DATA-MBDoE papers. For usage details, please refer to the README file in this folder.

3. utility.py
   Core library of Python functions for:

   • Loading and storing nested MATLAB .mat data.
   • Performing parameter estimation and providing information for model ranking.
   • Performing Fisher Information Matrix (FIM) analysis.
   • Visualization of experimental and simulation results.

4. DATA1_model_demo.ipynb
   A Jupyter Notebook demonstrating:

   • Dynamic diafiltration Pyomo modeling.
   • Reproduce DATA1 analysis for NF90 membranes.
   • [WIP] Generating contours for sensitivity analysis/DoE in the DATA1 paper.

5. DATA2_model_demo.ipynb
   A Jupyter Notebook demonstrating:

   • Dynamic diafiltration Pyomo modeling.
   • Analysis of NF270 membranes for DATA2 paper.

6. DATA2_visualization.ipynb
   Notebook for generating publication-ready plots and visualizations for the DATA2 paper.

7. run_cross_verification.py
   Python script for cross-verifying empirical solute permeability coefficient (B) models with additional datasets, and store visualizations.

8. run_DATA2_model_variations.py
   Script for exploring model variations (e.g., including startup dynamics and/or time correction) and performing Fisher Information Matrix (FIM) calculations to evaluate information gain for the DATA2 paper.

9. run_pre_B_dependence.py
   Preliminarily investigates the dependence of solute permeability coefficient (B) on interface concentrations. Outputs visualizations and insights for modeling and optimization.

---

Key Features

• Dynamic Diafiltration Modeling: Captures startup dynamics, concentration-dependent transport properties, and solute flux mechanisms.
• Data Analytics: Implements advanced techniques like weighted least squares (WLS) and Akaike Information Criterion (AIC) for parameter estimation and model discrimination.
• Support for Multiple Membranes: Includes NF90 (near neutral) and NF270 (negative-charged) membrane analysis for comparing transport properties.
• Visualization Tools: Built-in scripts for generating model diagnostics and experiment comparisons.
• FIM Analysis: Calculates the Fisher Information Matrix for experimental design optimization.

---

Usage

Running the Model

1. Prepare Data: Place experimental .mat files in the data/ directory.
2. Configure Parameters: Modify initial conditions and parameters in utility.py or the notebook as needed.
3. Run the Notebook: Execute DATA2_model_demo.ipynb to:
   • Load data.
   • Run the Pyomo model.
   • Visualize results.

Visualization

Plots include:

• Time evolution of mass and concentration in vials.
• Comparison of experimental and simulated results.

FIM Analysis

Use calc_FIM to optimize experimental design:

• Configure step size and finite difference scheme.
• Analyze parameter sensitivity printout.

---

References

This repository accompanies the studies:

DATA2

"Characterizing Transport Properties of Surface-Charged Nanofiltration Membranes via Model-based Data Analytics", authored by Xinhong Liu et al., William A. Phillip, and Alexander W. Dowling.

DATA-MBDoE

"Membrane Characterization with Model-Based Design of Experiments", authored by Xinhong Liu et al., William A. Phillip, and Alexander W. Dowling.

DATA1

"DATA: Diafiltration Apparatus for high-Throughput Analysis", authored by Jonathan A Ouimet, Xinhong Liu et al., William A. Phillip, and Alexander W. Dowling.

For details on the methodology, refer to the manuscript or contact the corresponding authors.