# An Electrical Equivalent Model of an Electromembrane Stack with Fouling Under Pulsed Operation

## TL;DR

This paper presents a new hybrid model for electromembrane stacks that combines electrical and empirical fouling data to improve desalination predictions under pulsed operations.

## Contribution

The novel hybrid model integrates electrical circuit parameters with an empirical fouling model for electromembrane stacks under pulsed operation.

## Key findings

- The model achieves a prediction error of less than 10% in simulating membrane fouling during pulsed reversal operations.
- The hybrid approach simplifies traditional modeling by combining electronic and electrochemical data into a single framework.
- Calibration using correction factors improves the accuracy of electrical current signal predictions.

## Abstract

This study introduces a novel hybrid model for an electromembrane stack, unifying an equivalent electrical circuit model incorporating specific resistance (RM,Rs) and capacitance (Cgs,Cdl) parameters with an empirical fouling model in a single framework. The model simplifies the traditional approach by serially connecting N (N=10) ion exchange membranes (anionic PC-SA and cationic PC-SK) and is validated using NaCl and Na2SO4 solutions in comparison with laboratory tests using various voltage signals, including direct current and electrically pulsed reversal operations at frequencies of 2000 and 4000 Hz. The model specifically accounts for the chemical stratification of the cell unit into bulk solution, diffusion, and Stern layers. We also included a calibration method using correction factors (αi) to fine-tune the electrical current signals induced by voltage stimulation. The empirical component of the model uses experimental data to simulate membrane fouling, ensuring consistency with laboratory-scale desalination processes performed under pulsed reversal operations and achieving a prediction error of less than 10%. In addition, a comparative analysis was used to assess the increase in electrical resistance due to fouling. By integrating electronic and empirical electrochemical data, this hybrid model opens the way to the construction of simple, practical, and reliable models that complement theoretical approaches, signifying an advance for a variety of electromembrane-based technologies.