One-Stack Electrodialysis with a Concentrate Fluid Recirculation


Electrodialysis (ED) is a promising technology for desalinating brackish waters and has been deployed at industrial scales [1]. It utilizes electrical potential to drive ion diffusion through anion and cation exchange membranes, resulting in the dilution of the feed stream while producing a concentrated brine. A single ED stack is an assembly of multiple flow-by cells separated by alternating cation and anion exchange membranes positioned between a pair of electrodes. When a voltage is applied, ions in the cell pair are driven from one channel (forming the diluate channel) to the other (forming the concentrate channel), thereby desalinating water. A one-stack ED desalination system represents a basic ED operation from which more complicated or larger-scale systems can be derived. Analyzing a one-stack ED system therefore provides valuable information on the technology’s performance and cost-effectiveness for a given treatment task.

Equal flow conditions through the diluate and concentrate channels would result in a product water recovery of 50%. Larger water recoveries are commonly achieved by operating the system in a feed-and-bleed mode, where a portion of the concentrate outlet is recirculated back to its inlet, thus increasing the portion of product water from the diluate outlet. This flowsheet simulates a one-stack ED system operated in feed-and-bleed mode. A simpler ED flowsheet without fluid recirculation is presented as


The modeled one-stack ED system is illustrated by Figure 1. The feed solution is split into two fluids through a separator unit, entering the diluate and concentrate channels of the ED stack. Two pump units are placed respectively on the two channels entering pipelines to counterbalance the pressure drops across ED stack channels. On the outlet side of the ED stack, all diluate fluids are collected into the total product water, and the concentrate fluids into the total brine stream. A second separator unit takes a portion of the brine back into the concentrate pump inlet, with the rest being sent to brine disposal. Water recovery in this model is volume-based, i.e., the ratio of product volume to total volume of feed solution. The flowsheet relies on the following key assumptions:

  • supports steady-state only

  • a property package (i.e., MCAS) is provided for all unit models


Figure 1. Flowsheet diagram: one-stack ED operated in feed-and-bleed mode

The electrodialysis 1D block is set up with the following configuration arguments:

m.fs.EDstack = Electrodialysis1D(,

These configurations enable the electrodialysis unit to use a flowsheet-unified property package, set a constant stack voltage, and adopt a favorable number of finite elements for 1-dimensional simulation and solving. The overall ED configuration represents the most comprehensive modeling that takes into account the pressure change, diffusion layer phenomenon, and non-ohmic potentials in the system.

In the given optimization case, the objective function is to minimize the levelized cost of water, which can be represented by the following equation where \(Q\) represents volumetric flow, \(f_{crf}\) represents capital recovery factor \(C_{cap,tot}\) represents total capital cost, \(C_{op,tot}\) represents total operating cost, and \(f_{util}\) represents the utilization factor:

\[LCOW_{Q} = \frac{f_{crf} C_{cap,tot} + C_{op,tot}}{f_{util} Q}\]

The product water salinity is set to 0.1 \(g L^{-1}\).

Documentation for unit models from WaterTAP:
Documentation for unit models from IDAES:
Documentation for the property model:

Degrees of Freedom

The number of degrees of freedom (DOF) is associated with the number of fixed variables (parameters) determined by the purpose of the modeling case. There are two implemented modeling cases in the flowsheet: (1) the prediction of desalination outcome (salinity of the product water and saline disposal) and (2) the optimization of key decision variables in system design. In the first case, DOF is set to zero by fixing all initial conditions of the feed solution fluid and definite ED stack parameters. All fixed values are presented in the section to follow. In the second case, the values of those chosen to be the decision variables in the optimization are unfixed. The DOF number is therefore the number of decision variables. In this example, the decision variables are:

  • stack voltage applied

  • ED cell pair number

  • ED cell length

Flowsheet Specifications





Salinity (NaCl)


\(g L^{-1}\)

Volume flow rate

\(5.2 \times 10^{-4}\)

\(m^3 s^{-1}\)








Na^+ diffusivity

\(1.33 \times 10^{-9}\)

\(m^2 s^{-1}\)


Cl^- diffusivity

\(2.03 \times 10^{-9}\)

\(m^2 s^{-1}\)


NaCl mass diffusivity

\(1.60 \times 10^{-9}\)

\(m^2 s^{-1}\)


Cell pair number



Cell length




Cell width




Channel height

\(7.1 \times 10^{-4}\)


Water recovery



Stack voltage



Thickness, aem and cem

\(1.3 \times 10^{-5}\)



Areal resistance, aem

\(1.77 \times 10^{-4}\)

\(\Omega m^2\)


Areal resistance, cem

\(1.89 \times 10^{-4}\)

\(\Omega m^2\)


Water permeability, aem

\(1.75 \times 10^{-14}\)

\(m s^{-1} Pa^{-1}\)


Water permeability, cem

\(2.16 \times 10^{-14}\)

\(m s^{-1} Pa^{-1}\)


Water transport number, aem




Water transport number, cem




NaCl mass diffusivity, aem and cem

\(3.28 \times 10^{-11}\)

\(m^2 s^{-1}\)


Spacer porosity




Spacer specific surface area




Pump efficiency