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electrodialysis_1stack.rst
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One-Stack Electrodialysis
=========================
Introduction
------------
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%. This flowsheet simulates the simplest setup of a one-stack ED system without any fluid recirculation, i.e., the ED stack being operated in an in-and-out single direction flow mode. This flowsheet also does not take account of the frictional pressure drop in the channel so no pump is included. A more complicated ED flowsheet is presented as
* `One-stack electrodialysis with a concentrate fluid recirculation <https://watertap--1385.org.readthedocs.build/en/1385/technical_reference/flowsheets/electrodialysis_1stack_conc_recirc.html>`_.
Implementation
--------------
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. 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. Water recovery in this model is volume-based, i.e., the ratio of product volume to total volume of feed solution. The model simulates the steady state of the ED system. 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:: ../../_static/flowsheets/edfs.png
:width: 500
:align: center
Figure 1. Flowsheet diagram: one-stack ED system
The electrodialysis 1D block is set up with the following configuration arguments:
.. code-block::
m.fs.EDstack = Electrodialysis1D(
property_package=m.fs.properties,
operation_mode="Constant_Voltage",
finite_elements=20,
)
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.
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 :math:`Q` represents volumetric flow, :math:`f_{crf}` represents capital recovery factor
:math:`C_{cap,tot}` represents total capital cost, :math:`C_{op,tot}` represents total operating cost, and
:math:`f_{util}` represents the utilization factor:
.. math::
LCOW_{Q} = \frac{f_{crf} C_{cap,tot} + C_{op,tot}}{f_{util} Q}
The product water salinity is set to 1 :math:`g L^{-1}` (from a feed salinity of 9.9 :math:`g L^{-1}`).
Documentation for unit models from WaterTAP:
* `Electrodialysis_1D <https://watertap.readthedocs.io/en/latest/technical_reference/unit_models/electrodialysis_1D.html>`_
Documentation for unit models from IDAES:
* `Feed block <https://idaes-pse.readthedocs.io/en/latest/reference_guides/model_libraries/generic/unit_models/feed.html>`_
* `Separator <https://idaes-pse.readthedocs.io/en/latest/reference_guides/model_libraries/generic/unit_models/separator.html>`_
* `Product block <https://idaes-pse.readthedocs.io/en/latest/reference_guides/model_libraries/generic/unit_models/product.html>`_
Documentation for the property model:
* `Multi-Component Aqueous Solution (MCAS) Property Package <https://watertap.readthedocs.io/en/latest/technical_reference/property_models/mc_aq_sol.html>`_
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. We implemented two modeling cases in this 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
Flowsheet Specifications
------------------------
.. csv-table::
:header: Name, Value, Unit, Reference
:widths: 30, 20, 20, 10
"Salinity (NaCl)", ":math:`9.9`", ":math:`g L^{-1}`", "--"
"Volume flow rate", ":math:`8.7 \times 10^{-5}`", ":math:`m^3 s^{-1}`", [2]_
"Temperature", ":math:`298.15`", ":math:`K`", "--"
"Pressure", ":math:`101325`", ":math:`Pa`", "--"
"Na^+ diffusivity", ":math:`1.33 \times 10^{-9}`", ":math:`m^2 s^{-1}`",[3]_
"Cl^- diffusivity", ":math:`2.03 \times 10^{-9}`", ":math:`m^2 s^{-1}`",[3]_
"NaCl mass diffusivity", ":math:`1.60 \times 10^{-9}`", ":math:`m^2 s^{-1}`", [4]_
"Cell pair number", ":math:`100`", ":math:`1`", "--"
"Cell length", ":math:`0.79`", ":math:`m`", "--"
"Cell width", ":math:`0.1`", ":math:`m`",[5]_
"Channel height", ":math:`2.7 \times 10^{-4}`", ":math:`m`", "--"
"Stack voltage", ":math:`5`", ":math:`V`", "--"
"Thickness, aem and cem", ":math:`1.3 \times 10^{-5}`", ":math:`m`",[5]_
"Areal resistance, aem", ":math:`1.77 \times 10^{-4}`", ":math:`\Omega m^2`", [5]_
"Areal resistance, cem", ":math:`1.89 \times 10^{-4}`", ":math:`\Omega m^2`",[5]_
"Water permeability, aem", ":math:`1.75 \times 10^{-14}`", ":math:`m s^{-1} Pa^{-1}`",[5]_
"Water permeability, cem", ":math:`2.16 \times 10^{-14}`", ":math:`m s^{-1} Pa^{-1}`", [5]_
"Water transport number, aem", ":math:`4.3`", ":math:`1`",[6]_
"Water transport number, cem", ":math:`5.8`", ":math:`1`", [7]_
"NaCl mass diffusivity, aem", ":math:`1.25 \times 10^{-10}`", ":math:`m^2 s^{-1}`", [8]_
"NaCl mass diffusivity, cem", ":math:`1.8 \times 10^{-10}`", ":math:`m^2 s^{-1}`", [8]_
"Spacer Porosity", ":math:`1`", ":math:`1`", [2]_
"Pump efficiency", ":math:`0.8`", ":math:`1`", "--"
References
----------
.. [1] Strathmann, H. (2010). Electrodialysis, a mature technology with a multitude of new applications. Desalination, 264(3), 268-288.
.. [2] Wright, N. C., Shah, S. R., & Amrose, S. E. (2018). A robust model of brackish water electrodialysis desalination with experimental comparison at different size scales. Desalination, 443, 27-43.
.. [3] Vanýsek, P. (1993). Ionic conductivity and diffusion at infinite dilution. CRC handbook of chemistry and physics, 94.
.. [4] Vitagliano, V., & Lyons, P. A. (1956). Diffusion coefficients for aqueous solutions of sodium chloride and barium chloride. Journal of the American Chemical Society, 78(8), 1549-1552.
.. [5] Campione, A., Cipollina, A., Bogle, I. D. L., Gurreri, L., Tamburini, A., Tedesco, M., & Micale, G. (2019). A hierarchical model for novel schemes of electrodialysis desalination. Desalination, 465, 79-93.
.. [6] Breslau, B. R., & Miller, I. F. (1971). A hydrodynamic model for electroosmosis. Industrial & Engineering Chemistry Fundamentals, 10(4), 554-565.
.. [7] Larchet, C., Dammak, L., Auclair, B., Parchikov, S., & Nikonenko, V. (2004). A simplified procedure for ion-exchange membrane characterisation. New Journal of Chemistry, 28(10), 1260-1267.
.. [8] Kamcev, J., Paul, D. R., Manning, G. S., & Freeman, B. D. (2018). Ion diffusion coefficients in ion exchange membranes: significance of counterion condensation. Macromolecules, 51(15), 5519-5529.