Ion Exchange

Introduction

The simple ion exchange (IX) flowsheet can be simulated to predict the performance of an IX system to remove targeted ions and components. This flowsheet can be useful to expedite the setup, usage, and costing of an IX system for conventional water treatment applications using the Langmuir isotherm and the constant pattern assumption.

Implementation

Consisting of only a single unit operation, the assumptions for the flowsheet are the same as those outlined in the IX unit model documentation:

  1. Model dimensionality is limited to a 0D control volume

  2. Single liquid phase only

  3. Steady state only

  4. Single solute and single solvent (water) only

  5. Plug flow conditions

  6. Isothermal conditions

  7. Favorable Langmuir isotherm

Figure 1 presents the process flow diagram for the IX model. Blue text represents all of the unit blocks on the flowsheets, and red text represents process streams (or more specifically, an Arc that is connected to a Port on each unit block).

../../_images/ion_exchange.png

Figure 1. IX demonstration flowsheet.

The following modeling components are used within the flowsheet:

Documentation for property models:
Documentation for unit models:
Documentation for unit models from IDAES:
Documentation for costing models:

The ion exchange flowsheet demonstration proceeds through five steps:

  1. Building the model with ix_build:

    This function builds the flowsheet with a list of ions as the input. If the keyword argument target_ion is not used, the first ion in the list of ions provided is used as the target_ion configuration argument for the IonExchange0D model. The ion used in the demonstration is calcium (Ca_2+), but the local function get_ion_config can be used to get diffusivity, molecular weight, and charge data for sodium (Na_+), chloride (Cl_-), magnesium (Mg_2+), and sulfate (SO4_2-). This function will also add the flowsheet level and unit model costing packages, set default scaling for molar flow rates of water and the target ion, create Arcs to connect the feed, product, and regen blocks to the IX unit model, and calculate scaling factors for the entire flowsheet. The model is returned from this function.

  2. Defining the operating conditions with set_operating_conditions:

    This function is used to set the flow rate and concentration for the flowsheet via the flow_in and conc_mass_in keywords, respectively. It will also set the operating conditions for the IX unit process simulation. Specific variables fixed are in the sections below.

  3. Connecting and initializing individual unit models with initialize_system:

    Calling this function will initialize all unit models on the flowsheet (feed, ion_exchange, product, and regen), initialize the costing block, and propagate the arcs.

  4. Solving the model with solver:

    The solver object is returned by calling the WaterTAP function get_solver(). After the model is built, specified, and initialized, the model has zero degrees of freedom and is solved with solver.solve(m). The termination condition of the solve is checked and, assuming the solve is optimal, continues with the optimization demonstration.

  5. Optimizing IX design with optimize_system:

    Though not required, this function provides an example of optimizing the design of the IX system for a targeted effluent concentration of 25 mg/L. The initial model demonstration resulted in an effluent concentration of 0.21 mg/L, so this optimization results in longer breakthrough time and therefore, a less frequent regeneration schedule and lower operating costs. The optimization proceeds in four steps:

    • First, the function will set an Objective on the flowsheet to minimize the levelized cost of water (LCOW).

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

    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. Additional information on the costing package calculations and variables can be found in the WaterTAP costing framework documentation.

    • Then, the model fixes the effluent concentration of the IX model to 25 mg/L, propagates that concentration to the product block, and re-initializes the product block with the new targeted concentration.

    • Next, three variables are unfixed on the ion exchange model to allow for the model to solve for the new conditions (dimensionless_time, number_columns, and the bed_depth).

    • Finally, the model is solved for these new conditions.

    Note that stopping at this point will likely result in a non-integer value for number_columns. This value also corresponds to an optimal value for both bed_depth and dimensionless_time. The user can optionally ensure the number_columns is an integer by rounding the number_columns to an integer value after the initial optimization solve, fixing number_columns to that value, and then re-solving the model to obtain the final values for bed_depth and dimensionless_time. This is the approach taken in the demonstration file.

Degrees of Freedom

The degrees of freedom for the flowsheet can change depending on the configuration options specified during the build. Specifics for other configuration options are available in the IX unit model documentation. In this demonstration, the following variables are initially fixed for simulating the IX flowsheet (i.e., degrees of freedom = 0):

  • Feed conditions (component flows, temperature, pressure)

  • Langmuir equilibrium coefficient for target ion

  • Resin capacity, diameter, porosity, and density

  • Number of columns for the system

  • Service flow rate (loading rate)

  • The dimensionless time for the constant-pattern solution

Flowsheet Specifications

Description

Value

Units

Feed molar flowrate of water

2777.5

\(\text{mol}/\text{s}\)

Feed molar flowrate of target ion

0.125

\(\text{mol}/\text{s}\)

Feed temperature

298.15

\(\text{K}\)

Feed pressure

101325

\(\text{Pa}\)

Langmuir equilibrium coefficient

0.7

\(\text{dimensionless}\)

Resin capacity

3.0

\(\text{mol/kg}\)

Resin bulk density

0.7

\(\text{kg/L}\)

Constant pattern dimensionless time

1

\(\text{dimensionless}\)

Number columns

4

\(\text{dimensionless}\)

Bed void fraction

0.5

\(\text{dimensionless}\)

Bed depth

1.7

\(\text{m}\)

Service flow rate (in bed volumes)

15

\(\text{1/hr}\)

Future Refinements

The following modifications to the IX flowsheet are planned for development:

  • Add examples of the Freundlich (Clark) ion exchange model.

  • Improve auto-scaling of model for ease of use

Code Documentation

  • watertap.examples.flowsheets.ion_exchange

References

LeVan, M. D., Carta, G., & Yon, C. M. (2019).
Section 16: Adsorption and Ion Exchange.
Perry’s Chemical Engineers’ Handbook, 9th Edition.
Inamuddin, & Luqman, M. (2012).
Ion Exchange Technology I: Theory and Materials.
United States Environmental Protection Agency. (2021). Work Breakdown Structure-Based Cost Models
https://www.epa.gov/sdwa/drinking-water-treatment-technology-unit-cost-models