Flowsheet documentation for IX (#1418)

docs/technical_reference/flowsheets/index.rst

@@ -13,4 +13,5 @@ Flowsheets
    electrodialysis_1stack_conc_recirc
    electrodialysis_1stack
    crystallization
+   ion_exchange
    gac

docs/technical_reference/flowsheets/ion_exchange.rst

@@ -0,0 +1,148 @@
+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 :doc:`IX unit model documentation </technical_reference/unit_models/ion_exchange_0D>`:
+
+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).
+
+.. figure:: ../../_static/flowsheets/ion_exchange.png
+    :width: 1000
+    :align: center
+
+    Figure 1. IX demonstration flowsheet.
+
+The following modeling components are used within the flowsheet:
+
+    Documentation for property models:
+        * :doc:`/technical_reference/property_models/mc_aq_sol`
+    Documentation for unit models:
+        * :doc:`/technical_reference/unit_models/ion_exchange_0D`
+    Documentation for unit models from IDAES:
+        * :doc:`idaes:reference_guides/model_libraries/generic/unit_models/feed`
+        * :doc:`idaes:reference_guides/model_libraries/generic/unit_models/product`
+    Documentation for costing models:
+        * :doc:`/technical_reference/costing/watertap_costing`
+        * :doc:`/technical_reference/costing/ion_exchange`
+
+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).
+
+    .. math::
+        
+        LCOW_{Q} = \frac{f_{crf}   C_{cap,tot} + C_{op,tot}}{f_{util} Q}
+    
+    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. Additional information on the costing package calculations and variables can be found in the :doc:`WaterTAP costing framework documentation </technical_reference/costing/costing_base>`.
+
+    * 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 :doc:`IX unit model documentation </technical_reference/unit_models/ion_exchange_0D>`.
+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
+------------------------
+
+.. csv-table::
+   :header: "Description", "Value", "Units"
+
+   "Feed molar flowrate of water", "2777.5", ":math:`\text{mol}/\text{s}`"
+   "Feed molar flowrate of target ion", "0.125", ":math:`\text{mol}/\text{s}`"
+   "Feed temperature", "298.15", ":math:`\text{K}`"
+   "Feed pressure", "101325", ":math:`\text{Pa}`"
+   "Langmuir equilibrium coefficient", "0.7", ":math:`\text{dimensionless}`"
+   "Resin capacity", "3.0", ":math:`\text{mol/kg}`"
+   "Resin bulk density", "0.7", ":math:`\text{kg/L}`"
+   "Constant pattern dimensionless time", "1", ":math:`\text{dimensionless}`"
+   "Number columns", "4", ":math:`\text{dimensionless}`"
+   "Bed void fraction", "0.5", ":math:`\text{dimensionless}`"
+   "Bed depth", "1.7", ":math:`\text{m}`"
+   "Service flow rate (in bed volumes)", "15", ":math:`\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
+------------------
+
+* :mod:`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