Add documentation for OARO flowsheet

docs/technical_reference/flowsheets/index.rst

@@ -6,6 +6,7 @@ Flowsheets
 
    BSM2
    extended_BSM2
+   oaro
    ASM1
    ASM2d
    ADM1

docs/technical_reference/flowsheets/oaro.rst

@@ -0,0 +1,121 @@
+Osmotically Assisted Reverse Osmosis
+====================================
+
+Introduction
+------------
+
+Osmotically assisted reverse osmosis (OARO) is a non-evaporative membrane-based desalination technology that can treat
+high-salinity brines. Compared to conventional reverse osmosis (RO), a saline sweep is added to reduce the osmotic pressure
+difference across the membrane as well as enhance water transport. This OARO flowsheet includes numbers of
+`OARO <https://watertap.readthedocs.io/en/latest/technical_reference/unit_models/osmotically_assisted_reverse_osmosis_0D.html>`_ units,
+pumps, energy recovery devices (ERDs) and a
+`RO <https://watertap.readthedocs.io/en/latest/technical_reference/unit_models/reverse_osmosis_0D.html>`_ unit
+depending on the number of stages. It can be used to implement techno-economic analyses and optimize costing metrics
+with specified number of stages and system water recovery.
+
+Implementation
+--------------
+
+Figure 1 shows the process flow diagram for an n-stage OARO system.
+After pressurized by the primary pump, the incoming feed water enters the feed-side of the first OARO module,
+then the water permeates across the membrane and the resulting concentrated brine flows out of the system from the feed-side,
+In addition, the permeate water will dilute a saline sweep solution in the permeate-side
+and the diluted sweep solution will flow into the feed-side of the next stage of OARO module.
+Similarly, the resulting concentrate flows out of the feed-side, gets energy recovered by the ERD and
+pressurized by the recycle pump, and flows back into permeate-side of the last stage.
+Meanwhile, the diluted sweep solution in the permeate-side flows into the next stage and finally into a conventional RO module.
+Costing relationships for each of the unit models is described in the
+`WaterTAP Costing Package <https://watertap.readthedocs.io/en/latest/technical_reference/costing/watertap_costing.html>`_ .
+The flowsheet relies on the following key assumptions:
+
+   * supports steady-state only
+   * supports optimization and minimizes levelized cost of water (LCOW) with constraints
+   * `NaCl Property Package <https://watertap.readthedocs.io/en/latest/technical_reference/property_models/NaCl.html>`_ is utilized
+   * number of stages and system recovery should be specified for optimization
+
+
+.. figure:: ../../_static/flowsheets/OARO.png
+    :width: 800
+    :align: center
+
+    Figure 1. OARO flow diagram
+
+Documentation for each of the unit models can be found here:
+   * `OARO <https://watertap.readthedocs.io/en/latest/technical_reference/unit_models/osmotically_assisted_reverse_osmosis_0D.html>`_
+   * `RO <https://watertap.readthedocs.io/en/latest/technical_reference/unit_models/reverse_osmosis_0D.html>`_
+
+Documentation for the property model can be found here:
+    * `NaCl Property Package <https://watertap.readthedocs.io/en/latest/technical_reference/property_models/NaCl.html>`_
+
+Documentation for the costing relationships can be found below.
+    * `WaterTAP Costing Package <https://watertap.readthedocs.io/en/latest/technical_reference/costing/watertap_costing.html>`_
+
+This flowsheet aims to solve optimization problem that minimizes levelized cost of water (LCOW) with specified
+number of stages and system mass recovery.
+LCOW can be represented by the following equation where :math:`Q` represents product 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}
+
+Degrees of Freedom
+------------------
+Firstly, the number of stages and water mass recovery of the system need to be specified. In addition, the following variables needs to be specified based on the default settings:
+   * feed water conditions (flow, temperature, pressure, component concentrations)
+   * pump efficiency of primary pumps and recycle pumps
+   * ERD pump efficiency and outlet pressure
+   * OARO solvent and solute permeability coefficients, membrane structural parameter, channel height and spacer porosity of both feed-side and permeate-side
+   * RO solvent and solute permeability coefficients, feed-side channel height and spacer porosity, and permeate pressure
+
+Flowsheet Specifications
+------------------------
+
+.. csv-table::
+   :header: "Description", "Units", "Value"
+
+   "**Primary pumps**"
+   "Pump efficiency", ":math:`\text{dimensionless}`", "0.75"
+   "**Recycle pumps**"
+   "Pump efficiency", ":math:`\text{dimensionless}`", "0.75"
+   "**ERDs**"
+   "Pump efficiency", ":math:`\text{dimensionless}`", "0.75"
+   "Outlet pressure", ":math:`\text{Pa}`", "101325"
+   "**OAROs***"
+   "Solvent permeability coefficient", ":math:`\text{m/Pa/s}`", "1E-12"
+   "Solute permeability coefficient", ":math:`\text{m/s}`", "8E-8"
+   "Membrane structural parameter", ":math:`\mu \text{m}`", "1200"
+   "Feed-channel height", ":math:`\text{m}`", "2E-3"
+   "Feed-side spacer porosity", ":math:`\text{dimensionless}`", "0.75"
+   "Permeate-channel height", ":math:`\text{m}`", "2E-3"
+   "Peremeate-side spacer porosity", ":math:`\text{dimensionless}`", "0.75"
+   "**RO***"
+   "Solvent permeability coefficient", ":math:`\text{m/Pa/s}`", "4.2E-12"
+   "Solute permeability coefficient", ":math:`\text{m/s}`", "3.5E-8"
+   "Feed-channel height", ":math:`\text{m}`", "2E-3"
+   "Feed-side spacer porosity", ":math:`\text{dimensionless}`", "0.75"
+   "Permeate pressure", ":math:`\text{Pa}`", "101325"
+
+\*Settings for `OARO <https://watertap.readthedocs.io/en/latest/technical_reference/unit_models/osmotically_assisted_reverse_osmosis_0D.html>`_
+and `RO <https://watertap.readthedocs.io/en/latest/technical_reference/unit_models/reverse_osmosis_0D.html>`_
+can vary depending on the configurations.
+
+
+Additional Variables
+--------------------
+
+.. csv-table::
+   :header: "Description", "Symbol", "Value", "Units"
+
+   "Maximum product concentration", ":math:`M_{out, max}`", "500", ":math:`\text{mg/L}`"
+
+Additional Constraints
+----------------------
+
+There is an extra inequality constraint to ensure the product quality:
+
+.. csv-table::
+   :header: "Description", "Equation"
+
+   "Product Quality", ":math:`M_{out, NaCl} \le M_{out, max}`"