.. _OARO_flowsheet:

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
:ref:`OARO <OARO_0D>` units,
pumps, energy recovery devices (ERDs) and a
:ref:`RO <RO_0D>` 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
:ref:`WaterTAP Costing Package <watertap_costing>`.
The flowsheet relies on the following key assumptions:

   * supports steady-state only
   * supports optimization and minimizes levelized cost of water (LCOW) with constraints
   * :ref:`NaCl Property Package <nacl>` 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:
   * :ref:`OARO <OARO_0D>`
   * :ref:`RO <RO_0D>`

Documentation for the property model can be found here:
    * :ref:`NaCl Property Package <nacl>`

Documentation for the costing relationships can be found below.
    * :ref:`WaterTAP Costing Package <watertap_costing>`

This flowsheet aims to solve optimization problem that minimizes 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 :ref:`OARO <OARO_0D>`
and :ref:`RO <RO_0D>`
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}`"