Osmotically Assisted Reverse Osmosis (1D)

This osmotically assisted reverse osmosis (OARO) unit model

  • is 1-dimensional

  • supports a single liquid phase only

  • supports steady-state only

  • supports flat-sheet and spiral-wound module designs

  • is based on the solution-diffusion model and film theory

  • assumes isothermal conditions

  • assumes the feed-side flows in the forward direction

  • assumes the permeate-side flows in the backwards direction

Degrees of Freedom

Aside from the feed-side and permeate-side inlet state variables (i.e. temperature, pressure, component flowrates), the OARO model has at least 4 degrees of freedom that should be fixed for the unit to be fully specified. Unlike RO, which only accounts for concentration polarization on the feed side, the OARO model includes a structural parameter variable, which is used to calculate the membrane-interface concentration on the permeate side.

Typically, the following variables are fixed for the OARO model, in addition to state variables at the inlet:

  • membrane water permeability, A

  • membrane salt permeability, B

  • membrane area

  • structural parameter

On the other hand, configuring the OARO unit to calculate concentration polarization effects, mass transfer coefficient, and pressure drop would result in 6 additional degrees of freedom. In this case, in addition to the previously fixed variables, we typically fix the following variables to fully specify the unit:

  • feed-side spacer porosity

  • feed-side channel height

  • permeate-side space porosity

  • permeate-side channel height

  • feed-side Reynolds number or water mass recovery

Model Structure

This OARO model consists of a separate MembraneChannel1DBlock for the feed-side and the permeate-side of the OARO unit.

  • The feed-side includes StateBlocks indexed by time and space (feed_side.properties[t, x]) which are used for mass, energy, and momentum balances, and additional StateBlocks for the conditions at the membrane interface (feed_side.properties_interface[t, x]).

  • The permeate-side includes StateBlocks indexed by time and space (permeate-side.properties[t, x]) which are used for mass, energy, and momentum balances, and additional StateBlocks for the conditions at the membrane interface (permeate-side.properties_interface[t, x]).

Sets

Description

Symbol

Indices

Time

\(t\)

[0]

Inlet/outlet

\(x\)

[‘in’, ‘out’]

Phases

\(p\)

[‘Liq’]

Components

\(j\)

[‘H2O’, ‘NaCl’]*

*Solute depends on the imported property model; example shown here is for the NaCl property model.

Variables

Refer to the Variables section in the 0D OARO model.

Equations

Refer to the Equations section in the 0D OARO model.

Class Documentation