Membrane module

Inputs

• Temperature: The isothermal operating temperature.
• Retentate Pressure Drop: Pressure loss from the feed inlet to the retentate-side membrane chamber. Must be >= 0.
• Permeate Pressure Drop: Pressure loss from the sweep inlet to the permeate-side membrane chamber. Must be >= 0.
• Membrane Area: Total area for permeation. Must be greater than 0.
• Component Permeances: One non-negative permeance for each component in the fluid.

Connections

The membrane has two inlet streams and two outlet streams:

• Inlets:
  • Feed stream (bottom right)
  • Sweep stream (top left)
• Outlets:
  • Retentate stream (top right)
  • Permeate stream (bottom left)

Although a sweep stream is required, a zero-flow sweep stream can be used to represent no sweep.

Outputs

After solving, the membrane uses the standard process-editor result and safety-check panes:

• solved properties appear in the Results tab
• warnings appear in Safety Checks

The membrane reports the following solved properties:

• Stage Cut: Total permeation rate divided by total feed molar flow, i.e. the total fraction of the feed that permeated.
• Permeation: Component permeation rates in mol/s.
• Permeate Recovery: For each component, permeation divided by the component feed molar flow.
• Log-Mean Driving Force: Effective component driving force across the membrane. See section Model Equations below for details.

These values are reported per component where applicable.

Details

This is a single-stage, lumped (0D), isothermal model for a countercurrent membrane. The membrane driving force is approximated using the log-mean fugacity difference between the two membrane ends.

Only transport from the feed/retentate side to the permeate/sweep side is allowed. Reverse transport is not supported.

The solved unknowns are the component permeation rates.

• If the forward driving force is nonpositive at one or both membrane ends, the effective driving force is set to zero for that component and a warning may be shown.
• Multiphase streams are allowed, but may produce warnings.
• As a lumped model, it is most reliable at modest stage cuts.

Model Equations

For each component $i$, the membrane solves for the permeation rate $J_i$ such that

$$J_i = A \Pi_i \langle \Delta f_i \rangle$$

where:

• $J_i$ is the molar permeation rate of component $i$
• $A$ is the membrane area
• $\Pi_i$ is the component permeance
• $\langle \Delta f_i \rangle$ is the log-mean fugacity difference for component $i$

The end-point fugacity differences are

$$\Delta f_{i,\mathrm{in}} = f_{i,\mathrm{feed,in}} - f_{i,\mathrm{perm,out}}$$ $$\Delta f_{i,\mathrm{out}} = f_{i,\mathrm{ret,out}} - f_{i,\mathrm{perm,in}}$$

The effective driving force is taken as the logarithmic mean of these two end-point fugacity differences:

$$\langle \Delta f_i \rangle = \frac{\Delta f_{i,\mathrm{in}} - \Delta f_{i,\mathrm{out}}} {\ln\left(\Delta f_{i,\mathrm{in}} / \Delta f_{i,\mathrm{out}}\right)}$$

The component balances are

$$\dot n_{i,\mathrm{ret}} = \dot n_{i,\mathrm{feed}} - J_i$$ $$\dot n_{i,\mathrm{perm}} = \dot n_{i,\mathrm{sweep}} + J_i$$

If the forward driving force is nonpositive at one or both membrane ends, the effective driving force for that component is set to zero.