Table 5 Corresponding boundary conditions in major domains of GLMC considering non-wetted mode of membrane.
Position | Shell side | Membrane | Tube | |
|---|---|---|---|---|
Mass | Momentum | Mass | Mass | |
z = 0 | Convective flux | Outlet: Pressure, no viscous stress, p = 0 | Insulated | \({\text{C}}_{{\text{CO}}_{2},\text{t}}=0\) \({\text{C}}_{\text{AMP},\text{tube}}= {\text{C}}_{\text{initial}}\) |
z = L | \(\begin{array}{c}{\text{C}}_{\text{solvent},\text{s}}={\text{C}}_{\text{initial}}\\ {\text{C}}_{{\text{CO}}_{2},\text{s}}=0\end{array}\) | Inlet velocity V = V0,shell | Insulated | Convective flux |
r = 0 | – | – | – | Axial symmetry \(\frac{\partial {\text{C}}_{{\text{CO}}_{2},\text{t}}}{\partial \text{r}}=0\) |
r = r1 | – | – | \({\text{C}}_{{\text{CO}}_{2},\text{m}}={\text{C}}_{{\text{CO}}_{2},\text{t}}/{\text{m}}_{{\text{CO}}_{2}}\) | \({\text{C}}_{{\text{CO}}_{2},\text{t}}={{\text{m}}_{{\text{CO}}_{2}}\text{C}}_{{\text{CO}}_{2},\text{m}}\) |
r = r2 | \({\text{C}}_{{\text{CO}}_{2},\text{s}}={{\text{m}}_{{\text{CO}}_{2}}\text{C}}_{{\text{CO}}_{2},\text{m}}\) | No slip, Wall | \({\text{C}}_{{\text{CO}}_{2},\text{m}}={\text{C}}_{{\text{CO}}_{2},\text{s}}\) | – |
r = r3 | \(\frac{\partial {\text{C}}_{{\text{CO}}_{2},\text{shell}}}{\partial \text{r}}=0\) | No slip, Table Wall | – | – |
