Table 2.

Dynamic correlations and formulas applied for the CFD model for the bubble and emulsion phase.

Parameter	Formula	Reference
Bubble velocity	$v_{\mathrm{b}}=v_{\mathrm{o}}-v_{\mathrm{e}}+v_{\mathrm{b}\mathrm{r}}$	[36]
Bubble rise velocity	$v_{\mathrm{b}\mathrm{r}}=0.7119{(g{d}_{\mathrm{b}})}^{1/2}$	[37]
Emulsion velocity	$v_{\mathrm{e}}=\frac{v_0-\partial v_{\mathrm{b}}}{1-\partial }$	[38]
Bubble diameter	$d_{\mathrm{b}}=d_{\mathrm{b}\mathrm{r}}{[1+27(v_0-v_{\mathrm{e}})]}^{1/3}(1+6.84H)$ $d_{\mathrm{b}\mathrm{r}}=0.0085$ (Geldard B category)	[39]
Bubble phase fraction	$\partial =0.534(1-{\mathrm{e}}^{-\frac{v_0-v_{\mathrm{m}\mathrm{f}}}{0.413}})$	[40]
Emulsion phase porosity	${\mathsf{\chi }}_{\mathrm{e}}={\mathsf{\chi }}_{\mathrm{m}\mathrm{f}}+0.2-0.059e^{-\frac{v_0-v_{\mathrm{m}\mathrm{f}}}{0.429}}$	[40]
Bubble phase porosity	${\mathsf{\chi }}_{\mathrm{b}}=1-0.146e^{-\frac{v_0-v_{\mathrm{m}\mathrm{f}}}{0.439}}$	[40]
Volume of polymer phase in the emulsion phase	${\mathsf{\zeta }}_{\mathrm{p}\mathrm{e}}=AH\left(1-{\mathsf{\chi }}_{\mathrm{e}}\right)(1-\partial )$	[17]
Volume of polymer phase in the bubble phase	${\mathsf{\zeta }}_{\mathrm{p}\mathrm{b}}=AH\left(1-{\mathsf{\chi }}_{\mathrm{b}}\right)\partial$	[31]
Volume of the emulsion phase	${\mathsf{\zeta }}_{\mathrm{e}}=AH\left(1-{\mathsf{\chi }}_{\mathrm{b}}\right)$	[41]
Volume of the bubble phase	${\mathsf{\zeta }}_{\mathrm{b}}=A\partial H$	[37]
Minimum fluidisation velocity	$\mathsf{\beta }{e}_{\mathrm{m}\mathrm{f}}={\left[{\left(29.5\right)}^2+0.357\text{Ar}\right]}^{1/2}-29.5$	[37]
Mass transfer coefficient	$K_{\text{sg}}=4.5(\frac{\mathsf{\beta }{e}_{\text{mf}}}{d_{\text{pr}}})+5.85\left(\frac{PPC\cdot g^{4/1}}{{d_{\text{pr}}}^{5/4}}\right)$$K_{\text{gs}}=6.77\left(\frac{D_{\mathrm{g}}0.45v_{\mathrm{b}}}{{d_{\text{pr}}}^3}\right)$	[20]
Momentum exchange coefficient	$K_{\text{mn}}=150\frac{{\mathsf{\alpha }}_{\mathrm{s}}^2{v}_{\mathrm{g}}}{{\mathsf{\alpha }}_{\mathrm{g}}{d}_{\mathrm{p}\mathrm{r}}}+1.75\frac{{\mathsf{\alpha }}_{\mathrm{s}}{\mathsf{\rho }}_{\mathrm{g}}}{d_{\mathrm{p}\mathrm{r}}}\left|v_{\mathrm{b}}-v_{\mathrm{e}}\right|$	[12]