Table 2.

Dynamic correlations and formulas applied for the multiphasic model [15,42,43].

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