## Nomenclatures  
L molar flow rate of liquid, [kmol/s] V molar flow rate of vapor [kmol/s] F molar flow rate of feed, [kmol/s] N molar transfer rate, [kmol/s] K equilibrium ratio, [-] r reaction rate, [kmol/s] H Enthalpy, [kmol/s] Q heat input to a stage, [J/s] q heat transfer rate, [J/s] T temperature, [K] x liquid mole fraction [-] y vapor mole fraction [-] c\({}_{\text{p}}\) specific molar heat capacity, [J/kmol K] \(M_{\text{zw},L}\) molecular weight of the liquid phase \(\lambda\) Thermal conductivity, [w/m K] h Heat transfer coefficient [w/m\({}^{2}\)K] D diffusion coefficient, m\({}^{2}\)/s  
\begin{tabular}{l l} \(N_{i,G}\) & rate of mass transfer of component i through the gas boundary, \([\text{kmol/s}]\) \\ \(N_{i,L}\) & rate of mass transfer of component i through the liquid boundary, \([\text{kmol/s}]\) \\ \(a\) & The interfacial area between gas and liquid phases, m\({}^{2}\) \\ C\({}_{iG}\) & concentration of component i in gas bulk, \(\left[\frac{\text{kmol}}{m^{3}}\right]\) \\ \(C_{iL}\) & concentration of component i in liquid bulk, \(\left[\frac{\text{kmol}}{m^{3}}\right]\) \\ \(C_{iG*}\), & concentration of component i in the interface from the gas side, \(\left[\frac{\text{kmol}}{m^{3}}\right]\) \\ \(C_{iL*}\) & concentration of component i in the interface from the liquid side, \(\left[\frac{\text{kmol}}{m^{3}}\right]\) \\ \(k_{iL}^{V}\) & binary mass transfer coefficient for vapor, m/s \\ \(k_{iL}^{L}\) & binary mass transfer coefficient for liquid, m/s \\ \(D_{ijk}^{V}\) & diffusivity of the vapor, m\({}^{2}\)/s \\ \(D_{ik}^{L}\) & diffusivity of the liquid, m\({}^{2}\)/s \\ \(F_{s}\) & superficial F-factor, \(kg^{0.5}/m^{0.5}\) \\ \(t_{L}\) & average residence time for the liquid (per pass), s \\ \(V\) & total molar flow rate of, liquid, vapor, kmol/s \\ \(L\) & total molar flow rate of, liquid, vapor, kmol/s \\ \(a^{I}\) & total interfacial area for mass transfer, m\({}^{2}\) \\ \(\overline{\rho}^{V}\) & molar density of vapor, kmol/m\({}^{3}\) \\ \(\overline{\rho}^{L}\) & molar density of liquid kmol/m\({}^{3}\) \\ \(F_{f}\) & fractional approach to flooding, - \\ \(a\) & relative froth density, -, Equation (18) \\ \(A_{b}\) & total active bubbling area on the tray, m\({}^{2}\) \\ \(u_{s}^{V}\) & superficial velocity for the vapor, m/s \\ \(u_{s}^{L}\) & superficial velocity for the liquid, m/s \\ \(u_{sf}^{V}\) & superficial velocity of vapor at flooding, m/s \\ \(\rho_{t}^{V}\) & density of the vapor, kg/m\({}^{3}\) \\ \(p_{t}^{L}\) & density of the liquid, kg/m\({}^{3}\) \\ \(l_{w}\) & average weir length (per liquid pass), m \\ \(Q_{V}\) & volumetric flow rate for the liquid, vapor, m\({}^{3}\)/s \\ \(Q_{L}\) & volumetric flow rate for the liquid, vapor, m\({}^{3}\)/s \\ \(\sigma\) & liquid surface tension N/m \\ \(FP\) & flow parameter, - \\ \(\varnothing\) & fractional hole area per unit bubbling area on the tray, - \\ \(h_{cl}\) & clear liquid height, m \\ \(h_{w}\) & average weir height, m \\ \(A_{b}\) & total active bubbling area on the tray, m\({}^{2}\) \\ \(N_{p}\) & number of liquid flow passes, - \\ P & sieve tray hole pitch, m, Equation (24) \\
**Subscripts** & \\ L & liquid \\ V & vapor \\ F & feed \\ G & gas \\ m\({}^{3}\)/h & cubic meter per hour \\ i & component \\ n & number of components \\ I & interface \\ f & film \\ j & stage number \\
**Abbreviations** & \\ NRTL & non-random two-liquid model \\ Nm3/h & cubic meter of gas per hour at the normal temperature and pressure \\ \end{tabular}