Eqns. (9.16, 9.18) form a system of nonlinear, coupled differential equations that must be solved numerically in most cases. In practice, at least for non-reactive separations, the Nij are obtained from the Maxwell-Stefan equations (9.16) modified as follows
with a similar relation for the vapor phase. The KLk represents the mass-transfer coefficient of the i-k pair in the liquid phase; this coefficient is estimated from information on the corresponding Maxwell-Stefan diffusivity fiLk using the standard procedures discussed in Taylor and Krishna . a is the interfacial area.
Equation (9.17) is based on a film model of interphase transport. For this model Eqs. (9.14, 9.15) may be solved analytically, subject to some simplifying assumptions, of course .
The energy transfer rates are given by fiTL °
with a similar relation for the vapor phase. hJ is the heat transfer coefficient in the liquid phase.
At the vapor-liquid interface we assume phase equilibrium
where the subscript I denotes the equilibrium compositions and Kj is the vapor-liquid equilibrium ratio for component i on stage j. The K-values are evaluated at the temperature, pressure, and composition of the interface from appropriate ther-modynamic models (the same models used in conventional equilibrium stage models).
Furthermore, in the NEQ model we take account of the pressure drop across a stage
where Pj and Pjare the stage pressures and Apjis the pressure drop per tray from stage (j - 1) to stage j. The pressure drop over the stage is considered to be a function of the stage flows, the physical properties, and the hardware design. In the NEQ model, hardware design information must be specified so that mass-
transfer coefficients, interfacial areas, liquid hold-ups, and so on can be calculated. The NEQ model requires thermodynamic properties, not only for calculation of phase equilibrium but also for calculation of driving forces for mass transfer. In addition, physical properties such as surface tension, diffusion coefficients, and viscosities, for calculation of mass (and heat) transfer coefficients and interfacial areas are required. The steady-state model equations most often are solved using Newton's method or by homotopy-continuation. A review of early applications of NEQ models is available .
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