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NEQ Cell Model

An issue that is not adequately addressed by most models (EQ and NEQ) is that of vapor and liquid flow patterns on distillation trays or maldistribution in packed columns. Since reaction rates and chemical equilibrium constants are dependent on the local concentrations and temperature, they may vary along the flow path of liquid on a tray, or from side to side of a packed column. For such systems the residence time distribution could be very important, as well as a proper description of mass transfer. On distillation trays, vapor will rise more or less in plug flow through a layer of froth. The liquid will flow along the tray more or less in plug flow, with some axial dispersion caused by the vapor jets and bubbles. In packed sections, maldistribution of internal vapor and liquid flows over the cross-sectional area of the column can lead to loss of interfacial area.

To deal with this shortcoming of earlier non-equilibrium models, both steady state and dynamic NEQ cell models have been developed [12-15]. The distinguishing feature of this model is that stages are divided into a number of contacting cells, as shown in Fig. 9.6. These cells describe just a small section of the tray or packing,

Fig. 9.6 The non-equilibrium cell model

and by choosing an appropriate set of cell connections, one can very easily study the influence of flow patterns and maldistribution on the distillation process.

Flow patterns on distillation trays are modeled by choosing an appropriate number of cells in each flow direction. A column of cells can model plug flow in the vapor phase, and multiple columns of cells can model plug flow in the liquid phase as depicted in Fig. 9.7. Back-mixing may also be taken into account by using an appropriate number of cells. This may be derived from calculating an equivalent number of cells from eddy diffusion models. Flow patterns in packed columns are evaluated by means of a natural flow model. The flows are split up according to the ratio of the cell surface areas between the cells. Other flow patterns may be approximated using different flow splitting policies.

The unit cell for homogeneous systems (and for heterogeneous systems modeled as though they were homogeneous) is depicted in Fig. 9.8. The equations for each cell are given in Table 9.1.

A schematic diagram of the unit cell for a vapor-liquid-porous catalyst system is shown in Fig. 9.9. Each cell is modeled essentially using the NEQ model for heterogeneous systems described above. The bulk fluid phases are assumed to be completely mixed. Mass-transfer resistances are located in films near the vapor-liquid and liquid-solid interfaces, and the Maxwell-Stefan equations are used for calculation of the mass-transfer rates through each film. Thermodynamic equilibrium is assumed only at the vapor-liquid interface. Mass transfer inside the porous catalyst may be described with the dusty fluid model described above.

Liquid entering stage vapor leaving stage

stage

Fig. 9.7 Details of flows in and out of multiple cells used to model the hydrodynamics of trayed columns

Liquid entering stage vapor leaving stage stage vapor entering stage

Liquid leaving si age

Fig. 9.7 Details of flows in and out of multiple cells used to model the hydrodynamics of trayed columns

Fig. 9.8 The non-equilibrium stage (cell) for homogeneous catalyzed reaction

Fig. 9.8 The non-equilibrium stage (cell) for homogeneous catalyzed reaction

Table 9.1 Equations describing dynamic NEQ cell model

Equation type and number

Liquid phase

Vapor phase

Equations describing conservation laws for an NEQ cell

0 0

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