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Phase Transfer Catalysis - Publications of the IAS Fellows

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Model<br />

Model A<br />

Table 3. Summary <strong>of</strong> Models for Homogeneous Solubilization*<br />

Step(s) Contributing<br />

to Overall Rate<br />

Characteristic<br />

Features <strong>of</strong> <strong>the</strong> Model<br />

Organic phase reaction Constant Q+ Y- concentration<br />

Pseudo-first-order rate<br />

Model B Organic phase reaction<br />

and ion exchange<br />

Model C Organic phase reaction, ion Rate <strong>of</strong> solid dissolution<br />

exchange, and solid dissolution important at low values <strong>of</strong> ksla<br />

Model D Organic phase reaction, ion Mass-transfer limitations<br />

exchange, solid dissolution, and<br />

mass-transfer steps<br />

slow down reaction<br />

*Adapted from Naik and Doraiswamy (1997).<br />

change step. Considering a volume reaction model, similar to<br />

those developed for gas-solid reactions, <strong>the</strong>y developed <strong>the</strong><br />

following equations for <strong>the</strong> PTC cycle<br />

0 50 100 150 200 250<br />

time (min)<br />

time (min)<br />

Figure 10. Comparison <strong>of</strong> models for homogeneous<br />

solubilization.<br />

Adapted from Naik and Doraiswamy (1997).<br />

Regime<br />

<strong>of</strong> Ion<br />

Exchange<br />

(4, at equilibrium)<br />

Regime <strong>of</strong><br />

Organic<br />

Reaction<br />

1<br />

Changing Q’ Y- concentration 1 1<br />

Between 1 and 2 1<br />

3 1, 2, or 3<br />

- = k2cRXbcQYb - kqafcQXb - cQXs 1<br />

dt<br />

GXb<br />

- = - k2ClzX$QYb<br />

dt<br />

with CQyb calculated from a quat species balance as<br />

c QYb = % - cQXb - ‘;Xa - ($Ya<br />

where Cixa and Ciya are <strong>the</strong> volume average concentrations<br />

<strong>of</strong> QX and QY in <strong>the</strong> solid. Initial conditions (IC)<br />

Boundary conditions (BC)<br />

r=R,D dC;Y<br />

- = kqKQyb - G&l<br />

q dr<br />

Constant diffusivity ( Dq) and <strong>the</strong> solid-liquid mass-transfer<br />

coefficient (kg) are assumed for QX and QY. The model<br />

equations are nondimensionalized in terms <strong>of</strong> <strong>the</strong> Thiele parameter<br />

+2, Biot number for mass transfer Bim, and nondimensional<br />

time and distance. An important conclusion from<br />

<strong>the</strong> subsequent analysis <strong>of</strong> <strong>the</strong> model simulations is <strong>the</strong> importance<br />

<strong>of</strong> <strong>the</strong> solid phase on <strong>the</strong> conversion <strong>of</strong> <strong>the</strong> organic<br />

substrate in <strong>the</strong> organic phase. Results <strong>of</strong> <strong>the</strong>ir simulation are<br />

shown in Figure 11. It can be noticed that at low $J~, corresponding<br />

to low diffusional limitations, <strong>the</strong> overall organic<br />

reagent conversion is lower than at higher values <strong>of</strong> +2. This<br />

result is <strong>the</strong> exact opposite <strong>of</strong> what is observed in analysis <strong>of</strong><br />

AIChE Jourual March 1998 Vol. 44, No. 3 627

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