Doing Material Balance On Brewery

Next the total material balance for the tray is: dMe which may be Laplace transformed to:

sMf{s) = F(s) + Lf+1(s) - Lf(s) + Vf^(s) - Vf(s) (18.28)

Note that

From equations (18.20) through (18.28) we can prepare the signal flow diagram of Figure 18.3. Note that q is a measure of the thermal condition of the feed; q is approximately the heat necessary to vaporize 1 pound mole of feed divided by the molar latent heat of vaporization of the feed. On a McCabe-Thiele diagram (see Section 2.4), the slope of the so-called q line is q/(q — 1); the intercept on the 45° line is always zF.

The top tray can be represented by a signal flow diagram similar to that of the basic tray (see Figure 18.2) if we make the simplifying assumption that the reflux, L0, enters the top tray at its boiling point. Then LR = L0. This is not usually true, but if the reflux is subcooled only a few degrees, subcooling has only a small effect on reflux enthalpy. Further, the reflux temperature is sometimes controlled, so the reflux enthalpy does not change significandy. For those cases where it is not practical to control reflux temperature, it is usually possible to control internal reflux rate. This we are doing more frequently today. Ignoring subcooling, therefore, in most cases leads to small errors in the calculated values of static gains and top-tray mixing time constant.

We assume further that the vapor from the top tray is totally condensed. We can then write the following transfer function relating the vapor composition yT and reflux composition xR:

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