## Heatstorage Effect On Column Pressure

These assumptions permit us, at least for atmospheric or pressurized columns, to lump the column contents together and to assume an average temperature, Tcp, and an average pressure, PCP, as shown by Figure 17.1. Note that the reboiler is lumped with the column base but the condenser and overhead receiver are not lumped with the column top.

We may now write a heat-balance equation similar to equation (15.30) but with terms for reflux added:

cpTFwe(s) + cpwFTF(s)+ qj{s) - cp[{wc + wB) + sWml] Tcp(s)

+ cpTrwr(s) + cpwRTR(s) - cpTcpwB(s) - cpsTcpWmi(s) (17.1) = (\p + cpTcp) wc(s)

### Reboiler with Steam Flow or Flow-Ratio Controlled

If we treat reboiler dynamics as negligible, and if we assume that steam will be flow or flow-ratio controlled, we may combine the above equations as shown in the preliminary signal flow diagram of Figure 17.2. This, in turn, may be reduced to the form of Figure 17.3.

### Reboiler with Direct Throttled Steam

For the case where the steam valve is manipulated by some variable other than flow or flow ratio, we may need to account for reboiler dynamics to calculate qT. Referring to Figure 15.8, we may make a partial signal flow diagram as shown on Figure 17.4 where:

CR = reboiler hot-side acoustic capacitance, ft5/lbf

Ar = reboiler heat-transfer area, ft2

Pa = reboiler hot-side pressure, lbf/ft2

Qv = heating-medium flow, actual ft3/sec pa = heating-medium (vapor) density, lbm/ft3

kst = heating-medium latent heat, pcu/lb

UR = reboiler heat-transfer coefficient, pcu/sec

The material-balance equation is:

'Cft2