## RTl Xal1112

dt Ha

The condenser characterises the first tray and the holdup tank contains an amount of liquid Hc which is kept constant at all times. The component balance for the holdup tank is:

The reflux ratio (internal) is defined as:

L = rV (III.4) The distillate-rate to the accumulator or product tank is therefore:

LD=V(l-r) (III.5) Internal Plates, i-2 to (N-l): i = 1 to n„

Like the condenser, the molar plate holdup remains at a constant value. The component balance on tray j is:

dxn v

dt Hj

The vapour liquid equilibrium relationship is written as:

The amount of mixture left in the reboiler depends on the liquid and the vapour flow rate through the column. The total mass balance is written as:

The component mass balance is:

The vapour liquid equilibrium relationship is same as the equation (III.7) with j = N.

Converse and Huber (1965), Robinson (1970), Mayur and Jackson (1971), Luyben (1988) and Mujtaba (1997) used this model for simulation and optimisation of conventional batch distillation. Domenech and Enjalbert (1981) used similar model in their simulation study with the exception that they used temperature dependent phase equilibria instead of constant relative volatility. Christiansen et al. (1995) used this model (excluding column holdup) to study parametric sensitivity of ideal binary columns.

A liquid binary mixture with Bo = 10 kmol and xBo = <0.6, 0.4> molefraction is subject to conventional batch distillation shown in Figure 4.3. The relative volatility of the mixture over the operating temperature range is assumed constant with a value of (a=) 2. The total number of plates is, N = 20. The vapour boilup rate is, V = 5.0 kmol/hr and the reflux ratio is, r - 0.75. The condenser and total plate holdups are 0.2 and 0.2 kmol respectively.

Figure 4.3 shows the accumulated distillate amount, the bottom product amount and the compositions at the end of 5 hr operation, obtained using the simple model outlined in section 4.2.3. Figure 4.4 shows the instant distillate composition profile.

Distillate

Final Bottom Product Hn= 3.75 kmol xw = <0.09, 0.91>

Figure 4.3. Batch Distillation using Simple Model Time, hr

Figure 4.4. Instant Distillate Composition Profile (Example 4.2.3.1)

Time, hr

Figure 4.4. Instant Distillate Composition Profile (Example 4.2.3.1) Figure 4.5. CBD with Notations for Detailed Model (Type IV-CVH) 4.2.4. Rigorous Model - Model Type IV

4.2.4.1. Constant Volume Holdup (CVH) Model

The model equations are presented in the following section, with reference to the column configuration shown in Figure 4.5. The main assumptions are listed below:

i) constant volume holdup for reboiler, condenser and internal plates.

ii) total condensation without sub-cooling.

iii) negligible vapour holdup.

iv) perfect mixing of liquid and vapour on the plates.

v) negligible heat losses.

vi) theoretical plates vii) feed mixture at its bubble point viii) adiabatic column

Condenser and Accumulator. i=l:i= 1 to nc Accumulator total mass balance:

Component bass balance: a) Accumulator d{HaXai)=LDxDi (IV. 2)

dt b) Condenser Holdup Tank d(HcxDi)

Energy balance:

Physical properties and other equations:

Total mass balance:

Component mass balance: d(H jXjj)

Energy balance:

Equilibrium: