Page 108 - Analysis, Synthesis and Design of Chemical Processes, Third Edition

where ρ is the liquid density, C is the liquid heat capacity, T is the temperature of the liquid in the tank
p
(95°C is desired value in 1.5 h), U is the overall heat transfer coefficient from the jacket to the liquid in
the tank, A is the heat transfer area of the jacket (cylinder surface), and T is the temperature of the
s
condensing steam. (Normally, there is also a jacketed bottom to such a vessel, but this added heat-transfer
area is ignored in this example for simplification.) Integration of this equation yields

(E3.1d)

where T is the initial temperature in the tank (assumed to be 25°C). The following “typical” values are
o
assumed for this design:

C p = 2000 J/kg°C

T s = 120°C (200 kPa Saturated Steam)

U
2
= 300 W/m °C
Tank Height to Diameter Ratio = 3/1 (so H = 3D)

Assuming the tank to be cylindrical and ignoring the volume of the bottom elliptical head, the tank volume
3
2
2
is V = πD H/4 = 3πD /4. Thus, the tank diameter, D, is 1.689 m. The height of fill is H = 4V/(πD ) =
tank fill
2
2.806 m. The area for heat transfer is A = πDH = 14.89 m , because we assume negligible heat transfer
fill
to the vapor space. When these values are used in Equation (E3.1d), it is found that the time required for
preheating the reactor, Δt, is 3288 s (55 min). Thus, the step time requirement of 1.5 h for this step is met.
The additional time is required for filling, sealing, and inspecting the vessel prior to heating. It should be
noted that there may be process issues that require a slower temperature ramp, which can be
accomplished by controlling the steam pressure. Note also that it is assumed that the time requirement for

cleaning the vessels in this example is included in the step times given in the problem statement.

Step 2: Reaction Vessel—Reaction

It is assumed that the reaction of one mole each of A and B to form one mole of the product is second
-4
3
order (first order in each reactant) and that the rate constant is 7.09 ×10 m /kmol s. The relationship for
a batch reactor is

(E3.1e)