Lesson 11 - Jacketed Vessels SAQ

** Using this example, answer the questions below.

The mashing process has three temperature stands, namely 62°C, 65°C, and 72°C. Furthermore, at the end of the mash profile, the mash is heated up to 76°C before transfer to the lauter tun. A minimum heat up rate of 1 °C min^-1 is required.

• Maximum mash vessel volume is 500 hL. Mash vessel diameter is 4 m.

• Heat is provided by steam at 130°C. The heat of evaporation of steam at 130°C is 2,200 kJ kg^-1.

• Typical overall heat transfer coefficient for an agitated jacketed vessel using steam the way this one does is 1,100 W m^-2 K^-1.

• Specific heat capacity and density of mash are 3,600 J kg^-1 °C^-1 and 1,060 kg m^-3 respectively.

(a)  What is the required heat transfer area of the mash vessel?

(b)  What would be the approximate height of the jackets, assuming they were positioned only on the side walls?

(c)  What is the maximum required mass steam flow rate?

Response

Let’s start with part (a) and work through the question step by step.

Firstly, we need to understand that we are dealing with unsteady state heat transfer and we need to calculate the solution for the worst-case scenario (highest rate of heat transfer scenario) which is where the mash temperature is 76°C which has the smallest ΔT.

First, we calculate the mass of mash (M_mash):

Next, we need to calculate the heat transfer rate:

To find out the amount of specific heat required to increase the mash temperature we can use the formula:

Therefore:

The heat transfer from the surface to the mash can be calculated using:

From this we can derive the amount of surface area required to achieve this heat transfer rate as follows:

Next let’s tackle part (b) and work through it step by step.

Using the formula for calculating the surface area of a cylinder, we can determine the approximate height of the jackets.

To achieve this heat transfer, the required height of the jackets for this vessel is 4.26 m.

It may be the case that the liquid level of the mash vessel is below 4.26 m. This is not ideal, as part of the heating surface may not be covered and this can cause vessel fouling. Rather than using a single jacket on the shell, we could use two jackets: one covering the bottom cone and one on the sides. Adding a cone jacket means the shell jacket can be smaller, and thus not exposed above the mash.

Finally, let’s cover part (c) and work through it step by step.

As the heating medium is changing state, we will use the latent heat formula for the heat transfer:

We need to work out the mass flowrate of steam and therefore can divide both sides by time:

And because :

We can now rearrange to isolate m_steam: