Lesson 10 - Jacketed Vessels

Let’s expand further on the example given in the previous section about cooling in a fermentation vessel. The fermentation has the following fermentation profile:

1. Free rise from 12°C to 15°C

2. Active fermentation at a constant temperature of 15°C

3. Cool down from 15°C to 4°C

The capacity of the fermentation vessel is 2,000 hL. The fermentation vessel has a radius of 2.5 m. There are three cooling jackets around the shell of the fermenter and each is 1.5 m high.

The jackets are supplied with liquid ammonia at 2°C. At this temperature, the heat of vaporisation of liquid ammonia is 1,446 kJ kg^-1.

The overall heat transfer coefficient for this vessel is 350 Wm^-2 K^-1.

The specific heat and density of beer is 4,040 J kg^-1°C^-1 and 1,030 kg m^-3 respectively.

The rate of heat generated during the fermentation per kg of wort is 0.9 J kg^-1 s^-1.

a)     How many cooling jackets need to be operated during the fermentation step?

b)     How long will it take to cool down the fermenter using all three jackets?

c)     A cool down rate of at least 0.25°C hr^_-1 is required throughout the cool down. Is this achievable with the current design?

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

1. Calculate the heat generated during active fermentation.

q (fermentation) = H (fermentation) × volume × density

q (fermentation) = 0.9 × 2000 / 10 × 1,030 = 185,400 J s^-1

2. Calculate the heat transfer area required to remove this heat.

During the fermentation step, the temperature in the fermenter remains constant, so heat transfer is steady state. The equations for steady state heat transfer can be used.

3. Calculate the heat transfer area per jacket.

4. Calculate the required number of jackets.

If the surface area of each jacket is 23.56 m² and the total surface area required for heat transfer is 40.75 m², then:

number of jackets required = total surface area / surface area per jacket

number of jackets required = 40.75 / 23.56 = 1.73

Therefore, during active fermentation at least two jackets will have to be operated to ensure that the heat generated during fermentation is removed and that the temperature remains at 15°C.

Let’s now look at part b)

During cool down, the product temperature is changing, so heat transfer is unsteady state. We can use the equation for unsteady state heat transfer to determine the time taken for cool down:

The total time required to cool down 2,000 hL of beer in this fermentation vessel from 15°C to 4°C will be 17.5 hours.

Finally, let’s look at part c) and work through the example step by step.

Because the cool down step is unsteady state, the cool down rate will be different at each point of the cool down process. To simplify the calculation, we will look at the two extreme points of the cool down. It is then safe to assume that all other points of the cool down will fall between these two extremes. These two points are:

i)    the start of cooling down, when the beer temperature is 15°C; and

ii)  the end of cooling down, when the beer temperature is 4°C. 

1. First, let’s calculate the time required to cool the fermenter by 0.25°C starting at 15°C:

2. Next, let’s calculate the time required to cool the fermenter by 0.25°C, ending at 4°C:

From this, we can see that initially the rate of cool down will be well within the requirements. However, this will not be the case at the end of the cool down. It is not possible to achieve a cool down rate of 0.25°C hr^-1 throughout the fermentation.

3. So what will be the actual rate at the very end of the cool down?

In this example, we selected a one hour interval during which it is assumed that the heat transfer is at steady state and thus so is the rate of cool down. In reality, this is not the case and even during this one hour period, the heat transfer rate is changing. The smaller the time interval used, the more accurate the calculation will be. In commercial designs, computer programs are used to calculate this integration.

You have now learned how to calculate the size and performance of jacketed vessels. In the next sections, we will look at some practical considerations for controlling jacketed vessels in the brewing process.