Question

A beverage is prepared by combining fresh juice (12% solids) with sugar and water to achieve a final concentration of 8% juice solids and 4% sugar. The beverage is pasteurized continuously in a regenerative heating/cooling plate heat exchanger. The juice first enters the pasteurizer at 500 kg/h, 20°C through the regeneration section, where it is being warmed up to 65°C by the outgoing hot product. The juice then flows through the heating section, where it is heated to a target temperature by the heating medium (hot water). The hot water enters the heating section at 95°C and exits at 87°C, at a flow rate of 841 kg/h. The juice then passes back through the regeneration section where it is being cooled by the incoming product. The juice finally flows through the cooling section, where it is cooled to 4°C. In the cooling section, the cooling water enters and leaves the pasteurizer at 0°C and 8°C, respectively. The hot water in the heating section is heated in a heat exchanger using steam at 120°C with a mass flow rate of 12.9 kg/h. The steam condensate leaves the heat exchanger at 98°C. Heat capacity of juice is 3.75 kJ/kg.K, and water is 4.18 kJ/kg.K.

(a) draw a schematic diagram of the process indicating all streams

(b) calculate the quantities of juice, water and sugar required

(c) determine the temperature of the product exiting the heating section

(d) calculate the purity of the steam (i.e., steam quality) required in the heat exchanger

(e) calculate the mass flow rate of the cooling water

Answer 1

I bilieve the juice reffered in the third sentence and in the following sentences actually refers to the beverage, because juice is mixed to make beverage and beverage is the material that is being pasteurized.

All the notations of the temperature and flow rate given are indicated in the diagram,

(a)

(b) The total amount of the beverage is given as 500 kg/h

Taking mass balance around mixer,

Now we will take balance on sugar around the mixer,

Now taking balance on the juice solids around the mixer we get,

Now from the total balance we get the amount of water as,

So the amount of sugar required is 20 kg/hr

amount of water required is 146.67 kg/hr

amount of juice required is 333.33 kg/hr

(c) Given that the specific heat capacity of juice is and water is

Taking energy balance around the heating section we get,

H is the amount of hot water and is given as,

So the temperature of the product exiting is 800C

(d) purity or quality of the steam is the fraction of the steam that is vapour. let x be the fraction of steam that is vapour.

So we will take the heat balance around the heat exchanger we get,

heat needed to raise the sensible of hot water = latent heat supplied by vapour in the steam + sensible heat supplied by the condensate and water that was already in the steam.

condensate and water that was already in the steam = total amount of steam

So mathematically we can write,

Here S is the amount of steam.

Temperature of the steam entering heat exchanger,

Temperature of the condensate leaving heat exchanger,

is the latent heat of vapourisation at 1200C and

so,

So the purity of the steam should be 94.823% required in heat exchanger to heat the recycle hot water from 870C back to 950C.

e) To calculate the mass flow rate of cooling water first we have to find the temperature of the hot beverage coming out the regeneration section. So doing heat balance around the regeneration section we get,

Now we will calculate the heat balance around the cooling section to get calculate the amount of cooling water,

Here C is the amount of cooling water.

So the amount of cooling water required is 1738.188 kg/hr