Question

The popularity of orange juice, especially as a breakfast drink, makes it an important factor in the economy of orange-growing regions.Marketed juice has either gone through a process in which it was concentrated, or it may be a not-from-concentrate juice. Frozen concentrated juice is reconstituted before consumption. Although concentrated juices are less popular in the United States than at one time, they still have a major segment of the market.The approaches to concentrating orange juice include evaporation, freeze concentration, and reverse osmosis. Here we examine the evaporation process by focusing only on two constituents in the juice: solids and water.Fresh orange juice contains approximately 10.0 wt% solids (sugar, citric acid and other indigenous ingredients) and frozen concentrate contains approximately 45.0 wt% solids. The frozen concentrate is obtained by evaporating water from the fresh juice to produce a mixture that is approximately 67.0 wt% solids. However, so that the flavor of the concentrate will closely approximate that of fresh juice, the concentrate from the evaporator is blended with fresh orange juice (and other minor additives) to produce a final concentrate that is approximately 45.0 wt% solids.Assume a basis of 100.0 kg of fresh juice fed to the process.a) What is the mass of final concentrate produced?b) What is the fraction of fresh juice that bypasses the evaporator?

Answer 1

Answer:

A) 22.22 kg

B) 0.1364

Explanation:

When we perform a degree of freedom (DOF) analysis on the bypass subsystem, we will have 2 unknown masses which are; (m1, m2).l with degree of freedom as 1.

Secondly, when we perform a degree of freedom analysis on the overall system, we will have 2 unknown masses namely (m3, m5) with degree of freedom as 0.

Thirdly, when we perform a degree of freedom analysis on the evaporator, we will have 3 unknown masses namely (m1, m3, m4) with Degree of freedom as 1.

Lastky,when we perform a degree of freedom analysis on mixing point, we will have 3 unknown masses namely, (m2, m4, m5) with degree of freedom as 1.

We are given;

Fresh orange = 10.0 wt% solids

Frozen juice concentrate = 45.0wt% solids

Mixture produced = 67.0 wt% solids

Final concentrate = 45.0 wt% solids

Now, making use of the overall solids balance, we have;

0.1 × 100 = 0.45(m5)

m5 = (0.1 × 100)/0.45

m5 = 22.22 kg

Making use of overall mass balance, we have;

100 kg = m3 + m5

m3 = 100 - 22.22

m3 = 77.78 kg

Now, making use of the Mixing point mass balance, we have;

m4 + m2 = m5

So; m4 + m2 = 22.22 - - - (eq 1)

Also, making use of the Mixing point solids balance, we have;

0.67m4 + 0.1m2 = 0.45m5

0.67m4 + 0.1m2 = 9.999 - - - (eq 2)

Solving eq 1 and eq 2 simultaneously, we have;

m2 = 13.64 kg

m4 = 8.58 kg

Final concentrate is m5 = 22.22 kg

Now, fraction = m2/100 = 13.64/100 = 0.1364