Problem Statement A fruit juice concentrate plant works based on the process shown in Figure 1. Fruit juice with 10% solid particles (Feed Stream 1, X5,1=0.1) is to be freeze-concentrated to 40% solids (Stream 5, X.,5=0.4). The dilute juice is firstly fed to a freezer where the ice crystals are formed, and then the slush is separated in a centrifugal separator into ice crystals (Stream 4 contains no solid particles), and concentrated juice. It should be noted the Stream of fresh fruit juice is combined with the recycle stream (Stream 6) before entering the freezer. Stream 6: Recycled liquid (recycled ratio: 20%) Stream 2 Freezer Stream 3 Separator Unit Feed Stream 1 Xs,1 = 0.1 Recycle Mixer Stream 5: Concentrated juice X,5 = 0.4 Stream 4: Ice = 0 X5,4 Figure 1. Simplified process flow diagram of the plant Tasks: You should perform a simulation using Microsoft Excel to determine the following items: a. Calculate the mass flow rate of fruit juice (Stream 1), Ice (Stream 4) and recycled Stream (Stream 6) in order to deliver 2000 kg/h of concentrated juice (Stream 5). The recycle fraction is 20%. b. Now, assume that due to a change in the feed Stream, the mass fraction of solids in the fruit juice (Stream 1) changes from 0.1 to 0.15. What is the required flow rate of fruit juice to maintain the same flow rate of 2000 kg/h of concentrated juice? Comment on the trend you observed in the flow rate of Stream 1 with respect to changing of solid concentration. c. The efficiency of the freezer has the following characteristics: For every 0.01 decrement in the mass fraction of water Stream 2, the efficiency of the freezer increases by 7.5%. At the same time, for every 200 kg/hr increment in the total mass flow rate of Stream 2, the efficiency of the freezer decreases by 4%. Taking zero recycling as the basis for this optimization study, what is the optimal recycle ratio to produce the 2000 kg/hr of 40% concentrated juice? (solid concentration of Stream 1 is 10%] How does change in the recycle ratio affect the energy aspect of the process? Discuss these in terms of sustainability in your report