Fresh orange juice with 12% soluble solids content in concentrated to 60% in a multiple effect evaporator.

2. Fresh orange juice with 12% soluble solids content in concentrated to 60% in a multiple effect evaporator. To improve the quality of the final product the concentrated juice is mixed with an amount of fresh juice (cut back) so that the concentration of the mixer is 42%.
Calculate how much water per hour must be evaporated in the evaporator, how much fresh juice per hour must be added back and how much final product will be produced if the inlet feed flow rate is 10000 kg/hour juice. Assume steady state.
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Solution:

Step 2:

Write the total and component mass balances in enveopes I and II:

i) Overall mass balances in envelope I

10000 = W + X                                         (1)

ii) Soluble solids mass balance in envelope I

0.12 * 10000 = 0.60 * X           

                        ⇰ X = 1200 / 0.60

                        ⇰ X = 2000                                            (2)

From equation (1),

                        10000 = W + 2000

                        ⇰W = 10000 - 2000

                        ⇰W = 8000

iii) Overall mass balance in envelope II

X + F = Y                                                (3)

iv) Soluble solids mass balance in envelope II

0.60 * X + 0.12 * F = 0.42 * Y             

                        ⇰ 0.60 * 2000 + 0.12 * F = 0.42 * Y

                        ⇰ 1200 + 0.12 * F = 0.42 * Y                (4)

                        

                        

From eqn (2) find X=2000 kg/h. Substituting X in eqn (1) and find W=8000 kg/h. Solve equations (iii) and (iv) simultaneously and Substitute X in eqn (1) and find=1200 kg/h and Y=3200 kg/h. Therefore 8000 kg/h of water will be evaporated, 1200 kg/h of fresh juice will be added back and 3200 kg/h of concentrated orange juice with 42% soluble solids will be produced.