Question

3. (5 points) Species A and B are separated using a distillation column according to the process flow diagram below. How many more process variables must be measured or defined before all flowrates and compositions can be calculated? Justify your answer. а. 0 X2A = b. 1 X2,B с. 2 = 100 h d. 3 Half of the A fed to the column x1,A = 0.70 exits in stream 2 X,8 = 0.30 (by mass) Хз.л Vз хзв 4. (5 points) Consider the process flow diagram below. In this process, saltwater is fed to an evaporator. Part of the feed bypasses the evaporator and is combined with the concentrated salt water that exits the evaporator. Which sub-system(s) in this process have zero degrees of freedom? Circle all that apply. Justify your answer a. Overall process b. Mixing point c. Evaporator d. Splitting point m3 x3w= 1 m= 70 lbs. m450 lbs. mg mo evaporator X4,s = 0.7 X4,w = = X0,s X1,w= x5,w = X0,w m2 30 lbs. x2,s X2w Distillation Column

Answer 1

2,4:2 x2 B=2 33cron Valoolyn X,A = 0.7 & B = 0.3 [tim 3,4 - 2 B = 9 to the column exits in stream at Given: Half of the A feed Degrees of freedom = Unknown variables 1 - Independent Equation Unknown variables = { 2, Y , KQA, *3A3 Note: R2R 8 X3. B are not unknown variables because it is a binary mixture. [aga+RaB = 1] Independent Equations = a [two chemical species 1. A&B ] Additional equation ( Half of A fed to column exits in strean 2) - 2 + 1 - Dof=4-3= 1 3

m3 r tzwal So salt W= Water m, =70b] 4= 5obbe me Evaporator 14,5077 X56 11:87 *w = My= 3016 x = 2 Xw,sz? (a) overall process Independent Chknown variables - - Equations Degrees of freedom = unknown variables = { mo, nos, Paum3, M5, ass, ta] Independent Equations = a chemical species { salt & unter Note ) Take tas of now as unknown - Howol-dois variable Binary mature] Dof - 5-723 (6 mising point Unknown variables = {ms, trs, &5,s} ... Dof a 3 -d = 1 (1) Evaporator : Unknown variable = { m3, x,s} = 2 Independent Equations =% :. Dof -2-2 20

m, = mz+m4 70 = mg + 50 ) Mz 2016 solid balance around evaporatori 70 (2,5) = 20 (1) + 50(0.7) = 20 + 35 55 US 53 0.785 70 *,w+" ,s=1 0.215 wo -0.785 = (d) point: splitting Unknown variables = { mo, Ros, as}. xs, & xas compositinans are same that is why we are not taking xis as another unknown variable 3-2 = 1 - DOF =