Flake caustic soda, NaOH, is produced from a feed consisting of 40% NaOH by weig

Question

Flake caustic soda, NaOH, is produced from a feed consisting of 40% NaOH by weight. The aqueous feed is first concentrated by evaporation in which 40% of the water in the feed is removed and the resulting concentrated caustic solution is cooled to bring about crystallisation of the NaOH. The resultant slurry is filtered on a rotary vacuum filter to produce a filtrate of 45% by weight NaOH and a filter cake consisting of 90% by weight NaOH flake and the balance is residual filtrate. The unfinished diagram below is a simplified PFD of the process in which the crystallisation and filtration stages have been combined into a single unit process. You have to complete the labelling of the PFD and answer the following questions [10%) F2 xy Cake Evaporator Crystallizer/Filter Fi Fa Filtrate the last page of this Paper. (a) For the overall system, the evaporator and the crystallizer, conduct a Degrees of Freedom analysis. Show that there is not enough information available to allow you to proceed to balance the PFD [15%] (b) Assuming a feed, Fi5000kg/h proceed to solve for all unknown flow rates and compositions. [40%) (c) The process as described above produces a caustic stream at 45% by weight and is very wasteful of the NaOH. It is decided to recycle this stream to mix with stream 1, maintaining the composition and flowrate of stream 1 to the evaporator. Determine the mass flow rate and composition of the make-up stream of caustic required to achieve this result. [20%] (d) Determine the molar flowrate and composition in mole fractions of the recycle stream. [15%]

Explanation / Answer

a. For degree of freedom analysis, we will write down number of unknown and number of equation formed.

Unknown variable = F1, F4, F5

Number equation formed = 2 (Overall balance and composition balace equation.

Hence, degree of freedom = number of variable- number of equation = 3-2 =1

So, one more variable need to be define for complete balance of PFD.

b. Feed Stream, F1= 5000 kg/h, x1(NaOH composition) = 0.4, y1(Water composition) = 0.6

40% of water in feed is evaporated in evaporator,so

F2= 0.4*F1*y1 = 1200 kg/hr

Balance across evaporator ,

F1=F2+F3; F3= 3800 kg/hr

Component Balance across evaporator , x2=0 (Stream 2 is pure water)

x1*F1=x2*F2+x3*F3; x3= 0.5263

Balance across Crystallizer ,

F3=F4+F5;

Component Balance across Crystallizer , x4= 0.9 & x5 = 0.45

x3*F3=x4*F4+x5*F5;

F4= 645 kg/hr & F5=3155 kg/hr.

c.

Overall Balance system,

F1=F2+F4;

overall component Balance , x2=0 (Stream 2 is pure water), x4=0.9, F2= 1200 kg/hr

x1*F1=x2*F2+x4*F4; F4= 2222.23 kg/hr

Balance across Crystallizer ,

F1-F2=F3=F4+F5;

Component Balance across Crystallizer , x4= 0.9 , x3= 0.5263

x3*F3=x4*F4+x5*F5; F5=1577.77,

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