I\'m struggling with setting up the mass balance I need. I have already coded th

Question

I'm struggling with setting up the mass balance I need. I have already coded the code to solve the equation with Newton-raphson, but I can't get the equation itself. Thanks!

Problem 3: Flash unit A feed stream (F) composed by propane (z! = 0.30), n-butane (Z-0.10), n-pentane (z,-0.15) and n-hexane (z4- 0.45) is to be split into a vapor (V) and liquid (L) phase by entering into a flash evaporation unit at a rate of 100 moles/h, where zi represents the molar fraction of each component in the feed stream. Inside the flash tank, the operating conditions are T-50C and P-200 kPa. Using the Newton-Raphson method (Vo-0 moles/h as initial guess) and ,-0.1%, obtain the molar flow rate for the liquid and vapor phase that are produced in the flash tank under those conditions and compare your answer with any MATLAB built-in function. You may use the following data taken from the DePriester chart at 50 and P = 200 kPa: omponent Kyx 7.0 n-C5H12 0.80 n-CGHi4 0.30

Explanation / Answer

Setting up of mass balance equaiton for the gigen probelm

Let propane be component 1 , butane be component 2, pentane be component 3 and hexane be component 4

Let F be the feed flow rate , L be the bottom flow rate coming out of the flash column , V be the top flow rate coming out of the column

Let Xfi be the mole fraction of Component 'i'present in feed

Yi be the the mole fraction of Component 'i' present in Vapor phase

Xi be the mole fraction of Component 'i' present in liquid phase

Now we will write overall mass balance

F = L + V. .......1

Now we will write component balance for all the 4 compnents

Component balance for 1st compoennt

F*Xf1= V*Y1 + L*X1. .....2

For component 2

F*Xf2 = V*Y2 + L*X2 .....3

For component 3

F*Xf3 = V*Y3 + L*X3 . .......4

For component 4

F*Xf4= V*Y4 + L*X4 .....5

Now we are provided Ki values hence we can form another 4 equaitons

Yi/Xi = Ki

Y1 = K1*X1

Y2= K2*X2

Y3=K3*X3

Y4=K4*X4

Hence with this we will get additional equaitons

Now our mass balance is ready to solve the above problem

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