We are interested in determining the vapor-liquid equilibria for the system of n

Question

We are interested in determining the vapor-liquid equilibria for the system of n-Butane and n-Pentane at 14.7 psia. You may assume that the mixture behaves ideally and Raoult's law can model it's properties. Use Antoine's equation for the vapor pressure. Calculate the boiling points of the two pure substances at this pressure. Use about 8 points (including the boiling points and approximately well- spaced) and plot the Txy diagram. For this, you may use Excel. However, you are expected to use one representative temperature and show how the calculations are done. You can print out the plot and table from Excel. A 40/60 (butane/pentane) mixture flowing at 100 kmol/h and 14.7 psia is heated so that 50% of the feed is vaporized. Assuming the vapor and liquid streams are in equilibrium, calculate the flow rates, composition of the vapor and the liquid. Also calculate the temperature of the vapor leaving the system.

Explanation / Answer

Antoine constants :

n-pentane, ln Psat( Kpa) = 13.7667-2451.88/(T-41.136) butane   lnpsat( kpa): 13.6608-2154.70/(T-34.611), t is K

14.7 psia= 101.3 Kpa

At this pressure , for n-pentane ,ln(101.3)= 13.7667-2451.88/(T-41.136)

4.62= 13.7667- 2451.88/(T-41.136)

2451.88/(T-41.136)= 9.1467. T-41.136= 2451.88/9.1467= 268.06, T= 268.06+41.136= 309.2 K

For n-butane, 4.62= 13.6608- 2154.7/(T-34.611),

2154.7/(T-34.611)= 13.6608-4.62= 9.0408

T-34.611= 2154.7/9.0408= 238.33, T= 238.33+34.611= 272.9K

The boiling point of mixture of these compounds lie between 309.2 K and 272.9 K

Assume some temperature between 272.9 and 309.2 and calculate P1sat and P2sat.

Since y1P=x1p1sat and y2P= x2p2sat , addition of these equations gives P= x1p1sat+x2p2sat

Since x2= (1-x1), P= x1p1sat+(1-x1)p2sat

(P-P2sat)/(P1sat-p2sat)= x1 . Calculate x1, then calculate y1 from y1P=x1p1sat. The Calculations are shown below along with the graph.

given x1=0.4 and x2=0.6

x1p1sat +x2p2sat= 101.3 Kpa

assume a temperatuere such that the above equation is satisfied. The calculations done in excel are shown

y1=0.712 and y2= 0.287 T= 16.17 deg.c

since F= V+L ( overall balance)

100= V+L

50% of the feed is vaporized, V= 50

L= 50

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