Chapter 14-Part VII Applications of VLLE

problem Toluene (1) and water (2) are essentially immiscible as liquids. Determine the dew point T and the composition of the first drop of liquid formed when vapor mixtures of these species with mole fractions z1 = 0.2 and z1 =0.7 are cooled at constant P of 101.33 kPa. What is the bubble point T and the composition of the last bubble of vapor in each case?

Let’s first find T* Since the liquids are immiscible, x1b =1, x2a =1 We solve the equation to find T*, using Antoine equations T*= 84.3 oC Then y1* = x1b P1sat/P = 0.444 Therefore, one of the z1 is at the left and the other at the right of y1*

For z1 < y1*  the first liquid is pure 2

Lets write the VLE equations For the first composition, y1 = 0.2, solve for T T=93.85 oC

For z1 > y1*  the first liquid is pure 1

Again, write VLE equations Now, use the first equation with y1 =0.7 and solve for T T=98.49 oC Note that the bubble point temperature is T* and the mole fraction of the last vapor is y1*

Second problem Consider a binary system of species 1 and 2 in which the liquid phase exhibits partial miscibility. In the regions of miscibility, the excess Gibbs free energy at a particular temperature is expressed by the equation: The vapor pressures of the pure species are 75 kPa and 110 kPa respectively (comp. 1 and 2). Prepare a P-x-y diagram for this system at the given temperature

What type of diagram do we expect?

Lets find the solubility limits For the simple GE model, the activity coefficient equations are: For LLE and this model, because the solubility curves are symmetric about x1 = 0.5, see equation E in example 14.5 Solve for x1a = 0.224; and x1b = 0.776 (only because the model is symmetric!!!)

Now find the 3-phase equilibrium point P* =160.7 kPa y1* =0.405 Now draw the actual diagram

Calculate VLE in the 2-phase regions First solve for P (for increasing x1b values) and for the corresponding y1 Similar procedure for the a-V equilibrium

Third problem The system water (1)-n-pentane (2)-n-heptane (3) exists as a vapor at 101.33 kPa and 100oC with mole fractions z1 = 0.32, z2 = 0.45, z3 = 0.23. The system is slowly cooled at constant P until it is completely condensed into a water phase (b) and a hydrocarbon phase (a) . Assuming that the two liquid phases are immiscible, that the vapor phase is an ideal gas, and that the HCs obey Raoult’s law, determine: a) the dew-point T of the mixture and the composition of the first condensate.

Calculate dew point T and liquid composition assuming the hydrocarbon layer (a) forms first: Only two components in the HC phase (a phase) : components 2 and 3; VLE for the HC phase Since there are 3 unknowns Tdew 1, x2a and x3a, we need only 3 equations, Use the last three because the first is a combination of the 2nd and 3rd Solve for Tdew 1 ; x3a ; x2a

Calculate dew point T assuming the water layer (b) forms first: x1b =1 Solve for Tdew 2; Tdew 2 = 70.85 oC Then Tdew 1 =65.12 oC; Tdew 2 = 70.85 oC Since we are cooling, we will find Tdew 2 first, the water layer will form first

Next step explanation In the previous two slides we determined which phase condenses first.  In the vapor phase the compositions were z1, z2, and z3. We found out that water condenses first.   Next, we have a system that has vapor (water, C5 and C7) coexisting with a liquid water phase (pure water).  Now we want to find out at what temperature the second phase is going to condense.  The vapor composition has changed because some water is being condensed, but the HC components have not condensed yet, so for them, their compositions must be in the same ratio as the original: y2/y3 = z2/z3, at the temperature where the first drop of HC phase shows up.

b) What is the temperature at which the second layer forms 6 equations and 6 unknowns y1, y2, y3, T dew 3, x2a, x3a y1= 0.24, y2 =0.503, y3 =0.257, T dew 3 = 64.298 oC, x2a = 0.21, x3a = 0.79

Last step Finally (next slide) we calculate the bubble temperature where we have the two phases with their final liquid compositions, (x1 = 1 for the water phase), x2=z2/(z2+z3) and x3=z3/(z2+z3) for the HC phase, and we can calculate the composition of the last vapor.

c) Calculate bubble point given the total molar composition of the two phases Find T (bubble point) = 43.94 oC And compositions of the last bubble of vapor