Recent Question/Assignment

Thermaldynamic
PROC2080 PROCESS THERMODYNAMICS
Assignment (30%)
Submission deadline: Tuesday 09/06/2020 at 11:55 pm
Submit your work in Canvas before the deadline. Do not email your work. Late submission will not be accepted.
• All components in this assignment add up to a mark of 100 points which corresponds to the weight of this assignment (30%).
• You may choose to (i) work individually and submit the work on your own, or (ii) work in pair and submit a joint report, for assessment. For the latter, you may choose who you want to work with.
• Your report MUST include the following three components:
1. A typed Summary Header (the template is available for download in the assignment page) [5 points],
2. A scanned copy of your handwritten work that clearly articulates the method used and the calculations performed in answering the assignment question [85 points, see the breakdown in the question page], and
3. Raw calculations – This assignment requires iterative calculations and the use of spreadsheets to perform such calculation is recommended. All raw calculations including iterative calculations performed in spreadsheets must be appended and submitted as a separate file. [10 points]
The importance of bubble point and dew point calculations
Four common types of vapor-liquid equilibria calculations are illustrated by the four quadrants in Figure 1. In a bubble-point calculation, the liquid-phase mole fractions of the system are specified, and the vapor mole fractions are solved for. The solution represents the composition of the first bubble of vapor that forms when energy is supplied to a saturated liquid.
Figure 1. Common VLE calculations.
Conversely, in a dew-point calculation, the liquid mole fractions are determined given the vapor mole fractions. This case corresponds to the composition of the first drop of dew that forms from a saturated vapor. Bubble- and dew-point calculations are represented by the two columns in Figure 1. In addition to knowing the composition, the value of either the temperature or the pressure needs to be specified to constrain the state of the system. The former case is represented by the first row in Figure 1, while the latter case is represented by the second row. Hence, the grid in Figure 1 represents four typical combinations of independent and dependant variables found in VLE problems. They are defined by the quadrants I, II, III, and IV for reference in the examples and problems presented in Modules 6-8 of this course.
When confronted with such a calculation, it is important to identify the independent and dependent variables systematically. For binary systems that follow Raoults law, it is possible to solve for the vapour and liquid mole fractions when temperature and pressure are known.
Before you attempt the problem in this assignment, it is important that you get yourself familiarised with the materials and concepts presented in Sections 12.1 – 12.3 and 13.1 – 13.5 of SVAS. Section 13.3 of SVAS provides the method and the techniques to support the calculations in this assignment. In addition, the approaches and iteration techniques adopted in the following examples are highly relevant to the problem in this assignment:
• Example 13.1 in the prescribed textbook,
• Example 6 in the pre-lectorial screencast of Module 6, and
• Example 3 in the pre-lectorial screencast of Module 7.
Assignment question
The Wilson model is versatile and has been widely adopted to describe the VLE behaviour of many binary mixtures including the mixture of methanol (1)/acetone (2). The Wilson equation, like the Margules equations, contains just two parameters for a binary system.
?
ln(????1) = - ln(????1 + ????2?12) + ????2 12
????1 + ????2?12 ?21
-
????2 + ????1?21 (1)
?
ln(????2) = - ln(????2 + ????1?21) -????1 12
????1 + ????2?12 with ?21
-
????2 + ????1?21 (2)
????2 (-????12)
?12 = ???? ????????
????1 ????1 (-????21)
?21 = ???? ????????
????2
Alternatively, a simpler model developed by Wilsak et al. can be used for methanol (1)/acetone (2) mixtures.
Wilsak et al. successfully developed a set of two-parameter (or three-suffix) Margules equations to model the VLE behaviour of methanol (1)/acetone (2) mixtures over a wide range of temperatures. However, the coefficients of infinite-dilution (????12 and ????21) in their two-parameter Margules model are not constant. To reflect the temperature dependent nature of ????12 and ????21, Wilsak et al. introduced two temperature dependent parameters ???? and ???? to replace ????12 and ????21, respectively. Using the terms ???? and ????, the activity coefficients (????????) can be calculated from Equations (3) and (4) at different temperatures:
????????(????1) = ????22[???? + 2????1(???? -????)] (3)
????????(????2) = ????12[???? + 2????2(???? -????)] (4)
where ???????? is the activity coefficient for component ????
???????? is the mole fraction of component ???? in the liquid phase
Using Equations 5 and 6, the values of ???? and ???? can be calculated based on the system temperature, ????, in Kelvin scale.
-79000 927
???? = 2 + ???? - 1.497
???? (5)
-79000 804
???? = 2 + ???? - 1.064
???? (6)
You may assume the validity of the modified Raoult’s law and use the two parameter Margules equations developed by Wilsak et al. in your calculations. Parts (b) – (e) require iterative calculations.
a) Quadrant II calculation – Calculate the bubble point pressure and the vapour composition when ????1 = 0.69 and ???? = 60 ?. [5 points]
b) Quadrant I calculation – Calculate the dew point pressure and the liquid composition when ????1 = 0.69 and ???? = 60 ?. [10 points]
c) Quadrant III calculation – Calculate the bubble point temperature and the vapour composition when
????1 = 0.28 and ???? = 101.325 ????????????. [20 points]
Suggestion: Based on the equation, ???????????????????????? = ????1????1????1???????????? + ????2????2????2????????????, set up the iteration in the form:
????1
????????????|????+1 = ????1????1 +????????????????????????????2????2 ????1????????????????????????||???????? (7)
????2
where ???? represented the ????th literation. You can apply Equation (7), a new saturation pressure of component 1, i.e. ????1????????????|????+1, can be iterated from a set of old saturation pressure values i.e. ????1????????????|???? and
????2????????????|????.
d) Quadrant IV calculation – Calculate the dew point temperature and the liquid composition when ????1 =
0.57 and ???? = 101.325 ????????????. [20 points]
Suggestion: Based on the equation,
1
???????????????????????? = ????1????????11 + ????2????????????
???????????? ????2????2
set up the iteration in the form:
????
????1????????????|????+1 = ???????????????????????? ????11 + ????????22 ????????21????????????????????????||???????? (8)
where ???? represented the ????th literation. Using equation (8), a new saturation pressure of component 1,
i.e. ????1????????????|????+1, can be iterated from a set of old saturation pressure values, i.e. ????1????????????|???? and ????2????????????|????.
e) Show that methanol and acetone will form an azeotrope at ???? = 313.15 ????. Hence, determine the pressure (????????????????????????????????????????) and the compositions of liquid and vapour at which this azeotropic mixture is formed. [30 points]
Reference
R.A. Wilsak, S.W. Campbell, G. Thodos, Vapor-liquid equilibrium measurements for the methanol-acetone system at 372.8, 397.7 and 422.6 K, Fluid Phase Equilibria (1986), 28(1), 13-37.

Looking for answers ?