homework5 - PGE 312 – Homework 5 Solutions ...

Info iconThis preview shows page 1. Sign up to view the full content.

View Full Document Right Arrow Icon
This is the end of the preview. Sign up to access the rest of the document.

Unformatted text preview: PGE 312 – Homework 5 Solutions Problem 12 ­1 To determine the liquid fractions, start with Raoult’s law: ∑!! = ∑!! !!" = ! ! = !! !!! + !! !!! Since x1+x2 = 1, ! − !!" !! = !!" − !!" and ! − !!" !! = !!" − !!" To determine the vapor fractions, use Dalton’s law: !! = !! ! Substitute for P in Raoult’s law: !!" !! = !! ! Substituting for xj from above, ! − !!" !!" !! = !!" − !!" ! ! − !!" !!" !! = !!" − !!" ! Problem 12 ­7 Component lb MW ni zi Pvap ziPvap zi/Pvap 2,2 ­dimethylbutane 3 86.17 0.0348 0.6653 9 5.9884 0.0739 2,2,4 ­trimethylpentane 2 114.23 0.0175 0.3346 1.75 0.5855 0.19121 ∑!! !!,!"# = !! = !. !"!"#  ! ! = !! = !. !!!"# ∑! ! !,!"# PGE 312 – Homework 5 Solutions Problem 12 ­12 Find zi’s 1 SCF n ­butane (C4) 2 SCF n ­pentane (C5) Note: SCF is proportional to number of moles. Therefore SCF fraction = mole frac. !!"# !! = = !. !!! ! + !!"# !!"# !! = = !. !!! ! + !!"# Bubble point calculation First, calculate the bubble and dew points as if it was an ideal mixture. These will be your initial guesses to begin iteration on the K ­factors: Component zi Pvap zjPvap zj/Pvap c4 0.666 27 17.982 0.024666667 c5 0.333 7 2.331 0.047571429 SUM: 20.313 psi 13.843 psi First guess Kj @ 60F and 20 psi: Component Zi Ki ZiKi C4 0.666 1.2 0.7992 C5 0.333 0.35 0.11655 SUM: 0.91575 We can see that the sum of ziKi is too low, and should approach unity, thus guess again at P = 19 psi, and obtain the K ­factors from Appendix A for 60F and 19 psi: Component Zi Ki ZiKi C4 0.666 1.3 0.8658 C5 0.333 0.38 0.12654 SUM: 0.99234 The sum is approximately 1. Without an equation to describe the K ­factor dependence on temperature and pressure, this is the best we can do. Thus: !! = !"!"#$ PGE 312 – Homework 5 Solutions Dew Point Calculation Begin by a starting pressure guess of 14 psi. Obtain the K ­factors for the two components at 60F and 14psi from Appendix A in your text: Component Zi Ki ZiKi C4 0.666 1.8 0.37 C5 0.333 0.5 0.666 SUM: 1.036 Thus, !! = !"!"#$ Compute compositions and volumes of gas and liquid at 60F and 14.7 psia K4 = 1.75 K5 = 0.48 The flash calculation is performed using goalseek on the gas phase mole fractions such that: !! ∑!! = ∑ = 1 1 1 + !! ! − 1 ! Zi Ki xi yi C4 0.666 1.75 0.412662481 0.722159342 C5 0.333 0.48 0.57977988 0.278294342 0.992442361 1.000453684 Goal ­seek converged on the following values for !! and !! : !! = !. !"!# !! = !. !"!# To determine the volume of liquid and vapor simply multiply the above values by the total number of moles in the mixture: 1.198!"#$% !!"!#$ = 3!"# ∙  = 3.594!"#$% !"# Thus: PGE 312 – Homework 5 Solutions !! = !. !"!# ∙ !. !"#!"#$% = !. !"#!!! !"# !"#$% !. !"# !"# !! = !!!! − !. !"#!!! = !. !"#!!! !"#$"% Problem 12 ­14 This is a simple flash calculation. Follow the procedure for goal ­seek outlined in the previous problem: Component zi Ki yi xi C3 0.65 1.42 0.772191082 0.543796536 n ­C4 0.35 0.55 0.243439772 0.442617768 n ­C5 0.05 0.23 0.017914168 0.077887686 SUM: 1.033545022 1.06430199 Again, a trial ­and ­error approach yielded the following: !! = 0.535 !! = 0.465 Problem 12 ­17 a) Bubble Point Pressure Calculation First, determine the number of moles: Components Mass, lb MW n zi (lb/lbmol) C3 25 44 0.568181818 0.465394982 n ­C4 15 58 0.25862069 0.211834957 n ­C5 20 72 0.277777778 0.227526436 n ­C6 10 86 0.11627907 0.095243624 As in previous problems, do iterate P to find an acceptable solution: Component Zi Ki ZiKi C3 0.465394982 1.7 0.79117147 n ­C4 0.211834957 0.65 0.137692722 n ­C5 0.227526436 0.27 0.061432138 n ­C6 0.095243624 0.11 0.010476799 SUM: 1.000773129 PGE 312 – Homework 5 Solutions !! = !""!"#$ b) Composition of vapor at bubble point At the bubble point, !! ≅ 0, thus !! !! = !! Component yi C3 0.79117147 n ­C4 0.137692722 n ­C5 0.061432138 n ­C6 0.010476799 c) What is the dew-point pressure? Component C3 n ­C4 n ­C5 n ­C6 Zi 0.465394982 0.211834957 0.227526436 0.095243624 Ki 4.2 1.58 0.64 0.24 SUM: Zi/Ki 0.110808329 0.134072758 0.355510056 0.396848435 0.997239578 !! = !"!"#$ d) What is the composition of the liquid at the dew point? At the dew point, !! = 0, thus !! = !! /!! : Component C3 n ­C4 n ­C5 n ­C6 xi 0.110808329 0.134072758 0.355510056 0.396848435 e) Calculate the composition of the liquid and the gas at 150 psia Component C3 n ­C4 n ­C5 n ­C6 zi Ki 0.465394982 2.2 0.211834957 0.83 0.227526436 0.34 0.095243624 0.13 SUM: yi 0.68623925 0.188996039 0.106058388 0.019247118 1.000540795 xi 0.311926932 0.227706071 0.311936435 0.148054756 0.999624193 PGE 312 – Homework 5 Solutions f) Calculate the masses of the two phases at 150 psia First, calculate the average molecular weight of each phase: Component MW ML MG C3 44 13.724785 30.19452701 n ­C4 58 13.2069521 10.96177024 n ­C5 72 22.45942333 7.636203933 n ­C6 86 12.73270898 1.655252168 SUM: 62.12386942 50.44775335 !! = !! ∙ !!"!#$ ∙ !! = !. !" ∙ !. !!" ∙ !". !" = !!. !"!" !! = !! ∙ !!"!#$ ∙ !! = !. !" ∙ !. !!" ∙ !". !! = !". !"!" Problem 12-19 Component Composition Mole Fraction Ki ! 30 Methane x 1+! .1 0.55 n ­C4 0.1 1+! .3 0.195 n ­C5 0.3 1+! .6 0.065 n ­C6 0.6 1+! The criteria for reaching bubble point is such that ∑!! !! = 1. We wish to determine the amount of methane we can add (at 100F) such that the vapor pressure of the solution, does not exceed the applied pressure of 100 psia. That is, we want to determine how much methane we can add to create a solution with a bubble point at 100F and 100 psia. ∑!! !! = 1 = 0.55 0.1 0.3 0.6 ! + 0.195 + 0.065 + 30 1+! 1+! 1+! 1+! Solving for x, ! = 0.02922 Solubility is then defined as follows: !"!"#$!$%& = ! !"!"#$!"#$%&" = !. !"#$ !+! !"!"#$!"#$%&' ...
View Full Document

This note was uploaded on 11/25/2011 for the course MATH 325K taught by Professor Shirley during the Spring '11 term at University of Texas at Austin.

Ask a homework question - tutors are online