Thermodynamic Computation Systems
Why study Thermo of mixtures: Motivation
-Example, i.e. SCF measurements, others?
-UO
UO systems (discuss general PFD and where separations fits in
plus other things like HT, MT, staged processes, etc)
-Simulators: AspenPlus,
p
, Fluent,, Comsol,, ChemSep,
p, others.
1
2
Course Overview
- Homework given
Clix
Course Overview
3
Course Overview
------16 Dec 2009
4
Course Overview
Chapter 5
Chapter 6
-
Thermodynamic Web
Departure Functions
Review Equations
q
of state (chapter
( p 4,, briefly)
y)
Equilibrium (chemical potential)
* Pure Component
* Mixtures
Chapter 7
- Fugacity (chemical potential  fugacity  equilibrium calculations)
* Vapor (overview), liquid, solids
- Activity Coefficients [Fugacity Coefficients (overview)]
Chapter 8
- Phase
h
Equilibrium
ilib i
* Diagrams
* Vapor – Liquid (VLE)
* Liquid
Li id – Liquid
Li id (LLE)
* Solid – Liquid (SLE)
Chapter 9
- Reaction Equilibria
5
Lecture 2
Chapter 5
- Review Equations of State (chapter 4)
- Thermodynamic
y
Web
- Departure Functions
6
7
Equations of State
Simplest:
PV =nRT
or
P=RT
When Ideal Gas Law not valid, account for:
1) size of molecules that interact
2) specific interactions (attractive forces)
Non-Ideal, or “Real” gases (how do we describe these)
•P  = Z R T
RT
•P
v  b 
Z – Compressibility Factor
RT
a
P
 2
v  b  v
vdw EOS
(van der Waals)
(1873)
Equations of State
RT
a
P
 2
v  b  v
Pv 3  ( RT  Pb)v 2  av  ab  0
vdwEOS cubic in 
1 real root
T > Tc
3 reall roots
T < Tc
T
 smallest is  liquid phase
 largest is  vapor phase
Where do we get values for a and b
•Data
D t (PvT);
(P T) regression
i
•Corresponding States Theory
27 RTc 
a
64 Pc
2
RTc
b
8Pc
8
Example
C l l t the
Calculate
th vdw
d constants
t t a andd b for
f ttoluene
l
Example
Calculate the vdw constants a and b for toluene
Example
P = 1 bar
v [m^3/mol]
Superheated
water:
0.08
Pressure [bar]
1
P = 10 bar
10
0.008
Data stm
tables
50
Ideal 1
Ideal 10
Ideal 50
vdw-50
P = 50 bar
0.0008
200
400
600
Temp [oC]
800
1000
12
Modern Cubic Equations of State
Based on vdw EOS
•Redlich Kwong (RK)
RT
P
 attractive forces
v  b 
a
1

T vv  b) 
1873
1949
•Souve-Redlich Kwong (SRK)
a *  (T )

vv  b 
1972
•Peng
Peng Robinson (PR)
a * (T )

vv  b   bv  b 
1976
Modern Cubic Equations of State
•Redlich Kwong (RK)
0.42748 R 2Tc2.5
a
Pc
0.08664 RTc
b
Pc
•Peng Robinson (PR)
0.45724 R 2Tc2
a
Pc


 (T )  1   1  TR
0.07780 RTc
b
Pc

2
  0.37464  1.54226   0.26992  2
13
14
Other Equations of State
Virial (derived from 1st principles with statistical mechanics)
Pv
B C D
Z
 1  2  3       
RT
v v
v

 ( r )

( kT )  2
B  2N A  1  e
 r dr

0
Benedict-Webb-Rubin (modified virial EOS)
1940
Ao
Co  1 
a   2 a 5

Z  1   Bo 

v 
v  b 
v 
3 
RT RT 
RT 
RT


      
1  2  exp  2 
3 2 
RT v  v 
 v 
1901
EOS Summary
3 classes of Equations of State:
• Virial – 2nd/3rd order can represent non ideal gases, but not
liquid properties
•Semi-theoretical [analytic] (i.e. PR, SRK) – represent vapor
and liquid
q
behavior for certain ranges
g of T & P for manyy
substances
•Emperical [non-analytic] (i.e. BWR, Wagner) – represent
broader range of T & P for vapor and liquid substances, but
more fitting parameters required.
Poling, B.E., J.M. Prausnitz, and J. P. O’Connell, “The Properties of Gases and
Li id ” McGraw-Hill,
Liquids”,
M G
Hill 5th Edition,
Editi New
N York
Y k (2001)
15
Liquid Densities
•Measure in the lab
•Compiled data
•BWR reasonable estimates for hydrocarbons
•Compressibility charts (Lee-Kesler extension of BWR EOS)
•Correlations
Rackett equation
q
((liquid
q
volume at saturation))
v
l , sat
1 1T 2 7 
RTc
0.29056  0.08775   R 

Pc
16
Liquid Densities
•P
P=ZRT
Z  Z ( 0)   Z (1)
Z ( 0) Contribution from simple molecules
Z (1) Contribution due to nonsphericity
Z functions depend only on TR and PR
Z functions available via:
•Charts
•Tables
•Equations
E ti
17
Liquid Densities
Z ( 0)
18
Liquid Densities
Z (1)
19
Z ( 0)
Liquid Densities
20
Liquid Densities
21
Liquid Densities
Thermosolver program
22
Liquid Densities
Compiled
data:
23
Liquid Densities
Compiled
data:
24
Problem Solving Exercise
Determine the density of n-butane
n butane at 50 bar and 60 oC.
C
General information:
3
m
 bar
5
R  8.314 *10
mol  K
25
Example