ThermoSolver
An Integrated Educational
Thermodynamics Software Program
Connelly Barnes
What is ThermoSolver?
•
Programmed by Connelly Barnes.
•
Software program used to teach Chemical
Engineering (ChE) thermodynamics.
•
Available for free from Web (Google it).
•
Allows students to "explore"
thermodynamics
–
make nontrivial
calculations, and compare different
thermodynamic models.
Motivation
•
Thermodynamic equations can become
complicated, must be solved by lookup
tables or computer algorithms.
•
Tables are available for a limited set of
pure species.
Motivation (continued)
•
Computer solutions: spreadsheets, scripts,
Computer Algebra System worksheets can
be used, but it's hard to let the student use
different number of species,
thermodynamic models, etc.
•
We would like students to not have the
burden of programming every solution,
especially for routine calculations.
Objectives
•
Standalone educational software program.
•
Easy to use interface
–
reduce all
"barriers" to using the software.
•
Research and develop algorithms needed
to solve equations.
•
Integrate with chapter problems in
Engineering and Chemical
Thermodynamics
by Milo Koretsky.
Use at Universities
•
At OSU, ThermoSolver used in ChE
thermo course, graduate reactors course,
plant design.
•
In plant design, ThermoSolver not
specifically named, but 10/39 students
used it.
•
Don't track usage by other Universities,
but Web search reveals it has been used
at Univ. Notre Dame, Indiana and Univ. of
Colorado at Boulder.
Features
•
Database, 350+ chemical compounds.
•
Calculate saturation pressure, temp.
•
Solve equations of state (LK and PR).
•
Find pure, mixed fugacity coefficients.
•
Fit excess Gibbs energy models to
experimental data.
•
Bubble point and dew point calculations.
•
Plot phase diagrams for binary systems.
Features (continued)
•
Calculate
K
eq
for single chemical reaction.
•
Multiple chemical reaction equilibria.
•
Plotting.
•
HTML docs provided, numerical methods
and equations described.
Tour of Program:
Saturation Pressure Calculator
•
Solve for saturation pressure or saturation
temperature.
•
Saturation pressure/temp determines
where liquid/vapor phase transition occurs.
•
Example problem: Find saturation
pressure of 1,4

dioxane (C
4
H
8
O
2
) at 50
o
C.
Tour of Program:
Equation of State Solver
•
Finds one of the state properties pressure,
molar volume, or temperature given the
other two, using the LK or PR equations of
state.
•
Example problem: Find molar volume of
propane at 35 bar and 50
o
C. Compare w/
ideal gas: 0.77 L/mol.
Tour of Program:
Fugacity Coefficient Solver
•
Finds the pure fugacity coefficient or the
fugacity coefficient of a species in a
mixture, using the LK or PR equation of
state.
Tour of Program:
Fugacity Coefficient Solver
Tour of Program:
Models for excess Gibbs energy
•
Fits activity coefficient models to
experimental data for binary Vapor

Liquid
Equilibrium (VLE) systems.
•
Objective function.
•
Example: Chloroform

heptane.
Tour of Program:
Bubble point / Dew Point Calculator
•
Dew point: gaseous system, when first
drop of liquid forms
–
achieved by
decreasing temperature or increasing
pressure.
•
Bubble point: liquid system, when first
bubble forms.
•
Solver finds temp./pressure where first
bubble or dewdrop forms, and composition
of chemicals in bubble or dew

drop.
Tour of Program:
Bubble point / Dew Point Calculator
Tour of Program:
Binary Phase Diagrams
•
Make plots of phase transitions in binary
vapor

liquid systems.
•
Example: Plot pressure vs. liquid mole
fraction for methylcyclohexane

benzene
system at 50
o
C.
Tour of Program:
Equilibrium Constant Solver
•
Finds
K
T
at a single temperature, for a
single chemical reaction.
•
Plots
K
T
vs
T
.
Tour of Program:
Equilibrium Constant Solver
Tour of Program:
Multiple Chemical Reaction Equilibria
•
Gas

solid equilibrium.
•
Found by minimizing excess Gibbs energy.
Tour of Program:
Multiple Chemical Reaction Equilibria
Tour of Program:
Multiple Chemical Reaction Equilibria
Numerical Algorithms
•
Newton root finder with backtracking.
•
Downhill simplex method for minimization.
•
Iterative substitution.
Multidimensional Newton Method
•
Vector

valued function
F
:
R
n

>
R
n
.
•
Newton step
•
Iterate
Newton Backtracking
•
Use full Newton step
δ
if norm

F

2
is less
than its value at
x
i
, otherwise try
δ
/2
, δ
/4,
δ
/8, ...
until

F

2
is less than its value at
x
i
.
•
This is guaranteed to happen, as
δ
is a
descent direction for

F

2
.
Simplex Method
•
J.A. Nelder and R. Mead, "A simplex
method for function minimization,"
Computer Journal 7 (1965) 308

313.
•
Simple, derivative free method for finding
minimum of function of form
F
:
R
n

>
R
.
•
Does not use derivatives, so constrained
minimization possible by setting
F
to
infinity.
Algorithms
•
Equation of state solver: Newton method.
•
Excess Gibbs energy model fitting: Simplex.
•
Bubble point / dew point: Custom iterative
methods based on those of Smith, Van Ness,
and Abbott.
•
Multiple chemical reaction equilibria: Newton
and simplex. Typically converges, however
Dr. Koretsky found a problem where this
method does not converge.
Conclusion
•
Objectives met?
•
User interface is straightforward to use.
•
Numerical methods converge with one
known exception.
•
A practical tool integrated with problems in
a textbook.
Acknowledgements
•
Milo Koretsky, Mentor.
•
Rubin Landau, Computational Physics.
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