# ThermoSolver - Connelly Barnes

Μηχανική

27 Οκτ 2013 (πριν από 4 χρόνια και 8 μήνες)

87 εμφανίσεις

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.

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 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
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

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.