Modelling chemical reactins for chemical formulae

[masseys@bre.co.uk]

Dear Systems Dynamic Community,

re: Modelling chemical reactions from reaction equations


I am interested in using SD to model chemical reactions from the appropriate
system of chemical equations and the reaction rates. From looking at the SD
modelling programmes with their stocks and flows it would seem reasonably
straight forward to model the reactions. However, not being familiar with SD
techniques I would value some help in starting out in this direction. Are there
any papers or text books dealing with this subject ?

I note that all the VenSim examples come mostly from basic physics where the
differential form of the problem is standard fare.

Since solving the chemical equations is effectively solving a system of linear
equations I presume that there must also be a means of solving (or simulating)
linear and non-linear systems of equations using SD.

Dr S W Massey
Building Research Establishment
Garston, Watford, WD2 7JR. UK.
Tel : +44 1923 664297
Fax : +44 1923 664786
e-mail : masseys@bre.co.uk

[Mats Svensson]

I can recommend the Elsevier Journal Ecological Modelling for several
projects where SD has been used and where it has been used to solve
chemical equations. Many of the papers also include SD diagrams, a thing I
think is very nice instead of these tiresome (and linear) rows of
differential equations.

For some more introductory examples see the following;
The nice book by Bruce Hannon and Mattias Ruth - Modeling dynamic
biological systems, published by Springer 1997, as well as their previous
book, includes examples of chemical reactions solved by SD tools (in this
case, STELLA).

Leonard Soltzbergs book The Dynamic Environment (1996, University Science
Books) also covers chemical examples.

Well, that was a few.

All the best & good luck

Mats Svensson

_______________________________________________________________
Mats G E Svensson e-mail: mats.svensson@chemeng.lth.se
Dept. of Chemical Engineering, LTH phone (office): +46-(0)46-222 04 08
Box 124 phone (mobile): +46-(0)70-58 707 59
S-221 00 LUND phone (home): +46-(0)46-12 83 97

["Magnus Sterky"]

Dear Mr. Massey

Should your interst in Chemical reactions SD also include the process
plant, you may find the SW you need at :
http://www.vtt.fi/aut/tau/ala/apros.htm

/Magnus
From: "Magnus Sterky" <magnus.sterky@mailbox.hogia.net>

["Richard G. Dudley"]

The book "Dynamic Modeling" by Hannon and Ruth has some chemistry examples of the
type you are asking about.

--
Richard G. Dudley

rdudley@indo.net.id
http://home.indo.net.id/~rdudley

[Peter Bispham]

Although I dont know exactly which chemical systems you are dealing with,
I thought I would respond with a description of how our simulation modeling
package, ModelMaker, can be effective for solving chemical reactions.

An example of the use of ModelMaker for this purpose is contained on the
web page:

http://www.cherwell.com/modelmaker/mm-kintu2.html


This page contains an description of how to use ModelMaker to simulate:

* First order chemical reactions
* Consecutive reactions
* Reversible reactions
* Second order reactions
* The effects of independent events


Brief example: If we have the reaction A + B -> C.

Modeling this reaction may be done by introducing the variable "extent of
reaction". Call this variable x, with x a function of time x=x(t), and
initially set x = 0.
If at time t=0 we have concentrations of reactants Ao and Bo, then the
concentrations of reactants at time t are Ao-x(t) and Bo-x(t).

The equation governing the change in reaction is then:

dx(t)
---- = K * (Ao-x(t)) * (Bo-x(t))
dt

This model is easily constructed with ModelMaker.

Using the optimization techniques available, the parameter K of this model
may be adjusted to fit the model to experimental concentration
measurements. the model may be developed further, e.g. making K a function
of temperature etc.

A demo version of ModelMaker (and online demo guide) is available on the
ModelMaker home page:

http://www.cherwell.com/modelmaker/index.html


Examples from other diverse applications are contained on the page:

http://www.cherwell.com/modelmaker/mm-examples.html


I hope this is of some use.

Peter.


--- ---
Dr. Peter Bispham Ph.D. C.Phys. | email: peter.bispham@cherwell.com
Technical Consultant | Phone: +44 (0)1865 784800
Cherwell Scientific Publishing | Fax: +44 (0)1865 784801
Oxford OX4 4GA, UK | URL: http://www.cherwell.com
--- ---

[Peter Tebbutt]

HI all,

If I might add to my colleagues (Peter Bispham of Cherwell Scientific)
comments about modeling chemical equations (since I wrote the fairly simple
models he has listed)

Tom Fiddaman wrote

By "solving" here I assume you
>mean solving a set of simultaneous equations (i.e. to find a chemical
>equilibrium), by algebraic or other means. This is actually not standard SD
>fare - in fact its sometimes considered antithetical to the method (this
>is mainly a reaction to foolish applications of equilibrium models to
>problems that are fundamentally dynamic).

Solving a set of equations for a system in equilibrium is only a relatively
small part of modeling chemical systems - and a fairly old one at that.
Chemists are taught at a fairly early age that equilibrium is not static
but dynamic and that most reactions although related to equilibrium theory
lean so far to one side as to be easily considered a single direction
transaction.

Traditionally, systems of reactions are broken down into series of single
reactions (some forward some reverse). These are fairly idealised but the
maths works for most things so it is considered OK (as an aside, great
tracts of theory are devoted to how a single molecule reacts, but that is a
different story). This results in a series of simple differential
equations. About the most complex it gets is when we have to cosider
transport properties such as diffusion and then you get some interesting
second order equations.

A great number of chemists use anlytical methods and these are solved by
whatever means are available (Laplace transform was the favourite of my PhD
supervisor) making approximations along the way to make things easier. The
approximations are usually made depending on the actual experimental
conditions e.g at very high concentration the (relative) concentration (c)
does not change much so therefore dc/dt=0 - sweeping maybe but very
effective. Another is that short lived intermediates do not change
concentration much and so again dc/dt=0. In this way it is possible to
reduce a set of several equations down to two or three which fit the
standard model one way or another.

More and more chemists are now using simulation modeling whether it be with
prgrams such as ModelMaker from Cherwell Scientific or writing code in
Quick basic to C. The advantages are that you can keep everything intact
and allow the model to effectively make the approximations itself - in a
teaching environment you can allow students to find for themselves where
these sweeping simplifications come from and where they apply.

Using these methods it is alo easy to use the chemical equations centrally
- as a sub-model - and build up related systems (the dynamics of the
reaction vessel, all kinds of flow apparatus,reaction conditions etc.)
around these to model transfer of laboratory reactions to the pilot plant.

So I would add that SD methods are very capable of modeling chemical
systems although at a first glance it seesm that many systems are so simple
a nut as not to warrant the hammer of SD methods. However in a time when
many students do not get the training in classical mathematics that were
available and to whom diferential equations are an anathema SD modeling is
an excellent way to show how theoretical models of real systems are easily
(and usefully) derived.

So now its time for the plug - for thse interested in chemical systems I
have a text book Basic Mathematics for Chemists published by John Wiley &
Sons, much of which is devoted to the use of calculus in modeling chemical
systems. These chapters cover most of the standard chemical systems and
how complex systems are simplified.

Regards

Peter Tebbutt
Cherwell Scientific Publishing
From: Peter Tebbutt <peter@cherwell.com>

["Scholl Greg"]

You might try Anne Quaadgras; she has experience in modeling these types of
phenomena and is also likely to have a good handle on the existing literature.
She is located in New York City and is listed in the System Dynamics
directory.

Good luck,
Greg


Greg Scholl
Principal
Booz Allen & Hamilton
101 Park Avenue
New York, NY 10178

scholl_greg@bah.com

[Tom Fiddaman]

>Since solving the chemical equations is effectively solving a system of linear
>equations I presume that there must also be a means of solving (or simulating)
>linear and non-linear systems of equations using SD.

Im having a hard time dusting off my chemistry, especially because my
chemistry text is holding up my monitor. By "solving" here I assume you
mean solving a set of simultaneous equations (i.e. to find a chemical
equilibrium), by algebraic or other means. This is actually not standard SD
fare - in fact its sometimes considered antithetical to the method (this
is mainly a reaction to foolish applications of equilibrium models to
problems that are fundamentally dynamic).

Using "traditional" SD, youd have at least two options:
- Solve the system algebraically and implement the resulting equations as a
non-dynamic SD model
- Build the differential equation interpretation of the system and let it
run to equilbrium

Needless to say, SD software doesnt offer big advantages if this is all
youre doing. This kind of thing does crop up often in the context of a
dynamic model that contains a "stiff" subsystem with fast dynamics that
slow up model execution a lot unless you can replace the subsystem with its
equilibrium equivalent.

There are several ways to handle this:
- Solve algebraically for the equilibrium (as above). Frequently this is
hard or impossible.
- Link to an external model (spreadsheet, LP, ...) that solves the
subsystem in question. This can be accomplished via external functions
and/or DDE (Windows dynamic data exchange) in Vensim, via DDE in PowerSim,
and maybe in other packages as well.

Vensim also includes two functions, SIMULTANEOUS and FIND ZERO, that allow
numerical solution of nonlinear simultaneous equation systems within a
model. The standard Vensim external function library (Windows only) also
includes matrix inversion, and you can use external functions to implement
other solution methods.

A good example of this is Mosekilde et al.s model of chaos in rat kidneys.
The authors implemented the original model in Pascal, using an iterative
process to solve one subsystem of the model to equilibrium each time step.
A Vensim version of the model using FIND ZERO is available on my web site
in the model library.

>From my perspective, the biggest problem with simultaneous equations (in SD
models or otherwise) is that you lose track of causality. In a system of
equations like an economic general equilibrium model, effectively
everything is connected to everything else, and the real meat occurs in the
solution algorithm. This makes it hard to understand whats going on.
Reminds me of the quote that "time is what keeps everything from happening
all at once."

Regards,

Tom

****************************************************
Thomas Fiddaman, Ph.D.
Ventana Systems http://www.vensim.com
34025 Mann Road Tel (360) 793-0903
Sultan, WA 98294 Fax (360) 793-2911
Tom@Vensim.com http://home.earthlink.net/~tomfid/
****************************************************