Ventana software support forum

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>