Rates depending on "external" variables

[speth]

Transitioning side discussion from #2

@BoyangMichael asked:

In the ExtensibleRate class, is it possible to define a rate expression depending on an "external" variable (not just on T,P)? For example, k = x A exp(-Ea/RT)? Where x is a variable not in the mechanism, but rather a physical variable to model. Thank you very much in advance!

@speth replied:

Generally no, that's not currently possible. I think that would be a different enhancement proposal (which you're welcome to open). Having some concrete use cases would help think through the interface and how it would have to interact with other classes like ThermoPhase and Reactor.

@ischoegl replied:

I believe you can implement k = x A \exp(-Ea/RT) with a CustomRate, see https://cantera.org/dev/python/kinetics.html#customrate

It is not as formalized as ExtensibleRate, but may just work (the lambda function takes T as an argument, but can depend on other parameters that are in scope; at least if I recall correctly)

[speth]

While you can define either a CustomRate or ExtensibleRate so that it captures other variables as part of a closure, the problem is one of synchronization. The Kinetics object assumes that CustomRate depends only on temperature, and will re-use a cached value for the rate constant if the temperature of the mixture hasn't changed. In Cantera 3.0, ExtensibleRate is subject to similar caching based on the full ThermoPhase state, but that has been relaxed in the current main branch. So you may be able to do this with some combination of an ExtensibleRate and an ExtensibleReactor defined in the same scope, but this would be kind of a hack. Even then, I think you may risk running into some of the problems described in #201.

I think a relatively clean and flexible way to support this would be to introduce a way of attaching auxiliary state variables to a ThermoPhase object. In the case of a reactor network, updating these variables would be the responsible of the corresponding Reactor class (which would need to be an ExtensibleReactor or some other user-defined type). This approach should work both for the case where the extra variables are just parameters (for example, functions of time), or are additional state variables that need to be integrated in time.