Cantera/Isothermal and Nonisothermal Reactors

Begin with the Fundamentals

Let's talk fundamentals.

If we examine an infinitesimally small packet of gas, one that is so small that there are no inhomogeneities, no gradients, then the thermochemical state of that packet of gas can be fixed by specifying a number of characteristics, equal to the number of degrees of freedom of the gas's thermodynamic state - a.k.a. Gibb's Phase Rule (Wikipedia) - which is equal to:

$DOF=C-P+2$

where C is the number of components, and P is the number of phases. Because energy and reaction rates are so tightly coupled, it is important to understand how energy behaves in the reactor - when it enters or leaves the reactor, how much is generated, how it is distributed, etc.

Differential versus Integral Reactors

Differential reactors characterized by a single thermochemical state

• described by a differential equation
• small enough change that can approximate as differential
• differential change between inlet and outlet

Integral reactors are a continuum of gas thermochemical states

• described by same differential equations, but integrated over the continuum of gas thermochemical states
• can have a zero-dimensional integral reactor, but there you're just evaluating the integral
• series or continuum or distribution of states

In experimental systems:

• differential reactors are typically very small
  • the higher the surface area to volume ratio, the better the heat transfer, and therefore the higher the heat transfer coefficient
  • Heat transfer coefficient equation $Q=h(T_{2}-T_{1})$
  • More detail on how assumption works, how to add heat transfer coefficient into Cantera

• integral reactors are larger
  • adiabatic, generate own heat
  • commercial systems

Isothermal Reactors

Isothermal reactors are special because rate expressions are a function of temperature, and the isothermal reactor freezes the reaction rate

Isothermal and Differential Reactors

A preliminary assumption that can be made is that the amount of change that our reactor will affect, the amount of reactants it turns into products, will be very slight - differential - so that the change in the gas thermochemical state caused by the reactor can be examined differentially.

This would be perfect if you wanted to measure a kinetic rate expression. Create a very tiny reactor, very small amount of reaction occurs, isothermal, same temperature, measure your concentration step change, etc.

Isothermal and Integral Reactors

A reactor can also be an integral reactor, and be isothermal. This is the case in any isothermal reactor where the reaction goes to completion. The exit state of these reactors depends on the entire range of states (and gradients) in the reactor. Isothermal reactors can help keep operation simpler by removing functional dependence of the reaction rate on the (often experimentally unknown) temperature profile in the reactor.

Isothermal Integral Reactors in Cantera

Reactor models in Cantera are isothermal integral reactors. Cantera reactors are integrating concentration (and optionally energy) equations; you can turn off the energy equation, in which case Cantera will still integrate the concentration equations (hence, an integral reactor). You can turn off the energy equation in a reactor when you create it:

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or after you create it:

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Nonisothermal Reactors

Nonisothermal reactors are, by definition, integral. Multiple thermochemical states.

Some maths

how Cantera solves nonisothermal integral reactor equations - (ref the Cantera/Reactor Equations page

Adiabatic reactors

How to make an adiabatic reactor in Cantera (it is the default)

Reactor heat transfer profile

How to specify heat transfer coefficient in a reactor in Cantera? Install a wall, set the heat transfer coefficient.

Heat transfer coefficients can be static (fixed number), or change (function of temperature/composition/physical properties/reactor material/time/etc)

Reactor temperature profile

How to specify the reactor temperature profile - just make it isothermal and change the temperature manually at each timestep (with caveats - how ELSE is the thermochemical state changing?)