## Extensible Reactor¶

This page walks through the walks through defining modified governing equations and shows how to implement these changes to the equations in Python.

## Extensible Reactor Tutorial¶

The variables in the governing equations that are differentiated with respect to time are known as the state variables. The state variables depend on the type of Reactor base class chosen. For example, choosing an Ideal Gas Constant Pressure Reactor allows the user to modify the governing equations corresponding to the following state variables:

• $$m$$, the mass of the reactor's contents (in kg)

• $$T$$, the temperature (in K)

• $$Y_k$$, the mass fractions for each species (dimensionless)

As shown in the derivations of the governing equations for an Ideal Gas Constant Pressure Reactor, the user may modify the three equations below:

\begin{equation*} \frac{dm}{dt} = \sum_{in} \dot{m}_{in} - \sum_{out} \dot{m}_{out} + \dot{m}_{wall} \tag{1} \end{equation*}
\begin{equation*} m c_p \frac{dT}{dt} = - \dot{Q} - \sum_k h_k \dot{m}_{k,gen} + \sum_{in} \dot{m}_{in} \left(h_{in} - \sum_k h_k Y_{k,in} \right) \tag{2} \end{equation*}
\begin{equation*} m \frac{dY_k}{dt} = \sum_{in} \dot{m}_{in} (Y_{k,in} - Y_k)+ \dot{m}_{k,gen} - Y_k \dot{m}_{wall} \tag{3} \end{equation*}

There are two "sides" to each of these equations: the terms left of the equals sign and the terms to the right of the equals sign. This is the format in which the user will be editing the governing equations. For example, if the user wishes to add a term for a large mass (say a rock) inside the reactor to see the effects on temperature:

\begin{equation*} m c_p \frac{dT}{dt} = - \dot{Q} - \sum_k h_k \dot{m}_{k,gen} + \sum_{in} \dot{m}_{in} \left(h_{in} - \sum_k h_k Y_{k,in} \right) \tag{2} \end{equation*}

Will change to:

\begin{equation*} \left(m c_p + m_{rock} c_{p,rock}\right) \frac{dT}{dt} = - \dot{Q} - \sum_k h_k \dot{m}_{k,gen} + \sum_{in} \dot{m}_{in} \left(h_{in} - \sum_k h_k Y_{k,in} \right) \end{equation*}

A simple example is shown below to illustrate the process for implementing changes in Cantera's existing governing equations. We will be replacing the right-hand side (RHS) and left-hand side (LHS) of the temperature governing equation for an Ideal Gas Constant Pressure Reactor. All other governing equations defining an Ideal Gas Constant Pressure Reactor will remain as the default.

In this example

\begin{equation*} m c_p \frac{dT}{dt} = - \dot{Q} - \sum_k h_k \dot{m}_{k,gen} + \sum_{in} \dot{m}_{in} \left(h_{in} - \sum_k h_k Y_{k,in} \right) \tag{2} \end{equation*}

Will change to:

\begin{equation*} \left( m_{rock} c_{p,rock} + m_{gas} \right) \frac{dT}{dt} = - \dot{Q} \end{equation*}

The governing equations will be modified through the user created Python class' methods. For each method, the name should be prefixed with before_, after_, or replace_, indicating whether the this method should be called before, after, or instead of the corresponding method from the base class.

#1 Define objects, properties, and initial conditions.

#create gas object
gas = ct.Solution('h2o2.yaml')
gas.TPX = 500, ct.one_atm, 'H2:2,O2:1,N2:4'

# define properties of gas and solid
mass_gas = 20  # [kg]
Q = 100  # [J/s]
mass_rock = 10  # [kg]
cp_rock = 1.0  # [J/kgK]

#initialize time at zero
time = 0  # [s]
n_steps = 300

#2 Define a new custom Reactor class. Here we named it "RockReactor" and
# chose the Ideal Gas Constant Pressure Reactor as the base class to inherit
# governing equations from.

# define a class representing reactor with a solid mass and gas inside of it
class RockReactor(ct.ExtensibleIdealGasConstPressureReactor):

# modify energy equation to include solid mass in reactor

# after the initial solution for time t is computed ask Cantera to solve the modified
# equation. The index 1 refers to modification of governing equation 2 in the reactor
# documentation (recall that indexing begins at 0).
def after_eval(self, t, LHS, RHS):
# although the time variable t is not used directly in the method definition it is a
# required argument for the internal solver.
self.m_mass = mass_gas
# as the arguments for after_eval are positional arguments, you may name them as you wish
# rather than use the default RHS and LHS nomenclature.
LHS[1] = mass_rock * cp_rock + self.m_mass * self.thermo.cp_mass
RHS[1] = -Q

# Initialize the new Reactor class and Reactor Network.
r1 = RockReactor(gas)
r1_net = ct.ReactorNet([r1])

#3 Integrate custom equations over desired time.

for n in range(n_steps):
time += 4.e-4

Details on functions in addition to eval() that are able to be modified with before_, after_, or replace_ can be found here.