Continuously Stirred Tank Reactor

Description & Equations

The continuously stirred tank reactor (CSTR) is a system which converts species A to species B via the reaction: A → B. The reactor's temperature is controlled by a cooling jacket. The following system of equations describes the system:

\begin{align} \nonumber\frac{\mathrm{d}C_A}{\mathrm{d}t} &= \frac{q}{V}(C_{A_f} - C_A) - kC_Ae^{\frac{-E_A}{RT}}\ \end{align} \begin{align} \nonumber\frac{\mathrm{d}T}{\mathrm{d}t} &= \frac{q}{V}(T_f - T) -\frac{\Delta H_R}{\rho C_p}kC_Ae^{\frac{-E_A}{RT}} + \frac{UA}{\rho C_p V}(T_c - T) \end{align} where $C_A$, the concentration of species A in the reactor, and $T$, the temperature of the reactor, are the state variables, $\mathbf{x} = [C_A, T]^\intercal \in \mathbb{R}^2$ while, $u = T_c$, the cooling water temperature, is the action variable.

Observation

The observation of the CSTR environment provides information on the state variables and their associated setpoints (if they exist) at the current timestep. The observation is an array of shape (1, 2 + N_SP) where N_SP is the number of setpoints. Therefore, the observation when there exist a setpoint for both states is [CA, T, CA_Setpoint, T_Setpoint].

Action

The action space is a ContinuousBox of [290,302] which corresponds to a jacket temperature between 290 K and 302 K.

Reward

The reward is a continuous value corresponding to square error of the state and its setpoint. For multiple states, these are scaled with a factor (r_scale) and summed to give a single value.

Reference

This model implementation and its description were kindly provided by Akhil Ahmed. The original model was created by by Hedengren (2022).