Extraction Column

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}X_i}{\mathrm{d}t} &= \frac{L}{V_L}(X_{i-1}-X_i) - K_{La}\left(X_i - \frac{Y_i}{m}\right)\ \end{align} \begin{align} \nonumber\frac{\mathrm{d}Y_i}{\mathrm{d}t} &= \frac{G}{V_G}(Y_{i+1}-Y_i) + K_{La}\left(X_i - \frac{Y_i}{m}\right)\ \end{align}

Where the concentration of the solute in the liquid and gas at each stage, $X_i$ and $Y_i$ are the state variables, $\mathbf{x} = [X_1..X_{10},Y_1...Y_{10}]^\intercal \in \mathbb{R}^{10}$. The action variables are the flowrate of the gas and liquid phases through the column, $\mathbf{u} = [L, G]^\intercal \in \mathbb{R}^2$.

Observation

The observation of the Multistage Extraction 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, 10 + N_SP) where N_SP is the number of setpoints. Therefore, the observation when there a setpoint exists for $X_1$ and $Y_1$ is [X_n..., Y_n..., X_1, Y_1].

Action

The action space is a ContinuousBox of [[5,10],[500,1000]] which corresponds to a liquid phase flowrate between 5 m$^3$/hr and 500 m$^3$/hr and a gas phase flowrate between 10 m$^3$/hr and 1000 m$^3$/hr.

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 and its description were kindly provided by Akhil Ahmed. The original model was created by Ingham et. al. (2007).