Extraction Column
Description & Equations
The multistage extraction column is a key unit operation in chemical engineering that enables mass transfer between liquid and gas phases across multiple theoretical stages, described by coupled differential equations representing the dynamic concentration changes in each phase:
\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].
The observation space is defined by the following bounds corresponding to the ordered state variables:
An example, tested set of initial conditions are as follows: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).