The influence of dispersion on breakthrough curves

Obtaining predictive models for gas adsorption systems is extremely challenging due to the various coupled nonlinear mass and heat transfer mechanisms. Often, significant simplifications can be implemented to reduce complexity, and the 1D axially dispersed plug flow model is the most common model employed in the academic literature:

$$\epsilon_b (\frac{\partial y_i}{\partial t} + \frac{y_i}{P}\frac{\partial P}{\partial t} - \frac{y_i}{T}\frac{\partial T}{\partial t}) + \frac{T}{P} \frac{\partial}{\partial z}(\frac{u y_i P}{T}) - \epsilon_b \frac{T}{P}\frac{\partial}{\partial z}(\frac{D_{ax} P}{T} \frac{\partial y_i}{\partial z}) + \frac{RT}{P} \rho_b \frac{\partial q_i}{\partial t} = 0$$

This model lumps all of the axial dispersion mechanisms: molecular diffusion, turbulence, lateral mixing, Taylor dispersion and wall channelling into a single coefficient, $D_{ax}$. Empirical equations do not account for each mechanism explicitly, and thus are not always accurate in practice. For example, Wako and Funazkri suggest:

$$D_{ax} = \frac{20 D_{m,i}}{\epsilon_b} + 0.5 u_s d_p$$

This equation separates the molecular diffusion (first term) and axial dispersion mechanisms (second term). However, it does not account for any wall channelling dispersion that could occur in practice. Often, the rule of thumb used to suggest wall channelling is negligible is: $D_i > 20d_p$, but that is not always true.

As the axial dispersion coefficient influences the shape of the breakthrough curve, it is important to include it within the model when fitting mass transfer coefficients to experimental data. This dispersion term can also result in an artificial concentration front sharpening at the outlet of the bed from simulations. This sharpening effect is often ignored, but it has a significant impact on the shape of the breakthrough curve and can influence the parameters extracted.

The concentration front sharpening is an effect I have noticed in my work, developing adsorption modelling software AdSim. If you run the "Ward (2022)" example and visualise the CO2 mole fraction profile as it propagates through the bed with time, you will see the transition from constant pattern behaviour at the outlet.

One way to avoid this problem would be to measure the adsorbate concentration within the bed along the centre line. Thus, avoiding the influence of wall channelling effects in the experimental data, and avoiding concentration front sharpening in simulations.