Gas Absorption at Liquid Surface
|Introduction||Solve the PDE Model|
|Domain||Post-processing and Visualization|
|Mass Transport Model||References|
Physical and chemical gas absorption are an important separation processes and widely employed in various industries. Gas absorption is used to either separate undesirable components from a gas or for manufacturing purposes of chemicals.
This example reproduces a gas absorption model . The absorption process takes place in the gas-liquid interface section shown below in gray:
A gas is exposed to a fully developed laminar flow. The gas flows either co-currently or counter-currently with respect to the flowing liquid. The above image displays the co-current case. The solute in the gas flow is absorbed and removed by the liquid flow beneath it, and mass transfer of the solute takes place from the gaseous to the liquid phase. The time of contact between solute and liquid is long enough to presume a parabolic velocity profile. Steady state conditions are assumed to prevail. In the post-processing section we will compare the absorption effectiveness between the co-current case and the counter-current case.
To model the interphase mass transfer, we will define a thin interphase region between the gas and liquid flow, which will allow us to enforce an equilibrium condition (1) specified below via coupled fictitious mass sources and handle the discontinuous concentration of the solute between two different phases.
We start be generating a boundary ElementMesh that accounts for the different material regions and the interface region. On the boundary we specify markers that will be used later to set up boundary conditions for to co-current and counter-current case.
To accurately model the mass transfer between the gas and liquid phases, the interphase region should be finely meshed. For clarity we add the material regions as an Association.
Here and are the concentration of solute dissolved in the gas phase and liquid phase. To model the mass transfer between the two phases we add coupling mass source terms and in the governing mass balance equation (2), leading to:
Next, we specify the fluid flow velocities . The flow velocities are only active in their respective sub-regions. The gaseous flow velocity will initially be in the same direction as the liquid flow velocity .
Based on the two-resistance theory, the equilibrium at the interface is considered to be reached instantaneously and maintained at all times. This condition can be modeled by setting the mass transfer coefficient to be infinitely large. In practice, we can choose to be greater than the species diffusivity and ) by several orders of magnitude.
The coefficient depends on pressure, temperature and the chemical properties of the transported species and the media of both phases. The value can be determined by experimental measurement . In this example the equilibrium coefficient is given by .
Also, see this note about how to set up of computationally efficient PDE coefficients.
To measure the effectivity of the gas absorption, the net reduction of the solute is calculated between the gas inlet and outlet. For this the mean concentration at the outlet is computed with a boundary integration: