Simulation of nucleation and growth of aerosols in absorbers and condensers

Simulation of nucleation and growth of aerosols in absorbers and condensers

In industrial processes the formation of aerosols may occur due to spontaneous phase transition in supersaturated gas-vapour mixtures (saturation ratio S >1). The saturation ratio is defined as the ratio of the sum of the partial pressures of the condensable components and the dew point pressure of the gas phase.

pic 1

 Some processes in which supersaturation is possible are:

-    Mixing processes
-    Chemical reactions in the gas phase
-    Fast expansion of gases
-    Simultaneous heat and mass transfer processes

The formation of aerosols may be undesired, as for example during the absorption of strong acids such as HCl, HBr and H2SO4 in aqueous solutions. The supersaturation is particularly high in these cases as the azeotropic acid-water systems reveal strong vapor-pressure minima. As a result, during the quenching of a flue gas with traces of acid, small droplets may be formed carrying a considerable amount of the pollutant. As their sizes are often around 1 µm, they are difficult to precipitate (minimum between diffusion and impaction based precipitation). Additionally, the harmful gas may cause operational problems in the downstream equipment.

The heat and mass transfer processes in a cocurrent absorption packed column are shown in Fig. 1. The gas phase enters the column with a temperature of 200 °C. The two phases are neither in thermal nor in material equilibrium at the entrance of the column and the states of the gas and liquid phases change due to the simultaneous heat and mass transfer along the interface A, or length z, respectively. The circulating liquid is cooling the gas phase, partly evaporates and the acid component is absorbed.

Figure 1


As a consequence of these changes of the gas phase, the dew point may be exceeded and the gas phase gets supersaturated. Once the saturation is higher than the critical saturation, droplets are formed due to homogeneous or heterogeneous nucleation and grow subsequently. The changes of state of the three phases (gas, liquid, aerosol) have to be calculated simultaneously in order to consider the competing mass transfer between the phases. 

Figure 2 


For the calculation of the aerosol formation in gas-liquid contact devices, a simulation tool (AerCoDe) has been developed at this institute together with the Konrad-Zuse-Zentrum für Informationstechnik, Berlin [1,2,3]. It is shown schematically in figure 2. The gas and liquid flows are regarded as one-dimensional plug flows. It has been shown in experiments that this consideration provides a good description of the apparatus despite the complex configuration.
In the simulation, 4 different control volumes are considered for the liquid phase, the gas phase, the droplet phase and the phase boundary and one additional phase – the cooling phase – to consider heat losses. One-dimensional differential mass and energy balances are established for all control volumes along the length z. They are all linked by the heat and mass transfer processes between the phases. Together they build a differential algebraic equation system which is solved numerically at various nodes along the apparatus.
Figure 3 shows a process path of the absorption of HCl in a quench with a circulating liquid. The flue gas enters the column with a temperature of 200°C and is cooled by the liquid to 46°C (cooling limit). The acid concentration at the entrance is 1000 ppm.

 

Figure 3


On the ordinate, the sum of the partial pressures of water and HCl as a function of the gas phase composition is plotted (i.e. the dew point lines for temperatures between 45°C and 50°C). In addition, the process path is drawn. The process begins at high HCl concentrations and low partial pressures of the condensable component (water) and proceeds to lower concentrations of HCl and higher water partial pressures due to the combined absorption and evaporation. In order to observe the exceeding of the dew point, the points of the process path are marked with the temperature. The gas phase is supersaturated as soon as the dew point at the corresponding temperature is exceeded. Figure 3 shows that this is the case for temperatures below 47°C. However, the reached supersaturations are not as high. In this system there is no homogeneous nucleation, the formation of droplets takes place at the existing foreign particles.
If the heterogeneous nucleation is considered in the calculations, it can be seen that the supersaturation is depleted by the growth of the droplets. The extent of this depletion depends mainly on the number of foreign particles in the process. In figure 4 the saturation without aerosol formation and with typical foreign particle concentrations between 105 und 107 particles/cm³ as a function of the NTU is shown.

 

Figure 4


It can be seen that the supersaturation is depleted faster at higher numbers of foreign particles in the system. This can be explained by the higher exchange surface at higher number concentrations.
The resulting droplet diameters are about reciprocally proportional to the number concentrations. Figure 5 shows the droplet diameters for some number concentrations. At the end of the column, droplet diameters between 300 and 900 nm are reached.
Apart from the simulation of heterogeneous nucleation, the simulation of processes with homogeneous nucleation is possible with AerCoDe [4]. The number concentration then has to be calculated from the nucleation rate J (for example by means of the classical nucleation theory).
With the help of AerCoDe, not only processes in gas-liquid contact devices can be calculated. As long as a model for the heat and mass transfer is available, all processes where supersaturation may result from simultaneous heat and mass transfer can be calculated.  
Regarding heterogeneous nucleation, the good correlation between simulation and experiments has been proved already [2,5]. Concerning homogeneous calculation, the validation is part of the current research.

 

 

 

References:
[1]    R. Ehrig, O. Ofenloch, K. Schaber, P. Deuflhard: Modelling and simulation of aerosol formation by heterogeneous nucleation in gas - liquid contact devices. Chem. Eng. Science 57 (2002) 1151-1163.
[2]    K. Schaber, J. Körber, J., O. Ofenloch, R. Ehrig, P. Deuflhard: Aerosol formation in gas-liquid contact  devices - nucleation, growth and particle dynamics. Chem. Eng. Science 57 (2002) 4345-4356.
[3]    A. Wix, K. Schaber, O. Ofenloch, R. Ehrig, P. Deuflhard: Simulation of aerosol formation in gas-liquid contact devices. Chem. Eng. Commun. 194 (2007) 565-577
[4]    A. Wix, L. Brachert, S. Sinanis, K. Schaber: A simulation tool for aerosol formation during sulphuric acid absorption in a gas cleaning process. J. Aerosol Sci. 41 (2010) 1066-1079
[5]    A. Wix, Theoretische und experimentelle Untersuchungen zur homogenen und heterogenen Nukleation bei der Säureabsorption in Gas-Flüssigkeitskontaktapparaten, Fortschritt-Berichte VDI Reihe 3, Nr. 894. VDI Verlag Düsseldorf, 2008