Different companies (Babcock & Wilcox Power Generation Group, Inc., Alstom Power Italy, Idreco-Insigma-Consortium) propose methods and apparatuses for waste gases purification from SО2 using two-phase absorbent (CaCO3 suspension)  . The basic problem of the carbonate absorbents is that its chemical reaction with SO2 lead to CO2 emission (every molecule of SO2 absorbed from the air is equivalent to a molecule of CO2 emitted in the air), because the ecological problems (greenhouse effects) of SO2 and CO2 are similar. The large quantity of by-products is a problem, too. Another drawback of these methods is the impossibility for regeneration of the absorbents.
The theoretical analysis  -  of the method and apparatus for waste gases purification from SО2 using two-phase absorbent (CaCO3 suspension) shows the possibility to use an absorption-adsorption method. The use of synthetic anionites (basic anion-exchange resins-R-OH form of Amberlite, Duolite, Kastel, Varion, Wofatit) as adsorbents    for gas purification from SO2 provides possibilities for adsorbent regeneration. In the proposed method   the waste gas purification is realized in two steps-physical absorption of SO2 with water and chemical adsorption of from the water solution by synthetic anionite particles in a fixed bed adsorber. The adsorbent regeneration is made with NH4OH solution. The obtained (NH4)2SO3 (NH4HSO3) is used (after reaction with HNO3) for production of concentrated SO2 (gas) and NH4NO3 (solution). The proposed patent  makes it possible to create a waste-free technology for waste gases purification from sulfur dioxide by means of regenerable absorbent and adsorbent. The proposed method  permits to be used for the absorption columns, where are used the CaCO3 suspensions.
The efficiency of the waste gases purification from SО2 can be increased if the absorption is realized in co-current flows and the adsorption takes place in the flexible adsorbent. For this is proposed a new absorption-adsorption column apparatus with bubbling plates.
2. An Absorption-Adsorption Apparatus
In the proposed absorption-adsorption method for waste gases purification from sulfur dioxide   , the absorption is realized in the counter-current absorber (where practical gas velocity does not exceed 5 m∙s−1) and the adsorption is carried out in a fixed bed adsorber. The efficiency of the process can be increased if the absorption is realized in co-current flows and the adsorption takes place in the flexible adsorbent. For this it can use a new absorption- adsorption apparatus with bubbling plates. The bubbling of the gas at a plate through a layer of aqueous suspension of synthetic anionite allows an increasing of the gas velocity (reduction of the diameter of the absorption column), elimination of the adsorption column and carrying out the adsorption in a flexible adsorbent. The movement of the gas between the plates leads to mixing in the gas phase, which increases the absorption rate because the absorption of sulfur dioxide in water is limited by mass transfer in the gas phase.
The new absorption-adsorption apparatus with bubble plates  is shown in Figure 1. The gas enters tangentially into the column 1 through the inlet 2,
Figure 1. Absorption-adsorption apparatus.
passes through the distribution pipes 5, concentric bubble caps 6 of the plates 4 and exits the column through the outlet 3. The aqueous suspension of synthetic anionite enters the column 1 via the valve 11 and the pipes 7 and creates of plates 4 layer with a certain thickness. After saturation of the adsorbent with sulfur dioxide, the aqueous suspension is output from the column through the pipes 8 and valves 11 and enters in the system 9 for the regeneration of the adsorbent. The suspension of the regenerated adsorbent is removed from 9 by pump 10 is returned to the plates 4 in the column 1.
The operation of the absorption-adsorption apparatus is the following cyclic scheme:
1. Supply all the plates with the necessary amount (volume) of aqueous suspension of synthetic anionite.
2. Start the absorption-adsorption process and monitor the SO2 concentration of the exit 3.
3. When the increasing the SO2 concentration at the outlet of the gas 3 exceeds permissible limits, the suspension of the first (bottom) plate is transferred in the regeneration system 9 and the plate is loaded with a new (regenerated) suspension.
4. When the increasing the SO2 concentration at the outlet of the gas 3 exceeds permissible limits, the suspension of the second (next) plate is transferred in the regeneration system 9 and the plate is loaded with a new (regenerated) suspension.
5. The procedures are repeated until reaching the top plate, then starts again from the first plate.
3. Absorption-Adsorption Process Modeling
Tangentially supplying of the gas in the column  reduces the radial non-un- iformity of the velocity at the column cross-sectional area and the gas velocity is a constant , practically. Under these conditions, the concentration of SO2 in the gas phase is changed only in the height of the column ( ), which increases the rate of mass transfer rate. On the other hand the gas bubbling creates an ideal mixing regime in the liquid phase and the concentration of SO2 in the liquid phase is . The concentration of SO2 in the solid phase (capillaries) is and the concentration of active sites in the adsorbent is .
The interphase mass transfer rate of SO2 from the gas to the liquid is , while the liquid to the adsorbent is . The chemical reaction rate of the SO2 with the adsorbent is .
The modeling of a non-stationary (as a result of the adsorbent saturation) absorption-adsorption process on the plate number , for gas purification from SO2  , uses a combination of the physical absorption and chemical adsorption models  :
In (1) is the entrance to the gas input of the plate number , is the distance between the plates, is the diffusivity of SO2 in the gas phase.
The concentration of SO2 in the water of each plate is determined by the amount of absorbed SO2 ( ) and its distribution between liquid phase ( ), the solid phase (capillaries) ( ) and adsorbed on the surface of the capillaries is ( ):
where are the gas, liquid and solid phase volumes on the plates.
4. Generalized Analysis
The use of dimensionless (generalized) variables  allows to make a qualitative analysis of the models (1), (3), where as characteristic scales are used the inlet and initial concentrations, the characteristic time (saturation time of the adsorbent) and the distance between the plates :
When (4) is put into (1), (3), the model in generalized variables takes the form:
The following parameters are used in (5), (6):
Practically and as a result
The solution of the equations of the model (6), (8), (9) uses a two-stage algorithm. In the first stage must be solved the equations for . In the second stage must be applied consistently for every plate the algorithm for .
Algorithm of the solution
1. Put .
3. The solution of leads to
4. The solution of (9) leads to
5. The solutions in 3 and 4 must be introduced in (6) and as a result is obtained
6. Put in an as a result is obtained
7. A polynomial approximation of with respect to must be obtained.
8. The solutions of the equations with respect to permit to be obtained and the obtained solutions must be denoted as
9. A polynomial approximation of with respect to permit to be obtained
10. The introducing of in (8) and (9) permits to be obtained its solutions for .
11. The obtained solution of (8) in 10 permits to be obtained and as a result to be used the algorithm 1-11 for consistent solutions of the equations set (6), (8) for
5. Parameters Identification
The parameters in the model (6), (8), (9), which are subject to experimental determination are . They may be obtained from experimental data of the SO2 concentration at the gas outlet from the first plate , where is the time for the fully saturation of the adsorbent on the first plate. For this purpose must be minimized the function of the least squares with respect to :
The proposed utility model  uses an absorption-adsorption column and gives the possibility to create a waste-free technology for waste gases purification from sulfur dioxide by means of regenerable adsorbent, where the absorbent regeneration system is similar to the regeneration system in the patent   . The efficiency of the processes is increased in an absorption-adsorption apparatus, where the absorption is realized in co-current flows and the adsorption takes place in the flexible adsorbent. That’s why a new absorption-adsorption column apparatus with bubbling plates is offered. A mathematical model of the absorption-adsorption process in a plate column is presented too.
 Boyadjiev, Chr. (2011) Mechanism of Gas Absorption with Two-Phase Absorbents. International Journal of Heat and Mass Transfer, 54, 3004-3008.
 Boyadjiev, Chr., Doichinova. M. and Popova, P. (2011) On the SO2 Problem in Power Engineering. 1. Gas Absorption. 15th Workshop on Transport Phenomena in Two-Phase Flow. Sunny Beach Resort, Bulgaria, 94-103.
 Boyadjiev, Chr., Pantofchieva, L. and Hristov, J. (2000) Sulphur Dioxide Adsorption in a Fixed Bed of a Synthetic Anionite. Theoretical Foundations of Chemical Engineering, 34, 141-144.
 Hristov, J., Boyadjiev, Chr. and Pantofchieva, L. (2000) Sulphur Dioxide Adsorption in a Magnetically Stabilized Bed of a Synthetic Anionite. Theoretical Foundations of Chemical Engineering, 34, 439-443.