Petya Popova-Krumova

Perturbation Method Approach

A new approach for the column apparatuses modeling uses convection–diffusion-type models and average-concentration models. All these new types of models (Boyadjiev in Theoretical chemical engineering. Modeling and simulation. Springer, Berlin [1], Doichinova and Boyadjiev in Int J Heat Mass Transf 55:6705–6715 [2], Boyadjiev in J Pure Appl Math: Adv Appl 10:131–150 [3]) are characterized by the presence of small parameters at the highest derivatives. As a result, the model equations have no exact solutions and approximate (asymptotic) solutions have to be obtained (Мищенко and Розов in Дифференциальные уравнения с малым параметром и релаксационные колебания. Изд. “Наука”, Москва [4], O’Malley in Introduction to singular perturbations. Academic Press, New York [5], Boyadjiev et al. in J Eng Thermophys 24:371–380 [6]). In these cases, the use of the conventional software (MATLAB) for solving the model differential equations is difficult and this difficulty may be eliminated by an appropriate combination with the perturbation method.

Industrial Column Chemical Reactors

The new approach for the modeling of the processes in column apparatuses (Boyadjiev in Theoretical chemical engineering. Modeling and simulation. Springer, Berlin, Heidelberg, 2010, [1]; Doichinova, Boyadjiev in Int J Heat Mass Transf 55:6705–6715, 2012, [2]; Boyadjiev in Pure Appl Math Adv Appl 10(2):131–150, 2013 [3]) presents the convection–diffusion and average-concentration models of the column chemical reactors (in Chaps. 2 and 5), where the radial velocity component is equal to zero in the cases of a constant axial velocity radial non-uniformity along the column height:

Industrial Co-current Column Absorber

The new approach for the modeling of the processes in column apparatuses (Boyadjiev in Theoretical chemical engineering. Modeling and simulation. Springer, Berlin, Heidelberg, 2010, [1]; Doichinova, Boyadjiev in Int J Heat Mass Transf 55:6705–6715, 2012, [2]; Boyadjiev in Pure Appl Math Adv Appl 10(2):131–150, 2013 [3]) presents the convection–diffusion and average-concentration models of the column chemical reactors (Boyadjiev and Boyadjiev in Bulgaria Chem Commun 49(3):711–719, 2017 [4], in the cases of an axial modification of the axial velocity radial non-uniformity along the column height (see Chap. 10). This problem will be solved in the cases of the absorption processes in a co-current column (Boyadjiev and Boyadjiev Bulgaria Chem Commun 49(3):711–719, 2017 [5].

Bizonal Absorption Apparatus

The chemical absorption of average soluble gases (ASG) in the case of slow chemical reaction (e.g., absorption of CO2 with aqueous solutions of NaOH, where Henry’s number in the system CO2/H2O is \(\chi^{{20\;{^\circ{\text{C}}}}} = 1.16\)) is possible to be used for waste gas purification. The absorption process intensification has to be realized through intensification of the convective mass transfer in the gas phase (in gas–liquid drops system) and in the liquid phase (in liquid–gas bubbles system). This theoretical result is applied in a new method and bizonal apparatus for gas absorption [1]. In the upper equipment zone, a physical absorption (as a result of the short reaction time, i.e., short existence of the absorbent drops) is realized in a gas–liquid drops system and the big convective transfer in the gas phase leads to decrease of the mass transfer resistances in this phase. In the lower zone, a chemical absorption in a liquid–gas bubbles system takes place and the big convective transfer in the liquid phase lowers the mass transfer resistances in this phase.

Industrial Column Catalytic Reactors

In Chaps. 10– 13 were presented convection-type and average-concentration models of chemical (Boyadjiev and Boyadjiev in Bulg Chem Commun 49(3):706–710 [1]), co-current absorption (Boyadjiev and Boyadjiev in Bulg Chem Commun 49(3):711–719 [2]), countercurrent absorption (Boyadjiev and Boyadjiev in Bulg Chem Commun 49(3):720–728 [3]), and non-stationary adsorption (Boyadjiev and Boyadjiev in J Eng Thermophys 27(1):82–97 [4]) processes in industrial column apparatuses, where the radial velocity component is not equal to zero in the cases of an axial modification of the axial velocity radial non-uniformity along the column height. This problem will be solved in the cases of the catalytic reactions in gas–solid systems (physical and chemical adsorption mechanisms) in the industrial column apparatuses (Boyadjiev and Boyadjiev in J Eng Thermophys [5]).

Industrial Column Adsorber

In Chaps. 10– 12 were presented convection–diffusion and average-concentration models of chemical (Boyadjiev and Boyadjiev in Bul Chem Commun 49(3):706–710 [1]), co-current absorption (Boyadjiev and Boyadjiev in Bul Chem Commun 49(3):711–719 [2]) and countercurrent absorption (Boyadjiev and Boyadjiev in Bul Chem Commun 49(3):720–728 [3]) processes in industrial column apparatuses, where an axial modification of the axial velocity radial non-uniformity along the column height exists and the radial velocity component is not equal to zero. This problem is solved in the cases of the physical and chemical adsorption processes in the industrial column apparatuses (Boyadjiev and Boyadjiev in J Eng Thermophys 27(1) [4]).

Industrial Counter-current Column Absorber

In Chap. 11 were presented the convection–diffusion and average-concentration models (Boyadjiev in Theoretical chemical engineering. Modeling and simulation. Springer, Berlin, 2010) [1], (Doichinova and Boyadjiev in Int J Heat Mass Transfer 55:6705–6715, 2012) [2] and (Boyadjiev in J Pure Appl Math: Adv Appl 10(2):131–150, 2013) [3] of the gas absorption processes in the co-current columns, where the radial velocity component is not equal to zero, in the cases of an axial modification of the axial velocity radial non-uniformity along the column height (Boyadjiev in Bulg Chem Commun 49(3):711–719, 2017) [4]. This possibility will be used for modeling of the gas absorption processes in the counter-current columns, where the problem is complicated (Boyadjiev in J Eng Thermophys 24(3):247–258, 2015) [5], (Boyadjiev in Bulg Chem Commun 49(3):720–728, 2017) [6] because the mass transfer process models have to be presented in two-coordinate systems (in a one-coordinate system, one of the equations has no solution due to the negative Laplacian value).

Column Reactors Modeling

The theoretical procedure (II.5–II.15) presented in the Part II will be used for creation of average concentration models of simple and complex chemical processes in one-phase column apparatuses.

Interphase Mass Transfer Processes Modeling

The theoretical procedure (II.5–II.15) presented in Part II will be used for the creation of average-concentration models of absorption, adsorption, and catalytic processes in two-phase systems.

Bi-zonal Absorption Apparatus

The theoretical analysis (see Chap. 4) of the method and apparatus for waste gases purification from SO2 using two-phase absorbent (CaCO3 suspension), which are applied by some companies (Babcock & Wilcox Power Generation Group, Inc., Alstom Power Italy, Idreco-Insigma-Consortium) in the thermal power plants shows that the interphase mass transfer process in the system gas-liquid drops is practically physical absorption as a result of the low concentration of the dissolved SO2 and CaCO3 in the water and the short reaction time (short existence of the absorbent drops). It was shown that in these conditions the interphase mass transfer resistances in both phases are commensurate (44.4 % in the gas phase and 55.6 % in the liquid phase), but the possibility for intensification of the mass transfer in the liquid phase is very limited.