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This new edition includes brand-new developments in the modeling of processes in the column apparatuses. It analyzes the radial velocity component and axial variation in the axial velocity in the column. These models are described in five new chapters.

The book presents models of chemical and interphase mass transfer processes in industrial column apparatuses, using convection-diffusion and average-concentration models. It also introduces average concentration models for quantitative analysis, which use the average values of the velocity and concentration over the cross-sectional area of the column. The new models are used to analyze a broad range of processes (simple and complex chemical reactions, physical and chemical absorption, physical and chemical adsorption, catalytic reactions in the cases of physical and chemical adsorption mechanism), and make it possible to model sulfur dioxide gas purification processes.

### Chapter 1. Introduction

The logic and the intuition are the foundation of the human knowledge and the science. In the mathematics, the intuitions are the axioms (unconditional statements that cannot be proven), while the logic is the theorems (logical consequences of the axioms). The proportion between the logic and the intuition is different in the different sciences. In the mathematics, the logic predominates. In the natural sciences (physics, chemistry, and biology), the role of the intuition increases, but the “axioms” are not always unconditional. In the humanities, the role of the logic decreases.

### Chapter 2. One-Phase Processes

The fundamental problem of the one-phase processes modeling in the column apparatuses comes from the complicated hydrodynamic behavior of the flow, and as a result, the velocity distribution in the column is unknown.

### Chapter 3. Two-Phase Processes

The concentrations of the transferred substance in the phases are presented as kg mol of the transferred substance in 1 m3 of the phase volume.

### Chapter 4. Three-Phase Processes

The modeling of three-phase (gas–liquid–solid) interphase mass transfer processes in column apparatuses [1–4] is used in the case of absorption and adsorption in two-component ($$i_{0} = 2$$i0=2), three-phase ($$j = 1,2,3$$j=1,2,3) systems.

### Chapter 5. 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. On this basis, the effect of the velocity radial non-uniformity will be analyzed and methods for model parameter identification (Boyadjiev in Int J Heat Mass Transf 49:796–799 [1], Boyadjiev in Trans Acad 3:7–22 [2], Boyadjiev in Theoretical chemical engineering. Modeling and simulation. Springer, Berlin [3]) proposed.

### Chapter 6. Interphase Mass Transfer Process 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.

### Chapter 7. 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.

### Chapter 8. Two-Coordinate Systems Problem

In the cases of physical absorption [1–4] in a high countercurrent gas–liquid column, the mass transfer process model has to be presented in two-coordinate systems (see 3.1.8):

### Chapter 9. Multi-step Modeling Algorithms

In the cases of a non-stationary chemical adsorption in gas–solid systems, the presence of mobile (gas) and immobile (solid) phases in lengthy processes leads to a non-stationary process in the immobile phase and stationary process in the mobile phase, practically. As a result different coordinate systems have to be used in the gas and the solid phase model.

### Chapter 10. 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:

### Chapter 11. 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].

### Chapter 12. 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).

### Chapter 15. 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 $$\chi^{{20\;{^\circ{\text{C}}}}} = 1.16$$χ20∘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.

Different companies (Babcock & Wilcox Power Generation Group, Inc., Alstom Power Italy, Idreco-Insigma-Consortium) propose methods and apparatuses for waste gas purification from SO2 using two-phase absorbent (CaCO3 suspension). The adsorption (absorption) of SO2 on materials derived from natural carbonates (c) [3] has the drawback of waste accumulation. 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.