Mechanism of gas absorption with two-phase absorbents

doi:10.1016/j.ijheatmasstransfer.2011.02.050

International Journal of Heat and Mass Transfer

Volume 54, Issues 13–14, June 2011, Pages 3004-3008

https://doi.org/10.1016/j.ijheatmasstransfer.2011.02.050 Get rights and content

Abstract

A theoretical analysis of gas absorption with two-phase absorbents in the cases, when a component of gas phase reacts chemically with a component of solid phase after its dissolution in liquid phase, is presented. The interphase mass transfer in system with two interphase surfaces (gas–liquid and liquid–solid) is analyzed. The influence of the mass transfer resistant at the phase boundaries on the absorption mechanism is investigated. The kinetic models of gas absorption of high and low soluble gases is presented.

Introduction

The gas absorption of components in gas mixtures with high (HCl), middle (SO₂) and low (CO₂) solubility in the water, by means of two-phase absorbents, where the active components (CaCO₃, Ca(OH)₂) are water suspensions, is used in power plants for gas cleaning (absorption of SO₂ in waste gases) or solutions of lime neutralization by CO₂ absorption (in calcinated soda production plants). In the first case SO₂ is possible to be examined also as a high soluble gas.

The presence of the active component in the absorbent as solution and solid phase leads to an increasing of the absorption capacity of the absorbent, but the introduction of a new process (the solution of the solid phase) creates conditions for variation of the absorption mechanism (interphase mass transfer through two interphase surfaces – gas/liquid and liquid/solid).

Section snippets

Physical model

As a physical model will be used a laminar co-current gas–liquid flow in vertical canal with flat walls (Fig. 1), where the liquid flowing down as a liquid film.

The gas flow is a mixture and an active component dissolves in the liquid film, where reacts with the active component of the absorbent, dissolved in the liquid. The solid walls are made from the same active component of the absorbent and dissolve in the liquid film. The chemical reaction between active components (reagents) of the gas

Hydrodynamic model

Let us consider co-current flow of a laminar gas flow and laminar liquid film flow and ${\bar{u}}_{G}$ and ${\bar{u}}_{L}$ are the average velocities (m s⁻¹): ${\bar{u}}_{G} = \frac{Q_{G}}{2 r}, {\bar{u}}_{L} = \frac{Q_{L}}{2 h},$ where Q_G and Q_L (m³ m⁻¹ s⁻¹) are the gas and liquid flow rates in a canal with a width of one meter.

The velocity distributions in the gas and liquid phases will be obtained in the stratified flows approximations [1], [2]: $u_{G} = u_{G} (y), u_{L} = u_{L} (y) .$

The large difference between values of gas and liquid viscosity coefficients permit the friction force between

Interphase mass transfer model

The obtained solutions (6) of the hydrodynamic problem permit to be used the convection–diffusion equations for the formulation of the interphase mass transfer model in thin layer approximation $(0 = {(\frac{r}{l})}^{2} ≪ 1, 0 = {(\frac{h}{l})}^{2} ≪ 1) :$ $u_{G} \frac{\partial c}{\partial x} = D \frac{\partial^{2} c}{\partial y^{2}}, 0 ⩽ x ⩽ l, 0 ⩽ y ⩽ r - h;$ $x = 0, c = c_{0}; y = 0, \frac{\partial c}{\partial y} = 0; y = r - h, D_{1} \frac{\partial c_{1}}{\partial y} = D \frac{\partial c}{\partial y} .$ $u_{L} \frac{\partial c_{1}}{\partial x} = D_{1} \frac{\partial^{2} c_{1}}{\partial y^{2}} - {kc}_{1} c_{2}, 0 ⩽ x ⩽ l, r - h ⩽ y ⩽ r;$ $x = 0, c_{1} = 0; y = r, \frac{\partial c_{1}}{\partial y} = 0; y = r - h, c = χ c_{1} .$ $u_{L} \frac{\partial c_{2}}{\partial x} = D_{2} \frac{\partial^{2} c_{2}}{\partial y^{2}} - {kc}_{1} c_{2}, 0 ⩽ x ⩽ l, r - h ⩽ y ⩽ r;$ $x = 0, c_{2} = c_{20}; y = r, c_{2} = c_{20}; y = r - h, \frac{\partial c_{2}}{\partial y} = 0 .$ In (7), (8), (9) $D, D_{1}, D_{2}$ (m² s⁻¹) are the diffusivities of the reagents in

Absorption kinetics

The presented theoretical analysis of the gas absorption with two-phase absorbents shows, that the absorption rate depends on the rates of four processes:

–
mass transfer from the gas volume to the gas–liquid interphase surface;
–
mass transfer from the gas–liquid interphase surface to the liquid volume;
–
mass transfer from the solid–liquid interphase surface to the liquid volume;
–
chemical reaction in the liquid volume.

In the general case the absorption rate is possible to be obtained after solution of

Absorption mechanism

The identification of the absorption mechanism needs a mass balance of the reagents in the film flow volume Δv = hΔx (m³) with width of 1 (m), thickness of h (m) and length of Δx (m).

The diffusion mass flux of the active gas component J_D (kg mol m⁻¹ s⁻¹), which enters in the volume Δv across the gas–liquid interphase surface Δs₁ = Δx (m²) (with width of 1 (m)) is: $J_{D} = - D_{1} {(\frac{\partial c_{1}}{\partial y})}_{y = r - h} Δ x .$

The convective mass flux of the active gas component J_C (kg mol m⁻¹ s⁻¹), which enters in the volume Δv across the liquid

Absorption of gases with high solubility

The relations (24), (25), (26) permit to be obtained the influence of the mass fluxes at the phase boundaries on the process mechanism.

In the cases of gases with high solubility (SO₂, HCl) $χ ≪ 1$ and $γ_{1} ≫ 1$ (for example $χ_{{SO}_{2}} \sim 10^{- 2}, χ_{HCl} \sim 10^{- 3}$ ) and the problem (12) is possible to be solved in approximation $0 = γ_{1}^{- 1} ≪ 1$ . As a result $C_{1} \equiv 0$ and the model (11), (12), (13) must be reduced: $(α - β Y_{G}^{2}) \frac{\partial C}{\partial X} = Fo \frac{\partial^{2} C}{\partial Y_{G}^{2}};$ $X = 0, C = 1; Y_{G} = 0, \frac{\partial C}{\partial Y_{G}} = 0; Y = 1, Y_{G} = 1, {(\frac{\partial C}{\partial Y_{G}})}_{Y_{G} = 1} = δ γ_{2} {(\frac{\partial C_{2}}{\partial Y})}_{Y = 0} .$ $(2 Y - Y^{2}) \frac{\partial C_{2}}{\partial X} = {Fo}_{2} \frac{\partial^{2} C_{2}}{\partial Y^{2}};$ $X = 0, C_{2} = 1; Y = 0, C_{2} = 1; Y = 1, \frac{\partial C_{2}}{\partial Y} = 0,$

Absorption of gases with low solubility

In the cases of gases with low solubility (CO₂) $χ ≫ 1$ and $γ_{1} ≪ 1$ (for example $χ_{{CO}_{2}} \sim 1, γ_{1} \sim 10^{- 2}$ ) and the problem (11) is possible to be solved in approximation $0 = γ_{1} ≪ 1$ . As a result the problem (11) must be replaced by $C \equiv 1$ and the last boundary condition in (12) by Y = 1, C₁ = 1: $(2 Y - Y^{2}) \frac{\partial C_{1}}{\partial X} = {Fo}_{1} \frac{\partial^{2} C_{1}}{\partial Y^{2}} - K_{1} C_{1} C_{2};$ $X = 0, C_{1} = 0; Y = 0, \frac{\partial C_{1}}{\partial Y} = 0; Y = 1, C_{1} = 1 .$ $(2 Y - Y^{2}) \frac{\partial C_{2}}{\partial X} = {Fo}_{2} \frac{\partial^{2} C_{2}}{\partial Y^{2}} - K_{2} C_{1} C_{2};$ $X = 0, C_{2} = 1; Y = 0, C_{2} = 1; Y = 1, \frac{\partial C_{2}}{\partial Y} = 0 .$

The solution of (32), (33) permits to be obtained $(\frac{\partial C_{1}}{\partial Y})_{Y = 1}$ and k_L, using (16).

From (32) follows, that $K_{1} ≪ 1$ for

Conclusions

The two-phase absorbent (water suspensions of CaCO₃ or Ca(OH)₂) are used in power plants for waste gases cleaning (absorption of SO₂). This process is used in calcinated soda plants for solutions of lime neutralization by CO₂.

The presented theoretical analysis shows, that the using of two-phase absorbents leads to modification of the absorption mechanism as a result of the new mass transfer resistance at the liquid–solid interphase surface. The absorption mechanisms for the practically

References (4)

Chr. Boyadjiev et al.
Mass Transfer in Liquid Film Flows
(1984)
Chr. Boyadjiev et al.
Mass Transfer in Following Liquid Films
(1984)

There are more references available in the full text version of this article.

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