Development of a Model for Wet Scrubbing of Carbon Dioxide by Chilled Ammonia

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1 Development of a Model for Wet Scrubbing of Carbon Dioxide by Chilled Ammonia John Nilsson Department of Chemical Engineering, Lund University, P. O. Box 124, SE Lund, Sweden In this paper, the absorption of carbon dioxide in a solution of chilled aqueous ammonia, is studied. A literature survey has been performed in order to investigate the reaction mechanism that arises when chilled aqueous ammonia and carbon dioxide reacts, to determine which reactions that occur and to which extent they proceed. Further, the kinetics in the reaction mechanism is formulated. The model problem is eventually translated into mathematics. The two main concepts that this paper is founded upon are kinetics and mass- heat transfer. To utilize these concepts, a gas liquid contactor is required. The main purpose of this unit is to provide an extensive interface area to optimize the mass transfer performance. The reaction mechanism proposed by the pioneers in the research field was eventually chosen to represent the system. These reactions are highly exothermic and reversible. Hence, it was of outmost importance to obtain rate expressions that could embody these characteristics, to get an accurate description of the reaction mechanism in the mathematical model development. The continuity equations were subsequently solved by numerical methods. Moreover, it was found that the model could capture the real characteristics and properties of the system. Introduction CO 2 is considered to be one of the main contributors to the greenhouse effect by causing significant impact on the global climate, affecting precipitation, storm patterns and increased sea levels. The main source of atmospheric CO 2 originates from anthropogenic emissions as a consequence of the consumption of fossil fuels. The interest in CO 2 capture processes started in the 1970 s due to the interest in using CO 2 in the process of Enhanced Oil Recovery. Since then the awareness of the greenhouse effect emerged and the techniques for CO 2 capture had a new target. Typical processes for CO 2 -capture include gas-solid adsorption, gas-liquid absorption, cryogenic techniques and membrane systems. Among these, the gas-liquid absorption processes have been extensively studied and are currently considered the most effective and relative low cost method for reducing CO 2 emissions from fossil fuel fired power plants. The majority of the absorption processes rely on a specific solvent to either react or physically absorb the CO 2 in the flue gases. Reacting solvents rely on the characteristics to weakly bond with CO 2 to form intermediate compounds, the original solvent is then recovered when applying heat. Physical absorption solely utilizes the solubility of CO 2 in the solvent, which subsequently is regenerated by applying heat or pressure reduction [1]. Reaction Mechanism The reaction mechanism when carbon dioxide reacts with an ammoniated aqueous solution is relatively well understood. In the reaction mechanism there are reactions that will proceed at very low rates; other reactions will proceed with low probabilities. Due to the high solubility of the ammonium salts, the solid compounds expected to separate out will proceed at low probabilities. According to Astarita who was a pioneer in this field of research, the main product formation needed to be considered are the carbonated salts of carbamate and bicarbonate. Consequently, the reactions obviously promoting and influencing the absorption rate of can be represented by the two following reactions. These reactions will from now on be the basis for all mathematic modeling concerning the overall reaction mechanism [2]

2 The reaction rates of the two reactions are expressed with forward and reverse temperature dependent rate functions that can be evaluated by the expressions below. absorber at the height where the fluxes are calculated.,,,,, Conservation of mass in liquid film Conservation of mass in a countercurrent packed bed absorber Figure 1 displays the body of a countercurrent packed bed absorber with the gas and liquid flow rates denoted and. There is a fictional transition state of a stagnant boundary layer between the bulk phases, in which the only net transfer is due to intra phase molecular diffusion. Moreover, the reactions that proceed within the boundary are termed heterogeneous as they occur in neither bulk phase, but within the interface Fick s first law of diffusion states that in an isotropic media, the net transfer of diffusive flux is the negative concentration gradient proportional to a diffusion coefficient. The equation will be given here in one spatial dimension. This corresponds to the fact that the concentration of a component during molecular transport at a specific position on the x -axis in the boundary, is uniform over any plane normal to the x axis [3]. 0 Conservation read. PDE representing propagation of components through fictitious liquid film.,,,,,,,, Robin BC, describing molecular transfer over the gas interface for volatile components A and B.,, 0 5,,, 0, 6 Neumann BC, describing isolated gas boundary for non-volatile components C and D., 0 0, 7 Dirichlet BC at the liquid bulk side of the film describes the liquid bulk concentration in the Figure 1. Differential section in packed bed absorber. If the convective transport of gas and liquid phases is considered over the absorber height, a continuity equation for the concentration of a component at a specific height and time can be derived using the differential section, in figure 1. Conservation read. In the derivation of the continuity equations for the absorber height the following assumptions are stated [4]. Total absence of radial gradients of mass and momentum, and are uniform at all radial positions at a given axial location. Negligible axial mixing of gas and liquid phases, i.e. no dispersion. 2

3 Uniform flow, no fluid accelerations and decelerations. PDE representing heat evolution in fictitious liquid film, due to chemical reaction. PDE representing propagation of components in liquid-phase over height of absorption column.,,,,,, 15,,,,,,,,,,,,, 9 Dirichlet BC. Notice that the liquid phase propagates from the top of the absorber.,,,,,, 10 Robin BC, describing heat transfer at the gas interface., 0, 0 16 Dirichlet BC, describing the liquid bulk temperature in the absorber at the height where the heat fluxes are calculated., 17, 0,,,,, 11 PDE representing propagation of components in gasphase over height of absorption column.,,,,,,,,, 0, 12 Dirichlet BC. Notice that the gas phase propagates from the bottom of the absorber.,, 0,,, 0,,, Conservation of energy in liquid film If the reaction enthalpies are finite, the possibilities of non-isothermal conditions are more evident and it is essential to incorporate temperature as a dependent variable in the model development. The kinetics, diffusion and mass transfer coefficients are all functions of temperature and will to certain extent vary over the absorber height. The laws of Fourier describing thermal conduction are analogous to Fick s law of diffusion. Thus, the laws of conservation of mass and energy have a very similar appearance. The conservation of energy in the liquid film read. Conservation of energy in a countercurrent packed bed absorber PDE representing heat evolution in liquid-phase over height of absorption column.,,, 1,,, Dirichlet BC., 0,,, PDE representing heat evolution in gas-phase over height of absorption column.,,,,, 0, Dirichlet BC., , 23 3

4 Results The result section will be based upon the properties of the numerical solution of the mathematical model, developed in the previous section. The solutions of the continuity equations will be represented as three dimensional surface plots where the dependent variable is found on the z-axis and the independent variables respectively on the x- and y-axis. The purpose of the surface plots is to be a visualization of the propagation in time and space and to make conclusions based on these. The surface plots are not intended to be able to read exact numerical values from. Figure 2. Transient solution of continuity equation 9, describing liquid CO 2 propagation. Figure 3. Transient solution of continuity equation 12, describing gaseous CO 2 propagation. Gaseous CO 2 propagates from the base of the absorber and initially holds a concentration of 5 mol m -3. The resemblance with the surface plot of liquid CO 2 is evident. One can clearly see that during the initial state, the profiles form a very similar triangular shape due to the phases is in equilibrium. After the initial state when NH 3 is evident, the gaseous CO 2 provided to the system is rapidly consumed due to the strong reaction between CO 2 and NH 3 within the homogeneous interface. Thus, the flux to the liquid bulk is significantly decreased. The system will achieve a removal efficiency of 69 % under steady state operating conditions Liquid CO 2 propagates from the top of the absorber and initially holds zero concentration of CO 2. Since the superficial velocity of the gas is set to be a hundred times larger than the superficial velocity of the liquid, rapid dynamics in the model will initially force the gaseous CO 2 to be physically absorbed by the liquid phase. This occurrence is almost instantaneous, since the gas resistance in the model is approximately negligible. When the liquid propagation of NH 3 eventually reaches the physically absorbed CO 2 the consumption by chemical reaction is substantial. After approximately 100 seconds, liquid accumulation of CO 2 will cease. Figure 4. Transient solution of continuity equation 9, describing liquid NH 3 propagation. Liquid NH 3 propagates from the top of the absorber and initially holds a concentration of 800 mol m -3. It takes roughly 100 seconds for the liquid NH 3 to propagate to the absorber bottom, which correspond well to the ceased accumulation of CO 2, due to chemical reaction with NH 3. 4

5 Figure 5. Transient solution of continuity equation 12, describing gaseous NH 3 propagation. The gaseous NH 3 propagates from the base of the absorber and initially holds zero concentration of NH 3. In accordance with the relation of gas and liquid phases in CO 2 discussed earlier, the low resistance in the gas bulk will cause the gas and liquid bulk phases to reach chemical equilibrium virtually instantaneous. This explains why the two bulk phases of NH 3 show almost the same features. Figure 7. Transient solution of continuity equation 9, describing liquid NH 4 HCO 3 propagation. Liquid NH 4 HCO 3 propagates from the top of the absorber and initially holds zero concentration. NH 4 HCO 3 is the product when NH 2 COOH is hydrolyzed, according to reaction R2. The peak in this surface plot is more evident compared to the surface plot of NH 2 COOH. The peak is explained by the fact that hydrolyzation of NH 2 COOH is a slow reaction and will solely proceed in the homogeneous liquid bulk phase. Hence, the concentration of NH 4 HCO 3 will be greatly affected by the substantial homogeneous reaction that will occur when NH 3 reaches the accumulated CO 2 in the liquid bulk. Figure 6. Transient solution of continuity equation 9, describing liquid NH 2 COOH propagation. Liquid NH 2 COOH propagates from the top of the absorber and initially holds zero concentration. NH 2 COOH is the direct product formation of the reaction between CO 2 and NH 3 according to reaction R1. Product formation of NH 2 COOH will in general proceed within the heterogenic interface. Hence, the concentration will not be affected by the substantial reaction when NH 3 reaches the accumulated CO 2 in during the initial state. Figure 8. Transient solution of continuity equation 18, describing liquid heat evolution. Liquid propagates from the top of the absorber and initially holds a temperature of 285 K. The heat evolution in the liquid phase is entirely due to the highly exothermic reaction between CO 2 and NH 3. The liquid temparature show strong rescemblance to the surface plot of NH 2 COOH, as a consequence that all heat is generated by reaction R1. 5

6 ,,,, Concentration of component n, in liquid bulk Concentration of component n, in gas bulk Liquid phase heat capacity Gas phase heat capacity Figure 9. Transient solution of continuity equation 21, describing gas heat evolution. Gas propagates from the base of the absorber and initially holds a temperature of 285 K. Temperature rise in the gas bulk is entirely due to the heat transfer from the liquid bulk, since chemical reaction in the gas phase is totally absent. The steep transient at the base of the absorber is explained by the low heat transfer resistance between bulk phases. Conclusion The proposed reaction mechanism combined with the mathematical model is a powerful tool to predict and evaluate the performance of carbon dioxide absorption using chilled aqueous ammonia. Moreover, the mathematical model can effortlessly be adapted to suit any system of interest, as long as the reaction mechanism and kinetics are known. The mathematical model provides sufficient assistance to efficiently design a packed bed absorption column. Liquid diffusivity Gas phase flow rate, feed Height of absorption column Liquid hold-up Vector of reaction enthalpies Gas phase mass transfer coefficient 1 Forward reaction constant for reaction A. 1 Reverse reaction constant for reaction A. 2 Forward reaction constant for reaction B. 2 Reverse reaction constant for reaction B. Liquid phase flow rate, feed Abbreviations and Notations Liquid phase flow rate, effluents Boundary Condition Initial Condition Gas liquid partition coefficient for component / Partial Differential Equation Vector of reaction rates Carbon Dioxide Ammonia Ammonium Carbamate Temperature Gas phase temperature Boundary Carbonate Liquid phase temperature Interfacial area per unit packed volume Concentration of component n, in liquid film, Time Interstitional liquid velocity 6

7 , Interstitional gas velocity Axial coordinate along liquid film Axial coordinate along absorption tower Thickness of liquid film Liquid density Gas density Void fraction Liquid thermal conductivity Literature cited [1] Riemer, P. (1993). The capture of carbon dioxide from fossil fuel fired power stations, IEA Greenhouse Gas R&D Programme, pp 25,29,44,49 [2] Astarita, G. (1967). Mass Transfer With Chemical Reaction. Elsevier Publishing Company. pp 2-6, [3] Danckwerts, P.V. (1970). Gas Liquid Reactions. McGraw-Hill Book Company, pp 18, 30,31 [4] Carberry, J.C. (2001). Chemical and catalytic reaction engineering. Dover Publications, Inc. pp 12,17,19,194,251, Received for review May 6,

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