Carbon Dioxide Absorption Modeling for Off-Gas Treatment in the Nuclear Fuel Cycle

+e absorption of carbon dioxide is an important process in many practical applications such as reduction of greenhouse gases, separation and purification processes in the chemical and petroleum industries, and capture of radioactive isotopes in the nuclear fuel cycle +e goal of this research is to develop a dynamic model to simulate CO2 absorption by using different alkanolamines as absorption solvents. +e model is based upon transient mass and energy balances for the chemical species commonly present in CO2 gas-liquid absorption. A computer code has been written to implement the proposedmodel. Simulation results are discussed. +e reported model simulates well the response to dynamic changes in input conditions. +e proposed model can be used to optimize and control the separation of carbon-14 in the form of CO2 in the nuclear industry.


Introduction.
e off-gas stream produced from reprocessing used nuclear fuel containing a host of radioactive gases including tritium, iodine, methyl iodide, krypton, xenon, and carbon dioxide.ese gases are hazardous to human health, and some are of considerable economic value.Currently, there is interest in the efficient capture of these gases for recovery or storage purposes [1].
Presently, postcombustion separation of carbon dioxide from flue-gas streams is investigated using membrane separation, low-temperature distillation, physical adsorption by activated carbon and zeolites, chemical absorption by mineral oxides to produce the corresponding carbonates, and chemical absorption by suitable solvents [2].Chemical absorption by solvents is the most common form of the CO 2 capture process.Amines, and mixtures containing amines, are the most used solvents as these compounds react quickly with CO 2 , maintaining high mass transfer-driving forces [2].Industrially important amines are monoethanolamine (MEA), diethanolamine (DEA), diisopropanolamine (DIPA), and the tertiary amine N-methyldiethanolamine (MDEA).Most industrial processes are operated with aqueous amine solutions, but solvents consisting of a mixture of water and a nonaqueous solvent, for example, sulfolane in the Shell-Sulfinol process [3], are also frequently used [4].Blending of different amines is considered to be attractive because in this way the high absorption capacity of tertiary amines can be combined with the high absorption rates of primary or secondary amines [5].Blends are also more flexible than singular amines because the relative concentration of the amines can be varied [6].Other combinations have been considered, such as MEA and 2-amino-2-methyl-1-propanol (AMP).e latter amine is an attractive alternative since it offers higher absorption capacity and lower regeneration energy.Blending MEA with AMP is considered to combine all favorable characteristics of both amines and overcome the unfavorable characteristics [7].Some studies have been carried out considering the influence of the solvent mixed with the alkanolamines.For example, Usubharatana and Tontiwachwuthikul [8] studied the kinetics of CO 2 capture using methanol mixed into solutions of MEA. e goal of this work is to develop a theoretical model for dynamic simulations of CO 2 absorption using a generic blend of amines and/or other solvents.e proposed model can be used to simulate chemical absorption using a wide range of CO 2 input stream concentrations.rough computational implementation, the derived model can be used for design, optimization, and control applications.

Model Organization.
In this work, we will follow an approach similar to the one used by Greer et al. [9] in the dynamic simulation of the absorption/desorption of carbon dioxide from monoethanolamine (MEA).A dynamic model of the absorption process will be developed using a generic mixture of solvents to increase the absorption rate.
Mass transfer rates are calculated using the thin film model with chemical reactions confined to the liquid thin film.Henry's law is used for modeling the vapor-phase equilibrium of CO 2 .Henry's constant values for the different gas-phase species are calculated using fugacity ratios obtained by the Peng-Robinson equation of state (EOS).A kinetic scheme is proposed to represent the complex chemical reactions between CO 2 and the solvents.Liquid and vapor energy balances are developed to calculate the liquid and vapor temperature, respectively.A schematic of the column is shown in Figure 1. e model of the absorption tower is developed by taking a small slice of the tower of height dz. e height of the packing goes from z � 0 to z � H, where H is the packing height.

Kinetic Studies.
e most important part of the proposed model is the simulation of the complex chemical reactions involving the solvents and CO 2 .In the case of primary and secondary amines, the reaction mechanism is well understood as was originally proposed by Caplow [10] and reintroduced by Danckwerts [11].CO 2 reacts with the amine through a two-step process.e first step proceeds through the formation of a zwitterion intermediate: is step is slow and considered to be the ratecontrolling step; it is followed by a very fast removal of a proton by a base: It is important to notice that all bases present in the liquid phase will participate in reaction (2); therefore, B i represents a generic base participating in the reaction with the zwitterion.In this mechanism, the overall forward reaction rate equation can be derived using the quasi-steady-state assumption for the zwitterion intermediate [12]: where k 1 , k −1 , and k bi are the respective specific constants and  i k bi [B i ] represents the summation over the reaction rates of all the bases reacting with the zwitterion present in the solution.In dilute aqueous solutions, for example, the amine, OH − , and water act as a base, while in nonaqueous solvents, only the amine can be considered a base [12].
In the case of high amine concentration in the solvent, Equation ( 3) is simplified to For aqueous MEA solutions, the overall reaction rate is of second order, and is of first order with respect to the amine.is finding indicates that the deprotonation of the zwitterion by the bases present in the solution is very fast compared to the reverse reaction.erefore, Equation ( 4) is considered the main reaction in the absorption of CO 2 in high-concentration aqueous alkanolamine solutions.In the case of low-concentration solutions, more complex rate equations hold [2,13].Alvarez-Fuster et al. [14] and Sada et al. [15] showed that changes in the solvent lead also to changes in the order of reaction.
A different mechanism applies to the reaction of CO 2 with ternary amines.According to Littel et al. [16], the reaction of CO 2 with tertiary amines can be described satisfactorily using the base-catalysis reaction mechanism proposed by Donaldson and Nguyen [17]: is mechanism is essentially a base-catalyzed hydration of CO 2 ; thus, tertiary amines cannot react directly with CO 2 .
is finding was confirmed by Versteeg and Van Swaaij [18], who studied the absorption of CO 2 into a solution of MDEA and ethanol without water.
In all the cases discussed above, the following CO 2 reactions are also present: Reaction ( 6) is very slow and can be neglected in most circumstances.Reaction (7) e ionic species remain in the liquid phase, while the others are transferred from one phase to the other according to the scheme shown in Figure 2.
Only gas-phase mass transfer resistance is considered for liquid solvents (H 2 O, R 1 R 2 R 3 N, and RNH 2 ), while liquid-only mass transfer resistance for the gas species has been considered: CO 2 , N 2 , and O 2 ([2], among others).Under certain conditions, however, both resistances have to be considered for the reacting species CO 2 .In our computer code, we consider these situations by using a global mass transfer coefficient given by 1 where K l CO 2 is the overall mass transfer coefficient based upon liquid-phase concentrations; k l CO 2 is the liquid-phase mass transfer coefficient; k g CO 2 is the gas-phase mass transfer coefficient; g i is the concentration-based Henry's constant, in which C l i and C g i are the liquid-and gas-phase ispecies concentrations, respectively; and E is the enhancement factor defined in the subsection below.Typical values of these coefficients are given in Table 1.In Table 2, all the chemical species considered in the model are included.
1.4.2.Reactions.Mandal et al. [20] and Benamor and Aroua [21] proposed the following set of reactions occurring in the aqueous primary amine solution.A gasliquid equilibrium equation and six chemical equilibria equations are introduced to describe the chemistry involved in CO 2 absorption: Following Bosch et al. [6] who studied blends of alkanol amines, we add reaction (5) catalyzed by ternary amines and reaction (16) to account for the decomposition of the ternary ammonium ion: Reactions ( 5), (9), and (11) are the main reactions in CO 2 absorption by amines.e other reactions are required to complete the total reaction mechanism [6].
e CO 2 loading rate, defined as the ratio of CO 2 to alkanolamines, determines the relative weight of all reactions.For CO 2 loading rates below 0.5, Equation ( 9) is the main reaction.In the case of loading rates above 0.5, reaction (11) predominates, while reaction (5) will be important only for large amounts of ternary amine in the feed.In this work, we are interested in small loading rates and significant amounts of ternary amine present; therefore, the reactions with the amines will be the most important ones.A list of all OH -, and H + (no interphase transfer) Table 1: List of chemical species participating in the reaction scheme.reactions used in the model is included in Appendix.Equation ( 15) is considered by using the corresponding Henry's law constant for CO 2 .
e forward reaction ( 9) is thought to occur through a two-step mechanism.Initially, a CO 2 molecule and an alkanolamine molecule form a zwitterion intermediate which, in a second step, reacts with another alkanolamine molecule.e second step is much faster than the first step; hence, the first step is rate limiting and of second order.e reaction rate is given by e specific forward rate constant k 1f is calculated using the method in [22]: e bicarbonate ion formation, reaction (11), is the most important reaction for CO 2 /alkanolamine loadings above 0.5.It is of second order, given by e forward rate for the formation of bicarbonate is significantly fast, but the overall rate is usually quite small due to the low concentration of OH − ions used.At loadings of CO 2 /alkanolamines above 0.5, this becomes the dominant reaction for CO 2 removal.e forward rate is calculated from [23]: In order to complete the rate calculations, we collected literature data corresponding to the equilibrium rate constants of reactions ( 9)-( 14) from Bedelbayiev et al. [24] and Greer [2].In order to deal with reactions ( 5) and ( 16) for ternary alkanol amines, we followed many investigators including Haimour et al. [25], Critchfield [26], Littel et al. [16], and Rangwala et al. [27] who fit the rate constant of the reaction as a function of temperature using All values of kinetic parameters used are listed in Table 3.A full description of all the rate equations and calculation of generation terms is also included in Appendix.

Enhancement Factor.
e carbon dioxide absorption is accompanied by strong chemical reactions.erefore, the calculation of the CO 2 flux term requires the use of an enhancement factor (E) to account for the enhanced mass transfer.e enhancement factor is defined as the mass transfer rate under reactive absorption divided by the mass transfer rate under nonreactive absorption conditions [31].e CO 2 molar flow term (N CO 2 ,diff ) is given as follows [2,9,24]: where a w is the interphase area per unit volume.e enhancement factor (E) is a function of the Hatta number (Ha) defined as where D CO 2 is the diffusion coefficient and k if are the forward specific reaction rate constants.e influence of the different reactions on the total rate of CO 2 absorption is considered by the enhancement factor E. e Hatta number is the ratio of the rate of homogeneous reaction relative to the rate of gas dissolution.Ha is also a measure of the amount of dissolved gas that reacts inside the diffusion film near the gas-liquid interface compared to the amount that reaches the bulk of the solution without reacting.When Ha � 0, we have purely physical absorption.e higher the value of the Hatta number, the stronger the effect of chemical reactions on mass transfer.In the case of Ha > 2, the enhancement factor E is directly equal to Ha [31].
Versteeg et al. [32] recommended a different definition of the Hatta number including C CO 2 instead of C NaOH in Equation ( 23) to calculate the enhancement factor when all RNH 2 is consumed, and reaction (3) is the dominant CO 2 removal reaction.Other authors have used both formulations with similar results [24,33,34].In this work, however, we preferred to use the general definition of the Hatta number, Equation (23).

Mass Transfer Model 1.5.1. Mass Balances.
e mass balance of component i in the liquid phase was calculated using the following equation [2,35] where u l is the superficial liquid-phase velocity, R gen,i represents moles of species i generated/consumed by interphase reaction per unit volume, and N i,diff is the mass flow of component i from the liquid phase into the gas phase.In the model presented in this work, the effect of reaction on the CO 2 absorption is considered through the use of the enhancement factor.In the cases of ionic species, there is no interphase mass transfer; therefore, for these reactions, Equation (24) becomes e generic amines (RNH 2 and R 1 R 2 R 3 N) are the only chemical species for which we have to calculate a generation term plus an interfacial mass transfer term (N RNH 2 ,diff and N R 1 R 2 R 3 ,diff ).International Journal of Chemical Engineering 1.6.Energy Balances.
e reactions given by Equations ( 8) and ( 11) are highly exothermic; therefore, an energy balance has to be solved in order to consider temperature changes.
A two-equation model for the transient energy balance in the control volume depicted in Figure 1 leads to the following equations for all the components shown in the figure [9,36]: where C g pi and C l pi are the heat capacities of component i in the mixture, U T is the global heat transfer coefficient, u g is the superficial velocity inside the gas phase, and ΔH R is the heat released by the chemical reaction.e CO 2 molar flow term (N CO 2 ,diff ) is given by Equation (22), while the enhancement factor (E) is given by the Hatta number defined by Equation (23).

ermodynamics.
e molar flow of component i from the gas phase into the liquid phase (N g i,diff ) is calculated using where C * i is the interfacial liquid equilibrium concentration.In order to evaluate C * i , we use a formulation based upon the calculation of gas and liquid fugacity values [2]. is formulation avoids the use of an iterative procedure as the fugacity values can be calculated directly as is expression for the diffusion molar flow is valid for the RNH 2 , R 1 R 2 R 3 N, and H 2 O components when the resistance is assumed to be in the gas-liquid film [2].A similar expression for CO 2 , O 2 , and N 2 can also be derived by In Equations ( 29) and ( 30), R is the ideal gas constant; P is the pressure; T is the temperature; C l T is the total molar concentration in the liquid phase; Z g is the gas-phase compressibility factor; f l i and f g i , are the fugacities of component i in liquid and gas phases, respectively; and φ l i and φ g i , are the fugacity coefficients for component i in the liquid and gas phases, respectively.

Model Validation.
A FORTRAN computer code was developed based upon a previous one prepared for simulating CO 2 absorption using primary/binary amine solvents [30].An explicit finite-difference scheme was used to solve the relevant hyperbolic partial differential equations.For convenience, in our equations, all variables were made dimensionless, but the species concentrations were calculated in dimensional values (mM and mol/m 3 ).e residence time of the liquid phase (t r � H/u l ) was used to define a dimensionless time (t � time/t r ).In all our simulation runs, we used geometric parameters and operating conditions taken from the literature.A list of our input data is shown in Table 4. is list includes information about the packing, the ranges of all values, and the standard set used in most of our calculations.
Validation of the computer code was achieved by comparing calculated parameters with data from the literature, especially with the work of Greer [2].e validation process included checking against literature values [2,5,6,23,26,39] the values of our calculated geometric parameters (d p , a T , and a w ), transfer coefficients (k l i and k g i ), kinetic parameters (k if , k ir , K i , and E), and equilibrium parameters (H cc , f g i , f l i , φ g i , and ϕ l i ).It also included a comparison of calculated mass species concentration profiles against literature values [2,5,23,26,30].
In Figure 3, we show a comparison of calculated CO 2 axial concentration profiles against those values reported by Greer [2] for dimensionless time (t) equal to 0.328 (2000 s) and steady-state condition.e basic set of parameters and operating conditions reported by Greer ([2] Table 4.2 in page 90) was used in these calculations.It can be seen in the International Journal of Chemical Engineering figure that there is good agreement between our calculated data and those from Greer [2] for the CO 2 axial concentration profiles; our calculated values, however, were always slightly lower than those reported by Greer [2].Similar agreement, not shown in this work, was achieved when calculating the other chemical compounds' axial profiles.e accuracy of the reaction model was validated by carrying out a mass balance for the amine chemical species.A global mass balance for the amines and their reaction products at equilibrium gives e difference between both sides in Equations ( 31) and (32) was used as a way of estimating the accuracy of the reaction scheme.In all our calculations, the error between the calculated concentrations was on the order of the code precision (10 −6 ).A global mass balance for CO 2 was used as another way of estimating the global accuracy of the proposed model.e biggest relative error in all our calculations was 0.01%.

Simulation Results.
e time change of the CO 2 concentration is depicted in Figure 4, where typical axial concentration profiles are presented.At dimensionless time equal to 0, a gas mixture containing CO 2 is injected.e CO 2 concentration is highest at the base of the column, Z � 0, and drops as we approach the top, Z � 1. e results in Figure 4 show that as time increases, the concentration of CO 2 increases as we approach the top.We can also see that, at long times, the steady state is achieved.
In order to study the time evolution of the concentration of the generic amine, we chose to use monoethanolamine (MEA) due to the high amount of data available for this particular chemical compound.MEA reacts with CO 2 following reaction (9).Two amine ions, the ammonium-like ion   13) and ( 14), respectively.e interaction between these ions and MEA is very complex and varies with time.In Figures 5 and 6, we show contour plots which describe the variations of the ionic species axial profiles with time.In Figures 5 and 6, the depth axis depicts the axial variation of the concentration from the bottom to the top, i.e., it is a view from the bottom.e horizontal axis shows the time change of the concentration profile.Low values are represented by blue colors, while high values are represented by red colors.e "back" wall represents ionic input values, while the left-side wall represents initial conditions.e cation profile is shown in Figure 5. e figure shows that the values of the cation concentration are initially very high throughout the column and decrease as time increases.
e cation concentration is equal to zero at the column top (Z � 1), passes through a maximum, and decreases as it moves to the bottom (Z � 0).As time increases, the concentration of the cation decreases at the bottom of the column.Our results show that the decrease in the cation concentration leads to an increase in both the anion concentration and the neutral solvent. is behavior is produced by the complex interaction among the different chemical reactions.
Figure 6 depicts the time evolution of the carbamate ([RNHCOO − ]) ion concentration.e anion is not present in the input solution at the top (Z � 1); its concentration increases as CO 2 moves upwards in the gas phase, until a maximum is reached at the bottom, coinciding with the highest CO 2 concentration at the bottom of the column (Z � 0). e concentration values of the ammonium-like ion were also higher than the carbamate concentration values in all simulations.
e time variation of the solvent MEA concentration is shown in Figure 7.
It is shown in Figure 7 that as the amount of the reaction products increases, we can expect that the amount of the free amine will decrease.An analysis of the three contour plots shows that, at short times, there is a high rate of generation of the cation by consumption of the MEA solvent.As time increases, the concentration of the cation decreases, while the concentration of the anion increases, and some increase of the solvent concentration is observed until equilibrium is achieved.
e main goal of this project is to develop a dynamic simulator for nuclear energy applications.
e dynamic simulator is evaluated by how it describes sudden changes in input parameters.In order to test our model, we simulated the response to two sudden changes in input CO 2 concentrations: (i) a step which permanently increases the CO 2 input concentration and (ii) a discrete pulse which increases the input concentration during a fixed time; then, the input concentration is set to its original value (Figures 8 and 9).In the case of a step change in input concentration, we assumed that the column reaches the steady-state operating conditions shown in Figure 4; this is the starting time for the simulation (t � 0).At t � 0, we double the value of the CO 2 input concentration.
e results are shown in Figure 8 where the CO 2 gas-phase concentration starts increasing in value from the bottom of the column (input) towards the top (output) until a new equilibrium is achieved at higher concentration values (t > 0.1).
ere is a continuous increase in CO 2 concentration until the new steady-state values are reached.e area between both curves is proportional to the amount of extra mass added.
e simulation results for a discrete pulse are shown in Figure 9.We start from the final equilibrium concentration profile shown in Figure 8 (t � 0).At t � 0, the CO 2 input concentration is set to its original value (1.7 mol/m 3 ), and the CO 2 concentration starts decreasing throughout the column.
is behavior is more noticeable at the bottom of the column, as the extra amount of CO 2 injected during the pulse travels through the column.
e solid line in Figure 9 represents the final steady value to be reached, equal to the one depicted in Figure 4 for the same CO 2 input concentration.At this point in time, all the extra mass injected by the pulse has been absorbed and removed from the gas phase.e area in between the steady-state curve and the CO 2 concentration profile at a particular time represents the remaining extra CO 2 mass injected during the pulse.International Journal of Chemical Engineering e results presented in Figures 8 and 9 show that the proposed model can be successfully used to analyze the response of the absorption column to sudden changes in CO 2 input concentrations.

Conclusions
A model for the dynamic behavior of reactive CO 2 absorption using mixtures of alkanolamine solvents has been successfully developed.
e model is based upon transient mass and energy balances for several different chemical species commonly present in CO 2 gas-liquid absorption.
e phase equilibrium has been considered using a thermodynamic model and through the use of experimentally based Henry's law values.Typical values for the geometric parameters of the absorber and the packing characteristics have been collected.A reaction scheme that takes into account the different reactions between CO 2 and blends of amines in an alkaline environment has been proposed.A computer code has been written to implement the proposed model.
e computer code has been validated by checking the values of parameters calculated and comparing results to those reported in the literature.e mass balances for CO 2 have been close within a 0.01% relative error, while the alkanolamine solvents' mass balances have been closed within the computer code precision (10 −6 ).e results have been collected, and they are logical and agree with equivalent literature results.e computer code developed in this work can describe adequately the dynamic processes occurring due to sudden changes in operating conditions.erefore, it is a valuable tool to design, optimize, and control absorption processes in the nuclear industries.

A. Overall CO 2 Mass Transfer Coefficient
e computer code developed to implement our model calculates an overall mass transfer coefficient based upon liquid-phase concentrations (K l CO 2 ) and compares its value with the liquid-layer mass transfer coefficient (k l CO 2 ) value to decide which one should be used at each step of the calculations.Typical results are presented in Table 2. Equation (8) was used to calculate K l CO 2 .We can see that, in most of the calculations presented in this work, the relative error between using k l CO 2 E and K l CO 2 is around 10%; therefore, the overall mass transfer coefficient is used.

C. Reaction Rates
e equations used to calculate the forward and reverse reactions are Here, x H 2 O is the water molar fraction in the feed solvent phase.

E. Simulation Parameters
In our simulation runs, we used a Montz B 200 metal structured packing [2] as typical packing.Table 4 shows typical geometric parameters and operating variables used in the simulation runs.

F. Generation Terms
Assuming the pseudo-steady state for every chemical species, we can calculate the generation terms that enter into the chemical species mass balances.In order to simplify the calculations, we determined an overall rate per reaction according to R ai � r if − r ir . (F.1) Every generation term (R geni ) is calculated by a molar balance using Reaction rate for species i (mol•m −3 •s −1 ) R: Gas constant (J•mol −1 •K −1 ) t: Time (s) T i : Temperature of the i phase (K) u i : Superficial velocity of the i phase (m•s −1 ) U T : Global heat transfer coefficient (J•m −2 •K −1 •s −1 ) z: Column height (dim.)Z g : Compressibility factor (dim.) ΔH R : Heat released by chemical reaction (J•mol −1 ) φ j i : Fugacity coefficients for component i in phase j (dim.)Dim.: Dimensionless.

9 )R
gen9 � R a7 − R a8 .(F.10) Nomenclature a T : Mass transfer specific area (m 2 •m −3 ) a w : Packing specific area (m 2 •m −3 ) International Journal of Chemical Engineering B i :Concentration of base i participating in reaction (2) (mol•m −3 ) C * i : Interfacial liquid equilibrium concentration (mol•m −3 ) C j i : Concentration of species i in phase j (mol•m −3 ) C j pi : Heat capacities of component i in phase j (J•mol −1 K −1 ) D i : Diffusivity of component i (m 2 •s −1 ) E:Enhancement factor (dim.) E a :Activation energy (J•mol −1 ) f j i :Fugacities of component i in phase j (dim.or Pa) H cc :Concentration-based Henry's constant (dim.)Ha:Hatta number (dim.)k bi : Specific reaction rate constant of base i (m 3 •mol −1 •s −1 ) k i : Specific reaction rate constant (m 3 •mol•s −1 or s −1 ) k o i : Preexponential factor reaction i (m 3 •mol•s −1 or s −1 ) k if : Forward reaction specific rate constant (m 3 •mol•s −1 or s −1 ) k ir : Reverse reaction specific rate constant (m 3 •mol•s −1 or s −1 ) k j i :Phase j mass transfer coefficient of species i (m/s) K i :Equilibrium constant reaction i (dim.or mol m −3 ) K l i : Overall liquid mass transfer coefficient of species i (m/s) N i,diff : Flow of component i from the liquid phase into the gas phase (mol m −3 s −1 ) N g i,diff : Flow of component i from the gas phase into the liquid phase (mol•m −3 •s −1 ) R gen,i : Species i generated/consumed by chemical reaction (mol•m −3 •s −1 ) r i : , however, is fast and can enhance

Table 2 :
Typical values for CO 2 mass transfer calculations.

Table 3 :
Information used in solving the proposed reaction model.

Table 4 :
Typical values of column geometric parameters and operating variables.+ ) and the carbamate ion ([RNHCOO − ]), are produced by this reaction and consumed by reactions (

Table 3
summarizes all the rate equations used in the model.e first number in the first column is the equation number used in Appendix.e second number refers to the original equation number used in the article.