Pressure Dependence of the Nonequilibrium Kinetic Model That

Dec 1, 2010 - Hai Du, Armin D. Ebner, and James A. Ritter* ... A. D. Ebner , M. L. Gray , N. G. Chisholm , Q. T. Black , D. D. Mumford , M. A. Nichols...
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Ind. Eng. Chem. Res. 2011, 50, 412–418

Pressure Dependence of the Nonequilibrium Kinetic Model That Describes the Adsorption and Desorption Behavior of CO2 in K-Promoted Hydrotalcite Like Compound Hai Du, Armin D. Ebner, and James A. Ritter* Department of Chemical Engineering, UniVersity of South Carolina, Columbia, South Carolina 29208, United States

The reversible nonequilibrium kinetic model (RNEK) that describes the adsorption and desorption behavior of CO2 in K-promoted hydrotalcite like compound (HTlc) was further modified to account for different CO2 pressures. A complete set of model parameters were obtained by fitting it to experimental adsorption and desorption cycling data carried out with commercial K-promoted HTlc at four temperatures (380, 420, 460, and 500 °C) and five CO2 partial pressures (0.05, 0.19, 0.41, 0.86, and 1.0 atm). Four consecutive cycles were run, with each having a 30 min adsorption step in CO2 and a 30 min desorption step in He. The RNEK model fitted the experimental data very well over the wide ranges of temperature and pressure. This new version of the RNEK model should be very useful for designing temperature and pressure swing adsorption processes and sorption enhanced reaction processes via dynamic modeling, especially within the range of conditions studied. Introduction There has been considerable interest in K-promoted hydrotalcite like compound (HTlc) as a reversible adsorbent for CO2.1-12 This interest stems initially from work done at Air Products and Chemicals1,2 and subsequently that done by other research groups3-8 on sorption enhanced reaction processes (SERP) for the production of hydrogen. This material has also been touted for use in precombustion carbon capture by pressure swing adsorption (PSA).9-12 Understanding the adsorption and desorption behavior of CO2 in K-promoted HTlc at high temperature has been a challenge. Several models have been proposed that all consider equilibrium3,13-15 or nonequilibrium16-18 chemisorption and reaction processes taking place, coupled with a linear driving force (LDF) mass transfer resistance. One of the most comprehensive and experimentally validated models has been developed by Ritter and co-workers.16-18 In 2006, Ebner et al.16 proposed a simple mechanism that qualitatively describes the dynamics of the uptake and release of CO2 in K-promoted HTlc via three coupled, reversible reactions. This proposed mechanism was quantified in 2007 by Ebner et al.17 by formulating the three reactions in terms of an LDF mass transfer resistance driven by an equilibrium process, followed by two nonequilibrium processes. This three step model successfully predicted both short and long cycle time experiments carried out at 400 °C, and in particular, it was able to capture the very slow dynamic behavior of CO2 in K-promoted HTlc that becomes manifest only at very long cycle times. In 2010, Du et al.18 extended this reversible nonequilibrium kinetic (RNEK) model to account for changes in temperature by making each of the three reactions temperature dependent. This temperature dependent version of the RNEK model was successfully validated against experimental cycling data obtained over a wide range of temperatures from 300 to 500 °C for both long and short cycle times. This temperature dependent version of the RNEK model provides a much deeper understanding of the dynamic behavior * To whom all correspondence should be addressed. E-mail: [email protected]. Phone: (803) 777-3590. Fax: (803) 777-8265.

of CO2 in K-promoted HTlc. It is also suitable for temperature swing adsorption (TSA) process or SERP modeling, but only when the CO2 partial pressure stays fixed at about 1 atm because it cannot account for changes in the partial pressure of CO2. This limits its applicability and thus obviates its use in a PSA process or SERP modeling, when CO2 partial pressure changes are substantial. Therefore, the objective of this research note is to show how the temperature dependent version of the RNEK can be modified to also account for changes in the CO2 partial pressure. Pressure Dependent RNEK Model Formulation As a first approximation in the RNEK model, only the fractional surface coverage of phase A at equilibrium, i.e., θA,e,a, was given a pressure dependence, as noted but not formulated by Du et al.18 This was a logical choice, because phase A is associated with a reversible, chemisorption step through an equilibrium driven LDF process. Since it was the equilibrium loading in this term (or fractional surface coverage) that was assumed to be pressure dependent, this assumption made it possible to select a Langmuir or Langmuir-type adsorption isotherm model to account for pressure dependence. For reasons given in the Results and Discussion section, the well-known Toth adsorption isotherm model was selected to express θA,e,a in terms of pressure. This relationship is given in eq 1 θA,e,a )

bP [1 + (bP)t]1/t

(1)

where t is an adsorbent heterogeneity parameter and b is given by

(

b ) bo exp -

∆H RT

)

(2)

Here, bo is the pre-exponential coefficient, ∆H is the heat of adsorption, T is the absolute temperature, and R is the universal gas constant. The complete set of model equations is given in Table 1. Further description and discussion of the terms involved in the model are given in the work of Du et al.18

10.1021/ie100965b  2011 American Chemical Society Published on Web 12/01/2010

Ind. Eng. Chem. Res., Vol. 50, No. 1, 2011 Table 1. Temperature and Pressure Dependent Formulation of the RNEK Model That Describes the Adsorption and Desorption Behavior of CO2 in Commercial K-Promoted HTlc dqC ) -k1,fqC + k1,bqAqB dt

dqA ) km(qA,e - qA) + k1,fqC - k1,bqAqB + k2,fqB - k2,bqAqE dt

Materials and Experiments for Model Validation

qE ≡ qT - qB - qC

A commercial sample of K-promoted HTlc, namely, Puralox MG 70 (Sasol, Germany) was used in this study. It was reported to contain 20 wt % K2CO3 and was used as received. High purity grade CO2 (National Welders) and UHP He (National Welders) were also used as received. A Perkin-Elmer TGA-7 thermogravimetric analyzer was used to measure the dynamic adsorption and desorption behavior of CO2 on this K-promoted HTlc. To carry out the adsorption part of the cycle at different CO2 partial pressures, a 1000 psia gas mixture containing CO2 at a specified partial pressure in He was prepared. This was done volumetrically in a 2.25 L SS tank by charging this tank with different pressures of the two pure gases. The mole fraction of CO2 in the resulting mixture was determined using gas chromatography. The desorption step was carried out in pure He. A typical TGA run was carried out with a single pellet of K-promoted HTlc (∼90 mg, D ) 0.48 cm, L/D ) 1), as follows. First, the sample was activated at 500 °C for 8 h in He flowing at around 60 cm3/min and at 1 atm. With He still flowing, the temperature was changed to the temperature of interest (380, 420, 460, or 500 °C). Once this temperature was reached, the gas was switched from He to a mixture of CO2 in He (CO2 mole fraction of 0.05, 0.193, 0.41, 0.86, or 1.0) also flowing at around 60 cm3/min and at 1 atm. This adsorption step continued for 30 min. Then, the gas was switched back to He to initiate the 30 min desorption step.

qCO2 ≡ (qA - qA,o) + (qB - qB,o) + 2(qC - qC,o) For adsorption, km ) km,a, qA,e ) qA,e,a ) qA,maxθA,e,a qA,max ) η(qB + 2qE); η ) mn(T - T0)/[1 + n(T - T0)] bP -∆H ; b ) b0 exp RT [1 + (bP)t]1/t

(

)

For desorption, km ) km,d, qA,e ) qA,e,d ) 0

( ( ( ( ( (

) ) ) ) ) )

km,a ) Am,a exp

-Em,a RT

km,d ) Am,d exp

-Em,d RT

k2,b ) A2,b exp

-E2,b RT

k2,f ) A2,f exp

-E2,f RT

k1,b ) A1,b exp

-E1,b RT

k1,f ) A1,f exp

-E1,f RT

This temperature and pressure dependent RNEK model has 23 parameters, including the three additional fitting parameters associated with the pressure dependence, i.e. t, bo, and ∆H. Five of these parameters are known a priori, including To. Unlike the previous work,18 To in this study was arbitrarily defined a priori to be 250 °C. The value of 250 °C was chosen to be low enough to provide a wider range of conditions for the model but also high enough to describe the experimental trends with temperature. This leaves 18 parameters to be regressed to experimental data. The nonlinear regression analysis used to obtain reasonable values for each of the 18 parameters was carried out by the least-squares method using the Solver routine in MS Excel. The goodness of the fit of the model over the entire set of experimental results was evaluated by calculating the coefficient of determination, R2, defined as

R2 ) 1 -

∑ (q i

CO2,i,pre

∑ (q i

CO2,i,pre

- qCO2,i,exp)2 - qjCO2,exp)2

wi - wo 1 (1 + (qA,o + qB,o + 2qC,o)MCO2) wi MCO2 (4)

where wi represents the experimental mass obtained at a given time i during an experiment and wo represents the experimental mass just after activation.

dqB ) k1,fqC - k1,bqAqB - k2,fqB + k2,bqAqE dt

θA,e,a )

qCO2,i,exp )

413

(3)

where qCO2,i,pre, qCO2,i,exp, and qjCO2,exp are the predicted, experimental, and average loadings, respectively. The experimental CO2 loading qCO2,i,exp was estimated from the predicted loading at a reference state according to18

Table 2. Parameter Values for the RNEK Model That Describe the Adsorption and Desorption Behavior of CO2 in Commercial K-Promoted HTlc from 380 to 500 °C and at CO2 Partial Pressures from 0.05 to 1.0 atm parameter

value

unit

known a priori qA,o qB,o qA,e,d qT To

0.000 0.000 0.000 2.283 523.15

mol/kg mol/kg mol/kg mol/kg K

fit to experiment qC,o (avg) Am,a () km,a) Em,a Am,d Em,d A1,f () k1,f) E1,f A1,b E1,b A2,f E2,f A2,b E2,b m n b0 ∆H t

1.641 1.937 0.000 13.0085 16.0285 2.0 × 10-4 0.000 1.2835 × 10-5 -41.0 0.2841 20.7042 8.877 × 10-2 -12.6487 9.2 4.416 × 10-4 0.04537 -16.0 0.2874

mol/kg 1/min kJ/mol 1/min kJ/mol 1/min kJ/mol kg/(mol min) kJ/mol 1/min kJ/mol kg/(mol min) kJ/mol 1/K 1/kPa kJ/mol

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Figure 1. Experimental adsorption and desorption cycling results (symbols) and RNEK model predictions (lines) for the CO2 loading in commercial K-promoted HTlc at 380 and 420 °C and at five CO2 partial pressures (1.0, 0.86, 0.41, 0.19, and 0.05 atm).

Four consecutive adsorption and desorption cycles were carried out in this fashion at each temperature and CO2 partial pressure. Results and Discussion First note that the two previous studies17,18 used homemade K-promoted HTlc for contrasting the experimental data against

the constant temperature17 and temperature dependent18 versions of the RNEK model. In this third and final study on the development of the RNEK model, a commercial K-promoted HTlc was used because the results would clearly be more relevant to anyone interested in developing a CO2 adsorption process using this material. Nevertheless, since the homemade material was synthesized based on the original recipe,1 the

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Figure 2. Experimental adsorption and desorption cycling results (symbols) and RNEK model predictions (lines) for the CO2 loading in commercial K-promoted HTlc at 460 and 500 °C and at five CO2 partial pressures (1.0, 0.86, 0.41, 0.19, and 0.05 atm).

homemade and commercial K-promoted HTlc materials exhibited very similar CO2 adsorption and desorption cycling behaviors (results not shown). The only difference was that the commercial K-promoted HTlc exhibited moderately less absolute CO2 capacity and CO2 working capacity than the homemade version. Table 2 lists the values of the temperature and pressure dependent RNEK model parameters that were obtained by fitting it to the experimental cycling data. The following

nonlinear regression methodology was used to obtain the parameters in Table 2. To obtain reasonable initial guesses, the temperature dependent parameters were regressed first by fitting the experimental data obtained at the four different temperatures with the CO2 partial pressure fixed at 1 atm (i.e., pure CO2). Then, the pressure dependent parameters were determined by regressing all the experimental data at the four temperatures and five CO2 partial pressures simultaneously with the model. In this regression process, the aim

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Figure 3. Experimental results (symbols) and RNEK model predictions (lines) (using an average value of qC,o) for the CO2 working capacity as a function of CO2 partial pressure in commercial K-promoted HTlc at four different temperatures (380-500 °C). The CO2 working capacity is the difference between the CO2 loading at the end of the fourth adsorption step and that at the end of the fourth desorption step (refer to Figures 1 and 2).

was to predict the CO2 working capacity instead of the absolute CO2 loading because the former is more meaningful for adsorption process simulation and design. It is worth pointing out that different adsorption isotherm models were tested for adding the pressure dependence to the model. These included Langmuir, Freundlich, LangmuirFreundlich, and Toth adsorption isotherm models. During the arduous nonlinear regression process, it was determined that the Toth adsorption isotherm model shown in eq 1 fit the experimental cycling data the best. It is also important to explain the significant difference between some of the values reported in Table 2 and those reported in Du et al.,18 namely, Am,d, Em,d, A1,b, A2,f, A2,b, m, and n. The major reason for these differences was due to the K-promoted HTlc evaluated in this work being commercial Puralox MG 70, with that evaluated in ref 18 being homemade. Another reason was due to the regression analysis in this work covering different pressures in addition to different temperatures. Figures 1 and 2 display the experimental adsorption and desorption cycling behavior and the resulting RNEK model predictions at the four different temperatures and five different CO2 partial pressures. A coefficient of determination, R2 ) 0.9786, was obtained for the entire set of experimental data, which is quite acceptable when considering the wide ranges of pressure and temperature involved in the regression analysis. Note that for these model predictions the value of qC,o was allowed to vary at each temperature and CO2 partial pressure. These individual values of qC,o are shown in each panel; the average value of qC,o is listed in Table 2. This was necessary since a different pellet was used for each experiment, which gave rise to slight differences in the tare weight of the sample at the end of activation; however, these differences were only around 1.0 wt % of the unactivated sample weight and thus very small.

Figure 3 shows the experimental results and resulting RNEK model predictions for the CO2 working capacity as a function of CO2 partial pressure at four different temperatures. The CO2 working capacity was computed from the results in Figures 1 and 2 as the difference between the CO2 loading at the end of the fourth adsorption step and that at the end of the fourth desorption step. Note that for these model predictions, the average value of qC,o was used. This makes the temperature and pressure dependent RNEK model useful for process simulation. It is clear from the results shown in the Figures 1-3 that the temperature and pressure dependent RNEK model fit the experimental data very well, even when an average qC,o was used (Figure 3). This was quite a feat when considering the wide ranges of both temperature and CO2 partial pressure. This excellent fit of the model to experiments thus provided further evidence that the adsorption and desorption behavior of CO2 in K-promoted HTlc at high temperature is due to a combination of completely reversible chemisorption, diffusion and reaction phenomena, as envisioned in earlier works.16-18 The results in Figure 3 also show that the CO2 working capacity in K-promoted HTlc generally increased with increasing CO2 partial pressure. It also increased slightly with increasing temperature. Both of these trends were captured very well by the RNEK model. This temperature and pressure dependent RNEK model should thus be very useful for PSA, TSA, and SER process simulation carried out from 380 to 500 °C and up to 1 atm of CO2 partial pressure. Conclusions The reversible nonequilibrium kinetic model (RNEK) that describes the adsorption and desorption behavior of CO2 in K-promoted hydrotalcite like compound (HTlc) was further modified to account for different CO2 partial pressures. The Toth adsorption isotherm model was utilized for this purpose. It was easily incorporated into the previously developed temperature dependent form of the RNEK model.

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A complete set of model parameters were obtained by fitting this temperature and pressure dependent RNEK model to experimental adsorption and desorption cycling data carried out with commercial K-promoted HTlc at four temperatures (380, 420, 460, and 500 °C) and five CO2 pressures (0.05, 0.19, 0.41, 0.86, and 1.0 atm). Four consecutive cycles were run, with each having a 30 min adsorption step in CO2 and 30 min desorption step in He. The RNEK model fit the experimental data very well over the wide ranges of temperature and pressure. Overall, this new version of the RNEK model provided further evidence that the adsorption and desorption behavior of CO2 in K-promoted HTlc at high temperature is due to a combination of completely reversible adsorption, diffusion, and reaction phenomena. It should also be very useful for designing temperature and pressure swing adsorption processes, and sorption enhanced reaction processes via dynamic modeling. Acknowledgment The authors gratefully acknowledge financial support provided by DOE through Grant No. DE-FG26-03NT41799 and the Separations Research Program at the University of Texas at Austin.

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qCO2 ) CO2 loading relative to qo (mol CO2/kg of CO2-free K-promoted HTlc) qCO2,i,exp ) experimental CO2 loading relative to qo at time i (mol CO2/kg of CO2-free K-promoted HTlc) qCO2,i,pre ) CO2 loading predicted by the model relative to qo at time i (mol CO2/kg of CO2-free K-promoted HTlc) qo ) CO2 loading after activation (mol CO2/kg of CO2-free K-promoted HTlc) qT ) total number of reaction sites available for chemically bound CO2 (mol of sites/kg of CO2-free K-promoted HTlc) qX ) concentration of site X, with X ) A, B, C, or E (mol of sites/ kg of CO2-free K-promoted HTlc) qX,o ) concentration of site X after activation, with X ) A, B, C, or E (mol of sites/kg of CO2-free K-promoted HTlc) qjCO2,exp ) average of all experimental CO2 loadings relative to qo (mol CO2/kg of CO2-free K-promoted HTlc) R2 ) coefficient of determination for the data regression t ) parameter for the Toth model describing the fractional coverage of phase A at equilibrium To ) fitting parameter for η (K) w ) experimental mass (g) wo ) experimental mass just after activation (g) Greek Letters ∆H ) heat of adsorption (kJ/mol) θA,e,a ) fractional coverage of phase A at equilibrium η ) ratio of actual reaction sites to the maximum number of reaction sites

Nomenclature A ) reaction site for weakly chemisorbed CO2 in K-promoted HTlc Ai,j ) pre-exponential factor in the Arrhenius type relationships for the reaction and mass transfer processes: i ) m, 1, 2; j ) f, b b ) affinity coefficient for the Toth model describing the fractional coverage of phase A at equilibrium (1/kPa) bo ) pre-exponential factor of the affinity coefficient b (1/kPa) B ) reaction site for one molecule of chemically bound CO2 in K-promoted HTlc, i.e., Mg6Al2K2O9(CO3) C ) reaction site for two molecules of chemically bound CO2 in K-promoted HTlc, i.e., Mg6Al2K2O8(CO3)2 E ) reaction site free of CO2 in K-promoted HTlc, i.e., Mg6Al2K2O10 Ei,j ) activation energy in the Arrhenius type relationships for the reaction and mass transfer processes: i ) m, 1, 2; j ) f, b k1,f ) forward rate constant (1/min)17 k1,b ) backward rate constant (kg/(mol min))17 k2,f ) forward rate constant (1/min)17 k2,b ) backward rate constant (kg/(mol min))17 km,a ) mass transfer coefficient for adsorption of CO2 from the gas phase into phase A (1/min) km,d ) mass transfer coefficient for desorption of CO2 from phase A into the gas phase (1/min) m ) fitting parameter for η MCO2 ) molecular weight of CO2 (kg/mol) n ) fitting parameter for η P ) partial pressure of CO2 (kPa) qA,e ) concentration of site A at equilibrium (mol of sites/kg of CO2-free K-promoted HTlc) qA,e,a ) concentration of site A at equilibrium after adsorption (mol of sites/kg of CO2-free K-promoted HTlc) qA,max ) maximum concentration of site A formed during adsorption (mol of sites/kg of CO2-free K-promoted HTlc) qA,e,d ) concentration of site A at equilibrium after desorption (mol of sites/kg of CO2-free K-promoted HTlc)

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ReceiVed for reView April 27, 2010 ReVised manuscript receiVed October 21, 2010 Accepted November 12, 2010 IE100965B