Estimation Of Deactivation Kinetic Parameters Biology Essay

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In this work, the kinetic parameters of rice husk ash (RHA)/CaO/CeO2 sorbent for SO2 and NO sorptions were investigated in a laboratory-scale stainless steel fixed-bed reactor. Data experiments were obtained from our previous results and additional independent experiments were carried out at different conditions. The initial sorption rate constant () and deactivation rate constant () for SO2/NO sorptions were obtained from the nonlinear regression analysis of the experimental breakthrough data using deactivation kinetic model. Both the initial sorption rate constants and deactivation rate constants increased with increasing temperature, except at operating temperature of 170°C. The activation energy and frequency factor for the SO2 sorption were found to be 18.0 kJ/mole and 7.37.105 cm3/g.min, respectively. Whereas the activation energy and frequency factor for the NO sorption, were estimated to be 5.64 kJ/mole and 2.19.104 cm3/g.min, respectively. The deactivation kinetic model was found to give a very good agreement with the experimental data of the SO2/NO sorptions.

1. Introduction

Cleaning flue gases from sulfur oxides (SOx) and nitric oxides (NOx) has become an issue of great importance to governmental regulatory agencies and general public due to their negative effect towards the environment and human health. Normally SOx and NOx, which consists of more than 98% of sulfur dioxide (SO2) 1 and over 90-95% of nitric oxide (NO),2 are generated mainly from the combustion of fossil fuels in power stations as well as chemical plants and metallurgy processes. Attempts have been made to find a suitable method for the removal of SO2 and NO simultaneously. Dry sorption method is now considered to be the most attractive way to treat waste gases containing SO2 and NO due to the drawbacks of wet sorption methods.3,4 There are several dry-type sorbents that have been considered in the previous study for simultaneous removal of SO2 and NO.

Previously, we had reported the sorption characteristics of SO2 and NO over rice husk ash (RHA)-based sorbent at low temperature.5-11 RHA is an agricultural waste-siliceous materials produced from the burning of rice husk and available abundantly in rice-producing countries like Malaysia. Nevertheless, our previous reports only dealt with activity measurement related to sorbent preparation conditions and effects of reactor operating conditions. Our previous results also showed that the highest sorption capacity for the simultaneous removal of SO2 and NO was obtained using RHA/CaO/CeO2 sorbent. Currently, the optimum preparative parameters for this kind of sorbent had also been reported.12 On the other hand, the reaction between the siliceous/calcium dry-type sorbents and SO2/NO is very scarcely reported. The reaction between this siliceous/calcium dry-type sorbents and SO2/NO are very complicated due to the complex composition of the sorbent. The sorption of these pollutant gases (SO2/NO) on the sorbents is not a simple physical sorption processes, but also may be described as chemisorption or as gas-solid non-catalytic reactions.

There are various kinetic models that have been employed to estimate kinetic parameters in gas-solid reaction, mainly involves single component sorbent (such as CaO, Ca(OH)2 and CaCO3) and it was carried out mainly at high operating temperature. These kinetics models included shrinking unreacted core model,13 changing grain size model 14 and random pore model.15 Most of these models contain large number of adjustable parameters related to the pore structure, to the product layer and pore diffusion resistances as well as the surface sorption rate parameters. In addition, it is complicated to incorporate them without having to perform lengthy computer programs. Therefore in this study, the simplified deactivation kinetic model was used to estimate kinetic parameters against other models. The breakthrough curves data obtained from our previous results 11 (SO2 and NO sorptions) was fitted to deactivation kinetic model. In the present work, kinetic parameters such as deactivation rate constant, initial sorption rate constant, activation energy and frequency (pre-exponential) factor of the SO2 an NO sorptions were estimated from the breakthrough data through nonlinear regression analysis. In chemical engineering, the rate of reaction is a prerequisite to the design and evaluation of fixed-bed reactor performance especially under dry-type gas-solid reaction-sorption processes.

2. Experimental Section

2.1. Preparation of sorbent. RHA-based sorbents (RHA/CaO/CeO2) were prepared from rice husk ash (RHA), CaO (BDH Laboratories, England) and Ce(NO3)3. 6H2O (Fluka, 98%). The raw RHA was collected directly without any pretreatment from Kilang Beras & Minyak Sin Guan Hup Sdn. Bhd., Nibong Tebal, Malaysia. Prior to use, the RHA was sieved to produce less than 200 mm particle size. The chemical composition of raw RHA was 68.0% SiO2, 2.30% K2O, 1.20% P2O5, 0.71% MgO, 0.59% CaO, 0.32% SO3, 0.32% Cl2O, 0.16% Al2O3, 0.40% others and 26.0% LOI. The preparation method was based on the optimum hydration conditions reported in our previous studies.12

2.2. Activity Test. The sorption/activity of the prepared sorbents was tested in a laboratory-scale stainless steel fixed-bed reactor (Swagelok, 10 mm ID, 50 cm length) which was vertically fitted in a tube furnace (Linberg/Blue M). The schematic diagram and details of the activity study is presented elsewhere.5 The experiments were conducted at various reactor temperature range of 70°C to 170°C while maintaining the simulated flue gas under the fixed condition of 2000 ppm SO2, 500 ppm NO, 10% O2, 10% RH, balance N2 with total gas flow rate of 150 ml/min. Other operating conditions are given in our previous study.11

2.3. Kinetic Parameters Estimation of RHA/CaO/CeO2 Sorbent Using Deactivation Kinetic Model. The analysis of kinetic parameters was carried out using breakthrough data of single component gases of SO2 and NO, respectively. The deactivation kinetic parameters such as initial sorption rate constants () and deactivation rate constants () were calculated from breakthrough curve analysis. The outline of the analysis using deactivation kinetic modeling is given as follow. As in a typical gas-solid reaction, pore structure, active surface area and activity per unit area of the solid reactant have significant effects on the reaction rate. In the deactivation model, the effects of all these factors are combined in an activity term () introduced into the sorption rate expression and is written in Eq. (1).16

(1)

where is the deactivation rate constants (min-1), is the concentrations of the reactant gas (kmol/m3), is the reaction time (min), and and are exponential coefficients. Assuming that the concentration of the reactant gas is independent along the reactor (= 0) and the deactivation of the sorbent is first-order with respect to the solid active site (=1), integration of Eq. (1) give the following expression.

(2)

Furthermore, the following basic assumptions were made in the derivation of the deactivation model, such as isothermal and pseudo-steady state conditions, and axial dispersion in the fixed bed reactor and any mass transfer resistances were neglected. Considering these assumptions, and the initial activity () of the solid as unity, the pseudo-steady state species conservation equation for gases in the fixed bed reactor is given by Eq. (3).16-18

(3)

where is the volumetric flow rate (m3/min), is the sorbent mass (kg) and is the initial sorption rate constant (m3 kg-1 min-1). Combining Eqs. (2) and (3) and solving these equations will yield Eq. (4)

(4)

whereby is equal to and this kinetic model is known as the zeroth solution of deactivation model, which predicts the behavior of breakthrough curves for a gas-solid non-catalytic reaction. This solution assumes a fluid phase concentration that is independent of deactivation process along the reactor. However, it would be reasonable to expect the deactivation rate to be concentration dependent and axial position dependent in the fixed bed reactor.

In order to find analytical solutions of Eqs. (1) and (2) by considering concentration and axial position dependents in the fixed bed reactor (==1), iterative procedure was applied. The procedure used was similar to the procedure for the approximate solution of nonlinear equations suggested by Dogu.19 In this procedure, Eq. (4) was substituted into Eq. (1) with ==1 and the first estimated value for the activity () term was obtained by integrating the equation. Then, the estimated value for the activity () term expression was substituted into Eq. (3), and integration of this equation gave the following corrected solution for the breakthrough curve.

(5)

This Eq. (5) is also known as the solution of two-parameter deactivation kinetic model. Deactivation rate constant () and initial sorption rate constant () was then calculated by using a nonlinear regression technique.

A commercial software, MATHEMATICA ver. 5.2 (Wolfram Research Inc.), was used for nonlinear regression analysis together with the experimental/breakthrough data to find the rate constants for the model. In order to obtain the best fitting results, an error minimization technique was also applied and included after running the main program code of MATHEMATICA. MATHEMATICA software was run under Microsoft Windows XP Professional (ver. 2002) environment.

Based on the analysis of the experimental breakthrough data at different temperatures, the initial sorption rate constants () can be obtained by fitting Eq. (5) using nonlinear regression technique. Then, Arrhenius equation 16 was used for the determination of activation energy and frequency (pre-exponential) factor for SO2 and NO sorptions at different temperatures, and is given in Eq. (6).

(6)

where is a frequency (pre-exponential) factor, is the activation energy, is the gas constant (8.314 J/mole.K) and is the temperature (K).

3. Results and Discussion

Figure 1(a) & (b) shows the experimental SO2 and NO breakthrough curves obtained under various operating temperatures, respectively. The initial sorption rate constants () and deactivation rate constants () values were estimated by nonlinear fitting of Eq. (5) to the experimental SO2 and NO breakthrough curves at different temperatures. The results of rate parameters from the regression analysis of the data obtained with RHA/CaO/CeO2 sorbents at different temperatures are given in Table 1. The accuracy of the proposed deactivation kinetic model was assessed from the coefficient of determination (R2) which was found to be 0.95 or higher. Other kind of regression results (including statistical analysis) could be obtained from the nonlinear regression analysis after running the main program code of MATHEMATICA.

(a)

(b)

Figure 1. Effect of operating temperature on the (a) SO2 and (b) NO sorptions.

As expected, from Table 1, both the initial sorption rate constants and deactivation rate constants increased with increasing temperature. However, at operating temperature of 170°C, the initial sorption rate constant for SO2 was decreased. The decrease in the rate of SO2 sorption at higher temperatures might be due to water that accumulated and gas dissolving on the RHA/CaO/CeO2 sorbent surface was reduced.11 The predictions of the breakthrough curves from Eq. (5) at different temperatures using these rate constants are also shown in Figure 1, whereby the deactivation kinetic model shows good agreement with the experimental data at different temperatures. As predicted for SO2 sorption at high temperature (170°C), the breakthrough curves shifted to shorter time (Figure 1(a)). For NO sorption, the initial sorption rate constants still increased at high temperature (170°C) and the resulting breakthrough curves shifted to longer time (Figure 1(b)). This might be attributed to a lesser amount of water accumulated on the RHA/CaO/CeO2 sorbent surface thus allowing the metal species (CeO2) present in the sorbent to become more active.11

Table 1. Rate parameters obtained from the breakthrough data at different temperature.

Temp

(°C)

(cm3/g.min)

(min-1)

R2

SO2sorption

NO sorption

SO2sorption

NO sorption

SO2sorption

NO sorption

SO2sorption

NO sorption

70

4.06

10.22

1.22E+03

3.06E+03

0.12

0.11

0.987

0.989

87

5.84

11.00

1.75E+03

3.30E+03

0.15

0.12

0.975

0.990

100

8.57

11.45

2.57E+03

3.43E+03

0.20

0.126

0.972

0.954

120

10.85

13.38

3.25E+03

4.01E+03

0.21

0.128

0.983

0.976

150

13.12

14.56

3.93E+03

4.36E+03

0.23

0.130

0.991

0.964

170

11.69

15.78

3.50E+03

4.73E+03

0.24

0.135

0.965

0.957

Based on the data obtained in Table 1, Arrhenius equation (Eq. (6)) was used for the estimation of activation energy () and frequency (pre-exponential) factor () for SO2 and NO sorptions at different temperatures. Figure 2 (a) and (b) shows versus plots for SO2 and NO sorptions, respectively at different temperatures. The plots were found to yield a straight line indicating that the sorption rate constant obtained from deactivation kinetic model do follow the Arrhenius law as in Eq. (6). Accordingly, the slope of the plot equal to and intercept equivalent to , from which activation energy () and frequency factor () for SO2 and NO sorptions can be obtained, respectively.

The value of frequency factor () for SO2 and NO sorptions were calculated to be 7.37.105 cm3/g.min and 2.19.104 cm3/g.min, respectively. Whereas the activation energy () values determined for the SO2 and NO sorptions were 18.0 kJ/mole and 5.64 kJ/mole, respectively. The activation energy of the SO2 sorption at low temperature using the RHA/CaO/CeO2 sorbent was found to be slightly higher as compared to sorbent prepared from coal fly ash/Ca(OH)2 (14.94 - 15.47 kJ/mole),20 activated carbon from oil palm shell with KOH impregnation (13.2 kJ/mole) 21 and activated carbon from oil palm shell (12.6 kJ/mole).22 However, the activation energy obtained in this study was lower than the SO2 sorption when Ca(OH)2 (32 kJ/mole) 23 and coal fly ash/CaO/CaSO4 (22.9 kJ/mole) 24 were used as the sorbent, and also much lower than the reported value by Irabien et al.25 and Renedo & Fernandez 26 using Ca(OH)2 (75 kJ/mole) and coal fly ash/Ca(OH)2/CaSO4 (57.7 kJ/mole), respectively. Apart from that, this activation energy for SO2 sorption at low temperature was also found to be similar as compared to sorbents prepared from various type of CaCO3 (15.2 - 19.5 kJ/mole).27 For the case of the NO sorption, the value of activation energy was also much lower than previously reported in the literature which include the sorbent prepared from V2O5/NH4Br/TiO2/SiO2 (30.1 kJ/mole),28 V2O5-Al2O3 (53.56 kJ/mole) 29 and Fe-ZSM-5 (54 kJ/mole).30 However, most of the reported studies for NO sorption were carried out at high temperature processes. The relatively small activation energy obtained in this study suggested a feasible and easy sorption process of SO2 and NO by RHA-based sorbent. In other word, the sorption between SO2/NO and the reference sorbent synthesized from RHA/CaO/CeO2 is easier to occur due to the easier excess of SO2 and NO molecules to the active species in the sorbent.

(a)

(b)

Figure 2. Arrhenius plot of sorption rate constant versus reciprocal of operating temperature for (a) SO2 and (b) NO sorptions.

In order to verify the proposed deactivation kinetic model, additional independent experiments were carried out at different conditions using 0.5 g RHA/CaO/CeO2 sorbent. The first experiment was conducted at initial condition of 1500 ppm SO2, 1200 ppm NO, 10% O2, 60% RH, balance N2 and 150 ml/min of total flow rate at a reactor temperature of 80°C. While the second experiment was conducted at the following conditions of 1800 ppm SO2, 800 ppm NO, 10% O2, 40% RH, balance N2 and 150 ml/min of total flow rate at a reactor temperature of 110°C. Figure 3 shows the experimental versus predicted breakthrough curves of SO2 and NO sorptions at two different experimental conditions. It was shown that the deactivation kinetic model provided a very accurate description of the experimental data.

Figure 3. Comparison between predicted and experimental breakthrough curves at two different experimental conditions.

For further confirmation, the breakthrough curves data from our previous results 11 was fitted to the proposed deactivation kinetic model. The comparison between predicted breakthrough curves (obtained with deactivation kinetic model) with the experimental results was performed for all the SO2/NO sorption experiments under various operating conditions. Figure 4 (a) and (b) shows the comparison between the experimental C/Co versus predicted C/Co of SO2 and NO sorptions in all experiments, respectively. The results indicated that the proposed model prediction agrees reasonably well with the experimental data of the SO2/NO sorptions within the range of 10% experimental error.

(a)

(b)

Figure 4. Plot of all experimental C/Co vs predicted C/Co under various operating conditions for (a) SO2 and (b) NO sorptions.

4. Conclusions

In the present study, the deactivation model was applied successfully to describe the experimental breakthrough curves for the sorption of SO2 and NO from simulated flue gas in a fixed-bed reactor over RHA/CaO/CeO2 sorbent. The breakthrough data obtained for both SO2 and NO sorptions was fitted to the proposed deactivation kinetic model. Both the initial sorption rate constants and deactivation rate constants increased with increasing temperature, except at operating temperature of 170°C whereby the initial sorption rate constant for SO2 decreased. The activation energy and frequency factor for the SO2 sorption were 18.0 kJ/mole and 7.37.105 cm3/g.min, respectively. For the NO sorption, the activation energy and frequency factor were estimated to be 5.64 kJ/mole and 2.19.104 cm3/g.min, respectively. The breakthrough curves obtained by using the developed deactivation kinetic model were found to fit the experimental breakthrough curves very well.

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