regression modelling of thermal degradation kinetics, of concentrated, aqueous piperazine in carbon...

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Proceeding the Regional Conference on Chemical Engineering 2014 Yogyakarta, December 2-3, 2014

ISBN: 978-602-71398-0-0

Regression Modelling of Thermal Degradation Kinetics, of

Concentrated, Aqueous Piperazine in Carbon Dioxide Capture

Shaukat A. Mazari, Brahim Si Ali*

Department of Chemical Engineering, Faculty of Engineering, University of Malaya, 50603, Kuala

Lumpur, Malaysia.

*E-mail address: [email protected]

Abstract. Carbon dioxide (CO2) emissions are a rising concern for the climate change and

global warming. Postcombustion CO2 capture using amine-base solvents seems to be a viable

technology. Concentrated, aqueous Piperazine (PZ) is an advanced solvent that has promising

characteristics to capture CO2. Experimental, thermal degradation kinetics data of

concentrated, aqueous PZ, loaded with CO2 was regressed using MATLAB®. Data is fitted to

first and second order rate laws, by linear and nonlinear regression methods. Six different types

of expressions were used to describe the trend of thermal degradation of CO2 loaded aqueous

PZ. The findings revealed that the thermal degradation data followed both first order and

second order kinetics. Current model exhibited that rate constants (k1 and k2) can be predicted

by making use of six different expressions (1-6). Expression 3 and 5 are the most appropriate

expressions for predicting the thermal degradation kinetics for the first order and second order

rate laws. Coefficient of determination (R2) for both models are higher than 0.99.

Key words: CO2 capture, degradation kinetics, piperazine, regression, thermal degradation,

1. Introduction

The report of international energy agency (IEA) [1], exhibited that production of electricity

and heat from fossil fuel-fired power plants accounted for 41% of the global carbon dioxide

(CO2) emissions in 2010. The highest rate of CO2 emissions, i.e. 71.5% has been noticed in

electricity and heat sector for one decade, from 1990 to 2010, that is no doubt an alarming

sign to activate mitigation of these emissions [1]. Amine-based absorption/stripping process

is a viable approach for capturing CO2 from coal-fired power plant flue gases [2]. Solvent

selection is considered as a primary step to this technology because it has a major role in the

performance of CO2 capture and economics [3, 4]. However, the viability of a solvent

depends on several parameters, namely; CO2 capture capacity, volatility, absorption rate,

degradation resistance and environmental impact. One of an essential parameter for solvent

selection criteria is the thermal degradation, as the stripper temperature goes above 100 °C,

which causes a rise in steam requirements and ultimately lowers CO2 capture capacity [5, 6].

Piperazine is a newly established solvent that has higher capacity of CO2 capture, high CO2

absorption rate and lower thermal and oxidative degradation [5, 7-11]. Thermal degradation

rate of PZ is minimum compared to the conventional amines. However, the abundant thermal

degradation products of 8 m PZ are N-formyl PZ (FPZ), ammonium (NH4+), and N-(2-

aminoethyl)PZ (AEP) which accounts for a total of 57% of nitrogen and 45% of carbon loss

[9]. Thermal degradation PZ also produces nitrosamines, which are potentially carcinogens

compounds [12]. Nitrosation of PZ occurs either through oxidation of PZ or due to the

presence of nitrogen gas contents (NOx) [13, 14]. Further, research revealed that N-(nitroso)-

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piperazine (MNPZ) formed in absorber can be decomposed in stripper at 150°C with a

significant rate [15].

PZ thermal degradation follows secondary nucleophilic (SN2) reaction mechanism, which

supports the hypothesis of second order rate law and rate constant (k2), to be used for the

analysis of PZ loss [11].

Regression analysis is one the of basic tools used to analyze the chemical kinetics data [16].

Order of reaction, coefficient of rate constants and initial rate of reaction can be determined

by using linear and nonlinear methods of regression [17, 18]. Literature studies [9-11]

indicate, that the linear and exponential regression has been carried out for the data of current

system, concentrated aqueous PZ. However, the results obtained through the regression are

with lower R2 values, especially at 135°C. This suggests a detailed regression analysis of the

experimental data of the system is required. Six different expressions are produced from first

and second order rate laws. A comprehensive regression is conducted for all the expressions.

Detailed analysis of rate constants (k1 and k2) is discussed with respect to each model

(expression).

2. Methodology

Early PZ studies showed that PZ loss kinetics follow first order kinetics and rate constant (k1)

[10]. Recent studies revealed that PZ thermal degradation is believed to follow SN2 reaction

mechanism, which advocates a second order rate law and rate constant (k2) to analyze PZ loss

[11]. Thus, first order rate law and second order rate law expressions were rearranged in 6

different forms of linear and nonlinear expressions to get a better fit to the experimental data.

Integrated equations (at boundary conditions, t=0, and t=t) of the first order and order rate

laws are reported as in equation (1) and equation (2);

Experimental data for thermal degradation of aqueous, concentrated PZ was taken from

previous studies [9-11]. However, the subject data is for thermal degradation of 8 m PZ with

0.3 mole CO2 per mole alkalinity. Details of the materials and methods may be viewed from

the sources. In this study, MATLAB® R2012b is used. Regression analysis is conducted,

using the function curve fitting tool. Data for dependent and independent variables (X) and

(Y) are prepared as per Table 1. Expressions 1 to 4 employed polynomial first order and

expression 5 used second order polynomial whilst exponential function is used for expression

6.

CPZ (1)

(2)

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Table 1 Linear and Nonlinear forms of first and second order rate equations

Expression Type Equation Curve fitting (Y Vs X)

Expression 1,

First Order

Linear

lnCPZ Vs t

Expression 2,

Second Order

Linear

1/CPZ Vs t

Expression 3,

Second Order

Linear

1/CPZ.t Vs 1/t

Expression 4,

Second Order

Linear

CPZ/CPZ0 Vs CPZ.t

Expression 5,

Second Order

Quadratic

t/CPZ0 Vs t

Expression 6,

First Order

Exponential CPZ CPZ Vs t

3. Results and discussions

In this study, experimental data of concentrated, aqueous PZ are analyzed by using six

different expressions for the first and second order kinetics. Expressions for the first and

second order models for linearized and non-linearized forms with conditions are presented in

Table 1. Expression 1 and 2 are representing first order rate equation; however, expressions 2

to 5 represent a second order rate equation. First four expressions are in the linearized form

while fifth and sixth are in quadratic and exponential forms respectively. Expressions; 1, 2, 4

and 6 exhibited more or less similar results to those published in the literature previously.

However, two equations; expression 3 and 5 presented highly reliable results with R2 values

higher than 0.99.

3.1 First order kinetics

Expressions 1 and 6 in Table 1, are representing the first order rate laws. Expression 1 is in

the linear form and expression 6 is in exponential form. The results obtained through these

two expressions have identical R2 values. The highest R2, noticed for the first order

expressions 1 and 6 is at 150 °C, which is 0.96 and lowest R2 is observed at 135 °C.

However, overall k1 values are similar to those reported in literature, so the first order

reaction expressions are not of much interest in the case of this study. First order rate

constants, k1 of these two expressions and that from the literature are presented in Table 2.

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Table 2 First order rate models results for thermal degradation of 8 m PZ with 0.3 mole CO2

per mole alkalinity initially at 135 °C to 175 °C.

Temperature (°C) k1( s-1) R2 k1( s-1) R2

Expression 1, First order kinetics Literature results Model results

175 1.32*10-7 0.98 1.20*10-7 0.89

165 3.14*10-8 0.95 3.94*10-8 0.88

150 6.12*10-9 0.96 8.63*10-9 0.96

135 9.69*10-10 0.57 9.70*10-10 0.56


175 1.32*10-7 0.98 1.20*10-7 0.89

165 3.14*10-8 0.95 3.94*10-8 0.88

150 6.12*10-9 0.96 8.63*10-9 0.96

135 9.69*10-10 0.57 9.70*10-10 0.56

It is observed from Table 2 and 3 that the coefficients of determination, R2 are changing at

each temperature in virtually every equation. Change in R2 values at each temperature

advocates that the independent(X) and dependent(Y) variables data points are not uniform.

This reveals that there is a significant impact of temperature on the data fitting of

concentrated, aqueous PZ.

3.2 Second order kinetics

Second order kinetics is reported in expressions 2 to 5. Expressions 2 to 4 are in the first

order polynomial form while the expression 5 is in the quadratic form. Detailed k2 values for

each expression is shown in Table 3.

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Table 3 Results of k2 of second order models of thermal degradation of 8 m PZ with 0.3

mole CO2 per mole alkalinity initially at temperatures, 135 °C to 175 °C.

Temperature (°C) k2( kg/mmol.s) R2 k2( kg/mmol.s) R2


175 4.94*10-11 0.99 5.62*10-11 0.91

165 1.28*10-11 0.94 1.22*10-11 0.87

150 1.49*10-12 0.95 2.05*10-12 0.96

135 2.39*10-13 0.58 2.40*10-13 0.53


175 4.94*10-11 0.99 6.09*10-11 0.99

165 1.28*10-11 0.94 7.95*10-12 0.99

150 1.49*10-12 0.95 1.97*10-12 1.00

135 2.39*10-13 0.58 1.64*10-13 0.99


175 4.94*10-11 0.99 5.08*10-11 0.84

165 1.28*10-11 0.93 1.17*10-11 0.75

150 1.49*10-12 0.95 2.05*10-12 0.95

135 2.39*10-13 0.58 2.37*10-13 0.50


175 4.94*10-11 0.99 5.24*10-11 0.99

165 1.28*10-11 0.94 1.77*10-11 0.99

150 1.49*10-12 0.95 1.83*10-12 0.99

135 2.39*10-13 0.58 5.06*10-13 0.99

It is observed from Table 3, that the expressions, 2 and 4 R2 values are not consistent at each

temperature. This shows that either time or concentration data is in a highly haphazard

condition or expressions are not good representatives of the data. Generally, the most

appropriate fitting is found at 150 °C and the poorest at 135 °C except expression 3 in linear

models and expression 5 as quadratic. The expressions 2 and 4 presented poorest R2 values

while expression 3 and 5 showed higher R2 values. The expression 3 has R2 values nearly

equal to 1, which put forward the expression as a more suitable option, for predicting the

second order kinetic data by linear method. Similarly, on the basis of R2 values, the

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expression 5 also can be considered as a workable equation for predicting second order

kinetics data, as R2 values for this expression are also higher than 0.99.

Second order rate law fits data with more flexibility than the first order rate law due to its

versatility in alternate expressions formation, as provided in Table 1. Modeled expressions 2

to 4 describe the linear behavior of the second order kinetics whose results are more or less

similar in expressions, 2 and 4 with small changes. Consistency of the model for expression 3

can be tested by its R2 values, which demonstrates that expression 2 and 4 failed to provide

more reliable fit for the thermal degradation data in comparison to expression 3.

Linear method has nothing to do with process, either it is linear or not but it rather assumes

that the experimental data provided is linear [19]. In this method, dependent variable (Y) is

predicted on the basis of intercept and slope for given values of independent variable (X) for

the equation. To get the best fit, it is suggested to linearize the Y data with respect to X data,

as accomplished in expression 3.

3.3 Comparison between literature and models result

S.A Freeman et al, [9] used Null hypothesis (H0) for slopes of three different data sets

(including data of this work) of the same system and found the results using linear regression

for the first order rate constant, k1. In literature [10], exponential regression for the same

work exhibited slightly higher values of k1 under the same experimental data, however, there

is no appreciable variation in the results that may be discussed in details. Values of k1 in

previous literature [9-11] by the same author showed consistency nearly with same R2 values.

This study is in agreement with the linear and exponential regression of first order rate law

with literature. Model results of expressions 1 and 6 are compared in Figure1 for better better

understanding.

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Figure 1 Comparison of results obtained through expression 1 and 6 to those observed in the

literature.

It can be observed from Figure 1, that at 135 °C and 175 °C model results for expressions, 1

and 6 are slightly lower to those published in the literature. Somewhat higher results for

expression 1 and 6 were noticed at 150 °C and 165 °C.

Second order rate law, results of thermal degradation kinetics data are best fitted by the

models of this study than literature. R2 values of expressions 2 and 4 are nearly equivalent to

those reported in the literature. Higher coefficient of determination values has been noticed

for two expressions of second order kinetics, namely: expression 3 and 5. Results of k2 for

expression 2 and 4 are nearly equal to those reported in the literature, but for expressions 3

and 5 k2 values are different to those published in the literature. Expression 3 and 5 presented

somewhat similar k2 values to those of literature and expression 2 and 4 at 150 °C and 175 °C

only. However, deviation in k2 values is observed at 135 °C and 165 °C. A comparison of

results of k2 of the models is compared with the results of literature in Fig 2.

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Figure 2 Comparison of results of literature for k2 and second order models of the study.

4. Conclusions

Thermal degradation data o PZ is found to follow both first order and second order

kinetics.

Conventional equations failed to present better results for second order kinetics,

especially at 135 °C.

The results of first order rate models, expressions 1 and 6 and second order models,

expressions 2 and 4 are in agreement with the results of literature.

Expression 3, in the linear form and expression 5, in quadratic form provides the

most feasible fits with R2 values higher than 0.99.

5. Nomenclature

CPZ = concentration of piperazine at time, t

CPZ0 = concentration of piperazine at time, 0

CO2 = carbon dioxide

Exp = exponent

H0 = null hypothesis

k1 = coefficient of first order rate constant

k2 = coefficient of second order rate constant

Mmoles/kg= millimoles per kilogram

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MNPZ = 1-nitrosopiperazine

PZ = piperazine

R2 = coefficient of determination

SN2 = nucleophilic substitution reaction

SSR = sum of squares of residuals

6. References

[1] IEA, CO2 emissions from fuel combustion highlights, International Energy Agency

(2012) Edition (2012) 124. (http://www.iea.org/co2highlights/co2highlights.pdf)

[2] A.B. Rao, E.S. Rubin, A Technical, Economic, and Environmental Assessment of Amine-

Based CO2 Capture Technology for Power Plant Greenhouse Gas Control, Environmental

Science & Technology 36 (2002) 4467-4475. (Journal)

[3] G.T. Rochelle, Amine scrubbing for CO2 capture, Science 325 (2009) 1652-1654. Journal

[4] G. Rochelle, E. Chen, S. Freeman, D. Van Wagener, Q. Xu, A. Voice, Aqueous

piperazine as the new standard for CO2 capture technology, Chemical Engineering Journal

171 (2011) 725-733. (Journal)

[5] J.D. Davis, Thermal degradation of aqueous amines used for carbon dioxide capture,

University of Texas Libraries, Austin, Tex., 2009, pp. 1 online resource (xxix, 278

leaves). (Dissertation)

[6] J. Davis, G. Rochelle, Thermal degradation of monoethanolamine at stripper conditions,

Energy Procedia 1 (2009) 327-333. (Journal)

[7] A.J. Sexton, Amine oxidation in CO2 capture processes, University of Texas, Austin,

Tex., 2008, pp. 1 online resource (xxiv, 262 leaves). (Dissertation)

[8] S.A. Freeman, R. Dugas, D.H. Van Wagener, T. Nguyen, G.T. Rochelle, Carbon dioxide

capture with concentrated, aqueous piperazine, International Journal of Greenhouse Gas

Control 4 (2010) 119-124. (Journal)

[9] S.A. Freeman, Thermal degradation and oxidation of aqueous piperazine for carbon

dioxide capture, University of Texas, Austin, Tex., 2011, pp. 1 online resource (lvi, 734

leaves). (Dissertation)

[10] S.A.D. Freeman, Jason, Rochelle, Gary T., Degradation of aqueous piperazine in carbon

dioxide capture, International Journal of Greenhouse Gas Control 4 (2010) 1750-5836.

(Journal)

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[11] S.A. Freeman, G.T. Rochelle, Thermal Degradation of Aqueous Piperazine for CO2

Capture: 2. Product Types and Generation Rates, Industrial & Engineering Chemistry

Research 51 (2012) 7726-7735.

[12] P.N. Magee, Toxicity of nitrosamines: Their possible human health hazards, Food and

Cosmetics Toxicology 9 (1971) 207-218. (Journal)

[13] M.J. Goldman, N.A. Fine, G.T. Rochelle, Kinetics of N-nitrosopiperazine formation

from nitrite and piperazine in CO2 capture, Environmental science & technology 47

(2013) 3528-3534. (Journal)

[14] P.T. Nielsen, L. Li, G.T. Rochelle, Piperazine degradation in pilot plants, Energy

Procedia 37 (2013) 1912-1923. (Proceeding)

[15] N.A. Fine, P.T. Nielsen, G.T. Rochelle, Decomposition of secondary nitrosamines in

amine scrubbing, Environmental science & technology (2014). (Journal)

[16] O. Levenspiel, Chemical reaction engineering, Wiley New York etc.1972. (Book)

[17] K.V. Kumar, Linear and non-linear regression analysis for the sorption kinetics of

methylene blue onto activated carbon, Journal of Hazardous Materials 137 (2006) 1538-

1544. (Journal)

[18] T.P. Labuza, Application of chemical kinetics to deterioration of foods, Journal of

Chemical Education 61 (1984) 348. (Journal)

[19] D.C. Montgomery, E.A. Peck, G.G. Vining, Introduction to linear regression analysis,

John Wiley & Sons2012. (Book)

Acknowledgment

This research is supported by High Impact Research Chancellery Grant

UM.C/625/1/HIR/123 from University of Malaya.