Metallurgical Coke Gasification by Carbon Dioxide under Nonisothermal Conditions: A Kinetic Study.

Metallurgical coke gasification by carbon dioxide was kinetically investigated through the use of thermogravimetric analysis under nonisothermal conditions. The results showed that the activation energy, gained by the Cai-Chen iterative model-free method, was estimated to be 183.15 kJ·mol-1. Notwithstanding, the mechanism function f(α) cannot be directly determined due to the fact that f(α) and the pre-exponential factor A α were lumped together as [A α f(α)]; this situation may be tackled by means of the master-plot methods. The most probable mechanism function, determined by the Málek master-plot method (based on Z(α) master plots), was discovered to be the Johnson-Mehl-Avrami equation. The usefulness of the compound kinetic calculation technique founded upon complemental application of the Málek master-plot and Cai-Chen model-free methods in estimating reaction kinetics of metallurgical coke gasification was verified. The comparison between original and reconstructed kinetic curves judged the accuracy of the gained kinetic parameters. By means of gained nonisothermal kinetic results, the forecasting of kinetic curves in isothermal as well as nonisothermal conditions was performed. In this work, new kinetic equations were presented and applied to reproducing and forecasting kinetic curves.

Introduction

The characterization of the investigated reactive behavior is commonly exhibited in the form of a so-called kinetic triplet[1] (namely, the pre-exponential Arrhenius factor, the conversion factor, and the activation energy), which is the classic result of an ordinary kinetic study. The kinetic triplet is widely studied, probably because it can be used for describing the reaction process, forecasting the reactive behavior beyond the scope of the experimental temperature, enabling the rational planning of experimental programs, and designing gas–solid contacting systems. Ordinarily, it is not easy for one to derive the most precise kinetic triplet from the kinetic data. Under dynamic regimes, the rate of conversion is always affected by the conversion factor as well as the reaction constant; consequently, when evaluating a kinetic triplet, one will confront a situation: an imprecise evaluation of any constituent of the triplet would lead other constituents of the triplet to be incorrectly evaluated. Accordingly, during a kinetic computation, one should try one’s best to accurately evaluate all constituents of the triplet, especially the constituent that is first evaluated and afterward is used in the evaluation of other constituents. The first evaluated kinetic parameter, in the present work, is the activation energy, of which the calculation procedures were widely developed and could be generally categorized into two types:[2] model-free and model-fitting methods. The model-free methods are universally accepted to be more dependable than model-fitting ones.[3] An iterative linear integral isoconversional method, a model-free method published by Cai et al.[4] and designated as the Cai–Chen method,[5] was adopted.

This present study is aimed specifically at showing the usefulness of a compound kinetic approach, founded upon complemental application of the master-plot method[6] as well as the model-free method, in deriving the kinetic triplet from the experimental thermoanalytical (TA) data of carbon dioxide gasification of metallurgical coke under nonisothermal conditions. It is expected that the present research can be helpful for comprehending the process of metallurgical coke gasification and designing as well as operating the gasifier.

Experimental Section

The metallurgical coke, which Ansteel (China) generously supplied, and of which the properties are described in Table , was used as the material for the present research. In the present study, all experimental tests were performed in a SETSYS Evolution thermogravimetric analyzer (TGA) bought from Setaram Co., France. Prior to running each gasification test, the coke sample, of which the mass was 5 ± 0.1 mg, was set into an alumina crucible, of which the height and inner diameter were 7 and 3 mm, respectively. The four selected heating rates, at which the samples were heated from the ambient temperature to 1500 K under high-purity carbon dioxide (which is the gasification agent and of which the gas flow rate is 40 mL·min–1), are 2, 5, 10, and 15 K·min–1. So that the results of all tests can be reproduced, in the present work each test was redone at least twice.

Table 1

Properties of the Coke Employed[7]

parameter	value
ash yield (wt %)	11.43
moisture (wt %)	0.16
volatile matter (wt %)	1.11
fixed carbon (wt %)	87.30
C (wt %)	85.69
H (wt %)	0.19
N (wt %)	0.95
O (wt %)	0.26
density (kg·m–3)	1.820 × 103
average particle size (μm)	34
BET surface area (m2·g–1)	1.178

The carbon conversion can be defined as the next equation,[8,9] whereby one can change the experimental thermogravimetry curves into curves of α vs T.where m0, m, and m∞, are the initial, immediate, and final masses, respectively.

Figure displays the α vs T curves of the nonisothermal gasification of metallurgical coke at constant heating rates; from this figure, it can be seen that the more the heating rate increases, the higher temperature the curve of α vs T transfers to.

Figure 1

α vs T curves of nonisothermal gasification of coke at constant heating rates of 2, 5, 10, and 15 K·min–1.

Theoretical Basis

The following rate equation[10] widely represents the kinetics of the gas–solid reactions (e.g., carbon gasification).where α is the carbon conversion, t is the time, A is the frequency factor (i.e., the pre-exponential Arrhenius factor), k is the reaction constant, E is the activation energy, T is the temperature, R is the gas constant, f(α) is the conversion factor, also referred to as the mechanism function, and β is the heating rate expressed as dT/dt or (T – T0)/t (the parameter T0 is the initial temperature).

Integrating eq results in the integral form of f(α)where I(E, T) is identical to ∫0Texp[−E/(RT)]dT, u is identical to E/(RT), and p(u) is a more greatly performed temperature integral than I(E, T) and is identical to ∫∞u–2 exp(−u)du. Like both I(E, T) and p(u), these functions (π(u) and h(u)) have numeric rather than analytic solutions.

Accordingly, within a small range of conversion, from eq it followswhere the subscript α (or α – Δα) signifies the values when the conversion is identical to α (or α – Δα).

On the basis of the above equation and on the presumption that the value of E stays invariable within the conversion interval of [α – Δα, α], for a fixed conversion and a run of linear nonisothermal tests carried out with various heating rates β (i = 1, 2, ..., n), the expression of the Cai–Chen method is deduced

An iterative procedure, described in detail in the literature,[11] is applied because in eq the left-hand side term, which against reciprocal temperature is supposed to result in a direct line whose slope lets activation energy be calculated (see eq ), depends on and varies with Eα.where Sα is the slope of the plot of the left-hand side term in eq vs reciprocal temperature.

In case of the awareness of the activation energy, a method, put forward by Málek[12−15] and thus referred to as the Málek method, is helpful in finding out the mechanism function in nonisothermal conditions; the auxiliary function Z(α) employed in this method can be denoted by the next two equations.

A sequence of TA curves recorded under various heating rates is applied to acquiring experimental Z(α) values that are produced by plotting the right-hand side term in eq vs α. After the substitution of the often-quoted mechanism functions into eq , plotting the right-hand side of eq vs α produces theoretical Z(α) curves. Having compared the experimental and theoretical Z(α) curves, one is able to acquire the most probable mechanism function whose corresponding theoretical Z(α) curve corresponds closely to the experimental Z(α) curve of the investigated reaction process.

With the purpose of reproducing nonisothermal TA curves within the experimental heating rate range, in addition to Eα values, which have been known, the term Δ[Aαf(α)] could be calculated via the following expression.[16]

According to the above equation, if we use lowercase j to represent a left endpoint of a small interval of conversions, we get

Substitution of both Eα and Δ[Aαf(α)] into eq , after rearranging, yields the following equation, which can be used for reproducing the original nonisothermal experimental data and forecasting nonisothermal TA curves outside the experimental heating rate range.

This equation is subject to the initial value condition

For the purpose of forecasting isothermal TA curves by means of predetermined nonisothermal kinetic results, in addition to knowing Eα values, the term ∫α–Δαα {dα / [Aαf(α)]} could be calculated via the following expression.[17]where Iα is the intercept of the plot of the left-hand side term in eq vs reciprocal temperature.

With f(α) (or G(α)) presumed to stay invariable, the substitution of both Eα and ∫α–Δαα {dα/[Aαf(α)]} into eq , after some mathematical derivations, yields the following equation, which can be used for forecasting isothermal TA curves.where Tiso is the isothermal temperature.

It is worth mentioning that the equations for calculating Aαf(α), reproducing nonisothermal kinetic curves, and forecasting isothermal kinetic curves, i.e., eqs , 11, and 13, are originally put forward in the present study.

Results and Discussion

Calculating the Activation Energy

At various conversions, the Eα values evaluated by means of the Cai–Chen method appear in Figure . The errors within the beginning and end of the conversion range, as everyone knows, stand to be fairly high on account of the extremely small deflection of the TA curve away from the baseline. Accordingly, the conversion range in the present work is chosen as 0.1 ≤ α ≤ 0.9, in which the activation energy is found to be almost not connected with the conversion and then the mean activation energy E̅ is calculated to be 183.15 kJ·mol–1. Fuertes et al.[18] investigated the kinetics of CO2 gasification of metallurgical coke by means of a thermal analyzer, and the reported E value was 183 kJ·mol–1. This value is close to the value obtained in this work.

Figure 2

Relationship of Eα (calculated by the Cai–Chen method) to α for the gasification of coke.

Apart from the model-free method (i.e., the Cai–Chen method in the present work), a model-fitting method (i.e., the universal integral approach[19] denoted by eq ) is used to calculate activation energy.

For a particular mechanism function, after plotting the left-hand side term in eq vs reciprocal temperature, in agreement with eq a direct line is supposed to be gained. Values E and A may be estimated from the slope and intercept, respectively.

For different mechanism functions listed in Table ,[20] results of the application of the universal integral approach to the experimental TA data measured under 2, 5, 10, and 15 K·min–1 are expressed as Arrhenius parameters (E and A) and the linear correlation coefficient R2 and tabulated in Table . As seen in Table , values of E and lnA are found to be strongly influenced by the mechanism function and to be weakly influenced by the heating rate. Many mechanism functions listed in Table lead to better linear correlation coefficients, which are above 0.97; the most probable mechanism function cannot be unambiguously determined according to the linear correlation coefficient. It is agreed that different mechanism functions may ostensibly fit every TA curve well on account of there being a kinetic compensation effect (KCE) between Arrhenius parameters. Hence, it is obvious that the application of only the model-fitting method to working out kinetic parameters may introduce errors.

Table 2

Set of Mechanism Functions Widely Applied to Kinetic Analyses

	mechanism function	code	G(α)	f(α)
1	power law	P2/3	α3/2	(2/3) α–1/2
2	power law	P2	α1/2	2α1/2
3	power law	P3	α1/3	3α2/3
4	power law	P4	α1/4	4α3/4
5	parabolic law	D1	α2	(1/2) α–1
6	Valensi equation	D2	(1 – α) ln(1 – α) + α	[−ln(1 – α)]−1
7	Jander equation	D3	[1 – (1 – α)1/3]2	(3/2) (1 – α)2/3[1 −(1 – α)1/3]−1
8	contracting cylinder	R2	[1 – (1 – α)1/2]	2(1 – α)1/2
9	contracting sphere	R3	[1 – (1 – α)1/3]	3(1 – α)2/3
10	Johnson–Mehl–Avrami	A1.5	[−ln(1 – α)]2/3	(3/2) (1 – α)[−ln(1 – α)]1/3
11	Johnson–Mehl–Avrami	A2	[−ln(1 – α)]1/2	2(1 – α)[−ln(1 – α)]1/2
12	Johnson–Mehl–Avrami	A3	[−ln(1 – α)]1/3	3(1 – α)[−ln(1 – α)]2/3
13	unimolecular decay law	F1	–ln(1 – α)	(1 – α)

Table 3

Results from Using the Universal Integral Approach for Different Mechanism Functions

	β = 2 (K·min–1)			β = (5 K·min–1)			β = (10 K·min–1)			β = (15 K·min–1)
model	Ea	ln Ab	R2	E	ln A	R2	E	ln A	R2	E	ln A	R2
P2/3	377.89	27.13	0.913	358.33	24.37	0.937	354.15	23.34	0.946	353.58	22.92	0.948
P2	58.02	–3.12	0.805	65.01	–2.09	0.878	69.66	–1.37	0.900	71.57	–1.02	0.907
P3	4.70	–8.16	0.099	16.12	–6.50	0.605	22.25	–5.49	0.743	24.57	–5.01	0.777
P4	–21.95	–10.68	0.899	–8.32	–8.71	0.539	–1.46	–7.55	0.031	1.07	–7.01	0.016
D1	537.83	42.26	0.918	505.00	37.60	0.940	496.39	35.70	0.948	494.59	34.90	0.951
D2	595.69	47.45	0.948	556.78	41.99	0.965	546.12	39.73	0.970	543.71	38.78	0.972
D3	674.02	53.88	0.977	626.63	47.31	0.988	613.10	44.56	0.991	609.85	43.41	0.992
R2	266.74	16.27	0.962	255.27	14.72	0.978	253.74	14.26	0.982	253.90	14.10	0.983
R3	286.05	17.82	0.977	272.49	15.99	0.988	270.26	15.42	0.991	270.21	15.21	0.992
A1.5	185.97	9.49	0.997	180.48	8.82	1.000	180.93	8.79	1.000	181.63	8.82	1.000
A2	113.99	2.55	0.999	114.94	2.79	1.000	117.55	3.16	0.999	118.86	3.37	0.999
A3	42.02	–4.38	0.991	49.41	–3.25	0.991	54.18	–2.47	0.993	56.09	–2.08	0.993
F1	329.91	23.35	0.995	311.54	20.90	0.999	307.69	20.05	1.000	307.16	19.73	1.000

E expressed in kJ·mol–1.

A expressed in s–1.

Determining the Mechanism Function and Frequency Factor

As observed in eq , the mechanism function f(α) gets lumped in with the pre-exponential Arrhenius factor Aα; in other words, they are considered as a group rather than separately. The mechanism function f(α), therefore, cannot be isolated from the term Aαf(α) directly; yet, the determination of f(α) might be accomplished using the master-plot methods. It is observed that when the Eα value is not only calculated from a model-free approach but it is also virtually independent of α, the Málek master-plot method could be applied. On the condition that the Málek method is practicable, a mean activation energy E̅ (in this work, E̅ = 183.15 kJ·mol–1) can be substituted for the nearly invariable value of Eα and then be introduced into eq 7.(21) As mentioned earlier, the most probable mechanism function can be recognized from the situation in which the theoretical Z(α) values related to this mechanism function correspond closest to the experimental data transformed by eq . Figure compares the experimental and theoretical values of Z(α); as observed, the influence of β upon experimental values of Z(α) may seem trifling. As also observed in Figure , the nonisothermal gasification of metallurgical coke by carbon dioxide can be represented by the Johnson–Mehl–Avrami equation (An):[22−25]f(α) = n(1 – α)[−ln(1 – α)]1–1/. With the aim of evaluating the values of n in this f(α) under the heating rates of 2, 5, 10, and 15 K·min–1, after substituting the mean activation energy E̅ estimated formerly as well as the differential form of the An equation into eq , taking logarithms, and rearranging, we write

Figure 3

Comparison of experimental data transformed by eq with theoretical Z(α) values calculated by eq . Codes by the curves correspond to the codes in Table .

Then, for each heating rate, values of n and lnA are, respectively, found from the slope and intercept of the ln(βdα/dT) – ln(1 – α)+E̅/(RT) vs ln[−ln(1 – α)] curve, a plot which ought to be linear. Table shows n values as well as lnA values. As seen in Table , the parameters n and ln A are scarcely affected by β. As also seen in Table , the n values at 2, 5, 10, and 15 K·min–1, respectively, were calculated to be 1.73, 1.74, 1.76, and 1.77, thereby leading to the average n value of 1.75. Therefore, we reached a conclusion that the appropriate kinetic model for the CO2 gasification of metallurgical coke is the Johnson–Mehl–Avrami equation (A1.75), viz., f(α) = 1.75(1 – α)[−ln(1 – α)]1–1/1.75 as well as G(α) = [−ln(1 – α)]1/1.75. Li et al.[26] investigated the metallurgical coke–carbon dioxide gasification reactions with/without alkali carbonates and reached the similar conclusion that in the absence of alkali carbonates, the Johnson–Mehl–Avrami equation (A2) was discovered to be the suitable mechanism function of metallurgical coke gasification.

Table 4

Parameters n and lnA Acquired under Different Heating Rates

β (K·min–1)	n	ln A (A in s–1)
2	1.73	10.171
5	1.74	10.182
10	1.76	10.208
15	1.77	10.221
arithmetic averages	1.75	10.196

Reproducing and Forecasting TA Curves

According to eq , we applied the evaluated parameters of Eα as well as Δ[Aαf(α)] to reproduce original α vs T curves and forecast the reaction kinetics beyond the range of employed heating rates. Figure presents the comparison of the original and the calculated α vs T curves. As observed in this figure, original kinetic curves are in close accordance with the calculated ones, thereby indicating that eq is appropriate to simulate the gasification process under nonisothermal conditions.

Figure 4

Comparison of original (open symbols) and calculated (dash lines) α vs T curves for various linear heating rates.

We forecast the evolution of the carbon conversion with temperature for the various linear heating rates not employed in the nonisothermal tests (see Figure ). In low heating rate conditions, gasification starts at lower temperatures, while in high heating rate conditions, it starts at higher temperatures. For a given degree of conversion α, the corresponding temperature Tα increases with the heating rate.

Figure 5

Calculated α vs T curves of the gasification of coke for various linear heating rates not employed (3.5, 7.5, 12.5, and 20 K·min–1).

In addition, forecasts of conversion profiles under isothermal conditions have been given on the basis of the available nonisothermal kinetics previously determined. According to eq , at the chosen isothermal temperatures (1200, 1250, 1300, 1350, and 1400 K), the isothermal forecasted α vs tα curves are procured and appear in Figure from which we can notice that the entire reaction time becomes shorter with an increase in the isothermal temperature and that the evolution of α with tα exhibits a sigmoidal shape, implying that the rate of conversion originally increases and then decreases with increasing time.

Figure 6

Isothermal forecast α vs tα curves of the gasification of coke at the chosen isothermal temperatures of 1200, 1250, 1300, 1350, and 1400 K.

Conclusions

The gasification of metallurgical coke by carbon dioxide is kinetically gone into under linear nonisothermal heating programs. The activation energy, estimated from the iterative linear integral isoconversional method (the Cai–Chen method) in the absence of presuming any mechanism function in advance, is discovered to be barely affected by the conversion and therefore has a mean value of 183.15 kJ·mol–1. The Málek method discloses that the mechanism function f(α) = n(1 – α)[−ln(1 – α)]1–1/ (n = 1.75) well represents the reaction behavior. The frequency factor is also determined: the value of ln A is estimated to be 10.196. With the aid of the joint kinetic analysis, acceptably deriving the kinetic triplet from the kinetic data of the nonisothermal gasification of metallurgical coke is doable. In addition, the experimental data have been precisely reproduced. Also, the obtained kinetic results permit one to forecast the evolution of carbon conversion in isothermal as well as nonisothermal conditions. We should point out that account will be taken of the change in activation energy with conversion when the Cai–Chen method is applied to determine the activation energy and that the Málek method can be employed in the event that the activation energy obtained by a model-free method almost keeps unchanged. Furthermore, new kinetic equations developed from the Cai–Chen method have been presented for reproducing the experimental data as well as forecasting kinetic curves, and satisfactory results have been achieved.