J Therm Anal Calorim (2015) 122:1013–1021 DOI 10.1007/s10973-015-4761-3 The reactivity of cokes in Boudouard–Bell reactions in the context of an Ergun model 1 1 1 Andrzej Mianowski • Tomasz Radko • Tomasz Siudyga Received: 22 October 2014 / Accepted: 3 May 2015 / Published online: 28 May 2015 Ó The Author(s) 2015. This article is published with open access at Springerlink.com Abstract In previous studies, a kinetic equation based on List of symbols the Ergun mechanism and concept presented in 1956 was a Conversion degree of CO2,0B a B 1 applied to Boudouard–Bell reactions for granular coke Cf Free carbon sites (1–3 mm) in the temperature range T = 1173–1423 K. In Ccb Carbon as a carbon black contrast to several other works on this subject, the proposed Ct Total number of active carbon sites equation was based on only three kinetic constants: k1, the C(O) Carbon sites occupied by oxygen (oxy- rate constant for the Boudouard reaction; k-1, the rate carbon), acc. Ergun [1] constant for the Bell reaction; and k3, which is related to the C0 Combinations of kinetic constants in case oxy-carbon decomposition and CO desorption process. The when k3 = 0 dependence of these constants on temperature allows cer- C, C1 Combinations of kinetic constants tain values characteristic of the aforementioned processes to [CO2], [CO] Mole fraction, respectively, CO2 and CO, be calculated, including activation energy of gasification 0 B [CO2] B 1, 0 B [CO] B 1 reaction, enthalpy of disproportionation reaction of gasifi- [CO]m Maximum value of mole fraction CO, cation and activation energy of desorption process. When 0 B [CO]m B 1 k-1 [ 0, i.e., the Bell reaction and inhibitory effects occur, E Activation energy of gasification reaction -1 the kinetic constant k3 can be determined using a portion of (Boudouard reaction), J mol the experimental [CO] versus time data normalized to the E-1 Activation energy of disproportionation maximum contribution of CO in the outlet gases. reaction (Bell reaction), J mol-1 Edes Activation energy of desorption process, J mol-1 Keywords Boudouard–Bell reactions Á Gasification Á F Statistical test F Kinetics Á Coke reactivity DrH Enthalpy of reversible reaction of gasification (1), J mol-1 k Factor of proportionality in Eq. (9) k1 Kinetic constant of gasification reaction (Boudouard reaction), time-1 k-1 Kinetic constant of disproportionation reaction (Bell reaction), time-1 Electronic supplementary material The online version of this k3 Kinetic constant of desorption process, article (doi:10.1007/s10973-015-4761-3) contains supplementary -1 material, which is available to authorized users. time K Experimental constant of reaction, Eq. (6) & Tomasz Siudyga N Number of measurements/observations [email protected] H Fractional surface coverage of active sites 1 Faculty of Chemistry, Silesian University of Technology, acc. (5) Krzywoustego 6, 44100 Gliwice, Poland r2 Determination coefficient, 0 B r2 B 1 123 1014 A. Mianowski et al. -1 R_ Rate of complex process, time ½CO H k1 2 K ¼ ¼ ¼ idem: ð6Þ R Determination coefficient in nonlinear ½CO2 ðÞ1 À H kÀ1 regression, 0 B R2 B 1 q2 Determination coefficient in equation without intercept, 0 B q2 B 1 b) This system has the requirement of the steady-state sl Significance level assumption where T Absolute temperature, K v Rate of reaction/process, time-1 daf dH VM Volatile matter in dry and ash-free state, % ¼ 0: ð7Þ s Time, s ds x Conversion degree of solid phase, One can determine the value of H, and from Eqs. (4) 0 B x B 1 and (7), the well-known Langmuir–Hinshelwood equation (L–H) can be obtained [4–15]. Subscripts Condition (7) eliminates the inconvenience of simulta- des Desorption process neous occurrence of values in Eq. (4) that are related to the m At the maximum composition of the gas ([CO], [CO2]) and the solid phase r Reaction (H = C(O)/Ct) without invoking their analytical relation- ship. Finally, H can be obtained as: ½CO2 H ¼ k1 : ð8Þ Introduction k1½þCO2 kÀ1½þCO k3 TheleftsideofEq.(8) can be expanded by con- Ergun considerations and their consequences necting the Boudouard–Bell (B–B) reactions with the partial oxidation process that occurs in the presence of Assuming an Ergun mechanism gasification with carbon oxygen (POX-bis) [16–19] or by introducing second- dioxide [1] takes the form of the following reversible re- order terms including the partial pressure of CO2 0 action, i.e., where kÀ1 k1 and CðOÞCO: [16, 20]. k1 Other interpretations of Eq. (8) rely on assigning a rate CO2 þ Cf ! CO þ CðOÞ: ð1Þ kÀ1 of the process comprising the chemical reaction and the desorption to the left side of Eq. (8) and on introducing The C(O) decomposition and CO desorption process relationships between the products of the concentrations of (referred to throughout as the desorption process) can be the components in the gas phase and particular constants to described as: the right side of Eq. (8). k3 CðOÞÀ!CO þ Cf: ð2Þ The left-hand side of Eq. (8) is most often presented in a simple form as: Given the assumption that: R_ ¼ k Á H ð9Þ Ct ¼ Cf þ CðOÞð3Þ where k is a proportionality coefficient and R_ is the rate of one can obtain the equation: the complex process expressed as the conversion degree of dH the solid phase x in time: dx/ds [4, 12, 13], dx/(1 - x)ds ¼ k ½CO ðÞÀ1 À H k ½CO H À k H ð4Þ ds 1 2 À1 3 [8, 13, 15, 21] in [time-1] or with respect to the surface where area (specific) as the intrinsic reaction rate [6, 15]in [g m-2 s-1]. CðOÞ H ¼ : ð5Þ Ct Aim of the work For Eq. (4) to hold, according to [1, 2], two distinctive characteristics must be defined. Based on the general form of Eq. (4), a new kinetic ap- a) The experimental equilibrium constant of the re- proach to the B–B reaction is proposed as a result of re- versible reaction, which is the analog of the thermo- flections on the mechanism of this reaction and recent dynamic equilibrium constant, can be determined studies on the stability of the complex C(O), presented in from [3] as: [21], among others. In these presented considerations on 123 The reactivity of cokes in Boudouard–Bell reactions in the context of an Ergun model 1015 B–B reaction kinetics, a novel approach was used as a vr ¼ k1 exp½ÀðÞk1 þ kÀ1 s : ð16Þ conceptual framework to describe the complex process, specifically incorporating independence from the chemical In the literature concerning the B–B reaction, one can reaction and desorption process. often encounter a kinetic constant marked as k2, which is often identical to the constant marked as k-1 [5, 13–15, 21]. A kinetic approach to analyzing mechanism (1) By combining Eq. (16) and Eq. (13), a differential equa- and (2) tion is obtained, which eliminates the necessity of deter- mining the boundary conditions for individual stages of the General equation complex process in Eq. (12): dCO½ ¼ k1 exp½ÀÀðÞk1 þ kÀ1 s k3½CO : ð17Þ From a kinetic point of view, CO2 gasification monitored in ds the outlet gas composition can be described as a mole Equation (17) can be resolved using the constant vari- fraction of carbon monoxide as well as by the conversion ance method. Initially, Eq. (13) is solved for vr = 0, and degree of CO2 introduced into reaction system. The latter after that, variability of the integration constant is assumed. value does not require defining all of the products formed For the initial condition: [CO] = 0 for s = 0, the following in the reaction/process, and for only two components (CO relationship is obtained: and CO2), it leads to the condition: k1 ½þCO2 ½CO 1: ð10Þ ½¼CO ½expðÞÀÀk3s expðÞÀðÞk1 þ kÀ1 s : k1 þ kÀ1 À k3 As in [22], the conversion degree can be expressed as: ð18Þ 1 À ½CO ½CO a ¼ 2 ¼ : ð11Þ For k3 = 0, i.e., the desorption process does not occur, 1 þ ½CO2 2 À ½CO Eq. (18) simplifies to Eq. (15), which is valid for reversible reactions [22, 24]. If the combination of kinetic constants Based on our own experiences, it was demonstrated in Eq. (18) is denoted as C: that the use of CO mole fraction in these calculations is more reliable than using the conversion degree of CO . k1 2 C ¼ ; ð19Þ Use of CO mole fractions makes interpretation of the k1 þ kÀ1 À k3 kinetic constants and their relationships more credible. then it is easy to observe that the physical meaning of Calculations were performed for these two possibilities, Eq. (18) implies the inequality: i.e., using both a and [CO], but further considerations are presented only for mole fraction of CO. In accordance k1 þ kÀ1 [ k3: ð20Þ with the point of view expressed in [1] and its develop- Further analysis using the combined form of the kinetic ment, the rate of reaction/process was assumed to be the constants (19) in Eq. (18) leads us to the case where C B 1, result of two rates: the chemical reaction and the des- which implies another inequality: orption process: kÀ1 k3: ð21Þ v ¼ vr À vdes: ð12Þ However, the case with C [ 1 suggests that the kinetic Based on the experimental results, it can be assumed constant k-1 = 0; hence, the reaction proceeds irre- that the desorption process is the limiting stage of the versibly, and combination of the kinetic constants (19) complex process of gasification [4, 10, 23], and therefore, reduces to the form: Eq.