Char Gasification Kinetics in Mixtures of CO2 and H2O: The Role of

Nov 19, 2014 - This work also uses new data to demonstrate how reactant partial pressures can affect the availability of the reactive surface to a sec...
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Char Gasification Kinetics in Mixtures of CO2 and H2O: The Role of Partial Pressure in Determining the Extent of Competitive Inhibition Daniel G. Roberts* and David J. Harris CSIRO Energy, Post Office Box 883, Kenmore, Queensland 4069, Australia ABSTRACT: There is considerable interest in experimental studies investigating the kinetics of the reactions of carbonaceous chars with mixtures of CO2 and H2O. Several studies report a range of outcomes: some conclude that there is competition between CO2 and H2O for active sites, leading to inhibition of reaction rates of one reactant by another; others conclude that the two reactions occur independently. This work reviews and analyses this recent research activity, highlighting the importance of experimental conditions in generating appropriate gas−solid reaction rate data (many of the published studies have been performed under conditions where it is difficult to gain insight into the mechanisms of gas−solid reaction kinetics in isolation from other chemical and physical processes that may be occurring). This work also uses new data to demonstrate how reactant partial pressures can affect the availability of the reactive surface to a second reactant and, in turn, the extent to which a competitive effect is apparent; relatively low partial pressures of reactants (approximately 0.05 MPa and below) are less likely to show evidence of competition, whereas measurements at higher partial pressures (up to 3.0 MPa) are more likely to reveal competitive behavior. This is consistent with a reaction scheme that has CO2 and H2O competing for reaction sites and inhibitory effects that are only apparent when surface saturation becomes high enough for competition to impact observed kinetics. This result is important and provides further evidence that conventional Langmuir−Hinshelwood reaction schemes for representing char gasification reactions can be applied over a range of pressures and mixtures of reactants.

1. INTRODUCTION Char reactivity is one of the fundamentally important aspects of coal and biomass conversion in gasification. Accurate quantification of char conversion rates is key to understanding feedstock-specific behavior in a range of gasification technologies and, consequently, our ability to efficiently design, operate, optimize, and troubleshoot gasification-based systems. The importance of char conversion kinetics is reflected by the vast number of studies reported in the literature generating data under a range of laboratory and process-specific conditions, using chars made from many different feedstocks, including coal, biomass, and carbonaceous waste materials. The kinetics of the char gasification reactions, coal- and technology-specific issues affecting these kinetics, and how they interact with a range of other chemical and physical processes to influence the behavior of a feedstock under gasification conditions are all important to understand fuel performance. The complex nature of the char conversion process, involving a combination of chemical reaction rates, diffusion of gases through evolving pore structures, and a range of coal- and gasifier-specific impacts, means that it is important to effectively isolate these processes for study. Only then can the data be reliably reassembled and used in practical systems, where process-specific factors determine the relative importance of the key chemical and physical processes and in which combinations of factors control the overall coal and char conversion rates. One of these processes is the intrinsic rate of reaction of the solid carbon with CO2 and H2O. To assess these reactions reliably and to determine transportable rate data that can be used in appropriate gasification and conversion models, it is important that the reactions are studied under conditions free from heat- or mass-transfer limitations (so-called “regime 1” conditions, where the solid−gas reaction is the only process © 2014 American Chemical Society

contributing to observed reaction rates). These char gasification reaction kinetics (distinct from the observed rates of char conversion under industrial gasification conditions) have been studied extensively for more than 50 years, from a fundamental perspective,1−6 in support of the iron and steelmaking processes,7 and in the context of coal and biomass gasification for the production of power, fuels, and chemicals.8−14 The vast majority of these and related studies have isolated the two main heterogeneous reactions, those of carbon with H2O and CO2, and made significant progress in describing the reactions in a manner suitable for use in representing char conversion rates in relevant industrial applications, where the kinetics are often moderated by other physical factors, such as pore diffusion and surface area development. Most studies into char gasification kinetics are performed at atmospheric pressure. Some have been undertaken at higher pressures,11,13,15−17 providing data and insight applicable to higher-pressure, entrained flow coal gasifiers used for integrated gasification combined cycle (IGCC) power generation as well as the production of liquid fuels and chemicals. Some of these studies have quantified the role of reaction product species, CO and H2, on the reaction kinetics at these pressures,10,17−19 showing in most cases that our understanding developed at atmospheric pressure based on a Langmuir−Hinshelwood (LH) reaction scheme is relevant and can be applied to these higher pressure reaction conditions. Fewer still have investigated conversion kinetics in experiments where both reactants are reacting on the char surface in combination. The latter is Received: September 18, 2014 Revised: November 17, 2014 Published: November 19, 2014 7643

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Table 1. Overall (“Global”) Activation Energies for the Char−CO2 and Char−H2O Reaction Systems Published in Some Recent Studies, as Part of Investigations into Reaction Kinetics of Chars with Mixtures of CO2 and H2O study Nilsson et al.21,22 Guizani et al.24 Tagutchou et al.25

Ea CO2 (kJ mol−1)

Ea H2O (kJ mol−1)

163.5 154

171.0 139

comment low activation energies suggest that conversion rates are limited by reactant gas diffusion through pores low activation energies suggest that conversion rates are limited by reactant gas diffusion through pores not quantified; particle size and temperatures, however, using similar procedures to Guizani et al.,24 suggest that conversion rates are limited by reactant gas diffusion through pores

Table 2. Summary of Recent Char Reactivity Studies in Mixtures of CO2 and H2O, with the Outcome (Additive, Competitive, or Some Combination of the Two) Identified study

sample

reactant partial pressures

conditions

outcome

Nilsson et al.22,23 Guizani et al.24 Tagutchou et al.25 Bai et al.29 Chen et al.26 Umemoto et al.27 Roberts and Harris20 Zhang et al.28

biosolids char and wood char beech char charcoal bituminous coal char lignite char bituminous coal char bituminous coal char bituminous coal char

sub-0.1 MPa sub-0.03 MPa (0.1 MPa total) sub-0.04 MPa (0.1 MPa total) sub-0.1 MPa

800−900 °C chips, 800−900 °C 900 °C 800−900 °C in TGA, 125 μm

up to 2 bar 1−20 bar up to 1 bar

900−1000 °C in TGA 800−900 °C, 0.5 mm 900−1000 °C

additivea additivea additivea synergistic (additive)b partially competitive combination competitive competitiveb

Data generated under technology-specific conditions and not likely to be “regime 1” kinetics. bSamples used had different heat-treatment temperatures, and therefore, temperature effects on reaction rates are not clear. a

Table 1 are much lower than what might be expected for purely “regime 1” conditions (∼220−280 kJ mol−1). Such measurements are important for generating technology-specific data for particular industrial case studies (in the case of Nilsson et al., a fluidized bed system); however, these conditions are difficult to use to generate transportable data, which can be used in more general gasifier models, in combination with relevant computational fluid dynamics (CFD) and char structure models, or for developing insights into the mechanisms of reactions, because effects of pressure, temperature, and char structure will also affect the rates of diffusion. Umemoto et al.27 investigated mixed-gas kinetics on bituminous coal chars, at low temperatures in a thermogravimetric analyser (TGA), where diffusion processes were negligible, and at higher temperatures using a drop-tube furnace under more complex reaction conditions. The reactant pressures for their TGA studies were higher than atmospheric (up to 0.2 MPa) and provided data that supported a combination-style mechanism, whereby some part of the reaction of CO2 and steam occurred on separate discrete sites, with some occurring on sites for which the reactant gases competed. Chen et al.26 studied mixed gas kinetics using a Chinese lignite, revealing some degree of competition between CO2 and H2O, and that this was most evident in the inhibition of the rate of the char−CO2 reaction by H2O. Zhang et al.28 and Bai et al.29 also studied in detail the kinetics of reaction of chars in mixtures of CO2 and H2O, using char made from Chinese bituminous coals. The work by Zhang et al.28 reported data suggesting that there is some degree of “common active sites” for the reactions studied. The work by Bai et al.29 revealed some additive behavior and suggested an important contribution by the catalytically active species present. The study by Zhang et al. used char samples made at temperatures significantly lower than those at which the subsequent reactivity tests were performed, however. Similarly, Bai et al. used chars made at different temperatures for the reactivity tests at those temperatures, introducing dual effects of the temperature (one on char properties as part of the coal pyrolysis process and one

important because it raises questions regarding the mode of reaction under such conditions: do the reactants compete for an active surface, or do they proceed in isolation using separate sites associated with the char surface? This is an important question because it impacts the way in which gasification and gasifier models are developed and applied. If CO2 and H2O react on the same surface sites, then the presence of reaction intermediates from one reactant will affect the amount of surface available for the other and vice versa. One of the first experimental studies into the kinetics of gasification of bituminous coal chars in mixtures of CO2 and H2O by the authors20 reported data clearly demonstrating that the presence of CO2 led to a decrease in the C−H2O reaction rate. That work also demonstrated that a “standard” LH kinetic model (applied using a “relative rate” approach) based on sharing of active sites was able to describe well these experimental results. This suggested that CO2 and H2O competed for the same active sites on a reacting char surface and that the reaction intermediates from one reactant could lead to a reduction in the number of sites available to the other. Importantly, accepted LH kinetics were able to describe this without modification. This result is significant, because most models of char gasification do not account for this competition for reaction sites and, consequently, model the two reactions as if their rates are purely additive. In more recent years, there has been a number of similar investigations into reactivity of coal, lignite, and biomass chars with mixtures of CO2 and H2O.21−28 Nilsson et al.,21−23 Guizani et al.,24 and Tagutchou et al.25 studied the reactions of chars made from biomass and biosolids at atmospheric pressure using fractional (sub-atmospheric) partial pressures of reactants. In general, these studies suggest that, for these samples under these conditions, the kinetics of the C−CO2 and C− H2O reactions are additive, finding no evidence for the competitive behavior described above. The kinetic data published in these papers, however (see Table 1), suggest that there may be significant influences on the measured gasification reaction rates by diffusion of CO2 and H2O through the pores of the reacting particles; the activation energies in 7644

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on reaction kinetics) into the rate measurements. This means that samples reacted at different temperatures had been subjected to different heat treatment histories; consequently, it is likely that effects of the temperature on the measured reaction rate (and, therefore, quantification of rate constants) are due to more than just effects of the temperature on the rate of the gas−solid reactions and will include effects associated with char preparation conditions, extent of devolatilization, char thermal annealing, etc. Table 2 gives a summary of these studies, showing some of the key conditions used to generate the char samples and the type of char used for the studies. It also summarizes the outcome as “competitive” (whereby the results suggest that CO2 and H2O compete for the same reaction sites), “additive” (whereby the reactions occur independent of each other), and perhaps some combination of the two models. Only two of these studies were performed using reactant partial pressures above atmospheric pressure,20,27 and only one of these at pressures greater than 0.2 MPa.20 Furthermore, the variability in the feedstocks used means that there is a very large variability in the amount of surface available for reaction in the different studies. It is possible that the variability in the results reported (i.e., additive or competitive behavior) is related to these experimental conditions and properties of the samples used and possibly also by the complicating effects of high levels of catalytically active species. It is clear that the variations in conclusions drawn by these published studies require further attention, because such inconsistencies may point to a lack of understanding of the generally accepted reaction scheme for chars reacting with CO2 and H2O. However, it is also clear that the experimental conditions used to generate the published data vary significantly in terms of sample type (chars made from bituminous and lignite coals as well as biomass sources), reaction temperature, and reactant partial pressure. Interestingly, it is also possible that there is a link with a property related to feedstock type; the biomass-derived chars seem more likely to not show evidence of competition, while the coal-derived materials do, and the material falling in-between on a “rank” spectrum (lignite) shows some mixed results. This paper provides some further analysis and interpretation of previously published data and provides some new data that extend the pressure range of the previous work. This is performed to understand in more detail the apparent conflicts in the literature, how they may or may not be consistent with our understanding of the role of active sites on the char surface, and how these determine the reactivity behavior of samples as reactant pressure increases.

Table 3. Parent Coals Used To Produce Char Samples Analyzed in This Work CRC281

CRC272

Proximate Analysis (%, air-dried basis) moisture 1.5 3.4 ash 10.4 6.6 volatiles 8.8 38.6 fixed carbon 79.3 51.4 Ultimate Analysis (%, dry and ash-free basis) carbon 90.6 82.9 hydrogen 3.64 5.95 nitrogen 1.87 1.83 sulfur 0.67 0.88 oxygen 3.2 8.4

Reaction rates of these chars with CO2, H2O, and their mixtures were determined at 850 °C using a high-pressure TGA.11,20 This instrument allows for measurement of reaction rate profiles under truly differential reaction conditions. Experiments used to generate rate data in this work were stopped at 10% carbon conversion and the reaction rate at that level of conversion used in the subsequent analysis.

3. ANALYSIS 3.1. Surface Saturation. We know from previous work13 that, for some chars reacting (separately) with CO2 and H2O, the reacting surface can approach saturation at partial pressures of ∼1 MPa. This leads to a reduction in the sensitivity of the reaction rate to further increases in reactant partial pressure (i.e., a reduction in the apparent “reaction order” in the nthorder rate equation) such that, at CO2 or H2O pressures above ∼2.5−3 MPa, further increases in reactant partial pressure have a much reduced effect on measured reaction kinetics. This behavior is readily described by the accepted LH reaction scheme based on dissociative adsorption onto active sites, followed by desorption of the reaction intermediate as CO (this is discussed in more detail below). In the context of reaction systems in mixtures of CO2 and H2O, it follows that, if these reactants are using the same (or similar) reactive surface, then impacts of competition will only become apparent when there is not an excess of sites available. At low partial pressures or with samples having a particularly high surface area, the reacting surface is not likely to be at a high degree of saturation, and therefore, competitive effects would not be expected to be present in the measured data. While this discussion simplifies the situation for the two reactants of interest, a distributed surface reactivity model, reflecting the heterogeneous nature of the char surface and also the presence of catalytically active species present in different char types, will ultimately be required. The present discussion is based on the hypothesis that the lower energy sites are occupied first (and at lower pressures) for each reactant, that the inventory of occupied sites becomes limiting at high levels of surface coverage (at high reactant pressures), and that effects of catalysis are represented by the rate constants used in the rate equations. We can test this hypothesis by analyzing measured rate data using the generally accepted LH reaction scheme. When rate constants are calculated for chars reacting with CO2 and H2O, the LH reaction scheme can be used to quantify the degree of surface saturation. This can be compared to measurements of the degree of observed inhibition of one reaction rate by the presence of the other reactant and, consequently, ascertain its

2. MATERIALS AND METHODS The parent coals of the chars discussed in this work, the techniques used to prepare the chars for reactivity analysis, and those used for determining reaction rates have been detailed in previous work by the authors20 and will be discussed here only briefly. The parent coals were a bituminous coal from New South Wales and a sub-bituminous coal from Queensland, Australia (Table 3). Chars were prepared from these coals using techniques that have been used in this laboratory extensively to generate sufficient quantities of material for detailed kinetic analysis and removing possible complicating effects arising from annealing, further devolatilization, etc. This involved heating −1.0 + 0.6 mm samples at a heating rate of 0.1 °C s−1 under flowing nitrogen to 1100 °C, where they were held for 3 h. 7645

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Figure 1. Calculated fractional surface coverage during the char−gas reaction with different (left) H2O or (right) CO2 partial pressures based on measured pure gas reactivity data for two coal chars labeled CRC272 and CRC281.

likelihood as an important aspect of “competition and inhibition” in the C−CO2−H2O reaction system. The LH gasification reaction schemes for CO2 and H2O reacting with solid carbon have been presented and discussed many times in the literature. Using the char−H2O reaction as an example, the reaction scheme is Cf + H 2O ⇌ C(O) + H 2

k1′, k 2′

(1)

k 3′

C(O) → CO

the decrease in the overall order of reaction (when expressed using nth-order kinetics) as the reactant pressure increases. Here, a similar analysis can be used to relate this degree of saturation of the available surface to the extent of inhibition of the C−H2O reaction by the C−CO2 reaction. 3.2. Surface Availability and Potential for Inhibition. Figure 1 shows calculations of the extent of surface coverage (θ) based on measured pure gas reactivity data for two chars made at 1100 °C reacting in varying partial pressures of steam at 850 °C and CO2 at 900 °C, from below atmospheric to 2.0 MPa. These calculations have been made using pure gas kinetics published previously13 and the procedures described above. At partial pressures below 0.1 MPa, very little of the available surface of either char sample is used by either H2O or CO2; over 95% of it is available for reaction. Under these conditions, it is unlikely that the occupation of active sites by reaction intermediates from competing reactions will make a significant impact to the amount of surface available. It follows that, at these partial pressures, inhibitory effects are likely to be slight. Consistent with the accepted LH mechanism for these reactions, Figure 1 also shows that, as the partial pressures of reactants increase, the extent of surface coverage increases. At 1.0 MPa of reactant, these chars in both CO2 and H2O have more than half of the surface used (and, for CRC281 in H2O, this is closer to 75%). Further increases in the partial pressure lead to more use of the active surface. Under these conditions, the high extent of surface saturation (and the corresponding reduction in available surface) becomes significant, and we would expect inhibitory effects to begin to be apparent in a similar way because we reported a decrease in the effect of the partial pressure on the reaction rate in previous work.11 We can see this effect in Figure 2, which charts the extent of inhibition of the C−H2O reaction by CO2 (where 1 = no inhibition and 0 = complete inhibition) at different partial pressures of CO2. The expression for this “inhibition factor” is

(2)

with an additional consideration required to account for the complex mode of inhibition by H2, if H2 is present in significant concentrations (for this work, H2 concentrations are negligible). Here, Cf is a free active site; k1′ is the rate constant for the forward reaction in eq 1; and k2′ is the reverse. In the absence of H2, the rate of reaction with reactant i (ρi) can be expressed as a function of the reactant partial pressure (Pi) by the equation ρH O = 2

[C′f ]k1′PH2O 1+

k1′ P k 3′ H 2O

(3)

Because the rate of conversion is equal to the rate of desorption ρH O = k 3′[C(O)]

(4)

2

The degree of surface coverage (θ) is defined as θ=

[C(O)] [Ct ]

(5)

Then, we can use eqs 3−5 to quantify the degree of surface coverage as a function of the reactant partial pressure (and temperature via the rate constants) using eq 6. θ=

(k1′/k 3′)PH2O 1 + (k1′/k 3′)PH2O

(6) 13

4,5

Previous kinetic studies by the authors and others have used this approach to estimate the degree of saturation of the reactive char surface. This has been used in the past11 to explain 7646

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Figure 3. Calculated extents of inhibition of the C−H2O reaction by CO2 (lines) compared to experimental data (points).

Figure 2. Calculated extent of inhibition of the C−H2O reaction by CO2 as a function of the CO2 partial pressure (where 1.0 = no inhibition and 0.0 = complete inhibition). Log scale on the abscissa to highlight sub-1 bar effects.

Part of the challenge of understanding the way mixtures of CO2 and H2O react with a char surface is the complexity of the char gasification process under process conditions. As discussed in the introductory review of this work, many of the studies reporting conversion data in mixtures of CO2 and H2O are aimed at generation of gasification data under process-specific conditions (such as fluidized bed gasification of biomass), which is important for technology development and feedstock assessment. Such studies, however, are not well-suited for making reliable insights into gas−solid reaction kinetics, because of the confounding effects of pore diffusion and product gas inhibition or heat treatment histories of samples that lead to additional uncertainties in the results. There remains no clear picture of the nature of the interaction of CO2 and H2O over a reacting char surface. The LH reaction scheme is the commonly accepted mechanism for the char gasification reactions, which has been shown to represent the main char gasification reaction rates for individual reactant gases over a wide range of reactant and product gas partial pressures. Its use in this work to interpret char−gas reaction data obtained over a wide range of partial pressures has demonstrated the strong link between reactant partial pressure, surface availability, and presence of inhibitory effects arising from competition between CO2 and H2O for an active surface. At low reactant pressures (∼0.1 MPa), the proportion of active surface area used by reactions is low. The high availability of reactive surface leads to an absence of inhibition at these partial pressures. At higher partial pressures (above ∼1 MPa for the samples studied in this work), surface coverage by reaction intermediates is considerably higher and the availability of an active surface is lower. Under such conditions, the reduction in available reaction sites means that effects of inhibition become more prominent. This analysis can be extended to previous studies published in the literature and be used as an explanation of the variability in published results regarding competition and inhibition between CO2 and H2O. It is reasonable to expect that studies undertaken at low partial pressures of reactant (atmospheric pressure and below) will report no evidence of competition or inhibition. Even at higher partial pressures, samples with particularly high active surface areas may not lead to

k1 P k 3 CO2

inhibition factor = 1 −

1+

k1 P k 3 CO2

(7) 20

which was derived in the previous work by the authors but not presented explicitly (in this application, for simplicity, we are considering the inhibition of the C−H2O reaction by CO2, and there will also be inhibition of the C−CO2 reaction by H2O reaction intermediates; however, given the relative rates of the C−CO2 and C−H2O reaction, they have not been considered in this analysis). The data in Figure 2 show that inhibition factors at pressures below 0.1 MPa are indeed slight, ranging from 0.94 to 0.99. In many systems, this degree of inhibition will not be detectable, and it is not until CO2 partial pressure increases to ∼0.1 MPa that we begin to see significant inhibitory effects. Figure 3 compares these calculations to inhibition factors determined from measured rate data for the reaction of these same coal chars in mixtures of CO2 and H2O from atmospheric pressure to 3.0 MPa from our previous work11,13 using eq 8. ρ inhibition factor = mixture ρH O (8) 2

The abscissa on this chart is on a different scale to allow for representation of the experimental data, which were obtained over a narrower range of pressures. There is a generally good agreement between calculations of the expected extent of inhibition of the C−H2O reaction by CO2 with those observed experimentally.

4. DISCUSSION As we have seen in the Introduction, there is no general consensus in the literature regarding char gasification reaction rates in mixtures of CO2 and H2O and how these relate to the reaction rates measured separately. Published work reporting data for gasification rates in mixtures of CO2 and H2O presents a range of outcomes, including evidence for competition for active sites, reactions occurring separately and, therefore, overall rates being additive, and mixtures of these two models. 7647

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(20) Roberts, D. G.; Harris, D. J. Fuel 2007, 86 (17−18), 2672− 2678. (21) Nilsson, S.; Gómez-Barea, A.; Cano, D. F. Fuel 2012, 92 (1), 346−353. (22) Nilsson, S.; Gómez-Barea, A.; Ollero, P. Fuel 2013, 105, 764− 768. (23) Nilsson, S.; Gomez-Barea, A.; Fuentes-Cano, D.; Campoy, M. Fuel 2014, 125, 192−199. (24) Guizani, C.; Escudero Sanz, F. J.; Salvador, S. Fuel 2013, 108, 812−823. (25) Tagutchou, J. P.; van de Steene, L.; Escudero Sanz, F. J.; Salvador, S. Energy Sources, Part A 2013, 35 (13), 1266−1276. (26) Chen, C.; Wang, J.; Liu, W.; Zhang, S.; Yin, J.; Luo, G.; Yao, H. Proc. Combust. Inst. 2013, 34 (2), 2453−2460. (27) Umemoto, S.; Kajitani, S.; Hara, S. Fuel 2013, 103, 14−21. (28) Zhang, R.; Wang, Q. H.; Luo, Z. Y.; Fang, M. X.; Cen, K. F. Energy Fuels 2013, 27 (9), 5107−5115. (29) Bai, Y. H.; Wang, Y. L.; Zhu, S. H.; Yan, L. J.; Li, F.; Xie, K. C. Fuel 2014, 126, 1−7.

competitive behavior until very high partial pressures sufficiently use this surface. It follows that experimentation at high partial pressures (or on samples with very low active surface areas) is required to reveal significant evidence for CO2 and H2O competition. This is generally consistent with the outcomes of the review of the literature presented in the Introduction.

5. CONCLUSION Char−H2O and char−CO2 reaction rate data have been analyzed using the widely accepted LH reaction scheme and showed that there is a link between the reactant partial pressure, reactive surface saturation, and onset of inhibitory effects arising from competition between CO2 and H2O for reactive sites. This helps interpret the literature data in this area, which seem to provide a range of contradicting results; it explains why studies at low partial pressures (or on samples with high reactive surface areas) show no evidence of competition, while studies at higher pressures (or on samples with lower reactive surface areas) reveal competitive behavior. Importantly, this result suggests that the absence of inhibition of one reactant by the presence of another does not preclude a competitive reaction mechanism, which will only reveal inhibition at sufficiently high partial pressures, and that such a competitive reaction process is able to predict this behavior. More work under the appropriate experimental conditions is required to broaden the type of samples used (including chars from biomass and lignites), which will help to assess the extent to which high levels of catalytically active species or large variations in surface area may influence an analysis such as this.

■

AUTHOR INFORMATION

Corresponding Author

*E-mail: [email protected]. Notes

The authors declare no competing financial interest.

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REFERENCES

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