Full Length Article The kinetics and mechanism of the combustion of the carbon in biochar from oak, as studied in an electrically heated, fluidised bed of sand E.J. McMurchie , J. Olatunji , K.Y. Kwong , E.J. Marek , A.N. Hayhurst * Department of Chemical Engineering and Biotechnology, University of Cambridge, Philippa Fawcett Drive, Cambridge CB3 OAS, United Kingdom A R T I C L E I N F O Keywords: Combustion of a biomass in a fluidised bed Mechanism of combustion of a carbon in zone 1 Confirmation of Hurt and Calo’s outline mechanism Measurements of kinetic parameters of two rate-determining steps Catalysis of biomass combustion A B S T R A C T The oxidation of small particles (size 200 μm) of char from oak has been studied, by adding a small batch of them to an electrically heated bed of inert, silica sand, fluidised by mixtures of O2 and N2. The concentrations of CO, CO2, and O2, in the off-gases from the bed were continuously monitored, enabling the rate of combustion and also the fraction, X, of the carbon oxidised in each particle to be measured throughout combustion at different, well-controlled temperatures. The rate of oxidation declined as (1 – X) during burnout, because the O2 freely contacted the carbon in these tiny particles, whose oxidation was kinetically controlled at 700 ◦C and below. In fact, these tiny char particles burned in the fluidised bed at 500–700 ◦C in Zone 1 according to S0(1 – X)(k5CO2 + k6) per g of char. This matches Hurt and Calo’s three-step mechanism, whereby a porous char burns at a rate controlled by two reactions, one first-order in O2, the other zeroth-order in O2. Reactions (V) and (VI) were found to be, respectively, k5 = 1.7 × 103 exp (− 139 ± 18 kJ mole− 1/RT) m s− 1 and k6 = 1.5 exp (− 92 ± 20 kJ mole− 1/ RT) mole s− 1 m− 2. Reaction (V), between O2 and a surface complex containing oxygen, became faster as X increased, if the temperature exceeded 600 ◦C; catalysis by potassium was suspected as providing this extra reactive boost. 1. Introduction The study of the oxidation of carbon, particularly when it is in a particle of a char, made by heating either coal, wood or biomass in an inert atmosphere, has been one of the major pursuits of combustion research [1–5]. In spite of much prolonged activity on fundamental is sues, there is still much to be learned. For example, there is a need to identify the chemical reactions involved, when a solid carbon is burned, although some recent studies [6 –9] appear to have revealed as many new complications and questions as actual solutions. Of course, much of the current research is motivated by the practical concerns of replacing coal with a biomass as the renewable, sustainable, clean, solid fuel for generating electricity. Also, it is clear that the oxidation of carbon is horridly complicated by many features [6–9]. First, two basic chemical steps can be assumed [10] to proceed concurrently, if somehow indi rectly, viz. one producing the intermediate, CO, in the overall scheme: Cs + ½ O2 → CO, ΔH1 = − 110 kJ mol− 1. (I) The second appears to yield CO2 directly in the much more exothermic alternative: Cs + O2 → CO2, ΔH2 = − 393 kJ mol− 1. (II) There is, of course, the possibility that CO can be oxidised to CO2, as is usually achieved by reaction with an OH radical [11] in the homoge neous, gas-phase reaction: CO + OH → CO2 + H, ΔH3 = − 124 kJ mol− 1. (III) This latter reaction normally occurs without a surface [11,12], so that in a fluidised bed it is most likely to proceed inside a gaseous bubble (the bubble phase of the bed), and probably not in the gas percolating be tween the sand particles (i.e. the particulate phase), where any radicals usually disappear rapidly by recombining quickly on the extensive surface of the hot sand [12,13]. At temperatures below 800 ◦C, the oxidation of CO in (III) probably involves HO2 radicals, rather than OH [11]. Nevertheless, here is an important feature of a fluidised bed, viz. that a burning carbon particle inevitably resides with the sand in the particulate phase, where free radicals hardly exist, because they quickly recombine, forming stable molecules on the huge surface area of the sand. Consequently, the near-absence of free radicals around a char particle burning in a fluidised bed simplifies one’s thinking about the chemistry of combustion for a solid like a carbonaceous char. In * Corresponding author. E-mail address: anh1000@cam.ac.uk (A.N. Hayhurst). Contents lists available at ScienceDirect Fuel journal homepage: www.elsevier.com/locate/fuel https://doi.org/10.1016/j.fuel.2024.132677 Received 16 February 2024; Received in revised form 23 July 2024; Accepted 30 July 2024 Fuel 378 (2024) 132677 Available online 29 August 2024 0016-2361/© 2024 The Author(s). Published by Elsevier Ltd. This is an open access article under the CC BY license ( http://creativecommons.org/licenses/by/4.0/ ). mailto:anh1000@cam.ac.uk www.sciencedirect.com/science/journal/00162361 https://www.elsevier.com/locate/fuel https://doi.org/10.1016/j.fuel.2024.132677 https://doi.org/10.1016/j.fuel.2024.132677 http://crossmark.crossref.org/dialog/?doi=10.1016/j.fuel.2024.132677&domain=pdf http://creativecommons.org/licenses/by/4.0/ addition, CO is slow to oxidise in the particulate phase of a fluidised bed [13], because of the absence of free radicals like OH. Likewise, carbon particles, quite distinctly from in a normal burner [4,14], are not at all attacked by free radicals in a fluidised bed, but are inevitably attacked by molecules of O2, in more detailed versions of reaction (I) or (II). It will be seen below that mass transfer of O2 to a reacting char particle can be enhanced by the particle residing in the particulate phase. This is because the velocity of the gas moving around each char particle is increased considerably by the presence of the sand. Other complicating features of the oxidation of a solid carbon are that as intermediates in reactions (I) and (II), a whole host of surface oxide complexes are formed [8,9]. They include alcohols, carboxylic acids, ethers, anhydrides and even quinone, detected by e.g. infra-red spectroscopy or temperature-programmed desorption [8,9]. Some of these complexes can be tightly bound, but others less so. Likewise, their mobilities over a surface vary. Of course, a carbon atom’s reactivity depends on whether it lies on a planar or a flat surface or inside a pore or is more exposed on an edge. Inorganic catalysts can also be important [15–17] during the oxidation of a solid carbon. When an alternative solid fuel, such as a biomass char, comes to be burned, these various complexities must be borne in mind. This study follows previous work on the oxidation of tiny char par ticles (sieved to be ≈0.2 mm) from coal [6,18,19] in an electrically heated fluidised bed of sand. Then such small particles of char were found to have large mass transfer coefficients for oxygen diffusing to a char particle from the surrounding particulate phase. This gives tiny particles of char a greater tendency to burn under kinetic control in a fluidised bed, with the reactant O2 having such good access to the carbon in a char. In addition, the smallest char particles exchange heat fastest with the fluidised sand. This tends to prevent the exothermic reactions (I) and (II) from over-heating a burning char particle, i.e. to above the temperature of the fluidised bed. All this means that a flui dised bed has real advantages over alternative reactors, such as a ther mogravimetric analyser [5]. This paper examines the total rate of oxidation of the carbon (in small particles of char from oak) simulta neously via both reactions (I) and (II), as measured from the concen trations of CO and CO2 in the off-gases leaving the bed. 2. Literature survey: mechanism of oxidation The oxidation of a porous solid, like carbon can occur in one of three zones [1–3]. This study is only concerned with zone 1 [1], in which chemical kinetics alone dominate, because the temperature is then low enough and the carbon particles are sufficiently tiny for heat and mass transfer effects to be rapid enough to be ignored. To ensure this condi tion, it is necessary to be handling only tiny particles of carbon. Tradi tionally, kinetics in zone 1 have been considered [16] by writing the overall rate at which the two oxides of carbon are produced (from unit surface area) as k Cn O2, where k is a global rate coefficient and n is an overall order. Thus, recent measurements of n include n = 0.73 for burning char from beech [20]. Also, n has been found [21] to be between 0.75 and 0.85 for the oxidation of chars from hard woods. Di Blasi [16] in her 2009 review of the combustion of lignocellulosic chars reported n ranging from 0.5 to 0.87. Values of n equal to unity have been measured [3], e.g. for coal chars, so that in general the magnitude of n constitutes one important area of uncertainty. In addition, the rate of oxidation has Nomenclature A pre-exponential factor for k (mole1− n m3n− 2 s− 1) Abed cross-sectional area of the fluidised bed (m2) Ccorr corrected or deconvoluted concentration of a species in the off-gas (mole m− 3) Cf a “free” carbon atom on a char’s surface and exposed to the reactant O2 (–) Cj corrected concentration of a species j in the off-gas (mole m− 3) Cmeas measured concentration of a species in the off-gas (mole m− 3) Cp specific heat capacity of a char particle (J kg− 1 K− 1) CT total molar concentration of all species in the gas phase at a temperature T (mole m− 3) DO2,N2 diffusion coefficient of gaseous oxygen (m2 s− 1) in N2 d effective diameter of a char particle (m) E activation energy for k for the overall oxidation of carbon (J mole− 1) Ei activation energy of reaction (I) (J mole− 1) f(ki, CO2) rate law for the oxidation of 1 m2 of char h heat transfer coefficient from a fluidised bed to a char particle (W m− 2 K− 1) k overall (global) rate constant for the oxidation of a char particle (mole1− n m3n− 2 s− 1) ki rate constant for reaction (I) kg mass transfer coefficient (m s− 1) Nu Nusselt number for heat transfer (–) n effective order of the oxidation of carbon when both reactions (I) and (II) occur (–) rcomb rate of combustion of the carbon in a batch of char particles (mole s− 1) rdiff diffusional flowrate of oxygen from a fluidised bed to a char particle (mole s− 1) R gas constant Remf Reynolds number for minimum fluidisation (–) Sc Schmidt number = ν/DO2 for the fluidising gas (–) S0 initial, unreacted specific surface area of a char (m2 kg− 1) Sh Sherwood number for mass transfer = kgd / DO2 Sp external surface area of a char particle (m2) T temperature of the fluidised bed or char particle (K) t time (s) theat heating time for a particle of char of diameter d (s) U superficial velocity of gas fluidising a bed of sand (m s− 1) Umf value of U for incipient fluidisation (m s− 1) Vc volume of a char particle (m3) W initial mass of char added to a bed (kg) X fractional conversion of carbon in a char particle during oxidation to CO and CO2 (–) yi mole fraction of gas i in the gaseous phase at a bed temperature, T (–) Z any molecule acting as a third body in a termolecular reaction α power to which (1 – X) is raised in Eq. (5) (–) ΔHi enthalpy change for chemical reaction i (J mole− 1) Δp pressure difference across a bed of sand (N m− 2) δ thickness of external boundary layer for mass transfer to a reacting char particle (m) εmf fractional voidage in the particulate phase at incipient fluidisation (–) θ fractional coverage of the active sites of char with an oxygen-containing complex (–) κ effective thermal conductivity of the fluidising gas (W m− 1 K− 1) νg kinematic viscosity of the fluidising gas (m2 s− 1) ρg density of the fluidising gas (kg m− 3) ρ0 initial density of a particle of char (kg m− 3) τ mixing time for a gaseous sample from the fluidised bed (s) E.J. McMurchie et al. Fuel 378 (2024) 132677 2 sometimes been written [16] as proportional to (1 − X)α, where α is a simple power. However, such a dependence on the conversion, X, has often been ignored by several workers [16]. One purpose of this study was to settle whether the rate does depend on X and if so, how. Finally, the activation energy associated with the global rate constant, k, appears to be between 76 and 229 kJ mole− 1 [16]. This contrasts with Smith’s comprehensive compilation of global rate constants [22] for burning a very wide range of carbons, but largely from a coal; he deduced that the effective order, n, was unity and concluded that the activation energy was 179 kJ mole− 1. This general picture of widespread uncertainty is compounded by practical matters of how best to measure the kinetics of oxidation of any solid containing carbon. Different experimental tech niques and their problems have been reviewed [5]. This study develops the use of fluidised beds for measuring the rate of oxidation of tiny carbon particles at a well-controlled temperature. A likely mechanism for the oxidation of a solid carbon under kinetic control in zone 1 was formulated by Hurt and Calo [7]. In broad outline, it involves the following steps: 2Cf + O2 → 2C(O) (IV) C(O) + O2 → CO2 and/or CO + C(O) (V) C(O) → CO and/or CO2 (VI) Here Cf represents a free atom of carbon exposed on the char’s exterior; C(O) is a surface complex [8,9,23], such as a ketone, alcohol, acid, ether, etc, containing an atom of oxygen. It could be that the second step (V) also produces CO, in addition to CO2. Other variations on this theme have been published [24], but assuming the steady-state hypothesis for θ, the fractional coverage of a char’s surface with a complex, then yields: 2k4CO2 = k6 θ and also gives the rate of combustion per unit surface area of carbon as: k4CO2(k5CO2 + k6) (k4CO2 + k6/2) = f(ki,CO2) , (1) for the rate law, f(ki, CO2). The rate of burning given by (1) indicates that n, the overall order of the combustion reactions with respect to CO2, lies between zero and unity. This is certainly consistent with those measured in the literature to have n between unity and zero. Also, according to Eq. (1), the overall global rate constant, k, in general varies in a very com plex way with CO2 and the temperature. One reason [7] for n having a value between zero and unity would arise, if k4CO2≫ k6/2, so that the rate of oxidation per unit surface area becomes: f(ki,CO2) = (k5CO2 + k6) (2) In this case, the global order n would also depend on the temperature and CO2. Such a scenario looks very much like the rate of oxidation being determined by two parallel reactions, involving reaction (V), which is first-order in O2, and also (VI), a zeroth-order step. Such a situation does not appear as yet to have been tested by experiment, but it will be checked against experiments described below. However, although apparently hitherto hardly noticed, Hurt and Calo’s measured rates, reported in Fig. 5 of [7] do fit beautifully to expression (2) for their dependence on CO2. To investigate all this more fully, particularly including checking whether the measured rates of oxidation vary with CO2 according to (2), is another purpose of the experiments described below. If this is successful, measurements of the two rate constants, k5 and k6, might be possible. 3. Experimental Fig. 1 illustrates the apparatus, described in more detail elsewhere [25,26]. The fluidised bed was housed in a quartz tube (i.d. 30 mm, wall thickness 1.5 mm), containing 45 g of silica sand, sieved to 150–180 μm (geometric mean = 164 μm) and sitting on a porous sintered alumina distributor to a depth of 45 mm, when unfluidised. The quartz tube and sand were located inside a tubular electric furnace (1.1 kW). Immersed inside the sand was a K-type thermocouple, which measured the tem perature of the sand and provided a signal for its feedback control of the bed’s temperature, which could quickly reach 1100 ◦C. After metering the flowrates of O2 and N2 with rotameters, the chosen mixture of these gases was passed to the small plenum chamber at the bottom of the Fig. 1. The fluidised bed of silica sand, its supply of fluidising gas and the system for sampling the off-gases. TC represents the thermocouple measuring the bed’s temperature. The non-dispersive infra-red analyser was logged by a computer. (For interpretation of the references to colour in this figure legend, the reader is referred to the web version of this article.) E.J. McMurchie et al. Fuel 378 (2024) 132677 3 quartz tube. The mixture of gases then passed vertically upwards through the sand to fluidise it. In general, the gas originated from 3 cylinders, containing, respectively, N2, secondly 5.5 vol% O2 in N2 and thirdly air, with 21.0 vol% of O2. The off-gas from the fluidised bed was continuously sampled through a simple, quartz tube (o.d. 7 mm, i.d. 5 mm), whose tip was ≈ 100 mm above the sand. For this, a pump (0.5–1.0 L min− 1) passed the sampled gas through a drying tube of CaCl2 (renewed daily) and then to a non- dispersive, infra-red analyser (ABB EL3020) to measure the mole frac tions of CO and CO2 in the sampled gas. The instrument had a para magnetic cell to measure the concentration of O2 in the off-gas. These measurements were recorded every 0.5 s on a computer. The size of the sand fluidised was selected to avoid the added char being blown out of the bed. This would have occurred, if the terminal velocity of a char particle in the bed had been less than the superficial velocity of the gas fluidising the sand. In addition, the latter velocity was usually set at twice its value for incipient fluidisation to ensure the bed was a bubbling one [27]. Thus, cleaned silica sand was first sieved to provide particles from 150 to 180 μm. Then, the pressure difference, Δp, across the bed of sand (unfluidised depth 45 mm, o.d. 30 mm, particle density 2690 kg m− 3) was measured with a differential electronic manometer, open to the atmosphere at one end. Starting with the flowrate of air well above the minimum for the sand to be fluidised, Δp was recorded, whilst the flowrate was reduced gradually to zero. A plot of Δp versus the flowrate of the fluidising gas gave the usual two as ymptotes [27,28]: one was almost horizontal, for when the bed was fluidised, but the other was a straight line through the origin for the unfluidised, fixed bed of sand. The intersection of these two asymptotes occurred when the superficial velocity of the fluidising gas through the bed was Umf, i.e. its value at the point of incipient fluidisation [27,28]. The value of Umf depended on the temperature of the sand, as follows. For respective temperatures of 500, 600, 700 and 800 ◦C, Umf was, respectively, 0.069, 0.057, 0.045 and 0.037 m s− 1. The actual superficial velocity of the fluidising gas, U, was such that U/Umf was in the range 2.0–6.0. In each case, the bed bubbled nicely, without any slugs of gas appearing. In the work described below, U/Umf was usually 2.0, when the depth of the sand was measured to have grown to ~55 mm from a stagnant 45 mm. Observations indicated that immediately above the bed, bubbles were “bursting” on leaving the sand, so that on top of the bed, there existed a “splash zone”, roughly 10 mm deep, to where sand particles were carried in the wakes of bubbles [27]. All this was well below where the gas was sampled at ≈ 100 mm above the sand, when fluidised. The oxidation of char from oak, a frequently used hard wood, was studied. To prepare the char, first the wood was sawn into cubes of ~8 mm. Then 3 or 4 such cubes, held in a cage made from stainless steel wire, were inserted into the bed, when fluidised by only pure N2 and held at 900 ◦C. The volatile matter from the wood could be seen leaving the quartz tube for the first 100 s, but heating was continued for a total of 5 min, after which the heaters were switched off and everything left to cool for 3 more min. in flowing N2. The cold cubes of char were then crushed, using a pestle and mortar, and sieved to 180–212 μm (geo metric mean 195 μm), so the char particles were slightly larger than the sand (150–180 μm). Great care was taken to ensure that the flows of gas through the fluidised bed were low enough for newly added char par ticles not to be elutriated straight out of the bed. Even so, it was inevi table that some particles suffered such a fate in their final stages of burnout. Fig. 2 shows two SEM pictures of sieved char particles, taken, at room temperature using a benchtop Scanning Electron Microscope, employing an accelerating voltage of 15 kV. It appears that this biochar had running through it a network of straight channels, which appear in Fig. 2 as near- circular holes with a diameter of 3–4 μm. Most probably these holes were associated with pores, based on structural features remaining from the original wood. Smaller and more circular pores (diam. ≈ 0.4 μm) perpendicular to the channels were seen. It seems [29] that holes were left after the wood had been through a plastic state and gas bubbles formed to retain something of the morphology of the original wood during its carbonisation to a more graphitic structure. To characterise the char further, the absorption and desorption of N2 were analysed to provide values for the initial specific surface area, the mean size of the pores and the porosity of each char, i.e. the fraction of a particle’s volume, which is empty space. The results are shown in Table 1. Ultimate analyses were conducted on the oak char. On an ash-free basis, the sample was comprised of the following elements: carbon 81.1 wt%, hydrogen 0.92, nitrogen 0.16, balance (mainly oxygen plus metals 17.8 wt%). The ash content of oak char was measured in a thermogravimetric analyser (TGA: Mettler Toledo DSC 1), which sub jected a sample (~9 mg) to a linear temperature ramp to attain 900 ◦C after ~30 min., whilst being bathed in a steady stream of air to oxidise the char. The ash was analysed using inductively coupled plasma mass spectrometry; Table 2 shows the main metals found. They were pre sumably present as the oxides, together with various other trace ele ments. Catalytic rȏles have been attributed to the ash, although the mechanisms are not at all clear [31]. Table 2 clarifies that calcium and potassium are the main metals present in this char from oak. The density of a particle of oak char, ρ0, was estimated as follows. Fig. 2. Two SEM images of particles of oak char after having been sieved to 180–212 μm. The white bars denote the distance shown in μm. Table 1 Results of experiments absorbing and desorbing nitrogen, i.e. the Brunauer- Emmett-Teller surface area, Barrett-Joyner-Halenda mean pore diameter [30], ash-content, the initial density, ρ0, and the porosity of the char particles. Ash, wt % ρ0, Density / kg m− 3 S0, BET area/ m2/g BJH pore diam./ nm Porosity ~ 7 154 ± 40 58.1 ± 2.0 5.5 0.20 ± 0.05 E.J. McMurchie et al. Fuel 378 (2024) 132677 4 The density of the original oak had been measured to be 561 kg m− 3 [32]. By burning some wood in the TGA, the loss of mass on preparing the char was deduced; also, the accompanying decrease in volume was measured directly, yielding ρ0 = 154 ± 40 kg m− 3, as in Table 1, in agreement with previous measurements [32]. 4. Results For the combustion experiments, usually 0.010 g of char particles (sieved to 180–212 μm) was weighed out and mixed with a small amount of silica sand (~0.05 g; 150–180 μm). This mixture was quickly added to the hot fluidised bed and the lid on top of the quartz tube was then rapidly replaced. The sand, added together with the char, was there to limit elutriation and also any burning of the char before entering the bed of sand [18,19]. A typical example of the traces of the mole frac tions, y, of O2, CO and CO2, measured at ~100 mm downstream of the fluidised sand, is shown in Fig. 3. Also shown in Fig. 3 is yCOx, the sum of the mole fractions of CO and CO2, which are the only carbonaceous products from burning the char in what Fig. 3 shows to be gases con taining excess O2. A mass balance on the element carbon shows that the rate of oxidation of carbon in the char recently added to the bed is the rate at which carbon leaves the bed as CO and CO2, so that: rcomb = Abed U CCOx = Abed U yCOx CT (3) in units of moles of carbon s− 1, where CCOx is the sum of the concen trations of CO and CO2 (in mole− 1m− 3) in the sample, with CCOx = yCOx CT. Here CT is the total molar concentration of all the species in the gaseous phase and yCOx = yCO + yCO2. In addition, Abed is the internal cross-sectional area of the quartz tube and the product (Abed U) is the volumetric flowrate of gas (in m3 s− 1) leaving the fluidised bed. Equa tion (3) means that a measured concentration, such as CCO or CCOx, in dicates the rate of production of that species within the bed. This makes the effective rates of some chemical reactions easy to measure in a fluidised bed, so Eq. (3) enables the rate of production of COx, which is established below to be the rate of oxidation of the carbon in the added char, to be determined. This is a huge advantage of a fluidised bed, in that it produces directly and accurately a rate of reaction from a mea surement of a concentration, thereby obviating the need to differentiate measured concentrations with respect to time. Here, as noted earlier, above the fluidised sand was a splash zone, roughly some 10–15 mm in height, where bubbles burst and various intermediates, particularly CO, were probably oxidised. In that case, all the carbon in the char should end up being eventually detected as COx. It also should be mentioned that CO was detected in the off-gases well downstream of the sand, confirming that not all of it was burned to CO2 just above the bed. The maximum rate of production of CO is seen in Fig. 3 to slightly precede that for CO2. Fig. 3 indicates that CCO2/CCO does not vary much with time and is ~7, so that CO is the minor species. Fig. 3 can be used to ascertain how well the mass balance for the element carbon was obeyed. Thus the area under the plot of yCOx versus time, when multiplied by the total molar flowrate at which gases were leaving the fluidised bed, gives the total number of moles of carbon, which left the bed as CO or CO2, after the batch of char had been fed into the bed. That turned out to be ~93 % of the total number of moles of carbon added in the char to the bed. The small deficit is doubtless made up by a mixture of experimental error and the very smallest particles being elutriated from the sand, after shrinking considerably in both mass and size, just before their burnout. This closure of the mass balance establishes that elutriation of the added char was not a problem. As is conventional [18,19], the raw measurements of mole fraction in Fig. 3 had to be deconvoluted to correct for mixing in the sampled gas, when it was inside the quartz tube, as well as in the sampling line and detector. This involved taking the plot of each species’ measured con centration, Cmeas, versus time, t, and deducing the corrected concentra tions, Ccorr, from: Ccorr = Cmeas + τ dCmeas /dt. Consequently, the measured plots of CCOx versus time were first differ entiated numerically. To produce the profiles of corrected (or decon voluted) mole fractions in Fig. 3, the mixing time, τ, was measured to be 18.5 s by introducing a sudden, step-wise increase in e.g. the concen tration of either CO2 or O2 in the feed of pure N2 to the fluidised bed [33]. Then the difference between the measured and final concentra tions was found to decay exponentially with time, thereby confirming the above equation and yielding the value of τ. Fig. 3 shows a clear maximum for CCOx slightly before the minimum in CO2, consistent with the infra-red measurements of the mole fractions of CO and CO2 being slightly faster than the paramagnetic device registering the amount of O2 in the sample. The rise-time for the maximum in CCOx is ~8 s, which is much longer than the response time of the infra-red analyser (0.5 s), or the residence time of the gas in the quartz tube before sampling (~4 s) or the heating time of a particle (~0.01 s). To estimate the latter, a particle was assumed to be spherical and small enough to be at one temperature, when in the bed. In that case, the heating time is: theat = ρ0CpVC / hSp, where ρ0, Sp and VC are, respectively, the initial density, the external surface area (πd2) and volume of a char particle (πd3/6); Cp is its specific heat capacity. The heat transfer coefficient, h, is given by the Nusselt number, Nu = hd/κ = 2 [34] for a sphere of diameter d, with κ being the thermal conductivity of the fluidising gas, which is a mixture of O2 and N2 and often air. This results in h = 730 W m− 2 K− 1 and theat = 0.010 s. The observed long rise-time is much longer than 0.01 s and was most probably caused by the relatively slow mixing of the added batch of char particles in with the hot sand inside the bed. This is particularly the case for such a small fluidised bed as the one used here, given that the mixing of solids is normally effected by solids being transported in the wakes of large bubbles [35]. Consequently, mixing of the solids in the particulate Table 2 The amounts (in wt %) of certain elements present in the ash from the oak char studied. Al Ca K Na Si 1.63 34.88 5.68 0.49 0.65 Fig. 3. The deconvoluted mole fractions of O2, CO and CO2 measured down stream of the bed at 700 ◦C, with U/Umf = 2.0, fluidised by N2 with 5.5 vol% O2, after adding 0.010 g of oak char, sized to 180–212 μm. The dotted curve labelled COx is the sum of the mole fractions of CO and CO2 at each time. E.J. McMurchie et al. Fuel 378 (2024) 132677 5 phase is less rapid in a smaller, narrower bed. In addition, that theat is as brief as 10 ms reflects the rapidity of both heat and mass transfer be tween a fluidised bed and a particle of biomass burning inside the bed. 4.1. Effects of the fractional conversion of the carbon, X Looking at the concentration of COx (in effect, the rate of oxidation) rising in Fig. 3 to a maximum and subsequently falling to zero, previous workers [6,18,19] interpreted such a maximum for a coal char particle, again in a small fluidised bed (e.g. diam. 30 mm [18]), as a good approximation to the initial rate of reaction for a small particle of char being kinetically controlled with an effectiveness factor [36] of unity. In that case, the entire internal surface area of the added char would have been available to the surrounding oxygen to oxidise the carbon in the char. The fall after the maximum was assumed to be caused by a cor responding drop in the surface area of carbon available for oxidation [18] during burning. In that case, the maximum rate of combustion of a tiny char particle was written, purely for convenience, [18] as: rcomb, max = W S0 f(ki, CO2) (4) for a mass, W, of the added char, with total, initial surface area, (WS0), for oxidation in reactions (I) and (II) occurring concurrently according to the rate law, f(ki, CO2), for unit area of carbon, The units of the rate of combustion in Eq. (4) are moles s− 1. Implicit in these considerations is that they only refer to temperatures low enough for combustion to be kinetically controlled. The conditions for this are identified below. Transferring attention from the initial maximum rate in e.g. Fig. 3 to the subsequently measured, declining rates of burning of the added char, these falling rates have been attributed by previous workers [6,18,19] to the decreasing surface area of carbon still available for oxidation. One way of expressing this has been [16] to generalise the rate of oxidation of a piece of char of initial, unreacted mass, W, by rcomb = W S0 (1 − X)α f(ki, CO2). (5) This alters Eq. (4) for the maximum initial rate by introducing the factor (1 − X)α, where X is the fractional conversion of the carbon to CO or CO2 and α is an exponent to be determined. The rate of reaction of the carbon can also be expressed as − d(WX/12)/dt mole s− 1, with Eq. (3) still enabling the rate of combustion to be measured. Equation (5) is equiv alent to the surface area of carbon still available for further reaction in the added char being WS0 (1 − X)α. The value of the conversion, X, after a time t in e.g. Fig. 3 can be measured as follows from such a measured plot of CCOX against time, t. Because of Eq. (3), the carbon burned after a time t equals ∫ t o UAbedCCOxdt, so that the fractional conversion of the added carbon after having been burning for a residence time, t, can be expressed as: X = ∫t 0 CCOx dt ∫∞ 0 CCOx dt (6) Alternatively, since mole fractions, yCOx, were actually measured for COx, with CCOx = yCOxCT, where CT was assumed not to change on combustion, it is possible to express X as: X = ∫t 0 yCOx dt ∫∞ 0 yCOx dt (7) This enables X to be derived from a plot of yCOx versus time, t, as in Fig. 3, by measuring the area under the plot up to an increasing time, t. An example of the measured conversions, X, is shown in Fig. 4, using the bed at 700 ◦C. The shapes of these plots of X against time are very much as expected, with oxidation being quickest for fluidisation, when effected by the most oxygen-rich gas, i.e. air. The curve for the smallest con centration of O2 in the fluidising gas is conspicuous for taking a long time for CCOx to rise to a maximum. These curves in Fig. 4 can be ana lysed further by extending Eq. (5), for the rate of combustion of an added batch of char, as follows: rcomb = W S0 (1 − X)α f(ki, CO2) = d(WX/12)/dt, (8) so that dX/dt = 12 S0 (1 − X)α f(ki, CO2). (9) and taking logarithms yields: ln (dX/dt) = ln (12 S0 f(ki, CO2)) + α ln (1 – X). (10) This means that downstream of a maximum as in Fig. 3, a plot of ln (dX/ dt) versus ln (1 – X) at a fixed temperature and CO2 should become a straight line of slope α. This is checked in Fig. 5 after numerically differentiating the measurements of X presented in Fig. 4 for the bed at 700 ◦C. In Fig. 5, those first parts of Fig. 3 before the maximum there in CCOx, re-appear with X ~ zero, so ln (1 – X) is close to zero and ln (dX/dt) rises to a maximum. After that, ln(dX/dt) gradually decreases linearly, so the working point in Fig. 5 moves from right to left, as time passes. With air (yO2 = 0.21) fluidising the bed, the maximum in Fig. 5 occurs when X reaches ~0.020, but, for the fluidising gas containing 5.5 vol% of O2, the maximum occurs after X has grown to ~ 0.025, with the bed at 700 ◦C. This means that the maximum in CCOx in Fig. 3 occurred when X had grown to at least 0.2, depending on the concentration of O2 in the N2 fed to the fluidised bed. This corrects previous ideas [6,18,19] that X was close to zero at a maximum, as in Fig. 3. For the values of X larger than the value for a maximum in CCOx, the plots in Fig. 5 do eventually become linear, as predicted by Eq. (10). Furthermore, they continue to be linear, until ln(1 – X) reaches ~ − 4 or 82 % of the carbon has been oxidised. The mean slope of these linear regions of all four plots in Fig. 5 was found to be 1.05 ± 0.10. Equation (10) shows that this is the value of α for a bed at 700 ◦C; also, evidently α does not appear to depend on the oxygen-content of the fluidising gas. As for the other two temperatures of the bed, similar plots to Fig. 5 were obtained. Those for the bed at 600 ◦C are shown in Fig. 6, where the slopes of the final asymptotes indicated that alpha was 0.95 ± 0.10. 0 20 40 60 80 0 0.2 0.4 0.6 0.8 1 Fig. 4. The measured values of the conversion, X, when plotted against the residence time, for 0.010 g of tiny particles of oak char (sieved to 180–212 μm) added to the bed at 700 ◦C, with the fluidising gas containing the vol. % of O2 in N2, as shown. Here U/Umf = 2.0. E.J. McMurchie et al. Fuel 378 (2024) 132677 6 Here the slope, α, was constant until ln(1 – X) became ~ − 5, i.e. when the conversion, X, had grown to ~0.99. As for 500 ◦C, α was found to be 1.07 ± 0.14; here there was more noise, because of the weaker signals observed. In this situation, where no systematic dependence of α on either X or the temperature over the range 500 to 700 ◦C was found (or indeed expected), an average value of unity (with an error of 10 %) was deemed appropriate for alpha. This important conclusion of α being unity is discussed below, but it is hard to explain without assuming the O2 has free access to the carbon in the char. 4.2. Is combustion controlled by chemical kinetics or mass transfer? The maximum rates of burning, as revealed by the maximum values of yCOx in such as Fig. 3, were used to derive the maximum rate of oxidation, rcomb,max, in beds fluidised by air at 500–800 ◦C at the point, where yCOx was at its maximum at that particular temperature. These maxima were used, because their values were easy to measure accu rately. The third row of Table 3 lists these measured maximum rates of combustion (rcomb, max/W) in units of moles of carbon burnt per g of char s− 1 for four beds at different temperatures. In addition, the rate at which O2 was transported by mass transfer to the exterior of a char particle, was calculated using the fact that the maximum possible rate of mass transfer of O2 to the exterior of one burning char particle is given by: rdiff = kg πd2 CO2 (11) Here kg is the mass transfer coefficient, given by the Sherwood number, with Sh = (kgd /DO2, N2) = 2εmf + 0.7 Remf 1/2Sc1/3 (12) [37], a well-established correlation, found correct to ~25 % [38]. Here the Reynolds number, Remf = Umf d/ εmf ν. The diffusion coefficient, DO2,N2 of O2 in N2 is ~0.22 × 10− 4 m2 s− 1 at S.T.P. and varies as T1.75 bed [39]; the voidage, εmf, in the particulate phase is ~0.42 [35], ν is the kinematic viscosity of the fluidising gas and the Schmidt number, Sc = ν/DO2,N2 for the fluidising gas of O2 in N2. All this leads to a value for the rate of diffusion of O2 from the particulate phase to the exterior of a spherical particle of char with a diameter equal to the geometric mean of 180 and 212 μm. This enabled the rate of external mass transfer to be computed as the rate of diffusion of O2 to unit mass of the host char particles at the four different temperatures of Table 3. Quite strikingly, row 4 of Table 3 reveals that the computed rate of external mass transfer of O2 to a reacting particle is much larger than the measured rate of combustion at all four temperatures. Of course, combustion requires most O2 per atom of carbon, when reaction (II) operates to the exclusion of (I). However, the ratio of the yield of CO2 to that of CO is typically ~7, as seen in Fig. 3, so CO is not a very major consideration. The ratios of the computed rates of external mass transfer to the actual rates of reaction, in which some of this O2 is consumed, are shown in the final row of Table 3. These ratios vary from 196 at 500 ◦C to 6.2 at 800 ◦C. The values in Table 3 have associated errors of almost a factor of 2. All this indicates that com bustion is not controlled by external mass transfer at 700 ◦C or below, but is possibly partly so at 800 ◦C. Similar conclusions were deduced from combustion experiments in weaker mixtures of O2 in N2.This leaves chemical kinetics and internal mass transfer (through the char’s pores over a distance of one radius of a particle, i.e. ~98 μm) as the other two possible processes controlling the rate of combustion. For both internal and external diffusion, the rate of mass transfer is inversely proportional to the square of the distance over which diffusion occurs. The thickness, δ, of the boundary layer for external mass transfer to a burning particle is given [40] by: Sh = 2εmf(1 + (d/2)/δ), which indicates (δ/d) = 1.8. Comparison of the two distances for diffusion indicates that internal diffusion over only one particle radius is faster than external mass transfer over a distance of 1.8 di ameters by a factor of (2 × 1.8)2 = 13. In addition, the ratio of the re sistances to internal and external diffusion of O2 is proportional to (1 – char’s porosity)/(1 − εmf) = (1 – 0.2)/(1 – 0.42) = 1.4 [34], so this ratio becomes 1.4/13 = 0.11. This value should be increased, because a particle’s pores are narrow and possibly tortuous, although with char from oak, the pores might be fairly straight. However, these pores are -8 -6 -4 -2 0 -9 -8 -7 -6 -5 -4 -3 -2 Fig. 5. Plot of ln (dX/dt) versus ln (1 – X) for 0.010 g of oak char (sieved to 180–212 μm) added to the bed at 700 ◦C, with the fluidising gas containing the vol. % of O2 in N2 as shown. Here U/Umf = 2.0. -4 -3 -2 -1 0 -6 -5 -4 -3 Fig. 6. More plots of ln (dX/dt) versus ln (1 – X) for 0.010 g of oak char added to the bed at 600 ◦C, with the fluidising gas containing the vol. % of O2 in N2 as shown. U/Umf = 2.0. Table 3 Measured maximum rates of burning oak char (in moles of C g− 1 s− 1) in beds, fluidised by air and held at 4 different temperatures, together with the computed maximum rates of mass transfer of O2 from the bed to what was initially unit mass of char. Tbed / oC 500 600 700 800 CO2 mole− 1/m− 3 3.30 2.93 2.63 2.38 Meas’d 103×(rcomb/W) / mole of C g− 1 s− 1 0.224 1.66 5.0 9.1 Calc’d rate of supply / mole of O2 g− 1 s− 1 0.044 0.047 0.050 0.056 (supply of O2)/(Meas’d (rcomb/W) for C) 196 32 10 6.2 E.J. McMurchie et al. Fuel 378 (2024) 132677 7 short in length and plentiful, but a further factor of 10 would make the two resistances similar. One relevant piece of experimental evidence was deduced above, viz that in this case the rate of oxidation is always proportional to (1 – X). This finding is discussed below, but it does indicate that the reactive carbon surface is always freely available to the reacting O2. In this case, it seems that the char particles are too tiny for the effects of diffusion of O2 through narrow pores to cause much of an internal resistance to combustion. Thus, the figures in the last row of Fig. 3 might be reduced slightly, by, say, a factor of 2, to account for internal diffusion of O2. This would leave chemical kinetics as a major feature controlling the rate at which this char burns. It is consequently very possible that at 700 ◦C combustion is not limited by either internal or external diffusion of O2. It is an important assumption of this work that, because these char parti cles are so tiny, their combustion here is controlled by chemical kinetics at 700 ◦C and below. Of course, such an assumption must be checked later in this paper. Exactly what is happening at 800 ◦C is not totally clear; control is then most likely to be by a mixture of internal and external mass transfer, coupled possibly with chemical kinetics. Equation (12) is worth examining. The first term is for the diffusion of O2, which is inhibited by the presence of the sand. The second term is for the convection of O2 to the reacting char particles. Importantly, the convective flux is increased by the sand’s presence, which merely in creases the interstitial velocity of the fluidising gas moving over the reacting char particles. The overall result is that the mass transfer of oxygen to the active particles can be accelerated by being surrounded by the inactive sand. This is how a fluidised bed operates as a combustor. In particular, enhanced mass transfer of a gaseous reactant results in more extensive regions of kinetic control compared to most reactors for combustion. Herein lies a virtue of a fluidised bed. 4.3. Analysis of kinetics The assumption is that particles of oak char as small as 0.2 mm burn in a fluidised bed at 700 ◦C, or below, within the so-called zone 1, where the rate of combustion is determined entirely by chemical kinetics. This is now investigated in more detail. The literature, discussed above in Section 2, indicated that, according to Hurt and Calo [9], the chemical reactions limiting the rate of combustion in zone 1 could be summarised as (V) and (VI), for which the rate of combustion, with α = 1 was seen above to be given by: rcomb = W S0 (1 − X) (k5CO2 + k6), (13) in moles s− 1. Equation (13) is to be checked for describing the kinetics of burning the carbon in a char. For this it can be rearranged to: rcomb / W (1 − X) = S0 (k5CO2 + k6). (14) Given that kinetic control has been assumed at 700 ◦C and below, Fig. 7 is a plot of measured values of rcomb / W(1 − X) against CO2, for the fluidised bed at 700 ◦C. Were Eq. (14) to hold, a straight line of slope, S0k5 (m3/s g− 1), and intercept, S0k6 (mole/s g− 1), would be obtained. Fig. 7 has separate plots for three different stages of combustion, i.e. for X = 0.2, 0.3 or 0.5, all for the bed at 700 ◦C. At each of these extents of combustion, Eq. (13) is obeyed nicely, by the good straight lines in Fig. 7, with a positive intercept on the y-axis. Again, the model based on kinetic control is borne out well by these experimental checks. Inter estingly, within experimental error, all three plots in Fig. 7 have the same intercept on the y-axis, enabling the value of (S0k6) to be obtained for 700 ◦C as S0k6 = 0.7 × 10− 3 mol s− 1 g− 1. This indicates that at 700 ◦C, k6 = 1.2 × 10− 5 mol s− 1 m− 2, subject to an error of 20 %. However, the slope of the best fit straight line in Fig. 7 (S0k5) in creases with the conversion, X, of the carbon to its oxides, suggesting that k5 somehow increases with X. Given that reaction (V) involves gaseous molecules of O2 reacting with oxygen-containing, surface complexes, this observation could be explained by the nature of the complex changing during oxidation, whilst the extent of reaction, X, increases at the fairly high temperature of 700 ◦C. This could result in the oxygen-containing complex becoming in effect more reactive in step (V) at higher X. Alternatively, for there to be a metallic catalyst in the gas phase might require the passage of time. Fig. 8 plots the slope of the best-fit straight lines in Fig. 7 for 700 ◦C against the value of the frac tional conversion, X. The fitted curve in Fig. 8 shows the slope of Fig. 7, (S0k5), increasing non-linearly from a value of 2.7 × 10− 3 m3/s g− 1 at X equals zero up to 4.8 × 10− 3 m3/s g− 1 at X = 0.5. This corresponds to k5 increasing unexpectedly by a factor of ~1.8 after half the carbon had burnt away at 700 ◦C. The effect is discussed below, but it is worth noting that k5 and k6 can be measured from a plot like Fig. 7 for a selected value of X. It is important to check what is happening in fluidised beds below 700 ◦C, where the rate of combustion is inevitably still controlled by chemical kinetics, especially at lower temperatures. The experiments for Fig. 9 were just like those described for Fig. 7, but for 500 ◦C, where rates of combustion were much lower. Quite strikingly, Fig. 9 for the fluidised bed at the lowest temperature of 500 ◦C, can be fitted by one single straight line, without the increase in slope with X, observed at 700 ◦C in Fig. 7. Again, the intercept in Fig. 9 does not vary with X. Thus, Eq. (13) is confirmed for 500 ◦C. The situ ation at 600 ◦C is seen in Fig. 10. At 600 ◦C, the plots in Fig. 10 are again good straight lines with a positive intercept, establishing Eq. (13) as a good description of how the rate of combustion, rcomb, varies with CO2 in Zone 1 below 700 ◦C. Even so, the slope of the best-fit line does increase, but only slightly, with the conversion, X. This reveals a consistent pattern whereby the behaviour Fig. 7. Plots of rcomb / W(1 − X) against CO2 for the oxidation of oak char in a fluidised bed at 700 ◦C. Here 10 mg of oak char (sieved to 180–212 μm) were added to the bed at 700 ◦C, with the fluidising gas containing the vol. % of O2 in N2 as shown. Here U/Umf = 2.0. The three plots shown are for measurements made at different values of the conversion, X, of solid carbon to its gaseous oxides. Here +, □ and × are, respectively, for X = 0.2, 0.3 and 0.5. E.J. McMurchie et al. Fuel 378 (2024) 132677 8 at 600 ◦C is intermediate between those at 500 and 700 ◦C. Thus a modest extrapolation of the slope to X = 0 was required. Measurements of the intercepts in Figs. 7, 9 and 10 did not depend on X and were taken to be S0k6, whose value at 700 ◦C was read from Fig. 7 to be 0.7 × 10− 3 mol s− 1 g− 1. An Arrhenius plot of the actual intercepts in Figs. 7, 9 and 10 is seen in Fig. 11. The slope of the best-fit straight line indicates an activation energy for reaction (VI) of E6 = 92 ± 20 kJ / mole. Also, the best-fit straight line in Fig. 11 enables the rate coefficient for reaction (VI) at 700 ◦C to be written as k6 = 1.7 × 10− 5 mol s− 1 m− 2, so that in general k6 = 1.5 exp (− 92 kJ mole− 1 RT) mole/s m− 2. It is notable that unlike k5, the value of k6 does not increase with X, so any ageing effect boosting k5 does not affect reaction (VI). Fig. 12 is the Arrhenius plot of the slopes of Figs. 7, 9 and 10 (cor rected as necessary to X = 0, as in Fig. 8) versus 1/T. The fit to a straight line in Fig. 12 is a good one, giving this entire mechanistic interpretation based on Eq. (13) a definite coherence. The slope of the best-fit straight line in Fig. 12 indicates an activation energy for reaction (V) of E5 = 139 ± 18 kJ mole− 1. This enables the rate constant of (V) to be written as k5 = 1.7 × 103 exp (− 139 kJ mole− 1/RT) m/s. This ignores any boost in the effective value of k5 (noted in Figs. 7 and 10) at temperatures of 700 and 600 ◦C, whenever X exceeds zero. At 700 ◦C, in going from X = 0 to X = 0.5 resulted in almost a doubling of k5, but at 600 ◦C the increase in k5 with X was only by a factor of ~1.2. The significant boost to reaction (V) noted in Fig. 8 was sensitive to temperature in that it was most conspicuous at 700 ◦C, but absent at 500 ◦C, with intermediate behaviour at 600 ◦C. Furthermore, at the two higher temperatures, the effect grew with conversion (i.e. time), as if a metallic catalyst needed a high temperature and time before being able to function. The coherence of the above set of observations and in particular that Fig. 8. The slopes of the three best-fit straight lines in Fig. 7 for the bed at 700 ◦C, plotted against the value of X. Fig. 9. Plots of rcomb / W(1 − X) against CO2, as in Fig. 7, but for the lower temperature of 500 ◦C. The three plots shown are for measurements made at different values of the conversion, X, of solid carbon to its gaseous oxides, with +, ● and ○ referring to X = 0.2, 0.3 and 0.5, respectively. Here +, □ and × are, respectively, for X = 0.2, 0.3 and 0.5. Fig. 10. Plots of rcomb / W(1 − X) against CO2, as in Fig. 7, but for the inter mediate temperature of 600 ◦C. The three plots shown are for measurements made at different values of the conversion, X, of solid carbon to its gaseous oxides. Here +, □ and × are, respectively, for X = 0.2, 0.3 and 0.5. E.J. McMurchie et al. Fuel 378 (2024) 132677 9 the behaviour at 500 ◦C fits well with that at 700 ◦C confirms that this particular char was in fact burning under kinetic control at these tem peratures in this fluidised bed. Thus the major assumption of kinetic control has been justified. 5. Discussion 5.1. Experimental aspects It is worth noting that a fluidised bed has proved here to produce good, direct measurements of the rate of combustion of a biomass char under well-defined conditions. Such a reactor has the advantages of efficient heat and mass transfer between a reacting solid particle and its surroundings. This ensures these transfer processes are fast enough to be unimportant, so that tiny particles of this char were found to burn under kinetic control at 700 ◦C and below. In addition. the temperature in a fluidised bed can be accurately controlled. 5.2. Structural aspects The fact that α = 1 is a striking conclusion, which is often assumed, but rarely verified. The statement means that after combustion has removed a certain fraction of the carbon from a sample of a char, the same fraction of the active surface area of the carbon has also dis appeared. It is as if the carbon is mainly dispersed on a very thin surface, which is readily accessible to the reacting oxygen. To check the initial thickness of the carbon seen in Fig. 2, the initial surface area of the carbon was noted in Table 1 to be S0 = 58.1 m2/g, together with ρ0 = 154 kg m− 3; all this indicates that, if the char were imagined to have been previously spread out over a large area, the average thickness of the carbon film would be ≈ 1/ (2 × 58.1 × 103 × 154) ≈ 5.6 × 10− 8 m ≈ 56 nm, which can be described as “thin”, even on a molecular scale, given the separation between parallel layers in graphite is of the order of 33.5 nm [41]. Consequently, the reacting oxygen is likely to have un inhibited access to very nearly all the carbon, resulting in α = 1 and also the same rate of reaction everywhere around a particle, which is admittedly a fairly crumpled film. Thus, the case under consideration of a tiny particle of char from oak appears to have a thin film of carbon, which helps to ensure that the rate of oxidation is the same and uniform around each particle, thereby resulting in the simple situation of α = 1. All this enables the oxidation of these small char particles to be under kinetic control. In the language of catalysis, the effectiveness factor [36,42] for one of these little char particles burning in a fluidised bed is unity. Such a situation has also been found by others. Thus, Di Blasi [16] in her detailed review of previous work on the oxidation of various chars from wood, quoted instances when α = 1.0 ± 0.1. More recently, one instance of where α = 1.0 ± 0.1 includes the use of a fluidised bed [23], but a critical requirement is to burn only small particles of char. 5.3. The mechanistic approach to describing the kinetics Figs. 7, 9 and 10 provide strong confirmation of Hurt and Calo’s outline reactions (IV), (V) and (VI), which indicated that a biomass char might burn at a rate controlled by one reaction first order in oxygen, as well as another one of zeroth order. Reactions (IV) – (VI) do not strictly constitute a proper, detailed mechanism, but rather a semi-global one. Even so, they do have the advantage of helping to understand and formulate the rate of combustion of a biochar. Moreover, their rate constants were estimated in this study, together with their activation energies of E5 = 139 ± 18 kJ mole− 1 and E6 = 92 ± 20 kJ / mole. Previous measurements are hard to find. However, Niksa et al. [43] have recommended for chars from coals: E5 = 117 ± 18 kJ mole− 1 and E6 = 133.8 ± 20 kJ / mole. The values of E5 overlap, but the values of E6 do not. Clearly more work is necessary now that a useful experimental technique has been identified. 5.4. Is combustion of biomass catalysed? Figs. 7, 8 and 10 revealed that the basic mechanism of reactions (IV) – (VI) could be augmented by reaction (V) providing more oxides of carbon, provided the temperature was above 600 ◦C and that sufficient Fig. 11. Plot of the natural logarithm of the intercepts (S0k6) in Figs. 7, 9 and 10 (after extrapolation to X = zero for 600 and 700 ◦C) against the reciprocal of the absolute temperature of the fluidised bed. Fig. 12. Plot of the natural logarithm of the slope of the best fit straight line (for X = zero) in Figs. 7, 9 and 10 versus the reciprocal of the absolute tem perature of the fluidised bed. E.J. McMurchie et al. Fuel 378 (2024) 132677 10 time had elapsed. There is evidence that ash from a biochar is capable of catalysing the oxidation of carbon [5,15–17,31,44–46]. Thus there are examples of the activation energy associated with the global reaction for the oxidation of a char being measured to be as low as ~78 kJ mole− 1 [16,44–46]. Certainly, metals like K and Ca were found here in the oak char. Potassium has often been thought to be the catalytic metal [31,47], but the mechanism for its action has remained so far elusive. One new catalytic mechanism, which might be aired here to explain this extra boost, is as follows. It is very likely that, during the combustion of a char from a wood, potassium at ~700 ◦C forms an organic salt, like its oxalate, which then decomposes at such a high temperature into free atoms, K, and mole cules of KOH [48,49] in the gaseous phase. Also, in O2-rich situations, as here, there is the possibility that molecules of KO and KO2 are formed [48,50]. The superoxide, KO2, is stable [51] with a melting point of 400 ◦C, and the bond K–O2 has a dissociation energy of 247 ± 20 kJ mole− 1 [48]. In fact, these superoxides of Group (1) metals are found in the mesopause region of the earth’s atmosphere [52] at an altitude of ~90 km, as well as in O2 - rich flames at atmospheric pressure and temperatures up to ~2000 ◦C [48–50]. The formation of an oxide like KO2 turns out to be surprisingly rapid [48,52–55] in the gas phase, where in hot, O2 – rich gases it is produced by K + O2 + Z = KO2 + Z, (VII) where Z represents any molecule acting as a “third body” to remove energy from the colliding pair of K + O2. It appears that the termolecular reaction (VII) is faster than the normally expected rate of bimolecular collisions [48,52–55] between K and O2. The earlier failure to properly detect superoxides of the alkali metals by mass spectrometric sampling has now been explained [56]. It was noted above that a mechanism of the three reactions (IV) – (VI) suffices for explaining the oxidation of most carbons. If the metal K and its superoxide are to catalyse the oxidation of a carbon, they must accelerate a rate-determining step. The evidence here is that reaction (V) appears to have been catalysed to an extent depending on temperature and conversion, X, or time. If then KO2 is present in the gas-phase at the temperatures of this study, i.e. 500–800 ◦C, it could participate in oxi dising carbon in the reaction: C(O) + KO2 → CO2 and/or CO + C(O) + K (VIII) and accelerate (V), when followed by the fast step: K + O2 + N2 → KO2 + N2. (IX) This is because addition of these two reactions yields: C(O) + O2 → CO2 and/or CO + C(O) (V) as the overall reaction, which is being catalysed or accelerated by (VIII) and (IX) in this boost at 700 ◦C and probably above. Given that potas sium appears [31,47] to somehow act catalytically in the combustion of a char, here is a likely catalytic mechanism based on the participation of KO2. That catalysis of reaction (V) was seen above to be more profound at larger X could be explained by it taking time to transfer potassium to the gaseous phase. Reaction (VIII) would have to proceed at the surface of the reacting char, whereas (IX) would occur rapidly in the gas phase in the thin film close to a char particle. Such a sequence of oxidation and reduction reactions involves a pair of short-lived, but reactive, species, viz free atoms of K and the superoxide. These transitory species are enabled to function this way by the unexpected rapidity of (IX). For Ca it looks as if the reaction: Ca + O2 → CaO + O (X) is more likely than the equivalent of (IX) [48,54] for potassium, so catalysis by this route might be limited to just potassium, where the formation of KO2 can become appreciable. Even so, the sequence of reactions (VIII) and (IX) does not require KO2 or CaO2 to be long-lived, so Ca or even Mg might just provide species like CaO2 and Ca as short- lived catalytic intermediates in this situation. These questions merit further research, but here is a possible answer to an old question. 6. Conclusions (a) Electrically heated fluidised beds of inert silica sand have proved to be useful reactors, in which to measure the rate of combustion of small particles (~200 μm) of carbon over a relevant range of temperatures, when an effectiveness factor of unity was achieved. (b) The rate of oxidation of a tiny particle of oak char in a fluidised bed was found to be kinetically controlled (i.e. in Zone 1) at temperatures of 700 ◦C or below. (c) Small particles of oak char (diam. ~200 μm) were shown to be oxidised at a rate proportional to (1 − X), where X is the fraction of the carbon already reacted. This conclusion, and also the previous two, depend on tiny char particles being burned. (d) Tiny char particles can burn in a fluidised bed with quite different boundaries between the three zones of combustion [1–4]. (e) By expressing the rate of burning per unit area of oak char by the semi-global expression: (k5CO2 + k6), the experimental technique enabled k5 and k6 to be measured. In fact, this expression pro vided good fits to the measured rates of combustion at 500–700 ◦C at concentrations of oxygen as low as 2.5 mol % in N2. This confirms Hurt and Calo’s scheme [7] of reactions (IV) – (VI) for oak char burning in Zone 1 and also establishes that the rate of combustion per unit surface area is indeed (k5CO2 + k6). It was deduced that k5 = 1.7 × 103 exp (− 139 kJ mole− 1/RT) m/s and k6 = 1.5 exp (− 92 kJ mole− 1 RT) mole s− 1 m− 2. This infor mation helps to model the combustion of biochars in Zone 1. (f) At ≈ 700 ◦C combustion by reactions (IV) – (VI) was augmented by reaction (V) being accelerated. A scheme for potassium cata lysing reaction (V) by the participation of molecules of KO2 is presented. Also, there is experimental evidence that the catalytic effect grows with time or conversion, X. 7. Use of AI AI was not used in any form. CRediT authorship contribution statement E.J. McMurchie: Writing – original draft, Investigation. J. Olatunji: Writing – original draft, Investigation. K.Y. Kwong: Methodology, Investigation. E.J. Marek: Investigation, Writing – original draft. A.N. Hayhurst: Supervision, Methodology, Formal analysis. Declaration of competing interest The authors declare that they have no known competing financial interests or personal relationships that could have appeared to influence the work reported in this paper. Data availability Data will be made available on request. Acknowledgments The authors thank Krishna Vadiraj Kinal and Prof. Laura Torrente- Murciano for measuring the BET surface area of their char and also Nigel Howard (Department of Chemistry, University of Cambridge) for an elemental analysis of the char, and finally George Fulham for the SEM images in Fig. 2. E.J. McMurchie et al. Fuel 378 (2024) 132677 11 References [1] Marsh H. Introduction to carbon science. London: Butterworths; 1989. [2] L.D. Smoot (Ed.), Fundamentals of Coal Combustion, Elsevier, Amsterdam, 1993. [3] Tomeczek J. Coal combustion. Malabar, Florida: Krieger; 1994. [4] Williams A, Pourkashanian M, Jones JM, Skorupska N. Combustion and gasification of coal. London: Taylor and Francis; 2000. [5] Kwong KY, Marek EJ. Combustion of biomass in fluidized beds: a review of key phenomena and future perspectives. Energy Fuel 2021;35:16303–34. [6] Bews IM, Hayhurst AN, Richardson SM, Taylor SG. 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http://refhub.elsevier.com/S0016-2361(24)01826-X/h0270 http://refhub.elsevier.com/S0016-2361(24)01826-X/h0270 http://refhub.elsevier.com/S0016-2361(24)01826-X/h0270 http://refhub.elsevier.com/S0016-2361(24)01826-X/h0270 http://refhub.elsevier.com/S0016-2361(24)01826-X/h0275 http://refhub.elsevier.com/S0016-2361(24)01826-X/h0275 http://refhub.elsevier.com/S0016-2361(24)01826-X/h0280 http://refhub.elsevier.com/S0016-2361(24)01826-X/h0280 The kinetics and mechanism of the combustion of the carbon in biochar from oak, as studied in an electrically heated, fluid ... 1 Introduction 2 Literature survey: mechanism of oxidation 3 Experimental 4 Results 4.1 Effects of the fractional conversion of the carbon, X 4.2 Is combustion controlled by chemical kinetics or mass transfer? 4.3 Analysis of kinetics 5 Discussion 5.1 Experimental aspects 5.2 Structural aspects 5.3 The mechanistic approach to describing the kinetics 5.4 Is combustion of biomass catalysed? 6 Conclusions 7 Use of AI CRediT authorship contribution statement Declaration of competing interest Data availability Acknowledgments References