Particle Agglomeration of Biomass and Plastic Waste during Their Thermochemical Fixed-Bed Conversion

Abstract

The article provides state-of-the-art research on agglomeration processes during fixed-bed combustion and gasification of low-grade fuels such as biomass and waste (primarily plastic-containing waste). Such fuels demonstrate complex thermal behaviour: their decomposition and combustion are multistage, accompanied by phase transitions, and may lead to fixed-bed mechanical instability and the non-uniformity of air distribution over the cross-section. To clarify the role of physicochemical factors (fuel composition and properties, reactor conditions), data from different sources are compared. The review shows that the fixed-bed agglomeration regimes can, in a rough approximation, be classified by the sintering mechanism (due to the melting of the mineral part or the organic part), with the following search for each mechanism realisation conditions by comparing the fuel properties and characteristic temperatures. Attempts to theoretically describe and numerically simulate the agglomeration phenomenon as a change in the structure of a reacting dispersed medium are also considered: the main directions in which such approaches can be developed are indicated.

1. Introduction

The problems of agglomeration in the thermochemical conversion of solid fuels are associated primarily with the use of low-grade fuels, primarily biomass and waste. Agglomeration of fuel particles is their association, sticking, which occurs when their surface softens, usually when some components (ash, plastic) melt or liquid products (tars) are released. Low-grade fuels typically have a high tar yield and high ash content; municipal waste and refuse-derived fuel often contain a significant amount of plastic. As a result, the thermal processing of biomass and waste becomes complicated: the produced agglomerates (clinkers) prevent the uniform distribution of air (or other gaseous reagents) over the reactor cross-section, significantly increasing hydraulic resistance, and sometimes merely block the reaction zone and lead to conversion extinction and equipment shutdown. These two main agglomeration pathways (through the melting of the organic mass and the melting of the mineral part) will be the focus of this review

Agglomeration is especially critical for fluidised bed reactors, where the fluidisation conditions are determined by the average particle size and the speed of the fluidising agent. Therefore, many works (including reviews) are aimed at studying agglomeration in fluidised beds. However, fixed-bed agglomeration also leads to significant problems. Despite this, systematic studies of fixed-bed agglomeration have not yet been carried out, and we still cannot clarify its details and features and explain available experimental data (not to mention predicting agglomeration).

The composition and properties of biomass and waste are sensitive to many factors (species, season, geographical location, etc.). Data on typical compositions can be found in [1,2].

Reactors and experimental units for pyrolysis, gasification, and incineration of waste (including plastic-containing waste), are described in several reviews: [3,4,5,6,7,8]. The main way to prevent sintering and agglomeration during waste processing is by using mechanical devices, for example, special agitators, rotators, screws, mechanical grates, etc. [9,10]. During the thermal processing of biomass and plastics, a number of valuable products can be produced, such as biochar, combustible gas, and, in some cases, liquid products or ash.

Sometimes, agglomeration can be an aim of the processing, for example, when forming a coke mass for technological purposes: when heated, the organic mass of coal also softens (undergoes a metaplast state) [11,12]. On the other hand, the agglomeration of coal particles can lead, for example, to the formation of large aggregates and mechanical underburning in the pulverised coal flame [13,14]. Agglomeration is also used in the briquetting and pelletisation of fuels [15,16,17]. In the thermal processing of biomass and waste, agglomeration is usually an undesirable process.

Agglomeration is a complex multiphase process that includes heat and mass transfer, chemical reactions, and phase transitions. Often, agglomeration is also associated with mechanical phenomena, such as the formation of channels and cavities (burnouts) in porous media. Therefore, the fixed bed agglomeration phenomena can be associated with a change in the structure of the reacting porous media. Depending on the sintering mechanism and reaction conditions, agglomeration can be determined by the fuel composition, temperature (and its distribution along the reaction zone), heating rate, airflow, etc. A full detailed description of the agglomeration processes is currently impossible, therefore, the proposed physical models of agglomeration are limited and inevitably are mainly empirical nature. In some cases, however, it is possible to build explanatory models that allow one to determine the sintering conditions for a given equipment and fuel, but these models usually have very limited applicability.

This review is organised as follows. Section 2 briefly considers the features of melting of the mineral and organic matter for different fuels during their thermochemical conversion (without detailing the chemical aspects). Section 3 discusses experimental evidence on the agglomeration phenomena in fluidised bed reactors (to the extent necessary for the aims of the review) and fixed bed reactors (in more detail, with an assessment of the critical value of the plastic content). Section 4 gives an overview of the mathematical models that are used to describe the agglomeration processes, as well as models that can be used, and models that should be used for this (according to the author’s opinion).

2. Features of Phase Transitions of the Mineral and Organic Parts of Fuels

2.1. Ash Melting

The mineral part of plant biomass, as a rule, is characterised by a relatively low melting point (including due to the high content of alkali metals and the formation of eutectic mixtures [18]). During combustion, the ash turns into liquid slag, which can cover the particle (mineral salts, as a rule, are concentrated in the near-surface layer along the burnout, which was experimentally observed in many papers: [19,20,21]). In some cases, even a small concentration of melting centres on the particle surface is sufficient for sintering [22]. In addition, alkali metals are highly volatile elements, so, at relatively low temperatures (often under conditions of air gasification, but sometimes even during pyrolysis [23]), they diffuse in the gas phase [24], covering particle surfaces. Then, the interaction of two particles can lead to the formation of liquid slag bridges and adhesion (Figure 1).

Even with the conversion of low-ash fuels, ash can accumulate in the reactor. Due to sintering and the formation of large aggregates, the mechanical removal of ash may become difficult. Even solid ash, due to its small size, can form a bed with high hydraulic resistance, decreasing the flow rate of gaseous reagents.

Experimental work to determine the characteristic temperature points of softening and melting of different species of biomass ash was carried out in [25,26,27]. The authors of [28,29] investigate the melting of waste ash. The influence of partial demineralisation was studied in [30], and the influence of the atmosphere was studied in [31,32]. The characteristic sintering times of ash in a mixture with sand, when heated by the combustion products of an air–propane mixture, were measured in [33]. In [34], the effect of ash composition and ambient temperature on the proportion of sintered ash particles was studied. The behaviour of mixed coal ash and agricultural waste was studied in [35,36]. The depletion of ash in alkali and alkaline earth metals during the gasification of biomass in a fluidised bed was observed in [37]. One of the main tools for assessing the mineral part composition and phase state is thermodynamic modelling (often based on semi-empirical approaches) [38,39].

2.2. Organic Matter Melting and Decomposition

Mixtures of lignocellulosic fuels with plastics often turn out to be model compounds of refuse-derived fuel. Fuel decomposition is usually studied using analytical methods: thermogravimetry, elemental, and gas analysis (in some cases, Raman spectroscopy and X-ray diffraction). The complexity of the fuel composition and a large number of possible reactive combinations lead to the fact that the elementary chemical reactions that occur during decomposition and combustion practically do not allow individual study. In this regard, chemical reactions of biomass and plastics are considered in a simplified way, usually in the form of brutto-reactions. Their co-decomposition is often characterised by non-additivity of the product yield and macro-kinetics [40,41,42,43,44,45,46]. During co-pyrolysis, the ranges of thermal decomposition can overlap in the area of decomposition of plastics and lignin [47]. Polyolefins may act as hydrogen donors [48,49,50], whereas the combustion of wood and char allows for intensifying the cracking of heavy pyrolysis products [51,52]. Interaction can occur through the gaseous phase: volatile products of polyolefins pyrolysis interact with the char carbon surface and change its structure and reactivity [53,54]. In some works, the catalytic effect of the mineral portion is noted [55,56]. In the co-pyrolysis of chlorine-containing plastic, the interaction of cellulose with HCl can occur [57].

The thermochemical interaction between waste components is often associated with mechanical effects. The co-decomposition of biomass with plastics occurs through the formation of polymer melt films on the reacting surface, which prevents the access of the oxidiser [58,59]. Plastic also can act as a binder, sticking waste or biomass particles together [16,60]. Pyrolysis of polymers in the presence of porous sorbents results in clogging and coking of pores [61]. A melting polymer can fill the macropores in the wood [62], and with a large proportion of plastic, particle encapsulation occurs [63].

The sintering scheme of the packing containing melting particles is shown in Figure 2: the melt acts as a filler and a binder at the same time, covering the reacting surface and blocking the access of the oxidiser.

When heated, waste particles (usually pellets) swell up to 50–80% of their initial size under the pressure of the released gases [64,65]. The combustion of plastic particles on the plate occurs in the diffusion mode due to the melting and evaporation of combustible components [66,67]. Suspended polyethylene particles undergo covering with a layer of melt that flows down from the holder until complete decomposition is complete [68]. Naturally, such liquid particles may have high enough adhesion to stick to each other or the carbon surface, forming strong aggregates.

It can be assumed that the stronger agglomerates are formed by the alternation of reactor temperature. For example, the slag film formed at high temperatures allows the formation of liquid bridges between adjacent particles, and then solidifies when the temperature drops below the softening conditions; the melting plastic mass formed during the heating stage then undergoes charring in the high-temperature region. In fluidised bed reactors, gravitational separation can enhance temperature effects. For example, if the average temperature decreases towards the lower part of the bed, then massive agglomerates of particles with a liquid film get stuck together, descend, and solidify.

3. Agglomeration in Thermochemical Conversion Reactors

3.1. Fluidised Beds

The effect of agglomeration due to low-melting ash becomes especially important in fluidised bed reactors, where the sintering of particles leads to the formation of large pieces of material that cannot be supported by the gas flow. Sintering indicators are fluctuations (or other statistical characteristics) of temperature and pressure drop across the layer [69,70,71], but other metrics may be used, for example, the torsion resistance of a submerged body [72]. Depending on the combustion conditions, the composition of the ash (and, consequently, its thermal behaviour) changes [73,74]. The following mechanism is formulated in [75]: potassium is deposited on quartz sand particles, where it forms fusible silicates. Experiments and thermodynamic calculations show that potassium salts can interact with silicon oxide at temperatures below the decomposition temperature of potassium carbonate. The authors of [76] observed ash agglomerates whose formation led to a shutdown in their experiments on the gasification of wood and grass pellets at a temperature of 800 °C and a stoichiometric ratio above 0.1. Approximately the same temperatures at the beginning of defluidisation (770–800 °C) were observed in [77] during agricultural waste conversion with sand and olivine as the bed material. Agglomeration occurs not only during autothermal gasification but also during allothermal gasification with intense external heating (for example, during solar-driven gasification [78]).

The same problems can occur with coal conversion, although higher temperatures are required in comparison with biomass and waste [79,80,81]. In [82], particle agglomeration was observed during the co-combustion of charcoal and liquid biofuels. Similar problems also appear during the conversion of heavy oil residues [83].

In the gasification of plastics, defluidisation occurs due to the coalescence of molten particles [84]. For the decomposition of plastic gasification produced tars, special sections for cracking are used: oxidative [85], catalytic [86,87,88], and thermal [89,90].

The critical conditions for defluidisation of the bed depend on the fuel properties and mineral matter transformations. The authors of [91] proposed to use the critical thickness of the liquid film on the particle surface. Attempts to relate the thickness of the slag film to the ash composition during coal gasification were made in [92]. The authors of [24] suggested that this thickness may be of the order of 1–10 µm. In [93,94], instead of the film thickness, the critical concentration of alkali metals in the bed was estimated, and a dynamic model for the alkali metals accumulation in the combustion chamber was proposed.

3.2. Fixed Beds

The differences between fluidized bed agglomeration and fixed bed agglomeration are primarily related to the characteristic time of contact between particles. In the fluidized bed, particles move with significant inertia, and in the fixed bed, the particles weakly migrate, whereas the packing weight contributes to better contact, so agglomeration can occur under milder conditions. In addition, with fixed bed conversion, temperature stratification is sharper.

3.2.1. Basic Schemes of Fixed Bed Conversion and Control Possibilities

One of the main problems in the fixed bed conversion of waste is the non-uniform airflow distribution over the cross-section of the furnace or gasifier. The distribution of the particles in the packing is random, so the local gas permeability in the packing is also a random variable. Non-uniformity of filtration flow in random packings has been the subject of chemical engineering for a long time [95]. Due to the conversion of the particles, the packing structure changes: burnout affects the size and mechanical strength of the particles, and they undergo splitting, abrasion, aggregating, etc. Small particle fractions can clog the porous space and reduce the local permeability of the packing [96,97]. As a result, non-uniformities may grow up to the size of a reactor. Thus, for example, areas with reduced porosity connecting the upper and lower parts of the bed are formed (burnouts and channels). It was shown in [98] that the channelling during biomass gasification leads to an increase in the tar yield. Burnouts and even cavities within the packing can form due to the stable configurations of the particles, especially during the gasification of low-density fuels (e.g., straw) [99,100]. The authors of [101] observed the “fire jump” phenomenon, that is, the predominant propagation of the combustion front through regions with reduced porosity (they attribute this process to differences in the characteristic times for the devolatilisation and the ignition of volatiles in pores).

Diagrams of the most widely used combustion and gasification processes are shown in Figure 3. The updraft (counter-current) gasification process is characterised by a high temperature in the lower region of the reactor (combustion core). If the ash melting proceeds there, then liquid slag removal is realised. In the downdraft (co-current) gasification process, the ash melting can also occur in the combustion core, which is now located in the upper region of the bed. Below the temperature decreases, therefore, the formation of strong ash agglomerates becomes possible. High temperatures can be achieved even for low-calorific fuels, for example, in filtration combustion [102], due to heat recovery. Under special conditions, even the existence of several combustion fronts (volatile combustion and char combustion [103]) is possible. Downdraft gasifiers typically have a waist in the region of air supply: agglomeration in these throat regions can be critical to the operation of the gasifier.

During grate combustion, the fuel decomposes with the influence of the freeboard. Heat flows are organized in such a way that fresh fuel is heated from above, whereas air enters, as in updraft gasification, through the bottom. Therefore, the temperature zones can alternate as the fuel moves along the grate.

In some cases, controlling the composition of the mineral matter can be a way to control ash agglomeration. For example, it was experimentally found in [104] that with a fraction of wood in a mixture with straw above 50%, it is possible to avoid ash softening and thus prevent agglomeration. In [105], mineral additives were used to increase the ash melting point during peat gasification. Other methods are also possible, such as washing raw biomass in water or acid solutions to remove the minerals [106]. Mineral additives make it possible to change the reaction pathways of decomposition of the organic mass, preventing polymerisation and agglomeration [107].

3.2.2. Experimental Results

Fixed-bed agglomeration due to ash sintering can occur, for example, during oxygen gasification of wet fuel: in [108] bed agglomeration was observed at a biomass moisture content of 45% or more. Under agglomeration conditions, CO₂ and O₂ become the main components of the producer gas (as well as under channelling conditions [96]). The authors of [109] reported significant fluctuations in gas composition, which affected the flare stability. To decrease these fluctuations, the mechanical impact was used. In [110,111], the grate rotation speed was optimised to reduce the yield of sintered ash.

The scheme of channelling during agglomeration is shown in Figure 4. If a clinker appears in the bed, it becomes an obstacle to the filtering gas. The gaseous reagent flows around the agglomerate along the path of least resistance, and the particles on the path undergo deeper conversion, increasing permeability.

Published data show that plastic conversion leads to agglomeration. Filtration combustion of charcoal with polyethylene mixtures was studied experimentally in [112]. It was shown that at a plastic content of more than 20%, the combustion front becomes unstable due to the flow of the molten polymer and its interaction with the carbon surface. At the polyethylene fraction of 40%, combustion becomes impossible. Tarry products of plastic decomposition can be carried over the bed and deposited in colder regions. Similar effects were observed during the combustion of charcoal with polyurethane [113], however, the critical fraction of plastic, in this case, is higher (up to 40%), possibly due to the higher viscosity of the melt: quite a complete conversion of the mixture is possible even with an unstable combustion front. Filtration combustion with a non-uniform distribution of plastic (in the form of a “charge”) was studied theoretically and experimentally in [114,115], where the efficiency of carbon combustion heat used to decompose plastic was evaluated: in this case, however, it is necessary to have a sufficient gap in the packing for providing filtration. The decomposition of polyethylene during the filtration combustion of gaseous fuel was studied in [116], and in [117] with wood additives.

The paper [118] describes experiments on a downdraft gasifier (capacity of 100 kg/h) fed by pellets made of waste and straw. It was shown that with a waste fraction of more than 60%, the stationary gasification process becomes impossible due to intensive agglomeration. With an average plastic content in waste of 13%, a critical fraction of plastics in pellets can be estimated at 8%. However, it should be clarified that the waste contained a significant proportion of non-combustible matter (15–25%).

An experimental study of the sawdust and polyethylene co-gasification in a laboratory fixed-bed reactor (with heating up to 700 °C) was carried out in [119]. The authors obtained loose agglomerates with intense burnouts near the reactor walls. Examination of the reactor shows that most of the air passed through the near-wall region, resulting in partial entrainment of particles. With a high fraction of polyethylene, the self-sustaining process of combustion and gasification of the mixture becomes impossible, even with an external heat supply, whereas tar deposits in the gas cleaning system.

The paper [120] investigated the gasification of wood with polyethylene. The authors provide data for mixtures with a plastic mass fraction of less than 17%. In the study of the co-gasification of wood with sewage sludge [121], agglomeration was observed with a sludge fraction of more than 33%. The authors of [122] studied the co-gasification of wood with different types of waste (rubber, plastic, sewage sludge) with a waste fraction of 20%, polystyrene fraction of up to 30% was used in [123]. Charring polymers, on the one hand, may increase bed stability, but on the other hand, agglomeration worsens if the molten polymer has time to fill the porous space. Plastics are characterised by different melting temperature ranges and melt viscosity (including different grades of the same polymer). The agglomeration conditions are probably related to the ratio between the characteristic times of melt flow and its thermal decomposition. The emphasis on such details is made in works on the fire safety of polymeric materials [124,125,126].

Agglomeration of mixtures of garden waste with polyethylene (up to 25%) in a downdraft gasifier was observed in [127]. With an increase in the plastic content, the heating value of the mixture increases, as well as the heating value of the producer gas and the maximum temperature. Due to this, among other things, the tar content in the producer gas decreases, but the ash melting leads to clinker formation. Increasing the polyethylene content leads to a decrease in ash content, so the agglomerates become smaller. The authors of [128] also reported on the clinker formation during the gasification of plastic-containing waste (paper industry waste pellets). An increase in the plastic fraction also leads to an increase in the temperature in the combustion core (and, at the same time, to a decrease in temperature at the reduction zone). The size of the clinkers reached 10 cm, and their analysis showed that they contain 15–30% carbon (mainly these are encapsulates that are observed, for example, in the fixed-bed conversion of other fuels [129]). In similar conditions, the authors of [130] tried to stabilise the waste pellets’ gasification process (plastic content up to 30%) by adding wood chips, and they obtained clinkers up to 15 cm in size. The authors of [131], carried out fixed-bed combustion experiments using plastic-containing wastes (plastic fraction 30–35%), and they observed different ash behaviour depending on the airflow, which largely determines the thermal regime of the conversion, and hence, the temperature of the combustion front. The updraft gasification of waste was studied in [132] (the proportion of plastic is not indicated), which pointed out the problem of burnouts forming the adhesion of particles to the walls.

In some cases, agglomeration does not occur even with a high fraction of plastic. For example, the authors of [133] did not report any problems with bed agglomeration (even with a plastic fraction of 80%) during the fixed-bed co-gasification of sawdust and polypropylene (instead of air, a gas mixture with an oxygen concentration of 10% was used). The authors of [134] used a horizontal reactor for steam gasification of wood chips and polyethylene mixtures, which allowed for avoiding bed blockage. The authors of [135] did not observe agglomeration during steam gasification of biomass and plastic (up to 60%) mixtures, as well as the authors of [136] when studying the allothermal CO₂-gasification process of an equal coal-polyethylene mixture. Oxygen gasification of waste without sintering was reported in [137]. It is possible, however, that this is a consequence of the “survival bias”: scientific articles mostly contain the results of successful experiments, reporting on achieved stationary and efficient conversion regimes; then many experiments with agglomeration simply do not reach publication. In this regard, the boundaries of the agglomeration conditions are estimated from very limited experimental material (as was done, for example, in [130]). Table 1 gives a comparison of the experimental conditions under which agglomeration was observed. Depending on the fuel composition and the reaction zone dimensions, different agglomeration scenarios are observed (accumulation of ash or fines, ash melting at high temperatures, or plastics melting at low temperatures).

An example of an inefficient conversion of plastic-containing wastes is the experiments reported in [138] (producer gas contained 5–7% oxygen). The combustion of sea plastic waste mixed with wood pellets was experimentally studied in [139], where the authors found the instability of the combustion front associated with the mechanical instability of the packing, which is observed at a sufficiently large proportion of plastic (combustion becomes impossible at a plastic fraction of 80%). The authors of [140] studied fixed-bed combustion of polyurethane foam, and stationary conversion modes were observed (the authors of [141] used catalysts).

Table 1. Comparison of experiments with fixed-bed agglomeration.

Ref.	Conversion Process	Reactor Type and Dimensions	Gaseous Reagent	Fuel Composition	Phenomena Observed
[104]	Combustion	Grate combustor (0.5 MWth)	Air	Wood. agricultural waste	Ash sintering
[105]	Gasification	Shaft reactor (length 400 mm, internal diameter 66 mm)	Air, steam	Peat	Ash-sand sintering
[108]	Gasification	Updraft gasifier (bed height 1.5 m, internal diameter 0.28 m)	Air, oxygen, steam	Wood	Bridging at high fuel moisture
[98]	Gasification	Downdraft gasifier (bed height 0.8 m, internal diameter 0.92 m)	Air	Wood	Channelling
[109]	Gasification	Downdraft gasifier (bed height 0.4 m, internal diameter 0.35 m)	Air	Wood	Bridging
[110]	Gasification	Downdraft gasifier with rotating grate (bed height 0.26 m, internal diameter 0.22 m)	Air	Garden waste	Accumulated ash sintering
[111]	Gasification	Downdraft gasifier with rotating grate (bed height 0.26 m, internal diameter 0.22 m)	Air	Biomass waste, coal	Accumulated ash sintering
[112]	Gasification	Shaft reactor (bed height 0.3 m, internal diameter 45 mm)	Air	Charcoal, polyethylene	Oxidation front instability due to melting polymer flow
[113]	Gasification	Shaft reactor (bed height 0.3 m, internal diameter 45 mm)	Air	Charcoal, polyurethane	Oxidation front instability due to melting polymer flow
[118]	Gasification	Downdraft gasifier (reactor height 2.3 m, internal diameter 0.6 m)	Air	Municipal waste, straw	Agglomeration at MSW fraction of 60%
[119]	Gasification	Updraft gasifier (bed height 0.35 m, internal diameter 0.15 m)	Air	Sawdust, polyethylene	Agglomeration, deposition
[121]	Gasification	Downdraft gasifier (bed height 0.5 m, internal diameter 0.16–0.3 m)	Air	Wood, sewage sludge	Ash agglomeration
[127]	Gasification	Downdraft gasifier with rotating grate (bed height 0.26 m, internal diameter 0.22 m)	Air	Garden waste, polyethylene	Ash sintering
[128]	Gasification	Downdraft gasifier (bed height 0.4 m, internal diameter 0.35 m)	Air	Fiber-plastic waste	Ash agglomeration
[130]	Gasification	Downdraft gasifier GEK	Air	Paper industry waste	Agglomeration caused by plastic melting in the pyrolysis zone
[131]	Gasification	Downdraft gasifier (bed height 0.15 m, internal diameter 0.1 m)	Air	Refuse derived fuel	Ash agglomeration
[132]	Gasification	Updraft gasifier (bed height 1.1 m, internal diameter 0.15 m)	Oxygen	Waste	Difficult operation at bed height above 0.7 m
[139]	Combustion	Updraft gasifier (bed height 1.9 m, internal diameter 0.15 m)	Air	Wood, marine plastics	Flame extinction under high plastic content

Table 1. Comparison of experiments with fixed-bed agglomeration.

Ref.	Conversion Process	Reactor Type and Dimensions	Gaseous Reagent	Fuel Composition	Phenomena Observed
[104]	Combustion	Grate combustor (0.5 MWth)	Air	Wood. agricultural waste	Ash sintering
[105]	Gasification	Shaft reactor (length 400 mm, internal diameter 66 mm)	Air, steam	Peat	Ash-sand sintering
[108]	Gasification	Updraft gasifier (bed height 1.5 m, internal diameter 0.28 m)	Air, oxygen, steam	Wood	Bridging at high fuel moisture
[98]	Gasification	Downdraft gasifier (bed height 0.8 m, internal diameter 0.92 m)	Air	Wood	Channelling
[109]	Gasification	Downdraft gasifier (bed height 0.4 m, internal diameter 0.35 m)	Air	Wood	Bridging
[110]	Gasification	Downdraft gasifier with rotating grate (bed height 0.26 m, internal diameter 0.22 m)	Air	Garden waste	Accumulated ash sintering
[111]	Gasification	Downdraft gasifier with rotating grate (bed height 0.26 m, internal diameter 0.22 m)	Air	Biomass waste, coal	Accumulated ash sintering
[112]	Gasification	Shaft reactor (bed height 0.3 m, internal diameter 45 mm)	Air	Charcoal, polyethylene	Oxidation front instability due to melting polymer flow
[113]	Gasification	Shaft reactor (bed height 0.3 m, internal diameter 45 mm)	Air	Charcoal, polyurethane	Oxidation front instability due to melting polymer flow
[118]	Gasification	Downdraft gasifier (reactor height 2.3 m, internal diameter 0.6 m)	Air	Municipal waste, straw	Agglomeration at MSW fraction of 60%
[119]	Gasification	Updraft gasifier (bed height 0.35 m, internal diameter 0.15 m)	Air	Sawdust, polyethylene	Agglomeration, deposition
[121]	Gasification	Downdraft gasifier (bed height 0.5 m, internal diameter 0.16–0.3 m)	Air	Wood, sewage sludge	Ash agglomeration
[127]	Gasification	Downdraft gasifier with rotating grate (bed height 0.26 m, internal diameter 0.22 m)	Air	Garden waste, polyethylene	Ash sintering
[128]	Gasification	Downdraft gasifier (bed height 0.4 m, internal diameter 0.35 m)	Air	Fiber-plastic waste	Ash agglomeration
[130]	Gasification	Downdraft gasifier GEK	Air	Paper industry waste	Agglomeration caused by plastic melting in the pyrolysis zone
[131]	Gasification	Downdraft gasifier (bed height 0.15 m, internal diameter 0.1 m)	Air	Refuse derived fuel	Ash agglomeration
[132]	Gasification	Updraft gasifier (bed height 1.1 m, internal diameter 0.15 m)	Oxygen	Waste	Difficult operation at bed height above 0.7 m
[139]	Combustion	Updraft gasifier (bed height 1.9 m, internal diameter 0.15 m)	Air	Wood, marine plastics	Flame extinction under high plastic content

3.2.3. An Attempt to Classify the Plastic-Containing Fuel Conversion Conditions with Respect to Agglomeration

Estimating the critical fraction of plastic in a mixture with other fuels, one can obtain the picture shown in Figure 5. Circles mark the limiting values of the fraction of different plastics (in the mixture with char, biomass, or other higher-grade fuel), at which stable conversion was observed. The technical properties of fuel mixtures chosen as coordinates are ash content and heating value. It should be mentioned that this picture is the result of a significant simplification: different plastics, different types of biomass, reactor parameters, and conversion conditions are presented in the same graph. Due to this, close points in the chosen coordinates can exhibit significantly different behaviour. Usually, the composition mixture change step in experiments is too large to allocate critical behaviour of the process. However, some patterns can still be seen. With an increase in ash content, it is possible to use mixtures with a high content of plastic: it can be assumed that due to the heating of the inert matter, the conversion temperature decreases, and the ash is less likely to melt. For low-ash mixtures, an increase in the proportion of plastic requires an increase in the heating value and maximum temperature, apparently to ensure complete decomposition of the plastic. However, the authors of [112] showed that the decomposition degree of polyethylene correlates with the charcoal fraction, whose heating value is lower compared to plastic. It can be assumed that the second component should have a sufficiently high heating value to ensure combustion stability even at the low conversion of plastic. Interestingly, mixtures with low ash content and low heating value are most prone to agglomeration. A detailed analysis shows that these points correspond to experiments with ash accumulation [118,128]. The average value of the critical plastic fraction is about 20–25%.

4. Mathematical Modelling

4.1. Numerical Models of Combustion and Gasification Processes

In the field of numerical simulation of combustion and gasification processes, in contrast to experimental studies, high plastic fraction mixtures conversion is often considered (even if these regimes are unattainable in practice). Few mathematical models include a description of agglomeration processes; therefore, most of the models allow calculating the characteristics of the conversion processes for mixtures with arbitrary composition. In some cases, using empirical constraints, it is possible to limit the range of stable regimes. However, more valuable are those works in which an attempt is made to describe theoretically the agglomeration process and to relate its characteristics with the fuel composition and conversion conditions.

The combustion and gasification differ, basically, in the target composition of products: if during gasification the aim is to obtain combustible components (CO, H₂), then during combustion, on the contrary, the aim is to reduce the yield of combustible components. When modelling the processes of fixed-bed combustion, the freeboard region is of great importance, in which the gaseous products are oxidised (usually under conditions of turbulent flow). The bed surface and the freeboard space are usually connected in a simplified way, which allows, for example, combining models with different spatial detalization (2D and 3D models of the freeboard region with 1D models of the fixed-bed region [142,143]). During combustion, the concentration of harmful substances in the flue gases is of interest, so kinetic models often include detailed nitrogen reactions [144].

When evaluating the composition of combustion and gasification products, equilibrium thermodynamic models are most widely used, which allow taking into account the elemental composition and heating value of fuel components [145,146,147,148,149]. Statistical models make it possible to optimise conversion conditions for a given reactor configuration [150,151,152,153]. These models are used in the optimization of power plants [154]. The use of kinetic models is still limited, first, by insufficient understanding of the reaction mechanisms and phase transitions that accompany the thermal decomposition and oxidation of components (biomass, plastics, other organic wastes, and the mineral part), and, second, the mechanisms of interaction between the components. Even assessing the fuel composition and its thermophysical properties is a difficult task [155,156]. Finally, the most uncertain part of the models is the description of the mechanical interaction between components [157].

The kinetic mechanisms of pyrolysis of biomass and artificial polymers (as a rule, based on significant simplifications and a rough estimate of kinetic coefficients) are proposed in [158,159,160,161]. These mechanisms do not take into account the direct thermochemical interaction of the mixture components, although they allow reactions between gaseous products. Simpler kinetic models were proposed in [162,163,164,165]. The molecular dynamics of the oxidation processes of polymers mixtures with cellulose and coals were investigated in [166,167]. Numerical tools based on computational fluid dynamics (CFD) for reacting waste and plastic particles (for laboratory drop tube reactor conditions) were proposed in [168,169,170].

To assess the reactivity, the heterogeneous chemical reaction’s kinetic coefficients are often used. However, it is necessary to highlight their nature. The kinetic coefficients for brutto-reactions inevitably contain a significant amount of uncertainty associated with the reacting surface features and the lumping of a multistage and multi-route chemical transformation into one averaged stage. Extrapolation of the kinetic dependences obtained in the laboratory to the furnace conditions is not always justified. In this regard, the heterogeneous reaction’s kinetic coefficients are rather empirical constants (and sometimes optimized model parameters) than the physicochemical properties of the reacting materials. As a rule, kinetic analysis methods are used for experimental data on fuel conversion (for example, thermogravimetry); in rare cases, estimates or reference data are available (reactivity of fuels and its correlations with other properties of fuels can be found in original studies [43,171,172]).

The chemical and mechanical interaction of components was not taken into account in [173,174] when modelling the co-conversion of wood and coal with waste (plastics, sewage sludge), but the estimated gas composition was pretty similar to experimental data. CFD model of coal and PET co-gasification in a fluidised bed was proposed in [175], also without chemical and mechanical interaction of the components. CFD-modelling of fluidised bed gasifiers was carried out in [176] for mixtures of biomass and polymers, and in [177] for model municipal waste.

It is important to note that most of the published modelling work on the fixed-bed conversion of biomass and waste uses the assumption of constant fuel composition (at least its average composition). When processing waste and biomass, it is difficult to expect the stability of fuel characteristics. In the general case, it is necessary to analyse the influence of fuel properties variations on its conversion process. The authors of [178] evaluated the impact of the biofuel technical properties on the characteristics of fixed-bed combustion. The effect of a sharp change in fuel moisture content on the characteristics of its gasification was experimentally investigated in [179]; the effect of a sharp change in inert matter content on filtration combustion front characteristics was studied in [180].

4.2. Filtration in Reactive Media

The theoretical description of agglomeration processes requires mathematical models of the mechanics of dispersed deformable media. Flow models in multi-fractional packings and random porous media were considered in [181,182,183,184], and with turbulent motion in [185]. An important issue is the choice of the representative porous configuration (the Monte-Carlo method is often used) [186,187,188,189]. The instability of the combustion front in porous media (both mono-fractional and poly-fractional) was theoretically and experimentally studied in [190,191]. The influence of natural convection and changes in the thermophysical properties on thermal filtration regimes was considered in [192,193]. Percolation models of burnout development were proposed by [194].

There are many papers devoted to the study of filtration flow and heat transfer in heterogeneous media with a changing structure. Models of porosity reduction in granular beds were proposed in [195] for ball packing under mechanical pressure, in [196] for graph structures, and in [197] for hydrate-saturated rocks. The dynamics of porous media dissolving in a flowing liquid were studied theoretically and experimentally in [198,199,200]. The models of melting powder particles under intense radiation (laser) were proposed in [201,202]; filtration models in media undergoing phase transitions were proposed in [203,204,205]. A model of heating and shrinkage of polymer granule packing was proposed in [206]. Experiments on the melting of plastic samples during heating and combustion, and study of the geometry effects on their heating and combustion, were carried out in [124,126]. Conjugate modelling of the polymer plates combustion was carried out in [207,208]. Discrete elements method (DEM) models for melting particles sintering in a metallurgical furnace were considered in [209,210] and for sintering of ice particles in [205,211,212]. The formation of ash deposits on the pipes was considered in [213,214,215], and channel clogging problems were studied numerically in [216,217]. Simplified approaches have been proposed to take into account changes in the porous structure during the reaction, for example, the random pore model [218,219]. Changes in the flow characteristics of a polymerising mixture in a channel were studied in [220]. Similar models were used to estimate the thermal stability limits of reactors with an exponential dependence of viscosity on the temperature in [221,222].

Loose media mechanics models were used to describe solid fuel conversion reactors in [223,224] for mixing in a drum and in [225,226] for particle mixing on a moving grate (using diffusion approximation). DEM models for moving beds were proposed in [227] (with tabulation of particle states), [228] (taking into account aggregation), and [224] (for solid particles). Temperature gradients during combustion can be high enough to consider the particles to be inhomogeneous [229,230]. In addition, it is crucial to describe the shrinkage and fragmentation of particles [231,232]. The simplest way to consider bed shrinkage is by fixing the porosity and calculating the bed height based on the current particle density distribution [233]. In some cases, however, bed compaction has to be modelled using logical conditions (for example, by reaching a critical value of local porosity) [234,235,236] and taking into account the mechanical strength of the material [237]. Models of fixed-bed combustion, taking into account changes in both particles’ density and packing porosity, were proposed in [238]. Material mixing can be simulated by introducing artificial particle diffusion [239], or by direct permutation of bed elements [240].

The next step is a simulation of bed blocking and channelling. The clogging of the air nozzle with fines was modelled in [241]. The authors of [242,243] considered the channel development from a non-uniform porosity distribution along the bed height; pyrolysis and burnout of particles in the higher porosity area lead to deeper burnout and a decrease in the bed height. A one-dimensional model of a fixed-bed gasifier with particle fragmentation and agglomeration (at temperatures above the ash melting point) was proposed in [244].

A two-dimensional non-stationary model of a porous medium was developed in the papers [245,246] to study the growth and decomposition of agglomerates. In the model, local permeability depends on the state of particles: melting of particles lowers permeability, and their thermal decomposition restores permeability. The calculation results show that the bed heating conditions significantly affect the agglomerate shape. When heated through the wall, the agglomerate grows up to the size of a reactor, and then gradually decomposes (in this case, the gas flow in the near-wall region plays the role of thermal insulation). When heated with hot gas, the agglomerate is formed near the inlet boundary and quickly blocks the cross-section, preventing further heating.

The processes of heating and shrinkage of packings during melting and thermal decomposition of plastic mixed with ceramic material were studied experimentally in [247,248].

Thus, there is a large body of experimental and theoretical work related to the transport processes in media with a changing structure. However, numerical simulations require numerous empirical parameters that determine the mechanical strength, deformation, and interphase interactions. The description of agglomeration in fixed-bed conversion requires an appropriate choice of approximations and selection of coefficients. At the same time, the resulting model may not have predictive power when interpolating parameters and conditions. Furthermore, as mentioned above, the particle packings have random configurations, so the continuous models are approximations that predict the probability of experimental agglomeration observation rather than the certain conditions of its occurrence. It can be assumed that for large reactors with a significant bed height (i.e., when the characteristic non-uniformities are much smaller than the characteristic system size), the results will be more predictable due to averaging. However, for small beds, which are typical for gasifiers in small power plants, agglomeration conditions may be more blurry.

4.3. Interfacial Interactions

Since the main mechanism for the agglomeration is the surface interaction (adhesion) of particles, the prediction of the agglomeration conditions requires data on the characteristic scales of these interactions (energy scale, geometric scale, etc.). The situation is complicated by the fact that the surface itself often is reactive, that is, it undergoes the transformation processes and therefore changes physical and chemical properties during this transformation.

Models of ash melting in a burning carbonaceous particle were proposed in [249,250,251]. Molecular dynamics modelling was used in [252] to study the melting dynamics. Lattice models of coke–ash structure evolution were proposed in [253,254]. The evaporation of alkali metals was introduced in the fuel particle combustion model in [255]. Models of the slag deposits formation on heat exchange surfaces considering the solid and molten ash particles interaction, make it possible to describe the decrease in heat transfer efficiency in boilers [256,257,258,259,260,261].

A CFD model of particles sticking in a fluidised bed with a liquid component was proposed in [262]. The paper [263] gives an integrodifferential equation for the dynamics of a different-size particle population under fluidised bed conversion conditions, although the critical values for particle sizes and relative colliding particle velocities are determined from empirical data [264]. The probability of particles sticking together is determined by the balance of adhesion and inertia forces, as well as their deformation and the impact of surrounding particles; with increasing temperature, this balance shifts towards sticking [265,266,267,268]. For large agglomerates, the interaction can be described in simpler approximations [269]. The ability of particles to deform is usually associated with the effective viscosity of the material [270]. On the one hand, due to the high viscosity of the film, the stickiness of particles decreases, and surface deformation becomes possible at high mechanical stresses; on the other hand, at low viscosity, the bridges formed between the particles are less stable and easily collapse. The key factor is the temperature, which determines the phase state of the surface. Agglomeration as a process of chain-like structure formation was considered in [271], where it was shown that the highest probability of agglomeration is observed near the walls, where the particle velocity decreases due to friction effects. Random walk models [272] can be used to describe the probability of collisions. Based on these approaches, for example, models of random mixing for two-phase mixtures have been formulated [273].

Models of particle sintering during the processing of minerals are proposed in [274,275]. The interaction of a carbon surface with liquid slag is usually considered in the context of high-temperature processes, such as coal gasification, when fuel particles can be captured by a slag film [276]. In problems related to agglomeration, the interaction of molten slag droplets with the carbon surface and with each other is of interest. As mentioned above, the mineral matter of different components can mix and interact. A variety of influencing factors leads to the fact that it becomes almost impossible to isolate and study one of them.

It should be noted that the movement of the liquid phase on the surface of the particles occurs under the conditions of gravity and gas filtration, therefore, it can be accompanied by wave disturbances, rivulets, and droplets formation. Polymer melt demonstrates non-Newtonian behaviour. Some of these phenomena were considered in a recent review [277].

Using the analogy between fluidisation and phase transition [278], agglomerate may be considered a new phase. A granular bed at a temperature above the ash melting can be considered a supercooled phase that begins to crystallise in the presence of nuclei (aggregates) that overcome the energy barrier (shear stresses breaking aggregates).

In general, the current level of interfacial interaction models is insufficient to reliably assess the agglomeration onset in real reactors for waste conversion. At the same time, many promising approaches have been proposed (including those in areas not directly related to thermal processing) that can be applied to solve this problem. The author hopes that this review will inspire researchers to new works in this area.

Figure 6 shows levels of description for the agglomeration phenomenon. In addition to the particle level and the packing level, an additional level is required, considering inter-particle interaction in the bed. As mentioned above, the mutual arrangement of particles of different types can play a significant role in the development of agglomeration. The fully presented scheme, however, is not required for numerical simulation (especially in engineering applications). The study at one level provides the necessary closing relations for the next so that the higher-level models could use information about the reaction and surface properties of particles through the appropriate coefficients, criteria, or algebraic relations.

5. Conclusions

The paper considers the main physical mechanisms of agglomeration in the fixed-bed conversion of biomass and waste. The sintering of particles during the melting of the mineral part and organic mass (which is especially important for plastic-containing wastes) is considered. The agglomeration phenomenon is related to the development of non-uniformities in reacting porous media. Therefore, the theoretical description of fixed-bed agglomeration should be based on the theory of heat and mass transfer, chemical kinetics, and the mechanics of multiphase media, including the available tools for models of interfacial and surface interaction in dispersed media.

An attempt was made to estimate the critical fraction of plastic in the fixed-bed combustion of plastic-containing waste based on the analysis of published experimental data (mainly obtained in laboratory reactors). Agglomeration due to the ash melting is difficult to separate from organic matter melting, although, it is possible to distinguish (rather limitedly) characteristic parameter ranges in the coordinates “heating value—ash content”.

The paper does not provide a detailed physicochemical analysis of the chemical reactions of different plastics, which, of course, should be taken into account in the detailed study of specific cases. Some details are noted, which may depend on the composition and grade of the plastic.

Mathematical models of reacting disperse media are reviewed that can be applied to the problem of agglomeration. It is pointed out that the relations between the physicochemical state of particles and their mechanical properties are necessary for this purpose. The development of inhomogeneities (burnouts, cavities, agglomerates) plays an essential role in agglomeration processes. These inhomogeneities can be associated with both hydrodynamic features (instability of the filtration flow in the reacting medium) and the stochastic nature of the packings.