Modeling of fluidized bed combustion processes

Modeling of fluidized bed combustion processes

11 Modeling of fluidized bed combustion processes D. P a l l a r è s and F . J o h n s s o n, Chalmers University of Technology, Sweden DOI: 10.1533...

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11

Modeling of fluidized bed combustion processes

D. P a l l a r è s and F . J o h n s s o n, Chalmers University of Technology, Sweden DOI: 10.1533/9780857098801.2.524 Abstract: This chapter provides an overview of the aims, principles, and limitations of the different types of modeling used for fluidized bed combustion (FBC) systems with a focus on macroscopic modeling, which is currently considered the most suitable modeling approach for FBC units of industrial scale. Sub-models for the different regions characterizing FBC units are described, with emphasis on the most critical in-furnace phenomena. Guidelines and examples are given of how different sub-models can be linked into a comprehensive process model for FBC units. Key words: modeling, fluidized bed, combustion, comprehensive.

11.1

Introduction

This chapter first provides an overview of the aims, principles, and limitations of the different types of modeling used for fluidized bed combustion (FBC) systems. The focus of the work is on macroscopic modeling, which is currently considered to be the most suitable type of modeling for simulating fluidized bed combustion under conditions that are relevant for industrial systems. In addition, mathematical descriptions of regions and phenomena relevant to FBC systems are presented and discussed. Finally, guidelines and examples of how these different sub-models can be linked into a comprehensive process model are given. This chapter is limited to modeling that is specific for fluidized bed processes, i.e., that focuses mainly on the gas–solids side (e.g., the flue gas side in an FBC unit). Thus, general models required for full process simulations, including the water/steam side, are not considered.

11.1.1 Objectives In general, the goal of modeling is to provide information that can be used for the reliable design, scale-up, and process optimization of FBC systems. Modeling should rely on known inputs and provide outputs that are essential for the performance of the process. Thus, for industrial processes, such modeling tools reduce the need for costly experiments and full-scale testing and can typically be used in the following areas: 524 © Woodhead Publishing Limited, 2013

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Design. Models can be used to assess the performance of a new process and to identify critical requirements for new FBC processes, such as chemical looping combustion and CFB oxy-fuel firing. Scale-up. A key aspect of fluidized bed development is to increase the size of boilers and, in the case of new fluidized bed processes, to advance and adapt from laboratory scale to pilot scale, and thereafter to commercial conditions. An increase in the size of an FBC process may entail significant changes in the solid and gas phases in terms of mixing rates, mass fluxes, and residence times. As models can help to quantify these changes, they represent important tools for the scale-up of FBC processes. Process optimization and retrofit. Modeling can be used to determine how an existing process can be modified to enhance performance, e.g., from a fuel change or from the introduction of new process elements, such as an ash classifier or a secondary cyclone. Model-based evaluation of such modifications can avoid potentially expensive tests and prevent failures.

At present, the burning of various renewable fuels (biomass waste, sludge, refuse-derived fuel (RDF), municipal solid waste (MSW), etc.) in a way that complies with the climate and renewable targets set in Europe and elsewhere (e.g., the EU target of 20% RES-based energy by Year 2020; EC, 2009), represents a significant challenge. In this sense, FBC technology has the potential advantage of fuel flexibility. However, in spite of the fact that FBC technology has been commercially available for several decades, the development to date of this technology has to a large extent relied on empirical experience. However, over the last decade, the major FBC technology providers have started to explore the use of more comprehensive modeling systems. Currently, modeling is combined with experimental data gathered over time. For a model to be used in the above-listed activities, it must be reliable and it should ideally be capable of modeling FBC units that lie outside the operational range within which the model was originally developed. The establishment of such a modeling framework is not without its problems. The present chapter provides an overview of the state-of-theart and the capabilities of the different modeling types that are available for FBC. A key step in modeling is the identification of the required input parameters, which should be limited to a set of independent and known variables. Typically, the input variables for comprehensive FBC modeling are, in addition to the geometry of the unit, the operating parameters, which include fluidization velocity, furnace pressure drop, fuel type, and bed material properties. It should be noted that since a parameter such as the circulating solids flux in a CFB loop is both dependent upon other input variables and is generally

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not known, it should not be considered as an external input to the modeling. Furthermore, the particle size distribution of the solids inventory should not be considered as an input to FBC modeling but rather as an output, since it is the result of attrition, cyclone escaping, and external removals and feedings of the solids (as discussed in Section 11.3.1). Regarding the outputs, i.e., the results from the modeling, comprehensive FBC modeling typically provides as the main outputs the distributions of the concentrations and fluxes of the gases and solids (differentiating between the different solids fractions and gas species), temperature, and heat flux to the heat transfer surfaces. Thus, modeling can provide quantitative estimations for specific questions, e.g., in determining the extent of heat transfer surfaces required for a certain fuel type and fuel feed rate.

11.1.2 Scope The modeling discussed in this chapter is limited to FB boilers of commercial scale, which typically1 have the following characteristics: ∑ ∑ ∑ ∑

aspect ratio of the furnace (H0/Deq) of the order of less than 10; aspect ratio of the settled bed, i.e., the bed formed if the solids are not fluidized, whereby Hb,settled/Deq is less than 1; solids belonging to Group B in the Geldart classification; and solids net flux that typically ranges from 0.5 to 20.0 kg/m 2s (CFB boilers).

Regarding these characteristics, it should be pointed out that the experimental fluidized bed studies reported in the literature focusing on CFB systems were in many cases carried out in units with a riser aspect ratio >20, i.e., with units that are narrow compared with a CFB furnace. These discrepancies can be explained by the fact that these works deal with chemical engineering applications (cracking, coating, polymerization), which typically employ Geldart Group A particles and operate at solids net fluxes that are typically >30 kg/m2s. These factors limit the use of experimental data from such units in FBC modeling. Similarly, regarding the narrow units devoted to FBC, an aspect ratio of the settled bed >1 is often used, which according to Zijerveld et al. (1998) implies that the dense region under non-circulating conditions adopts a slugging regime, which is not found in commercial-scale FBC boilers. Regarding the circulating conditions (CFB) in narrow risers with Geldart Group B particles, Schlichthaerle and Werther (1999) found it difficult to 1

This refers to the majority of the fluidized bed systems that have been delivered for the production of electricity and combined heat and electricity over the last decades and that are operated under atmospheric conditions. Thus, rare pressurized systems are not considered in this chapter.

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maintain a dense zone in the bottom region, while in the upper freeboard a solids flux profile with a parabolic shape was formed (Rhodes, 1990). These characteristics differ from those of large-scale CFB with a dense bottom bed and a solids flux profile in the freeboard that is shown to be rather flat across the core region, with pronounced wall layers (Zhang et al., 1995). Thus, given the significant differences in fluid dynamics between smaller laboratory-scale units and FBC boilers, the use of experimental data from narrow FB units for the validation of modeling of large-scale FBC should be limited to phenomena that are less-dependent on the lateral processes, such as the fundamentals of fluidized bed char reactivity and gas reaction kinetics. Under the conditions listed above, the process established in the furnace is associated with typical key regions and characteristics with respect to fluid dynamics and mixing, which have important implications for combustion and heat transfer. These regions are schematized in Fig. 11.1 and discussed briefly below. Provided with sufficient high solids inventory, a dense and strongly fluctuating region, termed the dense bed, is established in the bottom part

Furnace Exit duct Cyclone

Bottom region

Freeboard

Exit zone

Transport zone

Downcomer

Splash zone Dense bed

Particle seal Return duct

11.1 Zone divisions and macroscopic solids flow pattern in a commercial-scale CFB boiler. Boiler sketch courtesy of Metso Power Oy.

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of the furnace. The dense bed can be maintained also when the superficial velocity exceeds the terminal velocity of a major part of (or all of) the bed solids (under CFB conditions). This is mainly due to the fact that the primary gas passes through the dense bed in a heterogeneous way, partially in the form of large bubbles, which, at high velocities, create a shortcut of gas between the gas distributor and the region above the dense bed. Thus, this flow results in bubbles/voids that contain strongly oxidizing environments and dense regions (emulsion phase) under reducing conditions (see Section 11.3.1). Although the bubble-induced gas fluctuations in the dense bed quickly lose amplitude above the dense bed, they have important implications for the characteristics of the gas–solids flow in the freeboard. Above the dense bed, there is a so-called splash zone that consists of solids, which after ejection by the fluctuating gas flow in the dense bed, follow a ballistic movement, leading to strong solids back-mixing with a pronounced decrease in solids concentration. If the FBC unit is operated under circulating conditions (CFBC), the gas velocity is sufficiently high to cause a significant portion of the solids to be entrained up through the furnace. Thus, above the splash zone, a transport zone is formed in which most of the back-mixing occurs at the furnace walls, with the result that the solids flow forms a core-annulus structure, i.e., with mainly up-flow in the core and continuous back-mixing at the furnace walls, thereby forming down-flowing wall layers of solids. Such continuous back-mixing represents the segregation of solids, up through the transport zone, whereby the coarser the solids the higher the probability that they are separated at the furnace walls. Therefore, there is a continuous decrease in average solids size with height in the freeboard of a CFBC. Myöhänen (2011) reported the formation of local layers of down-flowing solids by the surfaces of heat extraction panels located within the core region. In addition, significant size segregation due to size-dependent back-mixing occurs at the exit duct(s) that connect the furnace with the cyclone(s). Thus, a certain fraction of the up-flowing solids will reach the riser exit duct(s) and in a CFB boiler furnace, significant amounts of solids leave the furnace and are separated in the primary cyclone and circulated back to the bed through a particle lock (this may also constitute an external particle cooler, which is required in an oxy-fired CFB boiler to control the bed temperature).

11.2

Types of modeling

The modeling currently used in FBC research and development can be divided into three categories according to the extent to which the modeling is based on empirical expressions and the temporal and spatial levels of resolution that they provide (in decreasing order of empirical content): empirical correlations; semi-empirical modeling; and computational fluid

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dynamics (CFD). Empirical correlations are typically used to determine a specific process in the FBC unit such as the vertical profile of the solids concentration in the furnace. Semi-empirical modeling (sometimes termed ‘macroscopic modeling’) refers here to that typically used for comprehensive modeling with the aim of modeling an entire FBC process on the flue gas side. CFD, which represents modeling from first principles, has to date been limited to focused studies, such as those on secondary air penetration; CFD has not yet been used or validated for the modeling of an entire large-scale FBC process, particularly with respect to one that considers fluid dynamics, combustion, and heat transfer. The principles, advantages, drawbacks, and area of application of each type of modeling are summarized below.

11.2.1 Empirical correlations Owing to the relatively high complexity of the multiphase flow picture, expressions that are based entirely on experimental data have traditionally predominated as modeling tools in the FBC industry. These expressions are based on experimental experience gained over many years of FBC technology development. The correlations are generally used to provide simplified descriptions of certain variables, such as gas composition (with special attention to pollutants), furnace heat transfer, outlet temperature, and in the case of CFB furnaces, the externally circulating solids flow required for determining the heat balance of an external particle cooler. In FBC development, the use of empirical correlations has proven to be efficient and reliable for interpolative exercises and incremental (‘extrapolative’) scale-up, which, as exemplified by CFB boilers, has expanded from 5 MWe in 1979 to 550 MWe in 2015 (for a review on the development of FBC technology, see Koornneef et al., 2007). However, empirical correlations cannot be used for extrapolating far outside the range of parameters for which they were derived, which means that their use for large-step scaling-up is risky. In addition, recent trends in FBC development involve a greater variety of operational conditions, and this requires new data to support or modify existing correlations regarding the combustion of new fuels or fuel mixtures, the development of new gas injection strategies, and the introduction of designs with supercritical steam data. Another obvious drawback associated with correlation-based modeling is that it makes little or no contribution to process understanding, i.e., correlations are of little use in identifying the reason for a specific malfunction in a process. Nevertheless, empirical correlations have been, and continue to be, valuable to FBC manufacturers, since they represent many years of experience and empirical knowledge and, in most cases, have not been published in the open literature.

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11.2.2 Semi-empirical modeling In semi-empirical modeling (macroscopic modeling), expressions that combine a theoretical basis with certain empirical content are used to describe the FBC process. Such modeling is generally based on the closure of mass and heat (but not momentum) balances, while neglecting turbulence, for a number of cells into which an FBC unit is discretized. Typically, a 3- or 1.5-dimensional discretization is used for modeling the furnace (see Section 11.3.1), while other components (see Fig. 11.1), such as ash classifiers (if present) and return leg components (in the case of a CFB unit), are commonly assigned a ‘0-dimensional’ description. The degree of empirical content in semi-empirical models varies greatly; these models consist of various sub-models that range in content from empirical relations to the use of transport equations. The main advantage of semi-empirical modeling is that a so-called ‘comprehensive model’, which describes the fluid-dynamics, combustion, and heat transfer of an entire FBC system, can be formulated while keeping computational costs relatively low (see Pallarès, 2008; Ratschow, 2009; Myöhänen, 2011), while at the same time allowing the dependencies between the different zones depicted in Fig. 11.1 to be modeled. Thus, the cause–effect relationships provided by linking the sub-models enable a causal analysis of the model results and can enhance understanding of the FBC process. Macroscopic modeling of FBC has been gradually adapted by the major FBC technology providers as a tool for design and scale-up, as well as for structuring the knowledge of the FBC process and identifying critical knowledge gaps (see, e.g., Vepsäläinen et al., 2009; Palonen et al., 2011). The main disadvantage of semi-empirical models is that they rely to different extents on empirical correlations, thereby limiting their use in scale-up.

11.2.3 Computational fluid dynamics (CFD) In contrast to semi-empirical modeling, CFD solves the momentum balance of the gas–solids flow. Although CFD refers to the fluid dynamics, it can be used in combination with the modeling of combustion reactions and heat transfer. However, the application of CFD to two-phase flow systems, such as FBC, represents a challenge that requires long computational times and validation, which has in most of the cases studied to date shown limited agreement between the simulations and experiments, due to assumptions and simplifications made in the simulations, as discussed below. Thus, the addition of combustion reactions and heat transfer modeling is often associated with difficulties that increase computational time. In the present study, the focus is on fluid dynamics (modeling of combustion chemistry and heat transfer is discussed in Section 11.3.1 and Chapter 5), with a brief summary of the

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different CFD approaches used in gas–solids flows and their current areas of application in the field of FBC. The different CFD modeling approaches for gas–solids flow used in FBC applications can be divided according to the time and space scales resolved, as reviewed by Yu and Xu (2003) and Myöhänen (2011). Although modeling at a coarser resolution entails reduced computational effort, it requires the use of empirical expressions to account for phenomena that occur at the finer scales and influence the flow. In the most finely time- and space-resolved CFD modeling, direct numerical simulation (DNS) solves the original Navier–Stokes equations at scales that are sufficiently small to resolve fully the turbulence, i.e., at the Kolmogorov scale. In DNS modeling, the solids are treated in a discrete manner (Hu, 1996). Thus, DNS can be considered as Lagrangian modeling of the solids phase, which makes modeling of particle collisions the main challenge in Dns modeling, together with the fact that the computational cost increases with increasing Reynolds (Re) number. To date, the studies that have applied DNS modeling to the field of gas–solids flow have been limited to disperse solids suspensions, neglecting collisions between particles at low Re numbers (Reddy et al., 2010), i.e., conducted under conditions that are not relevant to FBC units. At less finely-resolved temporal and spatial scales, the Lattice Boltzmann method (LBM) uses fictive sets of particles that are governed by the Boltzmann equation, so as to characterize the fluid. A model for particle collisions must be applied to the particles, and this represents the major challenge associated with this method. For gas–solids flow, LBM is mostly used to simulate gas flows around one or several solid particles that are arranged in different geometries, and to obtain drag coefficients to be used in other CFD methods, as exemplified by van der Hoef et al. (2005) and Benyahia et al. (2006). The Lagrangian–Eulerian (L-E) approach is based on definition of the gas phase as a continuum and definition of the solids phase as the sum of discrete elements (particles). Volume-averaged transport equations are used to solve the continuity equation and the momentum balance for the gas phase: ∂ (e r ) + — ··((e r u ) = 0 g g g ∂t g g    ∂ (e r u ) + — ·( ·(e g rg ug u g ) = – e g —p + — ··((e gt g ) + e g rg g ∂t g g g   VpV p, g (u p – ug ) –S p es

[11.1]

[11.2]

where the last term accounts for the influence of all particles in the given computational cell on the gas phase momentum. Each solid particle in the system is described by the equation of motion, in which both translational and rotational components can be accounted for, although the latter is often

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neglected. Gatignol (1983) expressed all the relevant terms for Rep << 1 with corresponding corrections, to describe conditions at higher Re numbers. Neglecting those terms which are small in gas–solids fluidized bed flows, the expressions for the translational and rotational motion given by Jackson (1997) can be written as:    ∂u p  VpV p, g (u p – ug )  [11.3] mp = Vp — ·(– p + t g ) + m p g + + Fcoll ∂t es lp

  ∂w p  = T– gas + T– coll ∂t

[11.4]

where the last terms in these equations account for the translational and rotational momentum exchange through collisions with other particles. Submodels available for description of the collision term are based on balances over the linear and angular momentums. These models differ in that they have either soft (Maw et al., 1976) or rigid particles, depending on whether or not they are deformed during the collisions. The soft particle approach yields multiple non-instantaneous collisions and is therefore especially suitable for dense regions, while the simpler hard particle approach is appropriate only under dilute flow conditions (under which particle-particle interactions can be neglected). In addition, normal and tangential restitution coefficients, which express the inelasticity of the collision, must be given to determine the last term in Eqs [11.3] and [11.4]. If Eqs [11.3] and [11.4] are used as expressed above, the scheme is called ‘four-way coupling’, i.e., particle collisions are accounted for in this scheme. A first simplification, known as ‘two-way coupling’, involves neglecting the particle collisions, i.e., removing the last term in Eqs [11.3] and [11.4], which is obviously only suitable for flows with low frequencies of solids collisions. If the effects of the particles on the gas flow are also neglected (i.e., the last term in Eq. [11.2]), a so-called ‘one-way coupling’ scheme is created. It should be noted that one-way coupling lacks conservation of the total momentum and that its applicability is limited to regions with voidages >10–4 (corresponding to concentrations <0.1 kg/m3 for typical FBC solids). A key characteristic of FB boilers is that the bed material has a relatively wide distribution of solids sizes due to the presence of several solid fractions (ash, fuel, sorbent, and make-up material), each with its own particle size distribution. One of the main advantages of the L-E approach is that it permits relatively straightforward formulation of systems with polydisperse solids. However, problems arise because the drag force on a certain particle depends on the breadth of the size distribution of the solids mixture, as shown by Beetstra et al. (2007), who proposed a modified drag expression to account for this effect. hoomans et al. (2000) have presented simulations that include bi-dispersed solids with a size ratio of 2.66. For larger size differences, the

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implementation of such modeling may require several meshes that resolve each different solids size scale, as applied by Farzaneh et al. (2011) in their modeling of fuel particles immersed in a dense bed of smaller-sized particles. The highest number of particles reported to be modeled with the referred L-E approach is 4.5 × 106, as described by Tsuji et al. (2008), who simulated 15 seconds of a monodisperse bed with a cross-section of approximately 1.5 m2. However, given the number of particles present in large-scale FB boilers (about six orders of magnitude higher), the L-E approach does not appear to be a realistic method for large-scale FBC modeling, owing to high computational costs. However, the L-E approach can be used to investigate the flow in zones of an FBC unit with disperse solids, such as cyclones (Wan et al., 2008). It is noteworthy that the L-E approach has a significant empirical content regarding the description of gas–solids interactions, ~p,g,  and particle collisions, Fcoll . Finally, in order to reduce computational costs, the gas phase calculations in the L-E approach are often performed on a mesh with cell sizes that are coarser than the solids size, which means that microscopic particle structures cannot be recognized by the modeling of the gas flow. However, this yields certain errors in the descriptions of the gas and solids phases. In the Eulerian-Eulerian (E-E) approach, both the gas phase and particulate phases are described as interpenetrating continua. For simplicity, only one particulate phase is assumed hereinafter. Expressing the solids phase as a continuum, the following continuity and momentum balance equations for both phases are obtained: eg + es = 1

[11.5]

 ∂ (e r ) + — ·( ·(e g rg ug ) = 0 g g ∂t

[11.6]

 ∂ (e r ) + — ·( ·(e s rs us ) = 0 ∂t s s

[11.7]

   ∂ (e r u ) + — ·( ·(e g rg ug u g ) = – e g —p + — ··((e gt g ) + e g rg g ∂t g g g   – V s, g (uus – ug )

[11.8]

  ∂ (e r u ) + — ·( ·(e s rs u s u s ) = – e s —p – —p —ps + — ∙(e st s ) ∂t s s s    + e s rs g + V s, g (us – ug )

[11.9]

The main challenge in E-E modeling is to find proper closure expressions for the solids phase stress tensor, ts, and for the particle pressure, ps, to give Eq. [11.9]. While these parameters can be obtained through correlations of the viscosity of the solids–gas mixture and the modulus of elasticity

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(see Enwald et al., 1996), closure equations are frequently derived from the so-called ‘kinetic theory of granular flow’. This theory, which was originally developed by Anderson and Jackson (1967), is analogous with the kinetic theory of gases applied to the particulate phase which, based on the Maxwell–Boltzmann equations, sets the basis for describing discrete gas molecules in random motion as a continuum (Grad, 1949). Thus, the solids stress tensor and the solids pressure can, respectively, be expressed as: 2 ˆ    Ê t s = m s (—us + —usT ) + Á o – m s ˜ (— ∙us ) I 3 ¯ Ë

[11.10]

ps = e s rsq s + 2e s2 rsq s (1 + e)g0

[11.11]

in which qs is the granular temperature, i.e., the particulate analogy of the thermodynamic temperature of the gas phase, which represents a measure of the velocity fluctuations in the solids phase. This granular temperature is the transported scalar in the equation for the granular energy, i.e., 3qs/2, which can be derived from the kinetic theory of granular flow and reads: 3È ∂ (e r q ) + — ·(e r q u )˘ s s s s ˙ 2 ÎÍ∂t s s s ˚  = (– ps I + t s ): —u s + — ∙(ks —q s ) – g + j

[11.12]

Thus, from Eqs [11.10]–[11.12], expressions for the following unknown variables are required to close the problem: ms, l, g0, Ks, g, and j. In addition, a value for the restitution coefficient, e, must be provided. The choice of closure expressions (often with certain empirical content) has a strong impact on the results, and it distinguishes the granular flow models described in the literature. A summary of the expressions for variables ms, l, g0, Ks, g, and j has been provided by van Wachem (2000). It is important to note that a series of assumptions are made in the derivation of the kinetic theory of granular flow, so as to make it suitable for modeling gas–solids flows. Thus, it is assumed that particles are rigid in form and that their velocities follow a Maxwell distribution. While such a distribution has not been experimentally proven, the assumption of rigid particles allows only instantaneous (infinitely short contact time) and consequently binary particle contacts, which is not the case in the dense bed regions of FB boilers. Nonetheless, the kinetic theory of granular flow is often applied to model the gas–solids flows in FBC units, resulting in various levels of agreement between the experimental data and the simulations. An additional challenge in E-E modeling is that in practice the mesh resolution is limited and therefore may not be sufficiently fine to resolve the formation of particle flow structures at smaller scales than the mesh size. Assuming that the solids are homogeneously distributed within each

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cell leads to an overestimation of the inter-phase drag. Methods to correct this overestimation, by accounting for the formation of microscopic particle clusters, are under investigation, e.g., the energy minimization multi-scale (EMMS) method proposed by Li et al. (1999). A recently developed CFD modeling approach for gas–solids flows applied in some commercial codes is the so-called multiphase particle-in-cell method (for its three-dimensional formulation, see Snider, 2001). In this method, the gas phase is modeled as a continuum, while the particle phase is described by a probability density function (PDF) for the physical properties, location, and velocity of the particles. The PDF is discretized into classes, each of which is represented by a certain number of particles. The time derivative of the PDF, expressed by the Liouville equation, is applied to the particles of each class, i.e., the particulate phase is modeled in a Lagrangian framework. However, to avoid the main computational cost associated with a Lagrangian framework coupled to solve particle collisions, the multiphase particle-incell method employs a solids stress tensor that is analogous to that used in E-E simulations, i.e., in which particle collisions are modeled in an Eulerian framework. A major advantage is that, in contrast to the E-E approach, the solids stress tensor can be calculated at a sub-grid level from the solids flow properties solved in the Lagrangian framework. Thus, the main advantages of this method are: ∑ computational times similar to those required for the E-E approach; ∑ more reliable estimations of the solids stress tensor; and ∑ the ability to account for polydisperse solids. A critical aspect, which is often oversimplified in the studies in the literature that use CFD to simulate FBC units, is the choice of inlet boundary conditions for the gas phase and, indeed, of the domain to be modeled. Normally, a uniform gas velocity (or pressure) profile is applied at the primary gas distributor (and other gas inlet locations, if applicable). However, in FBC units, neither the gas velocity nor the gas pressure is constant or homogeneous, since the gas distributor has a limited pressure drop, which means that the bed-pressure fluctuations caused by bubble movement penetrate down into the air feeding system (Kage et al., 1991; Peirano et al., 2002; Johnsson et al., 2002). Sasic et al. (2006a, 2006b) studied the influence of the gas feeding arrangement on dense bed regimes and proposed an extension of the modeled domain to include the gas feeding system. Thus, they presented a model, which when coupled to E-E modeling of the bed, resembles the dynamics of experimental pressure data. The strength of CFD modeling is that it is derived from first principles. Thus, it is assumed to stand on a more solid theoretical ground than macroscopic modeling (and empirical correlations). However, as indicated above, CFD formulations are limited by closure relations and the assumptions made to

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resolve the system and to decrease computational costs. Given the strongly fluctuating nature of the phenomena in FB boilers, the ability to provide highly transient resolved descriptions represents an advantage of CFD modeling. In summary, in FBC development, CFD simulations have to date been used mainly for targeted studies in which the computational domain can be restricted, e.g., the penetration of lateral gas injections (Li et al., 2009) and cyclone separation efficiency (reviewed by Cortés and Gil, 2007). Regarding the modeling of a complete FBC under relevant operating conditions, further development work is required to establish realistic closure laws, including solids size distributions and fuel particles, and to reduce simulation times, which is a challenge if these factors are to be combined with combustion and heat transfer modeling.

11.3

Semi-empirical modeling: basic sub-models

As indicated above, semi-empirical macroscopic modeling has been applied to describe the entire FBC process with respect to fluid dynamics, combustion chemistry, and heat transfer, and is therefore described in more detail in this chapter. Such modeling is performed using sub-models for the various phenomena in the different regions (Fig. 11.1) of an FBC unit. Sub-modeling is carried out within the three main processes, fluid dynamics, combustion chemistry, and heat transfer, all of which interact with each other. Thus, in a comprehensive model, the output data from one sub-model are used as the input data for the other sub-models, as illustrated in Fig. 11.2, where the thickness of the arrows indicates how sensitive the modeling of one process is to inputs from the other processes. Thus, the fluid dynamics strongly influences the chemistry (through mixing), and the heat transfer (through the solids flow), while the fluid dynamics is less influenced by Heat generation Chemistry

Heat transfer Temperature profiles

Internal gas generation

Fluid dynamical parameters

Temperature profiles

Fluid dynamics

11.2 Input–output data exchange between the processes involved in FBC modeling. The thickness of each arrow indicates the extent to which one process influences other processes.

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chemistry (combustion) and heat transfer. In addition, the chemistry and heat transfer both have strong influences on each other. Below, a selection of the phenomena within each of the processes presented in Fig.11.2 is discussed in terms of modeling the different zones given in Fig.11. 1. Key expressions and/or references to the most widely used submodels are given.

11.3.1 Dense bed fluid dynamics The dense bed (Fig. 11.1) is the region that is established in the lower part of most FB furnaces, provided that there is enough bed material in the furnace (it is of course always present in a BFB unit). The dense bed is characterized by a constant vertical gradient of the time-averaged pressure. Accurate modeling of the dense bed is critical, as despite occupying a relatively small vertical extension of the furnace, it typically contains a substantial part of the furnace solids inventory, and for low-volatile fuels (coal), it accounts for a significant share of the fuel heat release. The bottom bed flow regime is characterized by a strongly heterogeneous bubble flow regime, with large bubbles/voids that rise across the emulsion phase and burst as they reach the dense bed surface. The dense bed dynamics typically gives rise to an average bubble frequency of the order of 1 Hz (Svensson et al., 1996). Therefore, the power spectra of measured in-bed pressure fluctuations give a characteristic frequency of around 1 Hz, although the spectra become wider as the bed cross sectional area increases; this occurs because in-wall pressure measurements are influenced by the many bubble passages distributed over the bed cross-section. The rise-and-burst cycles of the bubbles govern the mixing of solids (including fuel particles) in the bottom region of the furnace (Rowe and Nienow, 1976; Eames and Gilbertson, 2005). The bubble flow characteristics result in a large fraction of the primary gas (air or air/flue gas) passing the bed via bubbles at high velocities at short intervals, with the results that the bubbles are oxygenrich and the emulsion phase is oxygen-depleted (reducing conditions), since the char tends to stay in the emulsion phase. FBC bubbles have been described as being of an ‘exploding type’ (Svensson et al., 1996). However, as indicated above, CFB boilers may not have a dense bed in the strict sense (i.e., a region with a constant pressure drop gradient) if the furnace pressure drop is kept too low and the gas velocity is high in relation to the average solids size. This may impose a risk in the operation of a CFB with coarser, non-entrainable fuel particles, since lower dense beds have been associated with reduced lateral fuel mixing (Niklasson et al., 2006). Yet, operation with low bed pressure drop has been proposed (Su et al., 2009) in order to save auxiliary power (fluidizing fan power), but the exact influence of fuel mixing and combustion behavior is not reported in the literature.

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An important variable in the modeling of the vertical solids concentration profile and the mass balance is the dense bed voidage, eb . Experimental data on dense bed voidage are relatively abundant for laboratory-scale FB units (for a summary of such experimental studies, see Oka, 2004). However, in contrast to FBC boilers, laboratory units are commonly operated at low excess gas velocities and with a relatively high pressure drop over the gas distributor; such laboratory-scale data should not be used for the modeling of large-scale FBC units. Expressions based on large-scale FB measurements are given in Table 11.1 (Eqs [11.22]–[11.24]). Assuming that the emulsion phase remains under minimum fluidization conditions and that the bubbles are free of particles, the average bed voidage, i.e., bed expansion, can be derived as:

eb = (1 – dbub)emf + dbub

[11.13]

where dbub is the volumetric bubble fraction, and emf is the voidage at minimum fluidization. The latter can easily be determined by combining Eqs [11.16] and [11.17], as given by Ergun (1952) and Wen and Yu (1966), respectively (a summary of the values for C1 and C2 in Eq. [11.16] is available from Grace, 1986). Thus, the volumetric bubble fraction in Eq. [11.13] remains to be determined. It should be pointed out that emulsion voidages that exceed that under minimum fluidization conditions have been measured in the vicinity of bubbles and in between trailing bubbles (Yates et al., 1994). However, too little information is available to include these factors in the modeling, and they are likely to have a minor impact on the overall bed voidage. In the so-called original two-phase flow theory, Toomey and Johnstone (1952) assumed that the fluidizing gas flow (expressed as u0 when normalized to a superficial velocity) consisted of two phases: the above-mentioned emulsion phase, which is assumed to be under minimum fluidization conditions, umf; and the phase corresponding to the gas bubbles, ubub. Several studies (e.g., Toomey and Johnstone, 1952; Geldart, 1968; McGrath and Streatfield, 1971) found that this so-called two-phase flow theory agreed with the experimental data, although these were limited to fluidization velocities slightly above the minimum fluidization velocity. For higher velocities, it was shown that the two-phase flow theory overestimated the bubble flow, as highlighted by Grace and Clift (1974). Thus, an additional gas flow phase is required to attain the measured bubble flows. This flow has been identified as so-called ‘throughflow’, uth, through and between the bubbles, i.e., the flow through the low-resistance paths created by the presence of the bubbles. Grace and Clift (1974) proposed a formulation with three gas flow terms, called the modified two-phase flow theory, which can be written (expressed as volumetric flow per surface area [m3/s/m2]) as:

u0 = umf + ubub + uth

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[11.14]

Table 11.1 Summary of expressions for the dense bed expansion eb = (1 – dbub)emf + dbub

[11.13]

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emf

dbub

1.75 Re 2 p, mf + 3 emf fs

u0 = umf + ubub + uth u0 = umf + dbubUbub + uth

+

150(1 – emf ) 2 Rep, mf = Ar 2 emf fs2

2 Rep, mf mf = C1 + C 2 Ar – C1

[11.16] [11.17]

Ubub

umf umf =

[11.14] [11.18]

Rep, m mff mg d p rg

[11.19]

uth

Ubub = 0.71 g dbub

[11.20] y = 0.4

dbub = 0.54(u0 – umf )

0.8

(h + 4 A0 ) g

–0.2

[11.21]

ubub u – uth – umf = 0 u0 – umf u0 – umf

y = f · (h + 4 A0 )0.4 fBF BFB B = [0.26 + 0.7e

–3.3d p

[11.22] ]¥

[0.15 + (u0 – umf ))]] fCF CFB B

[11.15]

–1 3

[11.23]

= 0.31 + 0.13 – 16.6ds u0 – 2.61.10–5 Dpref

[11.24]

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Several studies have evaluated the magnitude of the throughflow in fluidized beds and concluded that at fluidization velocities well above the minimum fluidization velocity, most of the primary gas passes the dense region as throughflow (Clift and Grace, 1985; Hilligardt and Werther, 1986), and that the local throughflow velocity at the dense bed surface can reach values several times higher than the fluidization velocity (Olowson and Almstedt, 1990). Thus, this applies to both bubbling and circulating fluidized beds that operate at velocities many times the minimum fluidization velocity. Under such conditions, the throughflow characteristics of the flow occasionally create a ‘shortcut’ for the primary gas to migrate from the air distributor and up to the dense bed surface across the entire dense bed, forming so-called exploding bubbles (see Svensson et al., 1996). Figure 11.3 shows the dense bed expansion curves, in which the significant bed expansion with fluidization velocity that occurs at low excess fluidization velocities is observed to decrease gradually with fluidization velocity, i.e., the visible bubble flow tends to become saturated and most of the additional gas supplied flows as throughflow. In Eq. [11.14], the fluidization velocity, u0, is a known input. The term for the minimum fluidization velocity is calculated using the definition of particle Reynolds number under minimum fluidization (see Eq. [11.19]). The term that represents the bubble volumetric flux can be expressed as a function of the bubble velocity, Eq. [11.14], which can be estimated from semi-empirical correlations, e.g., Eqs [11.20] and [11.21] derived by Clift and Grace (1985) and Darton et al. (1977), respectively. Thus, only an expression for the throughflow term in Eq. [11.14] is required to close the mass-flow balance for the gas phase, so as to arrive at a reasonable value for the bubble volumetric fraction, and thereby a value for the average bed voidage (bed expansion), also at higher velocities. In the literature, the throughflow is usually expressed as the ratio between the bubble phase gas and the excess gas, as follows: y =

ubub u – uth – umf = 0 u0 – umf u0 – umf

[11.15]

Different values for this ratio are found in the literature. Ratschow (2009) gives y a value of 0.8 and Zijerveld et al. (1997) propose a correlation with the Archimedes number, y = 1.45ar–0.18. Johnsson et al. (1991) give a height-dependent expression, Eq. [11.22], which maintains the experimentally proven and above-mentioned fact that there is a constant vertical pressure gradient up through the bed. This expression was used in the modeled data shown in Fig. 11.3. Table 11.1 summarizes the above expressions for bed expansion, together with a structure that can be used to solve the dense bed voidage.

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Dense bed voidage, eb(–)

0.7

0.65

0.6

0.55

Cold BFB, Johnsson et al. (1991) 16 MW BFB, Johnsson et al. (1991) 12 MW CFB, Svensson et al. (1996) Model BFB, Johnsson et al. (1991) Model CFB, Pallarès and Johnsson (2006a)

0.5

0.45

0

1

2 3 4 5 6 Excess fluidization velocity, u0 – umf (m/s)

7

11.3 Bottom-bed expansion for BFB and CFB units; experimental data compared to modeling results (by Johnsson et al., 1991; Pallarès and Johnsson, 2006a).

Equation [11.22] is to be combined with one of the f-functions given by Eqs [11.23] and [11.24], which were proposed by Johnsson et al. (1991) and Pallarès and Johnsson (2006a), respectively. These functions are based on experimental bed expansion (pressure drop) data from large-scale boilers under bubbling (fBFB) and circulating (fCFB) conditions, as shown in Fig. 11.3. The reason that the function f differs for BFB and CFB at a given velocity is that there is a difference in primary gas distributor pressure drop at a given fluidization velocity; the BFB gas distributor has a higher pressure drop than the CFB distributor. This relates to the findings of Svensson et al. (1996), who showed that the gas distributor pressure drop had a significant influence on bubble flow characteristics. In-bed solids mixing is characterized by a gulf-stream pattern around the bubbles as they rise through the bed, with the solids ascending in the wake of the bubble and descending in between the bubbles. This pattern inspired the counter-current back-mixing (CCBM) model. The CCBM model, which is shown in schematic in the upper part of Fig. 11.4, was developed by van Deemter (1967) to describe axial solids mixing based on the vertical velocity of each solids phase (up-flowing and down-flowing) and a net exchange coefficient, Ks, between the phases. Thus, the mass balance for each solids phase, i, reads:

di

∂cs, i ∂c = – us, id i s, i + K s (Ci – C jπi ) ∂t ∂z

[11.25]

Although the CCBM model was originally developed for small units, as larger units were introduced and the presence of preferred bubble paths was

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Fluidized bed technologies for near-zero emission combustion Mixing cell

Ks Kg

ug,1 Ks,cell us,1

ug,2 us,2

Ks,cell

Ks,cell

Ks,cell

11.4 Schematic of the counter-current back-mixing (CCBM) model for solids and gas mixing in dense fluidized beds (after van Deemter, 1967).

confirmed (see Werther, 1977), the model was extended to include exchange of solids between the mixing cells related to each bubble path, Ks,cell, which allowed a description of the lateral mixing (see Abanades and Grasa, 2001), as indicated in the lower part of Fig. 11.4. however, application of the model is not straightforward, since the values of the exchange coefficients are difficult to estimate in advance. The lateral solids mixing in the bottom region of a large-scale fluidized bed is typically described by means of a dispersion coefficient, Ds,lat: ∂cs 2 = Ds, llat at — C s ∂t

[11.26]

With respect to the lateral mixing of bulk bed material, i.e., fuel ashes,

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sorbent, and make-up material (fuel mixing is discussed below), no semiempirical sub-models are available. As for experimental studies on solids mixing, the tracking of individual particles (e.g., using radioactivity; Stein et al., 2000) provides information on the solids flow pattern, upon which models can be formulated. Other experimental studies have focused on defining the dispersion coefficient (Shi and Fan, 1984; Berruti et al., 1986; Lim et al., 1993; Liu and Chen, 2011, 2012; Sette et al., 2012), which has been found to range from 10–4 to 10–2 m2/s, depending on the bed solids used, operational conditions, and nozzle arrangement. As far as axial gas mixing is concerned, a similar approach to that employed in the CCBM model for solids mixing is often used (Ratschow, 2009; Myöhänen and Hyppänen, 2011). The gas is divided into bubble and emulsion flows, in which the gas flowing through the emulsion phase comes in contact with fuel particles. Thus, formulating a mass balance for any species, g, in the gas phase, i, a similar expression to Eq. [11.25] is obtained, with an additional term that accounts for the generation and consumption of the gas species studied:

di

∂cisp ∂c sp sp = – ug, i d i i + K g (Cisp – C sp j ) + Si ∂t ∂z

[11.27] It is usually assumed that the gas in the emulsion phase flows at the minimum fluidization velocity, and that the excess gas corresponds to gas flowing in and through the bubble phase. The values for the exchange coefficient, Kg, given in the literature (Sit and Grace, 1981; Hannes, 1996) vary significantly (10–1–40 s–1) depending on the operational conditions. This is expected, since this model is formulated on the basis of low-velocity fluidization. However, as the fluidization velocity increases, the throughflow begins to dominate the gas flow, drastically reducing the gas exchange between the bubble and emulsion phases. The difference in flow at higher fluidization velocities, with strong bypass of the gas through voids that extend across more or less the entire dense bed height, requires other modeling approaches. Thus, for modeling the axial gas mixing in the dense beds of CFB units, Pallarès and Johnsson (2009) have proposed a dynamical model over a bubble cycle to account for the throughflow and gas-flow fluctuations. This model is in good agreement with gas probe measurements in the bottom zone of a CFB furnace. Lateral gas mixing on the macroscopic scale, i.e., between mixing cells, is commonly neglected in the dense bed due to the short residence time of the gas. The authors of this chapter argue that a physically sound description of the combustion process in the dense bed must be formulated in a timeresolved manner. In other words, time-averaged descriptions fail to provide general and realistic descriptions of the progress of in-bed combustion under conditions that are relevant to industrial-scale FBC units.

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11.3.2 Freeboard fluid dynamics The first fluid dynamical studies of FB freeboards were carried out in BFB units. While these studies provided knowledge on the splash zone only, they were followed by studies conducted under CFB conditions, which provided data on the transport zone. The assumption that solids back-mixing is proportional to the solids concentration yields an exponential decay in the vertical solids concentration, which was found to be in agreement with measurements (Kunii and Levenspiel, 1991). Thus, correlations of the solids decay constant for the splash zone, a, were derived as exemplified by the following expressions from Kunii and Levenspiel (1991), Hiller (1995), and Johnsson and Leckner (1995): a = constant 1 ug a = 200 a=4

d p0.572 ug

ut ug

[11.28]

[11.29] [11.30]

Johnsson and Leckner (1995) combined the splash zone decay characterized by Eq. [11.30] with a decay coefficient corresponding to the solids backmixing in the transport zone, since their work concerned CFB conditions. Thus, Johnsson and Leckner (1995) acknowledged the existence of two counteracting processes: back-mixing due to ballistic movement of clustered particles; and wall layer-induced back-mixing (see below), with the first back-mixing effect predominating in the splash zone and the latter effect predominating in the transport zone. Note that none of the above expressions depends on the height of the dense bed or of the pressure drop across the primary air distributor, which are known to influence the dense bed regime and thereby, the local velocities of the gas ejecting clustered solids into the freeboard (Svensson et al., 1996; Olowson and Almstedt, 1990). Thus, further work is required to improve the expression for the decay constant a. Regarding the disperse phase, an approach to describe the disperse solids phase was presented by Kruse and Werther (1995), who formulated a method to describe the detailed characteristics of the solids flux in rectangular geometries, which Knöbig (1998) subsequently applied to three-dimensional discretization of furnaces with rectangular cross section. The method of Knöbig provides details as to the lateral heterogeneities of the solids flux, although it requires experimental data on solids fluxes for the case to be modeled. The approach described by Johnsson and Leckner (1995) can be combined with the experimentally supported assumption of a flat horizontal

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solids flux profile over the core region and, in line with the flow description given above, an exponential decay of the vertical solids concentration, with the decay constant: b = 0.23 u g – ut

[11.31]

Expressions for the terminal velocity of a single particle used in Eqs [11.30] and [11.31] are available in the literature (Haider and Levenspiel, 1989). Thus, the vertical solids concentration profile in the freeboard is expressed as: Cs = Cclus + Cdisp

[11.32]

z =H b – a (z– Cclus = Cclus e z –H b )

[11.33]

z =H b – b (z– z –H b ) Cdisp, core = Cdisp , core e

[11.34]

With Eqs [11.32]–[11.34], the vertical solids profiles, as depicted by the solid lines in Fig. 11.5, are obtained. As seen, when modeling CFB units, two separate decay constants that account for each of the solids back-mixing processes occurring in the freeboard are required, to describe adequately the experimental data (a one-decay model will yield a straight line in the plot, making it impossible to fit the experimental data). The dispersed phase can be assumed to flow at the slip velocity. Thus the core upflow at any height can be determined using Eq. [11.35] and, by differentiation, the net solids flow transfer from the core region to the wall layers can be deduced using Eq. [11.36]:

Solids concentration, cs (kg/m3)

Fdisp,core = Cdisp,core(ug – ut)Acore

[11.35]

12 MW, u0 = 2.7 m/s, ds = 320 µm Johnsson and Leckner (1995)

1000

226 MW, u0 = 3.2 m/s, ds = 180 µm Werdermann (1992)

100

Model Pallarès and Johnsson (2006a)

10

1 0

5

10 15 Height above air distributor, h (m)

20

11.5 Vertical solids concentration profiles for two CFB boilers. The experimental data are compared with the results from the model.

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∂Fdisp, core ∂Fdisp,layer , =– ∂z ∂z

[11.36]

Fdisp,layer = Cdisp,layerus,layerAlayer

[11.37]

For greater accuracy, the value of the terminal velocity used in Eq. [11.35] should account for the collisions with surrounding particles, which is generally how faster-flowing fine particles transfer momentum to coarser particles. By accounting for particle interactions, the modeling is able to predict entrainment out of the riser of particles with a single particle terminal velocity that is higher than the gas velocity, as observed experimentally (Pallarès and Johnsson, 2006a). An expression for the effective particle terminal velocity of a particle in a suspension of other particles has been formulated by Palchonok et al. (1997) based on the momentum balance of a polydispersed particle cloud. However, it should be cautioned that the use of such an effective terminal velocity does not apply to the correlations given in Eqs [11.30] and [11.31], in which the value of the single particle terminal velocity was used as a correlating variable. Having determined the solids flow in the wall layer, two of the three parameters, wall layer thickness (and thereby the cross section, Alayer), wall layer solids concentration, and wall layer velocity, have to be expressed to close the problem using Eq. [11.37]. Empirical correlations for the thickness, tlayer, and solids concentration, cdisp,layer, of the wall layers can be found in the literature, such as those given by Myöhänen (2011) and Werther (1993), respectively: tlayer ÊH ˆ = 0.55 Ret–0.22 Á 0 ˜ Deq Ë Deq ¯ Cdisp, layer

0.21

Ê H 0 – hˆ ÁË Deeqq ˜¯

Cdisp, core ˆ Ê –m Cs, m max = Cs, m ˜ max Á1 – e ÁË ˜¯

0.73

[11.38]

m = 0.5

[11.39]

where cs,max corresponds to the maximum package solids concentration, which can be obtained from the literature (see, e.g., Brown, 1950) and is assigned a value of 0.6rs by Myöhänen (2011). The authors of this chapter do not know of any expression proposed for the downflow velocity of the wall layer solids (for a compilation of the experimental data, see Werther, 2005). Gas lateral mixing can be modeled through lateral dispersion, with experimentally determined dispersion coefficients that are typically in the order of 10–1 m2/s (Kruse et al., 1995; Sternéus et al., 2000). The modeling of secondary gas injections has been discussed by Massimilla (1985) and Knöbig (1998). Concerning axial gas mixing, in industrial units, oxygen-rich pockets of gas that originate from the gas bubbles in the dense bed (ghost

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bubbles) are assumed to flow upwards along the freeboard as plumes in the absence of any significant mixing with the surrounding gas, which is typically observed under reducing conditions. This concept of ghost bubbles was first suggested by Pemberton and Davidson (1984). Niklasson et al. (2003) observed fluctuating oxygen concentrations in the furnace of an FBC unit, whereby the fluctuations declined with height in the furnace as a consequence of mixing, which can be interpreted as the effect of ghost bubbles. Modeling of the axial gas mixing in relation to gas kinetics is discussed below (see Section 11.3.7). Scala and Salatino (2002) present a BFB combustion model which combines heat and mass balances over the dense bed, splash zone, and upper freeboard. The model predicts a large influence on the results of the axial mixing pattern assumed in each zone and strong interactions between these zones in terms of heat and mass transfer. Yet, there is no validation of the model published in the literature. At the furnace exit, the solids will either be entrained out from the furnace or separated from the bulk flow into the wall layer downflow. As indicated previously, this exit effect at the top of the furnace (also known as ‘backflow effect’) results in a solids size segregation, i.e., coarser particles in the upper freeboard are less likely than fine particles to be entrained out from the furnace. The backflow effect influences the particle residence time in the riser and the circulation of external solids. Despite its importance in CFB units, there is limited data in the literature on the magnitude of the backflow, as it is difficult to quantify from measurements. With respect to data relevant to large-scale CFB boilers, Werdermann (1992) presented data from two different units to show that the probability of solids in the exit region being recirculated internally (not entrained out to cyclone) ranged from 0.37 to 0.43, while Pallarès and Johnsson (2006a) examined experimental solids flux data and found that the backflow effect was size-dependent and decreased with increases in slip velocity and solids flux.

11.3.3 Pressure loop and return-leg fluid dynamics of a circulating fluidized bed (CFB) Modeling of CFB boilers requires the pressure balance over the circulating loop to be closed, since this determines the solids mass present in the downcomer from the cyclone, which is of importance for the overall solids population balance. This pressure balance can be expressed as in Eq. [11.40] (the letters A–E are explained in Fig. 11.6). DÆE AÆB BÆC CÆD EÆA Dpdc = – Dpriser – Dpduc D return t – Dpcycl – Dp

[11.40]

AÆB In the pressure balance, the furnace (riser) pressure-drop term Dp D riser can be obtained by integration of the modeled vertical profile of solids

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B

C

D E A

11.6 Division of partial pressure drops (indicated by letters A–E) according to [Eq. 11.40]. A = inlet of recirculating duct into the furnace; B = furnace outlet; C = cyclone inlet; D = top of solids column in downcomer; E = seal bed surface. Boiler sketch courtesy of Metso Power Oy. EÆA D return concentration, while the pressure drop across the return leg, Dp , can be neglected. In boilers, the furnace pressure drop is typically measured during operation to control the solids inventory. The pressure drop over the riser exit duct/s and the cyclone(s) can be modeled using the expressions given by Muschelknautz and Muschelknautz (1991) and Rhodes and Geldart (1987), respectively. Thus, the pressure drop provided by the column of fluidized DÆE solids formed in the downcomer, Dp D dc , can be determined. Therefore, the level of solids in the downcomer can be written:

H s, ddc =

DÆE Dppdc rs ((11 – e ddc )g

[11.41]

where the solids voidage in the downcomer, edc, can be calculated with the expressions for dense bed expansion given in Table 11.1. Note that when calculating this voidage, the relative gas–solids velocity urel,dc = ug – us,dc has to be applied, since, depending on the solids external circulation and the cross-sectional area of the downcomer, solids in the downcomer may

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flow downwards with a significant superficial velocity, us,dc, which can be determined from the modeled circulating solids flow and downcomer crosssectional area.

11.3.4 Solids inventory As indicated in Fig. 11.2, fluid dynamics plays a dominant role in the overall FBC process. This motivates the importance of accurate modeling of the solids inventory, which determines to a large extent the flow and mixing pattern of the gas and solids. The solids population balance, from which the solids inventory is obtained, has a number of critical terms, as discussed below. First, for CFB modeling, it is crucial to account for the solids present in the return leg (which, based on the authors’ experience, can represent up to 70% of the total solids inventory for some designs). The solids inventory is also highly sensitive to the separation efficiency of the cyclones (or other type of primary separator), which can be either modeled (see the review of Cortés and Gil, 2007) or experimentally estimated by solids sampling. Also of importance, although less critical, is the separation efficiency of any ash classifiers present in the system, as studied by Guo et al. (2006). When modeling the solids population balance, it is important to account for attrition of the solids that constitute the main bulk of the bed material. Attrition of different solid fractions present in FB boilers has been studied by Chirone and coworkers (see Chirone et al., 2000 and references therein). Attrition is due to a series of phenomena, such as interparticle contacts, effects from the gas distributor jets, and wearing of the solids in the cyclone (Redemann et al., 2009). Experimental tests carried out on fluidized beds to characterize coal ash attrition (Pis et al., 1991; Tomeczek and Mocek, 2007) have shown higher rates of attrition during the first hours with fresh bed material, while after 30 hours there is still significant attrition, albeit at a much lower rate. This high initial rate of attrition can also be observed in the results of the characterization test for coal ash attrition (Fig. 11.7). Such attrition patterns can be included in the transient modeling of the solids inventory, either as experimental patterns (Pallarès et al., 2010) or for fitting so-called ‘comminution coefficients’ in a sub-model of solids attrition (Myöhänen, 2011). Agglomeration, which is the process by which the melting of certain ash components creates clumps of larger particles, also influences the population balance, although this process is obviously difficult to characterize and is therefore usually neglected in modeling. Several processes, including the attrition patterns of the solids, the separation efficiencies of the cyclone(s) and ash classifier(s), and the operational conditions, combine to determine the amounts of external solids that need to be added (make-up material) or removed so as to maintain a constant solids inventory. Solids can be discharged from the dense bed and

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Cumulative mass fraction (%)

100 t=0 t = 0.02*T

80

t = 0.1*T t = 0.2*T

60

t = 0.5*T 40

t=T

20 0 0.01

0.1

1 ds (mm)

10

100

11.7 Results of an attrition test of total time length T performed on bituminous coal ash (source: Pallarès et al., 2010).

the particle seal, depending on whether there is a need to decrease or increase the average size of the solids. In practice, a fluidized bed combustor is typically operated by maintaining the furnace pressure drop within a certain range, and as the ash content of the bed increases, the furnace pressure drop increases until it reaches a certain threshold value. Thereafter, (coarse) bed material is discharged from the bed bottom, reducing the pressure drop (inventory) and the average solids size. Fluid dynamics modeling and the solids population balance can be combined in different ways. Redemann et al. (2009) considered that the fraction of solids undergoing attrition could be neglected in the total population balance and thus, particles that had already undergone attrition constitute the solids inventory in their CFB modeling. They reported that this simplification exerted a significant influence only for the finer-size intervals of the solids inventory (which, on the other hand, is critical in the determination of the fly ash rate). Wang et al. (2003) and Myöhänen (2011) included in their steady-state population balance a sub-model for solids attrition that applies attrition coefficients derived from attrition characterization tests. Pallarès et al. (2010) used the results from attrition tests (such as those shown in Fig. 11.7) directly in their transient modeling of the solids inventory.

11.3.5 Fuel conversion The conversion of solid fuel particles in fluidized beds, discussed in Chapter 7, can be described with reasonable accuracy by mathematical models available in the literature, provided the properties of the modeled fuel particle and its surrounding can be defined unambiguously. Sreekanth et al. (2008) proposed a two-dimensional transient model of the fuel conversion

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process, in which fuel anisotropy, shrinkage and internal stresses, and heat generation are considered. However, fuel flows fed into FB units are often difficult to characterize and vary significantly in both size and shape. Obviously, it is computationally demanding to model the conversion of each fuel particle, which is an issue that can be solved by categorizing fuel in a few representative classes (Myöhänen, 2011). Although this simplification appears to be reasonable, it implies that the particle conversion model cannot be overly detailed. Modeling the conversion of fuel particles is normally divided into drying, devolatilization, and char conversion. Simplified empirical correlations for the characteristic times of drying and devolatilization are available in the literature (La Nauze, 1982). However, these processes can be modeled in a proper fashion by formulating an energy balance inside the fuel particle, since the moisture release rate is defined by the velocity of the evaporation front (given as T = 373 K) and the devolatilization rate is temperature-dependent (it is usually expressed in an Arrhenius form; see, e.g., Anthony and Howard, 1976). Thus, for the region between the evaporation front and the fuel particle surface, a onedimensional energy balance for an arbitrary time step in pseudo-steady state reads as follows (n = 0, 1, 2 for linear, cylindrical, and spherical coordinates, respectively): 1 ∂ Ê r n l ∂T ˆ – 1 ∂ (r n u r C ) = 0 g g p, g Á ∂r ˜¯ r n ∂r r n ∂r Ë

[11.42]

where the heat conduction towards the particle center (first term) competes with the heat required to heat up the volatiles flowing outwards from the fuel particle (second term). The following boundary conditions apply at the evaporation front and the particle surface, respectively: T˚revap = 373 K

[11.43]

∂ – l ∂T = hef f (T ˚ rsurf – T• ) ∂r– rsurf

[11.44]

The effective heat transfer coefficient from the bed to the fuel particle, heff, can be obtained from Nusselt (Nu) correlations available in the literature (Palchonok, 1998). The time-dependent solution is obtained by moving the evaporation front towards the center of the fuel particle at a velocity that is related to the heat influx and time step chosen. Based on the use of non-dimensional variables for space, x, and temperature, q, Thunman et al. (2004) provided the analytical solution to Eq. [11.42] for ideal fuel particle geometries (see Table 11.2). Note that, despite requiring an iterative procedure to solve the coefficient , this represents a solution with low computational cost for modeling drying and devolatilization. Furthermore, if the heating of devolatilized matter

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Fluidized bed technologies for near-zero emission combustion Table 11.2 Analytical expressions used to solve the one-dimensional temperature profile of a fuel particle during drying and devolatilization (source: Thunman et al., 2004)

x= r rpart q (x) =

a=

q=

[11.45]

T – T• 373 – T•

ab + Bit ((e abG (x) – 1) ab + Bit ((e

abG (xevap )

[11.47]

– 1)

n xevap C p, g (T• – 373)

[11.48]

Hvap

b =–

Bit =

abBit e

abG (xevap )

n xevap (a ab b + Bit (e

abG (xevap )

– 1))

hef efff rpart ar

l plate, n= 0

G(x) cylinder, n = 1 sphere, n = 2

ab Æ 0 q (x) =

[11.46]

[11.49]

[11.50] 1–x

[11.51]

–ln (x)

[11.52]

1–x x

[11.53]

1 + Bit G(x) 1 + Bit G(xevap )

[11.54]

as it flows outwards from the fuel particle is neglected, i.e., if ab Æ 0, a simpler expression (Eq. [11.54]) is derived, which can be solved without any iterations. Figure 11.8 shows a comparison of the experimental data from thermogravimetrical tests and the results of the modeling based on the expressions are given in Table 11.3. Regarding char combustion modeling, the mass transfer and kinetics can be expressed in analogy with resistances, as illustrated by the resistance scheme in Fig. 11.9, with the corresponding expressions given in Table 11.3. The external mass transfer coefficient, hm, can be calculated through correlations for the Sherwood number (Sh) given in the literature (for a compilation of these correlations for different conditions and particle types, see Palchonok, 1998). Chapter 5 provides further discussion on the Sherwood and Nusselt numbers governing respectively mass and heat transfer between a fuel particle and its surroundings. Correlations for the relatively large fuel particles typically used in FBC yield intrinsic pore areas that are sufficiently large to allow the resistance coupled to the kinetics in the pores to be neglected. It is common to simplify the formulation so that the two resistances coupled to the kinetics at the particle surface and gas diffusion through the pores are combined into a single effective internal resistance, Ωint,

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0.025

Fuel particle mass (g)

0.02

0.015

0.01

0.005

Experimental, Guedea et al. (2012) Modeled, Thunman et al. (2004)

0 0

2

4

6 Time (s)

8

10

12

11.8 Transient curve of mass loss of a bituminous coal particle during drying and devolatilization at 850°C. Experimental data are compared to model results obtained using the expressions listed in Table 11.2. Data sourced from Guedea et al. (2012).

as expressed by Eq. [11.62], and yielding the total resistance expressed in Eq. [11.63]. Thus, k0,eff and Ea,eff are not purely kinetic parameters but include pore characteristics, and they have to be determined for each fuel (Smith, 1978). However, typically, the fuel sizes and temperatures in FBC yield diff Ωext  Ωint, i.e., char combustion is controlled by external mass diffusion to the particle surface. It is only for small fuel particles close to burnout that the internal resistance Ωint becomes dominant. Figure 11.10 compares the experimental data from thermogravimetrical tests to the modeled data obtained with the expressions given in Table 11.3. A critical phenomenon that influences fuel conversion is fragmentation (also called ‘comminution’) of the fuel particle, which represents an increase in the specific area and thereby involves a significant increase in conversion rate due to enhanced heat and mass transfer to the fuel particle. As the fuel particles are reduced in size by the conversion process itself and due to fragmentation, there is an increased likelihood of locating the finer fuel particles higher up in the furnace and, in the case of a CFB, in the return leg (thus increasing heat release in the upper furnace, cyclone return, and external particle cooler). For most fuels, fragmentation is an important process that must be included in the modeling. Therefore, the expressions given above for the combustion should at each step during conversion be applied to the fragmented solids. The characteristics of fragmentation (time, number, and size of fragments) have been reviewed by Chirone et al. (1991), and a sub-model of fragmentation has been proposed by Arena et al. (1991). However, a more common approach to account for fuel fragmentation in

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Table 11.3 Expressions for mass transfer and kinetic resistances relevant to char conversion

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CO ,• ∂mc = LC , O2 2 ∂t Wtot 1

diff Wtot = Wdiff ext +

1 kin n Wki surf

Wdiff ext = hm =

[11.55]

1 hm Assurf

Sh Di , j d part

+

Wdiff por pores

[11.56]

1 ki + Wkin pores ores or

[11.57]

ki Wkin surf =

1 k 0 Asu surf e

[11.58] Wint =



Ea RTsurf

1 k 0,ef efff Asurf e

diff Wtot = Wdiff ext + Wint

E – a ,eff RTsurf

[11.59]

Wdiff = por pores

d part Dpor pore e ,eff Asu surf

[11.60]

ki Wkin = por pores

1 k 0 Apor pores e



Ea RTpores pores

[11.61]

[11.62]

[11.63]

Modeling of fluidized bed combustion processes

Ω kin surf

kin Ω pores

555

Ω diff ext

diff Ω pores

11.9 Scheme for mass transfer and kinetic resistances relevant to char conversion.

a comprehensive model of FBC is to characterize the fragmentation using specific test methods (see Laine, 2008) and to include these experimental patterns in the conversion modeling (Pallarès, 2008; Ratschow, 2009; Myöhänen, 2011). Similar to fragmentation, attrition by collisions with the bed material is a critical phenomenon that must be accounted for in fuel conversion modeling. With attrition-generated char fines burning in the vicinity of the ‘mother’ char particle, attrition can be accounted for by means of an increased combustion rate for the ‘mother’ char particle (obtained from fuel reactivity tests in fluidized bed test reactors; see, e.g., Avedesian and Davidson, 1973) or by including the char fines in the population balance (see Barletta et al., 2003).

11.3.6 Fuel mixing As indicated above, the mixing of fuel (and solids in general) in the bottom regions of FB units is induced and governed by the bubble flow (Lim and

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Fluidized bed technologies for near-zero emission combustion 0.03

Experimental, Guedea et al. (2012) Modeled, Thunman et al. (2004)

Fuel particle mass (g)

0.025 0.02 0.015 0.01 0.005 0 0

20

40

60 80 Time (s)

100

120

140

11.10 Transient curve of mass loss of a bituminous coal particle during char conversion in an oxy-fired environment (40% O2, 60% CO2) at 850°C. Experimental data are compared to the modeling results obtained with the expressions listed in Table 11.3. Data sourced from Guedea et al. (2012).

Agarwal, 1994), and is thus highly convective. However, there is little information in the literature on this bubble-induced fuel mixing. The mixing process is typically modeled by imbedding all of the mixing processes (emulsion drift sinking, bubble wake lifting, and bubble eruption scattering) in an effective lateral dispersion coefficient, Dlat,fuel (Rowe et al., 1965), which describes fuel lateral dispersion (according to Eq. [11.26]) and assumes perfect axial mixing. However, this approach has been shown by Olsson et al. (2012) to be suitable only for FB units with a cross section that is sufficiently large to contain a number of bubble paths large enough to be treated as a continuum. Olsson et al. (2012) summarized the experimental values for Dlat,s relevant for the fuel in FBC units (Table 11.4). It is clear that there is a lack of experimental studies of three-dimensional, large-scale FB units, especially with respect to obtaining data under combustion conditions. To the best of our knowledge, only one such study has been published (Niklasson et al., 2003), which gives a value for the lateral fuel dispersion coefficient of the order of 0.1 m2/s. However, it should be noted that experimental studies on lateral fuel mixing that provide only a dispersion coefficient are not very informative regarding the underlying mechanisms governing the process. In this sense, there is a need for experiments that track the trajectories of fuel particles. To date, such fuel tracking studies have been limited and carried out under cold conditions in either two-dimensional units (Soria-Verdugo et al., 2011) or three-dimensional units (Snieders et al., 1999; Olsson et al., 2012).

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Table 11.4 Overview of experimental studies reported in the literature that provide experimental values for lateral fuel dispersion coefficients (source: Olsson et al., 2012) Ref.

Hot/cold

Bed size (m2)

Tracer type

U/Umf

Dlat,fuel (m2/s)

Niklasson et al., 2002 Chirone et al., 2004 Xiang et al., 1987 Olsson et al., 2012 Schlichthaerle and Werther, 1999 Bellgardt and Werther, 1986 Xiao et al., 1998 Salam et al., 1987 Pallarès et al., 2007 Pallarès and Johnsson, 2006b

Hot Hot Cold Cold Cold Cold Cold Cold Cold Cold

1.4  1.4 f0.37 2.6  1.6 1.44 m2 1.0  0.3 2.0  0.3 2.5  0.15 0.9  0.15 1.2  0.02 0.4  0.02

Wood chip Pine-seed shells Coal Phosphorescent fuel Sublimating CO2 Sublimating CO2 Mung bean Coal Phosphorescent capsule Phosphorescent capsule

13.5 3.8 1.08–1.63 5–7.5 12.8 1.2–4.3 5.3–13.2 2–5 5.8–29.2 3.3–14.5

0.1 0.01–0.1 0.8–12  10–3 0.34–0.94  10–3 0.12 0.7–2.5  10–3 0.009–0.14 0.3–2.2  10–3 0.3–4.24  10–2 0.14–2.06  10–2

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Axial mixing of fuel particles is modeled as for other solid particles (see Section 11.3.2). However, it must be noted that due to the differences in size and density between fuel and bed material particles, the particle interactions become significant and thus, a sub-model to account for these should be applied (such as that proposed by Palchonok et al., 1997). It is important for the initial fuel mixing to determine how the fuel particles move at the fuel inlet, i.e., the ratio of fuel particles dragged down into the bed to the particles entrained upwards with the gas flow. Wischnewski (2008) defined as an input a factor to describe this ratio. However, there is a significant gap in knowledge with respect to the initial fuel particle movements. Modeling fuel particle movement is obviously further complicated by the fact that any modeling of the particle movement has to account for the decreases in size and density experienced by fuel particles during conversion. A study that focuses on validating the modeling of fuel mixing in a large-scale CFB is that of Pallarès and Johnsson (2006a).

11.3.7 Gas combustion Homogeneous reactions (especially combustion) are to a large extent mixing-controlled. While lateral gas mixing can be explicitly included in fluid dynamical models of large-scale FB units (see Section 11.3.2), it is difficult to link axial gas mixing with fluctuations in the gas phase. Instead, axial gas mixing can be taken into account indirectly by slowing down the gas kinetics, as performed by some authors (e.g., Knöbig, 1998). Thus, in such works, the gas kinetics is fitted to match the measured time-averaged gas concentrations. Such ‘effective’ gas kinetics includes both the axial gas mixing and the real kinetics and therefore, depends strongly on the axial mixing pattern in the furnace (which in turn depends on the bed height, fluidization velocity, and nozzle characteristics). This makes this effective gas kinetics case-specific, i.e., the kinetics correlated to one specific case is not entirely suitable for other cases. A few attempts to model the axial gas mixing have been reported. Hamdullahpur and MacKay (1986) presented a model for the heterogeneity of the gas velocity in the splash zone attributable to bubble eruptions, while Fung and Hamdullahpur (1993) applied a similar approach to model combustion in the freeboard of a laboratory-scale BFB unit. Scala and Salatino (2002) included the concept of ghost bubbles as suggested by Pemberton and Davidson (1984) in their modeling of the splash zone of a BFB combustor. Lyngfelt et al. (1996) presented a CFB model validated at large scale which account for the above-described gas flow fluctuations. This was also done by Pallarès and Johnsson (2009) who, in addition, applied transient modeling to describe the time resolved gas concentrations over one bubble cycle.

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11.3.8 Heat transfer Here, the focus is on modeling of the overall distribution of temperature and heat fluxes that can be extracted to the furnace walls and other heat transfer surfaces such as superheaters in furnace panels and external particle coolers, which are of key importance for the design of FBC applications. Earlier studies on heat transfer focused on BFB units and on the heat transfer coefficient for tubes immersed in bubbling beds, for which a number of correlations are available (Botterill et al., 1984 and references therein). In addition, CFD simulations have been carried out to model heat transfer under bubbling conditions (Schmidt and Renz, 1999). In a bubbling bed, particle convection dominates the overall heat transfer. In most CFB boilers, the heat is mainly extracted via the furnace walls and other heat transfer elements in the upper part of the furnace, as well as to heat transfer surfaces in external particle coolers. As for furnace wall heat transfer, both particle convection and radiation are important. In oxy-fuel CFB combustion for CO2 capture, the heat balance differs significantly from air-firing CFB, implying both challenges and new opportunities, since the inlet oxygen concentration (adjustable through the recirculating flue gas flow) can be used as a parameter to control the heat balance (i.e., not limited to 21% O2 as in air firing). With the sparse experimental data generated to date, CFB modeling can be used as a first estimate for allocating heat transfer surfaces under oxy-fuel conditions (Jäntti et al., 2006; Seddighi et al. 2010; Bolea et al., 2012). The key issues in the modeling of fluidized bed heat transfer relevant to FBC are the differences between the one- and three-dimensional descriptions and the descriptions of radiative and particle convective heat transfer (which is linked directly to modeling of the fluid dynamics). Thus, the accuracy with which heat transfer can be modeled depends not only on the heat transfer formulations, but also on the gas–solids flow modeling (especially in the CFB application, where the wall layers govern the convective heat transfer to the furnace walls) and on the combustion modeling (see Fig. 11.2). One-dimensional descriptions (i.e., simple correlations) involve a crucial limitation in that they cannot differentiate between the core region and the wall layer in the freeboard of a CFB unit. There are correlations that relate the overall heat transfer to the furnace walls to the cross-sectional average solids concentration (for a compilation of these correlations, see Breitholtz et al., 2001). However, heat convection to the furnace walls is governed by the properties of the colder and denser wall layer of down-flowing solids at the furnace walls. Thus, the one-dimensional heat transfer correlations of large-scale CFB units rely on the assumption of a proportional relationship between the properties in the core or cross-section averages (used for expression correlation) and those in the wall layer (which typically accounts for most of the heat transfer to the walls). Based on experimental data from

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four large-scale CFB boilers, Basu and Nag (1996) expressed the overall heat transfer to the furnace wall layer of CFB boilers as: h = aCsb

[11.64]

where a = 40 and b = 0.5. Breitholtz et al. (2001) used data from five additional large-scale cases, yielding a = 110 and b = 0.21. The correlation given in Eq. [11.64] is typically based on total heat flux measurements at furnace walls and thus includes the total contribution from convective heat transfer by the gas and solids and radiative heat transfer. Based on the same data, Breitholtz et al. (2001) proposed separate modeling of convective and radiative heat transfer for the bed and the walls, yielding values for the constants in Eq. [11.64] of a = 25 and b = 0.58, which express only the particle convective heat transfer, while the radiative heat transfer is described as: hradd = hrrad

s (Ts2 + Tw2 )(T Ts + Tw ) 1 + 1 –1 es ew

c hrad = 0.86 – 0.14arctan ÊÁ s – 1.6ˆ˜ Ë 2.6 ¯

[11.65]

[11.66]

where the so-called radiation efficiency, hrad, represents the decrease in the radiative heat transfer coefficient in locations with high presence of solids, i.e. with more developed wall layers. In 1.5-dimensional models, the wall layers are modeled separately from the core region, to yield a more realistic description of the heat transfer process. however, this type of formulation cannot resolve either the presence of internal heat-exchanging panels in the freeboard, which is often the case in large furnaces, or local heterogeneities in the wall layers, such as corner effects. Some 1.5-dimensional models for convective heat extraction in CFB boilers have been provided by Basu (1990), Wu et al. (1990) and Mahalingham and Kolar (1991) based on the modeling of wall layer properties through heat and mass exchange with the core region and the inclusion of a gas gap between the solids wall layer and the wall surface. Wirth (1995) expressed the radiative heat transfer coefficient through a Nu number-based correlation. These models are discussed by Hannes (1996), who instead chose to adjust manually the constant heat transfer coefficient in his comprehensive 1.5dimensional FBC model. Finally, three-dimensional models for large-scale units describe heat transfer between and within the core and wall layer regions. These models can resolve local heterogeneities (see, e.g., Ratschow, 2009) by taking into account the effects of fuel and secondary gas injections, as well as internal heat-exchanging panels. Radiative heat transfer has been modeled separately in three-dimensional models as an extra diffusive term in the discretized

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energy equation (Ratschow, 2009; Myöhänen, 2011) and as radiation with the capability for long-distance transfer, by accounting for optical factors and cell absorptivities (Pallarès et al., 2012) through the expressions given by Baskakov and Leckner (1997).

11.3.9 Pollutant emissions – SOx and NOx Formation and control of pollutant emissions are dealt with in Chapter 9, where the main formation and reduction mechanisms are given and discussed. This chapter is limited to a description of how fluidized bed models deal with emissions of sulphur and nitrogen oxides. Works on other pollutant emissions in FB units such as dioxins, furans, soot or submicron particulate matter have so far been eminently experimental and models validated in FB units are still lacking. Sulphur capture by means of feeding a solid sorbent can significantly influence other processes than the sulphur capture process itself. This is especially the case for the fluid dynamics since typical solvent addition in FB units yields a bed material which to a large extent consists of sorbent particles, which have different physical properties from those of fuel ash and makeup material. Also local gas concentrations and temperatures will be influenced by addition of sorbent. The net consumption of O2 and production of CO2 will occur due to sulphur capture, as explained in Chapter 9. Local temperatures will be influenced due to the heats of reaction of sulphur capture mechanisms (see Chapter 9). In order to account for these effects, population balances of the sorbent fraction have to be formulated with respect to the different conversion degrees (carbonation, calcination, and sulphation) and size intervals considered. For each of these classes, SOx models must apply the reaction mechanisms discussed in Chapter 9 (calcination, carbonation, sulphation, direct sulphation, and desulphation) and account for these in the mass and heat balances. The three states (carbonation, calcination, and sulphation) were shown by Scala and Salatino (2003) to have substantially different fragmentation and attrition patterns, i.e. which must be taken into account in the population balances. Having such a complex problem setup in the determination of the sorbent inventory from the sorbent fed to the bed, most SOx emission models in the literature (see, e.g. Adánez et al., 2001; Gungor, 2009b) choose to assume a certain sorbent inventory, typically estimated from bed solids samples, i.e. these models are not fully predictive since they use experimental data as inputs. Results from such models have shown a good agreement with experimental SOx emission data. A similarly good agreement is also shown by comprehensive FB combustion models which include the prediction of the sorbent inventory, such as the one by Myöhänen (2011) which is further discussed in Section 11.3.2, and the model proposed by Montagnaro et al. (2011).

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In contrast to the modeling of SOx emissions, the NOx chemistry is considered not to influence any of the main in-furnace processes; fluid dynamics, formation and reduction of other gas components and the progress of combustion can therefore in a comprehensive modeling be included as a post-process modeling. Experiments have revealed that NOx formation depends strongly on temperature and concentrations of char, CO and O2 (see Chapter 9 and Leckner (1998) for a thorough summary of the literature). Thus, it is obviously important that these parameters are modeled accurately to be able to model NOx in a proper way. For modeling of NOx, CFD tools have been used (Gungor, 2009a; Zhou et al., 2011) and the results have been verified under laboratory-scale reactor conditions. Such calculations often include simplifications such as limitation to two dimensions and an assumed char concentration field. For larger units, semi-empirical modeling has been used. Liu and Gibbs (2002) and Kallio and Keinonen (2009) performed one-dimensional modeling of the NOx emissions in the Chalmers 12 MWth research CFB boiler, with results in reasonable agreement with experimental data. It is not an obvious task to incorporate NOx modeling in comprehensive (3D) modeling of large FBC units. Yet, Myöhänen (2011) has included the NOx reaction mechanism proposed in Vepsäläinen et al. (2009) in such modeling, claiming this to be in better qualitative agreement to experimental data than when using the mechanism given by Tsuo et al. (1995).

11.4

Semi-empirical modeling: comprehensive models

A selected set of sub-models can be combined into a comprehensive process model for FBC combustion by applying an iterative procedure in line with the couplings between fluid dynamics, heat transfer, and chemistry/combustion, as shown schematically in Fig. 11.2. The input data generally required by such comprehensive models can be divided into three categories: ∑

∑ ∑

Geometry. Dimensions of the furnace and other components in the modeled domain (ash classifier(s), elements in the return leg(s)), and locations of heat exchanger surfaces and ports for the feeding of solids (fuel, sorbent, makeup material), and gas injections. Operational conditions. Flow rates, temperatures and compositions of all gas and fuel feedings, pressure drop over the furnace, and steam-side temperature field. Solids properties. Physical properties (PSD, density, sphericity, attrition pattern) of the solids (fuel ash, sorbent, makeup material).

Examples of 1.5-dimensional comprehensive modeling of large-scale FBC have been published by Hannes (1996), Huilin et al. (2000), Costa

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et al. (2001), and Kettunen et al. (2003). Such models entail a much lower computational cost than three-dimensional modeling, which makes them a useful tool for simulating transient responses to load changes in FB boilers and for developing process control strategies. For studying control strategies, the modeling has to be combined with modeling of the water side, as carried out by Costa et al. (2001) for 125-MWe and 250-MWe units and by Kettunen et al. (2003) for a 235-MWe unit. The model of Hannes (1996) was developed in collaboration with the International Energy Agency and includes a wide variety of features, such as modeling of solids attrition, sulphur capture, and NOx emissions, and the model was validated against experimental data from six large-scale FB boilers. Table 11.5 lists the three-dimensional comprehensive models for largescale FBC available in the open literature. Considering the magnitude of the cross-sectional dimensions of commercial FB boilers, three-dimensional modeling is likely to be required to provide a sufficiently detailed description of the in-furnace processes of relevance for design and scale-up. The models listed in Table 11.5 are mainly intended for CFB boilers, although with minor modifications they can also be used to satisfactorily simulate BFB combustion. These models resolve similar energy and mass balances and the differences lie in the phenomena included and in the submodels and empirical coefficients chosen for each phenomenon. The models all have specific strengths and limitations. In brief, the particular strengths of the models in their present versions are that: the TUHH model is validated against the widest variety of large-scale units from different manufacturers; the LUT model includes descriptions of sulphur capture and char gasification reactions; and the CUT model includes a transient description of the solids inventory (bottom-bed flow dynamics) and a radiative heat transfer modeling, Table 11.5 Three-dimensional comprehensive models for FBC available in the open literature Model Years name

Industrial partner

Developer

TUHH 1989–present Stadtwerke Hamburg Duisburg University of Technology

Main references Ratschow (2009) Wischnewski (2008) Luecke et al. (2004) Knoebig et al. (1999)

LUT

1989–present Foster Wheeler

Lappeenranta Myöhänen (2011) University of Myöhänen and Hyppänen (2011) Technology Vepsäläinen et al. (2009) Hyppänen et al. (1991)

CUT

2005–present Metso

Chalmers University of Technology

Pallarès et al. (2012) Palonen et al. (2011 ) Pallarès and Johnsson (2009) Pallarès (2008)

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allowing for heat exchange between non-neighboring cells in the calculation domain. Figures 11.11 to 11.13 exemplify typical output results from the three models listed in Table 11.5. The examples are only meant to be illustrative, but it has elsewhere been shown that the results give reasonable agreement with experimental data (for details, see Wischnewski et al., 2010; Myöhänen et al., 2009; Pallarès et al., 2012). Figure 11.11 shows modeled results from the TUHH model with respect to oxygen concentration at different vertical sections of a coal-fired CFB boiler. As expected, the oxygen concentration reaches maximum values just above the air injections. As seen in Fig. 11.11, penetration and shape of secondary air injection jets play an important role and need to be properly described in order to obtain gas concentration fields in agreement with those observed experimentally. Note that there are significant lateral variations in the oxygen concentration as high up as 10 m above the secondary air injection ports. Figure 11.12 exemplifies LUT model results with the temperature field in a 460 MWe coal-fired CFB boiler. The lowest temperatures lie around 850 °C and are found at the top of the furnace where internal heat extracting surfaces are located, while the highest temperatures, around 890 °C, correspond to combustion enhanced by the secondary air. However, it is worth noting the relatively even temperature distribution observed all over the furnace despite the large size of the unit modeled, which is one of the main features of CFB units. Figure 11.13 gives the extracted heat flux in a CFB boiler co-firing petcoke and biomass as obtained from the CUT model. The left plot (Fig.

x = –1.4 m

y

y x 14

y x

EHE gas

O2

12

Secondary air

10 z (m)

x = 0 m

x = –0.6 m

8

x

Coal Ash

CO2 (mol.–%) Secondary air

20 18 16 14 12 10 8 6 4 2 0

6 Coal + air 4 2 0

11.11 TUHH model – oxygen concentration field in the bottom region of the Duisburg CFB boiler burning coal with a thermal input of 252 MWth (from Wischnewski et al., 2010).

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11.12 LUT model – temperature field for the Łagisza CFB boiler burning bituminous coal with a thermal input of 1020 MWth (from Myöhänen et al., 2009).

11.13(a)) shows the front wall and the right plot (Fig. 11.13(b)) the rear wall, i.e. the cyclone side. The petcoke is fed at the front wall (Fig. 11.13(a)) and the biomass in the rear wall (Fig. 11.13(b)) . The heat flux through the refractory-lined bottom region is in the order of a few kW. Besides that,

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kW 35

30

30

25

25

20

20 z (m)

z (m)

35

15

[W] x105 1.7 1.65 1.6 1.55

15

1.5

10

10

1.45

5

5

1.4

0 5 0 x (m) –5

–8

–4

0 y (m)

4

8

0 –5 0 x (m)

5

8

4

0

–4

–8

1.35

y (m)

11.13 The CUT model – extracted heat flux fields for a CFB boiler burning petcoke and biomass with a thermal input of 340 MWth. The dark areas in the bottom of the furnace indicate refractory lined walls.

the lowest heat flux values are found in the upper region of the wall at the petcoke feed, where temperatures are lower due to the presence of internal heat exchanging surfaces. On the rear wall, the heat flux is higher and is locally enhanced by increased solids down-flow due to the back-flow effects at the two exit ducts. Also, local corner effects leading to enhanced heat flux can be observed. However, similarly to the temperature field, the extracted heat flux presents a rather even distribution. The modeling examples given in Figs 11.11–11.13 illustrate that threedimensional modeling is required since there are significant cross-sectional variations in important parameters such as oxygen concentration, temperature, and heat flux.

11.5

Conclusion

Fluidized bed modeling is an important area for ongoing research and development and can be used for the reliable design, scale-up, and optimization of FBC units. Furthermore, modeling is an important tool for gathering and structuring empirical data for increased understanding of FBC processes

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and can be used to identify critical knowledge gaps and future research needs. This chapter provides an overview of the different types of models used for FBC, and incorporates empirical correlations, macroscopic models, computational fluid dynamics, and comprehensive modeling of fluidized bed boilers. There is of course no sharp division between these groups and other groupings of modeling types are possible. It is expected that fluidized bed modeling will continue to be an important topic in the future, driven not least by the requirements set for FBC use in carbon capture schemes and for systems that involve the burning of difficult fuels.

11.6

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11.7

Appendix: nomenclature

a A A 0 b d C C p D Deq e E a F f g g 0 h h m H 0 H b Hb,settled I k k 0 K m n p R S t tlayer T Ŧ u Ubub u 0 V

decay constant for solids cluster phase [1/m] area [m2] grid area per nozzle [m2] decay constant for solids disperse phase [1/m] diameter [m] concentration [kg/m3] specific heat [J/kg K] dispersion coefficient [m2/s] equivalent diameter [m] restitution coefficient [–] activation energy [J/mol] flow [kg/s] auxiliary function (Eqs [11.22]–[11.24]) gravitational acceleration, 9.81 [m/s2] radial distribution function heat transfer coefficient [W/m2K] mass transfer coefficient [m/s] furnace height [m] dense bed height [m] settled bed height [m] moment of inertia [kg m2] thermal conductivity [kg/m s] pre-exponential factor [m/s] interchange coefficient between phases [1/s] mass [kg] geometrical coefficient (Eq. [11.42]) pressure [Pa] universal gas constant, 8.314 [J/mol K] gas generation [kg/m3s] time [s] wall layer thickness [m] temperature [K] torque [kg m2/s2] velocity [m/s] local single bubble velocity [m/s] fluidization velocity [m/s] volume [m3]

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x,y,z,r w

spatial dimensions [m] angular velocity [rad/s]

11.7.1 Greek letters a b ~ s dbub t e e s e w r h m ϙ G l L x q Q g j f y ∞ W

auxiliary variable (Eq. [11.48]) auxiliary variable (Eq. [11.49]) drag constant [kg/m3s] stefan Boltzmann constant, 5.67∙10–8 [W/m2K4] visible bubble volumetric fraction [–] stress tensor [N/m2] volumetric fraction [–] solids emissivity [–] wall emissivity [–] density [kg/m3] efficiency [–] shear viscosity [Pa s] bulk viscosity [Pa s] auxiliary function (Eqs [11.51])–([11.54]) thermal conductivity [W/m K] mass conversion coefficient [–] dimensionless spatial dimension [–] dimensionless temperature [–] granular temperature [m2/s2] dissipation of granular energy [kg/m3s] generation of granular energy [kg/m3s] sphericity [–] bubble flow fraction in excess gas [–] surrounding environment mass transfer and kinetic resistance [s/m3]

11.7.2 Subscripts b bub clus cycl coll core dc diff disp duct

dense bed bubble solids cluster phase cyclone collisions core region downcomer diffusion solids disperse phase exit duct to cyclone

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eff g int kin lat layer mf p rad return s sp surf t th w

Fluidized bed technologies for near-zero emission combustion

effective gas phase internal kinetic lateral wall layers region minimum fluidization particle radiation return leg solids phase gas species surface terminal throughflow wall

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