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Mixing and reaction in the circulating fluidized bed – A three-dimensional combustor model
Chemical Engineering Science 54 (1999) 2151}2160
Mixing and reaction in the circulating #uidized bed } A three-dimensional combustor model T. Knoebig, K. Luecke, J. Werther* Technical University Hamburg-Harburg, Denickestr. 15, D 21071 Hamburg, Germany
Abstract Horizontal gas and solids mixing processes may play a dominant role in circulating #uidized bed (CFB) reactors with a small height-to-diameter ratio, which is typical for CFB combustors. A semi-empirical approach was chosen to describe the threedimensional combustion of coal in a circulating #uidized bed with a rectangular cross section. Since the combustion process is rather complex, the underlying gas}solid #ow structure was modeled in a simpli"ed semi-empirical way to keep the computational time within reasonable limits. In the upper part of the CFB the #ow domain is divided into two phases, a dilute up-#owing suspension and a dense downward #owing cluster phase. For both phases the mass balances for gas and solids are solved. Since no momentum balances are made up in the model, additional information is needed from measurements of the up and down #owing local solid mass #uxes. In the bottom zone a bubbling #uidized bed is assumed. As an application the combustion chamber of the 12 MW CFB boiler of the Chalmers University of Technology is modeled. The results demonstrate the strong in#uence of the coal feed and the solids return on the spatial distributions of volatiles, char, oxygen and carbon monoxide. Depending on the contents of volatiles and on the reactivity of the char the distributions of reactants and reaction products are far from being uniform over the cross section of the combustion chamber. The model is intended to serve as a basis for future modeling of gaseous emissions. 1999 Elsevier Science Ltd. All rights reserved. Keywords: Mixing and reaction; Circulating #uidized bed; 3D mathematical model; Coal combustion; Volatile release; Char hold-up
1. Introduction Modeling of coal combustion in the circulating #uidized bed (CFB) is rather di$cult. The #uid dynamics of this gas}solid two-phase #ow are very complex and strongly dominated by particle}particle interactions. Furthermore, the numerous homogeneous and heterogeneous catalytic gas-phase reactions and their kinetics for the description of the combustion phenomena and the pollutant formation and destruction are not completely known. Therefore, it is necessary to develop simpli"ed modeling approaches, which can describe both, the gas}solid #ow structure and the combustion process with su$cient accuracy. A three-dimensional model of the gas}solid #ow should consider the non-uniform spatial solid distribution and the internal recirculation of the * Corresponding author. Tel.: 0 49 40 7718 3039; fax: 0 49 040 7718 2678. E-mail address: [email protected] (J. Werther).
particles against their net upward motion inside the riser which is typical of CFB combustors. Combustion chambers of industrial large-scale CFB furnaces have typically cross-sectional areas exceeding 5;5 m and heights above 30 m. Reactants are locally introduced into the combustion chamber, i.e. the coal is fed through several feed points into the bottom section and secondary air is injected through nozzles located on the riser wall several meters above the distributor plate. Since the lateral mixing processes of gas and solids are slow in comparison to the dominating vertical convection and the reaction of the components, the gaseous species and the char particles inside the combustion chamber are not evenly distributed over the lateral cross section. Three-dimensional models describing the #ow behavior of gas and solids in CFB riser are either empirical or based on the fundamental equations of #uid dynamics. Computational #uid dynamic (CFD) models employ the full set of partial di!erential equations that describe the
0009-2509/99/$ } see front matter 1999 Elsevier Science Ltd. All rights reserved. PII: S 0 0 0 9 - 2 5 0 9 ( 9 8 ) 0 0 3 5 9 - 5
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conservation of mass, momentum, energy and chemical species. The grade of complexity of the CFD models is di!erent according to the desired application. However, these models are at present just too complex to serve as a basis for reactor modeling. Furthermore, their computational times are very long due to the unsteady character of the numerous partial di!erential equations, which restricts their application to pure #uid dynamical simulations at present. A semi-empirical model approach, which is based on experimental "ndings and empirical correlations obtained from measurements, provides the possibility to account for the complex #ow patterns inside CFB combustors with comparatively low computational e!ort. This allows an application of this type of model to the complex reaction schemes typical for the combustion process. But even the semi-empirical description of the #ow structure is for three dimensions still at the beginning of its development and such models are therefore relatively scarce in literature. HyppaK nen et al. (1991) reported a three-dimensional CFB combustor model for the design of CFB furnaces. However, this latter model is based to a large extent on measured data and will thus be limited to the database it was developed from. For more predictive semi-empirical three-dimensional models, some general experimental "ndings concerning the gas}solid #ow patterns inside CFB combustors which usually have rectangular cross-sections should be considered. Detailed probe measurements in a laboratory-scale CFB riser with square cross section were performed by Zhou et al. (1995). They presented time-averaged porosity and velocity pro"les on several horizontal planes in the CFB and concluded that just as in CFB risers of circular cross sections there is a dilute region in the core of the square riser where most particles move upwards, and a surrounding annular region, where the particle concentration is high and most particles move downwards. This result is also supported by measurements with "ber optical probes by Wang et al. (1993). They reported the iso-mass-#ux lines to be concentric rectangles. Werdermann (1992) performed measurements of lateral mass #ux pro"les in the cross-section of a large-scale CFB combustor (cross-sectional area 5.1 m;5.1 m). He reported the iso-mass-#ux lines to be concentric rectangles, too. All the above-mentioned authors found that the local #ow variables change signi"cantly in the annular wall layer of the CFB riser only, whereas in the center of the riser almost constant #ow variables were measured. In the present paper a three-dimensional CFB combustor model is suggested which is intended to serve as a basis for future emission modeling. In order to be able to account for the complex kinetics of pollutants formation and destruction the #uid dynamic part of the model is kept comparatively simple by using a semi-empirical
approach for the description of the three-dimensional gas}solid #ow in the CFB.
2. Theory The present CFB combustor model can be divided into three major parts: a submodel of the gas}solid #ow structure, a reaction kinetic model for local combustion and a convection/dispersion model with reaction. The latter formulates the mass balances for the gaseous species and the char at each "nite control volume in the #ow domain. It needs #ow-structure information (e.g. local gas and solids velocities and solid volume concentrations) which are provided by the submodel of the gas}solid #ow. Kinetic information for the reactions is supplied by the reaction kinetic submodel which contains descriptions of devolatilization and char combustion, respectively. Solving the mass balances of the convection/dispersion model results in three-dimensional distributions of the gaseous and solid species. 2.1. 3D Modeling of the yow structure The #ow structure submodel is based on the work by SchoK nfelder et al. (1994). According to the axial solid volume concentration pro"le, the riser is axially divided into four di!erent regions. In the bottom region of the combustion chamber with high solid volume concentrations, a shallow bubbling bed is assumed according to Svensson et al. (1993). The #ow domain is subdivided here into a suspension phase and a bubble phase. Both, the bubble gas and the suspension gas #ow upwards. The bubble rise velocity, the bubble size, the bubble volume fraction and the suspension porosity are calculated by extrapolating the Werther and Wein (1994) bubbling-bed model to the high gas velocities used in the CFB. The height of the bottom bed has to be determined from experimental data. The upper dilute region of the CFB combustion chamber is subdivided into an upward #owing lean suspension (lean phase) and descending clusters (dense phase). Both phases may coexist at any position in the #ow domain, but the volume fraction of the dense phase is higher in the vicinity of the wall. In order to account for gas backmixing, it is assumed that the gas of the dense phase is entrained in the downward direction by the descending clusters. Upper dilute zone and bottom zone are connected by the splash zone, which has the same structure as the upper dilute zone but with higher solid volume concentrations and therefore with higher solids mass #uxes. The solids of the suspension phase are accelerated in the splash zone, until they reach the fully developed zone in the upper part of the riser. Above the dilute region the exit region is modeled as a simple continuous stirred-tank reactor with an in"nitesimal small height.
T. Knoebig et al./Chemical Engineering Science 54 (1999) 2151}2160
2.1.1. The yow structure in the upper dilute zone The model of the gas}solid #ow in the upper dilute zone calculates solid volume concentrations of the phases, gas and solid velocities and volume fractions of the dense phase. For this purpose, solid and gas balances are formulated and solved for each phase. Since the momentum balances are not solved, additional information from measurements is necessary. Following the suggestions by Kruse and Werther (1995), one pair of horizontal pro"les of the up and down #owing solids mass #uxes measured in the combustion chamber with a suction probe is used as input data. However, the Kruse and Werther approach has to be extended to derive a complete picture of the 3D distributions of gas and solids velocities and solids volume concentrations in the upper dilute zone. Bearing in mind Werdermann's (1992) experimental "ndings, some model assumptions for the three-dimensional #ow structure in large-scale industrial plants are now made: (i) The local #ow variables change signi"cantly in the wall region of the riser only. (ii) In the core region of the riser the local #ow variables are constant. (iii) The pro"les of the #ow variables in the wall layer are invariant in the direction parallel to the wall.
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zone and the lower end of the upper dilute zone. The height of the splash zone is iteratively calculated until the #ow variables at the common boundary between the upper dilute zone and the splash zone are equal. 2.2. 3D Model mass balances The convection/dispersion model with reaction formulates the mass balances on a "nite control volume for the gaseous components involved in the combustion process, i.e. O , CO, CO , H O and for the char. This results in a set of nine second-order partial di!erential equations for three dimensions which are solved with a discretization method described by Patankar (1989) to obtain the 3D distributions of the gaseous species and the char. In order to keep the computational e!ort within reasonable limits, no enthalpy balance is included in the model. The cold wall layer in the vicinity of the membrane walls (cf. Werdermann, 1992) is taken into account by considering a lower temperature in the wall layer than in the core of the combustion chamber. The mass balance equations and their supporting correlations are summarized in Table 1.
With these assumptions, the information of one pair of horizontal solid mass #ux pro"les of the up- and down #owing solids in the combustion chamber obtained from suction probe measurements can be extrapolated to a mass-#ux distribution over the whole lateral cross section. The cross-sectional average solid volume concentration which varies with height h can be taken from pressure drop measurements as suggested by Kruse and Werther (1995). Alternatively, the solid volume concentration may be assumed to be invariant with height and can then be estimated with the slip factor criterion suggested by Pugsley and Berruti (1996).
2.2.1. Gas mass balances in the bottom zone Due to the large cross-sectional area of industrial combustion chambers and because of the very shallow bottom bed with a height less than 1 m (Svensson et al., 1993), horizontal gas mixing in the bottom region is neglected. Thus, vertical convection is the dominating transport mechanism for the gas. The bubble phase is assumed to be free from solid particles. The mass exchange coe$cient k between the two phases is calGE culated according to Sit and Grace (1978). Because of the increase of bubble size and velocity, the bubble volume fraction is decreasing with height. This is leading to a convective exchange #ux between the phases which is taken into account by introducing the coe$cient k . @X
2.1.2. The yow structure in the splash zone Basically, the #ow structure in the splash zone is the same as in the upper dilute zone. However, the average solid volume fraction is much higher here and its vertical gradient is signi"cant. The vertical change of the crosssectional average #ow variables in the splash zone is calculated according to the approach suggested by Pugsley and Berruti (1996). The splash zone submodel connects the upper dilute zone and the bottom zone. The particles are accelerated in the splash zone by the upward #owing gas, until they reach the fully developed region in the upper dilute zone. Hence the boundary conditions for the splash zone submodel are given by both the upper end of the bottom
2.2.2. Gas mass balances in the upper dilute and splash zones The control volume in the upper dilute zone of the combustion chamber is divided into a dense and a lean fraction. In contrast to the bottom region, horizontal dispersion is taken into account here. The dispersion coe$cient D describing the lateral dispersion #ux is taken from Kruse et al. (1995). The coe$cient is assumed to be equal in the x- and y-direction, respectively. The vertical gas convection #uxes of the dilute and dense phases have opposite orientations. Since the solid volume concentration in the dense phase is higher than in the lean phase, the char carbon concentration may also be higher in the dense phase. This leads to di!erent reaction rates in both phases and thus to a di!erence in the
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Table 1 Summary of mass balances and supporting correlations No. 1
2
3
4
Equation
Comment
*((1!e )c ) @ G Q !k a(c !c )!k c !(1!e )R Q GE G @ G Q @X G @ @ G Q *h h"0: c "c G @
Balance for species i in suspension phase; boundary condition at gas distributor
*(u!u (1!e )c ) Q @ G @ #k a(c !c )#k 0" c !e R GE G @ G Q @X G @ @ G @ *h h"0: c "c G Q
Balance for species i in bubble phase; boundary condition at gas distributor
0"u
*(u (1!e (h))) @ k (x, y, h)" Q @X *h
Convective exchange coe$cient in bottom zone
*(D(1!f )(1!c ) *c /*x) *(D(1!f )(1!c ) *c /*y) B T J G J B T J G J 0"! ! *x *y *(u (1!f )(1!c ) *c ) *(v c ) *(w c ) B T J G J # J G J # J G J # J *h *x *y
Balance for species i in lean phase; boundary conditions (cN is the local average of the G Q @ concentrations of the bubble and suspension phases at the surface of the bottom bed)
!ka(c !c )#k c !(1!f )R G B G J G J B G J *c *c x"0, ¸ : G J"0, y"0, ¸ : G J"0, h"H : c "cN W *y @X G J G Q @ V *x 5
*(u (h) f (x, y, h)(1!c (h))) B T B k (x, y, h)" B *h
6
*(u f (1!c )c ) T B G B #ka(c !c )!k c !f R 0" B B G B G J G J B G B *h h"H: c "cN G B G
7
*(u (1!f )(1!c )) *(u f (1!c )) *v *w B T J # B B T B # J# J 0" J *h *h *x *y GFFFFFFFHFFFFFFFI /
Convective exchange coe$cient in splash and upper dilute zones Balance for species i in dense phase; boundary conditions (cN is the average G concentration in the upper stirred tank)
Gas balance over an individual control volume
8
* *
*
*
0"Q# # , x"0, ¸ : "0, y"0, ¸ : "0 V *x W *y *x *y
Equation of #ow potential ; boundary conditions
9
c "o c w , c "o c w , c "o (1!e )w A J N T J A A B N T B A A Q N Q A Q
Char concentrations written in terms of char mass fractions
10
* * u c o (1!f )w B A Q 0"D o (1!e ) # w (x, y)!r(w (x, y))! N J T J N ! N Q *x *y A Q A Q H (1!e ) @X @ u c o f w ! N B T B N B A B H (1!e ) @X @ *w x"0, ¸ : A Q"0, V *x
*w y"0, ¸ : A Q"0 W *y
*(D(1!f ) *w /*y) *(D(1!f ) *w /*x) B A B A !c o T J N *y *x *(u (1!f )c w ) *(u f c w ) N J B T J A #o N B B T B A #o N N *h *h *(v w ) *(w w ) N J A #o c N J A !(1!f )R !f R #o c N T J *x N T J *y B A J B A B *w *w x"0, ¸ : A"0, y"0, ¸ : A"0, h"H : w "w V *x W *y @ A A Q
Char balance in bottom zone; boundary conditions; char combustion is denoted by a sink-term r; at both the coal feed and the solids return element additional sources have to be de"ned to account for char entering the combustor
11
0"!c o T J N
Char balance for the lean and the dense phase in the upper dilute and splash zones; boundary conditions
12
*c x"0, ¸ : "0 V *x *c *c c # !r , r " , 0"D ! *x t *y *c y"0, ¸ : "0 W *y
Mass balance of volatilable carbon; boundary conditions; at the coal feed element additional sources have to be de"ned considering the volatiles in the feed
T. Knoebig et al./Chemical Engineering Science 54 (1999) 2151}2160
concentrations of the gaseous species, which causes a mass transfer between the dense and the lean phase. The mass transfer is governed by the product of the mass transfer coe$cient k based on unit mass transfer area and the volume speci"c mass transfer area a between the two phases. A correlation for k ) a proposed by SchoK nfelder et al. (1996) was applied in the model calculations. Since the #ow conditions are changing with height in the upper dilute zone, a lateral convective exchange #ux between the dense and the lean phase occurs. Very similar to the bottom zone this convective exchange #ux is considered in the mass balance by introducing the exchange coe$cient k . The lateral velocities v and w in the mass balance of J J the lean phase also originate from the variation of the #ow parameters with height. In particular, the distribution of the upward gas velocity in the lean phase u over J the cross-sectional area is changing with height such that the pro"le is #attening out (Kruse and Werther, 1995). This change of the velocity distribution together with changes of the other #ow parameters requires the introduction of lateral convective volumetric #uxes in the xand y-direction, respectively, in order to close the gas mass balance on the individual control volume. Since the dense phase is a particulate phase which is dispersed in the lean phase the lateral convective #ux occurs in the lean phase only. Considering the area the #uxes are crossing they can be related to lateral velocities and the gas balance over an individual control volume can be written as in Eq. (7), Table 1. After introducing and solving the equation of the #ow potential , the velocities v and w can be calculated as the derivatives of . J J Between the bottom zone and the splash zone an intermediate gas mass balance is formulated to connect regions with di!erent #ow structures. 2.2.3. Char mass balance in the bottom zone For the char in the shallow bottom bed, complete vertical mixing is assumed, which reduces the system in the bottom region to two dimensions. Char is entering the bottom bed with the feed coal but also from the solid return leg with the recycled solids from the cyclone. The char is distributed over the crosssectional area by horizontal dispersion. The lateral solids dispersion coe$cient D is taken from the correlation by ! Bellgardt and Werther (1986). Originally derived from measurements in #uidized beds operating at low super"cial velocities its application to CFB conditions is certainly an extrapolation. At both the coal feed point and the solids return point no convective #ows are considered. Instead the coal and char, respectively, are assumed to be distributed via dispersion into the combustor. In the case of the solids return element any contribution of the in-#owing ash to the local state of #uidization in the bottom zone has been neglected.
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2.2.4. Char mass balance in the upper dilute and splash zones It is assumed that the char is #owing up- and downwards with the same velocity as the bed material in the lean phase and the dense phase, respectively. Since no information about the char mass transfer between the phases is available, a further assumption is necessary. As a "rst approximation, it is assumed that the char weight fraction w of the bed material is the same in both phases. A The solids dispersion coe$cient is assumed to be the same as for the gas. 2.3. Kinetic model The kinetic model as it is used here considers devolatilization and char combustion in a rather simple way, i.e. neither the coal feed particle distribution nor e!ects of fragmentation and attrition are considered. 2.3.1. The volatile release model Volatiles are entering the combustor with the feed coal particles. They are released while these particles are dispersed in the bed. In agreement with other authors (Adanez et al., 1995; Stenseng et al., 1997) it is assumed that the volatiles are released in the bottom zone of the CFB only. The volatiles are released during the devolatilization time t which may be calculated according to Pillai (1981). Each coal particle which contains at a given time t(t still some volatile matter is a source of volatiles. If we consider an element dx dy H in the bottom zone it @X will contain a certain mass of carbon bound in the form of volatile matter in the coal particles which may be used to de"ne a concentration c of volatilable carbon based on the unit bottom zone volume. The local rate of release of volatilized carbon per unit bottom zone volume is then assumed to be proportional to c . It is assumed that the volatile carbon is immediately upon its release converted to CO, i.e. the sink term r in the volatile release balance corresponds to a source term in the CO mass balance. This is again a simplifying assumption which implies, of course, that su$cient oxygen is locally available for the CO formation. 2.3.2. Char combustion The char combustion rate at each control volume is calculated from (cf. Bellgardt et al., 1987). r "!k M c c . A K ! A A -
(13)
The oxygen consumption caused by char combustion is described by R "!k cc . - K - A -
(14)
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For the CO and CO production by char combustion we have R "2(k !k )c c . (15) !- K ! K - A - (16) "(2k !k )c c . R K ! A - K - !- According to experimental "ndings by Hembach (1991) the ratio k /k is as a very "rst approximation asK - K ! sumed to be constant with a numerical value of 0.8. CO may be further oxidized to CO . The reaction rate for CO oxidation is taken from Bellgardt et al. (1987) who adjusted the rate expression suggested by Howard et al. (1973) to the conditions in a #uidized bed combustor.
3. Results and discussion 3.1. Application of the model to the Chalmers university CFB boiler The model has been used to simulate the geometry and the operating conditions of the 12 MW CFB boiler operated by the Chalmers University of Technology, GoK teborg/Sweden. The combustor which is described in detail elsewhere (e.g. A> mand and Leckner, 1988) has a square cross-sectional area of 1.6;1.6 m and a total height of 13.5 m. Fuel is injected from one side into the bottom part of the furnace. From the opposite side recycled bed material which still contains unburned char is returned into the riser (Fig. 1). The operating conditions were taken from Zhang (1992) with u"6.3 m/s, G "31.9 kg/(m s), oxygen conQ tent in #ue gas 3.5 vol%, combustion temperature 8503C and a total riser pressure drop *p "6000 Pa. The characteristics of the bituminous coal used, i.e. proximate and ultimate analysis were taken from A> mand and Leckner (1994). They found that the carbon content in the bed material at the riser exit was about 1 wt%. In order to demonstrate the e!ects of coal feed and solids return arrangement the present calculations were restricted to the case of single-stage combustion where all the combustion air is entering the combustor through the
Fig. 1. The CFB combustor operated by the Chalmers University of Technology, GoK teborg/Sweden.
gas distributor. The simulation of two-stage combustion which is the standard operating mode for utility boilers requires the additional consideration of the injection of secondary air into the riser the modeling of which is subject of ongoing work. The mass balances of the gaseous species and the char were solved simultaneously using the "nite-volume method. For this purpose the riser was subdivided into 288 000 control volumes: 180 slices in vertical direction, each slice containing 40;40 cells in the horizontal. One solution of the balances in the combustion chamber requires a computational time of approximately 2.5 h on a HP Exemplar S Class (SPP-2000) computer. Since the simulations contain an iterative determination of the mass #ux of recycled char the total calculation time for one operating condition may exceed 12 h. In the present case no information was available about the numerical value of k . However, the char mass K ! fraction at the combustor exit, w , could be calculated A from the information given by A> mand and Leckner (1994) about the measured char content in the bed material at the cyclone entry. The unknown rate constant k was iteratively "tted such that the calculated char K ! mass fraction at the riser exit matched the measured one. A numerical value of k "2.2 m/(kg s) was obtained K ! for the operating temperature of 8503C. Fig. 2 shows the release rate of volatiles and the char concentration distribution in the plane A (cf. Fig. 1) which is located at a height of 0.55 m above the distributor, i.e. at the upper end of the bottom zone. In the left part of this "gure the two-dimensional distribution of carbon released per unit time and per unit reactor volume in the form of volatiles is plotted. According to our simplifying assumption that the carbon in volatiles is immediately converted to CO the 2D distribution of carbon sources from the volatilization process is equivalent to a 2D distribution of CO sources. This calculation has been performed with a devolatilization time
Fig. 2. Release of volatiles and char concentration distribution on plane A, (F"coal feed, R"inlet of solids return line; r min 0.03 kg/(m s), max 0.5 kg/(m s), linear spacing of iso-lines; char carbon min 7.7 kg/m, max 51 kg/m, linear spacing between iso-lines).
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t "10 s. The non-uniformity of the distribution of the volatile release lies just between the two extremes of the instantaneous devolatilization at the feed point which is underlying the &&plume''-model by Park et al. (1980) and the uniform distribution over the riser's cross-sectional area. It should be noted here that the further combustion of the released volatiles depends on the local bed temperature. If the bed has not a homogenous temperature as assumed in the model the calculated gas pro"les may di!er from the reality. In the right part of Fig. 2 the char carbon concentration distribution is plotted. Not unexpectedly, we observe a local maximum at the coal feed point. A second, and much larger maximum exists at the inlet of the bed solids recycle. It is obvious that a lot of char is recycled with the cyclone ash. However, the appearance of the maximum is due to the particular way of the description of the char recycle in the model: the model ignores that a mixture of char and ash is #owing into the combustor at the solids recycle. This will in reality lead to mixing of bed suspension with recycled material details of which are not known at present. In particular, the magnitude of possible horizontal convective #ows is not known. The model assumes a dispersion of the char from the solids recycle point and this leads automatically to the occurrence of the maximum of char concentration. In addition, the amount of recycled char is a!ected by the collection e$ciency of the cyclone. The model assumes in a very
"rst approach a collection e$ciency of 100%. In reality carbon will be lost with the #ue gas lowering further the amount of recycled char and thus the char concentration near the solids return point. Fig. 3 shows the concentration distributions of O and CO, respectively, in the planes A and B, the latter being located at the height of the cyclone inlet at 11 m (cf. Fig. 1). The release and conversion of the volatiles as well as the char combustion lead to a strong oxygen consumption at both, the local feed point and at the inlet of the solids return which is re#ected in the plot of the plane A. Two minima of the oxygen concentration occur as a consequence the location of which is identical to the occurrence of local CO maxima. It is particularly the
Fig. 3. O and CO distributions on plane A (below) and plane B (above) for the reference case, (linear spacing between iso-lines for O , logarithmic spacing for CO; plane A: O min 0.5 vol%, max 10 vol%, CO min 0.94 vol%, max 6 vol%; plane B: O min 0.15 vol%, max 6.6 vol%, CO min 0.018 vol%, max 1.13 vol%).
Fig. 4. O and CO distributions on plane A (below) and plane B (above) for two-fold increase of boiler capacity by doubling the width of the combustor, (plane A: O min 0 vol%, max 14.5 vol%, CO min 0.70 vol%, max 9.7 vol%; plane B: O min 0 vol%, max 11.2 vol%, CO min 0.01 vol%, max 9.44 vol%).
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vicinity of the coal feed point where very large CO values are observed. As is seen from the concentration distributions in the plane B the basic non-uniformity which is created through the pointwise feeding of coal and recycled char remains throughout the riser. The non-uniform CO distribution which reveals the existence of a CO plume which extends from the bottom to the top may be critical with respect to the CO emissions of the boiler. For example, German regulations require the CO emissions to remain below 250 mg/m (day's average, standard conditions, dry basis) which corresponds to 0.020 vol% CO. In the present case at the exit of the riser this limit cannot be matched and one has to rely on a su$cient destruction rate in the cyclone. 3.2. Results of parameter variations The model enables to check the in#uence of operating and geometry parameters on the performance of the combustor. An important question in the design of CFB combustors is the minimum number of feed points which is required to distribute a given coal mass #ow over a given cross-sectional area of the combustion chamber. Fig. 4 presents the results of a simulation where the bed area was doubled by simply extending two side walls by a factor of two. Coal feed rate and air mass #ow were doubled, too, while all other parameters remained unchanged. The result is a strong CO plume which leads to an increase of the averaged CO-concentration at the inlet of the cyclone from 0.032 vol% in the reference case
described above to a value of 0.180 vol%. Obviously, one coal feed point serving 5.12 m of bed area is not enough from the emission viewpoint with the present riser height. In order to oxidize the CO in the plume further a much higher combustion chamber would be required. Fig. 5 shows the results of a similar calculation where only the two other sides of the combustor were extended by a factor of two. Basically the same e!ect as above is observed which leads to a CO concentration at the inlet of the cyclone of 0.217 vol%. In some industrial CFB combustors the coal feed is introduced into the solids return line between the siphon and the riser. The coal and the unburned char in the recycled bed material are then entering the combustor at the same point. As it is demonstrated by the results of the respective calculation depicted in Fig. 6 the added e!ects of the release of volatiles and the combustion of char create a strong plume in the vicinity of the inlet of the solids return line which increases the CO concentration at the cyclone inlet to about 0.419 vol%. Although introducing the feed coal into the solids return line may present operational and construction cost advantages this practice appears not to be advisable from the emissions point of view.
4. Conclusions In the present work a semi-empirical approach was chosen to describe the three-dimensional mixing and
Fig. 5. O and CO distributions on plane A (below) and plane B (above) for two-fold increase of boiler capacity by doubling the length of the combustor, (plane A: O min 0 vol%, max 12.2 vol%, CO min 0.84 vol%, max 10.6 vol%; plane B: O min 0 vol%, max 9.3 vol%, CO min 0.016 vol%, max 10.2 vol%).
T. Knoebig et al./Chemical Engineering Science 54 (1999) 2151}2160
D
D A f B G Q h H H @X k k k GE k K ! Fig. 6. O and CO distributions on plane A (below) and plane B (above) for introduction of the coal feed into the return line, (plane A: O min 0 vol%, max 12.1 vol%, CO min 0.80 vol%, max 9.52 vol%; plane B: O min 0 vol%, max 8.6 vol%, CO min 0.024 vol%, max 10.8 vol%).
combustion of coal in a circulating #uidized bed riser with rectangular cross section. The model enables the e!ects of geometry and operating parameters on the three-dimensional distribution of gaseous and solid species inside the combustion chamber to be examined. The application of the model is illustrated by simulating the 12 MW CFB boiler operated by the Chalmers Univer sity of Technology. The calculations demonstrate the strong e!ect of gas and solids mixing on gaseous emissions of the combustor. The model is intended to serve as a basis for future NO, N O and SO emission modeling. This task is being undertaken within the framework of a project founded by the European Coal and Steel Community (ECSC) by a joint e!ort of the authors' group together with groups from Finland (Prof. Hupa), Sweden (Prof. Leckner), Denmark (Prof. Dam-Johanssen) and Portugal (Dr. Gulyurtlu).
c c A c T c
¸ V ¸ W *p Q r r R t ¹ u u v w w A x y
interfacial mass transfer area based on reactor volume, m/m concentration, kmol/m char concentration, kg/m solid volume concentration, dimensionless concentration of volatilable carbon per unit
reactor volume, kg/m coe$cient of dispersion in the x- and y-directions for gas and solids in upper dilute and splash zones, m/s lateral dispersion coe$cient for solids in the bottom bed, m/s volume fraction of the dense phase, dimensionless external solid mass #ux based on reactor cross-sectional area, kg/m/s height above gas distributor, m total riser height, m height of dense bottom region, m coe$cient of mass transfer between dense and lean phase, m/s coe$cient of convective exchange between phases, 1/s coe$cient of mass transfer between bubble and suspension phase for species i, m/s overall reaction rate constant for char combustion, m/kg/s overall reaction rate constant for oxygen consumption, m/kg/s length of riser in the x-direction, m width of riser in the y-direction, m total pressure drop over riser, Pa source term, Eq. (8), 1/s char consumption rate, Eq. (10), kg/m/s release rate of volatilized carbon, Eq. (12), kg/m/s reaction rate, kmol/m/s time, s temperature, K vertical velocity, m/s super"cial gas velocity, m/s horizontal velocity component (x-direction), m/s horizontal velocity component (y-direction), m/s char mass fraction of bed material, dimensionless coordinate, m coordinate, m
Greek letters e e @
Notation a
k K -
2159
o N
porosity, dimensionless bubble volume fraction in the bottom bed, dimensionless apparent solid density, kg/m #ow potential function, m/s
Indices b bz
bubble phase bottom zone
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c conv d h i in l p s t vol x y
T. Knoebig et al./Chemical Engineering Science 54 (1999) 2151}2160
char convective dense phase in the h direction number of species inlet lean phase particle suspension phase top of riser volatiles in the x direction in the y direction
References Adanez, J., de Diego, L.F., Gayan, P., Armesto, L., & Cabanillas, A. (1995). Modeling of coal combustion in circulating #uidized bed combustors. In: K.J. Heinschel (Ed.), Proceedings of the 13th International Conference on Fluidized Bed Combustion (pp. 305}315). New York: ASME. A> mand, L.-E., & Leckner, B. (1988). Emissions of nitrogen oxide from a circulating #uidized bed boiler } the in#uence of design parameters. In: P. Basu & J.F. Large (Eds.), Circulating -uidized bed technology II (pp. 457}464). Oxford, New York: Pergamon Press. A> mand, L.-E., & Leckner, B. (1994). Reduction of N O in a circulating #uidized-bed combustor. Fuel, 73, 1389}1397. Bellgardt, D., & Werther, J. (1986). A novel method for the investigation of particle mixing in gas-solid systems. Powder ¹echnol., 48, 173}180. Bellgardt, D., Hembach, F., SchoK {ler, M., & Werther, J. (1987). Modeling of large-scale atmospheric #uidized bed combustors. In: J.P. Mustonen (Ed.), Proceedings of the 9th International Conference on Fluidized Bed Combustion (pp. 713}722). New York: ASME. Hembach, F.W. (1991).
Kruse, M., & Werther, J. (1995). 2D gas and solids #ow prediction in circulating #uidized beds based on suction probe and pressure pro"le measurements. Chem. Engng Proc., 34, 185}203. Kruse, M., SchoK nfelder, H., & Werther, J. (1995). A two-dimensional model for gas mixing in the upper dilute zone of a circulating #uidized bed. Can. J. Chem. Engng 73, 620}634. Park, D., Levenspiel, O., & Fitzgerald, T.J. (1980). A comparison of the plume model with currently used models for AFBC. Chem. Engng Sci., 35, 295}301. Patankar, S.V. (1989). Numerical heat transfer and -uid -ow. Washington, New York: Hemisphere. Pillai, K.K. (1981). The in#uence of coal type on devolatilization and combustion in #uidized beds. J. Inst. Energy, 54, 142}150. Pugsley, T.S., & Berruti, F. (1996). A predictive hydrodynamic model for circulating #uidized bed risers. Powder ¹echnol., 89, 57}69. SchoK nfelder, H., Kruse, M., & Werther, J. (1996). A two-dimensional model for circulating #uidized bed reactors. A.I.Ch.E. J., 42, 1857}1888. SchoK nfelder, H., Werther, J., Hinderer, J., & Keil, F.J. (1994). A multistage model for the circulating #uidized bed reactor. A.I.Ch.E. Symp. Ser., 90 (301), 92}104. Sit, S.P., & Grace, J.R. (1978). Interphase mass transfer in an aggregative #uidized bed. Chem. Engng Sci., 33, 1115. Stenseng, M., Lin, W., Johnsson, J.E., & Dam-Johansen, K. (1997). Modeling of devolatilization in circulating #uidized bed combustion. In: F.D.S. Preto, (Ed.), Proceedings of the 14th International Conference on Fluidized Bed Combustion (pp. 117}124). New York: ASME. Svensson, A., Johnsson, F., & Leckner, B. (1993). Fluid dynamics of the bottom bed of circulating #uidized bed boilers. In: L. Rubow (Ed.), Proceedings of the 12th International Conference on Fluidized Bed Combustion (pp. 887}897). New York: ASME. Wang, T., Lin, Z.J., Zhu, C.M., & Liu, D.C. (1993). Particle movement in a square section circulating #uidized bed. In: L.N. Rubow (Ed.), Proceedings of the 12th International Conference on Fluidized Bed Combustion (pp. 1011}1020). New York: ASME. Werdermann, C.C. (1992). Feststo+bewegung und =aK rmeuK bergang in zirkulierenden =irbelschichten von Kohlekraftwerken. Ph.D. thesis, Technical University Hamburg}Harburg. Werther, J., & Wein, J. (1994). Expansion behavior of gas #uidized beds in the turbulent regime. A.I.Ch.E. Symp. Ser., 90 (301), 31}44. Zhang, W. (1992). Particle #ow pattern in circulating #uidized bed boilers. Thesis Lic. Engng, Chalmers University of Technology, GoK teburg/Sweden. Zhou, J., Grace, J.R., Lim, C.J., & Brereton, C.M.H. (1995). Particle velocity pro"les in a circulating #uidized bed riser of square cross section. Chem. Engng Sci., 50 (2), 237}244.
Mixing and reaction in the circulating #uidized bed } A three-dimensional combustor model T. Knoebig, K. Luecke, J. Werther* Technical University Hamburg-Harburg, Denickestr. 15, D 21071 Hamburg, Germany
Abstract Horizontal gas and solids mixing processes may play a dominant role in circulating #uidized bed (CFB) reactors with a small height-to-diameter ratio, which is typical for CFB combustors. A semi-empirical approach was chosen to describe the threedimensional combustion of coal in a circulating #uidized bed with a rectangular cross section. Since the combustion process is rather complex, the underlying gas}solid #ow structure was modeled in a simpli"ed semi-empirical way to keep the computational time within reasonable limits. In the upper part of the CFB the #ow domain is divided into two phases, a dilute up-#owing suspension and a dense downward #owing cluster phase. For both phases the mass balances for gas and solids are solved. Since no momentum balances are made up in the model, additional information is needed from measurements of the up and down #owing local solid mass #uxes. In the bottom zone a bubbling #uidized bed is assumed. As an application the combustion chamber of the 12 MW CFB boiler of the Chalmers University of Technology is modeled. The results demonstrate the strong in#uence of the coal feed and the solids return on the spatial distributions of volatiles, char, oxygen and carbon monoxide. Depending on the contents of volatiles and on the reactivity of the char the distributions of reactants and reaction products are far from being uniform over the cross section of the combustion chamber. The model is intended to serve as a basis for future modeling of gaseous emissions. 1999 Elsevier Science Ltd. All rights reserved. Keywords: Mixing and reaction; Circulating #uidized bed; 3D mathematical model; Coal combustion; Volatile release; Char hold-up
1. Introduction Modeling of coal combustion in the circulating #uidized bed (CFB) is rather di$cult. The #uid dynamics of this gas}solid two-phase #ow are very complex and strongly dominated by particle}particle interactions. Furthermore, the numerous homogeneous and heterogeneous catalytic gas-phase reactions and their kinetics for the description of the combustion phenomena and the pollutant formation and destruction are not completely known. Therefore, it is necessary to develop simpli"ed modeling approaches, which can describe both, the gas}solid #ow structure and the combustion process with su$cient accuracy. A three-dimensional model of the gas}solid #ow should consider the non-uniform spatial solid distribution and the internal recirculation of the * Corresponding author. Tel.: 0 49 40 7718 3039; fax: 0 49 040 7718 2678. E-mail address: [email protected] (J. Werther).
particles against their net upward motion inside the riser which is typical of CFB combustors. Combustion chambers of industrial large-scale CFB furnaces have typically cross-sectional areas exceeding 5;5 m and heights above 30 m. Reactants are locally introduced into the combustion chamber, i.e. the coal is fed through several feed points into the bottom section and secondary air is injected through nozzles located on the riser wall several meters above the distributor plate. Since the lateral mixing processes of gas and solids are slow in comparison to the dominating vertical convection and the reaction of the components, the gaseous species and the char particles inside the combustion chamber are not evenly distributed over the lateral cross section. Three-dimensional models describing the #ow behavior of gas and solids in CFB riser are either empirical or based on the fundamental equations of #uid dynamics. Computational #uid dynamic (CFD) models employ the full set of partial di!erential equations that describe the
0009-2509/99/$ } see front matter 1999 Elsevier Science Ltd. All rights reserved. PII: S 0 0 0 9 - 2 5 0 9 ( 9 8 ) 0 0 3 5 9 - 5
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conservation of mass, momentum, energy and chemical species. The grade of complexity of the CFD models is di!erent according to the desired application. However, these models are at present just too complex to serve as a basis for reactor modeling. Furthermore, their computational times are very long due to the unsteady character of the numerous partial di!erential equations, which restricts their application to pure #uid dynamical simulations at present. A semi-empirical model approach, which is based on experimental "ndings and empirical correlations obtained from measurements, provides the possibility to account for the complex #ow patterns inside CFB combustors with comparatively low computational e!ort. This allows an application of this type of model to the complex reaction schemes typical for the combustion process. But even the semi-empirical description of the #ow structure is for three dimensions still at the beginning of its development and such models are therefore relatively scarce in literature. HyppaK nen et al. (1991) reported a three-dimensional CFB combustor model for the design of CFB furnaces. However, this latter model is based to a large extent on measured data and will thus be limited to the database it was developed from. For more predictive semi-empirical three-dimensional models, some general experimental "ndings concerning the gas}solid #ow patterns inside CFB combustors which usually have rectangular cross-sections should be considered. Detailed probe measurements in a laboratory-scale CFB riser with square cross section were performed by Zhou et al. (1995). They presented time-averaged porosity and velocity pro"les on several horizontal planes in the CFB and concluded that just as in CFB risers of circular cross sections there is a dilute region in the core of the square riser where most particles move upwards, and a surrounding annular region, where the particle concentration is high and most particles move downwards. This result is also supported by measurements with "ber optical probes by Wang et al. (1993). They reported the iso-mass-#ux lines to be concentric rectangles. Werdermann (1992) performed measurements of lateral mass #ux pro"les in the cross-section of a large-scale CFB combustor (cross-sectional area 5.1 m;5.1 m). He reported the iso-mass-#ux lines to be concentric rectangles, too. All the above-mentioned authors found that the local #ow variables change signi"cantly in the annular wall layer of the CFB riser only, whereas in the center of the riser almost constant #ow variables were measured. In the present paper a three-dimensional CFB combustor model is suggested which is intended to serve as a basis for future emission modeling. In order to be able to account for the complex kinetics of pollutants formation and destruction the #uid dynamic part of the model is kept comparatively simple by using a semi-empirical
approach for the description of the three-dimensional gas}solid #ow in the CFB.
2. Theory The present CFB combustor model can be divided into three major parts: a submodel of the gas}solid #ow structure, a reaction kinetic model for local combustion and a convection/dispersion model with reaction. The latter formulates the mass balances for the gaseous species and the char at each "nite control volume in the #ow domain. It needs #ow-structure information (e.g. local gas and solids velocities and solid volume concentrations) which are provided by the submodel of the gas}solid #ow. Kinetic information for the reactions is supplied by the reaction kinetic submodel which contains descriptions of devolatilization and char combustion, respectively. Solving the mass balances of the convection/dispersion model results in three-dimensional distributions of the gaseous and solid species. 2.1. 3D Modeling of the yow structure The #ow structure submodel is based on the work by SchoK nfelder et al. (1994). According to the axial solid volume concentration pro"le, the riser is axially divided into four di!erent regions. In the bottom region of the combustion chamber with high solid volume concentrations, a shallow bubbling bed is assumed according to Svensson et al. (1993). The #ow domain is subdivided here into a suspension phase and a bubble phase. Both, the bubble gas and the suspension gas #ow upwards. The bubble rise velocity, the bubble size, the bubble volume fraction and the suspension porosity are calculated by extrapolating the Werther and Wein (1994) bubbling-bed model to the high gas velocities used in the CFB. The height of the bottom bed has to be determined from experimental data. The upper dilute region of the CFB combustion chamber is subdivided into an upward #owing lean suspension (lean phase) and descending clusters (dense phase). Both phases may coexist at any position in the #ow domain, but the volume fraction of the dense phase is higher in the vicinity of the wall. In order to account for gas backmixing, it is assumed that the gas of the dense phase is entrained in the downward direction by the descending clusters. Upper dilute zone and bottom zone are connected by the splash zone, which has the same structure as the upper dilute zone but with higher solid volume concentrations and therefore with higher solids mass #uxes. The solids of the suspension phase are accelerated in the splash zone, until they reach the fully developed zone in the upper part of the riser. Above the dilute region the exit region is modeled as a simple continuous stirred-tank reactor with an in"nitesimal small height.
T. Knoebig et al./Chemical Engineering Science 54 (1999) 2151}2160
2.1.1. The yow structure in the upper dilute zone The model of the gas}solid #ow in the upper dilute zone calculates solid volume concentrations of the phases, gas and solid velocities and volume fractions of the dense phase. For this purpose, solid and gas balances are formulated and solved for each phase. Since the momentum balances are not solved, additional information from measurements is necessary. Following the suggestions by Kruse and Werther (1995), one pair of horizontal pro"les of the up and down #owing solids mass #uxes measured in the combustion chamber with a suction probe is used as input data. However, the Kruse and Werther approach has to be extended to derive a complete picture of the 3D distributions of gas and solids velocities and solids volume concentrations in the upper dilute zone. Bearing in mind Werdermann's (1992) experimental "ndings, some model assumptions for the three-dimensional #ow structure in large-scale industrial plants are now made: (i) The local #ow variables change signi"cantly in the wall region of the riser only. (ii) In the core region of the riser the local #ow variables are constant. (iii) The pro"les of the #ow variables in the wall layer are invariant in the direction parallel to the wall.
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zone and the lower end of the upper dilute zone. The height of the splash zone is iteratively calculated until the #ow variables at the common boundary between the upper dilute zone and the splash zone are equal. 2.2. 3D Model mass balances The convection/dispersion model with reaction formulates the mass balances on a "nite control volume for the gaseous components involved in the combustion process, i.e. O , CO, CO , H O and for the char. This results in a set of nine second-order partial di!erential equations for three dimensions which are solved with a discretization method described by Patankar (1989) to obtain the 3D distributions of the gaseous species and the char. In order to keep the computational e!ort within reasonable limits, no enthalpy balance is included in the model. The cold wall layer in the vicinity of the membrane walls (cf. Werdermann, 1992) is taken into account by considering a lower temperature in the wall layer than in the core of the combustion chamber. The mass balance equations and their supporting correlations are summarized in Table 1.
With these assumptions, the information of one pair of horizontal solid mass #ux pro"les of the up- and down #owing solids in the combustion chamber obtained from suction probe measurements can be extrapolated to a mass-#ux distribution over the whole lateral cross section. The cross-sectional average solid volume concentration which varies with height h can be taken from pressure drop measurements as suggested by Kruse and Werther (1995). Alternatively, the solid volume concentration may be assumed to be invariant with height and can then be estimated with the slip factor criterion suggested by Pugsley and Berruti (1996).
2.2.1. Gas mass balances in the bottom zone Due to the large cross-sectional area of industrial combustion chambers and because of the very shallow bottom bed with a height less than 1 m (Svensson et al., 1993), horizontal gas mixing in the bottom region is neglected. Thus, vertical convection is the dominating transport mechanism for the gas. The bubble phase is assumed to be free from solid particles. The mass exchange coe$cient k between the two phases is calGE culated according to Sit and Grace (1978). Because of the increase of bubble size and velocity, the bubble volume fraction is decreasing with height. This is leading to a convective exchange #ux between the phases which is taken into account by introducing the coe$cient k . @X
2.1.2. The yow structure in the splash zone Basically, the #ow structure in the splash zone is the same as in the upper dilute zone. However, the average solid volume fraction is much higher here and its vertical gradient is signi"cant. The vertical change of the crosssectional average #ow variables in the splash zone is calculated according to the approach suggested by Pugsley and Berruti (1996). The splash zone submodel connects the upper dilute zone and the bottom zone. The particles are accelerated in the splash zone by the upward #owing gas, until they reach the fully developed region in the upper dilute zone. Hence the boundary conditions for the splash zone submodel are given by both the upper end of the bottom
2.2.2. Gas mass balances in the upper dilute and splash zones The control volume in the upper dilute zone of the combustion chamber is divided into a dense and a lean fraction. In contrast to the bottom region, horizontal dispersion is taken into account here. The dispersion coe$cient D describing the lateral dispersion #ux is taken from Kruse et al. (1995). The coe$cient is assumed to be equal in the x- and y-direction, respectively. The vertical gas convection #uxes of the dilute and dense phases have opposite orientations. Since the solid volume concentration in the dense phase is higher than in the lean phase, the char carbon concentration may also be higher in the dense phase. This leads to di!erent reaction rates in both phases and thus to a di!erence in the
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Table 1 Summary of mass balances and supporting correlations No. 1
2
3
4
Equation
Comment
*((1!e )c ) @ G Q !k a(c !c )!k c !(1!e )R Q GE G @ G Q @X G @ @ G Q *h h"0: c "c G @
Balance for species i in suspension phase; boundary condition at gas distributor
*(u!u (1!e )c ) Q @ G @ #k a(c !c )#k 0" c !e R GE G @ G Q @X G @ @ G @ *h h"0: c "c G Q
Balance for species i in bubble phase; boundary condition at gas distributor
0"u
*(u (1!e (h))) @ k (x, y, h)" Q @X *h
Convective exchange coe$cient in bottom zone
*(D(1!f )(1!c ) *c /*x) *(D(1!f )(1!c ) *c /*y) B T J G J B T J G J 0"! ! *x *y *(u (1!f )(1!c ) *c ) *(v c ) *(w c ) B T J G J # J G J # J G J # J *h *x *y
Balance for species i in lean phase; boundary conditions (cN is the local average of the G Q @ concentrations of the bubble and suspension phases at the surface of the bottom bed)
!ka(c !c )#k c !(1!f )R G B G J G J B G J *c *c x"0, ¸ : G J"0, y"0, ¸ : G J"0, h"H : c "cN W *y @X G J G Q @ V *x 5
*(u (h) f (x, y, h)(1!c (h))) B T B k (x, y, h)" B *h
6
*(u f (1!c )c ) T B G B #ka(c !c )!k c !f R 0" B B G B G J G J B G B *h h"H: c "cN G B G
7
*(u (1!f )(1!c )) *(u f (1!c )) *v *w B T J # B B T B # J# J 0" J *h *h *x *y GFFFFFFFHFFFFFFFI /
Convective exchange coe$cient in splash and upper dilute zones Balance for species i in dense phase; boundary conditions (cN is the average G concentration in the upper stirred tank)
Gas balance over an individual control volume
8
* *
*
*
0"Q# # , x"0, ¸ : "0, y"0, ¸ : "0 V *x W *y *x *y
Equation of #ow potential ; boundary conditions
9
c "o c w , c "o c w , c "o (1!e )w A J N T J A A B N T B A A Q N Q A Q
Char concentrations written in terms of char mass fractions
10
* * u c o (1!f )w B A Q 0"D o (1!e ) # w (x, y)!r(w (x, y))! N J T J N ! N Q *x *y A Q A Q H (1!e ) @X @ u c o f w ! N B T B N B A B H (1!e ) @X @ *w x"0, ¸ : A Q"0, V *x
*w y"0, ¸ : A Q"0 W *y
*(D(1!f ) *w /*y) *(D(1!f ) *w /*x) B A B A !c o T J N *y *x *(u (1!f )c w ) *(u f c w ) N J B T J A #o N B B T B A #o N N *h *h *(v w ) *(w w ) N J A #o c N J A !(1!f )R !f R #o c N T J *x N T J *y B A J B A B *w *w x"0, ¸ : A"0, y"0, ¸ : A"0, h"H : w "w V *x W *y @ A A Q
Char balance in bottom zone; boundary conditions; char combustion is denoted by a sink-term r; at both the coal feed and the solids return element additional sources have to be de"ned to account for char entering the combustor
11
0"!c o T J N
Char balance for the lean and the dense phase in the upper dilute and splash zones; boundary conditions
12
*c x"0, ¸ : "0 V *x *c *c c # !r , r " , 0"D ! *x t *y *c y"0, ¸ : "0 W *y
Mass balance of volatilable carbon; boundary conditions; at the coal feed element additional sources have to be de"ned considering the volatiles in the feed
T. Knoebig et al./Chemical Engineering Science 54 (1999) 2151}2160
concentrations of the gaseous species, which causes a mass transfer between the dense and the lean phase. The mass transfer is governed by the product of the mass transfer coe$cient k based on unit mass transfer area and the volume speci"c mass transfer area a between the two phases. A correlation for k ) a proposed by SchoK nfelder et al. (1996) was applied in the model calculations. Since the #ow conditions are changing with height in the upper dilute zone, a lateral convective exchange #ux between the dense and the lean phase occurs. Very similar to the bottom zone this convective exchange #ux is considered in the mass balance by introducing the exchange coe$cient k . The lateral velocities v and w in the mass balance of J J the lean phase also originate from the variation of the #ow parameters with height. In particular, the distribution of the upward gas velocity in the lean phase u over J the cross-sectional area is changing with height such that the pro"le is #attening out (Kruse and Werther, 1995). This change of the velocity distribution together with changes of the other #ow parameters requires the introduction of lateral convective volumetric #uxes in the xand y-direction, respectively, in order to close the gas mass balance on the individual control volume. Since the dense phase is a particulate phase which is dispersed in the lean phase the lateral convective #ux occurs in the lean phase only. Considering the area the #uxes are crossing they can be related to lateral velocities and the gas balance over an individual control volume can be written as in Eq. (7), Table 1. After introducing and solving the equation of the #ow potential , the velocities v and w can be calculated as the derivatives of . J J Between the bottom zone and the splash zone an intermediate gas mass balance is formulated to connect regions with di!erent #ow structures. 2.2.3. Char mass balance in the bottom zone For the char in the shallow bottom bed, complete vertical mixing is assumed, which reduces the system in the bottom region to two dimensions. Char is entering the bottom bed with the feed coal but also from the solid return leg with the recycled solids from the cyclone. The char is distributed over the crosssectional area by horizontal dispersion. The lateral solids dispersion coe$cient D is taken from the correlation by ! Bellgardt and Werther (1986). Originally derived from measurements in #uidized beds operating at low super"cial velocities its application to CFB conditions is certainly an extrapolation. At both the coal feed point and the solids return point no convective #ows are considered. Instead the coal and char, respectively, are assumed to be distributed via dispersion into the combustor. In the case of the solids return element any contribution of the in-#owing ash to the local state of #uidization in the bottom zone has been neglected.
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2.2.4. Char mass balance in the upper dilute and splash zones It is assumed that the char is #owing up- and downwards with the same velocity as the bed material in the lean phase and the dense phase, respectively. Since no information about the char mass transfer between the phases is available, a further assumption is necessary. As a "rst approximation, it is assumed that the char weight fraction w of the bed material is the same in both phases. A The solids dispersion coe$cient is assumed to be the same as for the gas. 2.3. Kinetic model The kinetic model as it is used here considers devolatilization and char combustion in a rather simple way, i.e. neither the coal feed particle distribution nor e!ects of fragmentation and attrition are considered. 2.3.1. The volatile release model Volatiles are entering the combustor with the feed coal particles. They are released while these particles are dispersed in the bed. In agreement with other authors (Adanez et al., 1995; Stenseng et al., 1997) it is assumed that the volatiles are released in the bottom zone of the CFB only. The volatiles are released during the devolatilization time t which may be calculated according to Pillai (1981). Each coal particle which contains at a given time t(t still some volatile matter is a source of volatiles. If we consider an element dx dy H in the bottom zone it @X will contain a certain mass of carbon bound in the form of volatile matter in the coal particles which may be used to de"ne a concentration c of volatilable carbon based on the unit bottom zone volume. The local rate of release of volatilized carbon per unit bottom zone volume is then assumed to be proportional to c . It is assumed that the volatile carbon is immediately upon its release converted to CO, i.e. the sink term r in the volatile release balance corresponds to a source term in the CO mass balance. This is again a simplifying assumption which implies, of course, that su$cient oxygen is locally available for the CO formation. 2.3.2. Char combustion The char combustion rate at each control volume is calculated from (cf. Bellgardt et al., 1987). r "!k M c c . A K ! A A -
(13)
The oxygen consumption caused by char combustion is described by R "!k cc . - K - A -
(14)
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T. Knoebig et al./Chemical Engineering Science 54 (1999) 2151}2160
For the CO and CO production by char combustion we have R "2(k !k )c c . (15) !- K ! K - A - (16) "(2k !k )c c . R K ! A - K - !- According to experimental "ndings by Hembach (1991) the ratio k /k is as a very "rst approximation asK - K ! sumed to be constant with a numerical value of 0.8. CO may be further oxidized to CO . The reaction rate for CO oxidation is taken from Bellgardt et al. (1987) who adjusted the rate expression suggested by Howard et al. (1973) to the conditions in a #uidized bed combustor.
3. Results and discussion 3.1. Application of the model to the Chalmers university CFB boiler The model has been used to simulate the geometry and the operating conditions of the 12 MW CFB boiler operated by the Chalmers University of Technology, GoK teborg/Sweden. The combustor which is described in detail elsewhere (e.g. A> mand and Leckner, 1988) has a square cross-sectional area of 1.6;1.6 m and a total height of 13.5 m. Fuel is injected from one side into the bottom part of the furnace. From the opposite side recycled bed material which still contains unburned char is returned into the riser (Fig. 1). The operating conditions were taken from Zhang (1992) with u"6.3 m/s, G "31.9 kg/(m s), oxygen conQ tent in #ue gas 3.5 vol%, combustion temperature 8503C and a total riser pressure drop *p "6000 Pa. The characteristics of the bituminous coal used, i.e. proximate and ultimate analysis were taken from A> mand and Leckner (1994). They found that the carbon content in the bed material at the riser exit was about 1 wt%. In order to demonstrate the e!ects of coal feed and solids return arrangement the present calculations were restricted to the case of single-stage combustion where all the combustion air is entering the combustor through the
Fig. 1. The CFB combustor operated by the Chalmers University of Technology, GoK teborg/Sweden.
gas distributor. The simulation of two-stage combustion which is the standard operating mode for utility boilers requires the additional consideration of the injection of secondary air into the riser the modeling of which is subject of ongoing work. The mass balances of the gaseous species and the char were solved simultaneously using the "nite-volume method. For this purpose the riser was subdivided into 288 000 control volumes: 180 slices in vertical direction, each slice containing 40;40 cells in the horizontal. One solution of the balances in the combustion chamber requires a computational time of approximately 2.5 h on a HP Exemplar S Class (SPP-2000) computer. Since the simulations contain an iterative determination of the mass #ux of recycled char the total calculation time for one operating condition may exceed 12 h. In the present case no information was available about the numerical value of k . However, the char mass K ! fraction at the combustor exit, w , could be calculated A from the information given by A> mand and Leckner (1994) about the measured char content in the bed material at the cyclone entry. The unknown rate constant k was iteratively "tted such that the calculated char K ! mass fraction at the riser exit matched the measured one. A numerical value of k "2.2 m/(kg s) was obtained K ! for the operating temperature of 8503C. Fig. 2 shows the release rate of volatiles and the char concentration distribution in the plane A (cf. Fig. 1) which is located at a height of 0.55 m above the distributor, i.e. at the upper end of the bottom zone. In the left part of this "gure the two-dimensional distribution of carbon released per unit time and per unit reactor volume in the form of volatiles is plotted. According to our simplifying assumption that the carbon in volatiles is immediately converted to CO the 2D distribution of carbon sources from the volatilization process is equivalent to a 2D distribution of CO sources. This calculation has been performed with a devolatilization time
Fig. 2. Release of volatiles and char concentration distribution on plane A, (F"coal feed, R"inlet of solids return line; r min 0.03 kg/(m s), max 0.5 kg/(m s), linear spacing of iso-lines; char carbon min 7.7 kg/m, max 51 kg/m, linear spacing between iso-lines).
T. Knoebig et al./Chemical Engineering Science 54 (1999) 2151}2160
2157
t "10 s. The non-uniformity of the distribution of the volatile release lies just between the two extremes of the instantaneous devolatilization at the feed point which is underlying the &&plume''-model by Park et al. (1980) and the uniform distribution over the riser's cross-sectional area. It should be noted here that the further combustion of the released volatiles depends on the local bed temperature. If the bed has not a homogenous temperature as assumed in the model the calculated gas pro"les may di!er from the reality. In the right part of Fig. 2 the char carbon concentration distribution is plotted. Not unexpectedly, we observe a local maximum at the coal feed point. A second, and much larger maximum exists at the inlet of the bed solids recycle. It is obvious that a lot of char is recycled with the cyclone ash. However, the appearance of the maximum is due to the particular way of the description of the char recycle in the model: the model ignores that a mixture of char and ash is #owing into the combustor at the solids recycle. This will in reality lead to mixing of bed suspension with recycled material details of which are not known at present. In particular, the magnitude of possible horizontal convective #ows is not known. The model assumes a dispersion of the char from the solids recycle point and this leads automatically to the occurrence of the maximum of char concentration. In addition, the amount of recycled char is a!ected by the collection e$ciency of the cyclone. The model assumes in a very
"rst approach a collection e$ciency of 100%. In reality carbon will be lost with the #ue gas lowering further the amount of recycled char and thus the char concentration near the solids return point. Fig. 3 shows the concentration distributions of O and CO, respectively, in the planes A and B, the latter being located at the height of the cyclone inlet at 11 m (cf. Fig. 1). The release and conversion of the volatiles as well as the char combustion lead to a strong oxygen consumption at both, the local feed point and at the inlet of the solids return which is re#ected in the plot of the plane A. Two minima of the oxygen concentration occur as a consequence the location of which is identical to the occurrence of local CO maxima. It is particularly the
Fig. 3. O and CO distributions on plane A (below) and plane B (above) for the reference case, (linear spacing between iso-lines for O , logarithmic spacing for CO; plane A: O min 0.5 vol%, max 10 vol%, CO min 0.94 vol%, max 6 vol%; plane B: O min 0.15 vol%, max 6.6 vol%, CO min 0.018 vol%, max 1.13 vol%).
Fig. 4. O and CO distributions on plane A (below) and plane B (above) for two-fold increase of boiler capacity by doubling the width of the combustor, (plane A: O min 0 vol%, max 14.5 vol%, CO min 0.70 vol%, max 9.7 vol%; plane B: O min 0 vol%, max 11.2 vol%, CO min 0.01 vol%, max 9.44 vol%).
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T. Knoebig et al./Chemical Engineering Science 54 (1999) 2151}2160
vicinity of the coal feed point where very large CO values are observed. As is seen from the concentration distributions in the plane B the basic non-uniformity which is created through the pointwise feeding of coal and recycled char remains throughout the riser. The non-uniform CO distribution which reveals the existence of a CO plume which extends from the bottom to the top may be critical with respect to the CO emissions of the boiler. For example, German regulations require the CO emissions to remain below 250 mg/m (day's average, standard conditions, dry basis) which corresponds to 0.020 vol% CO. In the present case at the exit of the riser this limit cannot be matched and one has to rely on a su$cient destruction rate in the cyclone. 3.2. Results of parameter variations The model enables to check the in#uence of operating and geometry parameters on the performance of the combustor. An important question in the design of CFB combustors is the minimum number of feed points which is required to distribute a given coal mass #ow over a given cross-sectional area of the combustion chamber. Fig. 4 presents the results of a simulation where the bed area was doubled by simply extending two side walls by a factor of two. Coal feed rate and air mass #ow were doubled, too, while all other parameters remained unchanged. The result is a strong CO plume which leads to an increase of the averaged CO-concentration at the inlet of the cyclone from 0.032 vol% in the reference case
described above to a value of 0.180 vol%. Obviously, one coal feed point serving 5.12 m of bed area is not enough from the emission viewpoint with the present riser height. In order to oxidize the CO in the plume further a much higher combustion chamber would be required. Fig. 5 shows the results of a similar calculation where only the two other sides of the combustor were extended by a factor of two. Basically the same e!ect as above is observed which leads to a CO concentration at the inlet of the cyclone of 0.217 vol%. In some industrial CFB combustors the coal feed is introduced into the solids return line between the siphon and the riser. The coal and the unburned char in the recycled bed material are then entering the combustor at the same point. As it is demonstrated by the results of the respective calculation depicted in Fig. 6 the added e!ects of the release of volatiles and the combustion of char create a strong plume in the vicinity of the inlet of the solids return line which increases the CO concentration at the cyclone inlet to about 0.419 vol%. Although introducing the feed coal into the solids return line may present operational and construction cost advantages this practice appears not to be advisable from the emissions point of view.
4. Conclusions In the present work a semi-empirical approach was chosen to describe the three-dimensional mixing and
Fig. 5. O and CO distributions on plane A (below) and plane B (above) for two-fold increase of boiler capacity by doubling the length of the combustor, (plane A: O min 0 vol%, max 12.2 vol%, CO min 0.84 vol%, max 10.6 vol%; plane B: O min 0 vol%, max 9.3 vol%, CO min 0.016 vol%, max 10.2 vol%).
T. Knoebig et al./Chemical Engineering Science 54 (1999) 2151}2160
D
D A f B G Q h H H @X k k k GE k K ! Fig. 6. O and CO distributions on plane A (below) and plane B (above) for introduction of the coal feed into the return line, (plane A: O min 0 vol%, max 12.1 vol%, CO min 0.80 vol%, max 9.52 vol%; plane B: O min 0 vol%, max 8.6 vol%, CO min 0.024 vol%, max 10.8 vol%).
combustion of coal in a circulating #uidized bed riser with rectangular cross section. The model enables the e!ects of geometry and operating parameters on the three-dimensional distribution of gaseous and solid species inside the combustion chamber to be examined. The application of the model is illustrated by simulating the 12 MW CFB boiler operated by the Chalmers Univer sity of Technology. The calculations demonstrate the strong e!ect of gas and solids mixing on gaseous emissions of the combustor. The model is intended to serve as a basis for future NO, N O and SO emission modeling. This task is being undertaken within the framework of a project founded by the European Coal and Steel Community (ECSC) by a joint e!ort of the authors' group together with groups from Finland (Prof. Hupa), Sweden (Prof. Leckner), Denmark (Prof. Dam-Johanssen) and Portugal (Dr. Gulyurtlu).
c c A c T c
¸ V ¸ W *p Q r r R t ¹ u u v w w A x y
interfacial mass transfer area based on reactor volume, m/m concentration, kmol/m char concentration, kg/m solid volume concentration, dimensionless concentration of volatilable carbon per unit
reactor volume, kg/m coe$cient of dispersion in the x- and y-directions for gas and solids in upper dilute and splash zones, m/s lateral dispersion coe$cient for solids in the bottom bed, m/s volume fraction of the dense phase, dimensionless external solid mass #ux based on reactor cross-sectional area, kg/m/s height above gas distributor, m total riser height, m height of dense bottom region, m coe$cient of mass transfer between dense and lean phase, m/s coe$cient of convective exchange between phases, 1/s coe$cient of mass transfer between bubble and suspension phase for species i, m/s overall reaction rate constant for char combustion, m/kg/s overall reaction rate constant for oxygen consumption, m/kg/s length of riser in the x-direction, m width of riser in the y-direction, m total pressure drop over riser, Pa source term, Eq. (8), 1/s char consumption rate, Eq. (10), kg/m/s release rate of volatilized carbon, Eq. (12), kg/m/s reaction rate, kmol/m/s time, s temperature, K vertical velocity, m/s super"cial gas velocity, m/s horizontal velocity component (x-direction), m/s horizontal velocity component (y-direction), m/s char mass fraction of bed material, dimensionless coordinate, m coordinate, m
Greek letters e e @
Notation a
k K -
2159
o N
porosity, dimensionless bubble volume fraction in the bottom bed, dimensionless apparent solid density, kg/m #ow potential function, m/s
Indices b bz
bubble phase bottom zone
2160
c conv d h i in l p s t vol x y
T. Knoebig et al./Chemical Engineering Science 54 (1999) 2151}2160
char convective dense phase in the h direction number of species inlet lean phase particle suspension phase top of riser volatiles in the x direction in the y direction
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