The residence time distribution (RTD) of coal particles in a bubbling fluidized bed with continuous feeding is calculated with an extended convection-dispersion model, in which segregation of coal is accounted for. The effect of bed length on the RTD of coal is investigated, and the results are validated by experiments

Liu, Zhihong

Narukawa, Masahiro

Suda, Toshiyuki

Takafuji, Makoto

English

Engineering Conferences International

Refereed ProceedingsThe 13th International Conference onFluidization - New Paradigm in FluidizationEngineeringEngineering Conferences International Year 2010PREDICTION AND VALIDATION OFEFFECT OF BED LENGTH ON RTDOF COAL IN A BUBBLINGFLUIDIZED BEDZhihong Liu∗ Masahiro Narukawa†Makoto Takafuji‡ Toshiyuki Suda∗∗∗IHI Corporation, Yokohama, Japan, shikou ryuu@ihi.co.jp†IHI Corporation, Yokohama, Japan‡IHI Corporation, Yokohama, Japan∗∗IHI Corporation, Yokohama, JapanThis paper is posted at ECI Digital Archives.http://dc.engconfintl.org/fluidization xiii/16    Zhihong LIU, Masahiro NARUKAWA, Makoto Takafuji, Toshiyuki SUDA IHI Corporation  1, Shin-Nakahara-Cho, Isogo-Ku Yokohama 235-8501, Japan T:81-45-759-2867; F:81-45-759-2208; E: shikou_ryuu@ihi.co.jp    ABSTRACT  The residence time distribution (RTD) of coal particles in a bubbling fluidized bed with continuous feeding is calculated with an extended convection-dispersion model, in which segregation of coal is accounted for. The effect of bed length on the RTD of coal is investigated, and the results are validated by experiments.  1. INTRODUCTION  The residence time distribution (RTD) of coal particles has a great impact on the reaction in a bubbling fluidized bed with continuous feeding. It is necessary to predict RTD when a fluidized bed is scaled up for industrial projects. A relatively safe method to enlarge the bed while maintaining performance is to extend the bed length. Experimental and numerical methods can be applied to investigate RTD of the bed. It is very difficult to perform experiments, when the scale is very large. One of the numerical options is the Euler-Euler method (1), which takes the fluid as one phase and regards the particles as another continuous phase. It is difficult to model the interaction between the coal and sand particles correctly in this approach. Another alternative method is the Euler-Lagrange method (2), in which both, sand and coal particles, are treated as individual particles, and each particle is traced. This approach consumes too long computing time for practical applications, even when parallel computers are employed.   In order to investigate the effect of bed length on RTD, a semi-empirical, semi-numerical method is proposed here. First, a phenomenological semi-empirical model, namely an extended convection-dispersion model is developed, which takes segregation of coal into account. Second, the segregation model for binary solids is developed and partial differential equations are deduced. Third, experiments are performed to determine the model parameters in the derived equations, such as segregation index and dispersion coefficient. Then, using the so obtained parameters, predictions of the effect of bed length on RTD are made by solving the partial differential equations numerically. Last, experiments are carried out to validate the predictions.  PREDICTION AND VALIDATION OF EFFECT OF BED LENGTH  ON RTD OF COAL IN A BUBBLING FLUIDIZED BED 1Liu et al.: PREDICTION AND VALIDATION OF EFFECT OF BED LENGTH ON RTD OF COALPublished by ECI Digital Archives, 20102. EXTENDED CONVECTION-DIFFUSION MODEL  In this section a phenomenology model is constructed in which segregation is considered. The conceptual diagram of the model is shown in Fig.1. A one-fluid model is employed here, which considers the mixture of solids (sand and coal) and fluid (air) as one fluid. Continuous feeding of sand is expressed as convection, the effect of mixing due to bubbling is expressed as dispersion (3) (4), and the effect of difference in density and size of coal and sand particles is expressed as segregation.                        2.1 Segregation Model  Segregation occurs when binary solids with different size and density do exist in the fluidized bed (5). In the segregation model proposed here, it is assumed that the dimensionless concentration distribution of coal C(Z)/Caverage keeps invariant, even if the concentration Caverage of coal varies with time.   In order to quantify the segregation effect in the concentration equation, we define two segregation indices St,Sb as follows. For simplicity, we only show the one-dimensional model in vertical direction (z-direction).   St=Ct/C                                                             Sb=Cb/C                                                            where Ct denotes the concentration at top surface of the control volume, Cb the Fluidization flow  coal  ① convection: flow of particles  ②diffusion: mixing by bubble movement inlet outlet ③Segregation Non-uniformity of coal concentration seal Fig.1 Extended Convection-diffusion Model X Z feeding Flow out  sand   (1-1)  (1-2) Continous 2The 13th International Conference on Fluidization - New Paradigm in Fluidization Engineering, Art. 16 [2010]http://dc.engconfintl.org/fluidization_xiii/16concentration at bottom, Caverage the average concentration in the control volume. According to the assumptions stated above, St and Sb are invariant with time.                  The control volume (bold square) for concentration equation is shown in Fig.2 for upward flow (W>0). In this case, the concentration at surface S is StC(Z-⊿Z), the concentration at surface N is StC(Z), so concentration equation can be deduced as    That is, for upward flow we obtain    Similarly, the concentration equation for downward flow (W≤0) becomes    Note, that in the above equations the convection velocity (second term in equation) is StW when the particles move upwards, but SbW when downwards. One of St or Sb is larger than unity and the other smaller. Hence, the segregation phenomenon is described quantitatively.  2.2 Conservation Equations  Conservation equations can be written as:  Continuity equation      0=∂∂+∂∂zwxuZZCADWAZCSZZWAZZCStCZA ztt ∆∂∂+−∆−∆−=∂∂∆2)()()( ρρρρ22ZCDZCWStCzt ∂∂=∂∂+∂∂22ZCDZCWStCzb ∂∂=∂∂+∂∂   Fig.2 Segregation Model ⊿ZZ－⊿Z●●C(Z)StC(Z) WＷ(Z －⊿Z)ZC(Z －⊿Z)StC(Z－⊿Z)Surface S Surface N  (2)  (3-1)  (3-2)  (4-1) 3Liu et al.: PREDICTION AND VALIDATION OF EFFECT OF BED LENGTH ON RTD OF COALPublished by ECI Digital Archives, 2010Momentum equations         Concentration equation     where )0,max()0,max( wSwSwS bt −+=   Dx, Dz are the horizontal and vertical dispersion coefficients of coal, respectively; μs is the viscosity, given by (5)          where dp, ρp are diameter and density of sand, respectively. εis the void fraction of sand (coal may be neglected here) and  εmin is the void fraction when the sand is closely packed (quiescent bed). εcan be determined when the pressure gradient dp/dz is measured.   Segregation indices Sb and St as well as dispersion coefficients Dx and Dz are to be determined in experiments.  3. EXPERIMENT AND DETERMINATION OF PARAMETERS  3.1 Experimental Conditions  Table1: Operating Conditions     *) Umf_sand denotes minimum fluidization velocity of sand.   221xuxpzuwxuu s∂∂+∂∂−=∂∂+∂∂ρµρ)()(zCDzxCDxzCwSxCutCzx ∂∂∂∂+∂∂∂∂=∂∂+∂∂+∂∂221zwgzpzwwxwu s∂∂+−∂∂−=∂∂+∂∂ρµρ (4-2)  (4-3)  (4-4)  (4-5) 1)21(3112.87)21(3101.019.416401.0657minminminminminminmin2<≤+−−+<<+−−++<<=εεεεεεεεεεεεεερµppsd (5) 4The 13th International Conference on Fluidization - New Paradigm in Fluidization Engineering, Art. 16 [2010]http://dc.engconfintl.org/fluidization_xiii/16A quasi two-dimensional bubbling fluidized bed is used in the experiments (refer to Fig1.) The bed material is sand, and tracer is coal. A sintered plate is used as distributor for the fluidizing flow. Experiments are carried out under atmospheric pressure at room temperature. Further operation conditions are listed in Table1.  3.2 Segregation Experiment                   In order to determine the segregation indices St and Sb, we measure the concentration distribution of coal along the vertical direction. Under fixed superficial velocity (0.322m/s), a certain amount of coal (about 2%) is injected into the bed (no continuous feeding). After a certain time long enough to obtain steady conditions, the fluidized bed is quickly shut-down (superficial velocity reduced to zero) in a very short time. Then, samples are taken from the bed, layer by layer with a vacuum cleaner. Coal and sand are separated by a sieve. In this way the coal concentration at each layer is measured. Fig.3 shows a typical result of the coal distribution. We can see that the concentration is higher in the higher part of the bed. From this distribution, the segregation indices St and Sb can be determined.    3.3 Measurement Of RTD And Determination of Diffusion Coefficients  In order to determine the dispersion coefficients Dx and Dz, we measure the residence time distribution (RTD) of coal in a fluidized bed. Sand is fed continuously into the bed at the inlet at a certain rate. For steady conditions, sand will leave the bed at the outlet at the same rate. For the RTD measurements, pulse experiments have been performed: coal (2% weight of bed material) is injected into bed at a very short time (less than 1% of plug-flow timeτ). At the outlet, the amount of coal exiting the bed is sampled at fixed time intervals. By measuring the weights of exited coal and sand for each sample, the RTD function (E-curve) can be obtained.  00.20.40.60.811.20.6 0.7 0.8 0.9 1 1.1 1.2Concentration/Average Concentration  [-]Z [m]Fig.3 Measurement of Coal Segregation in Sand  5Liu et al.: PREDICTION AND VALIDATION OF EFFECT OF BED LENGTH ON RTD OF COALPublished by ECI Digital Archives, 2010             The flow in the bed has been computed by solving equations (4-1) ~ (4-3). The result for a bed length of 1m is shown in Fig.4(a). By solution of equation (4-4), RTD can be calculated, if St,Sb,Dx and Dz are given. By curve fitting, we can fix the dispersion coefficients Dx and Dz. Fig. 5 shows the RTD for the 1m bed.                  The normalized residence time distribution function E is defined as the ratio of exited coal per unit dimensionless time to total injected coal. In the figure, τdenotes plug-flow time (τ= Wt/Q), where Wt [kg] is the total weight of particles present in the bed at a certain time, and Q [kg/s] is the rate of sand supply.  4. PREDICTION AND VERIFICATION  4.1 Prediction the Effect of Bed Length Assuming that the dispersion coefficients and the segregation indices are constant, if only the length of bed is extended, predictions for RTD of coal particles for various bed lengths can be made by solving equations (4). RTD functions have been Fig.5 Determine Diffusion Coefficients by Curve Fitting (L=1m)  00.20.40.60.811.20 0.5 1 1.5 2 2.5dimensionless time t/τ [-]E [-]Exp.(L=1m)Cal.(L=1m)(a)  L=1m (b)  L=3m (c)  L=6m (d)  L=18m Fig.4 Flow in Beds of Various Lengths (Color by Solid Particle Velocity) 6The 13th International Conference on Fluidization - New Paradigm in Fluidization Engineering, Art. 16 [2010]http://dc.engconfintl.org/fluidization_xiii/16calculated for 3m, 9m and 18m long beds. The flow fields for each bed length is shown in Fig.4; RTDs for various bed length are presented in Fig. 6(a)                  4.2 Validation by Experiment    A validation experiment has been performed for a 3m long bed. With exception of bed length, all other conditions are the same as for the 1m bed. The plug flow time τ is also kept the same. The comparison between calculation and experiment (Fig.7) shows good agreement for RTD.                   5. DISCUSSIONS  We compare predictions of a two-dimensional model with segregation (2DS) with a one-dimensional model without segregation (1DN). For horizontal (x-direction) 00.20.40.60.811.20 0.5 1 1.5 2 2.5dimensionless time t/τ [-]E [-]Exp.(L=3m)Cal.(L=3m)Fig.7  Comparison of Experiment and Prediction (L=3m)  Fig.6 Prediction of The Effect of Bed Length On RTD 00.511.520 0.5 1 1.5 2 2.5dimensionless time t/τ [-]E [-]Cal.(L=1m)Cal.(L=3m)Cal.(L=9m)Cal.(L=18m)(a) 2D with segregation (2DS) (b) 1D without segregation (1DN) 0123456780 0.5 1 1.5 2 2.5dimensionless time t/τ [-]E [-]Equ.6 (L=1m)Equ.6 (L=3m)Equ.6 (L=9m)Equ.6 (L=18m)7Liu et al.: PREDICTION AND VALIDATION OF EFFECT OF BED LENGTH ON RTD OF COALPublished by ECI Digital Archives, 2010one-dimensional flow, the normalized RTD function E is given by (6)     This solution is plotted for various bed lengths in Fig.6 (b). We can see that the predictions for 2DS and 1DN are much different. The peak of 1DN is higher and appears later. Eq.(6) cannot predict RDT of coal correctly for the beds considered here. For 1DN, we can see that the peak of RTD curve becomes higher, and the initial exiting time delays to later times, when the bed length becomes longer (Fig.6(b)). This is caused by the dimensionless dispersion coefficient Dx/uL, which becomes smaller when bed length is longer. The same trend can be found in 2DS. However, the 1m long bed is an exception: the peak of RTD is higher than that of the 3m long bed. With recourse to Fig.4 it can be assumed that the different behavior of the short bed is caused by the different flow pattern.  6. CONCLUSIONS  We summarize our results as follows. 1) Segregation is accounted for in the extended convection-dispersion model. We measured necessary parameters for this model. Predictions on the effect of bed length on the residence time distribution of coal in a bubbling fluidized bed can be made by the model presented here. The predictions have been validated by experiments. It has been shown, that the one-dimensional model cannot give correct predictions for the beds considered here.  2) When the bed length becomes longer, the initial exiting time of coal becomes later, and the peak of RTD curve becomes higher and are delayed. It has been shown, that for similar flow patterns, the RTDs also look similar.   REFERENCE  [1] S.Rodríguez-Rojo, M.J.Cocero, J. of Supercritical Fluids 50 p.54 (2009)  [2] A.D. Renzo, F.P. Maio, R.G.B. Formisani, Powder Technology 184 p.214 (2008) [3]Y. Zhang, C. Lu, M. Shi, Chemical Engineering Research and Design 87 p.1400 (2009)  [4] N. Kobayashi, R. Yamazaki, S. Mori, Powder Technology 113 327 (2000) [5]H. Lu Y. Zhao, J. Ding, D. Gidaspow, W. Li, Chemical Engineering Science 62 p.301 (2007) [6] “Fluidization”, p. 261, Academic Press (1971) ])/)(/(4)/1(exp[)/)(/(412τττπ tuLDttuLDExx−−=  (6) 8The 13th International Conference on Fluidization - New Paradigm in Fluidization Engineering, Art. 16 [2010]http://dc.engconfintl.org/fluidization_xiii/16

PREDICTION AND VALIDATION OF EFFECT OF BED LENGTH ON RTD OF COAL IN A BUBBLING FLUIDIZED BED

https://dc.engconfintl.org/cgi/viewcontent.cgi?article=1008&amp;context=fluidization_xiii

PREDICTION AND VALIDATION OF EFFECT OF BED LENGTH ON RTD OF COAL IN A BUBBLING FLUIDIZED BED

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