- Email: [email protected]
Pitfalls in gas sampling from fluidized beds
Chemical Engineering Science 64 (2009) 2522 -- 2524
Contents lists available at ScienceDirect
Chemical Engineering Science journal homepage: w w w . e l s e v i e r . c o m / l o c a t e / c e s
Shorter Communication
Pitfalls in gas sampling from fluidized beds John Grace a,∗ , Hsiaotao Bi a , Yongmin Zhang b a b
Department of Chemical and Biological Engineering, University of British Columbia, 2360 East Mall, Vancouver, Canada V6T 1Z3 State Key Laboratory of Heavy Oil Processing, China University of Petroleum, Beijing, 102249, China
A R T I C L E
I N F O
Article history: Received 29 September 2008 Received in revised form 29 January 2009 Accepted 11 February 2009 Available online 20 February 2009
A B S T R A C T
It is shown that gas sampling from fluidized beds can provide misleading information due to hydrodynamic factors, biased sampling from the dense phase and radial gradients. Caution is needed to avoid these problems and in the interpretation of gas-sampling data. © 2009 Elsevier Ltd. All rights reserved.
Keywords: Sampling Fluidization Dispersion Chemical reactors Multiphase flow Multiphase reactors
1. Introduction
2. Pitfall #1: bubble-induced pressure fluctuations
Gas-fluidized beds experience significant axial and lateral dispersion, affecting the conversion and selectivity of fluidized bed chemical reactors. Their hydrodynamics are subject to complex two-phase behavior and several flow regimes. Reactor modeling requires recognition of the two-phase nature of fluidized beds. Models also require experimental confirmation, preferably by measuring concentrations within the individual phases (Chavarie and Grace, 1975; Atkinson and Clark, 1988). It is less useful, but better than measuring concentrations only at the exit, to perform in-bed gas sampling along the height of the column. Sampling is also required when measuring gas mixing in fluidized beds. Efforts have been made to sample gas in large-scale industrial systems (e.g. Cooper and Ljungstrom, 1988; Hansen et al., 1995; Hartge et al., 2005), e.g. to better understand generation of pollutants.x The two-phase nature of fluidized beds results in significant pitfalls when interpreting gas-sampling data which can cause significant errors. These issues have gone largely unrecognized. For simplicity and because this is where the challenges are greatest, we focus on the bubbling flow regime, although similar considerations apply in varying degrees to the other flow regimes (especially slugging and fast fluidization).
Local pressures recorded in gas-fluidized beds show substantial fluctuations. Among the various causes (Bi, 2007) are bubbles: As bubbles approach, the pressure rises, reaching peaks when their noses reach the measurement level, then falling to a minimum at the back before recovering in the wake (Davidson and Harrison, 1963). The overall amplitude of the bubble-induced pressure fluctuations is of order p (1 − mf )Ub2 . A gas-sampling port within a bubbling bed experiences similar pressure fluctuations as bubbles pass. If the pressure drop through the sampling line and analysis instrumentation is small relative to the amplitude of these fluctuations, the sampling flowrate will vary significantly with time, with more gas sampled from near the front of the bubble and less from the back. Thus the sampling flux will be skewed disproportionately to the nose region, causing the sampling to be biased. Overall, the time-mean concentration acts as if the sampling was carried out from below the actual sampling level. The extent of the bias, in addition to depending on the pressure drop through the sampling tubing and instrumentation, depends on the vertical length and velocity of the bubbles. To avoid sampling errors associated with in-bed pressurefluctuations, the pressure drop through the sampling system should be much larger than the amplitude of the pressure fluctuations. This is readily achieved in pressurized or deep beds, but shallow atmospheric-pressure beds will almost certainly require a vacuum pump at the exit of the sampling lines, requiring careful attention to avoid leakage which could dilute the sampled gas and cause further errors.
∗ Corresponding author. Tel.: +1 604 822 3121. E-mail address: [email protected] (J. Grace). 0009-2509/$ - see front matter © 2009 Elsevier Ltd. All rights reserved. doi:10.1016/j.ces.2009.02.012
J. Grace et al. / Chemical Engineering Science 64 (2009) 2522 -- 2524
3. Pitfall #2: two-phase flow averaging Consider a bubbling fluidized bed operating at statistically steady state with reactant A concentrations at height z of cAb (z) and cAd (z) in the bubble and dense phases, respectively. Constant flow sampling at that height will give a time-mean concentration of c¯ Asample (z) = b (z) × cAb (z) + [1 − b (z)] × cAd (z)
(1)
where b (z) is the time-mean fraction of bed volume occupied by the bubble phase. The time-mean concentration based on flow through the two phases at that level should be c¯ Aflow (z) = {Qb (z) × cAb (z) + Qd (z) × cAd (z)}/Q
(2)
where Q is the total gas volumetric flow, whereas Qb (z) and Qd (z) represent the flows associated with the bubble and dense phases, respectively. Since b (z) is likely to be ∼0.1–0.4, the average measured concentration from Eq. (1) is weighted heavily to the dense phase concentration. On the other hand, since the flow passes predominantly through the bubble phase, Eq. (2) shows that the actual (flow) mean concentration should be heavily weighted towards cAb (z). Hence there is significant error in sampling when the concentrations in the two phases, cAb (z) and cAd (z), differ appreciably. This difference between the two means can be large as illustrated by comparing the sampled time-mean and flow-average concentrations for an illustrative case. To make this comparison, we could utilize various fluidized bed reactor models. For simplicity, we consider an irreversible constant-volume first-order reaction and the bubbling bed model summarized by Grace (1986). All of the gas is assumed to pass through the bubble phase, the dense phase acting as a stagnant zone, but nevertheless contributing greatly to reaction due to interphase mass transfer. Radial gradients and temporal fluctuations are ignored. With these assumptions, steady state dimensionless mole balances on the two phases yield: Bubble phase : Dense phase :
dCAb + X(CAb − CAd ) + k∗1 b CAb = 0 dZ X(CAd − CAb ) + k∗1 b CAd = 0
(3) (4)
where CAb = cAb /cAo ; CAd = cAd /cAo ; cAo is the inlet concentration of reactant A, and Z the dimensionless vertical coordinate = z/H with H the expanded bed height. X and k∗1 are a dimensionless interphase mass transfer and rate constant, respectively, defined by X=
km ab b H , U
k∗1 =
k1 H U
(5)
b is the fraction of bed volume occupied by bubble-phase solids ≈ 0.001b –0.01b , d the fraction of bed volume occupied by dense phase solids ≈ (1 − b )(1 − mf ), km an interphase mass transfer coefficient, ab the bubble surface area per unit volume, b the fraction of bed volume occupied by bubbles, mf the bed voidage at minimum fluidization, k1 the first order reaction rate constant and U the superficial gas velocity. With boundary condition CAb = 1 at Z = 0, Eqs. (3) and (4) give
−k∗1 [X(b + d ) + k∗1 b d ]Z X + k∗1 d CAb X CAd = X + k∗1 d
CAb = exp
and (6)
For very slow reactions (k∗1 → 0) or very large interphase mass transfer (X → ∞), the concentrations of the two phases are nearly equal at the same level, nullifying the difference between the mean concentrations from Eqs. (1) and (2). However, consider an illustrative case with realistic values and rate-limiting interphase mass transfer. Let mf =0.5; b =0.2; d =0.4; b =0.001; X=1.0; and k∗1 =10.
2523
At Z = 0.1, substitution of these values into Eq. (6) gives CAb = 0.922, whereas CAd = 0.184. Steady sampling at this height would then give (from Eq. (1)) a time-mean concentration of 0.332cAo , whereas the true (flow-average) concentration, given the stagnant flow in the dense phase, would equal the bubble-phase concentration, 0.922cAo . This difference is substantial, with the sampled gas concentration only 36% of the flow-average value. Failure to recognize errors associated with sampling will lead to erroneous conclusions regarding the progress of reactions along the reactor and the merits of reactor models. This effect explains the finding (Askins et al., 1951) that measured in-bed oxygen concentrations in a commercial FCC regenerator were consistently much lower than in the freeboard. Interpretation of sampling data requires care and caution to avoid misinterpretation. We could find only a few other instances in the literature (Gilliland and Mason, 1952; Fontaine and Harriott, 1972; Cooper and Ljungstrom, 1988; van der Vaart, 1992) where this bias resulting from over-representation of the dense phase has been recognized. Similar errors occur when withdrawing gas samples in determining axial gas mixing in fluidized beds. For example, gas samples taken upstream of a steady-state tracer injector, predominantly come from the dense phase, where the concentration is likely to be significantly higher than in the bubble phase, leading to overestimation of gas backmixing. Sampling errors of this nature are likely one cause of the wide scatter of gas axial dispersion coefficients reported in the literature (van Deemter, 1980). In order to compensate for this problem, sampling data should be interpreted with the aid of a two-phase model appropriate to the flow regime which is present in the bed.
4. Pitfall #3: hydrodynamic interference Gas sampling lines need a screen or filter at their entrances to prevent ingress of particles. Excessive withdrawal of gas through a sampling port can cause local defluidization or build-up of stagnant solids, with the resulting lump of solids impeding the movement of particles. To minimize flow disruption, the average velocity along the sampling line should be small, preferably ∼Umf /mf . However, for typical fluidized bed catalyst particles, the resulting velocities will then be only millimetres/second, causing long delay times. Moreover, such velocities, coupled with small sampling-tube diameters, give such low Reynolds numbers that the sampling tube flow will be laminar, causing Taylor dispersion to distort transient signals. If sampling tubes intrude into the bed, their presence can also interfere with the flow, e.g. causing bubble splitting. Non-intrusive measurement techniques such as NMR species mapping, can overcome this problem. Ports flush with the vessel wall also avoid the problem. However, sampling from the wall region leads to challenges associated with radial gradients, as outlined in the next section.
5. Pitfall #4: neglect of radial gradients Most fluidized-bed reactor and dispersion models assume one-dimensional flow, ignoring radial gradients of concentration, voidage and velocity, despite considerable evidence that, for example, voidages are considerably greater in the interior than near the outer walls. Since gas samples are usually withdrawn from the walls (as suggested above), measured concentrations are atypical of cross-sectional averages at the given level. For example, solids downward flow occurs predominantly along the walls, inducing gas backmixing in this region. Taylor dispersion associated with non-uniform gas velocity profiles may also cause axial mixing. Interpretation in terms of a one-dimensional axial model is likely to inadequately represent the actual mechanisms of mixing, which are dominated by macroscopic phenomena such as gulf-streaming (Merry and Davidson, 1973). Given these circumstances, two- or
2524
J. Grace et al. / Chemical Engineering Science 64 (2009) 2522 -- 2524
three-dimensional dispersion mixing models are needed to provide a proper interpretation of the mixing phenomena. 6. Pitfall #5: adsorption and trapping Sampling errors can also occur if a gas species adsorbs on the particles. The species in question then travels in a different manner from non-adsorbing species. The consequences have been recognized (e.g. Nguyen and Potter, 1974; Bohle and van Swaaij, 1978; Krambeck et al., 1987) and are not discussed here. Note, however, that similar considerations apply to non-adsorbing species with nonporous particles. In such cases, resistance to internal diffusion will cause delays in gas species entering and leaving the particles. As a result, measured gas mixing and local concentrations differ according to whether the particles are porous or non-porous, the extent of the difference depending on the internal porosity and the effective diffusivity of the gas species of interest. 7. Conclusions Fluidized-bed reaction and mixing studies often require gas concentration measurements to test models, understand behavior, and derive mixing coefficients. However, the two-phase nature of gasfluidized beds and their radial gradients can cause substantial errors in gas sampling. It is critical to minimize the pitfalls identified in this paper and to interpret data derived from in-bed gas samples with great care. Failure to do so has doubtless contributed to wide variations in literature data and may cause misinterpretation of the relative merits of alternative reactor and dispersion models. Some suggestions for overcoming the pitfalls are provided in this paper. Acknowledgement The authors are grateful to the Chinese University of Petroleum and the Natural Sciences and Engineering Research Council of Cananda for financial support
References Askins, J.W., Hinds, G.P., Kunreuther, F., 1951. Fluid catalyst-gas mixing in commercial equipment. Chem. Eng. Prog. 47, 401–404. Atkinson, C.M., Clark, N.N., 1988. Gas sampling form fluidized beds: a novel probe system. Powder Technol. 54, 59–70. Bi, H.T., 2007. A critical review of the complex pressure fluctuation phenomenon in gas–solids fluidized beds. Chem. Eng. Sci. 62, 3473–3493. Bohle, W., van Swaaij, W.P.M., 1978. The influence of gas adsorption on mass transfer and gas mixing in a fluidized bed. In: Davidson, J.F., Keairns, D.L. (Eds.), Fluidization. Cambridge University Press, Cambridge, UK, pp. 167–172. Chavarie, C., Grace, J.R., 1975. Performance analysis of a fluidized bed reactor, part I—visible flow behaviour. Ind. Eng. Chem. Fundam. 14, 75–91. Cooper, D.A., Ljungstrom, E.B., 1988. In-bed gas measurements in a commercial 16 MW fluidized bed combustor. Chem. Eng. J. Biochem. Eng. J. 39, 139–145. Davidson, J.F., Harrison, D., 1963. Fluidised Particles. Cambridge University Press, Cambridge. Gilliland, E.R., Mason, E.A., 1952. Gas mixing in beds of fluidized solids. Ind. Eng. Chem. 44, 219–224. Fontaine, R.W., Harriott, P., 1972. Effect of molecular diffusion on mixing in fluidized beds. Chem. Eng. Sci. 27, 2189–2197. Grace, J.R., 1986. Fluid beds as chemical reactors. In: Geldart, D. (Ed.), Gas Fluidization Technology. Wiley, New York, pp. 287–341 (Chapter 11). Hansen, P.F.B., Bank, L.H., Dam-Johansen, K., 1995. In-situ measurement in fluidized bed combustors: design and evaluation of four sample probes. In: Proceedings of 13th International Conference on Fluidized Bed Combustion, ASME, vol. 1, pp. 391–397. Hartge, E.U., Fehr, M., Werther, J., Ochodek, T., Noskievic, P., Krzin, I., Kallner, P., Gadowski, J., 2005. Gas concentration measurements in the combustion chamber of the 235 MWe circulating fluidized bed boiler Turow no. 3. In: Proceedings of 18th International Conference on Fluidized Bed Combustion, ASME, pp. 813–822. Krambeck, F.J., Avidan, A.A., Lee, C.K., Lo, M.N., 1987. Predicting fluid-bed reactor efficiency using adsorbing gas tracers. A.I.Ch.E. J. 33, 1727–1734. Merry, J.M.D., Davidson, J.F., 1973. Gulf-stream circulation in shallow fluidized beds. Trans. Inst. Chem. Eng. 51, 361–368. Nguyen, H.V., Potter, O.E., 1974. Gas mixing in fluidized beds as a function of the adsorbency of the solids for the gas. Adv. Chem. Ser. 13, 290–300. van Deemter, J.J., 1980. Mixing patterns in large-scale fluidized beds. In: Grace, J.R., Matsen, J.M. (Eds.), Fluidization. Plenum, New York, pp. 69–89. van der Vaart, D.R., 1992. Prediction of axial concentration profiles in catalytic fluidized reactors. A.I.Ch.E. J. 38, 1157–1160.
Contents lists available at ScienceDirect
Chemical Engineering Science journal homepage: w w w . e l s e v i e r . c o m / l o c a t e / c e s
Shorter Communication
Pitfalls in gas sampling from fluidized beds John Grace a,∗ , Hsiaotao Bi a , Yongmin Zhang b a b
Department of Chemical and Biological Engineering, University of British Columbia, 2360 East Mall, Vancouver, Canada V6T 1Z3 State Key Laboratory of Heavy Oil Processing, China University of Petroleum, Beijing, 102249, China
A R T I C L E
I N F O
Article history: Received 29 September 2008 Received in revised form 29 January 2009 Accepted 11 February 2009 Available online 20 February 2009
A B S T R A C T
It is shown that gas sampling from fluidized beds can provide misleading information due to hydrodynamic factors, biased sampling from the dense phase and radial gradients. Caution is needed to avoid these problems and in the interpretation of gas-sampling data. © 2009 Elsevier Ltd. All rights reserved.
Keywords: Sampling Fluidization Dispersion Chemical reactors Multiphase flow Multiphase reactors
1. Introduction
2. Pitfall #1: bubble-induced pressure fluctuations
Gas-fluidized beds experience significant axial and lateral dispersion, affecting the conversion and selectivity of fluidized bed chemical reactors. Their hydrodynamics are subject to complex two-phase behavior and several flow regimes. Reactor modeling requires recognition of the two-phase nature of fluidized beds. Models also require experimental confirmation, preferably by measuring concentrations within the individual phases (Chavarie and Grace, 1975; Atkinson and Clark, 1988). It is less useful, but better than measuring concentrations only at the exit, to perform in-bed gas sampling along the height of the column. Sampling is also required when measuring gas mixing in fluidized beds. Efforts have been made to sample gas in large-scale industrial systems (e.g. Cooper and Ljungstrom, 1988; Hansen et al., 1995; Hartge et al., 2005), e.g. to better understand generation of pollutants.x The two-phase nature of fluidized beds results in significant pitfalls when interpreting gas-sampling data which can cause significant errors. These issues have gone largely unrecognized. For simplicity and because this is where the challenges are greatest, we focus on the bubbling flow regime, although similar considerations apply in varying degrees to the other flow regimes (especially slugging and fast fluidization).
Local pressures recorded in gas-fluidized beds show substantial fluctuations. Among the various causes (Bi, 2007) are bubbles: As bubbles approach, the pressure rises, reaching peaks when their noses reach the measurement level, then falling to a minimum at the back before recovering in the wake (Davidson and Harrison, 1963). The overall amplitude of the bubble-induced pressure fluctuations is of order p (1 − mf )Ub2 . A gas-sampling port within a bubbling bed experiences similar pressure fluctuations as bubbles pass. If the pressure drop through the sampling line and analysis instrumentation is small relative to the amplitude of these fluctuations, the sampling flowrate will vary significantly with time, with more gas sampled from near the front of the bubble and less from the back. Thus the sampling flux will be skewed disproportionately to the nose region, causing the sampling to be biased. Overall, the time-mean concentration acts as if the sampling was carried out from below the actual sampling level. The extent of the bias, in addition to depending on the pressure drop through the sampling tubing and instrumentation, depends on the vertical length and velocity of the bubbles. To avoid sampling errors associated with in-bed pressurefluctuations, the pressure drop through the sampling system should be much larger than the amplitude of the pressure fluctuations. This is readily achieved in pressurized or deep beds, but shallow atmospheric-pressure beds will almost certainly require a vacuum pump at the exit of the sampling lines, requiring careful attention to avoid leakage which could dilute the sampled gas and cause further errors.
∗ Corresponding author. Tel.: +1 604 822 3121. E-mail address: [email protected] (J. Grace). 0009-2509/$ - see front matter © 2009 Elsevier Ltd. All rights reserved. doi:10.1016/j.ces.2009.02.012
J. Grace et al. / Chemical Engineering Science 64 (2009) 2522 -- 2524
3. Pitfall #2: two-phase flow averaging Consider a bubbling fluidized bed operating at statistically steady state with reactant A concentrations at height z of cAb (z) and cAd (z) in the bubble and dense phases, respectively. Constant flow sampling at that height will give a time-mean concentration of c¯ Asample (z) = b (z) × cAb (z) + [1 − b (z)] × cAd (z)
(1)
where b (z) is the time-mean fraction of bed volume occupied by the bubble phase. The time-mean concentration based on flow through the two phases at that level should be c¯ Aflow (z) = {Qb (z) × cAb (z) + Qd (z) × cAd (z)}/Q
(2)
where Q is the total gas volumetric flow, whereas Qb (z) and Qd (z) represent the flows associated with the bubble and dense phases, respectively. Since b (z) is likely to be ∼0.1–0.4, the average measured concentration from Eq. (1) is weighted heavily to the dense phase concentration. On the other hand, since the flow passes predominantly through the bubble phase, Eq. (2) shows that the actual (flow) mean concentration should be heavily weighted towards cAb (z). Hence there is significant error in sampling when the concentrations in the two phases, cAb (z) and cAd (z), differ appreciably. This difference between the two means can be large as illustrated by comparing the sampled time-mean and flow-average concentrations for an illustrative case. To make this comparison, we could utilize various fluidized bed reactor models. For simplicity, we consider an irreversible constant-volume first-order reaction and the bubbling bed model summarized by Grace (1986). All of the gas is assumed to pass through the bubble phase, the dense phase acting as a stagnant zone, but nevertheless contributing greatly to reaction due to interphase mass transfer. Radial gradients and temporal fluctuations are ignored. With these assumptions, steady state dimensionless mole balances on the two phases yield: Bubble phase : Dense phase :
dCAb + X(CAb − CAd ) + k∗1 b CAb = 0 dZ X(CAd − CAb ) + k∗1 b CAd = 0
(3) (4)
where CAb = cAb /cAo ; CAd = cAd /cAo ; cAo is the inlet concentration of reactant A, and Z the dimensionless vertical coordinate = z/H with H the expanded bed height. X and k∗1 are a dimensionless interphase mass transfer and rate constant, respectively, defined by X=
km ab b H , U
k∗1 =
k1 H U
(5)
b is the fraction of bed volume occupied by bubble-phase solids ≈ 0.001b –0.01b , d the fraction of bed volume occupied by dense phase solids ≈ (1 − b )(1 − mf ), km an interphase mass transfer coefficient, ab the bubble surface area per unit volume, b the fraction of bed volume occupied by bubbles, mf the bed voidage at minimum fluidization, k1 the first order reaction rate constant and U the superficial gas velocity. With boundary condition CAb = 1 at Z = 0, Eqs. (3) and (4) give
−k∗1 [X(b + d ) + k∗1 b d ]Z X + k∗1 d CAb X CAd = X + k∗1 d
CAb = exp
and (6)
For very slow reactions (k∗1 → 0) or very large interphase mass transfer (X → ∞), the concentrations of the two phases are nearly equal at the same level, nullifying the difference between the mean concentrations from Eqs. (1) and (2). However, consider an illustrative case with realistic values and rate-limiting interphase mass transfer. Let mf =0.5; b =0.2; d =0.4; b =0.001; X=1.0; and k∗1 =10.
2523
At Z = 0.1, substitution of these values into Eq. (6) gives CAb = 0.922, whereas CAd = 0.184. Steady sampling at this height would then give (from Eq. (1)) a time-mean concentration of 0.332cAo , whereas the true (flow-average) concentration, given the stagnant flow in the dense phase, would equal the bubble-phase concentration, 0.922cAo . This difference is substantial, with the sampled gas concentration only 36% of the flow-average value. Failure to recognize errors associated with sampling will lead to erroneous conclusions regarding the progress of reactions along the reactor and the merits of reactor models. This effect explains the finding (Askins et al., 1951) that measured in-bed oxygen concentrations in a commercial FCC regenerator were consistently much lower than in the freeboard. Interpretation of sampling data requires care and caution to avoid misinterpretation. We could find only a few other instances in the literature (Gilliland and Mason, 1952; Fontaine and Harriott, 1972; Cooper and Ljungstrom, 1988; van der Vaart, 1992) where this bias resulting from over-representation of the dense phase has been recognized. Similar errors occur when withdrawing gas samples in determining axial gas mixing in fluidized beds. For example, gas samples taken upstream of a steady-state tracer injector, predominantly come from the dense phase, where the concentration is likely to be significantly higher than in the bubble phase, leading to overestimation of gas backmixing. Sampling errors of this nature are likely one cause of the wide scatter of gas axial dispersion coefficients reported in the literature (van Deemter, 1980). In order to compensate for this problem, sampling data should be interpreted with the aid of a two-phase model appropriate to the flow regime which is present in the bed.
4. Pitfall #3: hydrodynamic interference Gas sampling lines need a screen or filter at their entrances to prevent ingress of particles. Excessive withdrawal of gas through a sampling port can cause local defluidization or build-up of stagnant solids, with the resulting lump of solids impeding the movement of particles. To minimize flow disruption, the average velocity along the sampling line should be small, preferably ∼Umf /mf . However, for typical fluidized bed catalyst particles, the resulting velocities will then be only millimetres/second, causing long delay times. Moreover, such velocities, coupled with small sampling-tube diameters, give such low Reynolds numbers that the sampling tube flow will be laminar, causing Taylor dispersion to distort transient signals. If sampling tubes intrude into the bed, their presence can also interfere with the flow, e.g. causing bubble splitting. Non-intrusive measurement techniques such as NMR species mapping, can overcome this problem. Ports flush with the vessel wall also avoid the problem. However, sampling from the wall region leads to challenges associated with radial gradients, as outlined in the next section.
5. Pitfall #4: neglect of radial gradients Most fluidized-bed reactor and dispersion models assume one-dimensional flow, ignoring radial gradients of concentration, voidage and velocity, despite considerable evidence that, for example, voidages are considerably greater in the interior than near the outer walls. Since gas samples are usually withdrawn from the walls (as suggested above), measured concentrations are atypical of cross-sectional averages at the given level. For example, solids downward flow occurs predominantly along the walls, inducing gas backmixing in this region. Taylor dispersion associated with non-uniform gas velocity profiles may also cause axial mixing. Interpretation in terms of a one-dimensional axial model is likely to inadequately represent the actual mechanisms of mixing, which are dominated by macroscopic phenomena such as gulf-streaming (Merry and Davidson, 1973). Given these circumstances, two- or
2524
J. Grace et al. / Chemical Engineering Science 64 (2009) 2522 -- 2524
three-dimensional dispersion mixing models are needed to provide a proper interpretation of the mixing phenomena. 6. Pitfall #5: adsorption and trapping Sampling errors can also occur if a gas species adsorbs on the particles. The species in question then travels in a different manner from non-adsorbing species. The consequences have been recognized (e.g. Nguyen and Potter, 1974; Bohle and van Swaaij, 1978; Krambeck et al., 1987) and are not discussed here. Note, however, that similar considerations apply to non-adsorbing species with nonporous particles. In such cases, resistance to internal diffusion will cause delays in gas species entering and leaving the particles. As a result, measured gas mixing and local concentrations differ according to whether the particles are porous or non-porous, the extent of the difference depending on the internal porosity and the effective diffusivity of the gas species of interest. 7. Conclusions Fluidized-bed reaction and mixing studies often require gas concentration measurements to test models, understand behavior, and derive mixing coefficients. However, the two-phase nature of gasfluidized beds and their radial gradients can cause substantial errors in gas sampling. It is critical to minimize the pitfalls identified in this paper and to interpret data derived from in-bed gas samples with great care. Failure to do so has doubtless contributed to wide variations in literature data and may cause misinterpretation of the relative merits of alternative reactor and dispersion models. Some suggestions for overcoming the pitfalls are provided in this paper. Acknowledgement The authors are grateful to the Chinese University of Petroleum and the Natural Sciences and Engineering Research Council of Cananda for financial support
References Askins, J.W., Hinds, G.P., Kunreuther, F., 1951. Fluid catalyst-gas mixing in commercial equipment. Chem. Eng. Prog. 47, 401–404. Atkinson, C.M., Clark, N.N., 1988. Gas sampling form fluidized beds: a novel probe system. Powder Technol. 54, 59–70. Bi, H.T., 2007. A critical review of the complex pressure fluctuation phenomenon in gas–solids fluidized beds. Chem. Eng. Sci. 62, 3473–3493. Bohle, W., van Swaaij, W.P.M., 1978. The influence of gas adsorption on mass transfer and gas mixing in a fluidized bed. In: Davidson, J.F., Keairns, D.L. (Eds.), Fluidization. Cambridge University Press, Cambridge, UK, pp. 167–172. Chavarie, C., Grace, J.R., 1975. Performance analysis of a fluidized bed reactor, part I—visible flow behaviour. Ind. Eng. Chem. Fundam. 14, 75–91. Cooper, D.A., Ljungstrom, E.B., 1988. In-bed gas measurements in a commercial 16 MW fluidized bed combustor. Chem. Eng. J. Biochem. Eng. J. 39, 139–145. Davidson, J.F., Harrison, D., 1963. Fluidised Particles. Cambridge University Press, Cambridge. Gilliland, E.R., Mason, E.A., 1952. Gas mixing in beds of fluidized solids. Ind. Eng. Chem. 44, 219–224. Fontaine, R.W., Harriott, P., 1972. Effect of molecular diffusion on mixing in fluidized beds. Chem. Eng. Sci. 27, 2189–2197. Grace, J.R., 1986. Fluid beds as chemical reactors. In: Geldart, D. (Ed.), Gas Fluidization Technology. Wiley, New York, pp. 287–341 (Chapter 11). Hansen, P.F.B., Bank, L.H., Dam-Johansen, K., 1995. In-situ measurement in fluidized bed combustors: design and evaluation of four sample probes. In: Proceedings of 13th International Conference on Fluidized Bed Combustion, ASME, vol. 1, pp. 391–397. Hartge, E.U., Fehr, M., Werther, J., Ochodek, T., Noskievic, P., Krzin, I., Kallner, P., Gadowski, J., 2005. Gas concentration measurements in the combustion chamber of the 235 MWe circulating fluidized bed boiler Turow no. 3. In: Proceedings of 18th International Conference on Fluidized Bed Combustion, ASME, pp. 813–822. Krambeck, F.J., Avidan, A.A., Lee, C.K., Lo, M.N., 1987. Predicting fluid-bed reactor efficiency using adsorbing gas tracers. A.I.Ch.E. J. 33, 1727–1734. Merry, J.M.D., Davidson, J.F., 1973. Gulf-stream circulation in shallow fluidized beds. Trans. Inst. Chem. Eng. 51, 361–368. Nguyen, H.V., Potter, O.E., 1974. Gas mixing in fluidized beds as a function of the adsorbency of the solids for the gas. Adv. Chem. Ser. 13, 290–300. van Deemter, J.J., 1980. Mixing patterns in large-scale fluidized beds. In: Grace, J.R., Matsen, J.M. (Eds.), Fluidization. Plenum, New York, pp. 69–89. van der Vaart, D.R., 1992. Prediction of axial concentration profiles in catalytic fluidized reactors. A.I.Ch.E. J. 38, 1157–1160.