Gas-Phase RTD Measurement in Gas and Gas− Solids Reactors

The measured concentration, average residence time, and degree of mixing in the ... Phase Mass Transfer Using Tracer Injection and Ultrasound Experime...
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Ind. Eng. Chem. Res. 2003, 42, 5506-5515

Gas-Phase RTD Measurement in Gas and Gas-Solids Reactors Using Ultrasound A. H. G. Cents, S. R. A. Kersten,* and D. W. F. Brilman Department of Chemical Engineering, University of Twente, P.O. Box 217, 7500 AE Enschede, The Netherlands

This paper describes gas-phase residence time distribution (RTD) measurements using a novel method for fast concentration measurements of binary gas mixtures that is based on differences in the ultrasonic velocities of the mixture’s components. It is shown that systems with holding times as low as 0.1 s can be interpreted, although an increase of the sampling frequency would be desirable. The technique was validated using single-phase gas reactors (tubular reactors and an intensely stirred reactor). The measured concentration, average residence time, and degree of mixing in the single-phase reactors were in good agreement with the experimental conditions and results from the literature. The method was applied to study the hydrodynamics of a novel gas-solids multistage circulating fluidized-bed reactor for biomass gasification, using a prototype measurement cell to evaluate the gas-phase RTD. From the measured RTD curves of this reactor, which consists of five fluid-bed stages, it can be concluded that there are overall no dead zones/ bypass streams with low exchange rates to the main flow field. The gas-phase hydrodynamics can be described by a series of six CISTRs compared to the five actual fluid-bed stages of the base-case design. The employed ultrasonic detection technique has several advantages. The composition of binary gas mixtures can be measured at a high sampling frequency in the presence of solids, and moreover, the average local solids fraction can be determined simultaneously. The method can be completely noninvasive, and measurements through reactor walls and even in industrial installations are expected to be possible. 1. Introduction In this work, the gas-phase hydrodynamics of a novel multistage fluid-bed reactor for biomass gasification are under investigation. This requires a technique for gasphase residence time distribution (RTD) measurements in the presence of solids that is nonintrusive, can be employed with a minimum amount of flow disturbance, and is preferably capable of characterizing reactors with holding times (defined in eq 12) as low as 0.1 s. Most reported techniques for gas-phase RTD measurements are based on (laser) light transmission,1 thermal conductivity,2 or radioactive tracers.3 For singlephase systems, all of these methods can be applied with good performance characteristics and at high sampling frequencies. The main disadvantage of light-based techniques is their inability to measure through nontransparent reactors and reactor walls. Thermal conductivity can only be applied with intrusive probes, which is undesirable because of the resulting disturbance of the flow pattern. However, intrusive sampling can also provide opportunities when local concentration profiles (e.g., radial) are to be determined. The presence of a solids phase decreases the applicability of most techniques. Laser light absorption, for instance, is often not applicable because of scattering of the light by the solids. Also, gas-phase sampling probes are more difficult to operate if solids are present in the reactor. Of the above-mentioned techniques, only the radioactive tracer-gas method (for instance, using 41Ar; see Viitanen3) meets all requirements, but it requires extensive safety procedures. * To whom correspondence should be addressed. E-mail: [email protected].

In this work, a method for RTD measurements was developed that makes use of the dependence of the ultrasonic velocity on the gas-phase composition. This method meets all requirements and has the advantage that the solids fraction and the tracer-gas concentration in the measurement cell can be determined simultaneously. Another benefit associated with this technique is that it offers the opportunity to measure through reactor walls (e.g., steel), which, as mentioned above, is impossible for photometric methods. This paper begins with an explanation of the measurement principle involved, followed by a description of the experimental setups used and the experimental methods applied. Results are then presented regarding the validation of the presented ultrasound RTD detection method in single-phase reactors (PFR and CSTR). In addition, results of gas-phase RTD measurements in a novel multistage circulating fluidized-bed reactor for biomass gasification are presented. Finally, the gasphase hydrodynamic characteristics of this novel reactor are discussed in terms of these RTD measurements. 2. Measurement Principle The measurement principle makes use of the dependence of the speed of sound in a material on the bulk modulus (of elasticity) and density of the medium. This dependence is given for a fluid by eq 1. (See the Notation section for the definitions of variables.)

υ)

x(dpdF) ) x F

Ev

(1)

The average density and bulk modulus of a binary

10.1021/ie021058k CCC: $25.00 © 2003 American Chemical Society Published on Web 10/01/2003

Ind. Eng. Chem. Res., Vol. 42, No. 22, 2003 5507

mixture of ideal gases are given by

F ) (1 - φ)F1 + φF2

(2)

1 1 1 ) (1 - φ) +φ Ev Ev,1 Ev,2

(3)

Both the density and the bulk modulus of pure components are well-tabulated or can be calculated. For an ideal gas undergoing an isotropic change (pressure wave), for instance, the bulk modulus of elasticity is defined as

Ev )

dp ) γp dF/F

(4)

Appearing in this equation is γ, the ratio of the constantpressure and constant-volume heat capacities, Cp and Cv, respectively. Povey4 suggests that the bulk modulus of the pure components be calculated from their tabulated density (F) and ultrasonic velocity (υ) values according to

Ev,i ) υi2Fi

(5)

When doing so, the composition of the binary mixture can be expressed as a function of the measured velocity of sound in the mixture and the known F and υ values of of the pure components

φ)

-B ( xB2 - 4AC 2A

(6)

where

( ) ( ) ( )

A ) υ12 1 B ) υ22

F1 F2 + υ22 1 F2 F1

F2 F1 - 2 + υ12 F1 F2

(

C ) υ22 1 -

)

υ12 υ2

(6a)

(6b)

(6c)

In this work, eq 6 was used to convert the experimentally determined sound velocity values to the mixture composition. Note that, in the above analysis, the term binary is not restricted to two pure components. The relation also holds when a component, the tracer gas, is considered with a mixture of components (e.g., air) whose relative composition does not change during the measurement. Furthermore, the calculation is based on a uniform radial tracer gas profile. This concentration measurement technique can be used to determine the system’s response to a step function in the inlet concentration of a tracer component. 3. Influence of Solid Particles An advantage of the measurement technique described here is its applicability in the presence of solid particles. The influence of solid particles on the speed of sound can be described by scattering theory, which was originally derived for liquid droplets in a gas phase by Epstein and Carhart5 and modified for solid particles in a fluid by Allegra and Hawley.6 The change in the

Figure 1. (a) Ultrasonic velocity and (b) attenuation coefficient of a mixture of air and sand for different volume fractions of 200µm sand particles. The calculations using the model of Allegra and Hawley6 were done for transmitted signals with frequencies of 200 kHz, 800 kHz, and 4 MHz.

sound velocity due to the presence of the solid particles in the measurement cell depends on the size of the particles, their volume fraction, and the frequency of the ultrasonic wave. For a more detailed description of the model describing the speed of sound and the attenuation coefficient in the case of particles in a fluid, the reader is referred to Cents et al.7 These authors have also shown that this technique is capable of determining the solids concentration and size distribution in a fluid accurately. Determination of a gas-phase concentration in the presence of solid particles is somewhat more laborious compared to single-phase systems: the presence of the particles causes a shift in the ultrasonic velocity that must be discriminated from the effect of a change in the gas-phase composition. Also, the particles cause extra attenuation (decrease in amplitude of the signal), which can give rise to problems concerning the acquisition of the received signal. The transmitted signal frequency and the fraction of tracer gas are degrees of freedom that can be optimized either to completely filter out the effect of the solids or to simultaneously measure the solids fraction and the tracer-gas fraction (see Figure 1). The tracer-gas concentration that needs to be applied depends on the fluctuations of the solids-phase fraction in time. When this fluctuation is small, the tracer-gas concentration can be low, because the effect of the solids on the speed of sound is relatively small compared to the effect of the tracer gas. For large fluctuations in the solids-phase fraction, however, higher tracer-gas concentrations are needed for a good distinction between the effect of the solids and the effect of the tracer gas to be made. When, for instance, helium (υHe ) 983 m/s at 23 °C) is added to a stream of air (υair ) 345 m/s at 23 °C), the velocity difference of 10% helium in air compared to pure air is 18 m/s, according to eq 6. To obtain accurate measurements, the velocity change due to solids fluctuations should be much less than this value, which can imply that, in some cases, high tracer gas concentrations are required. For the selection of the appropriate transmitted signal frequency, the fraction of solids, the path length of the measurement, and the particle size are important parameters. In Figure 1, the influence of the volume fraction, β, of 200-µm sand particles on the velocity of sound (υ ) x/t) and the attenuation coefficient [R ) -ln-

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(I2/I1)/x] at different frequencies is shown. These values are determined using scattering theory with the parameters for glass and air from Cents et al.7 From this graph, it can be seen that, at higher frequencies, the solid particles hardly have an influence on the speed of sound through the medium. Unfortunately, applying higher frequencies results in a substantial increase of the attenuation coefficient, which causes a loss of the measurement signal. At these higher frequencies, it is also not possible to actually measure the local solids content in the measurement cell. In this work, low solids fractions ( 50). 4.1. Application to a Novel Multistage Circulating Fluidized Bed for Biomass Gasification. The ultrasound method was also applied to determine the gas-phase RTD of a novel reactor design that was specifically developed to overcome a number of problems often encountered in circulating fluidized-bed gasification of biomass.9 This multistage circulating fluidized bed consists of several (seven in the present base-case

5. Interpretation of RTD Measurements It is common practice to use the probability functions (E, F) to describe the distribution of residence times

∫0∞ E(t) dt ) 1 F(t) )

∫0t E(t) dt

(9) (10)

The mean residence time (first moment) can be calculated from the E and F curves as follows

ht )

∫0∞ tE(t) dt ) ∫01 t dF(t)

(11)

It is interesting to compare the mean residence time found with the holding time of the actual reactor. Such a comparison yields information regarding the presence of dead zones and/or bypass streams with hardly any exchange to the main flow field. The holding time is defined as

τ)

Vgas Φv

(12)

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Normally, the E curve is presented using the reduced time

θ)

t ht

(13)

The spread in residence time is characterized by the variance

σ2 ) MO2 - ht 2, σθ2 )

σ2 1 , N) 2 2 ht σθ

(14)

where

MO2 )

∫0∞ t2E(t) dt ) 2∫0∞ t[1 - F(t)] dt

In this work, the step function was used as the input function, which yields the F curve as the output signal. Another, frequently used input function is the pulse function. The RTD curves obtained were interpreted in three ways. (a) The first mathod involved using a model consisting of a cascade of N equal mixed tanks. A numerical fit procedure was used to minimize the deviation between the measured F curve and the model. If the input step is assumed to be perfect, the analytical solution is

F(θ) )

N N-1

N θ e-Nθ dθ ) ∫0θ (N - 1)!

Γin(N,Nθ) Γ(N)

Figure 4. Parity plot of φ(He) calculated on the basis of the measured ultrasonic velocity of the mixture and φ(He) calculated according to the readings of the mass flow controllers (MFC).

(15)

in which

Γ(x) )

Figure 5. Response just after the tracer-gas injection valve.

∫0∞ ux-1x-u du

Γin(x,y) )

In the case of solids being present in the reactor, the available volume for the gas phase, and thus the gas holding time of the reactor, was corrected for the volume of the solids according to

∫0y ux-1e-u du

(b) In the second method, the axially dispersed plugflow model (with closed-open and open-open boundary conditions10). In this case also, a fit procedure was applied to find the best model parameters (Pe, ht). (c) Finally, in the third approach the RTD curves obtained were interpreted directly on the basis of the F curve using eqs 11 and 14 to obtain N and ht. The RTD data obtained in the novel reactor for biomass gasification were interpreted with a model consisting of a PFR in combination with a number of CISTRs in series. In this case, the total mean residence time can be described by

ht tot ) ht pfr + ht N-CISTR

(16)

The PFR was introduced into the model to account for the tubing between the tracer-gas injection valve and the riser and between the riser and the measurement cell. After it was verified (with the ultrasound method) that this tubing indeed had PFR characteristics compared to the rest of the reactor, it was decided to subtract the mean residence time of the PFR (the volume of the tubing was known) initially within the fit procedure. This reduced the number of fit parameters to two, viz., the mean residence time in the riser (five segments) and the number of CISTRs by which the five segments are best described. For comparison, the mean residence time was also calculated directly from the measured F curve (eq 11).

τ)

Vgas Vreactor(1 - βgrav) ) Φv Φv

(17)

6. Results and Discussion 6.1. Validation of the Method. To validate the ultrasonic technique regarding the ability to determine the composition of a binary gas mixture, the helium fraction in air calculated from the measured ultrasonic velocity of the mixture using eq 6 was compared with the helium fraction of a known mixture. The latter was based on the readings of the mass flow controllers placed in the air and He supply lines. The results are shown in Figure 4, from which it can be concluded that the ultrasound technique can be used to determine the composition of a binary gas mixture. Obviously, the nature of the components has to be known (Fi and υi in eq 6). The quality of the input step function, which is determined from the speed at which the valve opens, can be very important in the analysis of the RTDs in different reactors. For this reason, the concentration profiles at the outlet as well as at the inlet of the reactors were measured. An example of this input step function (with 10 cm of tubing after the valve) is presented in Figure 5, from which it can be seen that the valve opens very rapidly. However, the actual profile is difficult to determine, at least within the maximum

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Figure 6. Typical step response of one of the PFRs used. Experimental data and the best-fit line (NCISTR model) are plotted.

Figure 7. Parity plot of the mean residence time (calculated by interpretation of the measured F curves with the NCISTR model) and the holding time of the PFRs.

sampling frequency of 33 Hz of the prototype measurement cell. Although exact values for the variance of the valve opening (σv2) cannot be determined, the variance that can be determined from this curve is maximally 5 × 10-5 s2 (σθ2 ) 5 × 10-3). For pipe-flow experiments at high gas velocities, such a value can still be important at short residence times. In this case, the F(t) curve in the tube should be determined using deconvolution of the responses at the outlet and inlet. In all other experiments, the assumption of an ideal input step function is justified. Figure 6 shows a typical measured step response (helium fraction detected by the measurement cell after a step change in the input helium fraction) of one of the PFRs used (Dt ) 19 mm and L ) 1635 mm). In Figure 6 also, the best fit of the NCISTR interpretation model is plotted. Note that this fit is very good. Figure 7 shows the mean residence time calculated from the measured RTD curves of the PFR versus the holding time. In this case, the RTD data were interpreted with the NCISTR model. Comparing the mean residence time calculated on the basis of the F curve, the axial dispersion model, and the N-equal-CISTR model never resulted in a deviation of more than 5% when a sufficiently high He fraction (say 15%) was used. In the case of lower He fractions, the noise level caused that direct integration of the raw F curve to became more difficult. Smoothing of the data by spline interpolation solved this problem.

Figure 8. Typical step response of the CISTR. Experimental data and the best-fit line (NCISTR model) are plotted.

Figure 7 clearly shows that this prototype of the measurement system is already able to determine the gas-phase RTD of reactors with holding times as low as 0.08 s. Note that, according to the Nyquist theorem,11 only frequencies of less than 16.5 Hz can be reconstructed with the present sampling frequency (33 Hz). However, because, in principle, the theoretical maximum sampling frequency is 10 000 Hz with the current measurement cell, even systems with much smaller residence times can be analyzed when the problem of data transfer is solved. Note that, for such very short holding times (say, τ < 0.05 s), the dynamic behavior of the tracer-gas injection valve might become dominant, and the input step must be determined in all cases. In general, a higher sampling frequency will improve the accuracy of the RTD curve analysis, because more data are available on the slopes of the curves. It was found that using the standard dispersion model as the interpretation model does not influence either the accuracy of the fit or the information obtained from the fit. In fact, for all responses, both models were used, and it turned out that the approximate equation (for Pe > 10) Pe/2 ≈ NCISTR - 1 was always satisfied within 10%. The Bodenstein numbers found (in the range 0.63.0) were in good agreement with the values determined according to the correlations of Taylor12 and Wen and Fan13 for single-phase turbulent fluid flow in tubes. Figure 8 shows a typical step response of the CSTR. Also, for the CSTR, the mean residence time was in good agreement with the holding time. Several RTD curves were obtained: the number of CISTRs calculated varied between 0.9 and 1.1, indicating that the CSTR actually can be regarded as a CISTR. On the basis of the results described above, it was concluded that the ultrasound method developed satisfies the demands for the measurement of the gas-phase RTD of single-phase reactors. 6.2. Analysis of the Novel Multistage Fluidized Bed for Biomass Gasification. The ultrasound technique was also used to determine the gas-phase RTD of the novel multistage CFB reactor for biomass gasification as a function of the applied gas velocity (holding time), the solids flux, and the solids fraction in the segments. The data obtained from these RTD measurements will contribute to the understanding of the overall gas-phase mixing of the novel reactor. Combining the RTD information with information from stationary mixing experiments provides a first idea of the gas mixing per segment.

5512 Ind. Eng. Chem. Res., Vol. 42, No. 22, 2003 Table 1. Typical Results of Gas-Phase RTD Measurements in the Novel Reactora parameters

results βgrav (%)

httot (s)

htpfr (s)

htNCISTR (s)

Vrtd (mL)

no. of CISTRsb

Vrel

-

-

0.62 0.62 0.62 0.86 0.86 0.85 1.12 1.12 1.11

0.10 0.10 0.10 0.13 0.13 0.13 0.17 0.17 0.17

0.52 0.52 0.52 0.73 0.73 0.72 0.94 0.95 0.94

202 203 202 210 209 207 207 209 207

4.9 4.9 5.1 5.1 5.1 4.9 4.8 4.7 5.0

0.97 0.98 0.97 1.01 1.00 1.00 1.00 1.00 1.00

-

-

-

0.30 0.30 0.29 0.43 0.42 0.43 0.66 0.66 0.66

0.075 0.075 0.075 0.11 0.11 0.11 0.17 0.17 0.17

0.23 0.22 0.22 0.32 0.31 0.32 0.49 0.49 0.49

256 252 250 248 245 249 250 249 248

4.8 5.2 5.6 5.0 5.4 5.3 4.6 5.1 5.2

1.02 1.00 1.00 0.99 0.98 0.99 1.00 0.99 0.99

17 17 17 31 31 31 71 71 71 35 35 35

250 275 250 325 275 300 400 400 375 425 425 400

3.8 3.8 3.8 7.2 7.2 7.2 9.6 9.6 9.6 16.5 16.5 16.5

0.55 0.37 0.36 0.37 0.43 0.41 0.41 0.51 0.51 0.51 0.65 0.59 0.61

0.11 0.08 0.08 0.08 0.10 0.10 0.10 0.12 0.12 0.12 0.16 0.16 0.16

0.44 0.29 0.28 0.29 0.33 0.31 0.31 0.39 0.38 0.38 0.49 0.43 0.45

233 221 218 227 216 209 212 207 203 204 180 172 175

5.0 6.4 5.5 7.0 4.1 6.3 4.5 6.4 6.2 6.0 4.9 6.4 3.9

0.99 0.98 1.02 1.00 0.97 0.99 0.99 0.97 0.97 0.93 0.89 0.90

exp. no.

τ (s)

Vreactor (mL)

Gs [kg/(m2 s)]

1 2 3 4 5 6 7 8 9

0.63 0.63 0.63 0.85 0.85 0.85 1.12 1.12 1.12

208 208 208 208 208 208 208 208 208

-

10 11 12 13 14 15 16 17 18

0.29 0.30 0.29 0.43 0.42 0.43 0.67 0.67 0.67

251 251 251 251 251 251 251 251 251

19 20 21 22 23 24 25 26 27 28 29 30 31

0.54 0.38 0.37 0.36 0.42 0.42 0.42 0.50 0.50 0.51 0.70 0.67 0.68

232 232 232 232 232 232 232 232 232 232 232 232 232

∆pbc (Pa)

a Results obtained by interpretation of the RTD curves with the N b CISTR model described earlier. Number of CISTRs corresponding to only the riser () five segments in series).

In the case of gas-solids flow through the riser, the gas holding time of the system is calculated on the basis of the reactor volume corrected for the presence of the solids phase (βgrav, Table 1). The pressure drop over the bottom cone of the fifth segment (∆pbc in Table 1) is indicative of the solids hold-up in the riser segments. A drop of 400-425 Pa corresponds to a situation for which the bottom cone (height ) 4 cm) of each segment is completely filled with solids (giving the maximum amount of solids in a segment). In general, each 100 Pa represents approximately 1 cm of solids in the bottom cone of a segment. In addition to the RTD measurements, stationary tracer-gas tests (CO2 for IR detection, He for TCD detection) were performed (port A, see Figure 3b). Judging from the results of these tests, the following conclusions can be drawn (the conclusions hold for normal operating conditions, viz., solids in the bottom cones of the riser segments and a solids flux between the segments, unless stated otherwise): (a) The absence of tracer gas upstream of the segment in which the tracer gas was injected indicates that no back-mixing of gas between the segments occurs. This means that the overall gas hydrodynamics cannot be described with a dispersion model, because such a model includes both forward and backward mixing. The NCISTR model is more appropriate, as only forward mixing is considered in this model. (b) Downstream of the injection segment, the tracer was always uniformly distributed within the segments, which indicates that mixing of the gases occurs. The exact location and rate of this mixing are not yet clear.

(c) Gas mixing inside a single segment was investigated as well. Stationary tracer injection experiments indicated that CO2 injected into the top cone of a segment does not penetrate completely into the fluidized bed located in the bottom cone (say, only 1-2 cm). Apparently, gas back-mixing through the interface of the fluidized bed is difficult. These results show that, overall, one segment cannot be regarded as a single perfectly mixed cell. When no solids are present in the segment, the gas mixing between the top and bottom cones (circulation streams) turns out to be much more intense. For an empty riser, it was found that He injected into the top cone penetrated to the entrance of the bottom cone of the same segment. (d) CO2 injected into the fluidized bed of the bottom cone was quickly distributed uniformly over the whole bottom cone, which indicates that gas mixing occurs in the bottom cone (fluid bed) at high rates. By combining the last three items of the above list, it can be concluded that, under normal operating conditions, even though the gas mixing in an individual segment is not completely perfect (top cone to bottom cone), there is renewed mixing in each segment. When the riser is operated with the riser velocity (Ur) above 3 times the terminal velocity of the bed particles, gas jets (with a typical diameter of 1 cm) were observed in the fluidized beds present in the bottom cone of each segment.9 However, these jets did not seem to reach the top of these fluidized beds. A very turbulent solids flow pattern was observed at these high gas velocities, which might ensure optimal solids mixing. Note that Ur is defined at the smallest riser diameter (Do).

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Figure 9. RTD curve of the novel reactor without solids in the riser.

Figure 11. (a) Two RTD curves of the novel reactor for identical conditions [Gs ≈ 31 kg/(m2 s), Ur/Ut ) 5] after correction of the measured velocity for the presence of solids. (b) Raw velocity data corresponding to one of the RTD curves presented in part a. Figure 10. Parity plot of the mean residence time versus the holding time for both single-phase gas flow and gas-solids flow through the novel reactor. For the case of solids being present, the normalized velocity through the riser is also indicated.

The signal between the injection valve and the first segment of the riser showed PFR behavior, and a good agreement between the calculated (on the basis of the RTD curve) mean residence time and the holding time was observed. This provides a basis for the use of an interpretation model that consists of a PFR for the interconnecting tubes combined with a number of CISTRs for the segments of the riser (see section 5, eq 16). 6.2.1. Results without Solids in the Riser (Empty Riser). The results for the empty riser (example in Figure 9) show that the mean gas residence time calculated on the basis of the measured RTD curves is in very good agreement with the holding time (see Table 1 and Figure 10). This means that there are no dead zones/bypass streams with absolutely no exchange to the main flow field. The overall gas-phase hydrodynamics can be described with a model consisting of a cascade of equal CISTRs, in which the number of CISTRs closely resembles the actual number of segments in the riser (see Table 1). This could be expected as stationary mixing experiments showed that gas-phase mixing was present in each segment. The results obtained with the NCISTR fit model and by direct use of the F curve are nearly identical, and the reproducibility is good (see Table 1). No effect of the gas velocity on the mixing behavior was found (the number of CISTRs does not change, see Table 1) in the experimentally applied range (Ur ) 2-11 m/s).

6.2.2. Results with Solids in the Riser. Figure 11a shows step responses of the novel reactor operated at normal operating conditions. This figure shows clearly that no tailing occurs. In fact, on average, the endconcentration was reached after 2-3 times the holding time. Also, with solids present in the riser, the results show clearly that the mean gas residence time, calculated on the basis of the measured RTD curves (direct use of the F curve and the NCISTR model), is in very good agreement with the holding time (see Table 1 and Figure 10). Hence, also with solids, there are no dead zones and/or bypass streams (the observed jets) with a low exchange rate to the main flow. The mean residence time for the hypothetical case in which all of the gas passes through the segments of the riser as a jet is also given in Figure 10 (assuming that the diameter of the jet is equal to the diameter of the interconnecting tubes between the segment and there is no exchange between the jet and the rest of the system). Only in the case of solids being present combined with a relatively low gas velocity is the mean residence time about 10% lower than the holding time (see Table 1, experiments 29-31 and Figure 10), which might indicate the presence of some dead volume. By comparing Figures 9, 11a, and 12, it becomes clear that the presence of solids in the measurement cell induces fluctuations in the measured gas concentration. The fluctuations are caused by changes in the solids concentration in the measurement cell. Because of these fluctuations, it becomes difficult to determine whether the last data points on the slope of the RTD curve toward the steady-state concentration (end concentration) are actually part of the line or should be considered

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Figure 12. RTD curve measured in the presence of solids and model lines including the best fit.

already as scatter. Because the calculation of the second moment from the F curve contains the term [1 - F(t)] dt, this arbitrary decision affects the calculation of the variance. The results obtained by direct use of the F curve were found to depend on what was determined to be scatter and what not. The scatter level (error bars in the figures) was chosen to be the maximum deviation from the mean value in the stationary part of the curve. Figure 11a shows two RTD curves that could be regarded as identical by visual inspection. However, the fit procedures showed that these curve could represent between 4.6 and 8 CISTRs and 5.5 and 7.5 CISTRs depending on the interpretation method used. Figure 12 shows that, when taking into account the scatter in the data, one could not really distinguish visually between the agreement of the experimental data and a fit model including between 4 and 8 CISTRs, although the best fit was obtained for N ) 6.4. Typically, with solids present in the riser, it has been found that the error in the number of CISTRs obtained is in the range of 1-2 CISTRs for a single experiment. Despite the increased scatter in the data, it can be concluded that, after averaging, the number of CISTRs that describes the gas-phase hydrodynamics probably increases from 5 to 6 (average of 4-8) when solids are present in the riser. Apparently, the presence of solids in the riser reduces gas-phase back-mixing so that there are more theoretical CISTRs than actual segments. This could very well be the case, as stationary tracer-gas injection tests showed that, with solids in the bottom cone, the individual segments are not ideally mixed, i.e., one segment is characterized by more than one CISTR. No clear effects on the mixing behavior were found for varying gas velocity, solids flux, and solids hold-up in the riser (see Table 1). For the calculation of the mean residence time, the scatter due to the presence of solids is of minor importance, and so differences between the models are negligible. Performing a larger number of experiments might overcome the scatter found in the number of CISTRs (MO2), as the error induced by the solids is randomly orientated. Furthermore, using higher signal frequencies, at which the velocity is independent of solids hold-up, can reduce the scatter. 7. Conclusions In this work, a technique has been developed that can measure the gas-phase RTD of gas and gas-solids reactors. The prototype, having an overall sampling

frequency of 33 Hz, can already characterize systems with holding times typically as low as 0.1 s. The technique was validated using tubular reactors and a stirred vessel, showing excellent results in case of single-phase gas flow. In the presence of solids, the technique is somewhat more complex, but it was possible to separate the effects of the gas and the solids phase on the ultrasonic velocity accurately. The technique was applied to a novel multistage CFB reactor for biomass gasification. It was found that the overall gas-phase hydrodynamics could be described by a model of N equal mixed tanks in series, in which the number of tanks corresponds closely to the actual number of segments in the riser. Analysis of the RTD curves also showed that there are no dead zones/bypass streams with a low exchange rate to the main flow field present in the new reactor. The ultrasonic technique employed can determine the composition of binary gas mixtures at a high sampling frequency in the presence of a fluctuating solids holdup and is, furthermore, able to measure the local solids fraction simultaneously. The method can be completely noninvasive and can be used in highly scattering media and through reactor walls, possibly also for industrial reactors (although in that case, lower frequencies should be used to offset the longer measurement path length). Acknowledgment The authors thank P. J. Wijnstra for his contribution to the experimental work, B. Knaken for technical support, and G. F. Versteeg and W. P. M. van Swaaij for cooperating in the discussions. The Netherlands Energy Research Foundation (ECN) and The Netherlands Organization for Scientific Research (NWO-CW) are gratefully acknowledged for financial support. Notation A ) parameter defined in eq 6, m2/s2 B ) parameter defined in eq 6, m2/s2 Bo ) Bodenstein number (Bo ) Pe Dt/L) Cp ) heat capacity at constant pressure, J/(kg K) Cv ) heat capacity at constant volume, J/(kg K) C ) parameter defined in eq 6, m2/s2 dp ) particle size, µm D ) dispersion coefficient, m2/s Do ) inlet (smallest) diameter ()0.01 m) of the bottom cone, m D1 ) diameter at the solids level in the bottom cone, m Dt ) reactor diameter, m Ev ) bulk modulus of elasticity, Pa E(t) ) E function defined in eq 9, 1/s F(t) ) F function defined in eq 10 Gs ) solids flux, kg/(m2 s) L ) length, m I ) intensity, V MO2 ) second moment, s2 NCISTR ) number of CISTRs P ) pressure, Pa Pe ) Pe´clet number (Pe ) UL/D) Rxy ) cross-correlation function defined in eq 8, V2 ht ) mean residence time, s htNCISTR ) mean residence time according to the NCISTR interpretation model, s htpfr ) mean residence time according to the PFR interpretation model, s httot ) mean residence time defined in eq 16, s t ) time, s

Ind. Eng. Chem. Res., Vol. 42, No. 22, 2003 5515 U ) velocity, m/s Ur ) riser velocity at the smallest cross section (Do), m/s Ut ) terminal velocity, m/s V ) volume, m3 or mL Vrel ) relative volume (Vrel ) Vrtd/Vgas) Vgas ) volume of the reactor corrected for the presence of solids, m3 or mL Vreactor ) volume of the reactor, m3 or mL Vrtd ) volume of the reactor calculated on the basis of the RTD curve, m3 or mL x ) path length, m Greek Symbols R ) attenuation coefficient, 1/m βgrav ) solids fraction determined by weighing ∆t ) time difference, s ∆pbc ) pressure drop over the bottom cone of the elements of the novel reactor for biomass gasification, Pa Φv ) volumetric flow rate, m3/s γ ) ratio of Cp to Cv Γ ) gamma function defined in eq 15 Γin ) incomplete gamma function (eq 15) φ ) tracer-gas volume fraction θ ) reduced time defined in eq 13 F ) density, kg/m3 σ2 ) variance defined in eq 14, s2 σθ2 ) normalized variance defined in eq 14 τ ) holding time defined in eq 12, s υ ) speed of sound , m/s Subscripts r ) reference v ) valve

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Received for review December 19, 2002 Revised manuscript received August 21, 2003 Accepted August 25, 2003 IE021058K