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Radioisotope tracer study in a sludge hygienization research irradiator (SHRI)
Applied Radiation and Isotopes 54 (2001) 1±10
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Radioisotope tracer study in a sludge hygienization research irradiator (SHRI) H.J. Pant a,*, J. ThyÂn b, R. Zitny b, B.C. Bhatt c a Isotope Applications Division, Bhabha Atomic Research Centre, Trombay, Mumbai 400 085, India Department of Process Engineering, Czech Technical University, Prague 6, Technicka 4, 166 07, Czech Republic c Radiological Physics and Advisory Division, Bhabha Atomic Research Centre, Trombay, Mumbai 400 085, India
b
Received 11 September 1999; received in revised form 15 November 1999; accepted 10 December 1999
Abstract A radioisotope tracer study has been carried out in a batch type sludge hygienization research irradiator with ¯ow from top to bottom, the objective being to measure ¯ow rate, circulation and mixing times and to investigate the hydrodynamic behaviour of the irradiator for identifying the cause(s) of malfunction. A stimulus±response technique with NH82 4 Br as a tracer was used to measure the above parameters. Experiments were carried out at three dierent ¯ow rates, i.e 1.0, 0.64 and 0.33 m3/min. Three combined models based on a set of dierential equations are proposed and used to simulate the measured tracer concentration curves. The obtained parameters were used to estimate dead volume and analyse hydrodynamic behaviour of the irradiator. The nonlinear regression problem of model parameter estimation was solved using the Marquardt±Levenberg method. The measured ¯ow rate was found to be in good agreement with the values shown by the ¯ow meter. The circulation times were found to be half of the mixing times. A simple approach for estimation of dose based on a known vertical dose-rate pro®le inside the irradiator is presented. About one-fourth of the volume of the irradiator was found to be dead at lower ¯ow rates and this decreased with increase in ¯ow rate. At higher ¯ow rates, a semi stagnant volume was found with slow exchange of ¯ow between the active and dead volumes. 7 2000 Elsevier Science Ltd. All rights reserved. Keywords: Sludge hygienization research irradiator; Stimulus±response technique; Radioisotope tracer; Tracer ®rst appearance time; Flow rate; Circulation time; Mixing time; Dead volume; Stagnant region; Mean residence time; Residence time distribution; Models; Marquardt±Levenberg method; Runge±Kutta method; Covariance matrix; Minimum absorbed dose; Most probable dose
1. Introduction Many industrial process systems involve ¯ow of one or more ¯uids. Desired ¯ow patterns (hydrodynamics) are the key to the success of these processes. The
* Corresponding author. Tel.: +91-22-550-5161; fax: +9122-550-5151/551-9613. E-mail address: [email protected] (H.J. Pant).
industrial process systems are normally designed to have either of the two ideal ¯ow patterns, i.e. plug ¯ow or well mixed ¯ow (Levenspiel, 1991). However, in practice some deviation from the designed ¯ow pattern is quite common due to a number of reasons such as, improper design, scale-up eects, malfunction, improper operating conditions etc.. In bioreactors, even a small degree of deviation from the designed ¯ow pattern or any malfunction could lead to failure of the process itself. Irradiation of sludge by gamma
0969-8043/00/$ - see front matter 7 2000 Elsevier Science Ltd. All rights reserved. PII: S 0 9 6 9 - 8 0 4 3 ( 0 0 ) 0 0 1 0 1 - 9
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H.J. Pant et al. / Applied Radiation and Isotopes 54 (2001) 1±10
radiation is one such process. The irradiation of sludge is aimed at reducing the microbial load by several log cycles. After irradiating a batch of sludge for a predetermined period of time, the coliform counts should be below 102/ml. The pre-determined time depends upon the strength of the source used and irradiation time of the sludge in the vessel. Each element of the sludge should receive the appropriate minimum required dose while undergoing the irradiation process. In order to receive the uniform dose, all the ¯uid elements should have a minimum residence time in the irradiation zone. Liquid sludge irradiators can be designed to operate either in batch or continuous ¯ow modes. The continuous ¯ow irradiators developed till date use high-energy electron accelerators as the source of irradiation. The advantage of a continuous ¯ow irradiator over a batch irradiator is that the time is not lost in evacuating and ®lling the irradiation vessel. This results in better utilisation of the radiation energy. In a continuous type irradiator, the sludge ¯ow rate needs to be accurately controlled in order that the residence time of the sludge in the irradiation zone is more than the minimum irradiation time required to receive the desired dose. In addition, the velocity of sludge is much lower when compared to the velocity in recirculating batch type irradiators. This allows settling of the sludge since there is absence of turbulence inside the irradiator. Variation in the spatial dose rate also exists in the irradiation vessel and the value is given by the geometry of the source (cylindrical, line or grid source) and the sludge ¯ow pattern through the irradiator. For these reasons, in the irradiation zone, a thorough agitation of the sludge is required either by mechanical means or using pressurised air. Lavale et al. (1998) have described several dierent types of batch and continuous irradiators for sludge irradiation and a number of
Fig. 1. Regrowth of coliforms in post irradiated sludge (dose 500 krad).
designs of batch type irradiators have been proposed and tested (Krishnamurty, 1986). Mixing in a batch type process can be achieved either by agitation or continuous recirculation of the sludge. An important criterion is the absence of any dead volume in the recirculation loop or inside the irradiator away from irradiation zone (Lessel, 1998). The presence of dead volume in any system may either be due to improper design or improper operating conditions. Routine microbiological measurements (Rawat, 1995) in a sludge hygienization research irradiator (SHRI) described below, have shown regrowth of coliform counts in post irradiated sludge stored at room temperature (308C). An example plot of regrowth of coliform counts as a function of time is shown in Fig. 1. The regrowth of coliform in post irradiated sludge can be due to one or more of the following reasons: (1) segregation of pathogens in clusters and nonuniformity in the dose received; (2) presence of dead volume away from the irradiation zone; (3) contamination of the associated recirculation pipeline; and (4) improper ¯ow characteristics. The aim of the present radioisotope tracer study has been to measure hydrodynamic parameters such as ¯ow rate, mixing times and mean residence time of sludge, and to investigate the hydrodynamic behaviour of the irradiator with the main objective of proving or disproving the existence of a dead volume. 2. Description of the irradiator Studies over the last two decades have shown that a gamma radiation dose of 3±4 kGy is adequate for disinfection of liquid sludge (Suess et al., 1977). In collaboration with the Municipal Corporation of Vadodara, the Bhabha Atomic Research Centre (BARC), Mumbai, India, has set up a pilot-scale plant for hygienization of liquid sewage sludge (02% solids) using 60 CO as the source of gamma irradiation (Iya and Krishnamurty, 1984; Krishnamurty et al., 1992; Lavale et al., 1998). Subsequent use is made of the product as a safe fertilizer. The irradiator consists of a stainless steel vessel of 3.7 m3 volume, including the volume of the recirculation loop and excluding the volume occupied by the source assembly. The facility is designed to irradiate a batch of 3.0 m3 sludge. The level of the sludge is about 39 cm above the source assembly. A conical distributor, mounted at the top of the vessel, distributes the sludge uniformly across the cross-section of the vessel. A planar grid source assembly consisting of 13 tubes is mounted a little above the centre of the vessel. The maximum design capacity of the source in each cell is 18.5 PBq (500 kCi). During the course of the study, the irradiator was loaded with a source of strength about 3.0 PBq (55 kCi). However,
H.J. Pant et al. / Applied Radiation and Isotopes 54 (2001) 1±10
tracer experiments were carried out without source. A schematic diagram of one such irradiator and the source arrangement is shown in Fig. 2. The digested sludge is fed into the irradiation vessel by gravity from an overhead silo in a batch of measured volume (3.0 m3). The sludge in the irradiator is then kept under constant circulation using a pipeline of 10 cm diameter and a pump, pumping at a rate of 1.0 m3/min to prevent settling and also to achieve uniform exposure to gamma radiation. After irradiating the sludge for a predetermined period, the contents are drained into drying beds for subsequent use as fertilizer. The process cycle is then repeated with a fresh batch of sludge. It was the regrowth of coliforms in post-irradiated sludge, which led to the following investigation using radiotracer techniques.
3. Experimental A stimulus±response technique was used for the determination of hydrodynamic characteristics of liquid sludge in the irradiator. A series of radioisotope tracer experiments was carried out in the normal recirculation
3
mode, where sludge is kept under constant circulation, with ¯ow from top to bottom. The experiments were carried out at three dierent ¯ow rates, i.e. 1.0, 0.64 and 0.33 m3/min, whereas in the reverse circulation mode, the experiments were carried out at a ¯ow rate of 40 m3/h only. The sludge level in the irradiator was maintained constant during the experiments. Use was made of 82 Br in the form of ammonium bromide dissolved in aqueous solution as the tracer for the study, and about 250±370 MBq (7±10 mCi) activity was used in each experiment. The tracer was instantaneously injected at the suction end of the recirculation pump using compressed air (pressure 05 kg/cm3) and monitored at the inlet and outlet of the irradiator using collimated NaI(Tl) scintillation detectors. The experimental set-up for the normal recirculation mode is shown in Fig. 3. In order to measure the ¯ow rate, an additional detector D0 was mounted on the inlet pipeline. The detectors were connected to a ®ve-channel data acquisition system (DAS) which was set to record 1000 data points with a sampling time of 1 s. For further analysis, the recorded data were transferred to a laptop computer connected to the DAS. The mean solid content in the sludge during the experiments was about 1.25%.
Fig. 2. Schematic of irradiator and source assembly.
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H.J. Pant et al. / Applied Radiation and Isotopes 54 (2001) 1±10
4. Data analysis
4.2. Tracer ®rst appearance time
During ®rst recirculation, the inlet peaks of the tracer response curves, recorded by detectors D0 and D1 in the normal recirculation ¯ow mode, were used to determine the ¯ow rate produced by the centrifugal pump. The tracer concentration distribution curve recorded by one of the detectors D1 was used for the determination of the tracer ®rst appearance time (TFAT) of the tracer, in addition to circulation tc and mixing tm times. The dead and stagnant volumes were estimated by modelling the response curves recorded by detectors D1 and D2.
The tracer distribution curve recorded by detector D1 shows a sharp peak at the beginning, which returns to the background level and starts increasing again after one circulation (see Fig. 4b). The tracer ®rst appearance time is the minimum time required by sludge for one circulation through the irradiator. TFAT is important for estimation of the minimum dose received by sludge in one circulation. The values of TFAT determined for dierent ¯ow rates are presented in the Table 2. 4.3. Circulation and homogenization or mixing times
4.1. Flow rate measurement A transit time method (IAEA, 1990) was used to evaluate the ¯ow rate, Q, from the data recorded by detectors D0 and D1 and is given as: Q
pd 2 Ltt 4
1
where, d is the diameter of pipeline, L is the distance between the two detectors and tt is the transit time determined as the dierence between the ®rst moments of the two tracer distribution curves. Fig. 4(a) shows a representative plot of tracer distribution curve recorded by the detectors D0 and D1 for the transit time of 1 s. The results of the ¯ow rate measurement are presented in Table 1, with Vpipe being the volume of the pipe. The mean value of ¯ow rate was determined to be 1.0 m3/min, with a one-sigma standard deviation s of 0.068 m3/min.
The data recorded by detectors D1 and D2 were used to determine the circulation and homogenization or mixing times. The circulation time tc ), was estimated as the time lapse between two successive peaks of tracer concentration curves as shown in Fig. 4(b). The homogenization or mixing time (tm), is the minimum time required for the tracer to mix homogeneously with the entire volume of the sludge and is estimated to be complete when the tracer concentration changes becomes constant. The standard deviation s of a group of a readings is calculated and plotted as a function of time (IAEA, 1990). Adequate mixing or homogenization is deemed to have been achieved when s becomes constant. The mixing times determined are presented in Table 2. 4.4. Modelling 4.4.1. Dead volume and stagnant region If the stimulus±response technique is sensitive enough for the measurement of residence time distribution (RTD), then the relative dead volume Vdead =V can be estimated as: Vdead =V 1 ÿ Veff =V 1 ÿ texp =ttheo
2
where, Ve is the eective volume, V is the total geometric volume of the irradiator, ttheo is the theoretical
Table 1 Flow rate measurement
Fig. 3. Experimental setup for normal circulation mode.
Sr. No.
Vpipe pd 2 L=4 (m3)
Transit time, tt (s)
Flow rate, Q (m3/min)
1 2 3 4
0.040 0.040 0.023 0.023
2.5 2.6 1.3 1.3
0.97 0.93 1.06 1.06
H.J. Pant et al. / Applied Radiation and Isotopes 54 (2001) 1±10
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Fig. 4. (a) Flow rate measurement; (b) time of ®rst appearance, circulation and homogenisation or mixing time.
mean residence time ttheo V=Q and texp is the mean residence time which is determined from measured tracer curves. The dead volume is the part of the geometric or total volume of the system, which does not take part in the
¯ow and is ignored in the measurement of residence time distribution curves. The Stagnant region is a perfectly mixed part of the dead volume with slow exchange of ¯uid (cross ¯ow) between the eective and dead volumes.
Table 2 Tracer ®rst appearance time, circulation time and homogenization or mixing time Sr. No.
Flow rate, Q (m3/min)
TFAT (s)
Circulation time, tc (s)
Standard error (%)
Mixing time, tm (s)
Standard error (%)
1 2 3
0.33 0.64 1.0
160 145 61
300 215 150
7.0 ± ±
580 560 400
± ± 5.0
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H.J. Pant et al. / Applied Radiation and Isotopes 54 (2001) 1±10
A methodology of determination of dead volume or stagnancy from measured residence time distribution has been developed for continuous ¯ow systems (Himmelblau and Bischo, 1968; Levenspiel, 1991) and has been applied to the present closed batch type recirculating system (irradiator). The data between zero time t0 and homogenization time are used for model simulation. Three simple combined models with limited number of parameters, based on a set of dierential equations, were used for description of the measured RTD. The set of equations is solved numerically in the time domain using the Runge±Kutta method. The estimation of model parameters is a nonlinear regression problem and is solved by a modi®ed Marquardt± Levenberg method adapted for models de®ned by a set of ordinary dierential equations. RTD analysis software developed by Zitny and ThyÂn (1996) was used for data treatment, normalization, determination of process parameters and identi®cation of model parameters. As a criterion of ®t, either the sum of squares or the sum of the absolute deviations can be selected. Estimation of the model parameters is based upon the least squares method, i.e. minimizing the sum of squares or absolute deviations of dierences of measured and model computed responses, and is given as: s2
n X
ÿ 2 yi ÿ y ti , x i , p~ minimum
i1
3a
p~ p1 , p2 , . . . ,pm or jY ÿ Yp j
n X ÿ jyi ÿ y ti , x i , p~ j minimum
3b
i1
where n is the number of measured stimulus x 1 , . . . ,x n and response y1 , . . . ,yn data points and m is the number of model parameters p1 , . . . ,pm with condition m n). The Marquardt±Levenberg method is an iterative method, which estimates values of model parameters pi such that the value of s 2 is minimum. In each iteration, the system of dierential equations is solved based upon the approximate values of model parameters pi obtained from previous iteration. On the basis of the computed matrix, Ckm , and the estimated standard deviation s between measured yi and model predicted data points, it is possible to estimate the accuracy of the computed model parameters as s pk : ÿ1 , s 2 pk s 2 C kk
k 1, 2, . . . ,m:
4
where C ÿ1 denotes the inverse of the matrix called the covariance matrix.
The dead and stagnant volumes were estimated by means of regression analysis. Three simple combined models described by a set of dierential equations are proposed and these have been used to analyse the recorded data. 4.4.1.1. Model-A: ideal mixers in series with plug ¯ow in recirculation loop. This model assumes that the ¯uid mixing in the irradiator is created by the distributor, the ¯uid impact on the source tube and ¯ow through the source grid. The irradiator is represented by a series of N ideal mixers each of volume V1, in series with a plug ¯ow component of volume Vp, in the recirculation loop. The physical representation of the model is shown in Fig. 5(a). The model parameters are mean residence time texp ), ratio of volume of plug ¯ow component to volume of ideal mixers a Vp =Vim and number of ideal mixers in series (N ). The total volume is sum of the volume of individual ideal mixers and plug ¯ow component V Vp Vim ), where Vim NV1 : The curve recorded by detector D1 alone was used for the evaluation of parameters after normalization. The ®rst peak was considered as the stimulus x i and the remaining part of the curve as the response yi of the irradiator and the recirculation pipeline. A typical tracer distribution curve recorded by detector D1 is shown in Fig. 6(a). The results of model simulation and reproducibility are given in Tables 3 and 4, respectively. 4.4.1.2. Model-B: ideal mixer in series with plug ¯ow inside the irradiator and in recirculation loop. The volume of the plug ¯ow component, Vp, estimated from Model-A is higher than the volume of the recirculation pipeline (Vr), thus indicating the existence of the plug ¯ow inside the irradiator. Therefore in Model-B, a plug ¯ow component is connected in series with the ideal mixers in addition to the plug ¯ow component in the recirculation loop. The physical representation of the model is shown in Fig. 5(b). The model parameters are mean residence time texp of the sludge in the irradiator, the ratio of the volume of the plug ¯ow component in the recirculation loop to the total volume a Vr =V), the ratio of the volume of the plug ¯ow component inside the irradiator to the volume of the ideal mixers in series b Vp =Vim and the number of ideal mixers (N ), where, Vim NV1 : In the present model, the data recorded by the two detectors (D1 and D2) have been used for simulation and estimation of model parameters. The curves recorded by detectors D1 and D2 were used to represent the stimulus x i and response yi ), respectively. The experimentally measured and model simulated curves are shown in Fig. 6(b). The results of model
H.J. Pant et al. / Applied Radiation and Isotopes 54 (2001) 1±10
7
Fig. 5. Physical representation of (a) RTD Model-A; (b) RTD Model-B; (c) RTD Model-C.
Table 3 Reproducibility of results for Q 1 (m3/min): Model-A Sr. No.
texp 2s pt (s)
a Vp =Vim 2s pa
N
jY ÿ Yp j
Veff =V
Vdead =V
1 2 3 Mean2s Standard error (%)
158.7820.2 174.1620.48 168.1920.48 167.0426.33 03.8
0.6120.004 0.2920.004 0.5220.006 0.4720.135 028.7
4 4 4 4
0.019 0.018 0.040 ± ±
0.882 0.967 0.934 0.92820.029 03.6
0.118 0.033 0.066 0.07220.029 014.5
8
H.J. Pant et al. / Applied Radiation and Isotopes 54 (2001) 1±10
Fig. 6. Example of identi®cation from: (a) data of one detector; (b) data of two detectors.
simulation and reproducibility for ¯ow rate Q = 1 m3/ min are presented in Table 5. 4.4.1.3. Model-C: ideal mixers in series with stagnant volume and plug ¯ow in recirculation loop. This model was used to estimate stagnancy in the irradiator. The local turbulence or vortices create exchange of ¯uid
between the stagnant and eective volume. The physical representation of the model is shown in Fig. 5(c). The model parameters are the mean residence time texp ), the ratio of the volume of the plug ¯ow component to that of ideal mixers a Vp =Vim ), the ratio of the volume of the stagnant region to that of the eective region b Vp =Vim ), and the number of ideal
Table 4 Results of model simulation: Model-A Q (m3/min)
texp 2s pt (s)
a Vp =Vim 2s pa
N
jY ÿ Yp j
Veff =V
Vdead =V
0.33 0.64 1.0
413.421.9 277.521.1 167.0426.33
0.7820.006 0.6420.01 0.4720.135
2 3 4
0.04 0.04 0.03
0.758 0.987 0.928
0.242 0.013 0.072
H.J. Pant et al. / Applied Radiation and Isotopes 54 (2001) 1±10
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Table 5 Results of model simulation and reproducibility for Q =1.0 (m3/min): Model-B Sr. No.
texp 2s pt (s)
a2s pa Vr = Vp Vim
b2s pb Vp = Vp Vim
N
jY ÿ Yp j
Vdead =V
1 2 3 Mean2s Standard error (%)
156.020.2 163.320.3 168.220.6 162.525.01 03.1
0.0620.001 0.0720.002 0.0520.003 0.0620.008 013.3
0.3820.001 0.1620.02 0.3620.003 0.3020.099 033
3 4 3 3.320.5 015
0.022 0.018 0.052 ± ±
0.133 0.093 0.065 0.09720.025 011
mixers (N ). The total volume is the sum of the volume of the plug ¯ow component and the volumes of the individual ideal mixers V Vp Vim ), where, Vim NV1 V2 ). The stagnant volume is represented by a parallel series of perfect mixers, each of volume V2, with exchange of ¯uid between N mixers each of volume, V1, representing the main ¯ow. The data recorded by detector D1 were used for model simulation, in a similar manner to that of Model-A. Results of the model simulation are given in Table 6.
5. Results and discussions One of the main reasons for regrowth of coliform counts in the post-irradiated sludge is considered to be insucient dose received by some of the sludge molecules as a result of nonuniform dose rate pro®le inside the irradiator. Knowledge of the dose rate pro®le and residence time of the sludge can be used to estimate optimum irradiation time and assess the eciency of the irradiation process. The minimum absorbed dose Dmin and most probable dose (D ) received in one circulation are estimated from knowledge of TFAT and tc , respectively, provided the dose rate pro®le inside the irradiator is known. The vertical dose rate pro®le in water, produced by a planar grid source assembly of cobalt-60 (Activity: 3.7 PBq) consisting of 13 tubes, has been published by Krishnamurty (1986). The dose rate is minimum along the vertical walls and maximum along the centre of the irradiator. The dose rate dD=dt at a point depends upon the distance l from the grid and is estimated using the following relation:
dD=dt k1 exp ÿ k2 l Gy=min
5
where values for k1 and k2 are obtained by exponential regression and are found to be 84 Gy/min and 7.8 mÿ1 for regions near the wall, and 94 Gy/min and 7.5 mÿ1 for regions close to the vertical axis of the irradiator, respectively. The dose at a point in a horizontal plane is obtained by integrating Eq. 5. Thus: D
t k1 ÿ 2 ÿ e ÿk2 L1 ÿ e ÿk2 L2 Gy L k2 1 L 2
6
where, time t is equal to TFAT or tc : L1 and L2 are considered to be equal to each other and their value is taken as 0.5 m for estimation of dose. The minimum absorbed dose Dmin is received by sludge molecules which ¯ow with maximum velocity or have a residence time equal to TFAT, and which travel along the vertical walls of the irradiator. Similarly, the most probable dose (D ) is received by the sludge molecules which ¯ow along the vertical axis and have residence time equal to tc : The dose received by the sludge molecules for residence times equal to TFAT and tc are calculated to be about 20 and 60 Gy, respectively. This implies for ¯uid elements which ¯ow along the wall of the irradiator only and receive minimum dose that these needs to be recirculated some 100 times more than the rest of the ¯uid elements ¯owing along the centre of the irradiator in order to receive the desired value of dose, i.e. 3±4 kGy. The irradiation times for sludge ¯owing close to the vertical walls and along the vertical axis are estimated to be 2.7 and 2.4 h, respectively. However, the mean dose received may be equal to the desired value for sludge molecules which undergo a number of circulations over a period of time. The ratio of minimum absorbed dose to most
Table 6 Results of model simulation: Model-C Q (m3/min)
texp 2s pt (s)
a2s pa Vp =Vim
N
f 2 s pf
b 2 s pb V2 =V1
jY ÿ Yp j
Veff =V
Vdead =V
0.33 0.64 1.0
473.4216.2 285.622.3 193.4214.1
0.4220.02 0.4420.02 0.2920.03
6 8 5
0.2920.01 0.2820.02 0.0120.003
0.9920.06 0.7120.06 0.2520.1
0.03 0.04 0.015
0.868 01 01
0.132 0 0
10
H.J. Pant et al. / Applied Radiation and Isotopes 54 (2001) 1±10
probable dose, i.e. Dmin =D is a measure of the degree of uniformity of dose inside the irradiator, and is estimated to be about 0.3. For an ideal case of complete uniformity, this ratio has to be equal to unity. As the solid particles in sludge may form clusters during recirculation and may therefore have less absorption ability than water, the minimum desired irradiation time should be multiplied by the appropriate correction factor. Analysis by Model-A showed that about one-fourth of the total volume is dead at the lowest ¯ow rate (0.33 m3/min) and is minimum at intermediate ¯ow rate (0.64 m3/min). At the highest ¯ow rate (1.0 m3/ min), the dead volume is higher than the intermediate ¯ow rate, indicating the creation of local turbulence or vortices with slow exchange of ¯uid between eective and dead volume. The existence of a stagnant volume was further con®rmed by analysis with Model-C, which showed that at higher ¯ow rates (>0.64 m3/ min) no dead volume exists inside the irradiator because of vortices, with slow exchange of ¯uid. With a ¯at vertical dose rate pro®le inside the irradiator, the existence of the plug ¯ow region is important for dose uniformity. The results of analysis by Model-A and Model-C show that the volume of the plug ¯ow region decreases with increase in ¯ow rate. The ratio of the geometric volume of the recirculation pipeline to the total volume Vr =V is 0.057. The same ratio has been estimated to be 0.06 by Model-B. The estimated value is within acceptable accuracy. 6. Conclusions A stimulus±response technique used in conjunction with model simulation provides important information about the hydrodynamic behavior of a closed recirculating batch type sludge irradiator. From the present study, the following main conclusions have been drawn: 1. The measured ¯ow rates are in good agreement with values shown by the ¯ow meter. This indicates that calibration of the ¯ow meter and pump capacity has not changed. 2. For presently reported conditions, the minimum time of irradiation has to be more than 3 h. 3. About one-fourth of the volume of the sludge in the irradiator behaves as dead volume at lower low ¯ow rate (0.33 m3/min). The dead volume decreases at higher values of ¯ow rates. 4. At a ¯ow rate of 1.0 m3/min, local turbulence or vortices with small exchange of ¯uid are produced. 5. The volume of plug ¯ow component decreases from 2/3±1/3 with increase in ¯ow rate from 0.33±1.0 m3/ min.
6. The irradiation vessel can be described by a series of four ideal mixers N 4 with stagnant volume and a plug ¯ow component in series. 7. Poor degree of uniformity was observed in dose received during one circulation.
Acknowledgements The authors wish to thank Dr. S.M. Rao, M.R. Shah, Dr. S.V. Navada, P. Walinjkar, K.P. Rawat and M. Assadullah for their help and useful suggestions during the course of this study. J. ThyÂn and R. Zitny would also like to acknowledge ®nancial support provided from the International Atomic Energy Agency (IAEA) to develop the software for data analysis.
References International Atomic Energy Agency, Guidebook on Radioisotope Tracers in Industry, 1990. Technical Report Series No. 316, IAEA, Vienna, Austria. Himmelblau, D.M., Bischo, K.B., 1968. Process Analysis and Simulation: Deterministic Systems. Wiley, New York. Iya, V.K., Krishnamurty, K., 1984. Radiation treatment of sewage sludge in India. Radiat. Phys. Chem. 24, 67. Krishnamurty, K., 1986. Parameteric relationships for gamma dose and irradiation homogeneity in a sewage sludge irradiator. Radiat. Phys. Chem. 28, 381. Krishnamurty, K., Naik, A.D., Patel, S.S., Sinha, M.K., Ramakrishna, G.S., Lavale, D.S., Shah, M.R., 1992. Sewage sludge irradiation technology development programme in India. In: Proc. Symposium, Karlsruhe, 1992, IAEA, Vienna, Austria. Lessel, T., 1998. European experiences with gamma irradiation of sewage sludge for disinfection and alternative treatments. In: Proc. of international Conference on Applications of Radioisotopes and radiation in Industrial Development (ICARID-98), Mumbai, India. Lavale, D.S., Shah, M.R., Rawat, K.P., George, J.R., 1998. Sewage sludge irradiators. In: Proc. Symp. on Radiation Technology for Conservation of the Environment, Zakopane, Poland, 1997, IAEA-TECDOC-1023, Vienna, Austria. Levensiple, O., 1991. Chemical Reaction Engineering, 2nd ed. Wiley Eastern Limited, New Delhi. Rawat, K.P., 1995. Studies on disinfection of sewage euents by gamma radiation. Isotope Division, Bhabha Atomic Research Centre, Mumbai, India, unpublished work. Suess, A., Lessel, T., 1977. Radiation treatment of sewage sludge: experience with an operating pilot plant. Radiat. Phys. Chem. 9, 353. ZitnyÂ, R., ThyÂn, J., 1996. Residence Time Distribution Software Analysis. Computer Manual Series No. 11, IAEA, Vienna, Austria.
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Radioisotope tracer study in a sludge hygienization research irradiator (SHRI) H.J. Pant a,*, J. ThyÂn b, R. Zitny b, B.C. Bhatt c a Isotope Applications Division, Bhabha Atomic Research Centre, Trombay, Mumbai 400 085, India Department of Process Engineering, Czech Technical University, Prague 6, Technicka 4, 166 07, Czech Republic c Radiological Physics and Advisory Division, Bhabha Atomic Research Centre, Trombay, Mumbai 400 085, India
b
Received 11 September 1999; received in revised form 15 November 1999; accepted 10 December 1999
Abstract A radioisotope tracer study has been carried out in a batch type sludge hygienization research irradiator with ¯ow from top to bottom, the objective being to measure ¯ow rate, circulation and mixing times and to investigate the hydrodynamic behaviour of the irradiator for identifying the cause(s) of malfunction. A stimulus±response technique with NH82 4 Br as a tracer was used to measure the above parameters. Experiments were carried out at three dierent ¯ow rates, i.e 1.0, 0.64 and 0.33 m3/min. Three combined models based on a set of dierential equations are proposed and used to simulate the measured tracer concentration curves. The obtained parameters were used to estimate dead volume and analyse hydrodynamic behaviour of the irradiator. The nonlinear regression problem of model parameter estimation was solved using the Marquardt±Levenberg method. The measured ¯ow rate was found to be in good agreement with the values shown by the ¯ow meter. The circulation times were found to be half of the mixing times. A simple approach for estimation of dose based on a known vertical dose-rate pro®le inside the irradiator is presented. About one-fourth of the volume of the irradiator was found to be dead at lower ¯ow rates and this decreased with increase in ¯ow rate. At higher ¯ow rates, a semi stagnant volume was found with slow exchange of ¯ow between the active and dead volumes. 7 2000 Elsevier Science Ltd. All rights reserved. Keywords: Sludge hygienization research irradiator; Stimulus±response technique; Radioisotope tracer; Tracer ®rst appearance time; Flow rate; Circulation time; Mixing time; Dead volume; Stagnant region; Mean residence time; Residence time distribution; Models; Marquardt±Levenberg method; Runge±Kutta method; Covariance matrix; Minimum absorbed dose; Most probable dose
1. Introduction Many industrial process systems involve ¯ow of one or more ¯uids. Desired ¯ow patterns (hydrodynamics) are the key to the success of these processes. The
* Corresponding author. Tel.: +91-22-550-5161; fax: +9122-550-5151/551-9613. E-mail address: [email protected] (H.J. Pant).
industrial process systems are normally designed to have either of the two ideal ¯ow patterns, i.e. plug ¯ow or well mixed ¯ow (Levenspiel, 1991). However, in practice some deviation from the designed ¯ow pattern is quite common due to a number of reasons such as, improper design, scale-up eects, malfunction, improper operating conditions etc.. In bioreactors, even a small degree of deviation from the designed ¯ow pattern or any malfunction could lead to failure of the process itself. Irradiation of sludge by gamma
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radiation is one such process. The irradiation of sludge is aimed at reducing the microbial load by several log cycles. After irradiating a batch of sludge for a predetermined period of time, the coliform counts should be below 102/ml. The pre-determined time depends upon the strength of the source used and irradiation time of the sludge in the vessel. Each element of the sludge should receive the appropriate minimum required dose while undergoing the irradiation process. In order to receive the uniform dose, all the ¯uid elements should have a minimum residence time in the irradiation zone. Liquid sludge irradiators can be designed to operate either in batch or continuous ¯ow modes. The continuous ¯ow irradiators developed till date use high-energy electron accelerators as the source of irradiation. The advantage of a continuous ¯ow irradiator over a batch irradiator is that the time is not lost in evacuating and ®lling the irradiation vessel. This results in better utilisation of the radiation energy. In a continuous type irradiator, the sludge ¯ow rate needs to be accurately controlled in order that the residence time of the sludge in the irradiation zone is more than the minimum irradiation time required to receive the desired dose. In addition, the velocity of sludge is much lower when compared to the velocity in recirculating batch type irradiators. This allows settling of the sludge since there is absence of turbulence inside the irradiator. Variation in the spatial dose rate also exists in the irradiation vessel and the value is given by the geometry of the source (cylindrical, line or grid source) and the sludge ¯ow pattern through the irradiator. For these reasons, in the irradiation zone, a thorough agitation of the sludge is required either by mechanical means or using pressurised air. Lavale et al. (1998) have described several dierent types of batch and continuous irradiators for sludge irradiation and a number of
Fig. 1. Regrowth of coliforms in post irradiated sludge (dose 500 krad).
designs of batch type irradiators have been proposed and tested (Krishnamurty, 1986). Mixing in a batch type process can be achieved either by agitation or continuous recirculation of the sludge. An important criterion is the absence of any dead volume in the recirculation loop or inside the irradiator away from irradiation zone (Lessel, 1998). The presence of dead volume in any system may either be due to improper design or improper operating conditions. Routine microbiological measurements (Rawat, 1995) in a sludge hygienization research irradiator (SHRI) described below, have shown regrowth of coliform counts in post irradiated sludge stored at room temperature (308C). An example plot of regrowth of coliform counts as a function of time is shown in Fig. 1. The regrowth of coliform in post irradiated sludge can be due to one or more of the following reasons: (1) segregation of pathogens in clusters and nonuniformity in the dose received; (2) presence of dead volume away from the irradiation zone; (3) contamination of the associated recirculation pipeline; and (4) improper ¯ow characteristics. The aim of the present radioisotope tracer study has been to measure hydrodynamic parameters such as ¯ow rate, mixing times and mean residence time of sludge, and to investigate the hydrodynamic behaviour of the irradiator with the main objective of proving or disproving the existence of a dead volume. 2. Description of the irradiator Studies over the last two decades have shown that a gamma radiation dose of 3±4 kGy is adequate for disinfection of liquid sludge (Suess et al., 1977). In collaboration with the Municipal Corporation of Vadodara, the Bhabha Atomic Research Centre (BARC), Mumbai, India, has set up a pilot-scale plant for hygienization of liquid sewage sludge (02% solids) using 60 CO as the source of gamma irradiation (Iya and Krishnamurty, 1984; Krishnamurty et al., 1992; Lavale et al., 1998). Subsequent use is made of the product as a safe fertilizer. The irradiator consists of a stainless steel vessel of 3.7 m3 volume, including the volume of the recirculation loop and excluding the volume occupied by the source assembly. The facility is designed to irradiate a batch of 3.0 m3 sludge. The level of the sludge is about 39 cm above the source assembly. A conical distributor, mounted at the top of the vessel, distributes the sludge uniformly across the cross-section of the vessel. A planar grid source assembly consisting of 13 tubes is mounted a little above the centre of the vessel. The maximum design capacity of the source in each cell is 18.5 PBq (500 kCi). During the course of the study, the irradiator was loaded with a source of strength about 3.0 PBq (55 kCi). However,
H.J. Pant et al. / Applied Radiation and Isotopes 54 (2001) 1±10
tracer experiments were carried out without source. A schematic diagram of one such irradiator and the source arrangement is shown in Fig. 2. The digested sludge is fed into the irradiation vessel by gravity from an overhead silo in a batch of measured volume (3.0 m3). The sludge in the irradiator is then kept under constant circulation using a pipeline of 10 cm diameter and a pump, pumping at a rate of 1.0 m3/min to prevent settling and also to achieve uniform exposure to gamma radiation. After irradiating the sludge for a predetermined period, the contents are drained into drying beds for subsequent use as fertilizer. The process cycle is then repeated with a fresh batch of sludge. It was the regrowth of coliforms in post-irradiated sludge, which led to the following investigation using radiotracer techniques.
3. Experimental A stimulus±response technique was used for the determination of hydrodynamic characteristics of liquid sludge in the irradiator. A series of radioisotope tracer experiments was carried out in the normal recirculation
3
mode, where sludge is kept under constant circulation, with ¯ow from top to bottom. The experiments were carried out at three dierent ¯ow rates, i.e. 1.0, 0.64 and 0.33 m3/min, whereas in the reverse circulation mode, the experiments were carried out at a ¯ow rate of 40 m3/h only. The sludge level in the irradiator was maintained constant during the experiments. Use was made of 82 Br in the form of ammonium bromide dissolved in aqueous solution as the tracer for the study, and about 250±370 MBq (7±10 mCi) activity was used in each experiment. The tracer was instantaneously injected at the suction end of the recirculation pump using compressed air (pressure 05 kg/cm3) and monitored at the inlet and outlet of the irradiator using collimated NaI(Tl) scintillation detectors. The experimental set-up for the normal recirculation mode is shown in Fig. 3. In order to measure the ¯ow rate, an additional detector D0 was mounted on the inlet pipeline. The detectors were connected to a ®ve-channel data acquisition system (DAS) which was set to record 1000 data points with a sampling time of 1 s. For further analysis, the recorded data were transferred to a laptop computer connected to the DAS. The mean solid content in the sludge during the experiments was about 1.25%.
Fig. 2. Schematic of irradiator and source assembly.
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H.J. Pant et al. / Applied Radiation and Isotopes 54 (2001) 1±10
4. Data analysis
4.2. Tracer ®rst appearance time
During ®rst recirculation, the inlet peaks of the tracer response curves, recorded by detectors D0 and D1 in the normal recirculation ¯ow mode, were used to determine the ¯ow rate produced by the centrifugal pump. The tracer concentration distribution curve recorded by one of the detectors D1 was used for the determination of the tracer ®rst appearance time (TFAT) of the tracer, in addition to circulation tc and mixing tm times. The dead and stagnant volumes were estimated by modelling the response curves recorded by detectors D1 and D2.
The tracer distribution curve recorded by detector D1 shows a sharp peak at the beginning, which returns to the background level and starts increasing again after one circulation (see Fig. 4b). The tracer ®rst appearance time is the minimum time required by sludge for one circulation through the irradiator. TFAT is important for estimation of the minimum dose received by sludge in one circulation. The values of TFAT determined for dierent ¯ow rates are presented in the Table 2. 4.3. Circulation and homogenization or mixing times
4.1. Flow rate measurement A transit time method (IAEA, 1990) was used to evaluate the ¯ow rate, Q, from the data recorded by detectors D0 and D1 and is given as: Q
pd 2 Ltt 4
1
where, d is the diameter of pipeline, L is the distance between the two detectors and tt is the transit time determined as the dierence between the ®rst moments of the two tracer distribution curves. Fig. 4(a) shows a representative plot of tracer distribution curve recorded by the detectors D0 and D1 for the transit time of 1 s. The results of the ¯ow rate measurement are presented in Table 1, with Vpipe being the volume of the pipe. The mean value of ¯ow rate was determined to be 1.0 m3/min, with a one-sigma standard deviation s of 0.068 m3/min.
The data recorded by detectors D1 and D2 were used to determine the circulation and homogenization or mixing times. The circulation time tc ), was estimated as the time lapse between two successive peaks of tracer concentration curves as shown in Fig. 4(b). The homogenization or mixing time (tm), is the minimum time required for the tracer to mix homogeneously with the entire volume of the sludge and is estimated to be complete when the tracer concentration changes becomes constant. The standard deviation s of a group of a readings is calculated and plotted as a function of time (IAEA, 1990). Adequate mixing or homogenization is deemed to have been achieved when s becomes constant. The mixing times determined are presented in Table 2. 4.4. Modelling 4.4.1. Dead volume and stagnant region If the stimulus±response technique is sensitive enough for the measurement of residence time distribution (RTD), then the relative dead volume Vdead =V can be estimated as: Vdead =V 1 ÿ Veff =V 1 ÿ texp =ttheo
2
where, Ve is the eective volume, V is the total geometric volume of the irradiator, ttheo is the theoretical
Table 1 Flow rate measurement
Fig. 3. Experimental setup for normal circulation mode.
Sr. No.
Vpipe pd 2 L=4 (m3)
Transit time, tt (s)
Flow rate, Q (m3/min)
1 2 3 4
0.040 0.040 0.023 0.023
2.5 2.6 1.3 1.3
0.97 0.93 1.06 1.06
H.J. Pant et al. / Applied Radiation and Isotopes 54 (2001) 1±10
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Fig. 4. (a) Flow rate measurement; (b) time of ®rst appearance, circulation and homogenisation or mixing time.
mean residence time ttheo V=Q and texp is the mean residence time which is determined from measured tracer curves. The dead volume is the part of the geometric or total volume of the system, which does not take part in the
¯ow and is ignored in the measurement of residence time distribution curves. The Stagnant region is a perfectly mixed part of the dead volume with slow exchange of ¯uid (cross ¯ow) between the eective and dead volumes.
Table 2 Tracer ®rst appearance time, circulation time and homogenization or mixing time Sr. No.
Flow rate, Q (m3/min)
TFAT (s)
Circulation time, tc (s)
Standard error (%)
Mixing time, tm (s)
Standard error (%)
1 2 3
0.33 0.64 1.0
160 145 61
300 215 150
7.0 ± ±
580 560 400
± ± 5.0
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H.J. Pant et al. / Applied Radiation and Isotopes 54 (2001) 1±10
A methodology of determination of dead volume or stagnancy from measured residence time distribution has been developed for continuous ¯ow systems (Himmelblau and Bischo, 1968; Levenspiel, 1991) and has been applied to the present closed batch type recirculating system (irradiator). The data between zero time t0 and homogenization time are used for model simulation. Three simple combined models with limited number of parameters, based on a set of dierential equations, were used for description of the measured RTD. The set of equations is solved numerically in the time domain using the Runge±Kutta method. The estimation of model parameters is a nonlinear regression problem and is solved by a modi®ed Marquardt± Levenberg method adapted for models de®ned by a set of ordinary dierential equations. RTD analysis software developed by Zitny and ThyÂn (1996) was used for data treatment, normalization, determination of process parameters and identi®cation of model parameters. As a criterion of ®t, either the sum of squares or the sum of the absolute deviations can be selected. Estimation of the model parameters is based upon the least squares method, i.e. minimizing the sum of squares or absolute deviations of dierences of measured and model computed responses, and is given as: s2
n X
ÿ 2 yi ÿ y ti , x i , p~ minimum
i1
3a
p~ p1 , p2 , . . . ,pm or jY ÿ Yp j
n X ÿ jyi ÿ y ti , x i , p~ j minimum
3b
i1
where n is the number of measured stimulus x 1 , . . . ,x n and response y1 , . . . ,yn data points and m is the number of model parameters p1 , . . . ,pm with condition m n). The Marquardt±Levenberg method is an iterative method, which estimates values of model parameters pi such that the value of s 2 is minimum. In each iteration, the system of dierential equations is solved based upon the approximate values of model parameters pi obtained from previous iteration. On the basis of the computed matrix, Ckm , and the estimated standard deviation s between measured yi and model predicted data points, it is possible to estimate the accuracy of the computed model parameters as s pk : ÿ1 , s 2 pk s 2 C kk
k 1, 2, . . . ,m:
4
where C ÿ1 denotes the inverse of the matrix called the covariance matrix.
The dead and stagnant volumes were estimated by means of regression analysis. Three simple combined models described by a set of dierential equations are proposed and these have been used to analyse the recorded data. 4.4.1.1. Model-A: ideal mixers in series with plug ¯ow in recirculation loop. This model assumes that the ¯uid mixing in the irradiator is created by the distributor, the ¯uid impact on the source tube and ¯ow through the source grid. The irradiator is represented by a series of N ideal mixers each of volume V1, in series with a plug ¯ow component of volume Vp, in the recirculation loop. The physical representation of the model is shown in Fig. 5(a). The model parameters are mean residence time texp ), ratio of volume of plug ¯ow component to volume of ideal mixers a Vp =Vim and number of ideal mixers in series (N ). The total volume is sum of the volume of individual ideal mixers and plug ¯ow component V Vp Vim ), where Vim NV1 : The curve recorded by detector D1 alone was used for the evaluation of parameters after normalization. The ®rst peak was considered as the stimulus x i and the remaining part of the curve as the response yi of the irradiator and the recirculation pipeline. A typical tracer distribution curve recorded by detector D1 is shown in Fig. 6(a). The results of model simulation and reproducibility are given in Tables 3 and 4, respectively. 4.4.1.2. Model-B: ideal mixer in series with plug ¯ow inside the irradiator and in recirculation loop. The volume of the plug ¯ow component, Vp, estimated from Model-A is higher than the volume of the recirculation pipeline (Vr), thus indicating the existence of the plug ¯ow inside the irradiator. Therefore in Model-B, a plug ¯ow component is connected in series with the ideal mixers in addition to the plug ¯ow component in the recirculation loop. The physical representation of the model is shown in Fig. 5(b). The model parameters are mean residence time texp of the sludge in the irradiator, the ratio of the volume of the plug ¯ow component in the recirculation loop to the total volume a Vr =V), the ratio of the volume of the plug ¯ow component inside the irradiator to the volume of the ideal mixers in series b Vp =Vim and the number of ideal mixers (N ), where, Vim NV1 : In the present model, the data recorded by the two detectors (D1 and D2) have been used for simulation and estimation of model parameters. The curves recorded by detectors D1 and D2 were used to represent the stimulus x i and response yi ), respectively. The experimentally measured and model simulated curves are shown in Fig. 6(b). The results of model
H.J. Pant et al. / Applied Radiation and Isotopes 54 (2001) 1±10
7
Fig. 5. Physical representation of (a) RTD Model-A; (b) RTD Model-B; (c) RTD Model-C.
Table 3 Reproducibility of results for Q 1 (m3/min): Model-A Sr. No.
texp 2s pt (s)
a Vp =Vim 2s pa
N
jY ÿ Yp j
Veff =V
Vdead =V
1 2 3 Mean2s Standard error (%)
158.7820.2 174.1620.48 168.1920.48 167.0426.33 03.8
0.6120.004 0.2920.004 0.5220.006 0.4720.135 028.7
4 4 4 4
0.019 0.018 0.040 ± ±
0.882 0.967 0.934 0.92820.029 03.6
0.118 0.033 0.066 0.07220.029 014.5
8
H.J. Pant et al. / Applied Radiation and Isotopes 54 (2001) 1±10
Fig. 6. Example of identi®cation from: (a) data of one detector; (b) data of two detectors.
simulation and reproducibility for ¯ow rate Q = 1 m3/ min are presented in Table 5. 4.4.1.3. Model-C: ideal mixers in series with stagnant volume and plug ¯ow in recirculation loop. This model was used to estimate stagnancy in the irradiator. The local turbulence or vortices create exchange of ¯uid
between the stagnant and eective volume. The physical representation of the model is shown in Fig. 5(c). The model parameters are the mean residence time texp ), the ratio of the volume of the plug ¯ow component to that of ideal mixers a Vp =Vim ), the ratio of the volume of the stagnant region to that of the eective region b Vp =Vim ), and the number of ideal
Table 4 Results of model simulation: Model-A Q (m3/min)
texp 2s pt (s)
a Vp =Vim 2s pa
N
jY ÿ Yp j
Veff =V
Vdead =V
0.33 0.64 1.0
413.421.9 277.521.1 167.0426.33
0.7820.006 0.6420.01 0.4720.135
2 3 4
0.04 0.04 0.03
0.758 0.987 0.928
0.242 0.013 0.072
H.J. Pant et al. / Applied Radiation and Isotopes 54 (2001) 1±10
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Table 5 Results of model simulation and reproducibility for Q =1.0 (m3/min): Model-B Sr. No.
texp 2s pt (s)
a2s pa Vr = Vp Vim
b2s pb Vp = Vp Vim
N
jY ÿ Yp j
Vdead =V
1 2 3 Mean2s Standard error (%)
156.020.2 163.320.3 168.220.6 162.525.01 03.1
0.0620.001 0.0720.002 0.0520.003 0.0620.008 013.3
0.3820.001 0.1620.02 0.3620.003 0.3020.099 033
3 4 3 3.320.5 015
0.022 0.018 0.052 ± ±
0.133 0.093 0.065 0.09720.025 011
mixers (N ). The total volume is the sum of the volume of the plug ¯ow component and the volumes of the individual ideal mixers V Vp Vim ), where, Vim NV1 V2 ). The stagnant volume is represented by a parallel series of perfect mixers, each of volume V2, with exchange of ¯uid between N mixers each of volume, V1, representing the main ¯ow. The data recorded by detector D1 were used for model simulation, in a similar manner to that of Model-A. Results of the model simulation are given in Table 6.
5. Results and discussions One of the main reasons for regrowth of coliform counts in the post-irradiated sludge is considered to be insucient dose received by some of the sludge molecules as a result of nonuniform dose rate pro®le inside the irradiator. Knowledge of the dose rate pro®le and residence time of the sludge can be used to estimate optimum irradiation time and assess the eciency of the irradiation process. The minimum absorbed dose Dmin and most probable dose (D ) received in one circulation are estimated from knowledge of TFAT and tc , respectively, provided the dose rate pro®le inside the irradiator is known. The vertical dose rate pro®le in water, produced by a planar grid source assembly of cobalt-60 (Activity: 3.7 PBq) consisting of 13 tubes, has been published by Krishnamurty (1986). The dose rate is minimum along the vertical walls and maximum along the centre of the irradiator. The dose rate dD=dt at a point depends upon the distance l from the grid and is estimated using the following relation:
dD=dt k1 exp ÿ k2 l Gy=min
5
where values for k1 and k2 are obtained by exponential regression and are found to be 84 Gy/min and 7.8 mÿ1 for regions near the wall, and 94 Gy/min and 7.5 mÿ1 for regions close to the vertical axis of the irradiator, respectively. The dose at a point in a horizontal plane is obtained by integrating Eq. 5. Thus: D
t k1 ÿ 2 ÿ e ÿk2 L1 ÿ e ÿk2 L2 Gy L k2 1 L 2
6
where, time t is equal to TFAT or tc : L1 and L2 are considered to be equal to each other and their value is taken as 0.5 m for estimation of dose. The minimum absorbed dose Dmin is received by sludge molecules which ¯ow with maximum velocity or have a residence time equal to TFAT, and which travel along the vertical walls of the irradiator. Similarly, the most probable dose (D ) is received by the sludge molecules which ¯ow along the vertical axis and have residence time equal to tc : The dose received by the sludge molecules for residence times equal to TFAT and tc are calculated to be about 20 and 60 Gy, respectively. This implies for ¯uid elements which ¯ow along the wall of the irradiator only and receive minimum dose that these needs to be recirculated some 100 times more than the rest of the ¯uid elements ¯owing along the centre of the irradiator in order to receive the desired value of dose, i.e. 3±4 kGy. The irradiation times for sludge ¯owing close to the vertical walls and along the vertical axis are estimated to be 2.7 and 2.4 h, respectively. However, the mean dose received may be equal to the desired value for sludge molecules which undergo a number of circulations over a period of time. The ratio of minimum absorbed dose to most
Table 6 Results of model simulation: Model-C Q (m3/min)
texp 2s pt (s)
a2s pa Vp =Vim
N
f 2 s pf
b 2 s pb V2 =V1
jY ÿ Yp j
Veff =V
Vdead =V
0.33 0.64 1.0
473.4216.2 285.622.3 193.4214.1
0.4220.02 0.4420.02 0.2920.03
6 8 5
0.2920.01 0.2820.02 0.0120.003
0.9920.06 0.7120.06 0.2520.1
0.03 0.04 0.015
0.868 01 01
0.132 0 0
10
H.J. Pant et al. / Applied Radiation and Isotopes 54 (2001) 1±10
probable dose, i.e. Dmin =D is a measure of the degree of uniformity of dose inside the irradiator, and is estimated to be about 0.3. For an ideal case of complete uniformity, this ratio has to be equal to unity. As the solid particles in sludge may form clusters during recirculation and may therefore have less absorption ability than water, the minimum desired irradiation time should be multiplied by the appropriate correction factor. Analysis by Model-A showed that about one-fourth of the total volume is dead at the lowest ¯ow rate (0.33 m3/min) and is minimum at intermediate ¯ow rate (0.64 m3/min). At the highest ¯ow rate (1.0 m3/ min), the dead volume is higher than the intermediate ¯ow rate, indicating the creation of local turbulence or vortices with slow exchange of ¯uid between eective and dead volume. The existence of a stagnant volume was further con®rmed by analysis with Model-C, which showed that at higher ¯ow rates (>0.64 m3/ min) no dead volume exists inside the irradiator because of vortices, with slow exchange of ¯uid. With a ¯at vertical dose rate pro®le inside the irradiator, the existence of the plug ¯ow region is important for dose uniformity. The results of analysis by Model-A and Model-C show that the volume of the plug ¯ow region decreases with increase in ¯ow rate. The ratio of the geometric volume of the recirculation pipeline to the total volume Vr =V is 0.057. The same ratio has been estimated to be 0.06 by Model-B. The estimated value is within acceptable accuracy. 6. Conclusions A stimulus±response technique used in conjunction with model simulation provides important information about the hydrodynamic behavior of a closed recirculating batch type sludge irradiator. From the present study, the following main conclusions have been drawn: 1. The measured ¯ow rates are in good agreement with values shown by the ¯ow meter. This indicates that calibration of the ¯ow meter and pump capacity has not changed. 2. For presently reported conditions, the minimum time of irradiation has to be more than 3 h. 3. About one-fourth of the volume of the sludge in the irradiator behaves as dead volume at lower low ¯ow rate (0.33 m3/min). The dead volume decreases at higher values of ¯ow rates. 4. At a ¯ow rate of 1.0 m3/min, local turbulence or vortices with small exchange of ¯uid are produced. 5. The volume of plug ¯ow component decreases from 2/3±1/3 with increase in ¯ow rate from 0.33±1.0 m3/ min.
6. The irradiation vessel can be described by a series of four ideal mixers N 4 with stagnant volume and a plug ¯ow component in series. 7. Poor degree of uniformity was observed in dose received during one circulation.
Acknowledgements The authors wish to thank Dr. S.M. Rao, M.R. Shah, Dr. S.V. Navada, P. Walinjkar, K.P. Rawat and M. Assadullah for their help and useful suggestions during the course of this study. J. ThyÂn and R. Zitny would also like to acknowledge ®nancial support provided from the International Atomic Energy Agency (IAEA) to develop the software for data analysis.
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