Analysis Of Residence Time Distribution Of Fluid Flow By

Axial Dispersion Model

Sugihartoa,b, Zaki Su’udb, Rizal Kurniadib, Abdul Warisb and Zainal Abidina

aDepartment of Physics, Faculty of Mathematics and Natural Sciences, Bandung Institute of Technology,

Jl. Ganesha 10, Bandung 40132, Indonesia bCentre for Applications of Isotopes and Radiation Technology - National Nuclear Energy Agency,

Jl. Lebak Bulus Raya No. 49, Jakarta 12440, Indonesia.

Corresponding author. E-mail: sugi@batan.go.id

Abstract. Radioactive tracer 82Br in the form of KBr-82 with activity ± 1 mCi has been injected into steel pipeline to qualify the extent dispersion of water flowing inside it. Internal diameter of the pipe is 3 in. The water source was originated from water tank through which the water flow gravitically into the pipeline. Two collimated sodium iodide detectors were used in this experiment each of which was placed on the top of the pipeline at the distance of 8 and 11 m from injection point respectively. Residence time distribution (RTD) curves obtained from injection of tracer are elaborated numerically to find information of the fluid flow properties. The transit time of tracer calculated from the mean residence time (MRT) of each RTD curves is 14.9 s, therefore the flow velocity of the water is 0.2 m/s. The dispersion number, D/uL, for each RTD curve estimated by using axial dispersion model are 0.055 and 0.06 respectively. These calculations are performed after fitting the simulated axial dispersion model on the experiment curves. These results indicated that the extent of dispersion of water flowing in the pipeline is in the category of intermediate.

Keywords: Radioactive tracer, RTD, Dispersion number, Axial dispersion model. Pacs: 23.20.En, 28.20.Gd

INTRODUCTION

Concept of residence time distribution (RTD)

obtained from injection of various tracers has long been used for parameter characterization of flow

systems [1]. Among the various available tracer, -emitting radioisotopes offer several advantages over conventional ones such as high detection sensitivity, in-situ detection, availability in a wide range of compatible forms, stability under hostile industrial environment [2-4]

The measured RTD is used to analyze hydrodynamic behavior of system. In pilot scale industrial systems, the experimentally measured RTD is used to optimize the design parameters and to develop the mathematical model for prediction of the hydrodynamic behavior of the systems. In addition, RTD is also used to identify various malfunctions and qualification of degree of mixing in pilot scale and in large-scale industrial systems [5,6]

The knowledge of mean residence time (MRT) and

axial dispersion model are a basic requirement to evaluate the reactor performance The use of axial dispersion model has been reported for study of flow dynamics in various reactors, such as trickle bed reactor [7, 8], packed column [9,10], riser reactor [11]. Recent development of radiotracer methodology has also been reported [12]. This paper describes measurement of RTD, determination of MRT and implementation of axial dispersion model to qualify the extent dispersion of water flowing in the pipe using radiotracer technique.

EXPERIMENT A radiotracer experiments was performed to

measure the RTD of water flowing in a horizontal stainless steel pipeline of 3” (7.62 x 10-2 m) inner diameter. The water flows at ambient conditions gravitically from water tank. 82Br bromide isotope (half life: 35.7 h and γ energy 0.776 MeV (85%) as

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KBr-82 was used as a tracer). 82Br isotope was produced in nuclear reactor and about 1 mCi of activity was used in this experiment. The tracer was injected instantaneously into the inlet feed line through an injection point at the top of the pipeline using a disposable plastic syringe. The tracer was injected after the water flow achieving steady state. The tracer movement was monitored using two collimated NaI(Tl) scintillation detectors (Ludlum Measurement, U.S.A) separated by a distance of 3 m. The first detector (D1) and the second detector (D2) were placed at the distance of 8 m and 11 m from the injection point respectively. Due to the reason of interfered signal from injected tracer and the flow is not fully developed yet, no detector is placed near the injection point [13]. The detectors were connected to 12 channels data-logger (Ludlum Measurement, U.S.A). The data-logger has been setup to record 900 data points at time interval of 1 second. The tracer concentration was recorded until the radiation level comes to the background level. The recorded data was transferred to the computer for subsequent analysis.

RESULT AND DISCUSSION

The experimental data obtained from this

experiment is called residence time distribution (RTD) curves which represent relationship between radiation intensity ( vs. time ( , as presented in Figs. 1 and 2. Different signal height of these two curves is mostly due to difference of detector’s efficiency and contribution of geometrical arrangement of the collimators. No background correction was performed because half life of tracer is far high compared to time duration of the experiment. Most properties related to flow such as mean residence time, linear velocity or volumetric flow and flow pattern can be obtained from the experimental RTD curves. Determination of Mean Residence Time

Mean residence time (MRT) basically can be determined by peak to peak method and first moment method. As can be seen from Figs.1 and 2 that the shape of the RTD curves are fluctuated and are not perfectly Gaussian like. For such situation moment method gives better result in determining the MRT based on analyzing of RTD curves [2,7].

First moments ( ) of the experimental tracer concentration curves were determined using the following relation [1-2,7,9]:

(1)

where i= 1 for experimental RTD curve of D1 and i = 2 for experimental RTD curve of D2. The difference of the first moment of the two curves gives the MRT of process material in the system. Thus:

(2) where, and are values of the first moments of RTD curve of D1 and D2 respectively. The theoretical MRT ( ) of the fluid in a closed system is given as:

(3)

where is volume of pipeline within two detectors (m3) and is volumetric flow of water (m3/s). For a normally operating closed system the theoretical and the experimentally measured MRT should be the same. As the system was operated normally during the course of experimental time, it was assumed that the system was time-invariant that the quantity of measurement including the volumetric flow was considered constant. Based on Eq. 2, the calculated MRT was 14.9 s, and therefore the linear flow rate of water was 0.2 m/s. Residence time distribution and model simulation

The residence time distribution (RTD) is a

characteristic function of continuous process systems and is defined as a normalized response of the system to an ideal impulse injection of stimulant in the form of -Dirac function [1]. If an ideal impulse of tracer is injected at the inlet of the system at time t = 0 and it’s concentration is measured as a function of time at the outlet, then represents the fraction of the tracer having residence time between time interval ( ). In other words is the probability for a tracer element to have a residence time between interval ( ) and it is stated as:

(4)

Normalization of above equation becomes

= 1 (5) where : i = 1,2,….n, is the tracer concentration and is residence time distribution function.

Ideally, the slow water flow in the pipeline should be plug flow but some axial intermixing mainly due to fluid velocity gradients is always inevitable. The mass balance equation for axial dispersion model in dimensionless form is written as [1]:

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(6)

where: dimensionless tracer concentration, is vessel dispersion number (reciprocal to is Peclet number), is mean linear velocity, is axial dispersion coefficient,

is tracer concentration at time , is tracer concentration at time = 0, is dimensionless distance, is distance variable and is dimensionless time.

The Peclet number ( ) can be considered as the ratio between the transport rate by convection and transport rate by dispersion. The physical meaning could be understood from the following two extremes [2,7]. • In case is infinite the dispersion rate is

negligible compared to the convection rate and the flow is said to be ideal plug flow.

• In case approaches zero the convection rate is much slower than the dispersion rate and the flow is said to be completely mixed flow. Solution of Eq. (6) is different for different

boundary conditions. There are four physical boundary conditions encountered in industrial system, i.e. closed-closed, open-closed, closed-open and open-open. In this experiment, the system is considered as open-open system, therefore the solution of Eq. 6 for this experiment is written as [1]

(7)

with boundary conditions at (at the inlet):

and at (at the outlet): .

One of the oldest and the simplest techniques of parameter estimation is the moment’s method, which involves the comparison of variances of the model and experimental distribution function. Unfortunately there are some inherent computational errors involved in the variance of the measured response curves. In addition to inherent computational error, the presences of the “tail” due to the small value of concentration also contributes a large error for the computed moments [2,8].

The disadvantage of the moment method could be avoided by fitting the complete model RTD curve with the experimental RTD curve. The curve fitting method is used in this experiment to fit the two curves and to obtain the optimum model parameters. The quality of the fit is judged by choosing the model parameters to minimize the sum of the squares of the differences between the experimental and model computed curve The values of the model parameters (MRT and ) corresponding to the minimum value of root mean

square error (RMS) or absolute deviation error (ADE) are chosen as the optimum values [8]. Thus:

= minimum (8)

The model parameter for each of the two RTD curves (D1 and D2) calculated based best curve fitting of Eq. 7 were 0.05 and 0.06 respectively indicating that the extent of dispersion of water flowing in the pipeline is in the category of intermediate. Errors for each fitting curve as shown in Figs. 1 and 2, calculated based on Eq. 8 were 0.162 and 0.105 respectively.

FIGURE 1. Fitting RTD model on RTD experiment at the detector 1 (D1), 8 m from injection point.

FIGURE 2. Fitting RTD model on RTD experiment at the detector 2 (D2), 11 m from injection point.

It is worth to note that the Eq. 7 is based on

assumption that tracer injection should follows instantaneous injection as described by Dirac delta-function . In practice such pulse injection is difficult to realize. However, it is sufficient that the variance caused by a non-ideal injection is much smaller than the expected variance caused by the dispersion in the investigated system [14]

CONCLUSION

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Conclusion drawn from this experiment is that the flow velocity of water in the pipeline is 0.2 m/s. Model parameter estimated by axial dispersion model for each RTD curves is around 0.055 indicating the extent dispersion of water flowing in the pipeline is in the category of intermediate. Fitting error may result from inappropriate of tracer injection.

REFERENCES

1. O. Levenspiel, Chemical Reaction Engineering,

2ndEds, New York, John Wiley & Sons, 1972, Cp.9 2. IAEA, Radiotracer Residence Time Distribution Method for Industrial and Environmental

Applications, TCS, 31, Vienna, IAEA, 2008, Cp.5 3. J. Thŷn, R. Žitnŷ, J. Klusoň and T. Čechák, Analysis and Diagnostics of Industrial Processes

by Radiotracers and Radioisotope Sealed Sources, Praha, ČVUT, 2000

4. J.P, Leclerc, S. Claudel, H.G, Lintz, O.Potier and B. Antoine, Oil and Gas Science and Technology-Rev. IFP 55, 159 – 169 (2000)

5. G.Reed, “Measurement of Residence Times and Residence Time Distributions”, in Radioisotope Techniques for Problem Solving in Industrial

Process Plants, edited by J.S Charlton, Glasgow, Leonard Hill, 1986, pp. 112-137

6. IAEA, Guidebook on Radioisotope in Industry, Tech.Rep.Series, 316, Vienna, IAEA, 1990, Cp.4

7. H.J. Pant,”Studies on Process Dynamics of Industrial Systems Using Nuclear Techniques”, Ph.D. Thesis, University of Mumbai, 2001

8. H.J. Pant, A.K, Saroha and K.D.P, Nigam, Nukleonika 45(2), 235-241 (2000)

9. Z. Stegowski, , Nucl. Geophys 7(2), 335-341 (1993)

10. V. Blet, Ph. Berne, C. Chaussy, S. Perrin, and D. Schweich, Chem. Engg. Sci, 54, 91-101 (1999)

11. P. Vitanen, Measuring and Modelling of Particle Fluid Flow in a Riser Reactor, VTT Publication 88, 1992

12. P. Berne and J. Thereska, App. Rad and Isot, 60, 855-861 (2004)

13. V. Blet, P. Berne, F. Tola, X. Vitart and C. Chaussy, Appl. Rad and Isot 51, (1999)

14. A. Kreft and A. Zuber, Int. J of Appl. Rad and Isot 30, 705-708 (1979)

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