THE MEASUREMENT OF RIVERFLOW
WITH RADIOACTIVE ISOTOPES WITH PARTICULAR REFERENCE
TO THE METHOD AND TIME OF SAMPLING
P.R.B. WARD and P. WURZEL
Hydrology Research Team, Agricultural Research Council of Central Africa
ABSTRACT
Methods of riverflow gauging with radioactive isotopes involving withdrawal of sample from the
river and measurement in situ are investigated in streams of 10-250 cusecs.
The Total Counts method is favoured on account of its ability to sample large volumes and is found
to give reliable results at short sampling distances. An extension of the method to conditions of noninfinite geometry using a probe in the stream is offered. The extended method allows in situ gauging of
streams as shallow as two feet.
An empirical method for prediction of tracer passage times from tracer arrival times is given, based
on a series of measurements of 198
tracer passage in rivers at low flow.
The merits of colloidal Gold and Chromium51 EDTA as tracers for riverflow gauging are discussed.
Colloidal gold was found to be insignificantly adsorbed over a measuring reach of 3,000 ft.
1.
INTRODUCTION
The use of tracer dilution to measure small flows has been known to medicine and engineering
for more than a century and with the advent of commercially available radioactive isotopes new
horizons were opened in the measurement of river flows by this method. Following the use of
the method to measure fluid flows in industrial plants, Hull Q) first successfully applied the
method to flow measurement in natural streams and rivers.
Measurements of flow by tracer dilution involves the injection of a known amount of tracer
and the subsequent measurement of concentration over the duration of passage at a downstream
point. The location of the sampling station is critically dependent on the existence of complete
mixing. The tracer may be injected either at constant rate or instantaneously and the type of
injection determines the sampling procedure.
The importance of this method is as an addition to conventional river gauging methods.
Situations frequently arise in turbulent rivers and mountain streams where turbulence precludes
use of conventional flow-gauging, but stable sections are abundant. The primary advantage
of the tracer dilution method is that it is independent of the velocity and cross-section of flow.
Although this method is not directly applicable to continuous measurement of flow, its use in
gauging stable sections enables a rating curve to be constructed and thus a continuous record
of flow to be obtained from measurements of stage.
Using the instantaneous or pulse injection method the flow g in a river is calculated from
the amount A of tracer injected and the instantaneous concentration c by the following formula:
cat
Three systems of measurement are available when radioactive isotopes are used to determine
the integral and this work is concerned with assessing the merits of each. These are:
1) Sampling by retaining a sequence of samples (the Multiple Sample method) or a single
sample which is representative of the concentration in the river as a function of time (the
Integrated Sample method);
2) Sampling by measuring the tracer as it is carried past the immersed radiation counter (the
Total Counts method);
40
3) A sampling method which measures the tracer as it is carried past the radiation counter and
which relies upon a single sample for calibration (Gardner and Dunn's method).
In method 1 samples of volume 10-1,000 ml. (depending upon laboratory facilities and counting sensitivity) are taken at regular intervals during tracer passage. Following calibration of
the counting system a graph of tracer concentration versus time is constructed and the area
under the curve is determined. To avoid measuring many discrete samples, it is possible to make
a single measurement of concentration by mixing the samples collected at the end of the run.
Integration of samples by physical mixing provides an arithmetic mean concentrations which
when multiplied by the time of sampling gives the required integral.
MuJhple
fikricc/
of
Samples
&amp/i"nc)~
Fig 1 — Alternatives for obtaining the area under the concentration/time curve by Method 1.
Collection of an Integrated Sample is frequently carried out using a small pump which
extracts a sample of the river water at constant rate for the duration of tracer passage.
Method 2 was introduced and used by D.E. Hull and is uniquely applicable to radioisotope
gauging. The instantaneous count rate r equals the product of the instantaneous concentration
c times the detection sensitivity, F. r = F.c
Q
=
^J__
1/F
(2)
rat
The integral in equation (2) is very simply obtained: the radiation detector is immersed in the
river and the number of counts JV during radioisotope passage is measured.
A-F
e=N
(3)
The calibration of the detector must be carried out under conditions of geometry pertaining
to the measurement.
41
Method 3 was recently introduced by Gardner and Dunn (2) to combine the advantages of
in the river measurement with the simplicity of single sample calibration of counting rate. At
a convenient time during tracer passage a sample is withdrawn from the river and at the same
time the count rate recorded by the immersed detector is noted. Measurement of the single
sample in the laboratory under conditions of known detection sensitivity allows calibration of
the detector in the river.
2.
EQUIPMENT FOR SAMPLING AND MEASUREMENT
Field equipment for the measurement of radioactivity consisted of two Base portable scalers
and waterproof scintillation detectors. To obtain data on tracer passage when the detectors
were immersed in the river the scalers were linked to portable recorders with a chart speed of
six inches per minute and every one hundredth pulse was recorded.
Multiple samples were withdrawn from the river using an open necked container, and transferred to the laboratory in polythene bottles. To obtain integrated samples a constant head tank
and small electric pump were used assembled as a compact unit of only 30 lbs. weight using the
design of Guizerix (3). The sample volume collected was about six gallons and the duration of
sampling was matched with the expected passage duration time using a selection of outlet
nozzles of various diameters.
Laboratory facilities included a 4 gallon stainless steel counting vessel, housed in a cylindrical shield of 2 inches of old lead. The detection sensitivity in these conditions with Gold 198
was 2.35 x 107 c.p.m./fic/ml and the background was 130 c.p.m. In order to measure amounts of
water of about 4 gallons, a heavy duty scale was available and allowed very accurate measurement.
3.
A MODIFIED TOTAL COUNTS METHOD FOR USE IN SHALLOW STREAMS
Use of the Total Counts method was confined to measurement in deep sections of river in
Hull's work. This was because Hull confined his measuring site to conditions of infinite geometry
in order to make possible accurate calibration. With the gamma emitting radioisotopes commonly used in this work, a sphere of water of minimum radius three feet about the detector is
required to give "infinite" geometry counting. Under such conditions, radiation from beyond
the limits of the sphere has no effect upon the count rate. For shallow streams Hull placed the
detector in a counting vessel beside the stream and pumped a sample of the streamflow through
the vessel for the duration of tracer passage.
During infinite volume calibration measurements in a 1,000 gallons cylindrical tank of 6 ft.
diameter and 6 ft. depth we undertook some tests at shallow depths to determine the loss of
detection sensitivity. A tracer of medium strength gamma ray emission—Gold 198 was used.
It was found that by decreasing the depth to no less than two feet there was little loss of
detection sensitivity and further that at a depth of two feet the calibration was non-critical with
regard to depth. This is clearly indicated in the graph below. It may be noted that a depth
increase of six inches from 2\ ft. to 3 ft. produced a relative increase of count rate (based on the
value for infinite geometry) of only 1.4%.
Clearly the average depth of the river in the immediate vicinity of the immersed detector
need only be measured approximately and minor irregularities in bed level are unimportant.
Calibration in the large tank is then achieved by filling it with water to the approximate depth
of the river. Errors of up to six inches in the reproduction of depth for tank calibration purposes
are thus acceptable, as they lead to errors in the final flow value which are small compared with
other experimental errors.
42
Plate 1 — 1,000 gallon tank and Base scaler.
This extension of Hull's simple detector in the river method to shallow streams is of wide
application and its advantageous use is described in the next section.
Detection sensitivity for gold 198 as a function of depth
measured with a scintillation probe at half water
depth in a partially fi ed 1,000 gallon tank
Percentage
100
96
88 \
84
80
2'o-
yo'
4'0"
w~Dephh of measured
S'O-
solution
Fig 2 — Change of detection sensitivity with depth.
43
4.
A COMPARISON OF THE EXTENDED TOTAL COUNTS METHOD WITH OTHER SAMPLING PROCEDURES
In a series of seven experiments to measure theflowin small to medium rivers at different
types of site, samples were taken by the three methods listed in Section 1. The results are tabulated above, together with the flow result obtained by conventional gauging methods. Five
sites were used for the experiments, ranging from highly turbulent reaches mainly of rapids to
river sections of smooth streamlined flow.
Reference to table 1 shows that in all cases where sampling was carried out by the shallow
depth Total Counts method the results were self consistent and agreed well with the conventional methods. The results from the other sampling methods show occasional cases of large
disagreement with the metered flows, although sampling was carried out at the same stations
as for the Total Counts method. The errors are as large as 30%. We have carried out extensive
error analysis tests to determine the reproducibility of the laboratory measurement procedures.
These tests demonstrated that a single measurement of flow by the Integrated Sample method
has an error of ±2% (one standard deviation). The constant head integrated sampler was found
to work well and to provide a steady sampling flow. Thus when sampling by Methods 1 and 3
results are occasionally obtained which are well outside the limits of experimental error.
It has been suggested that even in circumstances where tracer dispersion from bank to bank
has occurred, incomplete mixing on a local scale
may still exist. This has been observed by
ground and aerial observations by H. B. Fischer (4) who used rhodamine B to observe dispersion
in a river of 250 cusecs. He found that although mixing had occurred between large pockets
of tracer in the leading and trailing edges of the cloud, small pockets of high and low tracer
concentrations existed. This phenomenon is evident in table 1, where flows calculated by the
small sample methods (1 and 3) give results which are at times in poor agreement with the check
value. In the Total Counts method, even when used for flow measurements in shallow streams
a large volume of water is sampled and the average tracer concentration of the water around
the counter is measured. Local inequalities in tracer concentration are thus smoothed out.
Experience in the use of Gardner & Dunn's method shows that two factors are of critical
importance. First, that the calibration sample is taken using a wide-necked container so that
instantaneous sampling is ensured. Use of a recorder attached to the scaler is desirable so that
the count rate of the detector in the river may be determined at precisely the correct time.
Instantaneous sampling and count rate determination is vital as the tracer concentration often
changes rapidly as a function of time. Secondly, the calibration sample must be collected from
a position as close as possible to the detector in the river. This is particularly important in
situations where large differences exist in velocity, and hence in the tracer concentration versus
time distribution across the river.
The Total Counts method, by virtue of its large volume "sampling" and its high detection
sensitivity (8.81 x 107 c.p.m./^c/ml with Gold198 in infinite volume) is the method of choice. It
has a further advantage in comparison with the Integrated Sample method, in that data on tracer
concentration versus time is available. The other sampling methods tested are small sampling
techniques, and are susceptible to errors from local tracer inhomogeneities.
5.
TIME AND DURATION OF SAMPLING
For the tracer concentration versus time measurement an approximate prior knowledge of
tracer transit time is needed. A sampling time which is too short results in incomplete sampling
of the tracer passage and hence a high value for flow. If sampling is carried out well beyond the
end of tracer passage an unnecessarily large number of background counts are accumulated,
making difficult the accurate measurement of the nett counts. The prediction of sampling
duration is also of importance in planning field experiments.
Flow gauging experiments in small to medium rivers (10-250 cusecs) draining the granite
plateau of Rhodesia showed that the (tracer passage time tracer arrival time) ratio was constant
(see table 2).
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The arrival time was easily determined from the first rise in tracer concentration. The tracer
concentration at the end of the passage curve decreased exponentially with time and no finite
end value could be measured. Hence an arbitrary value for the end of tracer passage was used,
defined as the time at which the concentration integral was 99% of the final value.
TABLE 2
Tracer passage characteristics, showing consistency
of tracer passage time/tracer arrival time ratio
River
Measured
flow
cusecs.
Station
Dist. below
injection
point feet
Arrival
mins.
Peak.
mins.
Passage
duration
mins.
Duration
Arrival
ratio
Upper
Inyagui
160
A
C
1,050
5
Upper
Inyagui
71
D
3,400
47
61
130
2.8
U m wind si
25
220
2.2
2.1
3.5
3.5
5.2
6.2
23
53
11.4
13.0
59
116
8
13.8
. electronic failure
2.8
Lower
Inyagui
170
3
D
1,260
2,640
15
36
Lower
Inyagui
135
B
D
1,260
2,640
20
40
65
146
Shawanoe
230
B
C
960
15
water leakage
23
46
3.1
B
C
590
740
29
39
101
116
3.5
3.0
Munenga
7.8
46
62
3.9
3.2
3.3
3.3
With the exception of the Umwindsi, the gauging reaches were of the same type, consisting
of stretches of long pools where the velocity was as low as 0,1 ft./sec. broken by short sections
of rapidly flowing turbulent water. The average velocity between injection and sampling stations
was 0.5 to 1.0 ft./sec. It may be seen from table 2 that the duration/arrival ratio for the Umwindsi
is abnormally high and this is due to the atypical nature of the reach. An initial stretch of highly
turbulent fast flowing water was followed by a large, wide pool which characterised the reach.
This caused the arrival time to be abnormally small in relation to the tracer passage time.
In typical conditions a method of predicting the passage time is thus available by making
a preliminary measurement of the arrival time using a dye such as fluoresceine. The tracer
passage time is approximately three times the tracer arrival time and hence the total time
required to conduct the flow gaugings is four times the value measured by the fluoresceine
observation. It has been shown (Ward and Wurzel (5)) that the concentration following continuous injection rises to 99% of the equilibrium value at the same time as the end of tracer
passage for pulse injection (defined above). In cases where the continuous injection method is
used, the time at which constant concentration conditions are reached at the sampling station
may be found, and hence the required injection period.
6.
GOLD 1 9 8 AND CHROMIUM 51 AS TRACERS FOR FLOW GAUGING
Gold 198 and Chromium 51 are radioisotopes which emit gamma radiation and hence are
detectable in situ. They have suitable radioactive half-lives for river gauging experiments (2.7
46
and 28 days respectively) and their maximum permissible levels in drinking water are favourable.
In the course of this work another important criterion, their tendency for adsorbtion, was
investigated.
Gold 198 was used in metallic form as a colloidal suspension stabilised with gelatin, of particle size 50-200 angstroms. The chromium was in solution form as the ethylene diamine tetraacetic acid complex. Sampling was undertaken at stations successively downstream of the
injection point. For example in one experiment, flow measurements were made at four stations
ranging from 1,000 ft. to 3,000 ft. from the injection point. No systematic rise in flow estimate
at stations progressively further downstream was noted with either Chromium 51 or Gold 198 ,
and hence no significant adsorbtion occurred.
This was a particularly important result for Gold 198 as its suitability for riverflow gauging
has been questioned by Smith (6). Hull (7) has found that negligible losses of tracer occur when
Gold 198 colloid was used for gaugings in a rocky gorge, although it was not suitable for gauging
a stream whose bed was lined with algae and organic debris. Typical reaches of rivers gauged
in this series of experiments included pools with sand-lined beds and well vegetated banks. In
these conditions no significant adsorbtion of colloidal gold occurred in 3,000 ft.
Gold 198 may be considered eminently suitable for river flow gauging for further reasons.
It is one of the most inexpensive radiotracers and its half-life is short enough for it to be favoured
by the Public Health authorities. Chromium 5 1 has a detection sensitivity smaller by a factor
of fifteen due to its low gamma-ray emission factor. Chromium may, however, be used advantageously on account of its short term storage potential due to its medium length half-life.
7.
CONCLUSION
The advantages of the Total Counts sampling in situ methodhave been stressed. The improvement which results from large volume measurement at short sampling distances has been
demonstrated in rivers of 10-250 cusecs. Consistent results by small sample techniques may be
ensured only when sampling stations are sufficiently far downstream for the tracer concentration
distribution (as a function of time or distance) to be flattened and elongated. In these circumstances of high dispersion, concentration gradients are greatly reduced and local tracer inhomogeneities at the leading and trailing edges of the passage curve are insignificant.
For flows of 5,000 cusecs and above, even the Total Counts method which offers the highest
detection sensitivity, requires excessively large tracer amounts. This incurs problems of
health hazards and expense. Thus the range of application of the Total Count method is to flows
of up to 5,000 cusecs. In order to reduce the tracer injection amounts in the measurement of
large flows, methods where samples are withdrawn from the river and enriched are essential.
This aspect is receiving particular attention by the Forschungsstelle fiir Radiohydrometrie,
Munich.
ACKNOWLEDGEMENTS
This work was carried out as part of International Atomic Energy Agency Research Contract RB-301 awarded to the Agricultural Research Council of Central Africa. The Hydrological
Branch, Ministry of Water Development were joint participants in this programme.
We wish to thank the Danbridge Co., Copenhagen whose portable radiation detection
equipment was used, for their co-operation.
REFERENCES
1
C ) HULL, D.E., The Total-Count Technique: A New Principle in Flow Measurement. Int. J. App.
Rad. and Isotopes, 4 (1958) 1.
(2) GARDNER, P.R. and DUNN, J.W., A Single Sample Radiotracer Technique for Determining Stream
Flow Rates. Int. J. App. Rad. and Isotopes, (1964), Vol. 15, pp. 330-344.
47
(3) GUIZERIX, J. et ah, Les mesures de débits effectuées en France à l'aide de traceurs radioactifs par la
méthode d'intégration. Radioisotopes in Hydrology, I. A. E. A. 1963. Proceedings, Tokyo Symposium,
March '63.
4
( ) FISCHER, H.B., Longitudinal Dispersion in Laboratory and Natural Streams. Report No. KH-R-12
California Institute of Technology, June 1966.
(5) WARD, P. R.B. and WURZEL, P., An Investigation into the Application of Radioisotope Tracers to
Riverflow Gauging with Particular Reference to Injection and Sampling Techniques. Unpublished
report to International Atomic Energy Agency, Vienna (1965).
6
( ) SMITH, D.B., Riverflow Measurement using Radioactive Tracers. Dilution Techniques for Flow
Measurement, Bulletin, No. 31. Paper 8, Dept. of Civil Engineering, Univ. of Newcastle (1964).
(?) HULL, D. E., Dispersion and Persistence of Tracer in Riverflow Measurement. Int. J. App. Rad. and
Isotopes, 13(1962)
48