Determination of the flow rate of streaming substances is one of the most important measurements in the chemical industry. In addition to direct flow rate determina­tion, movements based on mechanical principles (e. g., the rotation speed of a pro­peller built into the stream) need accurate calibration. Both can be performed by the radiotracer technique.

A great advantage of the flow rate measurements executed with the tracer tech­nique is that these measurements provide direct flow rate values in volume per time unit. This is in contrast to other methods that measure linear flow velocity, which also need to determine the flow cross section. In chemical technology, the cross section is not always well defined, e. g., there are pipes with changing cross sections where internal deposits can cause the change, or liquid flow with bubbles where the liquid volume is not defined, or open channels with changing cross sections.

In addition to this, in the case of several phases flowing together, the flow rate of the individual phases can be determined separately with the tracer technique. For instance, in the case of pneumatic powder transport, it is possible to label the transported air and powder separately, or in the case of suspensions transported with water, the water and the solid granules can be labeled separately. These exam­ples demonstrate the unique character of the radiotracer technique. When labeling
the phases individually and determining flow rates for the phases separately, the slip between the transporting (e. g., air and water) and the transported phases can also be determined.

Determination of the flow rates with the tracer method is based on measuring the dilution rate of the injected tracer in the pipe. The injected total activity is expressed as the volume and radioactive concentration of the radioactive tracer:

A = Va (11.5)

The dilution process of the tracer is described as integral to the radioactive con­centration by cross section and length as follows:

Introducing linear velocity of the flow: v = dL/dt (and from this, dL = v dt) Substituting dL into Eq. (11.4), we obtain:

Separating the double integral to members of cross section and time:

One member of Eq. (11.9) corresponds to the desired flow rate:

Technically, the measurement consists of a tracer injection at a given point of the pipe (Figure 11.4) and of a detector installed at another point over the mixing distance plotting the intensity function in time. Spreading the radioactive “cloud” is

Injection of radioisotope

Flow rate Q.|

V

Q. + Q2

Flow rate Q2

V

Sampling

Figure 11.5 Spreading the radioactive “cloud” in time.

demonstrated in Figure 11.5. Mixing distance is 100 X D, where D is the diameter of the pipe. For quantitative measurements, prior to the tracer injection, both the activity and volume of the radioactive tracer and its activity versus count rate are determined.

In addition to direct flow rate measurements, if the flow cross section is well — defined, linear velocity measurements with radiotracer technique are also possible. Such so-called peak-to-peak methods have practical importance in the calibration of rotameters.

In this method, the tracer is injected instantaneously and the passing of the tracer peak is sensed by two detectors installed onto the pipe at two points (Figure 11.6). The linear velocity of the flowing substance (v) can be calculated from the distance of detectors (L2—Lj) and from the time difference of intensity peaks (f2—tj):

L2 — Li

v =

t2 — tl

Injection of radioisotope

V

Recorder plotting intensity versus
time function

Practical examples for flow rate determinations with the radioisotope tracer technique (1—direct flow rate measurement; 2—linear velocity measurement):

• Testing for flow rate ventilation systems (1).

• Cooling water consumption determination in an oil refinery (1).

• Cooling water consumption determination in heat power stations (1).

• Determination of wastewater flow rates in various factories (1).

• Capacity measurement of pneumatic powder transport pipes in a cement factory (1).

• Flow rate measurement of moving solid grains in a drum furnace of a cement factory (2).

• The flow rate in natural streams, rivers, karst waters, surface waters, and irrigation sys­tems (1).

The peak-to-peak method (2) suitable for linear velocity measurement is used primarily for calibrating flow meters.