Flow parameters of substances processed in continuously operated chemical indus­trial systems are very important factors that influence chemical yield and product quality because the residence time of the substance in the system determines the contact time for reaction partners (namely, it defines the time of a chemical reaction).

If the residence time of a substance in an equipment is shorter than required, the chemical reaction will not be fully complete, but if it is unnecessarily long, the equipment efficiency will decrease. In addition to the length of time, there is the question of whether the full substance volume is involved in the entire reaction or only a part of it. This latter option may be due to dead spaces that have been formed with stagnating substances in the equipment, which also helps determine the efficiency.

A possible way to determine the important parameters of the chemical engineer­ing behavior of equipment and substances is to investigate and evaluate the mate­rial flow characteristics in an equipment or system. Material flows can be well studied by means of the radioisotope tracer technique using outer detectors. For such studies, a radioactive tracer is instantaneously injected into the inlet stream, and detector(s) are installed outside the system at the outlet stream. Detectors con­tinuously measure radioactive concentration of the tracer as count/time and plot the count rate versus time function. For obtaining chemical engineering parameters, these plots are evaluated.

Basic models of flow types are shown in Figure 11.9.

By quantitative evaluation of plots obtained from a radiotracer test, the follow­ing chemical engineering parameters can be determined:

• Average residence time of the substance.

• Extension of dead spaces.

In addition to quantitative parameters, the shape of plots provides important information on the character and deformation of flows.

The theoretical (designed) and actual (measured) residence time of a substance are determined on the basis of the following formulas:

V ml Qml/s

N

t, c(t)dt

Jo______

* N

c(t)dt

o where c(t) is the radioactive concentration. ml/s (milliliter/second) is the measuring unit.

The residence time of the substance in a chemical reactor corresponds to the reaction time for the chemical reaction. Optimally, the residence time is identical to the chemical reaction time. When designing continuously operated chemical reactors, the volume of the vessel and the flow rate of the substance passing
through the vessel are matched to the optimal residence time. The radioactive tracer test reveals if the experimentally measured residence time corresponds to the theo­retically designed residence time or not.

The theoretical residence time refers to the total volume of a vessel, while the experimental residence time obtained from the radiotracer test gives the active vol­ume of the vessel in which the material flow really takes place. The remaining space (difference of the theoretical and experimental) is the dead space where the material is stagnating, meaning that this material does not participate in the chemical reaction.

Vholtter = Velm — Veff (11-20)

Vholtter = Velm — ^ki’sS (11-21)

If there are dead space(s) in a vessel, average residence time becomes shorter and reaction volume and reaction efficiency will decrease.

Count rate versus time plots obtained from different measurements that used dif­ferent tracer activities can be compared to each other by converting them to stan­dard plots independent of the applied activity. This is performed by dividing each point (count rate) of the plot by the integrated count rate, i. e., the area under the curve on the plot.

This so-called density function (DE(t)) gives the relative frequency of the sub­stance portion, leaving the chemical reactor between t and the t + dt time interval. If values of the density function are integrated between 0 and t time-point, the so-called distribution function (DI(t)) is obtained, which represents the relative frequency of the occurrence of portions belonging to less than t time intervals. By combining the values of the density function and the distribution function, the so-called intensity function (I(t)) is obtained, which highlights flow irregularities (Figure 11.10). If an intensity function descends monotonously or has a maximum, these reflect a stagnating substance. In the case of ideal mixing or plug type flow, the intensity function is monotonously ascending.

From the shape of density, distribution, and intensity functions, the type of flow and flow irregularities can be concluded. On one hand, it can be determined if the flow pattern corresponds to the designed one or not (e. g., the tested flow is of plug or mixing type); on the other hand, it can be determined if deviation from the ideal flow pattern is significant or not and whether there are significant irregulaties in the flow pattern or not (Figure 11.11).

The plug flow characterizes chemical reactors where mixing of the substance portions representing different residence times is not needed. A simple physical example of this type of flow is the motion of heated water in a boiler passing through a drum without mixing with the entering cold water. However, there are several chemical reactors that operate on the principle of plug flow where reaction partners are introduced continuously into the reactor and only components repre­senting the same residence time are required to contact, and mixing with those portions entering or leaving the reactor earlier or later is not needed.

DE(t)

c(t) Ж J c(t)dt 0

DI(t)

t J c(t)dt 0____ Ж J c(t)dt 0

DI(t) =

Time

Figure 11.10 Standardized time functions of different flow types: density (DE(f)), distribution (DI(f)), and intensity (/(f)) functions.

DE(t) 1 — DI(t)

Plug type flow model

Real flow

Time

Fully mixed type model

Figure 11.11 Ideal flows (plug flow and mixed flow) and a practical case.

Contrary to this flow pattern, mixing-type chemical reactors ensure intensive mixing among substances of various residence times, e. g., entering and leaving the reactor in various timepoints. A typical example of this is the so-called equalization basin, which collects wastewater from various chemical plants with the aim of ega — lizing concentration peaks and fluctuations of various wastewaters by mixing and dilution.

None of these ideal flow types exists in pure form in practice. The actual flow pattern is always a combination of plug flow and mixing-type flow. It is important to know which type of theoretical flow pattern resembles the measured quantity and to what extent. To determine this, flow models are developed that provide quantitative parameters for expressing the extent of adequacy to one or the other basic flow type. In such models, compartments of ideal type flow are combined until an adequate description of the actual flow pattern is found.

The cascade model is built from n number of mixed tanks with identical volumes, connected to each other in series. In chemical engineering, by connecting an infinite number of mixed tanks in series, a plug flow pattern is obtained. When fitting a cascade model to the actual plot obtained for the measured system, the question is how many mixed tanks are necessary to connect in series to obtain a density function that fits well with the actual measured plot.

Figure 11.12 demonstrates density functions corresponding to cases when con­necting mixed tanks of n = 1, n = 2, n = 3, n = 4, n = 5, n = 6, n = 7 numbers. It is seen that as the number of mixed tanks connected in series increases, the density function gets closer and closer to the density function describing a plug type flow. NB: residence time of the moving substance is identical for each case.

The cascade model is based on mixed type flow compartments and quantita­tively gives the extent of deviation from the ideally mixed flow pattern with an increasing number of cascades (e. g., the number of mixed tanks). The higher the n number of tanks, the greater the deviation of the actual flow from the ideally mixed flow pattern. The cascade model is applied for equipment designed for mixed type flow (Figure 11.12).

Figure 11.12 Cascade model and density functions deduced for various cascade numbers.

The density function of the cascade model is found as follows:

where D is the dispersion coefficient and D/uL is the inverse of the Peclet number.

Mixed models combine the number, size, and connection way of plug flow and mixed tank units. As an example, one plug flow unit is connected to one mixed tank unit in a series in Figure 11.14. More complicated models can also be con­structed where the number, size, and method of connection (in series or parallel) of the units are varied until the density function of the theoretical model fits best to the plot measured with the radiotracer technique.

Deviation from ideal flow models can predict the types and effectiveness of the processes as well as expected quality of the material produced in the equipment.

In the case of serious deviations, the shape of the plots gained from the radio­tracer test itself refers to flow disturbances. Such serious flow disturbances are shown in Figure 11.15, demonstrating (a) plug type flow as designed with higher residence time than expected, (b) three channels formed within one flow, and (c) two channels within one flow.

Radiotracer investigations of such flow tests are justified partly by their simple technical implementation, partly because they do not require previous calibrations,

and partly because of significant information can be obtained about the efficiency of chemical reactors and expected product quality.

To cite a practical example, a chemical factory operates a mixed tank type basin for equalizing wastewater effluents originating from several plants. Flow tests car­ried out with the radiotracer technique resulted a much shorter residence time than calculated and test plots indicated a multichannel type flow. This test revealed that due to gradual sludge deposition, wastewater flows through several channels with­out the intended intensive mixing and dilution. A consequence of the radiotracer test was dredging and repeating the test.

Further industrial examples for the qualification of material flows include:

• Flow testing of the slurry in autoclaves digesting bauxite in an alumina factory.

• Measuring whitening reaction (residence) time of cellulose fibers in the pulp industry.

• Mixing of the benzine and gasoline fractions during flow in an oil pipeline.

• Mixing of the cold and warm water in electric boilers during flow.

• Testing the flow of melt in a bath furnace of a plate glass factory.