Model Studies of Flow through a Packed Bed of Liquids of Various Viscosities ^†

1. Introduction

Fluid flows through packed beds occur in many chemical processes. In shaft metallurgical units, such flow most often takes place in the lower parts of the furnace, where molten metallic and slag fractions flow. A special example of such an aggregate is a blast furnace in which the process of obtaining iron from ores is carried out using many phases (gas, lumpy and dusty particles, liquid).

Relatively much is known about the permeability of the charge column in a blast furnace [1,2,3,4,5]. However, the phenomena related to the flow of slag and iron between pieces of the charge, i.e., flow phenomena occurring in the lower part of the blast furnace, are also important for the course of the blast furnace process. The way the liquid phase flows in this region determines the course of many chemical reactions and influences heat and mass transfer. Therefore, it is very important to understand and know best the mechanism of slag flow through the packed bed in a blast furnace, where the temperature, at each height level and along the furnace radius, is different. The charge melts, gradually reducing its viscosity as the temperature increases. This suggests the possibility of liquid streams (slags) of different viscosities flowing side by side through the packed bed.

Due to the large size of the reactor and the process technology, some tests are very difficult (or even impossible) to be carried out on a working industrial metallurgical unit. Therefore, physical and numerical modeling is a commonly used research tool in a very wide range of metallurgical processes, from the blast furnace [1,2,3,4,5,6,7,8,9,10,11,12] through to steelmaking processes [13,14,15,16,17] and continuous steel casting [18,19,20,21].

Therefore, in order to obtain more information about the phenomenon of the flow of liquids with different viscosities through a packed bed, in conditions corresponding to the flow of liquid slag in a blast furnace, it was decided to perform experimental tests using a physical model. The tests were carried out to investigate the effect of changing the viscosity of the model liquid on the liquid flow rate in the bed.

2. Research Installation and Research Methodology

Figure 1 shows an outline of the research system. The packed bed is located in a PVC column. A flow curtain is installed in the upper part of the column, which prevents the liquids from mixing immediately after they are introduced into the bed, until the flow stabilizes. The curtain divides the column into two flow zones. Two liquid tanks were placed above the column. During the experiments, a liquid of a given viscosity or two liquids of different viscosities were introduced into the bed through two inlet ports located in the upper part of the column. A partition was placed in the lower part of the column, creating two collectors of equal volume, enabling the measurement of the volume of liquid flowing from two zones of the measuring column. A sieve was installed above the partition to prevent the packed bed from reaching the lower part of the column intended for liquid collection.

The movement of the model liquids was generated by opening simultaneous valves located in both inlet ports. After opening the valves, the liquid flowed gravitationally through the packed bed. The measurement of the time of liquid flowing through the bed began when the valves were opened and ended when all the liquid flowed through the packed bed and flowed to the collectors. After each test, the piece bed was rinsed with water and dried.

Table 1. Values of dimensionless numbers for model research conditions (at 20 °C) and for liquid slag in blast furnace.

	Modeling Fluid	Slag (Blast Furnace) 1500–1800 °C, [6]
$\mathrm{D}\mathrm{i}\mathrm{a}\mathrm{m}\mathrm{e}\mathrm{t}\mathrm{e}\mathrm{r} \mathrm{o}\mathrm{f} \mathrm{t}\mathrm{h}\mathrm{e} \mathrm{b}\mathrm{e}\mathrm{d} \mathrm{p}\mathrm{a}\mathrm{r}\mathrm{t}\mathrm{i}\mathrm{c}\mathrm{l}\mathrm{e}\mathrm{s} -dz$, m	0.008	0.03–0.04
$\mathrm{F}\mathrm{l}\mathrm{u}\mathrm{i}\mathrm{d} \mathrm{v}\mathrm{e}\mathrm{l}\mathrm{o}\mathrm{c}\mathrm{i}\mathrm{t}\mathrm{y} -U$, m/s	0.002–0.004	0.008–0.012
$\mathrm{F}\mathrm{l}\mathrm{i}\mathrm{u}\mathrm{d} \mathrm{d}\mathrm{e}\mathrm{n}\mathrm{s}\mathrm{i}\mathrm{t}\mathrm{y} -\rho$, kg/m3	1400–1490	2300–2600
$\mathrm{F}\mathrm{l}\mathrm{u}\mathrm{i}\mathrm{d} \mathrm{v}\mathrm{i}\mathrm{s}\mathrm{c}\mathrm{o}\mathrm{s}\mathrm{i}\mathrm{t}\mathrm{y} -\mu$, Pa·s	0.1–0.47	0.8–1.2
$\mathrm{S}\mathrm{u}\mathrm{r}\mathrm{f}\mathrm{a}\mathrm{c}\mathrm{e} \mathrm{t}\mathrm{e}\mathrm{n}\mathrm{s}\mathrm{i}\mathrm{o}\mathrm{n} -\sigma$, N/m	0.0322–0.0393	0.43–0.47
Shape coef. of the bed particles             −φ, -	1	0.5–0.6
Coef. of free space of bed                     −ε, -	0.38	0.4
Reynolds number                    ${Re}_m={\displaystyle \frac{\rho U{d}_Z\varphi }{\mu }}$, -	0.047–0.47	0.23–0.936
Capillary number                    ${Ca}_m={\displaystyle \frac{d_Z^2{\varphi }^2\rho g}{\sigma }}$, -	22–29	10–34
Galileo number                    ${Ga}_m={\displaystyle \frac{d_Z^3{\varphi }^{3}g{\rho }^2}{{\mu }^2}}$, -	44–1115	121–1432

shows the test conditions, which were compared with the values given in the literature [6], corresponding to the flow of liquid slag in the blast furnace.

Taking into account the movement of fluid in a packed bed, the most frequently used criteria are the numbers, the forms of which are presented in Table 1.

3. Research Results and Discussion

During the first stage of the research, the influence of changes in liquid viscosity on the liquid flow rate in the packed bed was analyzed. After filling tanks I and II with liquid of the same viscosity, tests were carried out according to the procedure described above. The time of liquid flow through the bed was measured each time. After each test, the same amount of liquid was found in both collectors. It was noticed that the viscosity of the model liquid affects its flow rate in the packed bed. In each case, even a slight decrease in the viscosity of the liquid results in an increase in the flow speed through the packed bed. The relationship between the viscosity of the model liquid and the experimentally obtained values of the liquid flow rate in the packed bed is expressed by an equation of the following form:

U = 0.0015μ^−0.415

The research results are presented in Figure 2.

In the second stage, the test was carried out by filling the tanks of the research installation with two model liquids of different viscosity. After the liquid flowed into the collectors, differences in liquid levels in the collectors were noticed. A higher level was observed in collector no. 2 (the collector on the flow side of the lower viscosity liquid). The test was repeated five times.

4. Conclusions

The influence of changes in liquid viscosity on the liquid flow rate in the packed bed was analyzed and, based on the research conducted on the behavior of streams of the two liquids with different viscosities flowing in a packed bed, the following were found:

• When two streams of liquids with different viscosities flow through the packed bed (at different speeds), an interaction occurs that causes the stream of the higher viscosity liquid to deflect towards the stream of the lower viscosity liquid.
• The test results may indicate that, in the operating conditions of the blast furnace, lateral movement of the flowing streams of liquid metal and slag can be expected, but this would require industrial verification.