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2019 International Conference on Computer Science, Communications and Big Data (CSCBD 2019) ISBN: 978-1-60595-626-8

Liquidus Temperature of Aluminum Electrolytes Detected by Statistics

Lei WU

School of Information, North China Univ. of Tech., 100144. Beijing. China

Keywords: Liquidus temperature, Data-density algorithm, Step-cooling algorithm, Statistics.

Abstract. This paper presents a novel method of data-density algorithm of statistics to identify on-line accurately and reliably liquidus temperature of aluminium electrolyte. Data-density algorithm of statistics utilizes the principal of aggregate category to characterize the relationship between temperature curve and data-density of temperature curve. Comparing with traditional step-cooling algorithm of statistics, Data-density algorithm of statistics made it possible to identify liquidus temperature even under the bad circumstance that inflection point of temperature curve display slight or not present. The technical activities and experimental results shown that direct measurements of the liquidus temperature in industrial cells by data-density algorithm of statistics is clearly outperforms conventional step-cooling methods of statistics for determining the liquidus temperature.

Introduction

Liquidus temperature of molten aluminium electrolyte is one of key parameters in the production of primary aluminium in the Hall-Héroult bath. Liquidus temperature (TL, primary freezing point) is in

principle the molten aluminium electrolyte does undergo phase transformation during solidification process. The bath temperature (TB) is temperature in an electrolysis cell. The temperature of reduction

cells normally should be higher than TL in aluminium production. Superheat value (ΔT) is the

difference between TB and TL, which can be presented by the following equation:

ΔT = TB – TL (1)

ΔT is around or slight below 10℃ to be generally considered the best value. Reasonable ΔT is ranges from 5 to 50℃. If we can pick up TL on potroom, we will simultaneously getΔT and directly

take it as reference value to timely adequate control TB for optimizes production processes. The other

way round, the higher the superheat, the more electrical energy is consumed. Therefore, TLto be

obtained is not only with theory significance, but also with economic value in production.

Literature Review

In terms of data processing, regression and step-cooling of statistical analysis, differential thermal analysis are the main methods, which all belong to thermal analysis. Regression analysis also belongs to non-experimental method and established on a few cell parameters which may require numerous physical measurements and off-line chemical analyses and largely dependents on some key chemical compositions of aluminum electrolyte to be carefully analyzed. Mr. Wang jiawei has clearly classified the test methods to TLof aluminum electrolyte and summarized static test by statistical method and

field dynamic test by setup with thermal analysis method.

Temperature-To-Voltage Conversion

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[image:2.595.218.372.72.116.2]

A T1 J1 v B J2 J3 T2 T2 T3 T3 J4 J5 C D EZ

Figure 1. Extension line of thermocouple.

The relation abouttemperature and voltage can be described as below equation:

EZ = EAB (T1) - EAB (T3), (2)

EAB (T1) = EZ + EAB (T3). (3)

T1 normally is placed in the "hot" end to feel the temperature of object measured.

T3 denotes temperature of the workshop can be direct measured by electric temperature sensor.

EZ is voltage under 10 microvolts, which picked up at the rate of one data point/10ms by our setup.

Table 1. K type thermocouple reference table.

℃ 10 20 30 40 50 60 …… 920 930 940 950 960 970

mV 0.40 0.80 1.20 1.61 2.02 2.44 …… 38.1 38.5 38.9 39.3 39.7 40.1

In order to get the value of T1, two steps are generalized.

Step1: take T3 as reference by table 1 to obtain voltage EAB (T3);

Step2: EAB (T1) usual gotten by EZ plus EAB (T3), take EAB to obtain temperature T1 by table 1.

For example, take T3 as reference to access reference Table 1 and the corresponding voltage of 30℃

is 1.20mV, which also present as following equation: EAB (T3) = EAB (30℃) =1.20mV.

EZ instantaneous read out by electric temperature sensor is 38.10 mV, the result given by Eq3 as the

following Eq:

EAB (T1) = EZ +EAB (T3) = 38.10 +1.20 = 39.3 mV.

Take 39.3 mV as index to access reference table 1 and corresponding temperature of 39.3mV is 900℃. The value of 900℃ is just the thermocouple temperature of front (hot) end. Normally the reference table 1 of temperature - to - voltage conversion of thermocouple in advance built-in the

ROM of embedded system, we can conveniently and quickly get temperature of aluminum electrolyte through looking-up reference table 1.

Data Processing with Step-cooling Algorithm

The Tradition Method of Step-cooling Derivative

First-order Derivative. Suppose two adjacent temperature are T1 and T2 respectively, the

first-order step-cooling derivative equation can then be defined as below: T1=(T2-T1)/(t2-t1).

The unit of Tiis degrees Celsius and the tiis millisecond. The interval time between two sample

temperatures is fixed and with 10 milliseconds. So the above equation can be simplified as below:

T1 = 10-1*(T2-T1)= (T2-T1)= (T2-T1)/10. (4)

If T1 = 0, it means T1 point is the arrest point of temperature curve of first-order derivative.

Second-order Derivative.Second-order derivative equation can also be defined as below:

2

T1 = (T1) = ((T2-T1)/(t2-t1))

= (10-1*(T2-T1)) = 10-1*(T2-T1) = 10-1*(T2 -T1) = 10-1(10-1*(T3-T2) –10-1*(T2-T1))

= 10-2( T3-2T2+T1) (5)

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Discussion.From theoretical, the point of TL is the arrest point of Ti=0 or the inflection point of 2

Ti=0. In order to increase the accurate of detection and avoid pseudo inflection points appearing,

multiply the temperature difference between adjacent sampling points, for example, the number of 10 replaced by 1 at equation of (4), that means the temperature difference between two adjacent sampling points is magnified by 10 times. In fact, the anticipated results of distinct temperature difference do not appear, shown at table 2.

Table 2. Check liquidus temperatures by different magnification factor.

Check method magnification factor/liquidus temperatures

first-order derivative *10/951.9℃ *20/951.9℃ *30/951.9℃

second-order derivative *10/952.4℃ *20/952.4℃ *30/952.4℃

As we known, the variation temperature of aluminium electrolyte at a pioriod of 10ms is slight or very small. Since we directly deal with the original data with discrete method rather than smooth curves. When the temperature of molten aluminium electrolyte is slightly disturbed, which will great influence the results judged by first-order derivative or second-order derivative, pseudo inflection points TL appearing on the temperature curve is not a strange phenomenon, but a normal situation.

The Second Method of Step Cooling Derivative

Find the Inflection Point by the Alter of Slop of Discrete Curve

Figure 2. Inflection point appear at the alter point of slop of discrete curve.

Refer Figure 2, another method of the discriminant equation about whether the point of P is the inflection point of the curve is expressed in the following:

(KAB - KBP)*( KPC - KCD) <0 (6)

KAB, KBP, KPC and KCD are all the slopes of AB line, BP line, PC line and CD line respectively.

Above discriminant equation (6) can be replaced by the following equation.

((TB-TA)/(tB-tA) - (TP-TB)/(tP-tB)) * ((TC-TP)/(tC-tP) - (TD-TC)/(tD-tC)) (7)

Since the sampling interval is fixed and equal to 10 milliseconds, that means:

tB-tA = tP-tB = tC-tP = tD-tC = 10ms. The above equation (7) can be simplified as below:

((TB-TA) - (TP-TB)) * ((TC-TP) - (TD-TC)) =(2*TB-TA - TP) * (2*TC-TP - TD) < 0 (8)

In order to get the inflection points with iterative method, formula (8) can be expressed as below:

(2*Tk-2 –Tk-3 – Tk-1) * (2*Tk – Tk-1 – Tk+1) <0 (9) Discussions.If above formula (9) constant below 0, after iteration calculation of many times to the formula (9), which means that there is not inflection point on the discrete temperature curve. When the above formula (9) alter from below 0 to equal to 0, that means the point of tk-1 is the inflection

point and the iteration calculation of formula (9) can be immediately ended up. As a matter of fact, there too much values meet the condition of formula (9),that means there are too much inflection point. We have calculated fourteen sets of data originated from 2606 datum, the result is there are 252 datum meet the condition of formula (9). The reason is the same as the variation temperature of molten aluminium electrolyte under the interval of 10ms is slight or very small. The above method is more sensitive to external interference, even the temperature disturbed is slightly, which will great influence the results. Too much pseudo inflection points TL appearing on the temperature curve may

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Data Processing with Data-Density

[image:4.595.170.424.190.250.2]

In order to understand the concept of data-density, firstly we bring a simple example to introduction. For example: there exist ten raw datum, such as: 2.2, 2.4, 1.3, 0.9, 2.1, 1.6, 2.2, 3.9, 3.2 and 4.4. Rounded to decimal places to deal with the raw datum of ten data, the dataset will cover new data of 2, 2, 1, 1, 2, 2, 2, 4, 3 and 4 respectively. After rounding, the identical data distributed at different area will be rearranged at different group, only the identical data near to each others can be rearranged at the same group, that means the data-density of the above dataset is three about 2 at the fifth position, but not five about 2 at the first position, which is shown at figure 3.

Figure 3. Identical data are grouped.

Technical Activity

The Relation between Temperature Curve and Data-Density

When there is a clear turning point on temperature curve, the value of TL obtained by step-cooling

algorithm is accordance with data-density algorithm. At right of figure 4, TL identified by first-order

step-cooling derivatives and at middle by data-density algorithm. At left of Figure 4 presents the TL

caught by data-density with the most number of 258 among the slices, and by first-order step-cooling

derivatives (right) with the lowest value of 0.0262 corresponding the minimum slope on the curve.

Figure 4. Liquids arrest identified by step-cooling curve algorithm and data-density algorithm.

Liquids Identified by Data-Density Not by Step-Cooling Curve Algorithm

Usually the values of TL calculated by the above mentioned two algorithms are fairly close to each

other, but they differ sharply when no clear marked sign of inflection point on temperature curve of molten aluminium electrolyte. Sometimes when curve presents barely certain trend and no evident inflection point, TL identified is difficult and often gives wrong value or position by step-cooling

algorithm. At the top of figure 5 is a typical example about TL mistaken by step-cooling algorithm, but

[image:4.595.57.537.408.566.2]
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[image:5.595.66.534.72.262.2]

Figure 5. Liquids identified by data-density but not by step-cooling algorithm.

Liquids Identified by Data-density Not by Step-cooling Algorithm

Extensive and varied strictly experiments and tests over a wide range of aluminium production cells are carried out in order to validate the performance of accuracy and reproducibility of our setups and data-density algorithm for identified TL during production process in four big famous enterprises of

China with six years, and the results some extent exhibit better performances than off-line apparatus and step-cooling algorithm in the respect of fast evaluation and determine the true TL. Real on-site

typical production cells at Hall-Héroult cells with 160KA at top and 300KA with another version at bottom for measuring TL by data-density algorithm is obtained and their temperature-time trace

shapes are shown at Figure 6.

Figure 6. Liquids identified at two different types of production cells.

Discussion Liquids Identified by Data-Density

[image:5.595.62.537.431.649.2]
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As a matter of fact, the system of aluminium electrolyte is a complex system and not a system of pure material. That means the latent heat of crystallization process in the system of molten aluminium electrolyte is lower than in pure materials and the temperature plateau is not obvious or small or no. On the other words, from the view of micro perspective, the platform of TL formed is a slow process

changed from molten into initial crystallization and also corresponding the process of releases heat. Whereas the decrease rate of temperature of molten aluminium electrolyte leaves delay, the number of temperature data to be collected is aggregated around the inflection point, the data (or data-density) near the vicinity of inflection point is much more than the other part interval. It is an attracted and normal phenomenon that the aggregate amount of temperature data on curve is little or more different. It can be explained, there is actually a difference in data-density at each segmented time slice. In fact, there is actually a biggest data-density among the whole temperature curve of molten aluminium electrolyte, and which corresponding the inflection point of temperature curve of liquids.

On the other hand, around the place of the biggest data-density always presents the decrease rate of temperature is close to zero and the slop rate of temperature curve also near to zero. This suggests some extent correlation between the temperature curve and temperature data-density, and the phenomenon is inherence feature of temperature curve of molten aluminium electrolyte, which led to

TL can be estimated by statistical analysis of different aggregate amount of temperature data but it

can't be measured in a precise.

Conclusions

When inflection point characteristics is not obvious or not desired, sometimes even have nothing, an alternative technical is data-density algorithm, which will correctly estimate the inflection points of TL

of aluminium electrolyte, and has a large potential of wide application. In addition, data-density algorithm can make up for the defect of conventional step-cooling discrete algorithms, thus improving the prediction accuracy.

Acknowledgments

The authors wound like to acknowledge the financial supported by “Beijing Key Laboratory on Integration and Analysis of Large-scale Stream Data, Beijing, China 100144” and “Social Science Foundation of Beijing, (Project No.: 18JYB015)” .

References

[1] Yu Jiang-yu, et al, Fast Measurement on Superheat of Aluminum Electrolyte by Using Differential Thermal Analysis Method: Chinese Journal of Non-Ffrrous Mining and Metallurgy; Vol. 31. No 2, April 2015, pp. 33-35.

[2] P. Verstreken, Employing a New Bath- and Liquidus-Temperature Sensor for Molten Salts: JOM, Volume 49, Number 11, 1997, pp. 43-46.

[3] Shi Dong, et al, A novel method for in-site measuring liquidus temperature of aluminum electrolyte: Chinese Journal of Journal of Wuhan University of Science and Technology; Vol. 38, No. 2, Apr. 2015, pp. 93-95.

[4] A. Solheim, Å. Sterten et al., Liquidus Temperature and Alumina Solubility in the System Na3AlF6-AlF3-LIF-CaF2-MgF2 : Light Metals 1995, pp. 451–460.

[5] A.Rostm, A.Solheim and A.Sterten. Phase Diagram Data in System Na3AlF6 - Li3AlF6 - AlF3 -

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[6] A.Sterten and O.Skar. Some binary Na3AlF6-MxOy phase diagrams. Aluminium, 1988, 64(10): p.

1051.

[7] Xiangwen Wang, Bob Hosler, Gary Tarcy, Alcoa STARprobe: Light Metals 2011, TMS2011, pp. 483-489.

Figure

Figure 1. Extension line of thermocouple.
Figure 3. Identical data are grouped.
Figure 5. Liquids identified by data-density but not by step-cooling algorithm.

References

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