L. R. Jaccard


Along the years 2005 and 2006 we conducted tests in submerged arc furnaces aiming to define the correlation between the furnace geometry and the ideal electrical parameters of operation ( V and I ). The experiences greatly confirmed the research made by Andreae, Morkramer, Kelly and others that, starting in 1923, studied the subject and concluded that the voltage and current values that promote the most efficient furnace operation are related with the electrode size. On the other side, we verified that the empirical relations presented by J. Westly in 1975 do not correspond to reality. According to Westly´s paper, the ideal voltage and current are dependent only on power ( V = P1/3 / C3 and I = C3 . P2/3 are the very well known Westly equations ).

We found that for a certain electrode space the ideal electrode-to-hearth voltage is proportional to the electrode diameter and inversely proportional to the active power fourth root: V = J0 . D / P1/4, where the J0 factor depends on the processed material and the electrode spacing. Additionally, it was inferred that, inside certain limits, the ideal voltage increases proportionally with the electrode spacing square root. The final equation is: V = J1 . D . S1/2 / P1/4, in which S is the space between electrode centers. That is, the ideal voltage and current, for each processed product, depends on: active power, electrode diameter and electrode spacing.


Electrode ideal position

Unlike direct arc furnaces, applied for steel production, in which the electrode position over the metallic charge does not have any effect on the energy consumption, for some ore reduction furnaces it is fundamental to operate at the right position of the electrode tip to obtain the lowest energy consumption and, consequently, the higher productivity. In the case of tin smelting and ferrosilicon production, which are the two cases we deal at this paper, a very small variation of just 2 to 3 volts around the ideal voltage produces a great increase of power consumption with the correlated productivity decrease. For the FeSi furnaces another consequence of the operation with the electrode out of the ideal position is a higher SiC deposition at the furnace hearth.

Research on electrode ideal position, since 1923 to 1970 - Andreae, Morkramer, Kelly and Persson - Power density concept

More than eighty years ago the fundamentals for the understanding of the ideal position parameters were being conceived. In 1923, F.V. Andreae developed the peripheral resistance concept, which he improved until its final publication at the A.I.E.E., in 1950. Andreae established that for each product exists just a unique ideal position of the electrode relative to the ore and carbon charge, which depends on the electrode diameter and the resistance between the electrode tip and the hearth. This concept was expressed by the equation: k = ( V / I ) . p . D where k is the electrode peripheral resistance, V is the electrode-to-hearth voltage, I is the current and D is the electrode diameter.

Many other researchers studied the subject of the electrode ideal position. Among them, we can mention Morkramer that used the power density concept ( also applied by Andreae ). According to that principle, the temperature at the neighboring of the electrode tip varies with the power density "pd" transmitted to the charge through the electrode, defining pd as the relation between the active power and the electrode cross sectional area ( kW / ) or kW / cm2 ). Based on the power density concept, the load temperature at the charge would be increased close to the electrode tip, in order to develop a higher power transfer rate, and to a higher distance of the electrode tip the heat would be dissipated prevailing the temperature of the chemical reactions. To a higher power density corresponds a higher charge temperature and, consequently, a lower load resistivity, concluding that k factor decreases as power density increases ( in fact, k represents the resistivity of the load ).

At the early 1940´s, after consultation with Andreae, W.M. Kelly "applied the k concept to an accumulation of ferro-alloy furnace data for various products and in 1950 ranges of k factor were established for the principal submerged arc operations, based on the furnace data then available". Figure 1 shows the Kelly´s straight line relationship for FeSi75. From this graphic it is possible to find the ideal voltages and currents for each active power and electrode diameter values.

FeSi75 k factor - (Kelly)

The methodology to design the submerged arc furnace using the k factor is complicated, mainly by the fact that the same variable ( electrode diameter ) appeared in both the ordinate and the abscissa parameters. That difficulty was verified by J.A. Persson who at his elucidating technical papers explained the theories of his antecessors and presumed, based in a simple arithmetical relation, that the straight line relationship between k factor and the power density pd, could be an hyperbola and, in this case, the electrode-to-hearth voltage would be directly proportional to the square root of the electrode diameter: V a D1/2 ( according with the experiences we made, the ideal voltage depends on both, electrode diameter and power, and the Kelly graphics should be hyperbolas but with a different curvature than that predicted by Persson ).

Critical parameters to define the ideal electrode position after J. Westly ( 1975 )

In 1975, J. Westly, from the Elkem company, presented a paper in which he raised doubts about all the concepts developed by the other previous researchers. He wrote: "when a furnace is operated on say 20 MW the operating resistance will be the same whether the electrode diameter is 1250 mm or 1550 mm provided the raw materials are the same, apparently in conflict with Andreae concept this conclusion certainly give rise to concern". And ends: "then what about the Andreae concept?" ( as we will mention later, the experiences that we realized proved us that Mr. Westly was wrong and the Andreae concept was correct ).

Westly deduced the following expressions to define the ideal electrode position: I a P2/3 and V a P1/3 ( he called C3 to the factor I / P2/3 ). In brief, according with J. Westly, the ideal voltage and current have not relation with the electrode size. After Westly´s paper the electrode size selection became to be made considering solely the electrode current density capacity.


In Brazil there are many small tin smelting furnaces. Most of them are rectangular two electrode furnaces with Scott connection transformers. The transformer power, except in few cases, varies between 150 kVA and 1250 kVA. The electrodes size goes from 8 inches to 24 inches. The charge materials are coal and cassiterite that form a floating layer over the slag. To achieve the optimum furnace performance, the electrode tip must be inserted in this layer at a position nor too dip neither too shallow.

After many years working with steel EAF´s, it was just between 1990 and 1992 that we had, for the first time, the opportunity to work with this kind of smelting furnaces and, making changes in voltage, current and electrode diameter we obtained significant performance improvement. The changes made at that period were based on J. A. Persson concept. At that time we had already read Westly´s paper, but the strong objections raised by Mr. Persson at the discussion session ( AISE electric proceedings 1975 ), induced us to believe that Westly´s empirical expressions were incorrect. Later on, when we made several jobs at FeSi75 furnaces and, also, after reading some technical papers, we verified that Westly´s equation ( I = C3 . P2/3) was the one considered certain by most of the furnace operators and designers. For that reason, in 2005, when we had a new opportunity to work with cassiterite reduction furnaces we decided to make experiences, changing values of power, voltage, current, electrode diameter and electrode spacing, in order to compare the different concepts and to find the real correlation among the ideal parameters.

The test details will be presented in the future; the following is a resume of the principal conclusions.


The experiences proved that, in opposition to the empirical C3 equation ( V = P1/3 / C3 ), the ideal electrode-to-hearth voltage is inversely proportional to active power. Consequently, in order to maintain the ideal electrode position after a power increase, the voltage, instead to be increased, as dictated by Westly´s equation, it should be diminished. And, the current should be increased in a higher proportion than the expected by the C3 expression ( I = C3 . P2/3). A major disagreement is the evidence that the ideal voltage and current have a strong correlation with electrode diameter.

We conclude that the electrode voltage which promotes the ideal position of the electrodes is directly proportional to the electrode diameter and inversely proportional to the fourth root of the active power: V = J0 . D / P1/4, where J0 is a factor that relies on the material to be processed and the electrode spacing. That is, the ideal voltage depends on power and electrode diameter.

In addition, it seems that the ideal voltage is proportional to the square root of the electrode spacing S ( center to center electrode distance ), then: V = J1 . D . S1/2 / P1/4, where J1 =V . P1/4/ D . S1/2 is a constant for each raw material.

Based on J equation, it is possible to conclude that higher electrode diameters permit to attain the ideal position with higher voltages and lower currents, leading to lower energy and electrode consumption. Presently, the electrode size is selected based in the higher density current allowed by it. This criteria must be provoking higher electrode and power consumption due to the necessity to use lower voltages and higher currents in order to find the ideal position.

Also, higher electrode spacing ( until a limit that must be quantified ) leads to higher ideal voltages, with the benefits mentioned above.

The J equation graphic, when represented as "Andreae´s k factor vs power density" shows a strong similarity with the Kelly graphic. Trusting on the experiences results we can conclude that as early as sixty years ago an excellent tool to define the submerged arc furnace ideal parameters was already available. Since 1975, the C3 fórmula, in spite of being wrong, became an absolute truth for most of the operators and the k factor concept, in part, due to its difficult application and, mostly, due to the C3 widespread disclosure, was forgotten ( see next picture ).

FeSi75 Kelly original k graphics vs k calculated with J1 and C3

As it will be explained in the next future, the experiences confirmed that for each material exists an ideal melting rate that can be attained just with one vertical position of the electrode.


After defining the J1 factor for a certain material it is possible to verify the alternatives of electrode size, electrode spacing, voltage and current that, for the desired active power level, promote the ideal positioning of the electrode. The implementation of the set of parameters that lead to the best performance ( lower energy and lower electrode consumption ) usually will require a higher investment and the final project must be based on economic reasons ( capital cost vs operational costs ).

Contact Mr. L R Jaccard