EFFECTS OF E.A.F. DESIGN AND OPERATION ON ELECTRODE CONSUMPTION *
L. R. Jaccard
INTRODUCTION
A deep knowledge of the correlation between the specific electrode consumption and the furnace operating and design parameters is the best tool to achieve the optimum economical conditions for the production of steel in electric arc furnaces.
A certain steel work can adopt an operating procedure different from that employed at another plant. However, it is important that the choice between one operating procedure or another is based on correct premises and that the results obtained confirm the previsions made.
EQUATION OF THE SPECIFIC ELECTRODE CONSUMPTION
After the tip consumption has been defined as being dependent on the square of the current intensity ( Qtip (kg/h) = K.I² 1), 2), 5), it became relatively simple to correlate the specific electrode consumption QS (kg/t) with the operating and design factors. On the basis of the expression above, the author4) arrived at an equation which enables to analyse the effects of the several variables on the specific electrode consumption without the need of dissociating the tip consumption from the sidewall consumption.
The overall electrode consumption, expressed in kilograms per hour, is proportional to the square of the current intensity and the ratio between the electrode initial cross section and the tip cross section (see figure 1):
Fig. 1 - Consumo Total
QTot(kg/h) = Qtip x D²/d² = K . I² . D² / d² ( 1 )
Where: D= electrode initial diameter, and d= tip diameter.
The specific electrode consumption (kg/t) is equal to the weight of electrode consumed in kilograms divided by the amount of steel produced at the same time in tons, and the production during a certain period is directly proportional to the active power and inversely proportional to the specific electrical energy consumption. Therefore, the specific electrode consumption (kg/t) is directly proportional to the specific energy consumption qee(kwh/t) and inversely proportional to the active power P(kW):
QS(kg/t) = QTOT(kg/h) . qee (kwh/t) / P (kW)(2)
By placing (1) in (2) and multiplying the result by 3, in the case of a furnace having three electrodes, it comes:
QS(kg/t) = 3 . K . ( I² / P ) . (D² / d² ) . qee (3)
The equation (3) enables to calculate the specific electrode consumption when the tip diameter is known. However, in order to have a better comprehension of the effects of the several parameters on the specific electrode consumption, it is necessary to find an expression which relates D² / d² with these parameters. This can be achieved by observing that the diameter reduction "D-d" due to the oxidation is proportional to the sidewall consumption intensity Kox, expressed in cm/h and the oxidation time Tox, expressed in hours.
But the oxidation time is inversely proportional to the tip consumption rate, also called linear consumption, and directly proportional to the height of the part of the column exposed to the oxidation. These premises lead to the following equation:
D - d = Kox . H . d² / ( K´. I² )
which, once resolved, becomes:
D²/d²= { 0,5 + [0,25 + ( Kox / K´ ) . ( D.H / I² )]1/2 }2 (4)
By placing the equation (4) in (3), the result is the final equation for the calculation of the specific electrode consumption as a function of the operating and design parameters:
QS(kg/t) = ( 3.K.I² / P ) . { 0,5 + [0,25 + ( Kox / K´) . ( D.H / I² )]1/2}2 . qee (5)
Where:
K is a coefficient representative of the electrodes quality from the viewpoint of the tip consumption. On a survey performed on 8 furnaces operating with electrodes manufactured in 1980, in Brazil, with diameters 350 mm and larger, the average consumption values collected corresponded to:
K = 0,0233 kg / kA² . h
I²/ P is a coefficient which depends on the electrical operating and design parameters. This coefficient is better understood by substituting 3 I²/P for tan(phi)/X or sin(phi)/cos(phi).X, thus enabling us to conclude that the specific electrode consumption is inversely proportional to the reactance and to the power factor. Other expressions equivalents to I²/P are: I/Va µ P/Va², which show that an increase in arc voltage decreases the electrode consumption. The expression I/Va can be written 1/Ra, where Ra is the resistance of the arc. In some smelting furnaces, there are not arcs and the current circulate by the slag. For that kind of furnaces, Ra is the slag resistance.
Kox is the sidewall consumption rate, expressed in centimeters per hour that the furnace remains "ON" . Its value ranges from 0.70 to 1.40 centimeters of diameter reduction per hour, for regular quality electrodes ( fig. 2 ).
Fig. 2 - Kox Sidewall consumption rate ( kg/h )
Kox = (D-d) / Tox = 0,7 to 1,4 cm/h
K' has the same meaning of K, and it is equal to 4.K/(p . Ws ), where Ws means the specific weight of the electrodes. For K = 0,0233 kg/kA2.h , K' is equal to 18,5 cm3 / h.kA2
D/I² is a coefficient inversely proportional to the current density in the electrode. D is the electrode initial diameter and I is the current intensity.
H is the furnace height as measured from the bath level to the roof rings.
qee is the specific electrical energy consumption.
Analysis of the Effects of the Several Factors lnvolved
Electrodes quality - K, K' and Kox
The better the electrodes are in quality, the lower will be the factors K and K' as well as the specific electrode consumption. However, any factor which causes a linear consumption decrease leads to a sidewall consumption increase, as it can be seen fron equation (5), through the factor K' in the denominator of the term Kox/K'. That means that if it were worked out an electrode quality with tip consumption 20% less than that of the regular quality electrode, without a parallel improvement of this electrode characteristic as regards to the sidewall consumption, the effective specific consumption reduction would be less than 20%.
Power factor and reactance
The specific electrode consumption decreases if the power factor or the reactance are increased. This can be seen from equation (5), by placing:
3 I² / P = tan (phi) / X = I . 1,73 / V.cos (phi)
At the beginning of the 1980´s, the power factor increase was the way used to reduce the specific consumption of electrodes in a great lot of arc furnaces. For those cases where the theories suitable to UHP operation had been applied with a certain exaggeration, through the use of power factors ranging from 0.60 to 0.70, also during the meltdown, the electrode consumption reduction reached values up to 40% after the power factors were increased to 0.80.
The power factor increase without voltage increase causes the active power to drop, thus reducing the production per unit of time. Above certain power factor values, the furnace production might fall below the minimum level required to reach the programmed goal. For this reason, the reduction of the specific electrode consumption by means of the power factor increase requires the observance of the production level desired. Anyway, in the great most of the steel works, the operation at low power factors seldom could be vindicated on account of the high rate of electrode consumption demanded by this kind of operation.
To hold the levels of production after the power factor increase it would be necessary to enhance the secondary voltage of the transformer. Unfortunately, most of the furnaces built in the 1970s and beginning of the 1980s had transformers with low secondary voltage. The maximum available voltage was such that the rated power of the transforrner would only be demanded by the furnace in case the operation were carried out with power factor close to 0.707 and no higher voltage tap were expected for operation at the rated power of the transformer with greater power factor. By that time, the furnace manufacturers had in their minds to reduce as much as possible the refractory consumption and so, they aimed at achieving low reactances and secondary voltages. At the end of the 1980´s, however, these protective measures were thought to be excessive, since the scrap protects the wall against the corrosive actions of the arc during the great most of the meltdown, and in this stage of operation, it is possible to use higher voltages.
In fact, the operation at higher power factors has become widespread after the introduction of the water cooled walls and roofs and concomitantly to the oil crisis, which raised the prices of the graphite electrodes. Once it has been understood that it was possible to operate in the meltdown at refractory erosion indexes much above those that had been used until then, due to the use of water cooled walls or the natural protection of the walls provided by the scrap, it became evident that, besides increasing the power factor, it would be possible to perform the project of furnaces for operation at higher voltage and reactance values.
ln small and medium-capacity furnaces with powers up to 15 MVA, in which the voltages applied are high if compared to the rated power and current, the use of high reactances should be considered a requirement of the circuit.
For example, a furnace of 3 MVA which operates at a voltage of 23OV requires an overall operating reactance of 10 mohms. Since the furnace reactance together with the primary system reactance are not enough for the matching of the voltages and currents expected, it is imperative that a serial reactor be inserted. Despite the utilization of high reactances, small capacity furnaces don't achieve exceptionally low electrode consumptions for two negative aspects: operation at high specific energyconsumption and the larger ratio D.H/I².
During the 1970 decade, before the positive effects of the operation with higher voltages and higher reactances were known, it started the elimination of the serial reactor from the designs of medium-sized furnaces with powers ranging from 15 to 25 MVA, with a preference to reduce the secondary voltage so that it could be eliminated a part that was considered to be just one more item which raised the furnace cost and took up space at the transformer compartment.
As it has been already said, in the 1970s, the search for low reactances turned out to be a design target for large capacity and high power furnaces. The manufacturers referred to the low reactances achieved as one of the main features of the furnace. This feature associated to a good triangulation so as to balance the phase reactances were thought to be primordial factors to make it possible the refining operation at low refractory erosion indexes.
Such a low reactance design together with the operation at low power factors resulted in high specific electrode consumptions.
During the 1990´s, the furnace circuit was designed in such a way as to have high reactances, so that the specific electrode consumption was reduced, and with higher secondary voltages to the attainment of the power needed.
For already existing systems with low impedance primary circuits, it was demanding that serial reactors were installed.
In order to increase the secondary voltage, the furnace transformer must be replaced or its secondary rewound. If it is desired a substantial productivity increment, the replacement of the transformer is mandatory.
The alternative of manufacturing a new secondary winding is very interesting if there is a spare transformer available, because it can be modified without the need to shut down the furnace. Whenever the transformer original specification doesn't enable to achieve the apparent rated power at operation with cos(phi) greater than 0.707, the modification in the secondary might result in an 10 to 20% increase of the furnace active power.
Up-dating to year 2003
Most of the existing E.A.F. over the world have been already revamped and they are operating, during the scrap melting period, with very high voltages and high reactances. The introduction of foammy slags allowed the use of very high voltages also during the refining period. We have the chance to verify that during operation with good foammy slags it is posible to employ power factors values closed to the unity, maintaining a perfect arc stability. The operation with extremely high power factors has some advantages. In first place, with the same transformer it is posible to obtain higher active powers. The other improvements are higher sensitivity of regulators( for the same percentage of arc length variation occurs at higher current variation ) and lower effect of phase reactances assymetries. To operate with the highest power factors it is necessary to by-bass the series reactor. Another great advantage of the operation with power factors close to 1 is the reduction of the electrode consumption, since I²/P is further reduced.
Electrodes diameter - D
In equation (5), the factor D.H/I² shows that the larger the electrode column surface is as to the square of the current intensity, the higher it will be the specific electrode consumption. Therefore, for the same current, a reduction of the electrodes diameter causes a consumption decrease. However, the current density can be increased only up to the maximum limit supported by the electrode.
In small capacity furnaces, specially those using electrodes with diameters 300 mm and smaller, the maximum allowable currents are such that the rate D.H/I²2 is greater than that of large capacity furnaces, being that one of the reasons for why the small capacity furnaces don't achieve very low electrode consumptions despite the installation of high reactances.
When an increase of the voltage and the reactance is made without a corresponding increase of the specific power, the current intensity decreases and so, the factor D.H/I² increases, thus causing the consumption due to the oxidation to raise. The overall specific consumption decreases as a consequence of the more intense reduction of the tip consumption; however, if this voltage and reactance increase were followed by a reduction of the electrodes diameter, then the specific consumption reduction would be still more significative. However, the electrodes diameter reduction could intensify the breakages due to scrap falls and electrodynamic forces. So, it follows that as regards to the low specific power furnaces, the difficulty in reducing significantly the electrodes diameter due to the risk of breakages is a limitation to the achievement of the lowest electrode consumptions. When the voltage and the reactance increase is followed by the power increase, the current intensity remains constant and, in consequence, the factor D.H/I² doesn't increase. ln the latter case, as it has been said elsewhere, the limitation to the adoption of more significative power and voltage increases is concerned to the refractory quality.
Furnace height
H. The part of the electrodes column subjected to the highest levels of oxidation intensity is the one that works inside the furnace, below the roof rings level, receiving all the heat coming from the furnace walls, the bath and the arc itself. The bigger the distance between the bath and the roof rings is, the longer every part of the electrode will be subjected to the oxidation, and the more intense will be the sidewall consumption.
In order to reduce the electrode oxidation length, the following techniques have already been attempted: recoating of the electrodes with refractory materiais, direct water cooling of the graphite electrodes and substitution of part of the electrode column for water cooled cylinders.
Up-dating to 1990´s
.Direct water cooling of electrodes is the only well succeeded solution to reduce the lenght of oxidation, used in most of the E.A.F´s furnaces. Anyway, the reduction in overall electrode consumption is small, in comparison with the reduction attained by voltage increase.
Specific electric energy consumption - qEE (kwh/t)
The specific electrode consumption is directly proportional to the specific electric energy consumption. For this reason, the use of the coefficient Qs/qee (kg/MWh) to determine the furnace design and operation conditions concerning to the specific electrode consumption is becoming generalized. For example, a furnace having such conditions of reactance, power factor and electrodes diameter that a consumption of 3 kg/MWh results, will have a specific consumption of 1.35 kg/t if it is operated at an energy consumption of 450 kWh/t, or 1.8 kg/t, if it is operated at 600 kWh/t.
Oxidation intensity - Kox (cm/h)
The factor Kox is equal to the horizontal consumption rate, expressed in cm/h. The main reason for the sidewall consumption is the electrode surface oxidation, which is caused by the oxygen contained in the furnace atmosphere due to the air drawn by the fume extraction and the use of oxygen lances.
In measurements performed by the author, in 1980, on furnaces using regular quality electrodes, values of sidewall consumption Kox corresponding to reductions of 0.70 to 1.40 centimeters of diameter per hour of furnace "ON" have been found. lf we consider that the electrodes continue to oxidize also when the furnace is "OFF", the most effective sidewall consumption rate would be somewhat lower than the values reported above.
Tap to tap time
In general, the tap to tap time is referred to as one of the principal causes for the specific electrode consumption increase. Actually, as it can be seen from equation (5), there is no direct correlation between the specific electrode consumption and the tap to tap time.
If the tap to tap time increase is achieved by decreasing the current intensity without a simultaneous decrease of the voltage, the power factor raises and the electrode consumption lowers. An increase of the sidewall consumption is noticed, but the proportionally larger reduction of the tip consumption causes the specific electrode consumption to lower, despite the higher tap to tap time.
A furnace with low specific power (kW/t) will certainly operate at higher tap to tap times than those obtained with a high specific power furnace.
However, the specific electrode consumption of such low specific power furnace, in spite of the higher tap to tap times, might be lower than the specific electrode consumption of the high specific power furnace, depending on the electrical parameters used.
The electrode conicity , “D²/d²" defines the effect of the sidewall consumption on the specific electrode consumption, and it is a function of the following factors only:
D²/d² µ (Kox/K´) . ( H. D / I² )
And it has not any correlation with the tap to tap time. For known qualities of electrodes and oxidation rates, the effect of the sidewall consumption on the specific electrode consumption depends only on the extent of the electrode lateral surface "H.D" and the inverse of the square of the current ( factor H.D/I² ).
* 2003 up-dated abstract of technical L.R. Jaccard paper “ Effects of E.A.F. design and operation on energy and electrode consumption” handed at the Third European Electric Steel Congress, Bournemouth, UK - 1989.
REFERENCES
1) COMMISSION OF THE EUROPEAN COMMUNITIES.: "Basic properties of high intensity electric arcs used in steelmaking" - Report FR/24176
2) JORDAN, G. R. : "Electrode erosion in electric arc furnaces-the controlling parameters." Ironmaking & Steelmakíng, 1978, no. 4.
3) BOWMAN, B. : "Optimum use of electrodes in are furnaces". Metallurgical Plant and Technology, 1983.
4) JACCARD, L. R. : "Consumo especifico de eletrodos em fornos a arco-correlaçáo com os fatores de operação". ABM. 439. Congresso Anual, Belo Horizonte, Brasil, 1988
5) SCHWABE, W.E. : "The mechanics of consumption of graphite electrodes in electric steel furnaces" Reprinted frorn Journal of Metais, November 1972.