On my fresh impression obtained during the foreign travel (Europe and U. S. A. 1960-1961), the new trend of the electrolytic process of Aluminium production is shortly described.
The condition for minimum production cost
The total production cost of aluminium will be able to be analysed into several terms, that is to say electric power cost, raw material cost, labor cost, indirect expense and tax. However these terms are also respective functions of current density, using a definite plant. [Refer to equ. 5 (electric power for electrolysis) 7 (electric power for mechanical power and lightning) 9 (material cost) 10 (labor cost) 11 (indirect expense) 12 (amortization) 13 (tax)] Thus, the total production cost (W) will be shown by equ. 14 and 15 (approximate equ.) in which current density is the most important variable. If we assume that all variable except current density are constant, and partialy differentiate the formula 16 (simplified form of 15) with variable Id to get the condition making W take the minimum value, the equ. 20 will be obtained. Letting ∂
W/∂
Id=O, and solve this formula regarding to Id. Thus the I
D=2
C11/
PC10√(
PC10)
2+4
C11(
PC9+
C8) satisfies the required condition that the production cost of aluminium is minimum. In this formula P is electric power price/kWh,
C10 is shown by equ. 18 in which
C3 is the slope of equation representing overvaltage (=
C2+
C3 logId), and
C11,
C9 and
C8 are given by the equations 19, 17and 13 respectively. In this equation (22) we can see that P and
C11 have remarkable influence for the value of the most preferable current density because of
C10 can not so greatly change whatever a kind of anode carbon is.
Operation with the most preferable current density
It is very sorry that I can't calculate the actual value of the most preferable current density because of I have no detail datas for industrial production of aluminium. Then, let us consider how do we can realize the best condition, if Id given by equ. 22 is larger than the current density now usefully used in plants. (1) Froced cooling of bed carbon will be required, otherwise bath temperature will rise and accordingly the current efficiency will be remarkably enlowered. (11) Keeping the Al
2O
3 conc. in bath as low value as possible to make specific resistance of bath low. And devising automatic controll of the Al
2O
3 conc.. (111) To apply rather large prebaked block carbon as anode and further, to design cell construction with slope or vertical surface as cathode, using new material.
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