On the Cost of Products from Energy Recovery Units in Open-Hearth Shops
Abstract Generated abstract
The paper examines how to calculate the cost of energy products generated by recovery units attached to open-hearth furnaces. It argues that the fuel component must be included in such calculations, since omitting it prevents evaluation of the reduction in primary heat consumption attributable to energy recovery. Treating the furnace and recovery unit as a single energy-technological aggregate, the paper derives heat-balance relations for allocating useful heat and losses between steel production and recovered energy, then formulates cost expressions for thermal and electric utilization of secondary energy resources. The resulting method combines the fuel component with depreciation, wages, materials, water, overhead, and other directly attributable costs to determine the unit cost of recovered energy.
Full Text
ON THE COST OF PRODUCTION OF ENERGY RECOVERY UNITS IN OPEN-HEARTH SHOPS
V. E. Tselebroskii
(For the principal notation, see pp. 102–103)
Energy recovery units at technological aggregates, as is known, make it possible to utilize part of the heat losses by converting them into energy products. As a result, the energy efficiency of the process is naturally increased and, consequently, the consumption of primary heat resources per unit of output is reduced.
Proceeding from this objective of the recovery unit, we must reject all methods for calculating the cost of producing its energy output that propose not to take into account the fuel component [1]. In fact, by adopting such a convention, we thereby deprive ourselves of the possibility of evaluating the economic benefit of the recovery unit at the site of its direct operation. In other words, we deprive ourselves of the possibility of determining by how much the consumption of fuel or of another primary energy resource per unit of technological output of the aggregate at which the energy recovery unit began to operate is reduced. Thus, what actually occurs is not reflected in this case in the calculations. This is quite obvious, since, having assumed nothing to its own account, the recovery unit cannot remove part of the fuel consumption either from the main technological process or, consequently, from the main technological product. From the economic point of view, a technological aggregate with an energy recovery unit may be regarded as a single energy-technological aggregate producing two kinds of products: technological and energy. Considering the heat balance of such an aggregate, we are able to determine heat expenditures and distribute them between the technological product and the energy produced in the recovery unit. We shall do this using the particular example of the operation of an open-hearth furnace with a recovery unit. Let us represent the heat balance of such an energy-technological aggregate in the schematized form given in Table 1.
We shall distribute the losses \(Q_n\) between the technological and energy processes in proportion to the quantity of heat used in each process. In this case, the magnitude of the losses charged to the technological process will be determined from the relation:
\[ Q_m^n=\frac{Q_n\cdot Q_u^1}{Q_u^1+Q_{yy}}, \]
and the losses charged to the recovery unit will be equal to:
\[ Q_{yy}^n=\frac{Q_n\cdot Q_{yy}}{Q_u^1+Q_{yy}}. \]
Table 1
| Components of the balance items | In calories per ton of steel | Share of each item in its part of the balance |
|---|---|---|
| Heat received | ||
| Chemically bound heat of the fuel | $Q^m$ | $\alpha$ |
| Heat from other possible sources | $Q^d$ | $\beta$ |
| Total received | $Q^m + Q^d$ | 100% |
| Heat used | ||
| For the main technological process | $Q_u^1$ | $\gamma$ |
| In the recovery unit for the production of energy products | $Q_{uy}$ | $\lambda$ |
| Total used | $Q_u$ | $\psi$ |
| Total heat losses in the process | $Q_n$ | $\xi$ |
| Total expended | $Q_u + Q_n$ | 100% |
It is evident that the sum $Q_m^n + Q_{uy}^n = Q_n$. If it is assumed that all primary heat sources of the energy-technological process under consideration participate in supplying the expenditure items of the balance in proportion to their specific weight in the incoming part, then the efficiency $\eta_{mэ}^m$ with respect to the fuel expended in the process is written in the form:
\[ \eta_{mэ}^m = \frac{Q_u^1 + Q_{uy} - \psi Q^d}{Q^m}, \tag{1a} \]
and with respect to the other heat sources of the incoming part of the balance in the form:
\[ \eta_{mэ}^d = \frac{Q_u^1 + Q_{uy} - \psi Q^m}{Q^d}. \tag{1б} \]
The overall thermal-economic efficiency of the energy-technological process is found from the relation:
\[ \eta_{mэ}^u = \frac{Q_u^1 + Q_{uy}}{Q^m + Q^d}. \tag{1} \]
All three efficiencies found from expressions (1a), (1б), (1) are equal to one another. This is easy to verify if one takes into account that the quantity $(Q_u^1 + Q_{uy}) = \psi (Q^d + Q^m)$, and the numerical value $\psi = \eta_{mэ}^u$.
The presence of the efficiency $\eta_{mэ}^u$ allows us to single out from the total heat expenditure in primary energy resources that part which should be charged to the energy installation $(Q_э^m + Q_э^d)$. This part is found from the expression:
\[ Q_э^m + Q_э^d = \frac{Q_{uy}}{\eta_{mэ}^u}. \tag{2} \]
Since the cost of heat in fuel may differ from its cost in other sources, it is necessary to determine separately the share of heat,
falling to the production of energy in one or another form of primary energy resources. This can be done from the following relations:
\[ Q_{e}^{m}=\frac{\lambda Q^{m}}{\eta_{te}^{m}} \quad \text{and} \quad Q_{e}^{d}=\frac{\lambda Q^{d}}{\eta_{te}^{m}} . \tag{2a} \]
Equations (2a) are obvious, since the quantity of heat used by the recovery unit can be represented as consisting of two components:
\[ Q_{uy}=Q_{uy}^{m}+Q_{uy}^{d}, \quad \text{where} \quad Q_{uy}^{m}=\lambda Q^{m}, \quad \text{and} \quad Q_{uy}^{d}=\lambda Q^{d}. \]
The quantity of heat in primary energy resources attributable to the share of the recovery unit can also be determined from the following relationships: for the electric-power variant of utilizing secondary energy resources,
\[ Q_{e}^{m}+Q_{e}^{d}=\frac{Q_{ue}}{\eta_{te}^{m}\eta_{uy}^{k}} \tag{2b} \]
and for their thermal-power utilization,
\[ Q_{e}^{m}+Q_{e}^{d}=\frac{Q_{utm}}{\eta_{te}^{m}\eta_{utm}} \tag{2v} \]
In these equations: \(Q_{ue}\) and \(Q_{utm}\) are the amount of energy obtained from the recovery unit, and \(\eta_{uy}^{k}\) and \(\eta_{utm}\) are the efficiencies of the corresponding recovery units. The quantity of heat \(Q_{e}^{m}+Q_{e}^{d}\) also determines the magnitude of the fuel component in the cost of producing energy in the recovery unit. This will be the direct benefit from operation of the recovery unit from the standpoint of reducing the cost of steel production. It is precisely by the amount \((Q_{e}^{m}+Q_{e}^{d})\) that we must reduce the quantity of heat previously taken as the basis in calculating the fuel component of the cost of producing steel in open-hearth furnaces.
The magnitude of the fuel component \((S_m)\) per unit of energy in monetary terms is determined from the following equations: for the thermal-power variant of utilizing secondary energy resources,
\[ S_m=\frac{K\left(Q_{e}^{m}+Q_{e}^{d}\right)}{Q_{utm}} =\frac{K\left(Q_{e}^{m}+Q_{e}^{d}\right)}{\eta_{te}^{m}\eta_{utm}\left(Q_{e}^{m}+Q_{e}^{d}\right)} =\frac{K}{\eta_{te}^{m}\eta_{utm}} \ \text{rub/Mcal}, \tag{3} \]
for the electric-power variant,
\[ S_m=\frac{K\left(Q_{e}^{m}+Q_{e}^{d}\right)}{860\,E\,10^{6}} =\frac{K\left(Q_{e}^{m}+Q_{e}^{d}\right)10^{-6}}{\eta_{te}^{m}\eta_{uy}^{k}\left(Q_{e}^{m}+Q_{e}^{d}\right)}, \]
whence
\[ S_m=\frac{K\,8.6\,10^{-4}}{\eta_{te}^{m}\eta_{uy}^{k}} \ \text{rub/kWh}. \]
Here, “\(K\)” \([\text{rub/Mcal}]\) is the cost of one megacalorie of heat in the primary energy resources of the open-hearth furnace. The value of “\(K\)” may be different for different types of primary energy resources, but this does not alter the logic of the reasoning in deriving the formula. If certain types of energy resources
are not included in the cost of technological production (in the production of steel in open-hearth furnaces, this category is usually taken to include: the heat of exothermic reactions and the physical heat of the charge), then, obviously, they should not be included in determining the cost of producing energy products. In addition to the fuel component, all the other components usually enter into the cost of producing energy products as well: depreciation, \(S_a\); wages, \(S_{zp}\); auxiliary materials and water, \(S_v\); overhead expenses, \(S_{nr}\); other expenses, \(S_{pr}\). All these components are calculated according to the expenditures that can be directly attributed to the production of energy in the recovery unit. The overhead expenses of the shop and the plant should be distributed between technological and energy products by the usual method, that is, in proportion to direct costs. Thus, the final equation for determining the cost of producing energy products in a recovery unit will take the form:
\[ S_{uu} = S_t + S_a + S_v + S_{zp} + S_{nr} + S_{pr} \quad \text{rubles/kWh (megacalorie).} \]
References
- Semenenko N. A., Secondary Energy Resources of Industry, Gosenergoizdat, 1951.
- Savostin D. Z., “Heat Balance of an Open-Hearth Furnace,” Steel, No. 3, 1951.