ON THE DETERMINATION OF ABSOLUTE FUEL SAVINGS WHEN USING SECONDARY ENERGY RESOURCES

V. E. TSELEBROVSKII

(For the principal notation, see pp. 102–103)

Working on secondary energy resources, a utilization installation creates the possibility of further use of part of the energy that previously was regarded as losses of the technological process. However, this amount of energy does not yet determine the absolute fuel saving obtained from operation of the utilization installation. If the use of heat resources for the production of technological product in the main unit and of energy product in the utilization installation is regarded as a combined energy-technological process, then the amount of energy used by the utilization installation may serve as a basis for reallocating the primary energy resources of this process between the two kinds of final product produced. This, for example, must be done when determining the cost of production of one or another kind of product. But in order to determine the absolute fuel saving from operation of the utilization installation, it is necessary to take into account also those interconnections which it always has, through energy consumers, with energy installations operating on primary energy resources: CHP plants, factory boiler houses, etc. In other words, we can correctly determine this absolute fuel saving only by comparing its expenditures for the production of the same amount of energy and technological product with and without participation of the utilization installation.

Let us consider a particular example of the operation of an open-hearth furnace with an energy utilization installation.

Suppose that, before construction of the utilization installation, the open-hearth furnace consumed for the technological process of producing \(G\) tons/year of steel \(Q^m + Q^0\) kcal/year of heat (\(Q^m\) is the heat of fuel, \(Q^0\) is the heat of other sources). Of this amount, \(Q'_u\) kcal/year was used, while the remainder constituted losses. For the production of \(E\) kWh/year of electric power and \(Q_{otb}\) kcal/year of heat, \(Q_{tets}\) kcal/year of heat in fuel was expended at the CHP plant. The utilization installation began to use, from the secondary energy resources of the open-hearth furnace, \(Q_{uu}\) kcal/year and, by virtue of this, to produce a certain amount of energy product. This reduced the process losses or, in other words, improved its thermal economic efficiency \((\eta^m_{te})\). This efficiency in the latter case may be determined from the expression:

\[ \eta^m_{te} = \frac{Q'_u + Q_{uu}}{Q^m + Q^0}. \]

The heat consumption for producing \(G\) tons/year of steel as a result of operation of the utilization installation decreased by the amount \(\dfrac{Q_{uy}}{\eta_{tez}^{m}}\),\(^{1)}\) that is, it became equal to

\[ Q^{m}+Q^{d}-\frac{Q_{uy}}{\eta_{tez}^{m}} . \]

At the same time, the fuel consumption at the TPP also decreased, since part of the necessary electric and thermal energy began to be supplied to consumers by the utilization installation.

Let us denote the new value of the heat consumption in primary energy resources for producing the former quantity of energy output by \(Q_{tets}^{uy}\). Then the total heat consumption in primary energy resources of the economic combined energy-technological system for the two cases under consideration will be determined as follows.

Without the utilization installation:

\[ Q^{m}+Q^{d}+Q_{tets}\ \text{kcal/year}. \tag{a} \]

With the utilization installation:

\[ Q^{m}+Q^{d}-\frac{Q_{uy}}{\eta_{tez}^{m}}+Q_{tets}^{uy}\ \text{kcal/year}. \tag{b} \]

The absolute saving of heat of primary energy resources of interest to us, obtained as a result of operation of the utilization installation, is determined as the difference between (a) and (b). Let us denote this difference by \(\Delta Q^{uy}\).

\[ \Delta Q^{uy}=Q_{tets}+\frac{Q_{uy}}{\eta_{tez}^{m}}-Q_{tets}^{uy}\ \text{kcal/hour}. \tag{1} \]

All quantities entering equation (1) can be determined from heat balances.

The greatest possibilities for taking account of all the principal factors affecting fuel consumption in the system are opened up by using the method for drawing up energy balances in combined production of heat and electric power, developed by Prof. I. N. Butakov (I. N. Butakov, Heat-Power Installations, Part 1, 1954). According to this method, the total heat consumption in the fuel expended at the TPP is determined from the expression:

\[ Q_{tets}= \frac{860\left(E-\dfrac{Q_{otb}}{q}\right)}{\eta_{k}} + \frac{860\dfrac{Q_{otb}}{q}+Q_{otb}}{\eta_{m}} + \frac{Q_{rou}}{\eta_{ku}\eta_{pot}} \ \text{kcal/year}; \tag{A} \]

where: \(E\) kWh/year is the total generation of electric power,
\(Q_{otb}\) kcal/year is the production of heat through extractions and back pressure of turbines,

\(^{1)}\) This question is considered in greater detail in the author’s article “On the Question of Choosing an Energy Installation Operating on Secondary Energy Resources of Open-Hearth Shops,” published in this same volume of Izvestiya.

$q\ \mathrm{kcal/kWh}$ — a specific index determining the amount of heat supplied to consumers through extractions or turbine back pressure for each kWh of electric power generated on heat consumption,

$\dfrac{Q_{\mathrm{t.c.}}}{q}\ \mathrm{kWh/year}$ — the amount of electric power generated on heat consumption,

$Q_{\mathrm{ext}}\ \mathrm{kcal/year}$ — heat delivered externally in live steam,

$\eta_k$ — efficiency of the condensing part of the CHPP,

$\eta_t$ — efficiency of the district-heating part of the same,

$\eta_{ku}$ — boiler efficiency,

$\eta_{\mathrm{pot}}$ — efficiency of the heat flow at the CHPP.

Secondary energy resources may be used to obtain, in a utilization installation, heat, electric power on heat consumption, and electric power on condensing turbines. The most general case will be the operation of a utilization installation consisting of a boiler and a turbine generator with steam extractions from intermediate stages.

Let $Q_{yy}^{\mathrm{ext}}\ \mathrm{kcal/year}$ denote the amount of heat that theoretically can be obtained from turbine extractions when using $Q_{yy}\ \mathrm{kcal/year}$ of heat from secondary energy resources. This amount is determined by the design features of the turbines used and may be calculated from the following considerations.

Let us denote by $G_1$ the amount of steam entering the turbine, and by $G_{\mathrm{ext}}$ the amount of steam that can theoretically be obtained from turbine extractions. The ratio

\[ \frac{G_{\mathrm{ext}}}{G_1}=\alpha . \]

Let the heat contents of steam and condensate at various points be denoted by $i$ with the corresponding subscripts: $i_1$ for live steam, $i_n$ for steam in the turbine extractions, $i_{fw}$ for feedwater, $i_k^{1}$ for condensate of the extraction-return flow, and $i_k$ for condensate from the turbine condenser.

In this case the heat content of the feedwater, which is a mixture of turbine condensate and condensate of the extraction-return flow, may be determined from the expression: $i_{fw}=\alpha(i_k^{1}-i_k)+i_k$. Using the adopted notation, we may write the heat balance of the utilization unit in the following form:

\[ G_1(i_1-i_{fw})=\alpha G_1(i_1-i_n)+\alpha G_1(i_n-i_k^{1})+(1-\alpha)G_1(i_1-i_k). \]

Making substitutions from the obvious equalities $Q_{yy}^{\mathrm{ext}}=\alpha G_1(i_n-i_k^{1})$, $G_1(i_1-i_{fw})=\eta_{ut}Q_{yy}$, where $\eta_{ut}$ is the efficiency of the utilization boiler with respect to the secondary energy resources used in the boiler, and expressing the heat content of the feedwater through $i_k$ and $i_k^{1}$, after elementary algebraic transformations we obtain:

\[ Q_{yy}^{\mathrm{ext}}= \frac{\alpha(i_n-i_k^{1})}{i_1+i_k-\alpha(i_k^{1}-i_k)} \,\eta_{ut} Q_{yy}. \tag{a} \]

Denoting the fraction entering equation (a) by $\xi$, we shall have the following expression:

\[ Q_{yy}^{\mathrm{ext}}=\xi \eta_{ut} Q_{yy}\ \mathrm{kcal/year}. \tag{2} \]

Since the demand for heat during the year may vary sharply, becoming in certain periods lower than can be obtained from the extractions of the utilization installation, the latter is forced during these periods to operate with increased generation of electric power on condensing

mode. If we denote by \(T\) the number of hours of utilization of the possible maximum extractions during the year, then the extraction utilization coefficient can be represented as:

\[ \eta_u=\frac{T}{8760}. \]

The energy output obtained from the waste-heat recovery installation during the year can be determined from an energy balance of the following form:

\[ Q_{uy}=\frac{860\,Э^k_{uy}}{\eta^k_{uy}}+\frac{860\,\eta_u Q^{otb}_{uy}}{\eta^t_{uy} q_{uy}}+\frac{\eta_u Q^{otb}_{uy}}{\eta^k_{uy}}\quad \text{kcal/year}, \tag{в} \]

All coefficients entering equation (в) have, for the waste-heat recovery installation, meanings analogous to those of the corresponding coefficients for the CHP plant in the expression for its energy balance given earlier.

From expression (в) it is easy to obtain equations for determining the amount of electric power generated in condensing mode \((Э^k_{uy})\),

\[ Э^k_{uy}=\frac{\eta^k_{uy}}{860}\,Q_{uy} -\left(\frac{1}{q_{uy}}+\frac{1}{860}\right) \frac{\eta^k_{uy}\eta_u}{\eta^t_{uy}}\,Q^{otb}_{uy} \quad \text{kWh/year} \tag{3} \]

and the electric power for heat consumption:

\[ Э^t_{uy}=\frac{\eta_u Q^{otb}_{uy}}{q_{uy}} =\frac{\xi \eta_u \eta_{ym}}{q_{uy}}\,Q_{uy}\quad \text{kWh/year}. \]

To determine \(Q^{uy}_{tez}\), let us compile the energy balance for the system with the waste-heat recovery installation, reduced to heat in primary energy resources. According to the adopted method, this balance is written by the following expression:

\[ Q^{uy}_{tez}= \frac{ 860\left[ Э-Э^k_{uy}-Э^t_{uy} -\frac{Q_{otb}-\eta_u Q^{otb}_{uy}}{q} \right] }{\eta_k} + \]

\[ +\frac{ 860\,\frac{Q_{otb}-\eta_u Q^{otb}_{uy}}{q} +Q_{otb}-\eta_u Q^{otb}_{uy} }{\eta_t} + \]

\[ +\frac{Q_{roy}}{\eta_{ky}\eta_{nom}} +\frac{Q_{uy}}{\eta^n_{tez}} \quad \text{kcal/year}. \tag{Б} \]

Substituting into expression (1) the values \(Q_{tez}\) and \(Q^{uy}_{tez}\) from expressions (A) and (Б), and making the corresponding substitutions on the basis of relationships (2) and (3), we obtain the following equation expressing the dependence of \(\Delta Q^{uy}\) on the value \(Q_{uy}\), for the case of operation of the waste-heat recovery installation on turbogenerators with steam extractions:

\[ \Delta Q^{uy}= \frac{\eta^k_{uy} Q_{uy}}{\eta_k} + \left[ \frac{860}{q}\left(\frac{1}{\eta_t}-\frac{1}{\eta_k}\right) +\frac{1}{\eta_t} \right. \]

\[ \left. +\frac{860}{\eta_k q_{uy}} -\frac{\eta^k_{uy}}{\eta_k \eta^t_{uy}} \left(\frac{860}{q_{uy}}+1\right) \right]\xi \eta_u \eta_{ym} Q_{uy} \quad \text{kcal/year}. \tag{4} \]

If the utilization installation generates electric power in a purely condensing mode, then the amount of generated electric power is determined from the expression:

\[ \mathcal{E}^{k}_{uy}=\frac{\eta^{k}_{uy}}{860} Q_{uy}\ \text{kWh/year}. \]

In this case the magnitude of extractions \(Q^{\text{otb}}_{uy}=\xi \eta_{ut} Q_{uy}\) is equal to zero. The general equation (4) for the particular case will take the form:

\[ \Delta Q^{uy}=\frac{\eta^{k}_{uy}}{\eta_k} Q_{uy}\ \text{kcal/year}. \tag{5} \]

When the utilization installation generates only thermal energy, its annual output will be determined from the expression: \(\eta_u \eta_{ut} Q_{uy}\). It should be borne in mind that the heat generated at the utilization installation may replace either the heat of live steam (RHP), or the heat of extractions, or both at once.

In the general case, all heat generation may be represented as consisting of two parts:

\[ \eta_u \eta_{ut} Q_{uy}=\eta_u \eta_{ut} Q'_{uy}+\eta_u \eta_{ut} Q''_{uy}. \]

Here, on the right-hand side of the equality, the first term determines the reduction in heat supply through the RHP of the CHP plant in connection with its replacement by the heat of the utilization installation. The second term, \(\eta_u \eta_{ut} Q''_{uy}\), determines the analogous reduction in heat supply through turbine extractions.

When only heat is generated at the utilization installation, \(\mathcal{E}^{k}_{uy}=0\), \(\mathcal{E}^{t}_{uy}=0\), \(G^{\text{otb}}=G_1\), \(i_n=i_1\), \(i_{nv}=i_k\), consequently \(q=\infty\), \(\eta^{k}_{uy}=0\), \(\eta^{t}_{uy}=0\), \(a=1\). Taking this into account, by means of the energy balance of the combined system (CHP plant—utilization installation), by a method analogous to the preceding one, one can obtain the following expression for determining the absolute saving of heat in fuel for the general case under consideration:

\[ \Delta Q^{uy}= \left[ \frac{860\,\eta_u \eta_{ut}}{q} \left( \frac{1}{\eta_{im}}-\frac{1}{\eta_k} \right) + \frac{\eta_u \eta_{ut}}{\eta_m} \right] Q''_{uy} + \frac{\eta_u \eta_{ut}}{\eta_{ky}\eta_{pot}} Q'_{uy} \ \text{kcal/year}. \tag{6} \]

The equation for cases in which the heat of the utilization installation displaces either the heat of extractions or the heat of the RHP is readily obtained if, in equation (6), the values \(Q''_{uy}\) and \(Q'_{uy}\) are successively taken equal to zero.

The third particular case will be when the utilization installation operates using the heat of back-pressure turbo-units.

Reasoning analogously to the case of operation of a turbine with steam extractions and applying the same notation, the dependence \(Q^{\text{otb}}_{uy}=f(Q_{uy})\) can be expressed by the following equation:

\[ Q^{\text{otb}}_{uy}= \frac{i_n-i_k}{i_1-i_k}\eta_{ut}Q_{uy}. \tag{7} \]

The amount of heat used during the year from back-pressure steam is determined analogously to the preceding case with the aid of the heat-utilization coefficient \(\eta_u\). In those periods when the back-pressure heat cannot

be used completely, the installation will operate “to exhaust” and generate electric power \(\mathcal{E}^{e}_{yy}\) with a very low efficiency, which we shall denote by \(\gamma^{e}_{yy}\). Taking the above into account, the energy balance of the back-pressure utilization installation, reduced to the heat of the secondary energy resources, will be written as follows:

\[ Q_{yy}= \frac{ 860\,\dfrac{\eta_u Q^{otb}_{yy}}{q_{yy}}+\eta_u Q^{otb}_{yy} }{ \eta^{m}_{yy} } + \frac{860\,\mathcal{E}^{e}_{yy}}{\gamma^{e}_{yy}} \quad \text{kcal/year}. \]

From this equation one can obtain the values of \(\mathcal{E}^{m}_{yy}\) and \(\mathcal{E}^{e}_{yy}\) in explicit form:

\[ \mathcal{E}^{e}_{yy} = \frac{\gamma^{e}_{yy} Q_{yy}}{860} - \frac{\gamma^{e}_{yy}}{\eta^{m}_{yy}}\,\eta_u \left(\frac{1}{q_{yy}}+\frac{1}{860}\right) Q^{otb}_{yy} \quad \text{kWh/year}, \tag{8} \]

\[ \mathcal{E}^{m}_{yy} = \frac{\eta_u Q^{otb}_{yy}}{q_{yy}} \quad \text{kWh/year}. \tag{9} \]

The operation of a back-pressure turbine “to exhaust” may be regarded as the operation of a condensing turbine unit at \(\gamma^{k}_{yy}=\gamma^{e}_{yy}\). When using the heat of the back-pressure steam, the economic effect of the back-pressure turbine as a converter unit will be the same as that of the district-heating part of a turbine unit with steam extractions, if their economic efficiencies \(\eta^{m}_{yy}\) are equal. This circumstance allows us to use formula (4), from which, at \(\gamma^{k}_{yy}=\gamma^{e}_{yy}\), we obtain the equation for determining the absolute annual saving of heat in fuel for the case under consideration. The same equation can be arrived at by using the previously considered method of derivation by means of the energy balance of the combined energy system. In final form the required relationship is expressed by the following equation:

\[ \Delta Q^{yy} = \left\{ \frac{\eta^{e}_{yy}}{\eta_k} + \left[ \frac{860}{q} \left( \frac{1}{\eta_m} - \frac{1}{\eta_k} \right) + \frac{1}{\eta_m} + \frac{860}{\eta_k q_{yy}} - \frac{\eta^{e}_{yy}}{\eta_k \eta^{m}_{yy}} \left( \frac{860}{q_{yy}}+1 \right) \right] \xi' \eta_u \eta_{ym} \right\} Q_{yy} \quad \text{kcal/year}. \tag{10} \]

The coefficient entering into the equation is

\[ \xi'=\frac{i_n-i_k}{i_1-i_k}, \]

and the values of all the other coefficients were given in the preceding exposition.

If the utilization installation and the thermal power plant have identical average annual economic indicators \((\eta_k=\eta^{k}_{yy},\ q=q_{yy},\ \eta_m=\eta^{m}_{yy})\), then relationships (4), (5), and (10) are considerably simplified. Thus, equations (4) and (5) prove to be identical and will be equal to:

\[ \Delta Q^{yy}=Q_{yy} \quad \text{kcal/year}. \tag{4a} \]

Equation (10) will take the form:

\[ \Delta Q^{uy}=\frac{\eta_{uy}^{B} Q_{uy}}{\eta_k}+ \]

\[ +\left[\left(\frac{860}{q}+1\right)\left(\frac{1}{\eta_m}-\frac{\eta_{uy}^{B}}{\eta_k \eta_m}\right)\right]\xi' \eta_u \eta_{ym} Q_{uy}\ \text{kcal/year}. \tag{10a} \]

Under practical conditions, the equalities \(\eta_{uy}^{k}=\eta_k\) and \(q=q_{uy}\) may occur very often. However, the efficiency \(\eta_{uy}^{m}\), as a rule, will always be higher than the efficiency \(\eta_m\). This is explained by the fact that, in calculating \(\eta_{uy}^{m}\), the higher efficiency \(\eta_{ym}\) is used instead of \(\eta_{ky}\), which enters as a multiplier in the value of the efficiency \(\eta_m\).

In the latter case, formulas (4), (5), (10) will take the form: formula (4),

\[ \Delta Q_{uy}=Q_{uy}+\left[\left(\frac{1}{\eta_m}-\frac{1}{\eta_{uy}^{m}}\right)\left(\frac{860}{q}+1\right)\right]\xi\,\eta_u \eta_{ym} Q_{uy}\ \text{kcal/year}, \tag{4b} \]

equation (5) will remain in the form: \(\Delta Q^{uy}=Q_{uy}\ \text{kcal/year}\),

equation (10) will take the form:

\[ \Delta Q^{uy}=\frac{\eta_{uy}^{B} Q_{uy}}{\eta_k}+ \]

\[ +\left[\left(\frac{1}{\eta_m}-\frac{\eta_{uy}^{B}}{\eta_k \eta_{uy}^{m}}\right)\left(\frac{860}{q}+1\right)\right]\xi'\eta_u \eta_{ym} Q_{uy}\ \text{kcal/year}. \tag{10b} \]

An analysis of the resulting relationships (4), (5), (6), (10) and their simplified variants makes it possible to clearly reveal the great advantages of organizing combined production of electricity and heat at a utilization installation as compared with separate production. Thus, for example, equation (4b) immediately shows that, in the case of using extraction turbines at a utilization installation, the saving of heat in primary energy resources at a CHP plant is always greater than the utilization installation uses from secondary energy resources. This is clear if one takes into account that this equation is drawn up for the case when \(\eta_{uy}^{m}>\eta_m\). The reverse case, when \(\eta_{uy}^{m}<\eta_m\), is practically difficult to imagine. Solving equation (10b) with specific values of the coefficients entering into it, it is easy to find that, also in the case of using back-pressure turbines, the saving of primary energy resources will be greater than the amount of heat taken by the utilization installation from secondary energy resources \((Q_{uy})\), down to quite a small value of \(\eta_u=0.35-0.4\). The value \(\eta_u=0.35-0.4\) corresponds, as is known, to a coefficient of the number of hours of use of the heat maximum \((T)\) of only 3000–3500 hours/year. Under the same conditions, in purely electric-power or heat-power variants of utilization installations, as shown by analysis of formulas (5) and (6), such saving of primary energy resources cannot be achieved.

In the most effective case for the heat-power variant, when the heat produced at the utilization installation replaces the heat of live steam delivered through a pressure-reducing and desuperheating unit, or obtained from independent boiler houses \((Q_{yy}=Q_{uy})\), at \(\eta_u=0.35-0.4\), the saving of heat in primary energy resources will amount to only 40–50% of the heat of the secondary energy resources used by the utilization installation \((Q_{uy})\).

In the same case, when the heat from the utilization unit replaces the heat from extractions of the turbines of the thermal power plant, the effect is reduced still further. Thus, for example, in the case when the heat from the utilization unit replaces extraction steam at a pressure of 3 ata with \(\eta_u = 0.4\), the saving in primary energy resources at the thermal power plant will amount to only 34% of \(Q_{uy}\). When replacing extraction at a pressure of 1.2 ata, the saving in primary energy resources will be still smaller and will amount to only 27% of \(Q_{uy}\).

In the case of the electric-power variant of the utilization unit, when \(\eta_k = \eta_{uy}^k\), as formula (5) shows, the saving of heat from primary energy resources will be equal to \(Q_{uy}\), that is, again less than for the variant using turbines with steam extractions under the same conditions.

It is quite obvious that all efficiencies entering equations (4), (5), (6), and (10), etc., must be taken as net efficiencies, i.e., with allowance for the consumption for the auxiliary needs of the power units. Otherwise we shall obtain neither a correct conclusion about the absolute fuel saving nor a correct basis for comparison of variants, since the expenditures for auxiliary needs differ for different variants of utilization units.