A New Method for Determining Losses in Testing Boiler Units

V. N. Smirenskii

Carrying out balance tests of boiler units is associated with well-known difficulties. Difficulties arise in the process of observations and measurements conducted during the test itself and, as a consequence, in processing the test materials—determining the individual losses and compiling the heat balance. Therefore, the reliability of the results obtained from a test often gives rise to doubts.

There are several methods for compiling heat balances, but all of them, to one degree or another, have various shortcomings. At the same time it is known that the compilation of a heat balance would be considerably simplified if it were possible to determine the volume of gases. Direct measurement of the quantity of gases as applied to tests of boiler units cannot be carried out, but the volume of gases can be found indirectly. This can be done in all cases when, during the test, it is possible to organize measurements that make it possible to determine with sufficient reliability the heat used by some heating surface (an economizer or part of it, a superheater, an air heater, a low-pressure economizer). This heating surface must be located in the gas duct where the combustion process has already ended. The most convenient case will obviously be an installation with a non-boiling economizer; moreover, no special measurements or observations during the test will be required. As for the analysis of gases for \(RO_2\) and \(O_2\), it must be carried out with sufficient care. The total loss from mechanical incompleteness of combustion in this method is determined without measuring the amount of slag, siftings, and carryover, and without analyzing them, when directly compiling the heat balance.

To find the volume of dry gases, the balance equation of the heat-utilizing heating surface may be used, written in the following form:

\[ (cVt)'_{g2} + (cVt)'_{vp} + Q_{pr} - (cVt)''_{g2} - (cVt)''_{vp} - Q_{5} = Q_{i}\ \text{kcal/kg}. \tag{1} \]

All the designations in this equation are clear.

If this equation applies, for example, to a non-boiling economizer, then

\[ Q_{i} = \frac{D_{ek}}{B}(i_{2} - i_{1})\ \text{kcal/kg}. \]

Bearing in mind that the volume of dry gases beyond the heating surface is \(a\) times greater than the volume before it, one can obtain from equation (1):

\[ V'_{g2} = \frac{ Q_{i} - (cVt)'_{vp} + (cVt)''_{vp} - Q_{pr} + Q_{5} }{ (ct)'_{g2} - a(ct)''_{g2} } \ \text{nm}^{3}/\text{kg}. \tag{2} \]

In these expressions \(D_{\mathrm{eq}}, B, i_2, i_1, t', t'', c'_{\mathrm{vp}}\) and \(c''_{\mathrm{vp}}\) are known from the test or are taken from reference data. The heat capacities of the dry gases are determined on the basis of gas analysis for \(RO_2\) before the heating surface and after it. If the composition of the dry gases before the surface is \(RO'_2 + R'_2 = 100\%\), and after the heating surface is \(RO''_2 + R''_2 = 100\%\), then

\[ c'_{c2}=\frac{c'_3 RO'_2 + c'_2 R'_2}{100}\ \text{kcal}/\text{nm}^3\text{ deg}, \tag{3} \]

where \(c'_3\) and \(c'_2\) are the heat capacities of triatomic and diatomic gases at temperature \(t'\). Similarly, \(c''_{c2}\) is determined.

The quantity

\[ a=\frac{RO'_2}{RO''_2}. \]

The quantities \(V'_{\mathrm{vp}}\) and \(V''_{\mathrm{vp}}\) are calculated by the known formula:

\[ V_{\mathrm{vp}}=\frac{8.94H^p+W^p+0.13\,a\,V_0^d+100W_{\phi}}{80.5}\ \text{nm}^3/\text{kg}. \tag{4} \]

In the present case it may be assumed that

\[ \alpha'=\frac{RO_{2\max}}{RO'_2} \quad \text{and} \quad \alpha''=\frac{RO_{2\max}}{RO''_2}, \]

or, better, \(\alpha\) may be determined from the known expression (10), but without taking \(CO\) into account.

The value \(V_0\) should be determined from the composition of the working fuel, and the heat of the air drawn into the gas duct from the expression:

\[ Q_{\mathrm{pr}}=(\alpha''-\alpha')V_0 c_v t_v\ \text{kcal}/\text{kg}. \tag{5} \]

The assumptions adopted above with regard to \(\alpha\) and \(V_0\) will have practically no effect on the desired value of the gas volume. The heat loss to the surroundings, \(Q_5\), may be estimated in accordance with the specific conditions.

Note 1. In expression (2), the quantities \(Q_{\mathrm{pr}}\) and \(Q_5\) are small and have opposite signs. Moreover, since \(Q_5\) is usually somewhat greater than \(Q_{\mathrm{pr}}\), the expression for \(V'_{c2}\) may be written in simplified form as:

\[ V'_{c2}= \frac{Q_u - V_{\mathrm{vp}}\left(c'_{\mathrm{vp}}t' - c''_{\mathrm{vp}}t''\right)} {(ct)'_{c2}-a(ct)''_{c2}} \ \text{nm}^3/\text{kg}, \]

where \(V_{\mathrm{vp}}\) is to be taken at \(a=1\). When the gas volume is found from this expression, the discrepancies in the calculation results, as a rule, do not exceed hundredths of a cubic meter for large boiler units.

The volume of dry gases found in this way considerably simplifies the further determination of the individual terms of the heat balance.

To determine all the principal losses of a boiler unit, it is necessary to know the conditional amount of burned carbon \(K^p_1\) and the \(CO\) content in the gases. It is known that

\[ K^p_1=0.539\,V_{c2}(RO_2+CO)\%. \tag{6} \]

If in this expression we substitute the value for \(CO\) [1]:

\[ CO=34.71-1.66\,RO_2-1.65\,O_2- \frac{7.25H^p-0.91O^p+0.28N^p+0.015S^p_l}{V_{c2}}\%, \tag{7} \]

then we obtain:

\[ K^p_1=(18.71-0.356\,RO_2-0.89\,O_2)V_{c2}-3.91H^p+0.49O^p- \]

\[ -0.15N^p - 0.008S_{\ell}^{p}\ \%. \tag{8} \]

After this, the quantity of unburned carbon is determined as \(C_{\text{mn}} = K^{p} - K_1^{p}\ \%\).

Since direct gas analysis for \(CO\) is not very reliable, for determining carbon monoxide one may use the analytical expressions (7), or the simpler one

\[ CO = \frac{K_1^{p}}{0.539\,V_{c2}'} - RO_2\ \%. \]

After substituting into this expression the corresponding values of \(V_{c2}'\) and \(RO_2'\), the percentage content \(CO'\) before the heating surface is determined. The content of carbon monoxide in the exit gases will be:

\[ CO^{yx} = CO'\frac{RO_2^{yx}}{RO_2'}\ \%. \tag{9} \]

Next, for the exit gases the following quantities are calculated:

the excess-air coefficient

\[ \alpha_{yx} = \frac{1}{ 1 - \dfrac{79}{21}\,\dfrac{O_2^{yx} - 0.5\,CO^{yx}}{N_2^{yx}} }; \tag{10} \]

the volume of water vapor according to expression (4), and the volume of dry gases

\[ V_{c2}^{yx} = V_{c2}'\frac{RO_2'}{RO_2^{yx}}\ \text{nm}^3/\text{kg}. \]

After this, in the usual way, the individual terms of the heat balance are found successively: \(Q_1, Q_2, Q_3, Q_4, Q_{\phi}\). \(Q_5\) is determined as the residual term of the balance.

Let us now consider the case when, in addition to \(CO\), the products of combustion contain \(H_2\) and \(CH_4\), and the gas analysis during the test is carried out with afterburning. In this case, corresponding additions must be made to some of the formulas given. In the presence of methane, formula (3) for heat capacity and formula (10) for the excess-air coefficient must be supplemented.

When calculating the volume of water vapor by formula (4), instead of \(H^p\) one should substitute the value \(H^p - H_{\text{gas}}^p\), where the amount of hydrogen in \(H_2\) and \(CH_4\) is

\[ H_{\text{gas}}^p = 0.09\,(H_2 + 2CH_4)\,V_{c2}\ \%. \]

Taking further into account that

\[ (H_2 + CH_4)^y = \frac{(H_2 + CH_4)'}{a}, \]

we obtain the following expression for the volume of dry gases before the surface:

\[ V_{c2}' = \frac{ Q_a - (cVt)_{vn}' + (cVt)_{vn}'' - Q_{pr} + Q_5 }{ (ct)_{c2}' - a(ct)_{c2}'' - 0.01(H_2 + CH_4)'\left[(ct)_{vn} - (ct)_{vn}''\right] } \ \text{nm}^3/\text{kg}. \tag{11} \]

In this expression, \(V_{vn}'\) and \(V_{vn}''\) are determined, as in the first case, from expression (4) without introducing any corrections, that is, with substitution only of the hydrogen of the working fuel \(H^p\).

The conditional quantity of burned carbon may be determined from the expression:

\[ K_1^{p} = 0.539\,V_{c2}\,(RO_2 + CO + CH_4)\ \%. \]

Remark 2. To check the percentage content of \(CO\) in the gases, expression (7) may be used, supplemented on the right-hand side, on the basis of [1], by the term \(+(0.306H_2 + 0.96CH_4)\). Accordingly, expression (8) for checking \(Kp\) is supplemented by the term \(+(0.165H_2 + 1.06CH_4)V_{c2}\).

When compiling the heat balance by this method, the results obtained will be the more accurate, the larger the heat-utilizing surface selected and the smaller the value of the heat loss to the external environment. Usually this corresponds to large boiler units.

The table below gives the results of calculations from a test of a Shukhov–Berlin A-7 boiler. In one case (\(A\)) the heat-utilizing surface was a water economizer; in the other (\(B\))—an air heater. The heat loss to the external environment was taken as \(0.6\%\) for case (\(A\)) and \(0.35\%\) for case (\(B\)). For comparison, the figures (\(V\)) obtained as a result of processing the test materials of the same boiler by the ash-balance method [2] are also given there.

REFERENCES

1. Smirenskii V. N.—On a new methodology for investigating the operation of boiler installations, “Izvestiya TPI,” vol. 63, 1944.

2. Gateev S. B.—Thermal-engineering tests of boiler installations, Gosenergoizdat, 1954.