New Methods for Drawing Up Direct Heat Balances in Testing Boiler Units

V. N. Smirensky

For balance tests of boiler units operating on solid fuel, the most difficult and least reliable operations are the selection of average samples of furnace residues and the determination of their quantity. Slag is often very heterogeneous, and with ash-bearing fuel a large amount of it accumulates during a test. Therefore, correct selection of an average slag sample is very difficult.

As for selecting an average sample of entrainment, it does not appear possible to traverse the gas duct at the sampling point either by fractional composition or by the process of its combustion, especially if one takes into account changes in the furnace operating conditions during the test. The qualitative state of the entrainment may differ greatly over the cross section of the gas duct. This will lead to the selected sample not representing the average entrainment sample. As a result, the loss due to mechanical unburned fuel, calculated from the test data, may differ greatly from the true value. At the same time, incorrect values will be obtained for the volume of dry gases, determined through this loss, as well as for the losses due to chemical incompleteness of combustion and with the outgoing gases. Ultimately, the heat balance will not close.

Incorrect values of individual losses are most clearly revealed when processing the materials of series of tests carried out to establish any regularities in the operating regime of the furnace and the boiler unit.

With regard to losses due to mechanical unburned fuel, one more remark should be made. Of the two methods for attributing this loss—either to unburned carbon or to proportional underburning of all combustible elements of the fuel—the first is the more correct. The process of formation of unburned combustibles in furnace residues, occurring under conditions of severely impeded access of air oxygen to the core of a burning particle, is similar to the coking process. A comparison of the composition of coke with the composition of the original fuel indicates that almost all the carbon of the fuel remains in the coke. Only 4–5% of it passes into the coke gas. As for hydrogen and oxygen, the greater part of them, up to 70% and more, passes into the gaseous state. Thus, in principle, it will be more correct to consider that the combustible matter of furnace residues consists mainly of carbon.

Below, two possible cases of operation of the furnace devices of the boiler units under test are considered: for the most general case

for chemical incomplete combustion and for the case when chemical incomplete combustion occurs mainly due to CO. For the first case an expression is given that makes it possible to determine at once the volume of dry gases, and for the second, the burned carbon. In both cases the determination of these quantities at once solves the problem of drawing up the entire heat balance.

Tests with direct compilation of the heat balance are carried out on all low-capacity boiler units and on many medium-capacity boiler units.

I. General case of chemical incomplete combustion

Let us consider the most general case of chemical incomplete combustion. In such cases, naturally, a complete gas analysis is required. Tests of this kind may be carried out when studying the operation of new designs of boiler units or furnaces, when changing over to new fuels differing in their properties, and in other cases when chemical incomplete combustion may be significant and may consist of different elements.

In tests of boiler units with direct compilation of the heat balance, the useful heat is determined quite reliably by direct measurements. The heat loss to the surroundings is always small and is usually of no interest, because it does not appear possible to influence the magnitude of this loss substantially. For the boiler unit being tested, the value of this loss may be taken with sufficient accuracy from reference data. Thus, three main losses may be of interest: with the flue gases, from chemical incomplete combustion, and from mechanical incomplete combustion. All these losses can be expressed through the volume of dry gases.

1) Heat loss with the flue gases

\[ Q_2 = (c_{\mathrm{g}} V_{\mathrm{g}} + c_{\mathrm{vp}} V_{\mathrm{vp}})\vartheta_{\mathrm{ukh}} - \]

\[ -\left[ V_{\mathrm{g}} + \frac{\mathrm{H}^{\mathrm{p}} - 0.126\mathrm{O}^{\mathrm{p}}}{100} - \mathrm{H}^{\mathrm{p}}_{\mathrm{gaz}} \frac{7.94}{1.429} - \frac{0.8\mathrm{N}^{\mathrm{p}}}{100} -\right. \]

\[ \left. - \frac{\mathrm{H}_2 + \mathrm{CH}_4 + \mathrm{C}_m\mathrm{H}_n}{100} V_{\mathrm{g}} \right](ct)_{\mathrm{kh}} \ \frac{\mathrm{kcal}}{\mathrm{kg}} . \tag{1} \]

The expression in square brackets represents the actual quantity of air, per kilogram of burned fuel, for the last gas duct downstream of the installation, \(\alpha_{\mathrm{ukh}} V_1^0\); the second term in the square brackets represents the oxygen of the air spent on oxidizing the completely burned hydrogen; the third term is the nitrogen of the fuel, conventionally taken to have passed into the gaseous state; the fourth is the increase in the volume of dry gases relative to the volume of air due to the chemical underburning of \(\mathrm{H}_2\), \(\mathrm{CH}_4\), and \(\mathrm{C}_m\mathrm{H}_n\).

The amount of hydrogen that has not burned to \(\mathrm{H}_2\mathrm{O}\) and has passed into the dry gases is

\[ \mathrm{H}^{\mathrm{p}}_{\mathrm{gaz}} = 0.09 \left( \mathrm{H}_2 + 2\mathrm{CH}_4 + \frac{n}{2}\mathrm{C}_m\mathrm{H}_n \right) V_{\mathrm{g}}^{0}. \tag{2} \]

The volume of water vapor is

\[ V_{\mathrm{vl}}^{p}=0.111(\mathrm{H}^{p}-\mathrm{H}_{\mathrm{gaz}}^{p})+0.0124\,W^{p}+0.0161\alpha_{\mathrm{ukh}}V^{0}\ \frac{\mathrm{n\,m}^{3}}{\mathrm{kg}} . \tag{3} \]

In this expression the theoretical quantity of air for the burned fuel, \(V_{1}^{0}\), has been replaced by the theoretical quantity of air for the working fuel, \(V^{0}\). This is entirely permissible in view of the negligible influence of this substitution on the result.

After substituting the corresponding values from (2) and (3) into expression (1), and after some transformations, we obtain

\[ Q_{2}= \left[ c_{\mathrm{sg}}t_{\mathrm{ukh}} - A\left(c_{\mathrm{vl}}t_{\mathrm{ukh}}-0.5c_{\mathrm{hv}}t_{\mathrm{hv}}\right) - P(ct)_{\mathrm{hv}} \right]V_{\mathrm{sg}} + \]

\[ {}-c_{\mathrm{vl}}V_{\mathrm{vl}}t_{\mathrm{ukh}} - f(ct)_{\mathrm{hv}}\ \frac{\mathrm{kcal}}{\mathrm{kg}}, \tag{4} \]

where

\[ A=\frac{ \mathrm{H}_{2}-2\mathrm{CH}_{4}+\dfrac{n}{2}C_{m}H_{n} }{100}, \]

\[ P=1-\frac{ \mathrm{H}_{2}+\mathrm{CH}_{4}+C_{m}H_{n} }{100}, \]

\[ V_{\mathrm{vl}}=0.111\mathrm{H}^{p}+0.0124W^{p}+0.0161\alpha_{\mathrm{ukh}}V^{0} \quad \text{and} \]

\[ f=\frac{ 5.55\mathrm{H}^{p}-0.7\mathrm{O}^{p}-0.8\mathrm{N}^{p} }{100}. \]

2) Loss due to chemical incomplete combustion

\[ Q_{3}= \left( 30.2\mathrm{CO}+25.8\mathrm{H}_{2}+85.5\mathrm{CH}_{4} + C_{m}H_{n}\frac{Q_{C_{m}H_{n}}}{100} \right) V_{\mathrm{sg}}\ \frac{\mathrm{kcal}}{\mathrm{kg}} . \tag{5} \]

3) Loss due to mechanical unburned fuel

\[ Q_{4}=81\left(K_{1}^{p}-K_{1}^{f}\right)\frac{\mathrm{kcal}}{\mathrm{kg}} . \]

where \(K_{1}^{f}\) and \(K_{1}^{p}\) are the conventional quantities of carbon in the working fuel and actually burned fuel, %.

Bearing in mind that

\[ V_{\mathrm{sg}}= \frac{1.86K_{1}^{f}} {\left(\mathrm{RO}_{2}+\mathrm{CO}+\mathrm{CH}_{4}+mC_{m}H_{n}\right)} \ \frac{\mathrm{n\,m}^{3}}{\mathrm{kg}}, \]

whence

\[ K_{1}^{f}=0.536\left(\mathrm{RO}_{2}+\mathrm{CO}+\mathrm{CH}_{4}+mC_{m}H_{n}\right)V_{\mathrm{sg}},\%, \tag{6} \]

we obtain

\[ Q_{4}=81K_{1}^{p} - 43.5\left(\mathrm{RO}_{2}+\mathrm{CO}+\mathrm{CH}_{4}+mC_{m}H_{n}\right)V_{\mathrm{sg}} \frac{\mathrm{kcal}}{\mathrm{kg}} . \tag{7} \]

If the volume of dry gases needed for compiling the heat balance cannot be determined by direct measurements during the test, it can be found indirectly.

Since

\[ Q_2 - Q_3 + Q_4 = Q_{n}^{p}\left(1-\frac{q_1+q_5}{100}\right), \tag{8} \]

then, substituting here the values of the losses from (4), (5), and (7), determining from the resulting equality the volume of dry gases and making certain possible simplifications, we finally obtain

\[ V_{\mathrm{sg}}= \frac{ 81K^{p}-Q_{n}^{p}\left(1-\frac{q_1+q_5}{100}\right) }{ 43.5RO_2-c_{\mathrm{sg}}^{\,n}\vartheta_{\mathrm{uh}} +P(ct)_{\mathrm{hv}}\cdot 13.3CO-25.8H_2-42CH_4 } \]

\[ \frac{ +c_{\mathrm{vp}}V_{\mathrm{vp}}^{\,n}\vartheta_{\mathrm{uh}} }{ -\left(\frac{Q_{\mathrm{sm}}H_n}{100}-43.5m\right)C_mH_n } \quad \frac{\mathrm{nm}^3}{\mathrm{kg}} . \tag{9} \]

The simplifications adopted in this expression are as follows: in the numerator the term \(f(ct)_{\mathrm{hv}}\) is omitted, and in the denominator \(+A(c_{\mathrm{vp}}^{\,n}\vartheta_{\mathrm{uh}}-0.5c_{\mathrm{hv}}t_{\mathrm{hv}})\), since this cannot have any effect on the final result.

If chemical incomplete combustion occurs only at the expense of CO, then

\[ V_{\mathrm{sg}}= \frac{ 81K^{p}-Q_{n}^{p}\left(1-\frac{q_1+q_5}{100}\right)+c_{\mathrm{vp}}V_{\mathrm{vp}}^{\,n}\vartheta_{\mathrm{uh}} }{ 43.5RO_2-c_{\mathrm{sg}}^{\,n}\vartheta_{\mathrm{uh}}+(ct)_{\mathrm{hv}}\cdot 13.3CO } \quad \frac{\mathrm{nm}^3}{\mathrm{kg}} . \tag{10} \]

As is evident from (9) and (10), the volume of dry gases is determined through large quantities. This can only have a positive influence on the accuracy of the quantity sought.

In these expressions the composition of the gases, the volumes, the heat capacities, and the gas temperature refer to the exit gases.

The sampling of gases for analysis and the measurement of temperature are most reliably carried out downstream of the induced-draft fan, if the latter is located close to the boiler unit. If the induced-draft fan is located so far away that the gases may cool considerably—not as a result of air in-leakage, but as a result of heat transfer—then the measurement of the temperature of the exit gases and the taking of samples for their analysis should be organized closer to the boiler unit, selecting for this purpose such measurement points where sufficiently good mixing of the gases can be counted on. The latter must also be borne in mind in the case of testing an installation with natural draft.

With a considerable loss of heat with the physical heat of slag—for example, with liquid slag removal or with a high ash content of the fuel and layer combustion—this loss can be taken into account in expressions (9) and (10). For this purpose the second term of the numerator should be written as

\[ -Q_{n}^{p}\left(1-\frac{q_1+q_5+q_6}{100}\right). \]

After the volume of dry gases has been determined, the further calculations for compiling the heat balance present no difficulties. The loss \(Q_2\) is calculated by the usual formula or by one of the modified formulas (1), (4). When calculating \(Q_2\) by the generalized formula

is first preliminarily determined, \(K_1^p\) (6), and from the known formulas \(V_1^0\) and \(\alpha_{\mathrm{ukh}}\). The losses \(Q_3\) and \(Q_4\) are found from formulas (5) and (7). This completes the compilation of the heat balance.

The method presented makes it possible simply, quickly, and with sufficient accuracy to compile the complete heat balance of a boiler unit for the most general case of chemical incomplete combustion. The accuracy of the balance quantities found is, naturally, determined by the accuracy of the observations and measurements carried out during the test. The total loss due to mechanical incomplete combustion can be determined without measuring the quantities of slag, siftings, and carryover, without taking average samples, and without analyzing their quality. In many cases this can greatly facilitate the work of the observers during the test. If it is necessary to determine individual components of the loss due to mechanical incomplete combustion, measurements should be organized for some of them, the most reliable and convenient ones. A component of mechanical incomplete combustion that is difficult to determine, for example the loss with carryover, can be determined by difference.

II. Chemical incomplete combustion occurs mainly at the expense of CO.

This case is encountered very often in operating boiler units. Therefore, in routine operational tests there is no need to complicate the work of observers and laboratory assistants with cumbersome gas analysis. Moreover, it is desirable to have a method that, with maximum simplification of the work during the test itself, makes it possible to reduce the complete heat balance sufficiently simply and correctly.

In this case it is more convenient to use the expression for the burned carbon; knowing this quantity, it is very easy to determine the volume of dry gases, and then all the principal losses. The quantities \(Q_1\) and \(Q_5\) are still regarded as known.

The expression for the conditional quantity of burned carbon \(K_1^p\) can be found without data on the quantity and quality of the furnace residues.

Bearing in mind that in the present case chemical incomplete combustion occurs at the expense of CO, let us write the expressions for the principal losses analogously to how this was done in case I.

\[ \begin{aligned} 1.\quad Q_2={}&(c_{\mathrm{sg}}V_{\mathrm{sg}}-c_{\mathrm{vp}}V_{\mathrm{vp}})\,\vartheta_{\mathrm{ukh}} +\left[ V_{\mathrm{sg}}\cdot \frac{\mathrm{H}^p}{100} -\frac{0.126\,\mathrm{O}^p\,7.94}{1.429} -\frac{0.8\,\mathrm{N}^p}{100} \right](ct)_{\mathrm{khv}} \\ &-\left[c_{\mathrm{sg}}\vartheta_{\mathrm{ukh}}-(ct)_{\mathrm{khv}}\right]V_{\mathrm{sg}} -c_{\mathrm{vp}}V_{\mathrm{vp}}\vartheta_{\mathrm{ukh}} -f(ct)_{\mathrm{khv}}\, \frac{\mathrm{kcal}}{\mathrm{kg}} . \end{aligned} \tag{11} \]

where

\[ f=\frac{5.55\mathrm{H}^p-0.7\mathrm{O}^p-0.8\mathrm{N}^p}{100}, \]

\[ V_{\mathrm{vp}}=0.111\mathrm{H}^p+0.0124W^p+0.0161\alpha_{\mathrm{ukh}}V^0\, \frac{\mathrm{N\,m}^3}{\mathrm{kg}} . \]

In the expression for \(V_{\mathrm{vp}}\), just as in (3), \(V^0\) has been substituted for \(V_1^0\), since in practice this changes nothing.

\[ 2.\qquad Q_3=30.2\,\mathrm{CO}\,V_{\mathrm{sg}}\, \frac{\mathrm{kcal}}{\mathrm{kg}} . \tag{12} \]

3.

\[ Q_4 = 81\left(K^p - K_1^p\right)\frac{\text{kcal}}{\text{kg}}. \tag{13} \]

Substituting into equality (8) the values of the losses given above, (11), (12), (13), and replacing the volume of dry gases \(V_{\text{dg}}\), \(CO\), and the characteristic of the burned fuel \(\zeta_1\) by their values,

\[ V_{\text{dg}}=\frac{1.86K_1^p}{RO_2+CO}\,\frac{\text{nm}^3}{\text{kg}}, \tag{14} \]

\[ CO=\frac{21-\zeta_1RO_2}{0.605+\zeta_1}\,(RO_2+O_2)\,\%, \tag{15} \]

\[ \zeta_1=2.35\,\frac{H^p-0.126O^p}{K_1^p}+0.005 \tag{16} \]

and solving the resulting equation with respect to \(K_1^p\), we obtain

\[ K_1^p= \frac{(21-0.4RO_2-O_2)M-(2.35L-58.3RO_2)(H^p-0.126O^p)} {520.8+0.605L-24.8(RO_2+O_2)+0.124RO_2}\,\%. \tag{17} \]

Here,

\[ M=81K^p-c_{\text{eg}}V_{\text{eg}}\vartheta_{\text{eg}} -Q_i^p\left(1-\frac{q_1+q_5}{100}\right), \]

\[ L=81RO_2+1.86\left[c_{\text{dg}}\vartheta_{\text{eg}}-(ct)_{\text{ca}}\right]. \]

In the expression for \(M\), the term \(-f(\alpha)_{\text{ca}}\) has been omitted because its influence is negligibly small.

After determining \(K_1^p\), the balance is brought to closure simply and quickly, since a number of quantities will already have been calculated.

The characteristics of the burned fuel \(\zeta_1\), \(CO\), and \(V_{\text{dg}}\) are found from expressions (16), (15), and (14).

The quantity of unburned carbon received is

\[ C_{\text{un}}=K^p-K^p_1q_0. \]

The loss \(Q_2\) can be determined from expression (11). When calculating this loss by the usual formula, it is first necessary to find the theoretical quantity of air for the burned fuel,

\[ V_1^0=0.0889K_1^p+0.265H^p-0.0333O^p\ \frac{\text{nm}^3}{\text{kg}}. \]

The losses \(Q_3\) and \(Q_4\) are determined from expressions (12) and (13). This completes the compilation of the heat balance.

Use of this method makes it possible, as in case I, to determine the total loss from mechanical incompleteness of combustion, bypassing all operations connected with measuring quantities and processing samples of bottom ash and fly ash. Gas analysis is performed only for \(RO_2\) and \(O_2\). As is known, absorption of \(CO\) in a gas analyzer proceeds slowly, and when its content in the gases is low, a considerable error can easily be introduced. In the present case, the chemical incompleteness of combustion is determined without analyzing the gas for \(CO\) during the test. Thus, application of this method for compiling the heat balance makes it possible to simplify considerably the work of the observers during testing, especially in those cases where one can confine oneself to the value of the total loss from mechanical unburned carbon.