On a New Methodology for Studying the Operation of Boiler Installations

V. N. Smirenskii
Associate Professor, Candidate of Technical Sciences

Introduction

The more modern the equipment of a boiler house is, the more difficult becomes the struggle for every fraction of a percent of fuel economy. This is entirely understandable. If, in some old installations, it often seems possible to detect easily some of the causes leading to excessive fuel consumption, without resorting at all to any investigations of the operation of the installation, then in more modern installations such obvious causes of fuel overconsumption are, as a rule, absent. But they may exist here in a hidden form, and in order to discover them one must organize careful heat-engineering investigations of the boiler installation.

Analysis of the results of such an investigation makes it possible to outline ways of eliminating individual shortcomings in the operation of the installation. At the same time, the results of the investigation can provide very valuable material for the operating personnel and for the design of new installations.

However, the existing methods of heat-engineering investigations of boiler-plant operation are insufficiently refined, which is explained by a whole series of difficulties in resolving the large number of questions connected with the investigation of an installation. But the ever more complicated struggle for economy of every fraction of a percent in fuel consumption, becoming more difficult together with the improvement of technology, persistently demands a more thorough investigation of the operation of installations. It is therefore quite understandable that recently a number of works have appeared on the methodology of investigating boiler installations, both by individual persons and by entire organizations directly interested in solving these questions.

On the Reliability of Certain Methods of Basic Measurements in Testing Boiler Installations

Let us consider certain basic measurements and observations in testing a boiler installation, the accuracy of which remains highly doubtful.

To determine the mechanical incompleteness of combustion during the test itself, it is necessary to determine the quantity and quality of furnace residues and carryover. Taking an average sample and measuring the quantity of fall-through material (in a grate-fired process) presents no particular difficulties. Careful observance of the rules for taking an average sample of fall-through material usually gives confidence in obtaining reliable data on the quantity of combustibles in it. Taking an average sample of slags for their technical analysis already presents known difficulties. The extreme nonuniformity in the distribution of combustibles in the slag requires special care in taking the average sample.

slag. With an increase in the capacity of the installation, i.e., with an increase in the hourly fuel consumption and with an increase in the ash content of the fuel, the proper selection of an average slag sample becomes still more complicated. Generally speaking, here too, as with grate siftings, there is every possibility of making a quantitative accounting and carrying out the sampling of slag sufficiently accurately.

As for the last component of mechanical incomplete combustion—carryover—here, first of all, we encounter the impossibility of a complete quantitative determination of it by direct measurement. To determine the amount of carryover, a very widespread method is that of the ash balance, in applying which it is necessary, among other data, to know the ash content of the carryover. The selection of an average carryover sample is carried out either from the ash pit of the last gas duct of the installation, or by traps of the simplest type, or by suction of gas with simultaneous separation of the carryover from it. Without dwelling on the first two methods mentioned for selecting a carryover sample, since in both these cases it is clear that only simple chance can give agreement between the composition of the selected sample and the true average carryover sample, let us consider in somewhat greater detail the last method of sampling.

The most advanced method in this case is considered to be the selection of a carryover sample by means of an Alner tube. But, obviously, reliable data cannot be expected with this method. There are no grounds for counting on uniformity in the composition of the carryover.

If we take any horizontal section in the furnace, then, considering it, we may note the following here.

a) A difference in temperatures, which, other conditions being equal, will lead to more complete combustion of the carryover in areas with higher temperatures.

b) A difference in the excess air at individual points across the section of the gas duct. In places with greater excess air, the conditions for oxidation of the combustibles in the carryover will be the most favorable, other conditions remaining unchanged (temperature, gas velocity, etc.).

c) A difference in the velocities of motion of the gas stream; moreover, an increase in velocities, i.e., a reduction in the residence time of particles in the furnace volume, will inevitably lead to less combustion of the combustibles in the carryover.

d) The presence of local vortex motions, which, by increasing the path of motion of solid particles and the time they remain in the furnace space, will lead to more complete combustion of the combustibles in them.

In addition, for one part of the carryover the time it remains in the furnace space will be considerably shorter than for another, because it will come into earlier contact with the cold heating surfaces of the boiler. In this case, less intensive combustion of the carryover will be observed. This will be especially noticeable in vertical water-tube boilers.

When considering the conditions under which carryover passes through the gas ducts, we again encounter a whole series of unclear factors which cannot be taken into account when organizing the selection of an average carryover sample: the difference in temperatures across the section of the gas duct, which is significant in the first gas ducts, where combustion of the carryover is possible; the difference in velocities and in the degree of concentration of the carryover; the deposition of carryover in the gas ducts themselves, inaccessible for sampling; and so forth. If all that has been set forth above is taken into account, it will become clear that it is impossible to select an average carryover sample with the same degree of reliability as we have for slag and grate siftings. Even by applying a preliminary calibration of the section in order to determine the degree of concentration of the carryover with the aid of an Alner tube, the sampling points can be indicated only approximately, since the degree and ratio of the carryover concentration at these points will not remain unchanged with a change in the operating regime of the furnace.

Thus, the question of the qualitative and quantitative determination of carryover, even with such a method—one that greatly complicates the experiment—as the use of Al’per tubes, remains extremely uncertain and unreliable.

As for a detailed determination of the composition of boiler gases, one may point to the unreliability of such analysis with the aid of the existing types of gas analyzers. Without dwelling here on a detailed examination of the reasons for this, let us note that, for gases rich in carbon monoxide, hydrogen, and hydrocarbons, such analysis gives results of quite sufficient accuracy; but with respect to boiler gases, the accuracy and reliability of the determination leave much to be desired. The poverty of boiler gases in combustible constituents does not permit the calorimetric method to be applied to them for the purpose of determining their calorific value. Thus, gas analysis gives sufficiently reliable data only with respect to the content of $\mathrm{RO}_2$ and $\mathrm{O}_2$. The absence of reliable data on the composition of the combustibles in boiler gases, which characterize the chemical incompleteness of combustion, makes it difficult to analyze the operation of the installation in this part. Determination of the CO content by the known formula is also unreliable, in view of what was said above concerning mechanical unburned loss.

In addition to the two imperfect basic measurements discussed above—sampling the carryover and detailed analysis of the gases—which are of enormous importance for the correct reduction of the heat balance, in thermotechnical investigations of boiler installations such observations as determination of the volume of gases and of the heat transfer to the external environment would be of no less importance. Carrying out these measurements would at once facilitate the correct reduction of the heat balance of the boiler installation and would thereby make it possible to approach the analysis of the results of the investigation with greater confidence. But the impossibility of directly measuring the quantity of gases, and the difficulty and unreliability in the present case of applying other methods for determining the quantity of gases—methods successfully used under other conditions—force experimenters to abandon such observations when testing boiler installations. The same may be noted with respect to setting up measurements to determine heat transfer to the external environment. The absence of these measurements is explained by the extreme difficulty of accounting for all heat losses from the cooling of the brickwork, metal parts protruding from the setting, pipelines, etc. All these heat-radiating surfaces have different temperatures and the most varied shapes. Moreover, in addition to radiation, convective heat transfer also takes place here. The uncertainty of certain calculations connected with determining heat-transfer coefficients makes even a theoretical calculation of the loss to the external environment impossible.

New proposals

From the foregoing it is evident that there are still quite a number of weak points in the measurement part when testing a boiler installation. The same is true in the computational part when reducing the heat balance. In the main, inaccuracies in heat-balance calculations may arise from incorrect accounting of unburned combustibles, and first of all unburned carbon $C_\mathrm{m}$ and then unburned hydrogen $H_\mathrm{m}$. The remaining combustible elements of the fuel that did not take part in combustion have a very insignificant influence.

Incorrect determination of $C_\mathrm{m}$ and underestimation of $H_\mathrm{m}$ give incorrect results in the calculations of $Q_4$, $V_{\mathrm{sg}}$, and $V_{\mathrm{vp}}$. Since the losses $Q_2$ and $Q_3$ are found through the volume of gases, they too will be determined incorrectly. Then the loss $Q_5$, as the residual term of the balance, will likewise receive an incorrect value. Therefore, in order to refine and more correctly determine the heat losses, it becomes necessary to seek some new additional paths. It is known, na-

for example, that the correct determination of the volume of gases would introduce sufficient accuracy into all balance calculations. However, the direct determination of the volume of gases, usually employed in other cases of flow-rate measurement (by pressure drop, velocity measurement, etc.), and giving satisfactory results there, cannot be carried out here, when testing a boiler installation, because of a whole series of known difficulties. The results of such a measurement would be extremely unreliable. What methods may be proposed for determining the volume of gases? A very simple solution of the question could be obtained if, for example, it were possible continuously to introduce into one of the cross sections of the gas duct, where the combustion process has already ended, some inert gas not present in the composition of the flue gases. By measuring its quantity \(V_R\) nm\(^3\)/h, arranging the introduction at such a place that, before the point at which gas is taken for analysis, it has mixed sufficiently well with the main mass of gas, and determining its percentage content in the dry gases \(R^0_0\), one could easily find \(V_{\mathrm{cg}}\) from the equality

\[ V_{\mathrm{cg}} B = \frac{V_R}{R} 100 - V_R \ \text{nm}^3/\text{h}, \]

whence

\[ V_{\mathrm{cg}} = \frac{V_R(100 - R)}{RB} \ \text{nm}^3/\text{kg}. \tag{1} \]

For the same purpose, one could also use the introduction of some gas forming part of the flue gases, with the application of a simple analysis for \(RO_2\) and \(O_2\). But the use of these methods for determining the volume of gases encounters certain practical difficulties, since it requires the availability of some gas for its additional introduction during the experiment.

The additional introduction of measured air, in the presence of leakage, does not make it possible to determine by a similar method the volume of gases, although such a method appears the simplest in its implementation. The impossibility of obtaining the corresponding equations in this case is explained by the fact that, together with the measured amount of additional air introduced, an unaccounted gas (air) of the same composition is drawn in through the leaks and pores of the brickwork.

But in some cases such a method for determining the volume of gases can be implemented.

A. Determination of the volume of gases by means of the additional introduction of air

If there is a section of gas duct in which there is no air leakage, then it appears possible to determine the volume of gas. Such a section may, for example, be an iron flue pipe (see Fig. 1). The points for taking gases for analysis and for introducing the additional air are visible in the drawing.

In this case it is possible to write the following balance equations for the amounts of \(RO_2\) and \(O_2\) at points \(A\) and \(C\):

\[ \frac{RO_2^c}{100}\left(V_{\mathrm{cg}}^a + \frac{V_{\mathrm{sv}}}{B}\right) = \frac{RO_2^a}{100} V_{\mathrm{cg}}^a \ \text{nm}^3/\text{kg} \]

and

\[ \frac{O_2^c}{100}\left(V_{\mathrm{cg}}^a + \frac{V_{\mathrm{sv}}}{B}\right) = \frac{O_2^a}{100} V_{\mathrm{cg}}^a + \frac{V_{\mathrm{sv}}}{B}\frac{21}{100} \ \text{nm}^3/\text{kg}; \]

Here \(\dot V_{sv}\) denotes the hourly quantity of air introduced, in \(\mathrm{Nm^3/hr}\). From these equations the volume of gases is determined:

\[ V_{sg}^{a}=\frac{V_{sv}RO_{2}^{a}}{B(RO_{2}^{a}-RO_{2}^{c})}\ \mathrm{Nm^3/kg}, \tag{2} \]

or

\[ V_{sg}^{a}=\frac{V_{sv}(21-O_{2}^{c})}{B(O_{2}^{c}-O_{2}^{a})}\ \mathrm{Nm^3/kg}. \tag{2'} \]

If the analysis of the boiler-room air gives an oxygen content in it different from 21%, this must be taken into account in the corresponding expression for \(V_{sg}^{a}\).

Expressions (2) and (2′) are simple. For the introduction of air, no special fan of any kind is required. The introduction may be carried out by means of the existing draft in the gas duct and the additional suction caused by the motion of the gas jet. Measuring the quantity of clean air, provided all the necessary conditions for this are observed, likewise presents no difficulties.

With a change in the gas flow rate, the quantity of air introduced will also change automatically in the same direction. As for the analysis of the gases, since here it is necessary only to determine \(RO_2\) and \(O_2\) (or even only one of them), such a simple gas analysis will not present any difficulties. It is only necessary to bear in mind that what will be measured is the quantity of moist air \(V_{v}^{vl}\), \(\mathrm{m^3/hr}\), at the corresponding mean temperature \(t_v^\circ\mathrm{C}\), mean static vacuum in the pipeline \(p_v\), mm water column, and barometric pressure \(B\), mm Hg.

Fig. 1. Layout of the principal measurement points. For determining the volume of gases by means of additional air suction.

The calculated mean hourly quantity of introduced dry air under normal conditions \((0;760)\) is determined from the expression

\[ V_{sv}=V_{v}^{vl}\frac{273\left(B-\frac{p_v}{13.6}\right)}{(273+t_v)\,760} -\frac{V_{sv}d}{0.805\cdot100}\ \mathrm{Nm^3/hr}, \]

whence

\[ V_{sv}=V_{v}^{vl}\frac{289B-21.3p_v}{(273+t_v)(805+d)}\ \mathrm{Nm^3/hr}, \tag{3} \]

where \(d\) is the mean moisture content in the air, determined, for example, by the gravimetric method, in \(\mathrm{g/Nm^3}\) of dry air.

From equations (2) and (2′) the volume of dry gases for section A is calculated. For any other section of the gas ducts, where a simple gas analysis has been performed, \(V_{\mathrm{dry}}^{x}\) can be found from the equality of the volumes of \(RO_2\)

\[ V_{\mathrm{dry}}^{x}=V_{\mathrm{dry}}^{a}\frac{RO_2^{a}}{RO_2^{x}}\ \text{Nm}^3/\text{kg}. \tag{4} \]

In this case it is obligatory that the given gas duct be located outside the limits of afterburning of the furnace gases.

From the operating standpoint, this method causes only a certain overload of the induced-draft fan, which must be taken into account in the case of a complete comprehensive test of the installation, allowing for the consumption of electric power for the plant’s own needs.

The accuracy of this method will depend mainly on the care with which the gas analyzer is operated. It is therefore necessary to analyze the gases with a gas analyzer equipped with a microburette, which makes it possible to take readings with an accuracy down to hundredths of a percent by volume. In addition, in order to obtain sufficient differences in the readings of the instruments for the two sections of the gas ducts, the amount of additionally introduced air must be at least \(3\div 5\%\) of the amount of gases. The greater the amount of air introduced, the more accurate the determination of the gas volume will be.

B. Determination of the gas volume by means of additional introduction of water vapor into the gas duct

Another way of determining the volume of gases may be outlined as follows. Into the gas duct immediately after the last heating surface (boiler, water or air heater), an additional introduction of water vapor is carried out continuously, the quantity of which is measured. Before the point of introduction and beyond it, where sufficient mixing of the vapor with the gases has already occurred, a simple gas analysis for \(RO_2\) and \(O_2\) is made. In these same sections of the gas ducts the moisture content of the gases is measured (see Fig. 2). The moisture content of the air is also determined. Let us note that the additional introduction of water vapor does not change the percentage composition of the dry flue gases.

Let us adopt the following notation:

\(\Delta V\) Nm\(^3\)/kg — air infiltration in the section \(A—C\);

\(G_{\mathrm{v}}\) kg/hour — average hourly amount of additionally introduced water vapor;

\(g_a\) g/Nm\(^3\) — moisture content per 1 Nm\(^3\) of dry gas in section A;

\(g_c\) g/Nm\(^3\) — the same for section C;

\(g'_c\) g/Nm\(^3\) — the same for section C under the condition of absence of additional introduction of water vapor;

\(d\) g/Nm\(^3\) — average moisture content of the air sucked into the gas duct, per 1 Nm\(^3\) of dry air.

Since in section C only the quantity \(g_c\) is determined by direct measurement, while in the subsequent calculations it is also necessary to know the quantity \(g'_c\), we shall find the corresponding expression for it. For this purpose we set up the following equations under the condition of absence of additional introduction of water vapor and the presence of air infiltration in the section \(A—C\):

\[ g_a V_{\mathrm{dry}}^{a}+d\,\Delta V=g'_c\left(V_{\mathrm{dry}}^{a}+\Delta V\right)\ \text{g/kg}; \tag{5} \]

\[ \frac{RO_2^{a}}{100}V_{\mathrm{dry}}^{a} = \frac{RO_2^{c}}{100}\left(V_{\mathrm{dry}}^{a}+\Delta V\right)\ \text{Nm}^3/\text{kg}; \tag{6} \]

\[ \frac{O_2^{a}}{100} V_{\mathrm{cr}}^{a} + \frac{\Delta V}{100}\,21 = \frac{O_2^{c}}{100}\left(V_{\mathrm{cr}}^{a}+\Delta V\right) \ \text{Nm}^3/\text{kg}. \tag{7} \]

From equations (5) and (6) we determine \(V_{\mathrm{cr}}^{a}\) and equate the two expressions obtained:

\[ V_{\mathrm{cr}}^{a} = \Delta V \frac{g'_c-d}{g_a-g'_c} = \Delta V \frac{RO_2^{c}}{RO_2^{a}-RO_2^{c}} \ \text{Nm}^3/\text{kg}. \]

Solving this equation with respect to \(g'_c\), we obtain

\[ g'_c = \frac{g_a RO_2^{c}+d\left(RO_2^{a}-RO_2^{c}\right)} {RO_2^{a}} \ \text{g}/\text{Nm}^3 \text{ of dry gas}. \tag{8} \]

Similarly, from equations (5) and (7) one can obtain an expression for \(g'_c\) through \(O_2\):

\[ g'_c = \frac{\left(21-O_2^{c}\right)g_a+d\left(O_2^{c}-O_2^{a}\right)} {21-O_2^{a}} \ \text{g}/\text{Nm}^3 \text{ of dry gas}. \tag{8'} \]

We now have all the data for determining the volume of dry gases in section C and in any other gas duct where the combustion process has ended.

Fig. 2. Diagram of the arrangement of the principal measurement points. For determining the gas volume by means of additional introduction of \(H_2O\).

Let us write the moisture-balance equation

\[ g'_c V_{\mathrm{cr}}^{c} + 1000\,\frac{G_{\mathrm{v}}}{B} = g_c V_{\mathrm{cr}}^{c} \ \text{g}/\text{kg}. \]

For the volume of dry gases in section C we obtain the expression:

\[ V_{\mathrm{cr}}^{c} = \frac{1000\,G_{\mathrm{v}}} {B\left(g_c-g'_c\right)} \ \text{Nm}^3/\text{kg}. \tag{9} \]

For any other section of the gas duct where the combustion process is completed, the volume of dry gases may be calculated from expression (4).

The addition of water vapor may be accomplished by feeding water into the gas duct, the water being completely evaporated by the heat of the flue gases. The apparatus for feeding, measuring, and evaporating the water can be made very simple. With regard to the amount of additional water vapor introduced, the following should be noted. It cannot be less than a certain minimum, depending on the magnitude of the air infiltration in section A--C, as well as on its humidity. Bearing in mind that for hard coals (with different methods of firing) the volume of dry gases downstream of the installation will on average be \(\sim 10 \div 12\ \mathrm{Nm^3/kg}\), and allowing for a certain margin, the following approximate expression may be given for determining the amount of water vapor to be introduced into the gas duct:

\[ G_{\mathrm{v}} \geq 0.02\,B\ \mathrm{kg/hour}. \tag{10} \]

For firewood, peat, and brown coals with a calorific value up to \(4000\ \mathrm{kcal/kg}\), for which the volume of dry gases downstream of the installation will average \(5 \div 6\ \mathrm{Nm^3/kg}\),

\[ G_{\mathrm{v}} \geq 0.01\,B\ \mathrm{kg/hour}. \tag{10'} \]

Naturally, the greater the amount of water vapor additionally introduced into the gas duct, the more accurately the gas volume will be determined. Measurement of the humidity of the gases and of the air is assumed to be by the gravimetric method, which guarantees considerable accuracy of the determinations.

B. Determination of the Gas Volume in the Case of Complete Combustion of Hydrogen

With complete combustion of the hydrogen of the fuel into \(\mathrm{H_2O}\), as is usually assumed, the volume of gases can be determined quite simply and at the same time with sufficient accuracy. In this case, during the test it is necessary to determine the moisture content in the gases. The gas analysis is carried out only in a simplified form for \(\mathrm{RO_2}\) and \(\mathrm{O_2}\). The percentage content of \(\mathrm{CO}\), required for calculating the chemical incompleteness of combustion, is found by calculation. Let us introduce the following notation:

\(g\) -- moisture content in the gases in the gas duct under investigation, in \(\mathrm{g/Nm^3}\) of dry gas;

\(\mathrm{RO_2}\), \(\mathrm{O_2}\), and \(\mathrm{CO}\) -- percentage content of the corresponding gases in the same gas duct;

\(d\) -- moisture content in the air, in \(\mathrm{g/Nm^3}\) of dry air;

\(V_{\mathrm{d}}^{\mathrm{a}}\) -- the actual amount of dry air supplied per \(1\ \mathrm{kg}\) of fuel for the gas duct of the boiler installation under investigation, taking account of infiltration through the brickwork, in \(\mathrm{Nm^3/kg}\);

\(\mathrm{H}\), \(\mathrm{O}\), \(\mathrm{S}\), \(\mathrm{N}\ldots\) -- percentage content of the corresponding elements in the working fuel.

The total amount of moisture per \(1\ \mathrm{kg}\) of fuel is

\[ G = 89.38\,H + 10\,W + V_{\mathrm{d}}^{\mathrm{a}}d\ \mathrm{g/kg}. \]

For the volume of dry gases we shall have the expression:

\[ V_{\mathrm{sg}}=\frac{G}{g} =\frac{89.38H+10W+V_{\mathrm{d}}^{\mathrm{a}}d}{g}\ \mathrm{Nm^3/kg}. \tag{11} \]

In this expression the only unknown is \(V_{\mathrm{d}}^{\mathrm{a}}\). To eliminate it, we shall first find the relation between \(V_{\mathrm{d}}^{\mathrm{a}}\) and \(V_{\mathrm{sg}}\). In the combustion of fue-

fuel according to the known reactions in an air atmosphere, the volume of the latter will change. To account for the change in volume during combustion, we shall use the combustion reactions and the molecular volumes of the gases.

\[ M_{\mathrm{O}_2}=22.394;\quad M_{\mathrm{CO}}=22.398;\quad M_{\mathrm{CO}_2}=22.258\ \text{and}\ M_{\mathrm{SO}_2}=21.892\ \mathrm{Nm^3/mol}. \]

1. Combustion reaction \( \mathrm{C}+0.5\mathrm{O}_2=\mathrm{CO} \).

As a result of chemical incompleteness of combustion, owing to the combustion of part of the carbon into CO, there will be an increase in the volume of the final combustion products as compared with \(V_d^{\mathrm{v}}\) by the amount

\[ V^{\mathrm{CO}}-V_{\mathrm{O}_2}^{\mathrm{CO}} = +\frac{\mathrm{CO}}{100}V_{\mathrm{cg}} -\frac{0.5\cdot 22.394}{22.398}V_{\mathrm{cg}}\frac{\mathrm{CO}}{100} \simeq +0.005\,V_{\mathrm{cg}}\,\mathrm{CO}\ \mathrm{Nm^3/kg}, \]

where \(V_{\mathrm{CO}}\) is the volume of CO obtained in burning 1 kg of fuel,
\(V_{\mathrm{O}_2}^{\mathrm{CO}}\) is the quantity of oxygen required for this.

1. Combustion reaction \( \mathrm{H}_2+0.5\mathrm{O}_2=\mathrm{H}_2\mathrm{O} \).

From the combustion of “free” hydrogen \( \mathrm{H}-\mathrm{O}/8 \) into \(\mathrm{H}_2\mathrm{O}\), there will be a decrease in volume by the amount of oxygen required for combustion

\[ -\frac{0.5\cdot 22.394}{2.0156}\frac{\mathrm{H}-\mathrm{O}/8}{100} = -0.0555\,(\mathrm{H}-\mathrm{O}/8)\ \mathrm{Nm^3/kg}. \]

1. Assuming that the nitrogen of the fuel passes into the flue gases, we obtain an increase in the volume of the final combustion products by

\[ +\frac{\mathrm{N}}{100\,\gamma_{\mathrm{N}_2}} = \frac{\mathrm{N}}{125.1} = +0.008\,\mathrm{N}\ \mathrm{Nm^3/kg}. \]

As a consequence of the deviation from Avogadro’s law for triatomic gases, in the complete combustion of C and S we shall also have a change in the volume of the gases.

1. Combustion reaction \( \mathrm{C}+\mathrm{O}_2=\mathrm{CO}_2 \).

In this case we have a decrease in volume by the amount

\[ V_{\mathrm{CO}_2}-V_{\mathrm{O}_2}^{\mathrm{CO}_2} = \frac{\mathrm{CO}_2}{100}V_{\mathrm{cg}} - \frac{22.394}{22.258}V_{\mathrm{cg}}\frac{\mathrm{CO}_2}{100} = -0.006\,V_{\mathrm{cg}}\frac{\mathrm{CO}_2}{100}\ \mathrm{Nm^3/kg}. \]

1. Combustion reaction \( \mathrm{S}+\mathrm{O}_2=\mathrm{SO}_2 \).

The decrease in volume in this case will be

\[ V_{\mathrm{SO}_2}-V_{\mathrm{O}_2}^{\mathrm{SO}_2} = \frac{\mathrm{SO}_2}{100}V_{\mathrm{cg}} - \frac{22.394}{21.892}V_{\mathrm{cg}}\frac{\mathrm{SO}_2}{100} = -0.0229\,V_{\mathrm{cg}}\frac{\mathrm{SO}_2}{100}\ \mathrm{Nm^3/kg}. \]

The relation between \(V_{\mathrm{cg}}\) and \(V_d^{\mathrm{v}}\) will be written in the following form:

\[ V_{\mathrm{cg}} = V_d^{\mathrm{v}} +0.005\,V_{\mathrm{cg}}\,\mathrm{CO} -0.0555\,(\mathrm{H}-\mathrm{O}/8) +0.008\,\mathrm{N} -0.00006\,V_{\mathrm{cg}}\,\mathrm{CO}_2 -0.000229\,V_{\mathrm{cg}}\,\mathrm{SO}_2\ \mathrm{Nm^3/kg}. \]

The last term of the expression may be split as follows:

\[ 0.000229\,V_{\mathrm{cg}}\,\mathrm{SO}_2 = 0.00006\,V_{\mathrm{cg}}\,\mathrm{SO}_2 + 0.000169\,V_{\mathrm{cg}}\,\mathrm{SO}_2. \]

We shall combine the first summand with \(\mathrm{CO}_2\) and denote the sum thus obtained by \(\mathrm{RO}_2\), while the second we shall express through the sulfur S.

Since in \(1\ \mathrm{Nm^3}\) of \(\mathrm{SO}_2\) there is sulfur

\[ \frac{32.06}{64.06}\,2.92623 = 1.4645\ \mathrm{kg/Nm^3} \]

and

\[ V_{\mathrm{SO}_2} = \frac{\mathrm{S}}{100\cdot 1.4645}\ \mathrm{Nm^3/kg}, \]

\[ \mathrm{SO}_2=\frac{V_{\mathrm{SO}_2}}{V_{\mathrm{cr}}}\,100 =\frac{S\cdot100}{100\cdot1.4645\,V_{\mathrm{cr}}} =\frac{S}{1.4645\,V_{\mathrm{cr}}}\% \]

and

\[ 0.000169\,V_{\mathrm{cr}}\,\mathrm{SO}_2 =0.000169\,V_{\mathrm{cr}}\frac{S}{1.4645\,V_{\mathrm{cr}}} =0.000115\,S. \]

Combining \(\mathrm{CO}_2\) and \(\mathrm{SO}_2\) in the expression for \(V_{\mathrm{cr}}\) and rewriting it for \(V_{\mathrm{d}}^{\mathrm{v}}\), we shall have:

\[ V_{\mathrm{d}}^{\mathrm{v}} =V_{\mathrm{cr}}\left(1-0.005\,\mathrm{CO}+0.00006\,\mathrm{RO}_2\right) +0.0555\,(H-O/8)-0.008\,N +0.000115\,S\ \mathrm{nm}^3/\mathrm{kg}. \tag{12} \]

On the other hand, we have the expression

\[ V_{\mathrm{d}}^{\mathrm{v}} =\frac{\dfrac{N_2}{100}V_{\mathrm{cr}}-\dfrac{N}{100\cdot1.251}}{79}\,100 =V_{\mathrm{cr}}\frac{N_2}{79}-\frac{0.8N}{79} \]

\[ =V_{\mathrm{cr}}\frac{100-(\mathrm{RO}_2+O_2+\mathrm{CO})}{79} -\frac{0.8N}{79}. \tag{13} \]

Equating both expressions (12) and (13) and carrying out certain transformations, we obtain the equation:

\[ V_{\mathrm{cr}}\left(21-1.005\,\mathrm{RO}_2-O_2-0.605\,\mathrm{CO}\right) =4.388\,(H-O/8)+0.168\,N+0.009\,S, \]

whence we find the expression for \(\mathrm{CO}\):

\[ \mathrm{CO}=34.71-1.66\,\mathrm{RO}_2-1.653\,O_2 -\frac{7.253\,H-0.91\,O+0.278\,N+0.015\,S}{V_{\mathrm{cr}}}\%. \tag{14} \]

Substituting \(\mathrm{CO}\) in expression (12) by (14), we have:

\[ V_{\mathrm{d}}^{\mathrm{v}} =(0.826+0.00835\,\mathrm{RO}_2+0.00826\,O_2)\,V_{\mathrm{cr}} +0.092\,(H-O/8) -0.0066\,N+0.0002\,S\ \mathrm{nm}^3/\mathrm{kg}. \tag{15} \]

Substituting the obtained expression for \(V_{\mathrm{d}}^{\mathrm{v}}\) into equation (11) and then determining \(V_{\mathrm{cr}}\), we obtain, in final form, the equation for calculating the volume of dry gases:

\[ V_{\mathrm{cr}} =\frac{89.38\,H+10\,W+\left[0.092\,(H-O/8)-0.0066\,N+0.0002\,S\right]d} {g-\left(0.826+0.00835\,\mathrm{RO}_2+0.00826\,O_2\right)d} \ \mathrm{nm}^3/\mathrm{kg}. \tag{16} \]

Bearing in mind that the value of the numerator will be of the order of several hundreds and that the influence of the terms with the factors \(N\) and \(S\) is negligible, they may be completely disregarded without detriment to the accuracy of the final results. The coefficients at \(\mathrm{RO}_2\) and \(O_2\) in the denominator may also be rounded.

Then we obtain:

\[ V_{\mathrm{cr}} =\frac{89.38\,H+10\,W+0.092\,(H-O/8)\,d} {g-\left[0.826+0.0083\,(\mathrm{RO}_2+O_2)\right]d} \ \mathrm{nm}^3/\mathrm{kg}. \tag{17} \]

Note: In expressions (14) and (16), the percentage values of \(O\), \(S\), and \(N\) should, strictly speaking, be substituted for the burned fuel, which differ somewhat from their values in the composition of the working ...

of the fuel. But in view of their insignificant influence on the final result, in the calculations one may use the composition of the working fuel. As for the value \(W\), then, with complete combustion of hydrogen, as is assumed in the present case, it must be expected that all the moisture of the fuel will pass into the gases. Therefore \(W^p\) should be substituted in the formula. What has been said will, obviously, also apply to the other fuel elements mentioned above.

Thus, with complete combustion of the hydrogen of the fuel, the volume of dry gases is determined by this method quite simply. In this case no analysis of the gases for CO is required, the percentage content of which is found from equation (14). The entire heat balance can be compiled without any difficulty.

In the case of a slight underburning of hydrogen, which occurs in most cases, formula (17) for determining \(V_{\mathrm{cr}}\) may be used successfully by substituting \(H^p\) into it instead of the actual volume of dry gases.

In the boiler laboratory of the TPI, a series of experiments was carried out on horizontal water-tube and locomotive boilers with a layer combustion process. Alongside the generally accepted testing procedure, the method analyzed here was also applied. The experiments were conducted in parallel with tests carried out by the Department of TCS for the heat-engineering investigation of various grades of coal. Determination of the moisture content in the gases was carried out with the aid of the apparatus schematically shown in Fig. 3.

Fig. 3. Schematic of the apparatus for determining moisture in gases.
\(a\)—sampling tube with filter, \(b\)—condenser, \(c\)—condensate receiver,
\(d_1\)—chemical moisture absorber with \(\mathrm{CaCl_2}\), \(d_2\)—control moisture absorber,
\(e\)—seal with \(\mathrm{H_2SO_4}\), \(f\)—gas meter, \(g\)—ejector.

The air humidity was determined by the gravimetric method. Special attention was paid to the thoroughness of taking an average fuel sample.

The quantity of moist gas \(v_g\), m³, was measured by a gas meter at the gas temperature in the meter \(t_g\) and at a vacuum \(\delta\) mm Hg. The volume of dry gas that passed through the meter, \(v_{\mathrm{cr}}\), was determined as follows.

If the barometric pressure of the air is denoted by \(B\) mm Hg, the partial pressure of the water vapor of the gas in the meter by \(p_p\), and the partial pressure of the dry gas in the mixture by \(p_{\mathrm{cr}}\), then \(v_{\mathrm{cr}}\), reduced to normal conditions (0.760), will be equal to

\[ v_{\mathrm{cr}} = v_g \frac{p_{\mathrm{cr}}}{760}\,\frac{273}{273+t_g} = 0.359\,v_g\frac{B-(\delta+p_p)}{273+t_g}\ \mathrm{nm^3}. \tag{18} \]

\(p_{\mathrm{p}}\) is found from the corresponding tables at \(t_{\mathrm{g}}\) and relative humidity \(\varphi = 100\%\), since the gas, after passing through the clock meters, will be saturated with vapors.

The same must also be noted with regard to determining the humidity of the air. Since in the tipping aspirator used to determine the humidity of the air the latter passes through a layer of water, in practice it was completely saturated with water vapor. If \(g'_{\mathrm{v}}\) is the weight gain of the chemical absorber of moisture, in g; \(v_{\mathrm{v}}\) is the volume of the air sample in m³ at \(\varphi = 100\%\), \(t_{\mathrm{v}}^\circ\mathrm{C}\), and \(B\) mm Hg; \(p'_{\mathrm{p}}\) is the partial pressure of water vapor at \(t_{\mathrm{v}}^\circ\mathrm{C}\) and \(\varphi = 100\%\), in mm Hg, then the volume of dry air at \(0^\circ\mathrm{C}\) and 760 mm Hg, according to the Boyle–Mariotte and Gay-Lussac laws, will be

\[ v_{\mathrm{sv}} = v_{\mathrm{v}} \frac{(B - p'_{\mathrm{p}})273}{760(273 + t_{\mathrm{v}})}\ \mathrm{nm}^3 \]

and the moisture content per cubic meter of dry air will be determined from the expression

\[ d = \frac{g'_{\mathrm{v}}}{v_{\mathrm{sv}}} = 2.784 \frac{(273 + t_{\mathrm{v}}) g'_{\mathrm{v}}}{(B - p'_{\mathrm{p}}) v_{\mathrm{v}}}\ \mathrm{g}/\mathrm{nm}^3 . \tag{19} \]

Note. When carrying out tests by the method set forth here, it is possible to dispense with the chemical absorbers that capture the water vapor from the gas after it has passed through the condenser. For this, it is additionally necessary only to measure the temperature and the gas rarefaction at the outlet from the condenser. In this case the weight of water vapor remaining in the gases after the condenser is found from the expression

\[ g'_{\mathrm{g}} = \gamma'_{\mathrm{p}} v_{\mathrm{g}} \frac{B - (b + p_{\mathrm{p}})}{B - (b' + p'_{\mathrm{p}})} \cdot \frac{273 + t'_{\mathrm{g}}}{273 + t_{\mathrm{g}}} \ \mathrm{g}, \tag{20} \]

where \(\gamma'_{\mathrm{p}}\) is the specific weight of water vapor at \(t'_{\mathrm{g}}\), in \(\mathrm{g}/\mathrm{m}^3\); \(b\), \(t'_{\mathrm{g}}\), and \(p'_{\mathrm{p}}\) are the rarefaction, temperature, and partial pressure of the water vapor of the gas at the outlet from the condenser. The remaining notation is as before.

The results of experiments carried out on various grades of coal and mixtures confirmed the full feasibility and advisability of conducting tests by this method, which was corroborated by comparative calculations of heat balances by different methods.

The total loss from mechanical incompleteness of combustion can be determined without taking into account the quantity of slag, grate siftings, and entrainment, and without their technical analysis. The conventional quantity of burned carbon required for calculating the loss \(Q_4\) is determined from the known expression

\[ K' = 0.539 V_{\mathrm{sg}}(RO_2 + CO)\%. \]

In the differentiated determination of \(Q_4\), the corresponding observations need be made only for slag and grate siftings, which can always be done with due care. Gas analysis may be applied only in the simplified form for \(RO_2\) and \(O_2\). The value of \(CO\), necessary for determining the chemical incompleteness of combustion and the conventional quantity of burned carbon, is found by a simple calculation using formula (14). The loss to the surroundings, determined as the residual term of the balance, assumes values closer to reality.

When conducting an experiment by the method given here, the following must be observed.

1. It is necessary to ensure careful selection of the average fuel sample and determination of its moisture content.
2. A careful determination of the moisture content of the air is also obligatory.
3. The trapping of water vapor from the gases must be carried out continuously from the beginning to the end of the fuel test. In addition, in order to approximate more fully the truly average composition of the gas, gas suction must be carried out simultaneously at several points over the cross-section of the gas duct, coordinating the suction rate with the overall velocity of the gases in the channel.
4. For a more careful performance of the test, approximately \(8 \div 10\ \mathrm{nm^3}\) of gas should be passed through the apparatus, which, for the average working composition of bituminous coals, will give about \(0.5\ \mathrm{kg}\) of water in the apparatus.
5. For the same reasons, before the beginning of the test, while establishing the operating regime of the boiler, gas should be passed through the apparatus for some time (but bypassing the chemical absorbents), so that at the beginning and at the end of the test the condition of the apparatus—on the inner walls of whose pipelines dew will be present—will be the same.

G. Allowance for the Incomplete Combustion of Hydrogen

Continuing the further development of the methodology for studying the operation of boiler installations, one may approach the question of determining the quantity of hydrogen completely burned to \(\mathrm{H_2O}\). Let us denote it by \(H'\), and the remaining elements of the fuel that have passed into the gases by \(C'\), \(O'\), \(N'\), \(S'\), \(W'\).

Let us take the general case of fuel combustion, when the final products of combustion contain \(\mathrm{CO}\), \(\mathrm{H_2}\), \(\mathrm{CH_4}\), \(\mathrm{C_mH_n}\), \(\mathrm{H_2S}\%\), and in the slag residues and carry-over—\(C_m\), \(H_m\), \(O_m\), \(N_m\), etc.

First let us find the relation between \(V_{\mathrm{cr}}\) and \(V_{\mathrm{d}}^{\mathrm{v}}\). Proceeding analogously to what was done in Section 2-B, here it is necessary additionally to take into account that the volume of dry gases will increase, as compared with the actual volume of air supplied for combustion, by the amount

\[ 0.01\left(\mathrm{H_2}+\mathrm{CH_4}+\mathrm{C_mH_n}+\mathrm{H_2S}\right)V_{\mathrm{cr}}\ \mathrm{nm^3/kg}. \]

The relation between \(V_{\mathrm{cr}}\) and \(V_{\mathrm{d}}^{\mathrm{v}}\) in this case will be expressed in the following form (we neglect the quantity \(0.00017\mathrm{H_2S}V_{\mathrm{cr}}\), which accounts for the correction for the change in volume due to part of the sulfur being burned to \(\mathrm{H_2S}\) and not to \(\mathrm{SO_2}\)):

\[ V_{\mathrm{d}}^{\mathrm{v}} = V_{\mathrm{cr}}\left[ 1-0.005\,\mathrm{CO} -0.01\left(\mathrm{H_2}+\mathrm{CH_4}+\mathrm{C_mH_n}+\mathrm{H_2S}\right) +0.00006\,\mathrm{RO_2} \right] + \]
\[ +0.0555\left(H'-O'/8\right)-0.008\,N' +0.000115\,S'. \tag{21} \]

Expression (13) in the present case is written as follows:

\[ V_{\mathrm{d}}^{\mathrm{v}} = V_{\mathrm{cr}}\, \frac{ 100-\left(\mathrm{RO_2}+\mathrm{O_2}+\mathrm{CO}+\mathrm{H_2}+\mathrm{CH_4}+\mathrm{C_mH_n}+\mathrm{H_2S}\right) }{79} - \]
\[ -\frac{0.8\,N'}{79}. \tag{22} \]

Equating the expressions for \(V_{\mathrm{d}}^{\mathrm{v}}\) (21) and (22), and omitting certain transformations, we obtain:

\[ \mathrm{CO} = 34.71 -1.66\,\mathrm{RO_2} -1.653\,\mathrm{O_2} -0.347\left(\mathrm{H_2}+\mathrm{CH_4}+\mathrm{C_mH_n}+\mathrm{H_2S}\right) - \]
\[ -\frac{ 7.253\left(H'-O'/8\right)+0.278\,N'+0.015\,S' }{V_{\mathrm{cr}}}\,\%. \tag{23} \]

and

\[ \mathrm{H}_2+\mathrm{CH}_4+\mathrm{C}_m\mathrm{H}_n+\mathrm{H}_2\mathrm{S} =100-4.786\,\mathrm{RO}_2-4.762\,\mathrm{O}_2-2.881\,\mathrm{CO} -\frac{20.895\,(H'-O'/8)+0.8\,N'+0.043\,S'}{V_{\mathrm{cr}}}\ \%. \tag{24} \]

After substituting expression (13) into (11), we obtain the following expression for the volume of dry gases:

\[ V_{\mathrm{cr}}= \frac{89.38\,H'+10\,W'-0.01\,N'd}{g-0.01266\,N_2d} \ \mathrm{nm}^3/\mathrm{kg}. \]

Since

\[ N_2=100-(\mathrm{RO}_2+\mathrm{O}_2+\mathrm{CO}+\mathrm{H}_2+\mathrm{CH}_4+\mathrm{C}_m\mathrm{H}_n+\mathrm{H}_2\mathrm{S})\%, \]

it may be written that

\[ V_{\mathrm{cr}}= \frac{89.38\,H'+10\,W'+0.01\,N'd} {g-1.266\,d+0.01266(\mathrm{RO}_2+\mathrm{O}_2+\mathrm{CO}+\mathrm{H}_2+\mathrm{CH}_4+\mathrm{C}_m\mathrm{H}_n+\mathrm{H}_2\mathrm{S})d} \ \mathrm{nm}^3/\mathrm{kg}. \tag{25} \]

From expression (25) one may eliminate either CO or \(\mathrm{H}_2+\mathrm{CH}_4+\mathrm{C}_m\mathrm{H}_n+\mathrm{H}_2\mathrm{S}\), using equations (23) and (24). After this, expressions can be found for the amount of completely burned hydrogen.

From formulas (23) and (25),

\[ H'= \frac{\{g-[0.826+0.00834\,\mathrm{RO}_2+0.00827\,(\mathrm{O}_2-\mathrm{H}_2-\mathrm{CH}_4-\mathrm{C}_m\mathrm{H}_n-\mathrm{H}_2\mathrm{S})]d\}V_{\mathrm{cr}}} {89.38+0.092\,d} + \frac{-10\,W'+(0.0115\,O'+0.0066\,N'-0.0002\,S')d} {89.38+0.092\,d} \ \%. \tag{26} \]

From (24) and (25),

\[ H'= \frac{\{g-[0.0479\,\mathrm{RO}_2+0.0476\,(\mathrm{O}_2+0.5\,\mathrm{CO})]d\}V_{\mathrm{cr}}} {89.38+0.265\,d} + \frac{-10\,W'+(0.033\,O'-0.0005\,S')d} {89.38+0.265\,d} \ \%. \tag{27} \]

Considering expression (26), it may be noted that its numerator will be measured by a number of the order of several hundreds (\(\sim 300 \div 400\)). Its term \(+0.00827(\mathrm{H}_2+\mathrm{CH}_4+\mathrm{C}_m\mathrm{H}_n+\mathrm{H}_2\mathrm{S})dV_{\mathrm{cr}}\), for boiler installations, where the quantity enclosed in parentheses is very small and even in the worst case does not exceed \(\sim 0.5\%\), will amount in all to no more than \(0.2 \div 0.3\). If this term is neglected, then the error in the final calculation for \(H'\) will be no more than 0.003, which even in precise work has no substantial significance. This is the worst case taken. Usually the magnitude of the error will be much smaller. Therefore the indicated term of the numerator may safely be neglected without any loss of accuracy in the calculation.

The other term of the numerator \((0.0115\,O'+0.0066N'-0.0002S')d\) will likewise be a quantity of the order of \(0.2 \div 0.4\) for most hard coals. For fuels with a high oxygen content it will be considerably higher. The second and third terms of the term under consideration, entering with different signs, constitute a quantity of no more than hundredths of a unit. We neglect them, and instead of the oxygen of the burned fuel we substitute \(O^p\). This will also serve as a certain compensation for the discarded terms of the numerator (in the presence of chemical incomplete combustion of hydrogen).

Thus, in final form expression (26) will take the form:

\[ H'=\frac{\{g-[0.826+0.00834RO_2+0.00827O_2]d\}V_{cr}-10W^p+0.0115O^p d}{89.38+0.092d}\%. \tag{26'} \]

As for formula (27), since a considerable percentage of CO can often be found in the flue gases, this term should not be neglected. The sulfur of the burned fuel may be neglected. The final expression for \(H'\) in this case will be

\[ H'=\frac{\{g-[0.0479RO_2+0.0476(O_2+0.5CO)]d\}V_{cr}-10W^p+0.033O^p d}{89.38+0.265d}\%. \tag{27'} \]

In both formulas, instead of \(W'\) one may substitute \(W^p\), and only in special, abnormal cases of bed combustion of fuel, with a very large amount of riddlings, should the unevaporated moisture of the fuel remaining in the riddlings be taken into account. Then, with the moisture of the riddlings \(W_{pr}\) and their hourly quantity \(G_{pr}\), the quantity to be substituted in the formula must be

\[ W'=W^p-W_{pr}\frac{G_{pr}}{B}\%. \tag{28} \]

From a comparison of both formulas for determining the amount of hydrogen of the fuel burned to \(H_2O\), it is clear that, while preserving the same accuracy, formula (26′) is the most convenient and simple, since here only a simplified gas analysis for the content of \(RO_2\) and \(O_2\) is required.

The percentage content of carbon monoxide in this case may be found (or checked) from equation (27′), which, after solution, gives the following expression for CO:

\[ CO=\frac{42}{d}\times \]

\[ \times\left[ g-\frac{(89.38+0.265d)H'+10W^p-0.033O^p d}{V_{cr}} \right]-2.01RO_2-2O_2\%. \tag{29} \]

If, with the availability of accurate gas analyzers, it is possible to determine the percentage content in the flue gases of hydrogen \(H_2\), methane \(CH_4\), and ethylene \(C_2H_4\), then the percentage of mechanical underburning of hydrogen can be found.

With insignificant rounding of the values of the specific gravities of the named gases, this expression will take the following form:

\[ H_m=H^p-\{H'+0.09V_{cr}[H_2+2(CH_4+C_2H_4)]\}\%. \tag{30} \]

With some approximation, the total determined quantity of heavy hydrocarbons may be referred to ethylene. But in the overwhelming majority of cases, the mechanical incompleteness of combustion of hydrogen will, obviously, be determined more simply from the expression

\[ H_m=H^p-H'\% \tag{30'} \]

in view of the fact that \(H_2\), \(CH_4\), and \(C_mH_n\) will be either equal or close to zero.

Conclusion

The existing methods of testing boiler installations and the methods of compiling heat balances possess a whole series of substantial shortcomings. Therefore, in the basic equation of the heat balance only two terms can be reliably determined:

1) the lower calorific value of the working fuel \(Q_{\mathrm{n}}^{\mathrm{p}}\),

2) the heat usefully utilized by the installation \(Q_{1}\).

All the other expenditure items of the heat balance do not give confidence in their correct determination, and at times even take on plainly implausible values.

The methods considered here make it possible to determine one of the basic quantities—the volume of gases. Methods 2-A and 2-B require special care in determining the composition of the gases (\(\mathrm{RO}_{2}\) and \(\mathrm{O}_{2}\)) and their moisture content, since these data enter into the denominator of the expressions for \(V_{\mathrm{sg}}\) in the form of a difference. Method 2-B may be applied in the overwhelming majority of cases, since the percentage of unburned hydrogen is usually small. All the heat losses of the installation, including the loss to the external environment (the residual term of the balance), are determined more accurately. At the same time, in order to determine the mechanical incompleteness of combustion as a whole, it is absolutely unnecessary to take account either of the quantity or of the quality of the slag, siftings, and carry-over. This circumstance may be of very substantial importance in testing large boiler installations, where such accounting presents very great difficulties.

In experimental verification, method 2-B proved justified. It may be recommended especially for fuels with a small yield of volatiles, during the combustion of which in normal furnaces the chemical incompleteness of combustion occurs almost exclusively at the expense of carbon monoxide.

When carrying out more thorough heat-engineering investigations of a boiler installation as a whole, by applying in this case, for determining the gas volume, one of the methods analyzed in Section 2, it is very simple to determine the incomplete combustion of hydrogen by formula (26′); for this only a simplified, but carefully performed, gas analysis is required.

The mechanical incompleteness of combustion of hydrogen, which has usually not been taken into account up to now but which sometimes constitutes a very substantial component in the total loss from mechanical underburning, is of considerable interest from two points of view: 1) from the standpoint of a correct assessment of the operation of the installation under investigation and the possibility of outlining expedient measures for eliminating deficiencies found in the operation of the firing equipment, and 2) from the standpoint of studying the behavior of hydrogen, the second most important combustible element of the fuel burned in a boiler furnace. This circumstance would subsequently make it possible to introduce certain corrections into calculations connected with the design of new boiler installations, where the mechanical incompleteness of hydrogen combustion is not taken into account at all.

The proposed moisture-balance method can likewise be extended to gaseous fuels.