Eng. V. N. SMIRENSKY.

ON THE ISSUE OF A NEW TESTING METHODOLOGY AND THE DETERMINATION OF LOSSES IN BOILER UNITS

The methodology now accepted in boiler practice for testing steam boilers, and the associated method of calculating the heat balance, are still far from accurate. The chief difficulty here is presented by one quantity: the mechanical incompleteness of combustion, $q_4$. This loss has hitherto usually been determined by the so-called ash balance, which, as is known, is very inaccurate and unreliable. Indeed, if one part of the total loss $q_4$ can be accounted for within the limits of the firing device (loss with slag and throughfall), then the other part, sometimes the predominant one (loss with carryover), is, for direct determination, an “elusive” quantity.

In determining the carryover component of $q_4$, the practice is to collect the carryover, then take it as an average sample, determine by technical analysis the combustible mass in the carryover, and, knowing the same in the slag and throughfall and their weights, determine $q_4$ by the ash-balance method.

If we were sure that the average sample of carryover had been selected correctly, then, in determining $q_4$ by the indicated method, we would be very close to the truth. But the whole trouble lies precisely in the fact that we are not able to select a truly average sample of the carryover. There are a number of reasons for this. First of all, the carryover collected directly in one or another gas duct of the boiler may partially burn out, while the conditions of its burning in the collecting device will be different from those under “natural” conditions. Conversely, in a device that sucks the carryover together with gas from the boiler gas duct, the process of afterburning of part of the carryover may be stopped somewhat earlier than in the flue itself. Moreover, a number of additional conditions must be observed here that promote the collection of a truly average sample of the carryover, at least at the given point of the gas duct, since otherwise either very fine or, conversely, coarse particles of carryover may escape capture. Thus, for example, the proper form of the simplest collector (a baking sheet) must be chosen in one case, or the proper suction velocity in another, and so on. Failure to observe the corresponding conditions inevitably already entails incorrectness in determining the average sample of carryover. Further, the composition and distribution of the carryover stream are not the same over the cross section of the gas duct. There are also a number of reasons for this: the presence of different areas of free sections along the gas duct and, consequently, of velocities, nonuniform—

temperature distribution, etc. Finally, in some places in the gas ducts we do not even have the possibility of taking a sample of entrainment during boiler operation.

All this, taken together, argues that, when determining the mechanical incompleteness of combustion \(q_4\) by the ash-balance method, it is very easy to depart very far from its true value, despite the thoroughness of all observations. And it is not surprising after this that often during tests \(q_4\) gives quite unexpected jumps over fairly wide limits, often not justified by anything.

Such a phenomenon is especially noticeable when carrying out a series of experiments on one and the same fuel.

Bearing in mind the methodology of heat-balance calculations, which is still widely used, it must be noted that an incorrect determination of the loss \(q_4\) inevitably entails inaccuracy also in the determination of other losses. In fact, according to the value found for the mechanical incompleteness of combustion \(Q_4\) cal/kg \((q_4\%)\), the following are determined:

the fictitious amount of carbon burned

\[ K_1^p = C^p - \frac{Q_4}{80.5} + 0.368 \cdot S_{\ell}^{p}; \]

the characteristic of the burned fuel, which serves for determining carbon dioxide, if the latter is not observed directly from the experiment,

\[ \beta' = 2.38 \frac{H^p - \dfrac{O^p}{8}}{K_1^p} + 0.005; \]

the loss with the outgoing gases

\[ Q_2 = \left[ 1.86 \frac{K_1^p}{RO_2 + CO} + 0.0124(9 \cdot H^p + W^p) \right] C_g (T_y - t_v) - C_m (t_m - t_v) \]

and the loss from chemical incompleteness of combustion

\[ Q_3 = 56.7 \frac{CO}{RO_2 + CO} K_1^p . \]

Consequently, the accuracy of determining the losses \(q_2\) and \(q_3\) is directly connected with the accuracy of determining the loss \(q_4\). In those cases where the loss to the surrounding medium \(q_5\) is found as a residual term, then all losses without exception may already be determined insufficiently accurately, especially if one has to deal with a large amount of entrainment.

But if the loss \(q_4\), necessary for a more correct compilation of the entire balance, is not amenable to direct determination, then another path may be proposed for its determination. This path will at the same time make it possible to determine the losses \(q_2\) and \(q_3\) more correctly.

It all comes down here to the installation of some additional, uncomplicated apparatus and to additional observations. The method itself includes determining the volume of gases downstream of the boiler. However, direct determination of the gas volume \(V_2\), \(\mathrm{m^3/kg}\), is no less difficult than direct determination of \(q_4\). But the volume \(V_2\) can be determined experimentally by means of the setup schematically shown in Fig. 1, the purpose of which is to condense and capture the water vapors from the gases drawn off by the ejector \(f\).

The gas drawn by the ejector \(f\) from the last gas duct of the boiler passes through a dry filter \(a\), which retains mechanically suspended particles in the gases. Ordinary glass wool may serve as the filter. It is better to place the filter in the boiler gas duct itself, at the end of the sampling tube, in order to avoid premature condensation of water vapor in it and unnecessary weighing. For the same reasons, the condenser \(b\) must be installed as close as possible to the place where the gas is sampled. The cooling water should have as low a temperature as possible, since calculations show that, at a water temperature of \(5^\circ\mathrm{C}\), for the average working composition of hard coals, the quantity of water vapor that remains in the gases after the condenser will amount to approximately 10% of its total content in the gases before the condenser. Therefore it becomes necessary to install an additional absorber of water vapor \(d_1\). The absorbing substance here may be phosphoric anhydride \((\mathrm{P_2O_5})\), sulfuric acid \((\mathrm{H_2SO_4})\), or calcium chloride \((\mathrm{CaCl_2})\), which should be used with some caution because of the possibility of partial absorption of \(\mathrm{CO_2}\) after unsuccessful calcination.

A second moisture absorber \(d_2\) is installed as a control, and to absorb water vapor that has not settled in the first absorber \(d_1\) in the event of its possible saturation. Thus, dry gases will pass through the gas meter \(e\), the quantity of which will be known as \(V_{c2}\), \(\mathrm{m^3}\) ¹). (\(V_{c2}\) is the gas volume reduced to normal conditions.) The weight of the water vapors deposited in the apparatus will also be known—\(g_v\), g, corresponding to the volume of dry gases \(V_{c2}\).

\[ g_v = g_1 + g_2 + g_3\ \mathrm{g}, \]

where \(g_1\), \(g_2\), and \(g_3\) are respectively the weights, in grams, of the condensed water vapors in the condenser receiver \(c\), in the first and second absorbers \(d_1\) and \(d_2\).

It is further necessary to take into account that the condensate formed in the apparatus, \(g_v\), is obtained not only at the expense of the moisture of the fuel \(W_p\) and as a result of the combustion of the hydrogen of the fuel \(H_p\), but also at the expense of the water vapor that entered the boiler gas duct with the air. The corresponding calculations show that neglect of this quantity gives an error in determining the volume of dry gases \(V_{c2}\), \(\mathrm{m^3/kg}\), of approximately

¹) If a wet gas meter is installed, when determining \(V_{c2}\) it is necessary to introduce a correction for the change in volume due to humidification of the gas in the meter. In this case, an additional moisture absorber is installed after the meter.

at 6% with an absolute air humidity \(\gamma_d = 3\ \mathrm{g/m^3}\) for the average working composition of hard coals.

If we denote

\(V_g^{v}\)—the actual quantity of air arriving per 1 kg of fuel in the last gas duct of the boiler, allowing for infiltration through the brickwork, in \(\mathrm{m^3/kg}\);

\(d\)—the moisture content in the air, in \(\mathrm{g/m^3}\);

\(H^p\) and \(W^p\)—the content of hydrogen and moisture in the working fuel, in %, then the total amount of moisture arriving per 1 kg of fuel will be

\[ G_v = 90H^p + 10W^p + V_g^{v}d\ \mathrm{g/kg}. \]

Then the total volume of dry gases is found from the expression

\[ V_{c2}=v_{c2}\frac{G_v}{g_v} = v_{c2}\frac{90H^p+10W^p+V_g^{v}d}{g_v}\ . \ . \ . \ . (1) \]

Here \(V_{c2}\), \(g_v\), and \(d\) are determined from the experiment; \(H^p\), \(W^p\) are known from the composition of the working fuel. The air volume \(V_g^{v}\) may be expressed through \(V_{c2}\) in the following way.

From the combustion reactions

\[ \begin{aligned} C + O_2 &= CO_2\\ S + O_2 &= SO_2\\ 2C + O_2 &= 2CO\\ 2H_2 + O_2 &= 2H_2O \end{aligned} \]

it follows that each cubic meter of oxygen entering with the air, upon reacting with the combustible elements of the fuel, yields, as a result of complete combustion of \(C\), \(S\), and \(H\), \(1\ \mathrm{m^3}\ CO_2\), \(1\ \mathrm{m^3}\ SO_2\), and \(2\ \mathrm{m^3}\ H_2O\), and, as a result of incomplete combustion of \(C\), \(2\ \mathrm{m^3}\ CO\).

Consequently, the change in the volume of dry gases \(V_{c2}\), as compared with the actual quantity of air supplied \(V_g^{v}\), will occur only due to incomplete combustion of carbon \(C\) to \(CO\) and due to the combustion of hydrogen \(H^p\) to \(H_2O\) (we assume the combustion of hydrogen to be complete). From the combustion of \(C\) to \(CO\), the volume will increase by the amount of oxygen required for the combustion of \(C\) kg of carbon to \(CO\). Since the amount of carbon burned to \(CO\) is equal to

\[ 0.536\,\frac{CO}{100}\,V_{c2}\ \mathrm{kg/kg}, \]

and per 1 kg of carbon, when it is burned to \(CO\), it is necessary to supply oxygen (according to the combustion reaction)

\[ \frac{\mu_{O2}}{\mu_{2C}\cdot \gamma_{O2}} = \frac{32}{24\cdot 1.429} = 0.93\ \mathrm{m^3/kg}, \]

then the increase in the total volume of gases from incomplete combustion of carbon \(C\) into \(CO\) will be

\[ 0.93 \cdot 0.536 \frac{CO}{100} V_{c2} = 0.005 \cdot CO \cdot V_{c2}\ \text{m}^3/\text{kg}, \]

which is equal to the volume of oxygen \((0.760)\) required for the combustion of \(C\) kg of carbon into \(CO\).

When hydrogen \(H^p\) burns to \(H_2O\), the volume will decrease by the amount of oxygen required for the combustion of \(H^p\). Since for each kg of hydrogen, in its complete combustion, it is necessary to supply \(5.6\ \text{m}^3\) of oxygen, and the amount of hydrogen in 1 kg of fuel is equal to \(0.01 H^p\ \text{kg}/\text{kg}\), the decrease in the volume of gases in this case will be

\[ 5.6 \cdot 0.01 H^p = 0.056 H^p\ \text{m}^3/\text{kg}. \]

Consequently, the volume of dry gases in the given gas duct will be

\[ V_{c2} = V_g^v + 0.005 \cdot CO \cdot V_{c2} - 0.056 \cdot H^p\ \text{m}^3/\text{kg}, \]

whence

\[ V_g^v = V_{c2} + 0.056 H^p - 0.005 \cdot CO \cdot V_{c2} \ . . . . . . \ (2) \]

Substituting the value of \(V_g^v\) from equation (2) into equation (1), we shall have

\[ V_{c2} = v_{c2} \frac{ 90 H^p + 10 W^p + [V_{c2}(1 - 0.005 CO) + 0.056 H^p]d }{ g_v }. \]

Solving this equation with respect to \(V_{c2}\), we obtain

\[ V_{c2} = v_{c2} \frac{ 90 H^p + 10 W^p + 0.056 H^p d }{ g_v v_{c2} d (1 - 0.005 CO) } \ , . . . . . \ (3) \]

Since the value of \(CO\) is usually small, the factor in parentheses in the denominator may be neglected. Then the direct determination from experiment of the percentage content of \(CO\) is not obligatory.

Further, from the equation for the volume of dry gases,

\[ V_{c2} = 1.86 \frac{K_1^p}{RO_2 + CO}\ \text{m}^3/\text{kg}, \]

knowing the gas composition from gas analysis, one can determine the fictitious quantity of carbon burned,

\[ K_1^p = 0.54 V_{c2}(RO_2 + CO)\% \ . . . . . . . . \ (4) \]

In the case when \(CO\) is not determined directly by gas analysis (and its determination by analysis is laborious and unreliable), the value \(K_1^p\) may be calculated in the following way. Carbon monoxide may be determined by the known formula

\[ CO = \frac{1}{0.6 + \beta'}[21 - \beta' RO_2 - (RO_2 + O_2)]\%, \]

where the characteristic of the burned fuel is

\[ \beta'=\frac{D}{K_1^p}+0.005; \qquad D=2.38\left(H^p-\frac{O^p}{8}\right). \]

Substituting the value of \(\beta'\) into the expression for \(CO\), we shall have

\[ CO=\frac{1}{0.605+\frac{D}{K_1^p}} \left[21-\frac{D}{K_1^p}RO_2-(1.005RO_2+O_2)\right]\%. \]

Taking the notation \(E=1.005RO_2+O_2\) and making the corresponding transformations, we have

\[ CO=\frac{(21-E)K_1^p-D.RO_2}{0.605K_1^p+D}\%. \]

Substituting the found value of \(CO\) into equation (4) and introducing the notation \(F=0.54\,V_{c2}\), we shall have

\[ K_1^p=F.RO_2+\frac{F(21-E)K_1^p-F.D.RO_2}{0.605K_1^p+D}\%, \]

whence, after the corresponding transformations, we obtain the quadratic equation

\[ 0.605K_1^{p2}-\left[(21-E)F-D+0.605.F.RO_2\right]K_1^p=0. \]

Denoting the expression in square brackets by \(M\) and solving this equation with respect to \(K_1^p\), we have

\[ K_1^p=\frac{M+\sqrt{M^2}}{2.0.605}=\frac{M}{0.605} =\frac{(21-E)F-D+0.605.F.RO_2}{0.605}\%. \]

Replacing \(D\), \(E\), and \(F\) by their values and carrying out the corresponding transformations, we obtain the expression for \(K_1^p\) in its final form

\[ K_1^p= \frac{ V_{c2}(11.34-0.54.O_2-0.216.RO_2)-2.38\left(H^p-\frac{O^p}{8}\right) }{0.605}\% \ldots (5) \]

In the expressions for \(K_1^p\) (4) and (5), the value \(V_{c2}\), determined from equation (3), is substituted. From \(K_1^p\), found from expression (5), \(\beta'\) is determined, and then \(CO\), necessary for calculating the loss \(Q_3\).

We now have data for determining all losses of the boiler unit. After determining, by formula (3), the volume of dry gases \(V_{c2}\), the heat losses with the outgoing gases are calculated as

\[ Q_2=\left[V_{c2}+0.0124(9H^p+W^p)\right]C_2(T_y-t_b)-C_m(t_m-t_b)\ \text{kcal/kg}. \quad (6) \]

and from chemical incompleteness of combustion

\[ Q_3=30.5\cdot V_{c2}\cdot CO\ \text{kcal/kg}. \ldots\ldots\ldots (7) \]

Thus, the losses \(Q_2\) and \(Q_3\) are now determined independently of the loss \(Q_4\), the incorrect determination of which, in the ash-balance method, immediately affects the values of the other losses.

The total loss from mechanical incompleteness of combustion will be found, after calculating the value \(K_1^p\) (by equation 5 or 4), from the expression

\[ Q_4 = 80.5\left(C^p + 0.368 S_{\ell}^{p} - K_1^p\right)\ \text{cal/kg} \ . . . (8) \]

Thus, in determining this loss \(Q_4\), it is entirely unnecessary to know the weight of slag and siftings; average samples and technical analysis of slag, siftings, and carryover are also not needed.

This circumstance can sometimes greatly facilitate carrying out the test, especially when one has to deal with large installations producing a large amount of slag, since, in view of the great heterogeneity of the latter, the average sample must be selected very carefully.

When tests are carried out in greater detail, the losses with slag \(Q_4^{ш}\) and with siftings \(Q_4^{п}\) may be determined separately by the usual method

\[ Q_4^{ш} = 80.5 \frac{G_{ш}\cdot Z_{ш}}{B}\ \text{cal/kg} \ . . . . . . . . (9) \]

\[ Q_4^{п} = 80.5 \frac{G^{п}\cdot Z^{п}}{B}\ \text{cal/kg} \ . . . . . . . . (10) \]

where \(G^{ш}\), \(G^{п}\), and \(B\) are the hourly (or for the entire test) quantities of slag, siftings, and fuel in kg.

\(Z_{ш}\) and \(Z_{п}\) are the combustible matter of slag and siftings in %, determined by technical analysis.

Here the calorific value of the combustible matter of slag and siftings is taken as \(8050\ \text{cal/kg}\).

The loss with carryover is then found as the difference

\[ Q_4^{у} = Q_4 - (Q_4^{ш} + Q_4^{п})\ \text{cal/kg} \ . . . . . . (11) \]

The loss \(Q_5\) to the surrounding medium, if there are no data for determining its magnitude, may be found as a residual term

\[ Q_5 = Q_{н}^{p} - (Q_1 + Q_2 + Q_3 + Q_4)\ \text{cal/kg} \ . . . (12) \]

When carrying out a test by the method presented 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) Careful determination of the moisture content of the air is also obligatory, since failure to take these circumstances into account will inevitably entail inaccuracy in all subsequent calculations.

3) The capture of water vapor from the gases must be carried out continuously from the beginning to the end of the fuel test.

In addition, for a more complete approximation to the actual average composition of the gas, gas extraction must be carried out simulta—

simultaneously at several points across the cross-section of the gas flue, coordinating the suction velocity with the overall velocity of the gases in the duct.

4) For a more accurate conduct of the test, approximately 8–10 m³ of gas (0.760) must be passed through the apparatus, which, for an average operating composition of bituminous coals, will yield about 0.5 kg of water in the apparatus. Then the possible inaccuracy in the test will be reduced to a minimum.

5) For the same reasons, before the start of the test, when establishing the operating regime of the boiler, gas must be passed for some time through the installation (but past 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.

In conclusion it is necessary to note that:

1) this method assumes complete combustion of hydrogen, which does not entirely correspond to reality, and

2) the described arrangement of the installation for trapping water vapors has not been finally adopted. It is accepted as the first for implementing the idea set forth here concerning a new arrangement of the test. Its improvement and, perhaps, the creation of a special instrument for determining the amount of moisture in the exhaust gases must be carried out in parallel with a broad experimental verification of this method, which is planned by the Department of TSU TII in 1935.

SUMMARY.

In the present paper an idea of a new way of running an experiment in testing boiler plants and a way of determining the heat balance is given. The essential feature of this method consists in the following: in testing a boiler plant the volume of dry gases falling to 1 kg of burned fuel is ascertained. The gas, the amount of which is measured by means of a clocktype volumeter gas during the whole trial is continuously sucked off by means of an ejector from the gaspipe of the boiler plant. On the passage of the gas, before the gas volumer, a condenser and chemical absorbers, catching the water vapours from the gases which are sucked off, are installed. During the trial the dampness of the air entering the furnace is carefully determined and an average sample of the fuel is also very carefully selected in order to ascertain most precisely the dampness of its power composition. All these data including the composition of the working fuel allow to determine the volume of dry gases falling to 1 kg of the burned fuel. By the volume of dry gases found in this way a fictitious amount of the burned carbon (sulphur being reduced to carbon) is determined, after this the total heat balance may be entirely settled up.

In the presented procedure of the trial the further calculation of the heat balance offers the possibility to determine the stack losses of heat and those due to the chemical incompleteness of combustion, this being quite independant from the mechanical incompleteness of combustion which, as it is known, is not as yet to be exactly determine, especially in those cases when the loss from flue gases forms a considerable value.

The loss from the mechanical incompleteness of combustion is determined in this case very simply, there being no need during the trial to weigh or take average samples of clinker ashes and flue gases. There is also no need in their technical analysis.

The advantages of this method so simple by its conception consist in the following.

1. The determination of particular losses of the heat balance of a boiler plant is not related to the but as yet imperfectly defined loss due to the mechanical incompleteness of combustion.

2. In those cases when no differential determination of losses from the mechanical incompleteness of combustion by its components is required the procedure of the trial is considerably simplified, as all the operations with clinker ashes and flue gases usual in boiler tests drop off when carrying the trial out by the method given. This being of a greatest meaning when testing large plants giving a great amount of hearth residues very heterogenous in their composition.

3. The entire heat balance of the boiler plant may be estimated with a greater accuracy.

Diagram labels:

• \(a\)
• \(b\)
• Cooling-water outlet
• Cooling-water outlet
• \(c\)
• \(d_1\)
• \(d_2\)
• \(e\)
• \(t\)