Research of Exhaust Gas Boiler Heat Exchange Surfaces with Reduced Corrosion When Water-Fuel Emulsion Combustion ^†

Abstract

The application of water-fuel emulsion (WFE) in internal combustion engines enables to reduce the consumption of sulfurous fuel oils, thereby protecting the environment from emissions of sulfur and nitrogen oxides, as well revealing a great potential for the heat utilization of exhaust gases. The efficiency of utilization of exhaust gas heat in exhaust boilers (EGB) depends on their temperature at the outlet of EGB, id est. the depth of heat utilization. Exhaust gas temperature is limited by the rate of low-temperature corrosion (LTC), which reaches a level of 1.2 mm/year at the wall temperature of about 110 °C for the condensing heat exchange surfaces (HES) and reduces the reliability of the HES operation. Therefore, decreasing the corrosion rate of condensing HES at wall temperature below 110 °C to an acceptable level (about 0.2 mm/year) when undergoing WFE combustion will make it possible to reduce the exhaust gas temperature and, consequently, increase the efficiency of EGB and fuel saving during the operation of the ship power plant. The aim of the research is to assess improvements to the reliability, durability and efficient operation of condensing HES in marine EGB undergoing WFE combustion in a diesel engine based on experimental studies of the LTC process. A special experimental setup was developed for investigation. The use of WFE with a decreased wall temperature of HES below 80 to 70 °C would improve the reliability of the EGB along the accepted service life, increase the lifetime of the HES metal by almost six times as well as the overhaul period, and reduce the cost of repairing condensing HES. Furthermore, due to the reducing corrosion rate under WFE combustion, the application of low-temperature condensing HES makes it possible to enhance the efficiency of deeper exhaust gas heat utilization and provide sustainable efficient operation of a diesel engine plant on the whole at a safe thermal and environmentally friendly level.

1. Introduction

Various methods are used to protect the environment from emissions of sulfur and nitrogen oxides during the combustion of sulfurous fuel oils. Most of them are associated with the impact on the combustion process in order to suppress emissions, primarily NO_x and SO_x: exhaust gas recirculation [1], two-stage [2] and three-stage combustion [3], non-stoichiometric combustion [4], structural and technological improvement [5]. A combination of several methods is recommended [6,7].

The thermochemical method is currently considered the most effective and economical method for reducing the concentration of nitrogen oxides in thermal power engineering. The supply of water to the reaction zone is mainly carried out in two ways: by injecting steam or water into the air or into the core of the torch and by using water-fuel emulsion (WFE). The supply of moisture together with air in the amounts of 1.5–2% of the nominal steam output of the boiler reduces emissions of nitrogen oxides by 20–25% [8,9]. The explanation for changes in the outlet of toxic ingredients should be sought in the kinetics of combustion reactions and the formation of NO. The combustion process is accelerated due to the partial dissociation of water with the formation of an additional amount of atomic oxygen and H⁺ and OH⁻ radicals, taking into account the chain mechanism of fuel burnout. The water introduced into the reaction zone plays not only the role of a coolant, but also a chemical reagent. It is a source of active OH⁻ and H⁺ radicals, which significantly affect the process of NO and CO formation. Atomic oxygen forming at high temperatures in the presence of water vapor primarily reacts with H₂ and carbon, and much more difficultly with N₂. So, the concentration of atomic oxygen, which could form nitrogen oxides, decreases [10]. When water is added to the chamber, there is an effect called “microexplosion”, as a result of which mixture formation improves, the evaporation surface of the fuel increases. It contributes to more complete combustion and a decrease in the content of oxides in gases. According to Wang, Z. et al. the concentration of particulate matter (PM) depends on the fineness of the emulsion too [11,12]. The curve of the change in PM concentration has a pronounced minimum of 19 mg/m³ within the range of the emulsion dispersed phase sizes from 35 to 45 µm. This is caused by more intensive combustion due to “microexplosions” of WFE droplets. The NO_x concentration has a maximum of 200 mg/m³ within the same range of dispersed phase sizes from 35 to 45 µm. The latter is caused by some increase in the temperature of the torch due to intensification of the combustion process with the largest number of “microexplosions” of emulsion drops. There is a decrease in the temperature of the torch due to the suppression (blocking, ballasting) of the zone of active combustion with water vapor at larger sizes of the dispersed phase. In this case, the NO_x concentration decreases to 113 mg/m³ [11,12]. Studies of the fractional composition of PM in WFE combustion products revealed that the fineness of PM does not depend on the size of the WFE dispersed phase. However, there is a significant difference in the sizes of aggregates of these particles. Kim et al. found that an emulsified fuel created by blending water with diesel oil reduced the NO_x and soot in a 2456-cc diesel engine [13,14]. Lim et al. researched the combustion characteristics of emulsified fuels in a ship diesel engine and reduced NO_x emissions by approximately 30%, depending on the water content [15,16]. According to Lee, T.H. et al. the WFE combustion with water content 25% effects on the improvement in exhaust gas emissions were as follows: the oxygen (O₂) concentration increased by up to 4.2%, and that of carbon dioxide decreased by approximately 2.1% [17,18]. Under the standard O₂ concentration of 4%, the concentration of nitrogen oxides decreased by up to 31.41%, and that of sulfur oxides decreased by up to 37.47%. However, the exhaust gas temperature decreased by approximately 14.3%, and the combustion efficiency decreased by approximately 2.6% [18,19]. In studies by K.R. Patel et al., emulsified fuel created by blending approximately 10.6% water with Bunker C oil NO_x and SO_x emissions were reduced by approximately 30% [20,21].

Many technologies have been developed for purification flue gases from NO_x and SO_x, based on the absorption of higher oxides of these components by water and solutions of other liquids. Their mechanism reveals and explains the possibility of increasing the NO₂ content in the flue gas flow and in the condensate of water and acid vapors. For example, the introduction of a strong oxidizing agent (ozone) into flue gases [22,23]. During radiolysis of a gas flow with an increase in the content of water vapor at the same energy of radiolysis, a rapid increase in the concentration of NO₂ is observed. A little irradiation energy is required to obtain an equimolar mixture. Moreover, the higher the content of SO₂ in flue gases, the more “steeply” the SO₃ concentration curves decrease depending on the irradiation dose [22,24]. Similar ionic reactions can take place in a flue gas flow under the influence of the energy of acoustic waves arising as a result of WFE “microexplosions” at a high concentration of water vapor, and hence H⁺ and OH⁻ radicals.

On the condensing heat exchange surface (HES) the sulfuric acid H₂SO₄ vapors are first formed during the interaction of water vapor and SO₃. At 300 °C, the flue gases contain comparable amounts of H₂SO₄ and SO₃ vapors. Below 200 °C, flue gases contain only H₂SO₄ vapors. Since the combination of SO₃ and water vapor with the formation of acid ends in 3 × 10⁻⁴ s [25], at any gas temperature at a wall temperature t_st below the dew point temperature (DPT) of the H₂SO₄ vapors, the process of condensation of these vapors on the HES and low-temperature corrosion (LTC) occur.

There are no specific data in the literature on the rate of corrosion processes during WFE combustion. There is only indirect evidence of a decrease in the intensity of pollution and corrosion processes due to factors such as an increase in the period between cleaning and repair of heating surfaces of boilers [26,27], a change in the nature of corrosion, for example, economizer (transition from pitting to uniform corrosion) [28], reduction in deposits and retardation of corrosion, which prolongs the campaign between boiler shutdowns for cleaning, facilitating operation and maintenance [29,30].

The LTC rate values obtained as a result of studies lasting up to 1000 h during the combustion of conventional standard fuel oils with water content W^r = 2%, various amounts of sulfur content S^r and excess air coefficient α up to 1.45 are presented in numerous literature sources, for example [22,31]. These values were obtained at different durations of flue gas flow exposure: from 2 to 100 h [22,32] and up to 1000 h [33]. Moreover, LTC studies were mainly carried out on operating boilers, during the operation of which it is impossible to ensure the constancy of the parameters and, consequently, the corrosive properties of flue gases even for several hours.

Goryachkin, A. carried out an experimental study of corrosion of HES of the exhaust gas boiler (EGB), installed after the gas turbine engine (GTE), when diesel fuel combustion with a sulfur content S^r = 0.1% at excess air coefficient α equal to 6.5 and 8.4 [22]. The duration of corrosion tests was 15–19 h, the LTC rate was 0.24–0.32 g/(m² × h) (the DPT was 115 °C). The deposits were black, sooty, moistened, in appearance and properties the same as in the condensing boilers. Consequently, at the condensing HES of EGB, washed by the combustion products of the GTE, processes similar to those that take place in boilers with deep cooling of the combustion products develop [34].

The corrosive aggressiveness of the flow of combustion products leads to a restriction of the limits of the use of their energy in boilers due to the need to maintain certain temperatures of the heating surfaces, at which the corrosion rate is within acceptable limits (0.2–0.3 mm/year) [22,35]. The lower limit is due to a sharp increase in LTC at temperatures of the HES wall below 130–140 °C, which is due to the condensation of H₂SO₄ vapors. The appearance of acid condensate on the HES also leads to electrochemical corrosion and a sharp increase in the rate of corrosion processes. The so-called “acid peak” of corrosion appears, which significantly limits the temperature of the exhaust gases [36,37], and, consequently, the depth of energy utilization of the combustion products [38,39]. Deep exhaust heat utilization increases the heat potential to be transformed to refrigeration [40,41] in trigeneration plants and for cooling sucked air in combustion engines [42,43] including gas turbines [44,45] and widens the application of low-temperature condensing surfaces in marine EGB. In turn, the use of refrigeration enabled due to deep exhaust heat utilization for engine cyclic air cooling allows fuel saving with a corresponding reduction of harmful emissions and sustainable, efficient operation of the engine at a safe thermal and environmentally friendly level [46,47].

According to Wang, Z. et al., the LTC mechanism under a layer of moistened deposits in boilers is similar to the processes of soil and atmospheric corrosion and therefore it becomes possible to use the results of studying the regularities of these processes [48]. The LTC intensity is determined primarily by the mass flow of H₂SO₄ vapors to the metal surface, which depends on their content in the flue gases and the temperature difference between the gases and the wall. In the steady (basic) mode of corrosion, the protective properties of the layer of corrosion products have a significant effect. As Melchers, R.E. et al. showed, in most cases the temperature has a significant effect on the electrochemical corrosion of metals [49].

The analysis of the literature data indicates that the combustion of WFE has a positive effect on the environmental and economic performance of fuel-burning devices and on the corrosion properties of combustion products at the same time. The data on the corrosion of condensing HES are scarce and qualitative, while quantitative data on the intensity of corrosion of such HES during WFE combustion are almost absent. It is necessary to studies of the corrosion process on condensing HES, when WFE combustion with water content 30%, the coefficient of excess air α = 2.9, which corresponds to the parameters of flue gases in the EGB.

The aim of the research is to assess improving the reliability, durability, and efficient use of condensing HES in marine EGB when WFE combustion in a diesel engine based on experimental studies of the LTC process. The following tasks are to be solved:

−

Data analysis and theoretical substantiation of the possibility of reliable prediction of corrosion processes for a long time on the basis of experimental studies of the scientific and technological complex for 2–12 h;

−

Development of a mathematical model to study the influence of variable values of wall temperature t_w and excess air coefficient α on the corrosion process intensity;

−

Conducting comprehensive studies of the effect of water content in WFE W^r, sulfur content in the fuel oil S^r and the excess air coefficient α on the LTC processes intensity;

−

Assessment of the reliability of the obtained results of studies of corrosion processes;

−

Determination of admissible values of LTC rate, that limit not only the reliability of condensing HES operation, but also the exhaust gas temperature values, on the value of which the efficiency of EGB depends.

2. Materials and Methods

Experimental Research

Flow chart of the research in the intensity of LTC on condensing HES is presented in Figure 1. Setting up industrial experiments to determine the development of corrosion process over time is fraught with great difficulties. It requires the stabilization of a large number of regime parameters and the invariance of the fuel composition throughout the experiments. However, the observance of these conditions does not ensure the reproducibility of the formation of SO₃ as a source of the appearance of H₂SO₄ vapors in flue gases. Therefore, it is desirable to conduct short, but reliable studies. A special experimental set-up (Figure 2) was used for studies.

In order to assess the intensity of the LTC, as well as to compare the LTC rate when different fuel oils undergo combustion in different combustion modes, it was decided that the kinetics of corrosion processes would be studied. This provides almost the same conditions for exposure to a corrosive environment with constant parameters when conducting research on the experimental setup and, consequently, sufficient reproducibility of the conditions for conducting experiments. In order to ensure the reliability of the experiments when conducting studies of corrosion processes during the combustion of WFE in an experimental setup, first, studies were carried out with the combustion of fuel oils for which there are literature data with the results of long-term experiments conducted on operating boilers or laboratory units, and then with the WFE combustion.

Furnace dimensions were 800 × 300 mm. The volumetric heat release density of the furnace space is 0.31 MW/m³ when 1 kg/h combustion. The hot air temperature was 150–180 °C. The removal of flue gases from the setup is carried out by a smoke exhauster. Much attention in the development and adjustment of the experimental setup was paid to supply to the burner 1–3 kg/h of fuel oil with a viscosity of 2–2.5 μm. Fuel oil from the tanks of the main reserve, where it is heated to a temperature of 70–90 °C, is fed by a gear pump through a double filter into the supply tank.

The complexity of the operation of this fuel system lies in the need to supply a small amount of fuel for consumption during the entire experiment (up to 100 h). Such a small flow rate is achieved by supplying fuel from the supply tank through the dropper by gravity. Since the supply of the gear pump is much larger, a fuel recirculation system is provided through the measuring tank to the main reserve tank. The operation of the gear pump, the presence of a recirculation system, through which most of the fuel is removed, also ensures the stabilization of the emulsion composition during WFE combustion.

Analysis of flue gas composition at the furnace outlet was carried out by a chemical gas analyzer (determination of RO₂, O₂, SO_x and NO_x) and chromatograph (determination of CO, H₂, and CH₄). Determination of the velocity and flow rate of flue gases in the gas duct was carried out using a high-speed pipe and a flowmeter (

Table 1. Equipment specification.

Parameter	Equipment	Range	Unit
Flue gas velocity	High-speed pipe	0–25	m/s
Flue gas flow	Flowmeter	0–25	m3/h
Flue gas temperature	Resistance thermoconverter	−40–270 °C	°C
Flue gases composition	Gas analyzers, chromatograph	0–100 mL -	mL Vol, %
Sample length	Digital calipers	0–200	mm
Sample diameter	Micrometer	0–25	mm
Sample weigh	Analytical balance	0–200	mg
Sample temperature	Resistance thermoconverter	−40–270 °C	°C

).

A working section of pipe samples for LTC research was installed at the flue gas temperature level of 350 °C. The pipe samples were simultaneously placed in the gas duct, which were then removed sequentially after the lapse of time intervals (2, 4, 8, 12 h). The scheme of the working area is shown in Figure 3.

The plate (1) was used for mounting a package of the collected pipe samples (2) from the studied steel grades. Each sample was fastened with a hollow screw (3), a nut (4), and a spring (5), thereby compensating for the thermal expansion of the samples. Samples were collected on the plate in a checkerboard pattern with steps S₁ and S₂ equal to 30 mm. Sleeves (6) were welded before and after the package for the installation of thermometers or thermocouples for flue gas temperature measurement. Pipes (7) for measuring vacuum before and after the stack of pipes and sampling flue gases for analysis were installed. Cooling of the pipe samples was carried out by supplying water through the hollow screw and the annular gap between the pipe and the screw. Flue gas dew point temperature (DTP) sensors (8) were installed before and after the working area for the LTC study. The investigation was performed within the range of wall temperature t_w from 70 to 140 °C [20,35]. Before the experiments, the samples were weighed on an analytical scale. The sample mass is designated as m₁. After the experiments pipe samples with corrosion products were weighed (mass m₂). Figure 4 shows a scheme of the sample treatment procedure for LTC studies. The removal of deposits and corrosion products from the metal surface was carried out by treating the samples in a 5% solution of hydrochloric acid inhibited by urotropin (1 g per 1 L of solution). Then, the sample was washed in water and B-70 gasoline, dried and weighed again (mass m₃).

The corrosion rate ΔG of the HES was calculated according to correlation

$$\Delta \mathrm{G}=\frac{{\mathrm{m}}_1-{\mathrm{m}}_3}{\mathrm{F}}$$

(1)

where m₁—mass of sample before experiment, g; m₃—mass of sample after cleaning of corrosion products and soot deposits, g; F—average area of the outer surface of the sample, m².

The corrosion rate K of the HES was determined as

$$\mathrm{K}=\frac{\Delta \mathrm{G}}{\mathsf{\tau }}$$

(2)

where τ—duration of experiment, h.

Approximation of the experimental data on the mass loss of metal (corrosion depth) was carried out in the form of a power relation, as suggested by many authors [20,22,35] in the form $\mathsf{\Delta }\mathrm{G}=\mathrm{A}\times {\mathsf{\tau }}^{\mathrm{n}}$; where A, n are constant coefficients, which determine the nature of the curve. The mathematical tools of the Microsoft Office software package, in particular Microsoft Excel, were used to search for the coefficients. Based on the obtained data, approximate dependences of the corrosion kinetics on the time of exposure to flue gases can be found: mass loss of metal ΔG = f (τ); corrosion rate K = f (τ) = (ΔG)′; acceleration of corrosion K′ = f (τ) = (ΔG)″.

3. Results

3.1. Influence of HES Metal Wall Temperature and Excess Air Coefficient on the Corrosion Process

The main factors influencing the intensity of LTC are the metal surface temperature t_w, on which H₂SO₄ vapor condenses, and the excess air coefficient α, which affects not only the intensity of the formation of SO₃ and H₂SO₄ vapor and the mass flow of acid to the surface, but also the rate of electrochemical LTC, since excess O₂ in air is a depolarizer. A change in the values of α is often observed when boilers operate in variable modes, for example, when combustion is regulated. Fluctuations of α lead to a change in the corrosion rate, especially in the area of the “acid peak”.

Accounting for these processes is necessary in the course of analysis of data on corrosion of boiler pipes under variable combustion conditions, and especially when these results compare with the results of laboratory studies that are carried out at constant α.

The patterns of change in corrosion characteristics with fluctuations of α are of the same nature as with temperature changes. A significant difference in the influence of α is the strict dependence of the direction of change in the corrosion intensity (mass loss of metal) on α: with decreasing α the mass loss of metal reduces, and vice versa, with rising α it increases, that is caused by changes in the amount of oxygen in the flue gases. Taking into account the theoretical provisions of electrochemical corrosion, the activation energy E_i of the corrosion process with oxygen depolarization is determined by the value of the partial pressure of oxygen ${\mathrm{P}}_{{\mathrm{O}}_2}$, therefore, when α changes, it should change too.

Since the spontaneous passage of electrochemical dissolution of the metal occurs if the reversible potential of the metal ${\left({\mathrm{U}}_{\mathrm{Me}}\right)}_{\mathrm{rev}}$ is less than the reversible potential of the oxygen electrode [22], the corrosion rate, other things being equal, will be equal to

$${\mathrm{K}}_{\mathrm{M}}=\mathrm{A}\times {\mathrm{e}}^{-\mathrm{E}/\mathrm{RT}}={\left({\mathrm{U}}_{\mathrm{Me}}\right)}_{\mathrm{rev}}-{\left({\mathrm{U}}_{{\mathrm{O}}_2}\right)}_{\mathrm{rev}}$$

(3)

$$\ln \frac{{\mathrm{P}}_{{\mathrm{O}}_2}}{{\mathsf{\alpha }}_{\mathrm{O}\overline{\mathrm{H}}}^4}=\left[{\left({\mathrm{U}}_{\mathrm{Me}}\right)}_{\mathrm{rev}}-{\left({\mathrm{U}}_{{\mathrm{O}}_2}\right)}_{\mathrm{rev}}^0-\mathrm{A}\times {\mathrm{e}}^{-\mathrm{E}/\mathrm{RT}}\right]\times 4\mathrm{F}/\mathrm{RT}$$

(4)

$${\mathrm{P}}_{{\mathrm{O}}_2}={\mathsf{\alpha }}_{\mathrm{O}\overline{\mathrm{H}}}^4\times \exp \left\{\left[{\left({\mathrm{U}}_{\mathrm{Me}}\right)}_{\mathrm{rev}}-{\left({\mathrm{U}}_{{\mathrm{O}}_2}\right)}_{\mathrm{rev}}^0-\mathrm{A}\times {\mathrm{e}}^{-\mathrm{E}/\mathrm{RT}}\right]\times 4\mathrm{F}/\mathrm{RT}\right\}$$

(5)

With complete combustion of fuel, α is related to ${\mathrm{P}}_{{\mathrm{O}}_2}$ (in kPa) by the equation ${\mathrm{P}}_{{\mathrm{O}}_2}=21-21/\mathsf{\alpha }$ whence $\mathsf{\alpha }=21/(21-{\mathrm{P}}_{{\mathrm{O}}_2}$). Therefore, with a known value of the activation energy E_i at a given temperature and other conditions being equal, it is possible to determine the value α_i corresponding to this mode

$${\mathsf{\alpha }}_{\mathrm{i}}=\frac{21}{21-{\mathsf{\alpha }}_{\mathrm{O}\overline{\mathrm{H}}}^4\times \exp \left\{\left[{\left({\mathrm{U}}_{\mathrm{Me}}\right)}_{\mathrm{rev}}-{\left({\mathrm{U}}_{{\mathrm{O}}_2}\right)}_{\mathrm{rev}}^0-\mathrm{A}\times {\mathrm{e}}^{-{\mathrm{E}}_{\mathrm{i}}/\mathrm{RT}}\right]\times 4\mathrm{F}/\mathrm{RT}\right\}}$$

(6)

Therefore, it is possible to determine the value of E_i with a known value α_i

$${\mathrm{E}}_{\mathrm{i}}=-\mathrm{RT}\times \ln \left[{\left({\mathrm{U}}_{\mathrm{Me}}\right)}_{\mathrm{rev}}-{\left({\mathrm{U}}_{{\mathrm{O}}_2}\right)}_{\mathrm{rev}}^0-\frac{\mathrm{RT}}{4\mathrm{F}}\ln \frac{21-21/{\mathsf{\alpha }}_{\mathrm{i}}}{{\mathsf{\alpha }}_{\mathrm{O}\overline{\mathrm{H}}}^4}\right]$$

(7)

Thus, the value of E_i depends on the value of α_i (when excess air coefficient α increases the content of O₂ in the flue gases increases, the activation energy decreases, which leads to the intensification of corrosion).

Consider the determination of the corrosion characteristics of a material with a stepwise change in α (on each i-th section, the processes proceed at a constant temperature and α), Figure 5.

Since α remains constant at separate time intervals, the total change in the mass of the metal is expressed as

$$\mathrm{g}={\mathrm{k}}_0{\displaystyle \sum }_{\mathrm{i}=1}^{\mathrm{m}}\exp \left(-{\mathrm{E}}_{\mathrm{i}}/{\mathrm{RT}}_{\mathrm{i}}\right)\left({\mathsf{\tau }}_{\mathrm{i}+1}^{\mathrm{n}\left({\mathsf{\alpha }}_{\mathrm{i}}\right)}-{\mathsf{\tau }}_{\mathrm{i}}^{\mathrm{n}\left({\mathsf{\alpha }}_{\mathrm{i}}\right)}\right)$$

(8)

(${\mathrm{k}}_0$—the pre-exponential factor in the Arrhenius equation).

or average corrosion rate

$$\overline{\mathrm{K}}\left(0,\mathsf{\tau }\right)={\mathrm{k}}_0{\mathsf{\tau }}_{\mathrm{m}+1}^{-1}{\displaystyle \sum }_{\mathrm{i}=1}^{\mathrm{m}}\exp \left(-{\mathrm{E}}_{\mathrm{i}}/{\mathrm{RT}}_{\mathrm{i}}\right)\left({\mathsf{\tau }}_{\mathrm{i}+1}^{\mathrm{n}\left({\mathsf{\alpha }}_{\mathrm{i}}\right)}-{\mathsf{\tau }}_{\mathrm{i}}^{\mathrm{n}\left({\mathsf{\alpha }}_{\mathrm{i}}\right)}\right)$$

(9)

The exponent n in this case depends only on α at a constant temperature. The specific change in the mass loss of metal over the time interval (${\mathsf{\tau }}_{\mathrm{k}+1},{\mathsf{\tau }}_{\mathrm{k}}$) is:

$${\mathsf{\Delta }\mathrm{g}}_{\mathrm{k}}\left({\mathsf{\tau }}_{\mathrm{k}+1},{\mathsf{\tau }}_{\mathrm{k}}\right)={\mathrm{k}}_0\left[{\displaystyle \sum }_{\mathrm{i}=1}^{\mathrm{k}+1}\exp \left(-{\mathrm{E}}_{\mathrm{i}}/{\mathrm{RT}}_{\mathrm{i}}\right)\left({\mathsf{\tau }}_{\mathrm{i}+1}^{\mathrm{n}\left({\mathsf{\alpha }}_{\mathrm{i}}\right)}-{\mathsf{\tau }}_{\mathrm{i}}^{\mathrm{n}\left({\mathsf{\alpha }}_{\mathrm{i}}\right)}\right)-{\displaystyle \sum }_{\mathrm{i}=1}^{\mathrm{k}}\exp \left(-{\mathrm{E}}_{\mathrm{i}}/{\mathrm{RT}}_{\mathrm{i}}\right)\left({\mathsf{\tau }}_{\mathrm{i}}^{\mathrm{n}\left({\mathsf{\alpha }}_{\mathrm{i}-1}\right)}-{\mathsf{\tau }}_{\mathrm{i}-1}^{\mathrm{n}\left({\mathsf{\alpha }}_{\mathrm{i}-1}\right)}\right)\right]$$

(10)

or corrosion rate over time $\Delta {\mathsf{\tau }}_{\mathrm{k}}={\mathsf{\tau }}_{\mathrm{k}+1}-{\mathsf{\tau }}_{\mathrm{k}}$

$$\mathrm{k}\left({\mathsf{\tau }}_{\mathrm{k}+1},{\mathsf{\tau }}_{\mathrm{k}}\right)={\mathrm{k}}_0{\left({\mathsf{\Delta }\mathsf{\tau }}_{\mathrm{k}}\right)}^{-1}\left[{\displaystyle \sum }_{\mathrm{i}=1}^{\mathrm{k}+1}\exp \left(-{\mathrm{E}}_{\mathrm{i}}/{\mathrm{RT}}_{\mathrm{i}}\right)\left({\mathsf{\tau }}_{\mathrm{i}+1}^{\mathrm{n}\left({\mathsf{\alpha }}_{\mathrm{i}}\right)}-{\mathsf{\tau }}_{\mathrm{i}}^{\mathrm{n}\left({\mathsf{\alpha }}_{\mathrm{i}}\right)}\right)-{\displaystyle \sum }_{\mathrm{i}=1}^{\mathrm{k}}\exp \left(-{\mathrm{E}}_{\mathrm{i}}/{\mathrm{RT}}_{\mathrm{i}}\right)\left({\mathsf{\tau }}_{\mathrm{i}}^{\mathrm{n}\left({\mathsf{\alpha }}_{\mathrm{i}-1}\right)}-{\mathsf{\tau }}_{\mathrm{i}-1}^{\mathrm{n}\left({\mathsf{\alpha }}_{\mathrm{i}-1}\right)}\right)\right]$$

(11)

Corrosion kinetic diagrams can also be used to determine the total value of Δg during corrosion, as shown in Figure 6. In this case, the ones shown in Figure 5 are designations.

Since the growth of the oxide film and corrosion products on the metal surface is a continuous process (assuming that there are no sharp changes in its structure during corrosion), the transition from one level of the value of α to another can proceed only along a line parallel to the time axis (in logarithmic coordinates). From here, according to the data (Figure 6), as well as from Equations (8) and (10), it follows that when the corrosion characteristics are calculated under conditions of a stepwise change in the value of α, it is necessary to follow the sequence of its change in time.

The change in Δg (along the abscissa axis) in value occurs differently, depending on the switching to a mode with a smaller or larger value of α. When switching to a mode with a smaller α, the value of Δg is less, and to a mode with a larger α, the value of Δg is greater. However, there will always be a horizontal movement of the transition point when switching from mode to mode. The slope angle of the line Δg depends on the intensity of the corrosion process. Thus, based on the stepwise change in α over time, using Equation (8) or using the kinetic corrosion diagram (Figure 6), it is possible to calculate the total mass loss of metal $\mathrm{g}={\displaystyle \sum }_{\mathrm{i}=1}^{\mathrm{m}}{\mathsf{\Delta }\mathrm{g}}_{\mathrm{i}}$ or depth $\mathsf{\delta }={\displaystyle \sum }_{\mathrm{i}=1}^{\mathrm{m}}{\mathsf{\delta }}_{\mathrm{i}}$ over time $\mathsf{\tau }={\displaystyle \sum }_{\mathrm{i}=1}^{\mathrm{m}}{\mathsf{\Delta }\mathsf{\tau }}_{\mathrm{i}}$.

For the general characteristics of metal corrosion under conditions of variable α, the concept of an equivalent excess air coefficient α_e is used, in which the total decrease in the specific mass of the corroding material is equal to the same value during corrosion under conditions of variable α during the actual operating time. The use of the concept of equivalent α allows us to conditionally replace its complex change with one value. In accordance with Equations (6) and (8), the equivalent α_e with a stepwise change in α can be defined as ${\mathsf{\alpha }}_{\mathrm{e}}={\displaystyle \sum }_{\mathrm{i}=1}^{\mathrm{n}}{\mathsf{\alpha }}_{\mathrm{i}}$.

The equivalent value of the activation energy E_e, which takes into account the change in flue gases, can be determined from the equation

$${\mathrm{k}}_0\exp \left(-{\mathrm{E}}_{\mathrm{e}}/{\mathrm{RT}}_{\mathrm{i}}\right){\mathsf{\tau }}^{\mathrm{n}\left({\mathsf{\alpha }}_{\mathrm{e}}\right)}={\mathrm{k}}_0{\displaystyle \sum }_{\mathrm{i}=1}^{\mathrm{m}}\exp \left(-{\mathrm{E}}_{\mathrm{i}}/{\mathrm{RT}}_{\mathrm{i}}\right)\left({\mathsf{\tau }}_{\mathrm{i}+1}^{\mathrm{n}\left({\mathsf{\alpha }}_{\mathrm{i}}\right)}-{\mathsf{\tau }}_{\mathrm{i}}^{\mathrm{n}\left({\mathsf{\alpha }}_{\mathrm{i}}\right)}\right)$$

(12)

If the exponent of the corrosion function does not depend on the value of α, then the value of E_e associated with α_e will be determined as follows

$${\mathrm{E}}_{\mathrm{e}}={\mathrm{RT}}_{\mathrm{i}}{\left[\ln \frac{{\mathsf{\tau }}^{\mathrm{n}}}{{{\displaystyle \sum }}_{\mathrm{i}=1}^{\mathrm{m}}\exp \left(-{\mathrm{E}}_{\mathrm{i}}/{\mathrm{RT}}_{\mathrm{i}}\right)\left({\mathsf{\tau }}_{\mathrm{i}=1}^{\mathrm{n}}-{\mathsf{\tau }}_{\mathrm{i}}^{\mathrm{n}}\right)}\right]}^{-1}$$

(13)

The value of E_i can be found from Equation (7). The value of E_e can be found as the sum ${\displaystyle \sum }_{\mathrm{i}=1}^{\mathrm{n}}{\mathrm{E}}_{\mathrm{i}}$.

With the dependence of the degree of the metal corrosion function on α, in order to find the equivalent energy E_e and, consequently, the excess air, it is necessary to solve the following equation:

$$\exp \left(-{\mathrm{E}}_{\mathrm{e}}/{\mathrm{RT}}_{\mathrm{i}}\right){\mathsf{\tau }}^{\mathrm{n}\left({\mathsf{\alpha }}_{\mathrm{e}}\right)}-{\displaystyle \sum }_{\mathrm{i}=1}^{\mathrm{m}}\exp \left(-{\mathrm{E}}_{\mathrm{i}}/{\mathrm{RT}}_{\mathrm{i}}\right)\left({\mathsf{\tau }}_{\mathrm{i}+1}^{\mathrm{n}\left({\mathsf{\alpha }}_{\mathrm{i}}\right)}-{\mathsf{\tau }}_{\mathrm{i}}^{\mathrm{n}\left({\mathsf{\alpha }}_{\mathrm{i}}\right)}\right)=0$$

(14)

The equivalent value of α_e with a stepwise change in α can be determined explicitly using the metal corrosion kinetic diagram based on experimental studies at various α (Figure 6). In this diagram, the equivalent α_e is on the line of constant α passing through a point with parameters (g, τ). This point is labeled A.

If the degree of dependence of the metal corrosion process depends on α, then

$${\mathrm{E}}_{\mathrm{e}}={\mathrm{RT}}_{\mathrm{i}}{\left[\ln \frac{{\mathsf{\tau }}^{\mathrm{n}\left(\mathsf{\alpha }\right)}}{{{\displaystyle \sum }}_{\mathrm{i}=1}^{\mathrm{m}}\exp \left(-{\mathrm{E}}_{\mathrm{i}}/{\mathrm{RT}}_{\mathrm{i}}\right){\mathsf{\Delta }\mathsf{\tau }}_{\mathrm{i}}{}^{\mathrm{n}\left(\mathsf{\alpha }\right)}}\right]}^{-1}$$

(15)

The above equations for calculating the corrosion characteristics are fundamentally applicable to the initial stage of the corrosion process.

With a simultaneous change in the temperature of the metal t_w and the excess air coefficient α, the intensity of the corrosion process due to their simultaneous action can increase in different ways depending on the values of t_w and α. If, with a simultaneous transition to new values of t_w and α, the corrosion rate increases from the action of each factor, then the total mass loss of metal Δg is taken equal to the sum ${\mathsf{\Delta }\mathrm{g}}_{{\mathrm{i}}_{\mathrm{T}}}$ and ${\mathsf{\Delta }\mathrm{g}}_{{\mathrm{i}}_{\mathsf{\alpha }}}$. If, with the same transition, the corrosion rate increases from the action of one factor, and conversely decreases from the action of the second factor, then the total mass loss of metal Δg will be equal to the difference in absolute values ${\mathsf{\Delta }\mathrm{g}}_{{\mathrm{i}}_{\mathrm{T}}}$ and ${\mathsf{\Delta }\mathrm{g}}_{{\mathrm{i}}_{\mathsf{\alpha }}}$, which can be equal to 0. If there will be a “zero” or “negative” situation in relation to the end point of the previous stage of the process, then in this case, during the change in time Δτ_i of this stage, the development of the process of mass loss of metal is represented by a horizontal line, since the metal loss achieved in the previous time intervals stays at this level.

When the durability of the metal under corrosion conditions is determined, it is necessary to proceed from the permissible depth of corrosion for a certain time of exposure to a gas flow Δδ, which can be represented as

$$\mathsf{\Delta }\mathsf{\delta }={\mathsf{\Delta }\mathsf{\delta }}_{\mathrm{p}}/{К}_{\mathrm{u}}$$

(16)

where Δδ_p—the permissible depth of corrosion for a certain operating time, at which sufficient strength of the cylindrical element of the boiler is still ensured; К_u—a safety coefficient that takes into account the unevenness of corrosion over the surface.

The value Δδ_p is determined by the equation

$${\mathsf{\Delta }\mathsf{\delta }}_{\mathrm{p}}={\mathsf{\delta }}_{\mathrm{in}}-{\mathsf{\delta }}_{\mathrm{w}}$$

(17)

where δ_in—the initial thickness of the metal subjected to corrosion; δ_w—the thickness of the metal wall, which provides the strength of the element.

The indicator that characterizes the lifetime of the metal, taking into account its corrosion resistance, is the allowable time of the metal, i.e., the durability (resource) of its work τ_r [22,50]. Since the mass loss of metal is approximated by the expression ΔG = A·${\mathsf{\tau }}_{\mathrm{r}}^{\mathrm{n}}$ (or $\mathsf{\Delta }\mathsf{\delta }=\mathrm{A}\times {\mathsf{\rho }}_{м}^{-1}{\mathsf{\tau }}_{\mathrm{r}}^{\mathrm{n}}$) and taking into account the fact that $\mathsf{\Delta }\mathrm{G}={\mathrm{k}}_0·\exp \left(-{\mathrm{E}}_{\mathrm{e}}/\mathrm{RT}\right)·{\mathsf{\tau }}_{\mathrm{r}}$, then τ_r is determined according to the equation

$${\mathsf{\tau }}_{\mathrm{r}}={\left(\frac{\mathsf{\Delta }\mathrm{G}}{{\mathrm{k}}_0\times \exp \left(-{\mathrm{E}}_{\mathrm{e}}/\mathrm{RT}\right)}\right)}^{\frac{1}{\mathrm{n}}}={\left(\frac{{\mathsf{\Delta }\mathsf{\delta }}_{\mathrm{p}}}{{\mathsf{\rho }}_{м}^{-1}\times \mathrm{A}}\right)}^{\frac{1}{\mathrm{n}}}$$

(18)

Since the values of k₀ and E_e at certain values of the metal surface temperature T are not known, a graphical method can be used to determine τ, expressing the total corrosion depth as a function of time for a given metal surface temperature based on the results of experimental studies.

3.2. LTC Kinetic Research

Relations and regression equations obtained as a result of processing the results of experiments, as well as the values of the determination coefficients R² during WFE combustion with a water content of 30% (S^r =1.5%; α = 2.9), at which the minimum corrosion intensity is observed, and when standard fuel combustion (S^r = 1.5%; α = 2.9), at which maximum corrosion is observed, are shown in Figure 7.

Corrosion studies have shown that the stabilization time of LTC is 2–3 h. This makes it possible calculating (predicting) the value of ΔG under the same operating conditions during any period of operation.

Corrosion studies with a duration from 0 to 2 h were not carried out due to methodological difficulties, and therefore, the nature of the process during this period can only be assumed, since it could go through any transition function, but study ceased within 2 h. Such an assumption is acceptable, since experimental data obtained for 2, 4, 8 and 12 h for all 25 modes, and for the main modes and for a longer time, are reliably approximated by a power function of the form ΔG = А·τⁿ, passing through the point at τ = 2 h (at high R² values). At the same time, it should be noted that in the area from 0 to 2 h, the measurement accuracy of ΔG and its influence on the evaluation of the process are of great importance. If the value of ΔG is at the level of measurement accuracy of 5.85 g/m² during this time, then the “acceleration” section ends at τ = 1–2 h process cannot be completed in all modes within one time—2 h.

Therefore, it is necessary to evaluate the influence of this initial section on the final values of ΔG, for example, during 8-h experiments, since on their basis the comparison of the influence of various factors (W^r in WFE, S^r in the fuel oil, α) on the intensity of corrosion processes was carried out.

It is necessary to evaluate the influence of the course of transient “acceleration” processes on the final results of the predicted corrosion values, which can develop according to a power function, a second-order aperiodic function, or along a signoidal function. The determination of the values of the coefficients of the approximation equations was carried out by processing the experimental data for 2–12 h using the Excel software package and is shown in Figure 8.

First, it was decided to evaluate the relative error of the research results corrosion, if we neglect the mass loss of metal during the first 2 h of exposure to the flue gas flow. When analyzing the relative error of more intense corrosion processes, the value of the error in estimating the mass loss of the metal is greater, and the accuracy of determining ΔG is somewhat reduced. So, when standard fuel oil combustion (S^r = 1.5%; W^r = 2%) at α = 2.9, the relative measurement error is 12.7%. The accuracy of determining ΔG is 87.3%. When taking into account the development of corrosion in the initial section according to the aperiodic function ΔG = 33 + 11ехр(−5.56τ) – 44ехр(−1.39τ), the relative error in this case will be 19.9%. The accuracy of determining ΔG will be 80.1%.

The impact of the initial section in predicting the development of corrosion for 100 h of stable exposure to the flue gas flow will be even less. If we do not take into account the initial section for a time of 0–2 h, determined by a power law, then the average value of the mass loss of metal for 100 h will be equal to 8241.71 g/m², and the relative error will be 0.3%. The accuracy of determining ΔG will be 99.7%. When taking into account the development of corrosion in the initial section according to the above aperiodic function equation, the relative error in estimating corrosion for 100 h will already be only 0.5%. The accuracy of determining ΔG for 100 h will be 99.5%.

If we assume that the “accelerating” line follows the equation of the signoidal curve ΔG = −0.3742 + 5.858/(1 + exp(−3.54τ + 4.22))^0.64, then the area under it in 2 h will be equal to 5.24 g/m², the accuracy of determining ΔG of an 8-h experience will be 85.6%, and predictions for 100 h will be 99.7%.

Then, when WFE combustion based on fuel oil (S^r = 1.5 %, W^r = 30 %) at α = 2.9, the relative error of corrosion measurements for 8 h will be 16.46% and the relative accuracy of determining ΔG will be 83.54%. If the transition function is determined by the found aperiodic function of the second order in the form of relation ΔG = 6 + 2exp(−5τ) – 8exp(−1.25τ) then the relative error is 13.1%, the relative accuracy of determining the mass loss of metal ΔG for 8 h is 86.9%. The influence of the initial section in predicting the development of corrosion for 100 h will be much smaller: the relative error is 0.6%, the accuracy is 99.4%.

If the transient process ends within 1 h, then the error in determining ΔG will be even less. We believe that such a time for the development of the corrosion process in the “accelerating” section during research on an experimental setup, provided that the parameters are constant, is more likely.

Thus, the values of mass loss of metal due to LTC predicted by power functions give somewhat overestimated values of the corrosion rate (at τ up to 8 h), taking into account the development of corrosion in the initial section from 0 to 2 h according to the power function. However, in this case, there is an acceptable agreement between the predicted values of ΔG and the values obtained for a longer time (for example, 100 h).

Based on the results of investigations of the relations ΔG = f (τ) obtained by combustion of various fuels, it was decided to determine the relation of the mass loss of metal ΔG on the S^r in the fuel oil, α and W^r in the WFE based on the data of 8 h experiments (Figure 9a–c).

On Figure 9a shows that starting from α = 1.4 and above, the relation ΔG = f (α) is almost rectilinear, similar to the data on the relation of the corrosion rate on α presented in [22]. However, with a decrease in α to 1.4 and 1.01, a sharp decrease in ΔG is observed. The reason is apparently that at such values of α, the content of SO₃, and hence the H₂SO₄ vapors in the flue gases, on which the corrosion rate depends, sharply decreases. The relation of SO₃ = f (α) has the same exponential character [35].

On Figure 9b the relation ΔG = f (S^r) is shown for various W^r in WFE: 2, 15 and 30%. With an increase in S^r more than 0.98% for any W^r in WFE, an increase in ΔG is observed, but the rate of increase in ΔG decreases with growth of W^r in WFE. When the fuel oil combustion (W^r = 2%) with an increase in S^r from 0.98 to 1.8% leads to an increase in ΔG from 9.4 g/m² to 30.5 g/m² (i.e., the value of ΔG increased by 3.2 times), then at W^r = 15% ΔG increases from 7.2 g/m² to 19.9 g/m² at S^r = 1.8% (i.e., the value of ΔG increased by 2.8 times). When WFE combustion with W^r = 30%, a slight increase in ΔG is observed: with an increase in S^r from 0.98 to 1.8%, ΔG grows from 5.2 to 10.8 g/m², i.e., mass loss of metal is 2.1 times lower than when fuel oil combustion.

On Figure 9c the relations of ΔG on the W^r in WFE during the combustion of fuel oils with a sulfur content S^r of 0.98, 1.5 and 1.8% are presented at values of α = 2.9. With an increase in W^r in the emulsion, ΔG decreases, and the higher the sulfur content in the fuel, the steeper the dependence curve ΔG = f (W^r) decreases. So, at S^r = 0.98% ΔG decreases from 9.4 g/m² at W^r =2% to 5.2 g/m² at W^r =30% (i.e., ΔG decreased in 1.8 times). At S^r = 1.8% ΔG decreases from 30.5 g/m² at W^r = 2% to 10.8 g/m² at W^r = 30% (i.e., ΔG decreased by 2.8 times). The value of R² is in the range of 0.98–0.99, which indicates the high reliability of the studies carried out on the experimental setup at constant parameters. The fact that the values of ΔG at W^r = 30% at different S^r practically converge at one point can only be explained by the fact that, in this case, W^r in WFE creates conditions for the appearance of metal passivation.

The equation for value of ΔG was obtained:

ΔG = −14.8326 + 7.3776α + 78.2079 S^r + 0.4531 W^r + 6.0669 (S^r)² − 0.5593 W^rS^r

(19)

The Equation (19) has reasonable values of ΔG in the range α = 1.5–2.9, S^r = 0.98–2%, and W^r = 2–30%.

The control studies were carried out with duration τ = 100 h, with WFE (W^r = 30%, S^r = 1.5%, α = 2.9) and with fuel oil (W^r = 2%, S^r = 1.5%, α = 2.9) combustion to evaluate the reliability of the results obtained in 8 h and the approximating equations for predicting corrosion rate.

The approximation equation of the corrosion rate K on t_w when the fuel oil combustion for 100 h was chosen [34,50]:

$$\mathrm{K}=370.16-16.582{\mathrm{t}}_{\mathrm{w}}+0.2905{\mathrm{t}}_{\mathrm{w}}^2-2.4863\times {10}^{-3}{\mathrm{t}}_{\mathrm{w}}^3+1.0411\times {10}^{-5}{\mathrm{t}}_{\mathrm{w}}^4-1.7108\times {10}^{-8}{\mathrm{t}}_{\mathrm{w}}^5$$

(20)

The Equation (20) is accepted for the ensuing features of the corrosion rate: t_w = 70–150 °C, W^r = 2%. Figure 10 represents the calculated values for K according to the received model.

Figure 10 represents prediction and confidence intervals. Compare of the calculated values of the corrosion rate K_C (Equation (23)) with the experimental K_E is δ_K = ±15% (Figure 11).

The approximation equation of the corrosion rate K on t_w when WFE combustion for 100 h was chosen:

$$\mathrm{K}=27.342-0.9715{\mathrm{t}}_{\mathrm{w}}+0.013{\mathrm{t}}_{\mathrm{w}}^2-7.7595\times {10}^{-5}{\mathrm{t}}_{\mathrm{w}}^3+1.7254\times {10}^{-7}{\mathrm{t}}_{\mathrm{w}}^4$$

(21)

The Equation (21) is accepted for the ensuing features of the corrosion rate: t_w = 80−140 °C, W^r = 30%. Figure 12 represents the calculated values for K with prediction and confidence intervals.

Compare of the calculated values of the corrosion rate K_C (Equation (21)) with the experimental K_E is δ_K = ± 20% (Figure 13).

If we take into account that variable modes lead to an increase in the corrosion rate, then the predicted values of the corrosion rate during fuel combustion in this mode should be considered reliable. Therefore, we believe that the results of corrosion studies and forecasts obtained with the same experimental setup for the combustion of WFE, for which there are no specific data on the corrosion rate, are also reliable.

The data of 100-h studies provide an opportunity to evaluate the accuracy of the long-term prediction of the corrosion process under WFE combustion, which is of primary interest to us. To do this, it is necessary to determine the average rate during the experiments using the obtained Equations for the corrosion kinetics. For example, for the WFE combustion mode at W^r = 30 %, S^r = 1.5 %, α = 2.9, the obtained predicted value of the average velocity for 100 h of the experiment is:

$${\mathrm{K}}_{\mathrm{av}}=\frac{1}{100}{\int }_0^{100}1.4322\times {\mathsf{\tau }}^{-0.4985}\mathrm{d}\mathsf{\tau }=0.1904\mathrm{g}/({\mathrm{m}}^2\times \mathrm{h}).$$

(22)

Experimental value К= 0.203 g/(m² × h).

Comparison of the obtained values of the average corrosion rate according to the equations of kinetics with the experimental data for 100 h, presented in Figure 14, shows that their discrepancy at t_w = 110 °C amounts to 6.6% [50].

Similar predictive calculations were performed for the combustion mode of standard fuel oil M100 at W^r = 2%, S^r = 1.5% and α = 2.9 to verify the reliability of the results of the study of corrosion kinetics (experimental data and calculations) for the considered fuel and its combustion mode.

It is possible to compare the predicted data with our experimental data at τ = 100 h and with the results of industrial studies presented in [22]. For 100 h, the predicted average rate is:

$${\mathrm{K}}_{\mathrm{av}}=\frac{1}{100}{\int }_0^{100}6.3218\times {\mathsf{\tau }}^{-0.5102}\mathrm{d}\mathsf{\tau }=1.2315г/({\mathrm{m}}^2\times \mathrm{h}).$$

(23)

Experimental value К= 1.288 g/(m² × h).

Comparing the corrosion rate predicted for 100 h, obtained for 2–12 h, with the experimental data for 100 h, presented in Figure 14, it can be seen that the discrepancy with the values in the area of the “acid peak” is also insignificant (the predicted value of K = 1.2315 g/(m² × h), the obtained value of the corrosion rate in the experiment is K = 1.288 g/(m² × h); i.e., the discrepancy is 4.6%.

4. Discussion

In real conditions, variable combustion modes are observed (α changes) along with variable t_w of heating surfaces, which leads to an increase in corrosion rates. If we assume that at variable values of t_w and α the level of corrosion rate at α = 1.05 in terms of τ = 100 h will be at the level of 0.25 mm/year [22], then we will obtain comparative characteristics K = f (t_w) during the combustion of WFE and standard fuels at different α and W^r, shown in Figure 15.

These relations make it possible to determine the minimum wall temperature in condensing HES according to the corrosion rate adopted according to the conditions of reliability and service life. The research results show a clearly pronounced “acid peak” when fuel oils undergo combustion with different α up to 1.025. When WFE combustion with W^r = 30% at two values of α (1.45; 2.9), the corrosion rate is below the limited level at α = 1.025 [22] with a practically absent “peak” of corrosion. Although this “peak” still “appears” (especially clearly when exposed to a flue gas flow for 8–12 h), but then it almost disappears after the formation of a dense salt layer and passivation of the metal.

The most dangerous in terms of the LTC level is the range t_w = 80–130 °C. When WFE undergoes combustion, the corrosion rate is less than fuel oil combustion. At a wall temperature of 105–110 °C, there is a significant difference in the corrosion rate. When the fuel oil combustion corrosion rate is K = 0.56 g/(m² × h), while under WFE combustion—K = 0.06 g/(m² × h); i.e., nine times less. Therefore, as the water content in WFE increases, the corrosion rate decreases. This is due to the passivation of the metal surface.

The lifetime of the condensing HES is accordingly increased. It indicates that the service time of the condensing HES is identical to that for a dry one under WFE combustion.

The obtained data on the corrosion rate at different t_w when WFE combustion with varying values of water content W^r from 4 to 30% make it possible to obtain the correlation for corrosion rate K = f (W^r) at characteristic wall temperatures t_w in the zones (Figure 16): dew point (130 °C); “acid peak” of corrosion (115 °C); minimum corrosion (80–100 °C); the second “peak” of corrosion (60–70 °C). Based on the experimental data and corresponding predicted values, it has been found that the value of K first sharply decreases when t_w = 70 °C is reached at W^r = 8–10%, then the corrosion rate K slowly decreases to 0.35 mm/year with a further increase in the water content W^r to 30%. Within the temperature range t_w = 80–90 °C at W^r up to 10–12%, the corrosion rate K first decreases, and then, with a subsequent increase in W^r to 30%, the value of K begins to slightly increase. At wall temperatures t_w = 100 °C and 130 °C, the value of K gradually decreases with an increase in water content W^r from 4 to 30%. However, at t_w = 100, 115, 120 °C (near the “acid peak” of corrosion), the corrosion rate K significantly decreases from 0.4–0.45 mm/year to 0.1 mm/year with an increase in water content W^r to 30%.

It is possible to determine the permissible corrosion rates K_per at wall temperature t_w = 115 °C and corrosion rates K_per at other values of t_w according to these relations. The relation curve K = f (W^r) at t_w = 115 °C characterizes the center of the zone of corrosion rates (with deviations of ±10%), at which a “passage” over the “acid peak” of corrosion is possible (Figure 16). At this wall temperature t_w the corrosion rate K_per is at the maximum, and at the other temperatures t_w it is lower (except for the corrosion rate at wall temperature 70 °C). The value of these corrosion rates K is determined vertically from the point of intersection with the coordinates K_per and W^r.

In addition, this makes it possible to determine the value of water content W^r in the WFE, which provides the accepted allowable value of corrosion rate K_per. For example, with the accepted allowable value of K_per = 0.25 mm/year, the water content in emulsion W^r = 17%. With this value of W^r in the WFE, the corrosion rate K_per is higher than its value K_per at wall temperature t_w = 70 °C. In addition, this makes it possible to accept the temperature of the flue gases as 110 °C (with a temperature difference between the gases and the wall of 30 °C) and lower.

5. Conclusions

The performed analysis of data from the literature indicates that WFE combustion has a positive effect on the environmental and economic performance of fuel-burning devices and on the corrosion properties of combustion products at the same time.

It is necessary to conduct analytical and experimental studies of the combustion of fuels, WFE, and thermochemical processes of corrosion on heating surfaces in order to achieve the goals set in the work.

The experimental studies of condensing HES corrosion processes of EGB that influence a depth of exhaust gas heat utilization and EGB working reliability was carried out using the described experimental setup.

It has been established that the stabilization of the corrosion process occurs within 1–2 h, when ensuring constant process parameters during WFE combustion. This makes it possible the reliable estimation of the intensity in corrosion processes and predict their development for a long time according to the experimental data obtained for 2, 4, 8 and 12-h durations, τ.

It is shown that the results of studies of corrosion kinetics are reliably approximated by power functions in the form of the relations of the mass loss of metal of the condensing HES ΔG = A × τⁿ with time τ, which is confirmed by the results of 100-h experiments.

Based on the obtained relations of the mass loss of metal ΔG = f (τ) according to the data of 8-h experiments at wall temperature of the condensing HES t_w = 110 °C, the relations ΔG = f (S^r), ΔG = f (α), ΔG = f (W^r) were obtained, which showed that at a water content W^r in WFE of about 30%, the LTC rate significantly decreases due to the appearance of the passivation process.

The obtained relations for corrosion rate K = f (t_w) (at τ = 100 h) show that with a decrease in excess air coefficient α the corrosion rate K (especially in the area of the “acid peak”) decreases. At water content in WFE W^r = 30% and increased values of excess air coefficient α = 2.9, the corrosion rate K is 1.85 times lower than at α = 1.45 with practically absence of “acid peak”.

The wall temperature range of condensing HES from 140 to 70 °C, at which the LTC rate K is in the range of 0.15–0.25 mm/year was determined and can be used as basic data in the design of more efficient environmentally friendly exhaust gas boilers with low-temperature condensing HES. The results of studies on condensing HES enable the acceptance of a suitable LTC rate when undergoing WFE combustion and demonstrate good prospects for their application in the exhaust gas heat utilization of diesel engines.

The use of WFEs with decreased wall temperatures t_w of condensing HES below 80 to 70 °C makes it possible to improve the reliability of the EGB during the accepted service life, increase the lifetime of the metal of HES by almost six times, the overhaul period, and reduce the cost of repairing the condensing HES. The application of low-temperature condensing HES enables the enhancement of the efficiency of exhaust gas heat utilization due to deeper exhaust gas temperature depression and provides sustainable, efficient performance of diesel engine plants on the whole at a safe thermal and environmentally friendly level.

The analysis of experimental data on LTC during WFE combustion helps with clarifying the mechanism and peculiarities of LTC according to “zone-by-zone” approach and enables further development of a method for protecting the metal of the condensing HES of the boiler from sulfuric LTC at a wall temperature below the dew point temperature of H₂SO₄ vapor.