The Effect of Firewood Moisture Content on the Atmospheric Thermal Load by Flue Gases Emitted by a Boiler

1. Introduction

The wood of deciduous trees, with its energetic properties in the seasoned state, and which is in accordance with the standard of STN EN 14961 Solid biofuels, is a biofuel with a heat value of Qn = 18.1 MJ·kg⁻¹, a high percentage of volatile flammable substance V = 85%, and a low ash content of A = 0.3%. In comparison to fossil fuels, the ash content of firewood from energy plantations or from forests is 15–30 times lower than the ash content of coal [1,2,3,4,5]. This can be considered a positive energetic property of firewood. The affinity to water and water vapor is a negative feature of firewood. The relative moisture contents of a freshly felled tree in the dormant season ranged from W = 35%–65%, depending on the wood species [1,6,7,8]. Firewood in branch form stacked under cover or against a sheltering wall dries naturally to an air-dried state, i.e., the moisture content of W = 18%–25% [6,9]. Unprocessed wood waste with a moisture content of W = 10%, or biofuel in the form of briquettes and pellets [10,11,12] made from wood with a specific size and moisture content, play an important role in terms of energy efficiency.

According to the authors [13,14,15,16,17], the efficiency of producing heat from firewood depends on the construction of the heat generator as well as on the energetic properties of firewood and energetic and environmental benefits delivered by the boiler. The energetic properties of firewood depend especially on its moisture content. The basic energetic properties include the gross calorific value (Qs) and heat value (Qn), but also the burning process in the furnace, including the flame temperature, amount of flue gases created, dew-point temperature of flue gases, and emission production, which are all affected by the wood moisture content in a negative way. The construction of a boiler heat exchanger affects the use of the calorific value of flue gases, namely the cooling rate of the flue gases before they are delivered into the atmosphere. Currently, the energy efficiency of mid-efficient energy firewood boilers is η_k = 80%–85%. On the other hand, the energy efficiency of modern biofuel boilers with guaranteed energetic properties is η_k = 92%.

Recently, biofuels have been at the center of our attention, not only because of their market accessibility, energy, and economic efficiency, but also because of their environmental benefits, as the authors of [18,19,20,21,22,23,24,25,26] mention. The results of the research into the effect of moisture content of firewood, and the temperature of flue gases on the atmospheric thermal load by flue gases emitted by a firewood boiler are presented in the paper.

2. Model Evaluation of the Atmospheric Thermal Load by the Heat of Flue Gases

The heat present in the exhaust gases from the boiler to the atmosphere is the thermal load of the atmosphere. The heat of emitted the flue gas related to the production of 1 GJ of heat is mathematically described by Equation (1), as follows:

$$Q_{fg}=m·V_{fg}·c_{fg}·\left(t_{fg}-t_{fg-e}\right)\left[\mathrm{MJ}·{\mathrm{GJ}}^{-1}\right]$$

(1)

The algorithm used to calculate the individual parameters of the atmospheric thermal load created by the flue gases is dependent on the chemical composition of the flammable substances of wood (C^daf, H^daf, O^daf, and N^daf), ash content in wood (A), relative moisture content of combusted firewood (W), excess of combustion air (λ), temperature of the flue gases delivered to the air from a boiler (t_fg), and temperature of the flue gases cooled to the temperature of the atmospheric air delivered to a boiler furnace (t_fg-e), which are described using the following equations:

The quantity of firewood burnt in the boiler furnace to produce the heat of 1 GJ is calculated using the following equation:

$$m_{p-1GJ}=\frac{{10}^6}{Q_n·{\eta }_K}\left[\mathrm{kg}·{\mathrm{GJ}}^{-1}\right]$$

(2)

The specific volume of humid flue gases produced in the combustion process of 1 kg of firewood, depending on the mentioned parameters, is described using the following equation:

$$\begin{array}{l}{V}_{fg}=\left[1.867·\frac{C^{daf}}{100}+11.2·H^{daf}+0.8·\frac{N^{daf}}{100}+V_{air}·\left(\lambda -0.21\right)\right]·\left[1-\frac{A}{100}-\frac{W}{100}\right]+\\ 1.24·\frac{W}{100}\left[{\mathrm{m}}_{\mathrm{n}}^3·{\mathrm{kg}}^{-1}\right]\end{array}$$

(3)

The production of humid flue gases produced in the combustion process of firewood to produce the heat of 1 GJ is calculated using the following equation:

$$V_{fg-1GJ}=m·V_{fg}\left[{\mathrm{m}}_{\mathrm{n}}^3·{\mathrm{GJ}}^{-1}\right]$$

(4)

The mean value of the specific heat capacity of 1 m_n³ of flue gases when the pressure is constant is described by the following equation:

$$c_{fg}=c_{CO2}·X_{CO2}+c_{CO}·X_{CO}+c_{O2}·X_{O2}+c_{N2}·X_{N2}+c_{H2O}·c_{H2O}·X_{H2O}\left[\mathrm{kJ}.{\mathrm{mn}}^{-3}·{\mathrm{K}}^{-1}\right]$$

(5)

The values of the mean specific heat capacity of 1 m_n³ of the i-th component of the flue gases when the pressure is constant (c_p-i) [ kJ.m_n⁻³·K⁻¹] are in

Table 1. Values of the mean specific heat capacity of 1 m_n³ of flue gases when the pressure is constant. [14].

Temperature [°C]	cp-i–Mean Specific Heat Capacity of 1 mn3 of Flue Gases When the Pressure is Constant [kJ·mn−3·K−1]
	CO2	O2	N2	H2O
0	1.620	1.306	1.302	1.491
100	1.725	1.319	1.306	1.499
200	1.817	1.336	1.310	1.520
300	1.892	1.357	1.315	1.537
400	1.955	1.382	1.327	1.557
500	2.022	1.403	1.336	1.583
600	2.077	1.419	1.348	1.608

. The values for X_i are the volumetric proportions of the i-th component of the flue gases [-].

The functional dependences of the mean specific heat capacity of 1 m_n³ of the individual components of the flue gases on the temperature (t) when the pressure is constant are described using the following equations:

Carbon dioxide CO₂: C_CO2 = 0.0008∙t + 1.6473 [kJ.m_n⁻³.K⁻¹]

(6)

Water vapor H₂O: c_H2O = 10⁻⁷∙t² + 10⁻⁴∙t + 1.4895 [kJ.m_n⁻³.K⁻¹]

(7)

Oxygen O₂: c_O2 = 5.10⁻⁸∙t² + 2.10⁻⁴∙t + 1.3036 [kJ.m_n⁻³.K⁻¹]

(8)

Nitrogen N₂: c_N2 = 9.10⁻⁸∙t² + 2.10⁻⁵∙t + 1.3022 [kJ.m_n⁻³.K⁻¹]

(9)

The volumetric proportions of the individual components in the flue gases from the firewood combustion are determined using the following equations:

Volumetric proportion of carbon dioxide in flue gases

$$X_{CO2}=\frac{1.867·\frac{C^{daf}}{100}·\left[1-\frac{A}{100}·\left(1-\frac{W}{100}\right)-\frac{W}{100}\right]}{V_{fg}}[-]$$

(10)

Volumetric proportion of nitrogen in flue gases

$$X_{N2}=\frac{\left(0.8·\frac{N^{daf}}{100}+0.79\lambda ·V_{air}\right)·\left[1-\frac{A}{100}·\left(1-\frac{W}{100}\right)-\frac{W}{100}\right]}{V_{fg}}[-]$$

(11)

Volumetric proportion of oxygen in flue gases

$$X_{O2}=\frac{0.21·V_{air}·\left(\lambda -1\right)·\left[1-\frac{A}{100}·\left(1-\frac{W}{100}\right)-\frac{W}{100}\right]}{V_{fg}}[-]$$

(12)

Volumetric proportion of water vapor in flue gases

$$X_{H2O}=\frac{11.2·\frac{H^{daf}}{100}·\left[1-\frac{A}{100}·\left(1-\frac{W}{100}\right)-\frac{W}{100}\right]+1.24\frac{W}{100}}{V_{fg}}[-]$$

(13)

The temperature of flue gases (t_fg) emitted to the atmosphere by fluid or steam boilers is dependent on the construction of the boiler heat exchanger and the temperature of the heated water, thermal oil, or water vapor produced. The temperature of the flue gases leaving the boiler ranges from t_fg = 120–200 °C, according to the prestigious producers of firewood boilers, such as Herz GmbH, Vincke Energietechniek n.v., TTS Group Třebič, Vissmann, and Justsen Energiteknik A/S.

The heating value of firewood is affected by the moisture content, as it has been described by many authors [1,6,12], using the following equation:

$$Q_n=18840-21351·\frac{W}{100}\left[\mathrm{kJ}·{\mathrm{kg}}^{-1}\right]$$

(14)

The thermal efficiency of a boiler with a controlled combustion process of firewood, in accordance with the environmental benefits and ecological criteria, BAT (the best available technologies), as it is mentioned in the literature [16,17,27], is dependent especially on the chimney heat loss. The dependence of the thermal efficiency of a boiler when the nominal thermal output performance ranges from P_nom = 1–5 MW on the temperature of the emitted flue gases from a boiler into the atmosphere at t_fg = 120–200 °C, and the moisture content of firewood of W = 10%–60%, is described using the following equation:

$${\eta }_k=[-0.001·{\left(\mathrm{W}\right)}^2-0.0019·W+91.52]-\left[\left(0.001·\mathrm{W}+0.058\right)·\left(t_{fg}-120\right)\right][-]$$

(15)

3. Dependence of Producing Flue Gases and Atmospheric Thermal Load by the Heat of Emitted Flue Gases on the Moisture Content of Combusted Firewood

The volume of flue gases of V_fg-1GJ = 656.43 m_n³ is produced and delivered to the atmosphere as a result of the combustion process of dried firewood, with the following chemical composition of flammable substances, namely, C^daf = 50.0% ± 1.0%, H^daf = 6.0% ± 0.1%, and O^daf = 44.0 ± 3.0, and an ash content in wood of A = 1.0% with an excess of combustion air λ = 2.1 necessary to produce 1 GJ of heat. The effect of the firewood moisture content ranging from W = 10%–60% on the energetic properties of the combusted wood, material, and technical conditions of heat production, and the atmospheric thermal load by flue gases with the temperature t_fg = 120 °C, is mentioned in

Table 2. The effect of firewood moisture content on the energy efficiency of a boiler, fuel consumption, and the production of flue gases when 1 GJ of heat is produced.

Fuel	Moisture Content	Heating Value	Specific Volume of Flue Gases from 1 kg of Wood	Thermal Efficiency of a Boiler	Consumption of Firewood to Produce 1 GJ of Heat	Production of Emitted Flue Gases when 1 GJ of Heat is Produced	Atmospheric Thermal Load by Flue Gases
	Wr	Qn	Vfg	ηk	mp-1GJ	Vfg-1GJ	Qfg
	[%]	[kJ·kg−1]	[mn3]	[-]	[kg]	[mn3]	[MJ·GJ−1]
Fuel wood	10	16,159	9.34	0.883	73.38	704.02	96.2
	20	14,075	8.44	0.878	87.49	738.47	101.3
	30	11,992	7.54	0.871	107.05	807.12	110.1
	40	9908	6.64	0.861	129.06	856.98	122.9
	50	7825	5.74	0.845	169.27	971.58	143.2
	60	5742	4.8	0.819	245.03	1188.87	179.8

Correlation between the volume of emitted flue gases resulting from the production of the heat of 1 GJ and the moisture content of combusted wood is shown in the graph in Figure 1.

.

Following the findings, we can state that in order to produce 1GJ of heat in the boiler furnace, a quantity of m = 73.5 kg of wood with a moisture content of W = 10% is burnt, and a volume of V_fg-1GJ = 704.02 m_n³ of flue gas is produced. Because of the lower heat value of the combusted wet wood with a moisture content of W = 60%, and a decrease in the energy efficiency of a boiler by o ∆η_k = 6.4%, 3.3 times more fuel is consumed, and a volume of V_fg-1GJ = 1188.88 m_n³ of flue gas is delivered to the atmosphere in order to produce the same amount of heat. Therefore, an increase in the flue gases of ∆V_fg-1GJ = 486 m_n³ in comparison to the combustion of dried wood is observed. An increase in flue gas production resulting from the combustion process of wetter wood is caused by a higher volume of water vapor in the flue gases from the evaporated water occurring in combusted wood, as well as by the heated nitrogen and unoxidized oxygen in the combustion air delivered to the boiler furnace in order to produce heat consumed in the drying process of firewood. The dependence of the atmospheric thermal load from the heat of the flue gases emitted to the atmosphere with the temperature of t_fg = 120 °C on the moisture content of combusted wood is illustrated in Figure 2.

A higher production of emitted flue gases from a boiler in the combustion process of firewood with a higher moisture content negatively affects the higher heat transfer by emitted flue gases into the atmosphere. This is confirmed by the gathered data, comparing the values of the atmospheric thermal load of flue gases with temperatures of t_fg = 120 °C in the combustion process of dried wood with a moisture content of W = 10%, to flue gases in the combustion process of wet wood with a moisture content of W = 60%. The atmospheric thermal load created by flue gases in the combustion process of dried wood is Q_fg = 96.2 MJ∙GJ^-1. On the other hand, the atmospheric thermal load created by flue gases in the combustion process of wet wood is Q_fg = 179.8 MJ∙GJ⁻¹. This indicates an increase in flue gases of ∆Q_fg = 83.6 MJ∙GJ⁻¹, as well as more heat delivered to the atmosphere.

Figure 3 illustrates the effect of the temperature of flue gases leaving a boiler, with temperatures ranging from t_fg = 120–200 °C, on the atmospheric thermal load, due to the combustion process of firewood with a moisture content of W^r = 10%–60% in the boiler furnace in the combustion process of firewood, with an excess of combustion air λ = 2.1 and average temperature of air delivered to the furnace t_vz = 10 °C.

Because of the higher temperatures of the emitted flue gases from a boiler, the atmospheric thermal load and heating of the atmosphere is higher. While the atmospheric thermal load created by the flue gases in the combustion process of dried wood and the temperature of flue gases t_fg = 120 °C is Q_fg = 96.2 MJ∙GJ⁻¹, the value of the atmospheric thermal load created by the flue gases in the combustion process of wet wood with a moisture content of W = 60 %, and the temperature of the flue gases t_fg = 200 °C is up to Q_fg = 3619 MJ∙GJ⁻¹. In comparison to the atmospheric thermal load by the flue gases in the combustion process of dried wood, an increase of 3.7 times can be seen.

When comparing the average atmospheric thermal load created by the heat of flue gases when the moisture content of combusted wood increases, we can state that the emitted heat in the flue gases with temperatures of t_fg = 120 °C, and with an increase in the moisture content of firewood by 1%, increases by ∆Q_fg = 1.7 MJ. When the temperature of the emitted flue gases is t_fg = 200 °C, then the increase observed is ∆Q_fg = 3.68 MJ. Following the presented data that describes the atmospheric thermal load created by the flue gases emitted from a boiler, depending on the moisture content of the combusted wood and the temperature of the flue gases, the moisture content of the combusted wood of W = 10–60% and the temperature of the emitted flue gases t_fg = 120–200 °C was used to derive the functional dependence in the form of a 3D graph Figure 4, using the program STATISTICA, for boundary conditions, and Equation (16).

$$Q_{fg}=271.69-3.79·W+2,28·t_{fg}+0.04·W^2+0.02·W·t_{fg}+0.01·t_{fg}^2\left[\mathrm{MJ}·{\mathrm{GJ}}^{-1}\right]$$

(16)

In order to compare the production of the flue gases and the atmospheric thermal load created by the flue gases resulting from the production of the heat of 1 GJ in the combustion process of firewood to other fuels,

Table 3. The production of flue gases and the atmospheric thermal load created by flue gases from a natural gas boiler.

Fuel	Heating Value	Production of Emitted Flue Gases When 1 GJ of Heat is Produced	Thermal Efficiency of a Boiler	Atmospheric Thermal Load
	[MJ·m−3]	[mn3]	[-]	[MJ·GJ−1]
Natural gas	33.9	297	0.95	51.6

shows the production of flue gases in a natural gas boiler with a thermal efficiency of η_K = 95%, and the atmospheric thermal load created by flue gases with temperatures of t_sp = 110 °C emitted from the boiler to the atmosphere.

The volume of flue gases emitted to the atmosphere as a result of the production of the heat of 1 GJ from natural gas is 2.4 times lower than the volume of flue gases produced and delivered to the atmosphere when 1 GJ of heat was produced from dried firewood with a moisture content of W = 10%. The volume value was four times lower than the value from the production of heat from wet wood with a moisture content of W = 60%. The values of the atmospheric thermal load created by the flue gases emitted in the production of 1 GJ of heat from natural gas with a temperature of t_fg = 110 °C, or of dried and wet firewood with a temperature of t_fg = 120 °C, are mentioned in the bar chart in Figure 5. The atmospheric thermal load created by the flue gases resulting from the combustion process of dried wood, with the temperature of flue gases of t_fg = 120 °C is 1.8 times higher, and the atmospheric thermal load created by the flue gases resulting from the combustion process of wood with a moisture content of W = 60%, and the temperature of flue gases of t_fg = 200 °C is seven times higher than in the combustion of natural gases.

The above arguments on the influence of wood moisture on the warming of the atmosphere by the flue gases emitted from the boiler illustrate the fact that the combustion of moist wood reduces the thermal efficiency of the boiler [16,27] and increases the production of the emission [20,23]. This is the reason for introducing the economically efficient pre-drying and seasoning of fuel wood. Such technologies, as mentioned in the literature [6,27], include the technology of the transpiration drying of the branches and top of trees before the production of wood chips, as well as the natural drying of stored firewood on the covered storehouses.

4. Conclusions

Following the results of the analysis of the effect of the moisture content of firewood on the atmospheric thermal load created by the heat of flue gases emitted from a firewood boiler, the following statements can be made:

(1)

in the production of 1 GJ of heat from dried wood with a moisture content of W = 10%, a volume of flue gases of V_fg-1GJ = 96.2–177.8 m_n³ with a temperature of t_fg = 120–200 °C is delivered to the atmosphere. In the combustion process of wet wood with a moisture content of W = 60%, a volume of flue gases of V_fg-1GJ = 179.8–361.9 m_n³ is emitted to the atmosphere.

(2)

An increase of 1% in the moisture content of firewood results in an increase in the atmospheric thermal load created by the heat of flue gases with a temperature of t_fg = 120 °C of ∆Q_fg = 1.7 MJ, on average. When the temperature of the flue gases is t_fg = 200 °C, it increases by ∆Q_fg = 3.68 MJ.

(3)

Comparing the values of the atmospheric thermal load created by the flue gases resulting from the combustion process of firewood to the thermal load caused by the combustion process of natural gas, we can state that the atmospheric thermal load caused by the combustion of firewood ranges from 1.8–7 times higher.

(4)

The heat of the water vapor from the evaporated water of the combusted wood, as well as the heat of the heated nitrogen and unoxidized oxygen in the combustion air delivered to the furnace of a boiler to dry firewood, are the reasons for the increasing volume of the flue gases. This, therefore, causes the increasing atmospheric thermal load created by the heat of the flue gases, resulting from the combustion of wood with higher moisture content.

(5)

Because of the effect of the moisture content of the firewood on the atmospheric thermal load created by emitted the flue gases from firewood, as well as the fact that, because of the moisture content, the energy efficiency of the boiler and the efficiency of the heat production decreases and the emission production increases. This justifies the use of economically-efficient forms of pre-drying and seasoning of firewood, such as the technology of transpiration used to dry branches and tree tops before the production of wood chips, or the natural pre-drying of stored firewood logs in a sheltered position.