Economic Efficiency Assessment of Using Wood Waste in Cogeneration Plants with Multi-Stage Gasification

Abstract

The aim of this work is to assess the effectiveness of biomass gasification power plants in Russia (Irkutsk region) and compare them with other types of electricity and heat cogeneration systems. Biomass, which is waste from logging and wood processing, is considered as fuel for gasification plants. As a criterion, the cost of energy is used. Analytical relations are obtained for the cost of electric energy at a given cost of thermal energy and vice versa, thermal energy at a given cost of electric energy. These relationships are applied to assess the economic efficiency and compare small-power plants (up to 200–500 kW) such as mini-combined heat and power (CHP) on fuel chips and fuel pellets, coal-fired CHP and gas and liquid fuel power plants (gas-piston and diesel power plants). The latter are equipped with heat recovery boilers and supply consumers with heat and the electric power simultaneously. The calculation results show that the cost of electricity when using wood fuel is significantly less than the cost of electricity from a diesel power plant due to the use of cheaper fuel. In this regard, for autonomous energy systems of small power, especially near logging points, energy supply from biomass gasification power plants is a preferable solution than the use of diesel power plants. Wood fired energy cogeneration systems (mini-CHP) can also successfully compete with coal and gas power plants if they have cheap wood fuel at their location. With the introduction of carbon dioxide emissions charges, the use of not only wood chips, but also pellets becomes competitive in comparison with coal and gas.

1. Introduction

In recent decades, the role of renewable energy sources (RES) in the global energy sector has significantly increased [1,2]. In the future, until 2050, their share in the energy balance will grow significantly faster than traditional energy sources [3].

This is due to public concern about climate change caused by carbon dioxide emissions from industry and energy sectors [4]. One option to reduce CO₂ emissions may be to replace fossil fuels with renewable alternatives [5]. This will be facilitated by programs to stimulating the use of renewable energy for electric and thermal energy production, adopted in more than a hundred countries [1].

Wood biomass has significant potential among renewable energy sources, along with widely developed hydropower, wind and solar energy. Development and implementation of technologies for biomass energy use has a positive effect on both the environmental situation and economic growth [6,7].

Wood processing for energy production does not change the balance of carbon dioxide in the atmosphere and causes significantly fewer pollutants (SOx, NOx) than burning fossil fuels (coal and petroleum products) [8,9]. At the same time, the object of energy use is not the forest itself, but the waste from the industrial harvesting of wood and its processing. It is necessary to utilize wood waste under controlled conditions rather than let it burn in forests without any treatment. Utilization of waste helps to avoid cluttering up territories, forest fires and pollution of surface and underground waters. This will positively affect the environmental situation in the areas of harvesting and processing of wood.

Timber processing waste can be used in the energy industry both directly, in the form of wood chips, and in the form of fuel granules (pellets). It is worth noting that the economically justified radius of using wood chips in energy sources does not exceed 150 km. This fact is explained by the significant costs of their transportation [10]. Pellets have a higher bulk density and stable calorific value, which makes them attractive for energy use despite the high value-added production. Currently, pellets are widely used instead of coal (or together with it) in the economically developed countries of Europe, America, and Asia in the production of thermal and electric energy. For example, the International Energy Agency states that in Europe the consumption of pellets is about 20 million tons/year, of which 36% is used to generate electricity [11]. The largest consumer of pellets for electricity production is the Drax power plant in the UK, which has four 660 MW power units operating on biomass, and two 660 MW coal-fired power units [12]. About 64% of pellets consumed in Europe are used to generate thermal energy in local heating systems, which typically use small boilers up to 50 kW [11].

Direct burning of wood raw materials is the simplest and most common type of energy use but it has low thermal efficiency. Another promising area is the use of gasification technologies that are thermally self-sufficient and more efficient than direct burning [13]. Moreover, the use of gasification in electric power generation plants provides a higher overall electrical efficiency [14].

Electricity production using gasification technologies should be supplemented by the production and recovery of heat from exhaust gases, which will contribute to the combined heat and power (CHP) production. Such a pattern of energy production is the most energy-efficient.

Combined heat and power plants can be used in both centralized and decentralized heating systems. Centralized heating systems employ large CHP plants that combine high efficiency and low operating costs. However, the acute issues of wood fuel availability and heat storage to cover peak loads [15] can arise. Small CHP plants are normally used in decentralized energy systems that use local resources. In this case, transportation costs are reduced and heat and electricity are supplied to consumers in a limited area [16]. Small CHP plants can also be used in systems with distributed energy generation in industrial or residential areas with low-rise buildings which are characterized by a low density of heat and electric load.

The areas with decentralized energy supply often face the choice of a more economically viable energy source using both fossil fuels (gas, coal, diesel fuel, etc.) and renewable energy sources (wind, sun, etc.).

The purpose of the work is to evaluate the economic efficiency of wood fuel firing mini-CHP (power plants with simultaneous production of electric and thermal energy) on wood fuel in Russia (Irkutsk region) and compare it with other types of electric and thermal energy cogeneration systems.

An economic comparison of various energy production technologies was carried out according to the criterion of energy cost, taking into account the uncertainty of technical and economic parameters. Particular attention is paid to the joint production of electric and thermal energy. Analytical relationships are obtained that allow us to compare the cost of energy of power plants using different fuels. They make it possible to take into account both the contribution of heat supply to lowering the cost of generated electricity, and the contribution of electricity supply to thermal energy cost. The proposed methodology was used to assess the competitiveness of gasification-based power plants and mini-CHPs for Russian conditions.

2. The Technology of Multi-Stage Gasification of Wood Fuel

A detailed analysis of the prerequisites for using biomass gasification technologies and their main development trends is presented in reviews [17,18,19]. It is shown that the main factors stimulating to the development and implementation of gasification technologies are:

–

Increase in energy consumption in developing and densely populated countries (China, India, Brazil);

–

Significant fluctuations in world hydrocarbon prices;

–

Countries’ policies aimed at diversifying energy structures in the fuel and energy balance;

–

Development of distributed energy generation, which allows reducing the distance of energy transport through the use of local fuels;

–

The pursuit of environmental friendliness (through the use of renewable solid fuel resources, including waste).

According to the International Energy Agency, in the countries included in the Organization for Economic Cooperation and Development (OECD), there are about 160 projects at various stages of design and construction of energy facilities using biomass gasification technologies. Typically, power facilities with a capacity of up to 300–500 kW use fixed-bed reactors and those with a capacity above 300 kW use fluidized-bed reactors [20,21]. However, despite a large number of projects, their practical implementation is slow due to some problems. This is confirmed by the fact that 46 projects have been suspended [22]. Although biomass is one of the most reliable and accessible renewable energy sources [23], it has specific features that make it difficult to be used in gasification plants.

Biomass is characterized by high humidity, high reactivity [24], and low ash content. At the same time, ash is characterized by increased corrosion and slagging properties due to the increased content of alkali metals [25]. Biomass gasification produces a large amount of tar [26]. It is worth noting that the capacity of biomass gasification plants is limited by the area of collection and logistic problems of transportation [27]. These circumstances worsen the technical and economic efficiency of the power plants. The producer gas may contain a significant amount of tar, which can lead to fouling of technological equipment and damaging of engines. The maximum permissible tar content in the gas supplied to the internal combustion engine is 50 mg/nm³ [28]. For a gas turbine, this value is 5 mg/nm³, and for a fuel cell–1 mg/nm³ [29]. Two methods are usually used to clean the producer gas from tar: 1) direct removal (decomposition) of tar in gasifier; and 2) the use of special cleaning devices after gasifier, including cyclones, various filters, and scrubbers. In addition, catalysts for tar cracking can be used. Direct removal of tar in the reactor is carried out by changing the process parameters (temperature, pressure, fuel residence time, the use of various additives), as well as by using special gasifier designs [30]. One of the methods to significantly reduce the tar in the producer gas and increase the efficiency of gasification is the organization of a staged process [31]. In this process, the exothermic stage of internal combustion takes place in a separate reactor (or zone), the produced combustible gas is completely or partially burned in the combustion chamber, and the combustion products are used as a gasifying agent in the second reactor, where charcoal from the first reactor is supplied. Such an organization of the process makes it possible to burn the tarry products released in the first stage, use their energy to force the gasification of charcoal and stabilize the composition of the final gas, as well as to obtain producer gas with a minimum amount of tar [32,33]. Figure 1 shows a diagram of a multi-stage gasifier. It is worth noting that the combustion chamber of the tarry pyrolysis gas can be either organized inside the reactor (shaft type gasifiers) or designed as a separate reactor.

The theoretical study [34] gives estimate of the efficiency of staged gasification in the combined production of electricity and heat at the level of 80–85%, which is 10–20% higher than that of traditional single-stage processes. The research presented in [35,36], however, state that the technology of multi-stage gasification develops at a noticeably slower pace than the technology of single-stage gasification in the 1990s. The widespread dissemination of multistage gasification technologies faces technical and economic obstacles. Therefore, special attention should be focused on the justification of the economic efficiency of new technologies in comparison with conventional energy sources.

Carpene et al. in [37] studied biomass competitiveness for large district heating schemes. It was concluded that, in most cases, biomass heating plants can compete with traditional coal and gas sources only if a fee of 40–60 euros per ton of CO₂ is introduced. Cogeneration plants will require even higher carbon prices.

In distributed energy generation systems, the degree of competitiveness of biomass plants is increasing. In autonomous energy supply systems of small power, biomass power plants are often economically effective in comparison with energy sources with expensive imported diesel fuel [32,38,39,40].

An important issue in the analysis of economic efficiency of cogeneration plants is the consideration of the simultaneous co-generation of thermal and electric energy. For this, various methods are used to divide the total costs by type of product. When analyzing the economic efficiency of biomass cogeneration plants, Nussbaumer and Neuenschwander [41] proposed distributing costs in proportion to the prices of electricity and heat.

In [42], the heat supplied to consumers was selected as the main product, and the generated electricity is considered as a by-product. This made it possible to obtain an analytical expression for calculating the cost of thermal energy at a given cost of electric energy. This cost is the difference between the unit costs for the production of thermal energy and the unit income from the supply of electric energy. In [35], it was proposed to choose electric energy as the main product, since it is always more expensive than heat, and heat is considered as a by-product.

Technical and economic barriers to the widespread adoption of multi-stage gasification technologies may arise. Therefore, the present research focuses on the economic efficiency of mini-CHP plants with a multi-stage gasifier.

3. Wood Fuel Resources in Russia

The total annual theoretical biomass potential in Russia, including agrobiomass, exceeds 100 million toe [43]. The most accessible for energy use was the waste of the timber industry, which at the beginning of the 21st century amounted to about 11–13 million toe/year [43,44]. In autonomous systems of energy supply of small power, it is advisable to use energy sources on wood biomass as fuel, significant reserves of which are available in the north of the European part of Russia and Siberia [40]. Below are the corresponding estimates for 2018, taking into account the waste generation standards adopted in [43,44]. We consider precisely the waste of logging and timber processing, since they are of the greatest importance for Russia in general and the Irkutsk region in particular.

Table 1. Production of the timber industry complex (2018) by federal districts, mln m³/mln t.

Federal District	Logging mln m3	Lumber mln m3	Plywood mln m3	Cellulose mln t	Wood Pulp mln t
Central	25.2	1.9	1.0	0.0	0.0
Northwestern	60.8	8.0	1.3	5.2	1.5
Southern	0.7	0.2	0.0	0.0	0.04
North Caucasian	0.3	0.0	0.0	0.0	0.0
Volga	34.4	3.0	1.2	1.0	0.8
Ural	17.1	0.9	0.4	0.0	0.02
Siberian	79.0	11.6	0.3	2.2	0.0
Far Eastern	21.0	2.8	0.0	0.1	0.0
Total	238.6	28.5	4.2	8.6	2.4

shows the production volumes of the main types of products of the timber industry in Russia.

Table 2. Waste generation (fuel resource) in the Russian timber industry complex in 2018 and 2030, mln m³_.

Products	Year
	2018		2030 (Forecast)
	Production	Waste	Production	Waste
Logging	238.6	53.9–82.1	230.5–286.1	52.1–98.4
Lumber	28.5	13.1–23.9	62.1–69.5	28.6–62.6
Plywood	4.2	6.5–8.0	5.1–5.9	7.9–11.2
Tare	0.4	1.1	0.5–0.8	1.4–2.2
Cellulose	38.8	4.7	43.4–63.3	5.2–7.6
Wood Pulp	6.3	4.4	6.8–10.5	4.8–7.3
Total	316.8	83.7–124.2	348.4–436.1	100.0–189.3

shows the calculation results, in accordance with the waste generation standards adopted in Russia [40], of the wood waste amount for the current and projected volume of production of the timber industry complex.

The total amount of wood waste currently stands at 84–124 million m³/year (about 14–21 million toe (tons of oil equivalent)), by 2030 it will increase to 100–189 million m³/year (18–34 million toe).

The main resources of wood fuel waste are currently concentrated in the Irkutsk region (about 17–18 million m³/year), which ranks first among all regions of Russia. Among other federal entities, the Krasnoyarsk Territory and the Arkhangelsk region stand out [40].

4. Energy Efficiency Assessment of Wood Fuel Gasification

In order to estimate gasification efficiency, we used the limit parameters of the process, i.e., the maximum characteristics that are sought for in optimization of technological modes with a given fuel composition. For example, a performance indicator of this kind can be the maximum efficiency of gasification process in terms of thermodynamic constraints. However, to calculate it, we need to know the thermodynamically achievable composition of the resulting syngas that, in turn, depends on the parameters of the technological process. We propose to evaluate the efficiency of gasification using dimensionless criteria. The first criterion is widely used cold gas efficiency (CGE) of the gasification process, equal to the ratio of the heat value of the generator gas to the heat value of origin solid fuel [45]. The second criterion that is used in this paper is the criterion of the process autothermality, which is equal to the ratio of the heat released during “ideal” gasification to the heat required for the transition of the reaction mixture to the autothermal (or allothermal) mode, i.e.,: C_g = q_g/q_h. “Ideal” gasification means the most complete conversion of the organic matter of the fuel into fuel gas (carbon monoxide and hydrogen) by the reaction:

$${\mathrm{CH}}_h{\mathrm{O}}_o{\mathrm{S}}_s{\mathrm{N}}_n+\left(\frac{1}{2}+s-\frac{o}{2}\right){\mathrm{O}}_2=\mathrm{CO}+\frac{h}{2}{\mathrm{H}}_2+s{\mathrm{SO}}_2+\frac{n}{2}{\mathrm{N}}_2$$

Therefore, the heat released during the gasification process, q_g, will be equal to the difference between the heat value of the fuel (which can be found using the known empirical correlations based on the elemental composition) and the heat value of the syngas produced by the above reaction:

$$q_g=-\Delta H_{comb,C{H}_h{O}_o{S}_s{N}_n}^0+\Delta H_{comb,CO}^0+\frac{h}{2}\Delta H_{comb,H_2}^0$$

The value q_h is sensible heat that is required to increase temperature of the fuel and gasification agent from the initial values (fuel temperature T_f and air temperature T_air, respectively) to the ignition temperature (T_ign) of the most active component of the volatile fuel (hydrogen was chosen with T_ign = 900 K). Thermochemical calculations are carried out in terms of enthalpy changes, therefore, the heat of phase transitions (moisture evaporation, ash melting) and the release of volatiles is very simple and fairly accurately taken into account in the heat balance [46]. The sensible heat of the organic mass of the fuel is determined by the difference in the total enthalpies of combustion products at the initial temperature and the accepted ignition temperature:

$$q_h=H_{air}(T_{ign})+H_{prod}(T_{ign})+H_{ash}(T_{ign})-H_{air}(T_{air})-H_{prod}(T_f)-H_{ash}(T_f)$$

where H_air is the enthalpy of air, H_ash is the enthalpy of ash, H_prod is the enthalpy of combustion products.

Thermodynamic analysis of the efficiency of gasification using similar models was carried out in [47,48,49,50], where other methods were proposed for assessing the efficiency of solid fuel gasification based on thermochemical relations. We propose to use criterion C_g for estimating the efficiency of the gasification process for a given fuel composition and technological parameters. It is obvious that the maximum efficiency of the process is achieved under the condition C_g = 1. In this case, the minimum fraction of the heat value of the initial fuel is spent on maintaining the gasification reaction: in the terminology of [51], this process is called “thermoneutral” gasification. Under given technological conditions, the optimal parameters of the gasification process are regulated by adding steam to the reactor to reduce the outlet gas temperature (C_g > 1), or by increasing the air stoichiometric ratio (C_g < 1) [52].

The results of calculations of the cold gas efficiency and heating value of syngas obtained from some solid fuels are shown in the

Table 3. Limit characteristics of gasification of some low-grade fuels.

Fuel	Moisture Content %	Ash Content %	Organic Matter Composition %					Heat Recovery MJ/kg	Cg	CGE	Heat Value of Syngas
			C	H	O	N	S				MJ/Nm3	MJ/kg of fuel
Wood (dried)	6.8	0.4	49	6	45	0	0	0	2.76 1.0	0.44 0.80	1.97 5.74	7.21 13.29
Wood (humid)	18.25							5.91	1.0	1.23	11.68	20.26
Brown coal (dried)	10	30	63	4	32	1	0	0	1.97 1.0	0.48 0.77	2.42 4.94	6.62 10.77
Brown coal (humid)	28.9							5.65	1.0	1.26	11.62	17.28
Peat	50	10	56	6	35	1	2	0.84	1.0	0.79	5.20	7.16

. Upper rows of the cells of the table contain the initial values of the corresponding values, lower rows contain optimal (limiting) values.

A feature of the staged gasification process is heat recovery, which allows to reduce the loss of useful energy with the sensible heat of the exhaust gases [53]. This heat is returned to the gasifier after the gas combustion gas in the engine; therefore, for the gasification process, such recovery is equivalent to external heating, i.e., an additional term ∆q_r appears in the heat balance equation:

$$q_h^{’}=H_{air}(T_c)+H_{prod}(T_c)+H_{ash}(T_c)-H_{air}(T_b)-H_{prod}(T_f)-H_{ash}(T_f)+\Delta q_r$$

when this heat is used for heating and carbonization of fuel, the production of useful heat energy for supplying the consumer is reduced. However, the fraction of recovered heat is usually low: our estimates show that no more than 10–15% of the heating value of the fuel is to be recovered [31]. With a high electricity price, the unit will primarily work for electricity production. Therefore, the use of waste heat to increase electricity production will be more efficient than heat production.

Table 3 presents the results of thermodynamic calculations. For wood and brown coal, the calculations were carried out with different values of moisture content. A less humid fuel has better gasification characteristics in autothermal gasification (C_g = 1). However, if heat recovery is possible, a more humid fuel is preferred. This is due to the use of evaporated moisture as a gasifying agent [34,54]. The syngas is enriched with hydrogen and its specific heating value increases. Calculations show that during gasification of wet biomass with heat recovery of 30%, the CGE can exceed 100% (due to the recovery of heat in the form of chemical energy [55]). Naturally, if we take into account all the components of the heat balance, then the gasification efficiency will be lower (for example, with high-temperature steam gasification, the thermal efficiency is usually less than 40% [48,56]). The obtained values of the CGE are, apparently, only the upper estimate of the thermodynamic efficiency. It should be noted that the efficiency of the gasification process, in addition to thermodynamic relationships, is determined by kinetic factors that limit the completeness of the processes in a reasonable time [45,57]. Nevertheless, experimental data and theoretical estimates show the possibility of achieving CGE of the order of 80–90% [58,59].

For comparison, Table 3 presents the values of the limit efficiency of the gasification process for another two common low-grade fuels (brown coal and peat). Dry biomass gasification is more efficient than brown coal gasification because wood contains a lot of hydrogen and oxygen that can participate in the carbon gasification process. Even using heat recovery, values of CGE for biomass and lignite gasification are close, while the specific heat value of the generator gas during gasification of biomass is higher. Peat gasification is only possible with heat recovery. That is, low-grade fuel with high initial moisture content cannot be autothermally gasified with C_g = 1. Thus, a simple model based on thermodynamic relationships allows to estimate the limits of thermal stability of fuel processing.

The average efficiency of internal combustion engines when running on syngas is about 20%, and with an increase in engine power, values of about 30% can be reached [60,61,62]. Then given limiting gasification characteristics the efficiency of electricity production from biomass about of 15–30% could be achieved. Further we assume that equipment is good enough to obtain net efficiency about of 25–30%.

5. Methodology for Economic Efficiency Assessment

To assess the competitiveness of wood-fired mini-CHPs, it is necessary to compare the indicators of its construction and operation project with those of competing energy sources. Usually, net present value (NPV) is used as a criterion for effectiveness assessment of an investment project. If NPV is non-negative, then participation in the project is preferable to rejecting it; of several projects, the best project is the one with maximum NPV.

It should be noted that NPV significantly depends on the scale of the project, therefore, with its help, the effectiveness of investment options is evaluated. To assess the effectiveness of energy technologies, when it is desirable to exclude the influence of the scale of the energy supply project on the results, in [63], as in many other studies, instead of NPV, the levelized cost of energy is used. Of the few energy sources, the best is the one that provides the lowest cost of energy.

When selling both electric and thermal energy to consumers, the problem of choosing a single indicator for comparing energy sources arises. In principle, knowing the characteristics of all power plants present on trade, it is possible, by solving the problem of mathematical programming, to simultaneously find the prices of both electric and thermal energy. However, the entire set of information required for this is often incomplete or unavailable.

Below, analytical expressions are obtained for determining the unit cost of producing electric energy in the case when the cost of thermal energy is known or, conversely, thermal energy at a known cost of electric energy. The choice of one of these options is determined by what types of energy the estimated energy source produces. With the simultaneous production of electric and thermal energy, it is advisable to choose the type of energy, the sale of which makes a greater contribution to NPV, as the main one.

The NPV of the project for the construction and operation of a source of electric and thermal energy can be represented as:

$$\hat{E}={\displaystyle \underset{-\Delta T_0}{\overset{\Delta T+\Delta T_1}{\int }}E(\tau )e^{-\sigma \tau }d\tau }$$

(1)

where ΔT₀ is the construction time, ΔT is the lifetime, ΔT₁ is the dismantling time, E(τ) is the cash flow, σ is the continuous discount rate associated with the annual discount rate d by the ratio σ = ln(1 + d) [64].

For simplicity, we assume that the construction costs of K₀ and the dismantling costs of K₁ are evenly distributed over the corresponding time periods. Unforeseen expenses during the construction period K*₀ are conditionally assigned to the moment of start-up, and cash flow during the operation period consists of two components–constant E₀ and variable E₁e^μτ. The latter value increases with the growth rate μ (μ = ln(1 + μ*), where μ* is the annual growth rate), i.e., E(τ) = E₀ + E₁e^μτ. Then;

$$\begin{array}{cc}\hat{E}={\displaystyle \underset{-\Delta T_0}{\overset{0}{\int }}\left(-\frac{K_0}{\Delta T_0}\right)e^{-\sigma \tau }d\tau }-K_0^{*}+{\displaystyle \underset{0}{\overset{\Delta T}{\int }}(E_0+E_1{e}^{\mu \tau })e^{-\sigma \tau }d\tau }+& \\ & +{\displaystyle \underset{\Delta T}{\overset{\Delta T+\Delta T_1}{\int }}\left(-\frac{K_1}{\Delta T_1}\right)e^{-\sigma \tau }d\tau }\end{array}$$

(2)

From here we find;

$$\begin{array}{cc}\hat{E}=-K_0\phi (\sigma \Delta T_0)-K_0^{*}+E_0\Delta T\psi (\sigma \Delta T)+E_1\Delta T\psi ((\sigma -\mu )\Delta T)-& \\ & -K_1{e}^{-\sigma \Delta T}\psi (\sigma \Delta T_1)\end{array}$$

(3)

where

$$\phi (x)=\frac{e^x-1}{x}=1+\frac{x}{2!}+\frac{x^2}{3!}+\frac{x^3}{4!}+\dots$$

(4)

$$\psi (x)=\frac{1-e^{-x}}{x}=1-\frac{x}{2!}+\frac{x^2}{3!}-\frac{x^3}{4!}+\dots$$

(5)

The representation of the functions φ(x) and ψ(x)in the form of power series is convenient for estimates at small values of the arguments, as well as when considering limiting cases when, for example, the duration of construction or dismantling periods can be taken equal to zero.

Total capital investments are proportional to the corresponding unit investments and installed capacity W (for the supply of electric or thermal energy):

$$K_0=K_{0}W,K_0^{*}=k_0^{*}W,K_1=K_{1}W.$$

(6)

The cash flow E(τ) during the operation period is equal to the difference in revenue from the sale of electric and thermal energy and costs (fuel costs, charges for emissions of harmful substances, in particular greenhouse gases, and constant operating costs):

$$E(\tau )=p_e{e}^{{\mu }_e\tau }{Q}_e+p_h{e}^{{\mu }_h\tau }{Q}_h-p_f{e}^{{\mu }_f\tau }F-p_c{e}^{{\mu }_c\tau }F-\delta K_0$$

(7)

where p is the price, μ is the rate of its growth, Q is the annual amount of energy supplied, F is the annual fuel consumption, δ is the annual fixed cost (share of capital investment); indices: e—electric energy, h—thermal energy, f—fuel, c—emissions. It is assumed that in the general case, different prices may increase at different rates.

Given the energy balances (see Figure 2):

$$Q_e=(1-{\beta }_e){\eta }_{e}F$$

(8)

$$Q_h=(1-{\beta }_h)(1-{\eta }_e){\eta }_{h}F$$

(9)

and equating NPV to zero, we find the cost of electric or thermal energy with a known cost of energy of another kind:

$$p_e=\frac{1}{(1-{\beta }_e){\eta }_e{\psi }_e}\left[\mathsf{\Omega }-p_h(1-{\beta }_h)(1-{\eta }_e){\eta }_h{\psi }_h\right]$$

(10)

$$p_h=\frac{1}{(1-{\beta }_h)(1-{\eta }_e){\eta }_h{\psi }_h}\left[\mathsf{\Omega }-p_e(1-{\beta }_e){\eta }_e{\psi }_e\right]$$

(11)

Here we have entered the notations

$$\begin{array}{c}\Omega =\frac{k_0}{\xi }\frac{1}{\Delta T}\phi (\sigma \Delta T_0)+\frac{k_0*}{\xi }\frac{1}{\Delta T}+\delta \frac{k_0}{\xi }\psi (\sigma \Delta T)+\\ +p_f{\psi }_f+p_c{\psi }_c+\frac{k_1}{\xi }\frac{e^{-\sigma \Delta T}}{\Delta T}\psi (\sigma \Delta T_1)\end{array}$$

(12)

$${\psi }_i=\psi ((\sigma -{\mu }_i)\Delta T)i=e,h,f,c$$

(13)

and value ξ is calculated by the formula

$$\xi =\frac{h_e}{{\eta }_e}$$

(14)

if in (6) W is the electric power, or by the formula:

$$\xi =\frac{h_h}{(1-{\eta }_e){\eta }_h}$$

(15)

if W is the thermal power.

In the latest dependencies, h is the annual number of hours of using installed capacity.

6. Initial Data for Calculations

The described methodology was used to evaluate economic efficiency and to compare power plants operating on different types of fuel: mini-CHP plants on biomass, CHP plants on coal and power plants on gaseous and liquid fuels. Their main technical and economic indicators according to [35,36,64,65,66] are given in

Table 4. Technical and economic indicators of power plants on different types of fuel (cogeneration of electricity and heat).

Fuel	k, $/kW	δ, 1/year	ηe	ηh	∆T, year	Fuel Price, $/toe
Fossil Fuel
Coal	1000–1250	0.07	0.28–0.30	0.52–0.55	20	36–57
Natural gas	650–700	0.05	0.30–0.32	0.53–0.56	15	93–100
Diesel fuel	450–550	0.07	0.30–0.32	0.40–0.48	15	890–990
Biomass
Wood chips	1100–1350	0.10	0.25–0.27	0.48–0.53	20	29–72
Pellets	900–1000	0.07	0.27–0.30	0.50–0.55	20	150–200

, some indicators are presented as an interval of uncertainty. An installation with multi-stage gasification of wood fuel, purification of syngas and its use for the production of electric and thermal energy was considered as a mini-CHP on biomass [35,36].

7. Results of Calculations and Their Analysis

The electric energy cost is shown in Figure 3a,b for options without a CO₂ emission charge and with a charge of $ 30/t CO₂. For the last option Figure 4 and Figure 5 shows the structure of cost components (capital, operational, fuel, and associated with the payment for emissions) in absolute and relative units, respectively.

Calculations show that the cost of electricity mini-CHP on wood fuel (wood chips) is significantly less than the cost of electricity of a diesel power plant. In this regard, for autonomous energy systems of small power, especially near the logging points, energy supply from gasification-based mini-CHP on biomass is more preferable than the use of diesel plants with a predominance of the fuel component in the energy cost.

Compared to coal and gas power plants, wood-fired mini-CHPs can be both more and less efficient, depending on specific conditions. If there is no charge for carbon dioxide emissions, then wood-based energy sources are on average inferior to competing mini-CHP plants on coal and gas, except for the option of using cheap fuel chips at a price of $ 30–40/toe (see Figure 3a).

With the introduction of an emission charge of $ 30/t CO₂, the competitiveness area of wood-fired power plants expands. In this case, wood firing mini-CHP plants on wood chips are more efficient than coal-fired and, in some cases, gas-fired power plants (see Figure 3b). This is because the cost of energy increases significantly when using fossil fuels, especially coal, due to the component associated with the payment for emissions (see Figure 4).

Pellet power plants will be competitive with diesel power plants over the entire range of parameter changes, and with power plants on coal and gas–with the introduction of emission charges and with relatively cheap pellets (for about 140–150 $/toe). This makes it possible to exclude rigid binding of the CHP to the place of logging and to transport fuel over considerable distances.

8. Conclusions

In the global energy sector, there is a steady tendency for the rapid development of new environmentally friendly energy technologies, including the use of biomass for the production of electric and thermal energy. In Russia, there are significant resources of wood fuel (waste from the timber industry)—more than 100 million cubic meters per year. A promising area for the use of wood fuel is gasification technology, including multi-stage thermochemical conversion of biomass, which allows you to get almost tar-free syngas.

The article assesses energy and economic efficiency of mini-CHP on wood fuel and compares it with energy sources on coal, natural gas and diesel fuel. Analytical relations are obtained for calculating the cost of electric energy at a given cost of thermal energy and vice versa, thermal energy at a given cost of electric energy.

This methodology was used to compare the economic efficiency of small power plants operating on different types of fuel for the conditions of Eastern Siberia (Irkutsk Region). The options are considered without introducing a fee for carbon dioxide emissions and with the introduction of such a fee.

It is shown that the cost of electricity of mini-CHP on wood fuel (wood chips or pellets) is significantly less than the cost of electricity of a diesel power station. Compared to the energy sources of other types, mini-CHP on wood fuel can turn out to be more or less efficient depending on specific conditions.

In the absence of a charge for carbon dioxide emissions, it is economically efficient to use power plants on cheap woodchips, with the introduction of a charge for emissions, the zone of their effectiveness expands, and they are more efficient than coal and, in some cases, gas energy sources.

Pellet plants are effective in competing with diesel fuel over the entire range of parameters, and can compete with coal and gas when introducing emission charges.