Methods of Increasing the Efficiency and Yield of a Methanol Production Plant in Waste-to-Fuel Technology with an Economic Analysis

Abstract

The article describes oxygen gasification installation for waste biomass in waste-to-fuel technology, in which the final product is liquid methanol (the reference case). A comprehensive techno-economic model integrates oxygen-based gasification of wet sludge with three waste-heat recovery technologies—expander, Stirling engine, and organic Rankine cycle—and directs the recovered electrical power to a PEM electrolyzer for additional hydrogen production. The model captures full material flows, thermodynamic efficiencies, CO₂ balances, and an economic analysis over a 20-year horizon. A comparison of the use of an expander, Stirling engines, and ORC modules to power the electrolytic hydrogen generation installation was proposed. The produced hydrogen is an additional substrate for the methanol reactor, which will consequently increase the methanol yield from the entire installation and reduce the specific CO₂ emissions. Oxygen from the electrolysis process can be used in the gasifier, which will reduce the energy consumption of the Air Separation Unit, and thus increase the efficiency of the entire gasification system. In addition to the technical evaluation, an economic analysis was carried out to assess the profitability of the proposed concepts, showing that process integration can significantly improve both energy performance and economic feasibility of methanol production in waste-to-fuel systems. Results show that proposed modifications have the potential to increase overall efficiency from 75.498% (reference scenario) to even 82.545% (best scenario), while specific emissions of carbon dioxide drop from 1.746 kg CO₂/kg CH₃OH (reference scenario) to 1.468 kg CO₂/kg CH₃OH (best scenario), with an increase in methanol yield of about 9.4% (from 0.255 kg CH₃OH/kg Bio in reference scenario to 0.279 in best scenario).

1. Introduction

Methanol, also known as methyl alcohol or wood spirit, is the simplest monosubstituted alcohol. It is characterized by its high solubility in water, a low boiling point (64.7 °C), and a strong distinctive odor. Under normal conditions, it occurs as a colorless liquid, and its molecule consists of a hydroxyl group (-OH) attached to a methyl group (CH₃-). Methanol plays an important role as a solvent, a raw material in chemical synthesis, and an alternative fuel in combustion engines and fuel cells. This chemical substance can be produced from natural gas or coal, but more ecological sources—like biomass—are also used. During these processes (for example biomass gasification), hydrogen is generated as a by-product and can be captured for use in other applications, such as hydrogen-fuel technologies. Hydrogen is the simplest and most abundant element in the universe. It is a major component of water, oil, natural gas, and all living matter. Despite its simplicity and abundance, hydrogen rarely occurs naturally as a gas on Earth. It is almost always combined with other elements. It can be generated from hard coal, lignite, oil, natural gas, biomass, and bio-waste or by splitting water. Demand for hydrogen, which has grown more than threefold since 1975, continues to rise [1]. Around 70 million tons of hydrogen per year are used today in pure form, mostly for oil refining and ammonia manufacture for fertilizers. A further 45 million tons of hydrogen per year are used in industry without prior separation from other gases. This hydrogen is almost entirely supplied from fossil fuels, with 6% of global natural gas and 2% of global coal going to hydrogen production. As a consequence, the production of hydrogen is responsible for massive carbon dioxide emissions of around 830 million tons per year [2].

Of course, hydrogen is a colorless gas, but the colors mentioned are related to the technology of its production. Usually, three main colors are given: green, blue, and gray, but in fact, we have a whole palette of hydrogen colors. The hydrogen color spectrum is presented in Figure 1.

While hydrogen offers compelling advantages as a clean energy carrier, its widespread adoption faces practical barriers like high-pressure storage, extensive refueling infrastructure, and limited energy density for transport applications. These challenges have caused interest in intermediate carriers that retain the environmental benefits of hydrogen yet are easier to handle with existing logistics networks. On the other hand, methanol that can be synthesized from renewable hydrogen and captured CO₂ emerges as a promising candidate, because—as a liquid medium—it can be stored and distributed using conventional fuel-handling equipment, while still providing a pathway to decarbonize sectors where direct hydrogen use is less feasible. It is worth noting that, in various hydrogen-production methods, the attractiveness of methanol becomes particularly visible [3,4].

Alternative sources of methanol are currently the subject of much research, particularly with regard to increasing the process efficiency and reducing CO₂ emissions. This includes, among others, the high-efficiency alternative presented in [5], combining the advantages of high-temperature electrolysis, methanol synthesis, heat recovery from a turbine, and carbon dioxide separation by amine scrubbing, or the techno-economical presented in [6], which includes the use of heat pumps, along with a forecast of how the profitability of the investment may change in the future. It is worth noting that extensive integration of methanol synthesis was also presented in [7], where it was possible to achieve a lower product cost than with conventional technologies, which in particular proves that modern energy technologies can be competitive not only in terms of environmental impact but also in economic terms. Similar conclusions are also drawn in article [8], which proposes the integration of CHP installations with gasification, electricity generation, and methanol synthesis, emphasizing the possibility of combining the production of alternative fuels and modern and conventional energy installations within a single installation, thus ensuring the high technological flexibility of this solution. In [9], the integration also included other modern energy solutions such as carbon dioxide electroreduction in the methanol production process chain, which shows how unconventional methods can develop new possibilities for the production of, among others, methanol. In [10], the authors analyzed different methods of methanol production, emphasizing that it is not only technology that is an important factor in environmental impact but, above all, the regional energy mix.

Methanol as a chemical substance has a wide range of applications not only in conventional industry. Its use has been considered, among others, in [11], where the possibility of integrating energy storage with a methanol production system for combustion in a turbine was demonstrated, while in [12], the potential for producing methanol from hydrogen from an electrolyzer powered by a PV farm for use in transport was proposed. It cannot be ruled out that, in the future, methanol will be able to widely power transport, as its liquid state will greatly facilitate its implementation. A practical approach to methanol combustion in engines was presented in [13], which showed how a methanol admixture in a compression ignition engine can improve engine stability, and [14] considered admixtures in spark ignition engines, comparing several different fuel additives. The role of methanol produced from waste in some conventional processes also seems to be important, which could be particularly significant in reducing their carbon footprint and environmental impact; in [15], a combined process was considered where methanol and methane are produced simultaneously from waste gases from the steel production process (blast furnace gas, coke oven gas, and basic oxygen furnace gas). As shown in [16], methanol production from biomass can be integrated with an electrolyzer, thereby improving the process parameters, achieving an optimal efficiency of 53.3% and a payback time of 4.8 years. The above concepts of methanol as a “green energy carrier” also highlight its potential not only as a raw material but also as an energy storage medium in the future, and additional links to renewable energy sources create a sustainable production cycle, reflecting the broader trend away from fossil fuels towards energy from renewable sources. Essentially, in the context of variable renewable energy production, methanol has the potential to become one of the energy storage options by converting surplus electricity first into hydrogen and then into methanol. Such storage options would make it possible to avoid direct hydrogen storage, which poses numerous technical challenges.

The growing interest in methanol stems from its multifunctionality, as it can not only serve as a chemical feedstock and precursor for other substances but also replace traditional fuels and support the decarbonization of the transport sector. This applies not only to the aforementioned road transport, but work is also underway on the use of this fuel in rail [17], air [18], and maritime transport [19].

In general, the integration of methanol production processes offers significant benefits in terms of improving the overall efficiency of the system, but at the same time, it remains significantly influenced by external factors (such as electricity prices), which is confirmed both by the analysis carried out in this article and in [20], while [21] analyzed a wind-powered system and showed the change in methanol yield at different times of the year.

The main topic of this article is sludge, which can be an input source for methanol production. A typical problem that could appear in practice is the unstable chemical composition of sludge. The simplest form of sludge management is simple combustion after drying. Recent research has shown that there is more efficient way to convert that resource. Many analyses show the potential of sludge-based systems, as in [22], where 67.28% efficiency was achieved in methanol synthesis installation integrated with Rankine, gasification, and solar power. There are also many simpler approaches, but the efficiency in such cases is lower, as in [23], where the gasification-based process achieved 37.9%.

The conducted research provides an original contribution to the development of waste-to-fuel technologies, as it goes beyond the classical assessment of efficiency and methanol yield in biomass gasification plants integrated with methanol synthesis. It identifies new opportunities for recovering and utilizing the waste heat of syngas. While the literature contains numerous studies on gasification or on methanol synthesis alone, there is limited analysis of system integration options involving additional waste-heat recovery modules—such as expanders, Stirling engines, or ORC modules—combined with their influence on electrolyzer operation and on the overall system balance.

The innovative aspect of this work lies in presenting a consistent methodology for assessing such solutions, simultaneously covering both energy and economic performance. A particular added value is the demonstration that integrating heat recovery with hydrogen production and its further utilization in methanol synthesis makes it possible not only to increase the yield of the final product but also to reduce the specific CO₂ emissions and the production cost of methanol.

The research gap addressed in this article is the absence of comprehensive studies that consider the simultaneous integration of biomass gasification, methanol synthesis, waste heat recovery, and water electrolysis processes, combined with a techno-economic assessment. Previous studies have typically focused on a single subsystem, whereas this work provides a holistic perspective, demonstrating significant potential to improve both energy efficiency and economic feasibility compared to conventional waste-to-fuel configurations.

2. Materials and Methods

2.1. System for the Production of Methanol from Sludge (Waste Biomass)—Reference Case

The main concept of methanol production from sludge is shown in Figure 2. The system consists of two installations: waste biomass oxygen gasification (including biomass drying, gasification, and syngas enrichment by means of the WGS reaction) and the production of liquid methanol. The biomass gasification installation converts it into H₂, with the additional by-products CO₂, CO, and H₂O. The hydrogen and carbon dioxide are then compressed to the appropriate pressure to act as substrates in the methanol-producing reactor.

2.2. Oxygen Gasification Unit

In order to analyze the biomass oxygen gasification system, based on an examination of the literature [24,25], sludge was proposed as the waste biomass, and its chemical composition is presented in

Table 1. Chemical composition of biomass (wt%).

Biomass	Organic Fraction					Organic Fraction	Moisture	Ash
	C	H	N	S	O
Sludge	50.2	7.09	5.63	1.77	34.9	41.8	32.5	25.7

.

A detailed diagram of the biomass oxygen gasification installation is presented in Figure 3. The installations were modeled using the Ebsilon Professional program. The main process line leading to methanol production is labeled S1–S9, the oxygen generation section O1–O3, the energy supply stream for the air separation unit as E1, the recovered heat streams as H1–H2, and the auxiliary mass streams as A1–A6. The raw biomass (S1) is first fed to the steam dryer, where it is dried using steam (A1) at a temperature of t14 = 250 °C. The moisture content in the biomass at the outlet of the steam dryer (S2) was assumed as X = 0.05. The gasification reactor operates at 850 °C and 2.5 MPa. The dried biomass (S2) is directed to the gasifier, where it is converted into syngas (S3) through thermal decomposition in an oxygen atmosphere. The oxygen stream (O2) required for gasification is supplied from the air separation unit (ASU), which receives air (O1) and consumes electric energy (E1), producing oxygen (O2) and nitrogen (O3) as by-products. The gasifier allows partial ash discharge (A3) at a rate of 10%. Dust and solid particles are separated in the cyclone, producing a cleaned syngas stream (S4) and removing solids via A4. The dedusted syngas (S4) is then cooled in a heat exchanger, generating the heat recovery stream (H1). Next, the cooled gas (S5) enters the water–gas shift reactor (WGS), where an exothermic WGS reaction takes place, converting CO and H₂O into CO₂ and H₂ according to Equation (1):

CO_(g) + H₂O_(g) ↔ CO_2(g) + H_2(g)           ΔH = −41.2 kJ/mol (298 K).

(1)

The steam feed to the reactor (A5) is controlled to achieve maximum CO conversion and minimal residual moisture in the outlet gas. The enriched syngas (S6), composed mainly of CO₂ and H₂, is then cooled again in the second heat exchanger, generating a heat stream (H2) and producing S7, which enters the membrane separation unit. In this stage, hydrogen (S8) is separated from carbon dioxide (C1–C3) and directed to the methanol production plant, where it reacts with CO₂ to produce methanol (S9) and water (A6). The membrane separation unit operates based on the differences in gas solubility and diffusivity across the polymer membrane, using a pressure gradient as the driving force. The entire biomass gasification model was set up for a reference hydrogen production rate of 1 kg/h, allowing direct comparison of the amount of biomass required to produce 1 kg of H₂, as presented in Section 4.

The need to cool the syngas resulted from the fact that the reaction equilibrium is shifted towards the products as the temperature is lowered. This means that, at lower temperatures, it is possible to achieve a lower CO content in the synthesis gas. The working pressure in the WGSR has no influence on the equilibrium of the CO conversion but may influence the kinetics of the reaction [26]. In the analyzed system, it was assumed that an LTS conversion that allowed for the reduction in the CO concentration to 0.1% took place in the reactor. The model assumed that the steam stream to the WGSR was selected so that the moisture content in the syngas was 0.3%. The synthesis gas enriched in this way consisted mainly of CO₂ and H₂. Due to the exothermic nature of the WGS reaction, it was necessary to cool the syngas again (cooling to 30 °C was assumed).

The waste heat from the installation was high-temperature (from Syngas Cooler 1: from 850 °C to 250 °C; from Syngas Cooler 2: from approx. 570 °C to 25 °C). According to the adopted methodology, the generated power could be added to the meter (8), which would increase the energy efficiency of the gasification installation and the entire analyzed system.

Membrane separation was used to separate hydrogen from CO₂. Membrane gas separation is based on the use of differences in the solubility and diffusivity of different gases in the specific polymers that make up the membrane. It is a process in which the driving force is the pressure difference between each side of the diaphragm. The aim of the process is to enrich or deplete a given gas stream with a selected component.

The entire biomass gasification model was set up for 1 kg/h of hydrogen, which also allowed us to compare the amount of biomass of a given type needed to produce 1 kg of hydrogen (the results are presented in Section 4).

2.3. Methanol Production Plant

The production of methanol is based on the exothermic reactions of hydrogen with carbon dioxide or carbon monoxide according to the reactions:

CO_(g) + 2H_2(g) ↔ CH₃OH_(l)                           ΔH = −128 kJ/mol (298 K)

(2)

CO_2(g) + 3H_2(g) ↔ CH₃OH_(l) + H₂O_(g)            ΔH = −87 kJ/mol (298 K).

(3)

In parallel, the endothermic reverse water gas conversion reaction also takes place:

CO_2(g) + H_2(g) ↔ CO_(g) + H₂O_(g)                    ΔH = +41.2 kJ/mol (298 K).

(4)

The mass of substrates and products in the methanol synthesis reaction (2) for 1 kg of H₂ was as follows:

7.277 kg CO_2(g) + 1 kg H_2(g) ↔ 5.298 kg CH₃OH_(l) + 2.979 kg H₂O_(g),

(5)

where M_CO2 = 44.00950 g/mol; M_H2 = 2.01588 g/mol; M_CH3OH = 32.04190 g/mol; M_H2O = 18.01528 g/mol [27].

The analysis of the methanol production and purification installation was carried out for 1 kg/h_H2(g), meaning that the amount of CO₂ supplied to the installation was in accordance with the stoichiometry of Equation (5) and amounted to 7.227 kg/h. The examined plant operated according to reaction (2), within the methanol synthesis reactor (R_MeOH). Figure 4 illustrates a schematic of the methanol synthesis facility, including its reaction loop. A detailed analysis of such an installation but linked to an electrolysis installation powered by excess energy from renewable energy sources, was presented by the authors in references [28,29].

The operation of the installation began with mixing hydrogen and carbon dioxide (from the biomass oxygen gasification installation). The recycled gas stream was mixed with H₂ and CO₂ and then heated to 210 °C in a heat exchanger, HX₁, before being injected into an adiabatic fixed bed reactor, R_MeOH. The gases leaving the reactor were separated into two streams: the first (60% of the initial stream) was used to preheat the gas mixture in the heat exchanger HX₁ at the reactor inlet, while the second was sent to the distillation column’s heat exchanger (Re) and also used to preheat the column’s feed HX₃. Afterwards, the two streams were recombined and cooled to 35 °C with water in heat exchanger HX₂. The water and methanol that had been condensed in HX₂ were separated from the unreacted gases in the separator (S₁). Some of the unreacted gases were cleaned to minimize the build-up of inert substances and by-products in the reaction loop. The medium exiting the separation tank (S₁), referred to as crude methanol, primarily contains methanol, water, and other dissolved gases. This crude methanol was then throttled down to 1.2 bar using a valve. The residual gases were then nearly entirely eliminated via the separator (S₂). The remaining stream was then heated to 80 °C in the heat exchanger HX₃ before being sent to the distillation column (DC). Water exiting the column bottom at 102 °C contained 23 ppb by weight of methanol, whereas the gaseous methanol taken from the top at 1 bar pressure and 64 °C held 69 ppm by weight of water along with unreacted gases. The methanol was then compressed (F₂) and cooled in the heat exchanger HX₄ to 40 °C. In the separation column (S₃), unreacted gases were withdrawn from the top of the column, while “pure” methanol was obtained from the bottom of the column in liquid form.

Table 2. Assumptions for the methanol production and purification installation (based on [30]).

Quantity (Symbol), Unit	Value
Reactor-inlet temperature for hydrogen and carbon dioxide (tin.R.MeOH), °C	210
Operating temperature inside the methanol synthesis reactor (tout.R.MeOH), °C	284
Throttle valve’s medium pressure downstream (pout.Va), MPa	7.36
Reboiler’s outlet medium temperature (tout.Re), °C	156
Distillation column’s feed temperature (tin.DC), °C	75
Inlet temperature of the fluid entering separator S1 (tin.S1), °C	35
Temperature of water leaving heat exchanger 5 (tout.HX5), °C	40
The gas pressure at the fan 2 exit (pout.F2), MPa	0.12
Medium’s temperature at separator 3 inlet (tin.S3), °C	40

shows the main assumptions for the installation calculation.

Additionally, it was assumed that the preparation of the substrates (hydrogen and carbon dioxide) for the methanol reactor took place in a three-section compression installation with intersectional heat removal (gas cooling to an assumed temperature of 25 °C). The gases were compressed from the gasification pressure (less pressure losses occurring in the gasifier, heat exchangers, and the WGSR) to a pressure of 7.8 MPa. The model assumed equal pressure between the individual sections of compressors (calculated separately for each gasification pressure), the internal efficiency of the compressors of η_i.C = 0.88, and the mechanical efficiency of the driving device η_m.C = 0.985.

2.4. Plant Modifications for Methanol from Sludge

Modifications aimed at improving the efficiency and increasing the methanol yield are shown in Figure 5. The oxygen gasification installation of waste biomass has two potential locations to use the waste heat of the generated syngas. The first such location is in front of the shift reactor, and the second is in front of the membrane. It was proposed to compare the use of an expander, Stirling engines, and ORC modules to power the electrolytic hydrogen generation installation. The generated hydrogen serves as an extra feedstock for the methanol reactor, thereby boosting the overall methanol yield of the plant and reducing its specific CO₂ emissions. Oxygen from the electrolysis process can be used in the oxygen gasifier, which will reduce the energy consumption of the oxygen generating unit (ASU) and thus increase the efficiency of the entire gasification installation.

The efficiency of the conversion of chemical energy is expressed as the ratio of the chemical energy of the produced fuel to the chemical energy of the converted (primary) fuel:

Efficiency of converting the chemical energy of biomass into hydrogen:

$${\eta }_{H2/Bio}={\displaystyle \frac{{\dot{E}}_{H2}}{{\dot{E}}_{Bio}}}={\displaystyle \frac{{\dot{m}}_{H2}·{HHV}_{H2}}{{\dot{m}}_{Bio}·{HHV}_{Bio}}}.$$

(6)

Efficiency (total) of conversion of biomass chemical energy to methanol:

$${\eta }_{CH3OH/Bio}={\displaystyle \frac{{\dot{E}}_{CH3OH}}{{\dot{E}}_{Bio}}}={\displaystyle \frac{{\dot{m}}_{CH3OH}·{HHV}_{CH3OH}}{{\dot{m}}_{Bio}·{HHV}_{Bio}}}.$$

(7)

The energy efficiency of the gasification installation is defined similarly to the conversion efficiency in Equation (6), with the following differences: the auxiliary power of the compressors (oxygen compressor N_C.O2 and the steam fan in the dryer N_F.SD), the energy supplied to the circulation in the form of heat (steam heat in the steam dryer Q_SD and steam heat in the WGSR Q_WGSR), and the energy consumption of air separation unit:

$${\eta }_{BG}={\displaystyle \frac{{\dot{E}}_{H2}+N_{el}}{{\dot{E}}_{Bio}+N_{C.O2}+N_{F.SD}+{\dot{Q}}_{SD}+{\dot{Q}}_{WGSR}+N_{ASU}}},$$

(8)

where N_el—electric energy generated from the expander, Stirling engine, and ORC (for reference case N_el = 0)

The CO₂ unit emission indicator from the biomass gasification installation was determined as the ratio of the difference between the CO₂ mass stream generated from the gasification installation and the CO₂ mass stream directed to the methanol reactor relative to the stream of hydrogen produced:

$$e_{BG.CO2}={\displaystyle \frac{{\dot{m}}_{CO2.out}-{\dot{m}}_{RMeOH.CO2}}{{\dot{m}}_{H2}}}.$$

(9)

The total CO₂ emission factor from the analyzed system was defined analogously to Equation (10), taking into account CO₂ emissions from the methanol installation:

$$e_{CO2}={\displaystyle \frac{{\dot{m}}_{BG.CO2}-{\dot{m}}_{RMeOH.CO2.in}+{\dot{m}}_{RMeOH.CO2}}{{\dot{m}}_{CH3OH}}},$$

(10)

where ${\dot{m}}_{BG.CO2}$—CO₂ mass stream generated from the gasification installation; ${\dot{m}}_{RMeOH.CO2.in}$—CO₂ mass stream required by the methanol reactor from the gasification installation; ${\dot{m}}_{RMeOH.CO2}$—sum of the CO₂ mass streams contained in the residual gases and the waste gas.

Unit yields were determined as the ratio of the mass stream of the produced fuel to the mass stream of the converted fuel (primary):

Hydrogen yield:

$$y_{H2}={\displaystyle \frac{{\dot{m}}_{H2}}{{\dot{m}}_{Bio}}}.$$

(11)

Methanol yield:

$$y_{CH3OH}={\displaystyle \frac{{\dot{m}}_{CH3OH}}{{\dot{m}}_{Bio}}}.$$

(12)

The production potential of the biomass gasification installation can also be presented from the side of the substrate, i.e., in the form of the amount of biomass required to produce 1 kg of hydrogen:

$$\alpha ={\displaystyle \frac{{\dot{m}}_{Bio}}{{\dot{m}}_{H2}}}.$$

(13)

2.4.1. Expander

Due to the fact that the gasification process takes place in overpressure (2.5 MPa), and the pressure change in the WGSR reactor does not affect the equilibrium state of the CO conversion reaction, it is possible to use the expander (Figure 5) to produce additional electricity. It was assumed that the isentropic efficiency of the expander is η_i.EXP = 0.9, the mechanical efficiency is η_m.EXP = 0.99, and the generator efficiency is η_G = 0.986. The final pressure of the expansion process was also assumed to be 100 kPa.

2.4.2. Stirling Engine

The Stirling engine is a heat engine that converts thermal energy into mechanical energy; however, without the internal combustion process of the fuel and due to the supply of heat from the outside, it is possible to supply it with heat from any source. The Stirling engine produces energy not by deflagration—like conventional internal combustion engines—but continuously; so, it produces much less noise and does not require large flywheels to improve the smoothness of rotation. Due to the necessity to use a very large radiator, these engines were not used in the automotive industry. A simplified diagram of the Stirling engine balance model is shown in Figure 6.

Figure 6 shows that the heat flux supplying the Stirling engine ${\dot{Q}}_{in}$ should be understood as the sum of heat fluxes: useful ${\dot{Q}}_{use}$, exhaust ${\dot{Q}}_{out}$, losses ${\dot{Q}}_{loss}$, and the electric power of this engine $N_{el.SS}$ in accordance with the equation:

$${\dot{Q}}_{in}={\dot{Q}}_{use}+{\dot{Q}}_{out}+{\dot{Q}}_{loss}+N_{el.SS}.$$

(14)

In the case at hand, the heat stream feeding the engine is the heat stream of syngas feeding the first heat exchanger. The loss stream takes into account the efficiency of the heat exchanger η_HX (η_HX = 0.99), the supply heat flux ${\dot{Q}}_{in}$, and the exhaust heat flux ${\dot{Q}}_{out}$ from the engine:

$${\dot{Q}}_{loss}=\left(1-{\eta }_{HX}\right)·\left({\dot{Q}}_{in}-{\dot{Q}}_{out}\right).$$

(15)

The electric power of the Stirling N_el.SS engine is understood as the difference between the supply heat flux ${\dot{Q}}_{in}$ and the outlet heat flux ${\dot{Q}}_{out}$, taking into account the electric efficiency of the motor η_el.SS in accordance with the equation:

$$N_{el.SS}={\eta }_{el.SS}·\left({\dot{Q}}_{in}-{\dot{Q}}_{out}\right).$$

(16)

The electricity generation efficiency of the Stirling engine was determined based on the electrical efficiency characteristics of the Stirling engine (Philips 1–98 [31]), including the temperature of the upper and lower heat source.

The Carnot efficiency was calculated as the difference between the average temperatures of the upper ${\stackrel{-}{T}}_{g.\mathrm{ź}}$ and lower heat source ${\stackrel{-}{T}}_{d.\mathrm{ź}}$ and the temperature of the upper heat source ${\stackrel{-}{T}}_{g.\mathrm{ź}}$:

$${\eta }_{ca}={\displaystyle \frac{{\stackrel{-}{T}}_{g.\mathrm{ź}}-{\stackrel{-}{T}}_{d.\mathrm{ź}}}{{\stackrel{-}{T}}_{g.\mathrm{ź}}}}.$$

(17)

2.4.3. Organic Rankine Cycle

The last proposed solution is the use of the ORC module for heat recovery. The diagram of the ORC module is shown in Figure 7. The organic Rankine cycle functions analogously to the classical Rankine cycle; however, it uses the organic factor as a circulating factor. In the analyzed case, benzene was used as a circulating medium. The main assumptions for the operation of the ORC module are presented in

Table 3. Assumptions for the calculations of ORC modules.

Quantity	Symbol	Value	Unit
Internal efficiency of the turbine	ηiEXP	84	%
Mechanical efficiency of the turbine	ηmEXP	98	%
Internal efficiency of the circulation pump	ηiCP	83	%
Electro-mechanical efficiency of a circulation pump	ηel-mCP	98	%
Generator efficiency	ηG	98	%
Relative pressure loss of the refrigerant on the economizer	ζECO	2	%
Cooling water temperature at the inlet condenser	t1c	15	°C
Cooling water temperature difference at the inlet of the ORC condenser and the temperature of the working medium at its outlet	∆tI	10	K
Temperature difference of the working medium at the outlet of the recuperator (4′s) and the temperature of the medium at its inlet (2s)	∆tII	5	K

. In the ORC module boiler, ΔT_pp was kept at such a level that the temperature of the medium at the boiler outlet was 250 °C. The pressure of the medium downstream of the turbine in the module was assumed as the saturation pressure for the temperature of 25 °C. The pressure at the inlet to the turbine was assumed to be 4.25 MPa.

3. Methodology of Economic Analysis

As part of this study, a net-present-value (NPV) economic analysis was conducted to calculate the break-even methanol price for each of the five process variants.

3.1. Basic Assumptions

The most important assumptions for the economic analysis are presented in

Table 4. Input data for economic analysis.

Symbol	Value	Unit	Explanation	Source
T	20	Year	Lifetime of investment	Assumption
τ	8000	Hour	Nominal annual operating time	Assumption
ṁBio	18.064	kg/h	Wet biomass stream for gasification	Assumption
kBio	0.0493	USD/kg	Biomass unit price	[32]
Ppom	3.694	kW	Auxiliary equipment power	Assumption
H	4.182	kW	Thermal power of equipment	Assumption
kQ	29.936	USD/GJ	Heat price	[33]
PASU	0.590	kW	Air separation unit power	Assumption
kel	0.151	USD/kWh	Electricity price	[34]
yMeOH	0.27	kgCH3OH/kgBio	Methanol yield	Assumption
r	0.05	-	Discount rate	Assumption

.

For currency conversions, the EUR to USD exchange rate was set at 1.1 and 3.75 for USD to PLN (as of 10 May 2025).

3.2. Capital Expenditures

Capital expenditures consist of four elements: Stirling engine, ORC, air separation unit, and gasification installation. In total,

$$CAPEX=C_{SS}+C_{ORC}+C_{ASU}+C_{EXP}+C_{PEM}+C_{GAS},$$

(18)

where—depending on the analyzed option—some of these components may be absent (could be equal to 0). They are expressed as follows:

$$C_{SS}=P_{Stir}\cdot J_{SS},$$

(19)

$$C_{ORC}=P_{ORC}\cdot J_{ORC},$$

(20)

$$C_{ASU}={PR}_{ASU}\cdot J_{ASU},$$

(21)

$$C_{EXP}=P_{EXP}\cdot J_{EXP},$$

(22)

$$C_{PEM}={\displaystyle \frac{P_{PEM}}{{\eta }_{PEM}}}\cdot J_{PEM},$$

(23)

$$C_{GAS}=P_{GAS}\cdot J_{GAS}.$$

(24)

The power of the electrolyzer was calculated based on the generated (specific variant from 5) stream of hydrogen:

$$P_{PEM}={\dot{m}}_{H2}\cdot 3600s\cdot \mathrm{119,960} {\displaystyle \frac{\mathrm{k}\mathrm{J}}{\mathrm{k}\mathrm{g}}}.$$

(25)

All assumed values of the capital expenditures are presented in

Table 5. Data of CAPEX calculation.

Variable name	Value	Unit	Source
JASU	100,000	USD/(MgO2/day)	[35]
JEXP	6105	USD/kW	Author’s assumption
JGAS	90	USD/kW	[36]
JORC	1861	USD/kWel	[37]
JPEM	2000	USD/kWel	[38]
JSS	400	USD/kW	[39]
PEXP	As in Table 4	kW	Author’s assumption
PGAS	50	kW	Author’s assumption
PORC	As in Table 4	kW	Author’s assumption
PPEM	Calculated (25) with 5. data	kWH2	Author’s assumption
PRASU	Calculated (26) with 5. data	MgO2/d	Author’s assumption
PSS	As in 5	kW	Author’s assumption
ηPEM	0.7	-	Author’s assumption

.

The amount of oxygen produced in ASU was calculated using the assumption that the energy consumption of the separation process is 0.18 kWh/kg_O2.

$${PR}_{ASU}={\displaystyle \frac{0.5899\mathrm{k}\mathrm{W}\cdot 24\mathrm{h}}{\frac{0.18\mathrm{k}\mathrm{W}\mathrm{h}}{{\mathrm{k}\mathrm{g}}_{{\mathrm{O}}_2}}}}={\displaystyle \frac{0.0787{\mathrm{M}\mathrm{g}}_{{\mathrm{O}}_2}}{d}}$$

(26)

3.3. Annual Rate of Return on Investment

The annual rate of return on investment (R) is expressed as follows (27):

$$R={\displaystyle \frac{r\cdot {\left(1+r\right)}^T}{{\left(1+r\right)}^T-1}},$$

(27)

where r is the discount rate, and T is the time of investment expressed in years.

3.4. Cash Flow

The cash flow consists of the methanol sold, (S_MeOH), the heat cost (K_Q), the electricity cost, (K_el) and the biomass cost (K_Bio).

$$CF=S_{MeOH}-K_Q-K_{el}-K_{Bio},$$

(28)

where the subsequent components of the sum are

$$S_{MeOH}=C_{MeOH}\cdot y_{MeOH}\cdot m_{bio},$$

(29)

where m_bio is the mass of biomass consumed in a given year, which is the product of the biomass stream (ṁ_bio) and the operating time of the installation (τ).

$$K_Q=\left({\displaystyle \frac{k_Q}{{10}^9}}\right)\cdot 8760\cdot \tau \cdot \left(1000\cdot H\right)\cdot {\displaystyle \frac{\left(\frac{m_{Bio}}{\tau }\right)}{{\dot{m}}_{{Bio}_{REF}}}},$$

(30)

where ${{\dot{m}}_{Bio}}_{REF}$ is a reference (this part of the formula only becomes relevant when the biomass flux is changed) biomass stream, equal to ṁ_Bio.

$$K_{el}=k_{el}\cdot \left({PR}_{ASU}+P_{pom}\right)\cdot {\displaystyle \frac{\left(\frac{m_{bio}}{\tau }\right)}{{\dot{m}}_{{Bio}_{REF}}}}$$

(31)

$$K_{Bio}=k_{Bio}\cdot m_{Bio}$$

(32)

3.5. Methanol Production and Its Break-Even Price

The annual methanol production depends solely on the amount of biomass gasified:

$$m_{MeOH.y}={\dot{m}}_{Bio}\cdot \tau \cdot y_{MeOH}=y_{MeOH}\cdot m_{Bio}.$$

(33)

The break-even price of methanol is expressed as follows (34):

$${BEP}_{MeOH}={\displaystyle \frac{K+\left(CAPEX\cdot R\right)}{m_{MeOH,y}}},$$

(34)

where

$$K=K_H+K_{el}+K_{Bio}.$$

(35)

4. Results

4.1. Thermodynamical Analysis

The analysis demonstrated that every proposed configuration enhanced both the overall efficiency and the methanol yield, as reported in

Table 6. Comparative analysis results (for 1 kg H₂/h produced from BG installation).

Case	I	II	III	IV	V	VI	VII
Quantity, Symbol, Unit	REF	EKS+	EKS+	SSI+	SSI+	ORCI+	ORCI+
		SSI	ORCI	SSII	ORCII	SSII	ORCII
Expander power EXP, kW	-	3.19	3.19	-	-	-	-
Stirling engine power SSI, kW	-	1.976	-	1.976	1.976	-	-
Stirling engine power SSII, kW	-	-	-	2.12	-	2.12	-
Module power ORCI, kW	-	-	1.065	-	-	1.065	1.065
Module power ORCII, kW	-	-	-	-	1.251	-	1.251
Produced hydrogen stream from electrolysis; kg/h	-	0.0914	0.0753	0.0725	0.0571	0.0563	0.041
Produced oxygen stream from electrolysis, kg/h	-	0.7259	0.5979	0.5756	0.4535	0.4476	0.3255
Oxygen compressor drive power, NC.O2, kW	0.539
Steam dryer fan power, NF.SD, kW	0.445
The heat of the supply steam SD, QSD, kW	1.201
The heat of the supply steam WGSR, QWGSR, kW	2.981
H2 compressor drive power, NC.H2, kW	1.635
CO2 compressor drive power, NC.CO2, kW	1.075
ASU Energy consumption, NASU, kW	0.6352	0.5425	0.5648	0.5686	0.5899	0.5909	0.6122
Conversion efficiency H2/Bio, %	84.914	92.675	91.308	91.07	89.763	89.695	88.395
Conversion efficiency CH3OH/Bio, %	61.008	66.584	65.602	65.431	64.492	64.443	63.51
Efficiency of the installation BG, %	75.498	82.545	81.293	81.075	79.878	79.816	78.628
Unit lift of CO2 from the installation BG, kg CO2/kg H2	14.631
Specific CO2 emissions from the installation BG, kgCO2/kg CH3OH	1.746	1.468	1.513	1.521	1.566	1.569	1.615
Specific CO2 emissions from the installation BG, kg CO2/kg Bio	0.445	0.410	0.415	0.417	0.423	0.424	0.430
Methanol yield, kg CH3OH/kg Bio	0.255	0.279	0.274	0.274	0.270	0.270	0.266

. When the expander and the Stirling engine were operated together, the plant achieved the greatest efficiency improvement, raising the total conversion efficiency by roughly 7 percentage points. This synergistic arrangement also increased the methanol recovery from the entire system by approximately 0.024 kg CH₃OH per kilogram of biomass processed. Conversely, the organic Rankine cycle (ORC) modules performed least effectively, contributing only an estimated 3.2-percentage-point increase in the biomass gasification efficiency. Additionally, the supplementary hydrogen stream produced by the waste-heat-driven electrolyzer and fed to the methanol synthesis unit reduced the specific CO₂ emissions of the installation to 1.468 kg CO₂ per kilogram of gasified biomass. These findings highlighted the relative advantages of the expander–Stirling combination and underscored the importance of integrating waste-heat recovery with hydrogen augmentation to maximize both energetic and environmental benefits.

From the thermodynamical point of view, option II seems to be most favorable. It has an increase in energy efficiency over the reference scenario from 75.498% to 82.545%, which at the same time causes a drop in carbon dioxide emissions from 1.746 kg CO₂/kg CH₃OH to 1.468 kg CO₂/kg CH₃OH. In this variant, there is also the highest stream of oxygen (approx. 17% more than in variant II) and hydrogen (approx. 21.3% more than in variant IV), compared to another modifications. However, the break-even price of methanol in this scenario is not the lowest: approx. 0.2% higher than in variant IV, which consists of two Stirling engines. From all the calculated modifications, the worst performance appeared in option VII, which consists of two ORCs. Compared to variant II, the installation efficiency is 78.628% (which is approx. 4 pp less), while the specific emissions are approx. 10% higher. It is worth noting that even this variant has better performance than the reference scenario.

4.2. Economic Analysis

The results of all the calculated variants are shown in

Table 7. Comparative analysis results.

Case	I	II	III	IV	V	VI	VII
Quantity, Symbol, Unit	REF	EKS+	EKS+	SSI+	SSI+	ORCI+	ORCI+
		SSI	ORCI	SSII	ORCII	SSII	ORCII
Methanol yield, kg CH3OH/kg Bio	0.255	0.279	0.274	0.274	0.270	0.270	0.266
Break-even price of methanol, USD/t (BEPMeOH)	623.88	591.34	603.75	590.54	601.56	600.92	612.28
Energy cost of methanol produced, USD/MWh	93.86	88.97	90.83	88.85	90.51	90.41	92.12

.

The cost structure is presented in Figure 8, distinguishing three main categories: heat, electricity, and biomass.

The largest share of the total cost of operating the installation is the cost of heat, which is USD 8773, 41.6% of all expenses. This indicates the crucial importance of the effective thermal management of the analyzed process. The second largest category is the biomass costs, which are USD 7128, equal to 33.8% of the total cost. The smallest share in the cost structure is held by the electricity costs, which amount to USD 5175, 24.6% of total expenses. The chart also shows that the costs are approximately evenly distributed, and none of them visibly dominates over the others. Figure 9 illustrates both the investment and operating costs that have the highest impact on the price of methanol, and it shows that capital expenditures have a small share in the cost of the product.

Sensitivity analysis

This sensitivity analysis compares the impact of changes in the following six parameters on the limit price of methanol:

• Mass flow of biomass gasified,
• Capital expenditures,
• Biomass price,
• Heat price,
• Electricity price,
• Discount rate.

All the above parameters were changed as shown in

Table 8. Sensitivity analysis variables and their ranges.

Variable	Minimal Value	Nominal Value	Maximal Value
Mass flow of biomass gasified, kg/h	12.645	18.0640	23.483
Electricity price, USD/kWh	0.106	0.151	0.197
Discount rate	0.0350	0.0500	0.0650
Capital expenditures, USD	17,445	24,922	32,399
Annual working time (τ), h	5600	8000	8000
Biomass price, USD/kg	0.0345	0.0493	0.0641
Heat price, USD/GJ	20.955	29.936	38.917

.

As can be seen from Figure 10, the installation is moderately sensitive to changes in capital expenditures, discount rate, biomass flow, operating time, electricity, and biomass cost. A 30% increase in CAPEX results in a cap price increase of just over 2%. Moderate sensitivity occurs for the discount rate; its increase of 30% increases the limit price by about 2.5%. The highest sensitivity occurs in the following cases:

• Changes in the price of electricity—an increase of 30% causes an increase in the limit price by almost 7%.
• Changes in the price of biomass—an increase of 30% results in an increase in the limit price by more than 9%.
• Changes in the price of heat—an increase of 30% results in an increase in the limit price by over 11%.

The diagrams below show how the cut-off price of methanol (marked on isolines) changes when selected installation parameters are changed (on the vertical axis) as a function of the installation operating time per year (horizontal axis). Figure 11 shows the change in the stream of biomass for gasification, Figure 12 shows the change in total capital expenditures, and Figure 13 shows the change in the price of electricity.

The graph in Figure 11 shows that the change in the price of the biomass stream for gasification has a higher impact in the case of short operating times; then, a higher density of isolines is visible. With the increase in the operating time of the installation, the increases in the limit price are not as strong. The course of the curves once again emphasizes the conclusions of the sensitivity analysis—the system is highly sensitive to changes in the stream of biomass to be gasified, but this does not cause significant changes in the limit price. In the case of a working time of 4490 h, an increase in the biomass stream from 14.93 kg/h to 26.10 kg/h results in a decrease in the limit price by approx. 4%.

The situation is slightly different in the case of the change in the capital expenditures presented in Figure 12. As shown, the curves are characterized by a high inclination, which emphasizes the high sensitivity of the analyzed system to changes in this variable; the longer the operating time of the installation, the lower the inclination. It is visible that with a working time of 5900 h, an increase in CAPEX from USD 24,930 to USD 46,680 raises the break-even price by as much as approx. 11%. With the decrease in working time, the increases are greater.

In the case of the change in electrical energy seen in Figure 13, a very strong correlation with the operating time is observed; in the case of low operating times, the curves are very steep, which emphasizes the significant sensitivity of the system to this variable; As the working time increases, the curves flatten. For an electric price of USD 0.12/kWh, a USD 0.04/kg_MEOH price reduction from USD 0.76 to USD 0.72 requires an increase in operating time of approximately 570 h, but with an electric price of USD 0.14/kWh, the same price decrease requires an increase in operating time of approximately 650 h.

5. Conclusions

The study uses three technologies for utilizing the waste heat of syngas downstream of the waste biomass gasification reactor (sludge) to produce additional electricity. Stirling engines, ORC modules, and an expander were examined.

• The additional electricity allowed the production of an additional stream of hydrogen (and oxygen) from the electrolysis process. The combination of the expander and the SS_I Stirling engine turned out to be the most effective, due to the fact that it was possible to generate 0.0914 kg H₂/h (remembering that it is calculated in relation to the unit production from the gasification installation—1 kg H₂/h).
• The produced electrolytic oxygen was directed to the gasification reactor, where the gasification process takes place in an atmosphere of pure oxygen. Additional oxygen from the electrolysis process relieves the ASU installation, which reduces its energy consumption and, as a result, improves the efficiency of the entire gasification installation. In the case of the best variant, it was possible to reduce the energy consumption of the ASU by approx. 0.9 kW, which allowed achieving an increase in the efficiency of the gasification installation by approx. 7 pp. to the level of 82.545%.
• The electrolytic hydrogen is directed to the installation for the production of liquid methanol. This means that, due to the additional amount of hydrogen in the methanol reactor, an additional amount of CO₂ is required, which ultimately reduces the CO₂ unit emissions from the installation and increases the methanol yield per unit of biomass. The reduction in the specific emissions in each analyzed variant is not much; in the best combination, it amounted to 0.278 kg CO₂ per kg of produced methanol. The methanol yield from the entire installation increased by approx. 0.024 kg CH₃OH/kg Bio.
• As shown in the economic analysis, the break-even price of methanol is strictly correlated with the structure of the analyzed system and may vary by more than 5%. Taking into account the tabulated data (Table 4), it was calculated that the system including two Stirling engines without any ORC can provide the lowest methanol break-even price.
• The achieved efficiency is slightly better than the integration proposed in [22] (approx. 13.8 p.p. higher compared to the lowest break-even price variant) and much better than standard gasification-based process as in [23] (approx. 43 p.p. higher) compared to the lowest break-even price variant)
• Emissions of carbon dioxide in the reference scenario are equal to 63,432 kg per year. The most thermodynamically efficient variant with an expander and Stirling engine (II) achieves emissions of 59,188 kg_CO2 per year, which means a reduction of 5153 kg_CO2 (approx. 8%). The most economically advantageous option—with two Stirling engines (IV)—emits 60,225 kg_CO2 per year, which is a reduction of 4116 kg_CO2 (approx. 6%) compared to the reference option.

Further work should be carried out with dynamic simulations of the integrated system to assess its behavior under variable operating conditions, separately extending the composition analysis to alternative types of biomass to verify the universality of the energy and environmental benefits obtained, and then running a pilot experiment of the most promising configuration, which will allow for the validation of the model cost and emission projections under real industrial conditions.

This scientific work was conducted as a part of the statutory research of the Silesian University of Technology.