Gasification of Lignocellulosic Waste in Supercritical Water: Study of Thermodynamic Equilibrium as a Nonlinear Programming Problem

: As one of the main industrial segments of the current geoeconomics scenario, agro-industrial activities generate excessive amounts of waste. The gasification of such waste using supercritical water (SCWG) has the potential to convert the waste and generate products with high added value, hydrogen being the product of greatest interest. Within this context, this article presents studies on the SCWG processes of lignocellulosic residues from cotton, rice


Introduction
Fossil fuels are limited, and the urgent need to increase the use of renewable energy sources, along with the alarming daily release of CO 2 into the atmosphere, is a major concern.Consequently, various economic and environmental factors are driving a renewed interest in developing and improving manufacturing alternatives to reduce greenhouse gas (GHG) emissions and support modern society [1].
In this context, using agro-industrial waste, especially in Brazil, presents an appealing alternative due to the country's high production rates and the large amount of waste generated.Lignocellulosic residues, in particular, are produced in significant volumes through various processes.Examples include sugarcane bagasse from the sugar and ethanol industries, as well as residues from other production chains like rice, cotton, and mustard [2,3].
Eng 2024, 5 1097 These wastes can be used in various value-added processes, including thermochemical processes, especially those aimed at hydrogen production.Hydrogen has a higher energy density compared to common and widely used fossil fuels, such as natural gas, with a key difference that hydrogen can be obtained from renewable sources and has water as its only oxidation product-thus contributing to avoiding climate change and reducing GHG emissions.A variety of such processes have been under investigation over the years, such as the thermochemical conversion of agro-industrial residues into hydrogen [4].
One pathway for producing hydrogen using thermochemical processes from biomass materials involves supercritical water (SCW).This is a promising reaction medium for organic components due to its unique physicochemical properties that at temperatures above 374 • C and pressures above 22.1 MPa allow overlap with the critical point of water, weakening the hydrogen bonds and resulting in a high dielectric constant and strong solubility of organic compounds such as biomass [5].
The composition of gasified biomass is primarily influenced by the reaction temperature [6].There are three key reactions involved in the gasification of lignocellulosic biomass, as shown in Equations ( 1)-( 3): The thermal characteristics of Equations ( 1)-( 3) were evaluated at a reference temperature of 298 K.Under SCWG conditions, the system exhibits low viscosity, which enhances mass transfer.This improved mixing of biomass with water hinders polymerization reactions, leading to the formation of simpler compounds, such as H 2 , and increases gasification efficiency [7,8].In biomass conversion processes, water can be said to fulfill all possible functions it can act as a solvent, catalyst, catalyst precursor, and reagent [9].
In Freitas and Guirardello [10], sugarcane bagasse was converted into syngas using SCW media with CO 2 as a co-reactant.This study was performed using the Gibbs energy minimization method in combination with the virial Equation of State (EoS).In Mitoura et al. [11], the methane cracking process was verified using ideal gas consideration in a thermodynamic study based on Gibbs energy minimization and entropy maximization methods.In Freitas and Guirardello [12], various glycerol (residue of biodiesel production) reforming technologies were studied to produce hydrogen.In all of these studies, the systems were thermodynamically considered using the Gibbs energy minimization method in combination with the virial EoS.Furthermore, the systems were thermodynamically evaluated using simple thermodynamic models (ideal gas and virial EoS); meanwhile, in other studies in the literature more complex thermodynamic models were used, such as Peng Robinson's state research.But in these cases, a stoichiometric approach (which does not consider all possible reactions) was used, as in Castello and Fiori [13].
This work addresses gasification processes using agro-industrial waste (composed of cotton, mustard and rice husk) using supercritical water as a reaction medium.Thermodynamic models based on Gibbs energy minimization and entropy maximization methods combined with the Peng-Robinson (PR) equation of state (EoS) were used to represent the phase behaviors of these complex systems.The models were formatted as optimization routines as non-linear programming problems using a non-stoichiometric approach (considering all possible reactions).
Process variables, such as temperature, pressure, and inlet composition were also evaluated to maximize hydrogen production and study the thermal behavior of all processes.The results of this work provide a complete thermodynamic analysis of this type of system, including the development of a robust, reliable, and efficient thermodynamic model.Moreover, its computational time is low despite the use of complex state equations such as the PR EoS.

Thermodynamic Approach
To predict the biomass gasification process in isothermal reactors, the thermodynamic Gibbs energy minimization method was employed.In this method, a thermodynamic equilibrium is reached when the system's total Gibbs free energy is minimized, making it a common objective function for evaluating equilibrium processes [6,14].To verify the thermal behavior of the reaction process, the entropy maximization method was utilized [15].
The use of Gibbs energy minimization and entropy maximization methodologies is crucial for evaluating the thermodynamic behavior of SCWG processes.MinG predicts equilibrium states by minimizing Gibbs energy, offering insights into isothermal reactor performance, while maxS assesses thermal behavior by maximizing entropy, key for adiabatic reactor dynamics.Both methods were formulated as nonlinear programming tasks with appropriate constraints.The following sections detail the thermodynamic approach for lignocellulosic biomass SCWG processes.

Chemical and Phase Equilibrium Formulated as a Gibbs Energy Minimization Problem: Calculation of Isothermal Reactor
The Gibbs energy of a system at constant temperature (T) and pressure (P) is described by Equation ( 4).In this context, the index i represents the different chemical species present, and k represents the different phases present: According to Sandler [16], the chemical potential can be defined as shown in Equation (5): Fugacity in a multicomponent and multiphase system can be determined using the Phi-Phi (φ-φ) method, which is more suitable for handling cubic state equations.Thus, the objective function for minimizing the total Gibbs energy of the system, at constant pressure and temperature, can be rewritten as Equation (6): By directly minimizing Equation ( 6), while taking into account mass balance and stoichiometry constraints, a unified chemical and phase equilibrium point is attained.To ensure the system reaches a suitable solution, two additional constraints must be incorporated.The first constraint involves ensuring the non-negativity of the number of moles, as outlined in Equation ( 7), for each component within each phase [10].
Gasification using supercritical water as a reactive medium occurs under conditions of high pressure and temperature.It is assumed that no components form in the liquid phase; however, both phases are still considered in the modeling process.To simplify the thermodynamic modeling, the solid phase is treated as ideal, as indicated by Equation (7), thus eliminating the need to estimate non-idealities.This approach seems reasonable given the significant amounts of water introduced into the reactive system during supercritical water gasification, which hinders the formation of solid phase components [10,12,17].
In contrast to the assumption of ideality for the solid phase, the vapor and liquid phases cannot be considered ideal due to the process conditions, which make such an Eng 2024, 5 1099 assumption impractical.Equations ( 8) and ( 9) describe the chemical potentials of the vapor and liquid phases, respectively: For predicting fugacity coefficients in reaction systems under supercritical conditions, the selection of equations of state (EoS) must be done carefully.There are reports of successful applications of the Peng-Robinson (PR) and Peng-Robinson Boston Mathias (PR-BM) EoS in studying supercritical biomass-in-water gasification reaction systems [6,18,19].In this study, the Peng-Robinson Palatino Linotype EoS was applied to calculate the fugacity coefficients of the verified system, using simplified mixing rules as reported by Downling et al. [20].

Chemical and Phase Equilibrium Formulated as an Entropy Maximization Problem: Calculation of an Adiabatic Reactor
The second stage of this work involves applying the entropy maximization methodology, as described in Equation (10), for the thermodynamic evaluation of gasification reactions with supercritical water from various biomass sources.These methodologies have been applied to a wide range of systems in the field of chemical reaction engineering, including systems that transform biomass into fuels [10] and methane cracking processes [11].
These problems are subject to the restrictions of Equations ( 8) and (9), which pertain to the non-negativity of the number of moles and the balance of atoms, respectively, as well as the minimization of Gibbs energy.Additionally, they must comply with the enthalpy balance restriction, as outlined in Equation (11):

Calculation of Fugacity Coefficients Using the Peng-Robinson Equation
The Peng-Robinson (PR) equation of state was utilized to assess the non-ideality of the system.This equation is noted for its balance of simplicity and accuracy.It was developed to perform as well as or better than the Soave-Redlich-Kwong (SRK) equation by altering the attractive pressure term of the semi-empirical Van der Waals equation [21].Equations of state can be formulated as cubic equations in terms of the compressibility factor Z, commonly represented by Equation (12): where A and B are dimensional coefficients that vary with temperature, pressure, and phase composition according to the classical mixing rule described by Downling et al. [20].The parameters u and w are set to 2 and −1, respectively, as specified in the Peng-Robinson equation of state.Equation (12) approximates the real behavior of the liquid and vapor phases for various fluids.Solving this equation yields either one or three real roots, which are then used to calculate the fugacity coefficients using the phi-phi method applied in this study [16].

Mathematical Formulation and Solution of the Equilibrium Problem
In their research, Kamath, Biegler, and Grossmann [22] established criteria for the cubic equation of state to ensure accurate root selection.They found that the first derivative with respect to Z must be positive to avoid selecting the root's mean value.Additionally, the second derivative plays a crucial role in determining the roots of the liquid and vapor phases.The larger root corresponds to the vapor phase, and its second derivative must be greater than or equal to zero.Conversely, the smaller root, representing the liquid phase, must have a second derivative less than or equal to zero.Equations ( 13)-( 16) present these constraints specifically for the Peng-Robinson equation: f To prevent the selection of a root lacking physical significance, Kamath, Biegler, and Grossmann [22] introduced slack variables (σ v and σ l ) into Equations ( 15) and ( 16).This strategy mitigates discontinuities caused by the disappearance of one of the system phases, leaving only either the gaseous or liquid phase.
A total of 12 potential components were taken into account during the biomass SCWG process.These components, along with their thermodynamic properties, are detailed in Table 1.They were chosen to represent the main compounds expected to emerge during the supercritical water biomass gasification.This selection stems from extensive literature findings, which suggest that these components are commonly present in notable quantities during gasification processes involving biomass from diverse origins [6,10,12,17,23,24].
The lignocellulosic residues were written as pseudocomponents.Table 2 shows the analysis for each biomass evaluated in this work, as well as their key parameters such as hydrogen/carbon and oxygen/carbon ratios.Kang et al. [25] and Vassilev et al. [26] reported the ultimate analysis for many agroindustrial residues.* The ratios of hydrogen to carbon and oxygen to carbon are represented on a molar basis.
The formulated nonlinear programming (NLP) problems were addressed using the TeS-Thermodynamic Equilibrium Simulation software and the trust-constr solver.This choice is informed by the numerous advantages offered by the trust-constr solver for the type of approach employed in this study.Specifically, it is suitable for models characterized by highly nonlinear constraints, designed to handle large-scale models, and can be applied to models without differentiable functions [28].This approach has consistently demonstrated high levels of accuracy and efficiency and has yielded excellent results in a variety of systems, particularly those involving chemical equilibrium and mixed phases [12,17,29,30].

Methodology Validation
This section aims to present results that support the application of the proposed methodology.The methodologies presented in Section 2 were validated using experimental data reported by Chakinala et al. [31] and Gomes et al. [6] who verified the SCWG processes of microalgal biomass in isothermal and adiabatic systems.

Methodology Validation for Isothermal Systems Using Gibbs Energy Minimization
Chakinala et al. [31] investigated the SCWG process of Chlorella vulgaris microalgal biomass using Ru/TiO 2 catalysts.This study was conducted at 240 bar, with the biomass feed set at 7.3% wt. Figure 1 presents a comparison between the results obtained by applying the previously described Gibbs energy minimization methodology, using the Peng-Robinson equation of state and the ideal gas model.The calculated results are plotted alongside those reported by Chakinala et al. [31] at 973.15 K.
TeS-Thermodynamic Equilibrium Simulation software and the trust-constr solver.This choice is informed by the numerous advantages offered by the trust-constr solver for the type of approach employed in this study.Specifically, it is suitable for models characterized by highly nonlinear constraints, designed to handle large-scale models, and can be applied to models without differentiable functions [28].This approach has consistently demonstrated high levels of accuracy and efficiency and has yielded excellent results in a variety of systems, particularly those involving chemical equilibrium and mixed phases [12,17,29,30].

Methodology Validation
This section aims to present results that support the application of the proposed methodology.The methodologies presented in Section 2 were validated using experimental data reported by Chakinala et al. [31] and Gomes et al. [6] who verified the SCWG processes of microalgal biomass in isothermal and adiabatic systems.

Methodology Validation for Isothermal Systems Using Gibbs Energy Minimization
Chakinala et al. [31] investigated the SCWG process of Chlorella vulgaris microalgal biomass using Ru/TiO2 catalysts.This study was conducted at 240 bar, with the biomass feed set at 7.3% wt. Figure 1 presents a comparison between the results obtained by applying the previously described Gibbs energy minimization methodology, using the Peng-Robinson equation of state and the ideal gas model.The calculated results are plotted alongside those reported by Chakinala et al. [31] at 973.15 K.
The results in Figure 1 indicate a noticeable divergence between the calculated data and the literature when using the ideal gas model, which is expected given the nature of the reaction system and the thermodynamic limitations of the ideal gas model.When the gas is considered real, by using the Peng-Robinson (PR) equation of state to calculate the fugacity coefficients the calculated results align satisfactorily with those reported by Chakinala et al. [31], achieving a correlation coefficient (R 2 ) greater than 0.999.This outcome underscores the necessity of employing more robust models to predict nonidealities.The PR equation offers better predictions than ideal models due to its high precision within the utilized temperature and pressure range and its accurate calculation of fugacity for the components present [32].Furthermore, the proposed methodology The results in Figure 1 indicate a noticeable divergence between the calculated data and the literature when using the ideal gas model, which is expected given the nature of the reaction system and the thermodynamic limitations of the ideal gas model.
When the gas is considered real, by using the Peng-Robinson (PR) equation of state to calculate the fugacity coefficients the calculated results align satisfactorily with those reported by Chakinala et al. [31], achieving a correlation coefficient (R 2 ) greater than 0.999.This outcome underscores the necessity of employing more robust models to predict non-idealities.The PR equation offers better predictions than ideal models due to its high precision within the utilized temperature and pressure range and its accurate calculation of fugacity for the components present [32].Furthermore, the proposed methodology proved effective for verifying the SCWG process of the C. vulgaris microalgal biomass.In terms of process design, robust models like the one presented in this work are essential for the development and scale-up of gasification processes with water in a supercritical state.

Methodology Validation for Adiabatic Systems Using Entropy Maximization
To validate this methodology, we used experimental data reported by Gomes et al. [6] who verified the SCWG process of Nannochloropsis sp. at 250 bar with 15% wt of biomass in the process feed.Figure 2 presents a comparison between data reported by Gomes et al. [6] and data calculated using the methodology described in this study for calculating adiabatic systems.
biomass in the process feed.Figure 2 presents a comparison between data reported by Gomes et al. [6] and data calculated using the methodology described in this study for calculating adiabatic systems.
The results reported in Figure 2 indicate that the methodology proposed in this study has a good correlation with the data used for validation (R 2 > 0.99).Thus, considering both results from the verified literature, the proposed methodologies produced satisfactory results.The next section presents a more detailed study of the behavior of the SCWG process of the selected lignocellulosic residues.

Study of Equilibrium Compositions of SCWG Processes of Lignocellulosic Waste
The approach presented in this paper for Gibbs energy minimization mimics the conditions of an ideal isothermal reactor.Therefore, hydrogen production rates are anticipated to be high given that hydrogen generation reactions are mainly endothermic and benefit from the thermal stability provided by the isothermal reactor [6,11,33].The thermodynamic study of this process was conducted under controlled conditions, with temperatures ranging from 723 to 1223 K and pressures from 200 to 300 bar.The proportions of biomass in the process input were maintained between 26% and 53%, with a constant amount of water of 2.0 mol.
Figure 3 shows the formation behavior of the main components throughout the SCWG processes of the verified lignocellulosic waste (hydrogen, methane, carbon monoxide, and carbon dioxide).However, other components were formed in smaller quantities (<5 × 10 −4 mol) for all verified reaction conditions, such as NH3, N2, and C2H6.As the model is based on chemical and phase equilibrium, the molar fractions of these components are orders of magnitude lower than the majority of products, regardless of the conditions used.Likewise, the impact of these components on the formation reactions The results reported in Figure 2 indicate that the methodology proposed in this study has a good correlation with the data used for validation (R 2 > 0.99).Thus, considering both results from the verified literature, the proposed methodologies produced satisfactory results.The next section presents a more detailed study of the behavior of the SCWG process of the selected lignocellulosic residues.

Study of Equilibrium Compositions of SCWG Processes of Lignocellulosic Waste
The approach presented in this paper for Gibbs energy minimization mimics the conditions of an ideal isothermal reactor.Therefore, hydrogen production rates are anticipated to be high given that hydrogen generation reactions are mainly endothermic and benefit from the thermal stability provided by the isothermal reactor [6,11,33].The thermodynamic study of this process was conducted under controlled conditions, with temperatures ranging from 723 to 1223 K and pressures from 200 to 300 bar.The proportions of biomass in the process input were maintained between 26% and 53%, with a constant amount of water of 2.0 mol.
Figure 3 shows the formation behavior of the main components throughout the SCWG processes of the verified lignocellulosic waste (hydrogen, methane, carbon monoxide, and carbon dioxide).However, other components were formed in smaller quantities (<5 × 10 −4 mol) for all verified reaction conditions, such as NH 3 , N 2 , and C 2 H 6 .As the model is based on chemical and phase equilibrium, the molar fractions of these components are orders of magnitude lower than the majority of products, regardless of the conditions used.Likewise, the impact of these components on the formation reactions of the main gaseous products is low, even though the biomass obtained from food production contains relative concentrations of elements such as nitrogen or sulfur [18].
The results in Figure 3 show the combined effects of temperature and biomass mass composition in the process feed on the formation of the majority of components at 257.14 bar.As expected, increases in temperature and amounts of biomass in the system feed tend to maximize the formation of hydrogen and carbon monoxide for both processes.This fact is justified by the endothermic nature of the gasification reaction.These results follow what was expected taking into account previous results already reported in the literature [6,13,18,[34][35][36].
of the main gaseous products is low, even though the biomass obtained from food production contains relative concentrations of elements such as nitrogen or sulfur [18].The results in Figure 3 show the combined effects of temperature and biomass mass composition in the process feed on the formation of the majority of components at 257.14 bar.As expected, increases in temperature and amounts of biomass in the system feed tend to maximize the formation of hydrogen and carbon monoxide for both processes.This fact is justified by the endothermic nature of the gasification reaction.These results follow what was expected taking into account previous results already reported in the literature [6,13,18,[34][35][36].
In addition to the formation of hydrogen and carbon monoxide, throughout the SCWG processes verified, the formation of methane and carbon dioxide is significant.Contrary to the behavior of hydrogen formation from carbon monoxide, the formation of methane is disfavored by increases in temperature, and this result is justified by the fact that the methanation reaction is exothermic, as observed by Jin et al. [37] and Guo et al. [36].Similarly to the formation of methane, the formation of carbon dioxide is favored with the addition of biomass in the feed of the reaction system.However, the formation of carbon dioxide presents maximum points at intermediate temperatures (800-900 K) for both processes.
It can be seen that the SCWG process of mustard husks presents higher rates of hydrogen and methane formation, this result is justified by the fact that this substrate presents a higher ratio of H/C atoms than the other substrates verified (H/C = 2.41), thus allowing more hydrogen and methane to be formed throughout the reaction process.Conversely, the rice husk SCWG process presents greater formation of carbon monoxide and dioxide due to its higher ratio of oxygen atoms to carbon atoms (O/C = 0.59) compared to other substrates.In addition to the formation of hydrogen and carbon monoxide, throughout the SCWG processes verified, the formation of methane and carbon dioxide is significant.Contrary to the behavior of hydrogen formation from carbon monoxide, the formation of methane is disfavored by increases in temperature, and this result is justified by the fact that the methanation reaction is exothermic, as observed by Jin et al. [37] and Guo et al. [36].Similarly to the formation of methane, the formation of carbon dioxide is favored with the addition of biomass in the feed of the reaction system.However, the formation of carbon dioxide presents maximum points at intermediate temperatures (800-900 K) for both processes.
It can be seen that the SCWG process of mustard husks presents higher rates of hydrogen and methane formation, this result is justified by the fact that this substrate presents a higher ratio of H/C atoms than the other substrates verified (H/C = 2.41), thus allowing more hydrogen and methane to be formed throughout the reaction process.Conversely, the rice husk SCWG process presents greater formation of carbon monoxide and dioxide due to its higher ratio of oxygen atoms to carbon atoms (O/C = 0.59) compared to other substrates.
Cotton husks present intermediate values for the O/C and H/C ratios, and, for this reason, the SCWG process for this substrate presents intermediate indices for the formation of both components among the processes verified.
In addition to the combined effects of temperature and the amount of substrate in feeding the reaction process, the influence of temperature on the behavior of the reactions is of great importance [17].Figure 4 presents the combined effects of temperature and pressure on the behavior of the equilibrium compositions for SCWG processes of lignocellulosic waste, fixing the mass composition of the biomass in the process feed at 31.19 %wt.
In addition to the combined effects of temperature and the amount of substrate in feeding the reaction process, the influence of temperature on the behavior of the reactions is of great importance [17].Figure 4 presents the combined effects of temperature and pressure on the behavior of the equilibrium compositions for SCWG processes of lignocellulosic waste, fixing the mass composition of the biomass in the process feed at 31.19 %wt.For both conditions verified in Figure 4, the SCWG process of mustard husks presents higher rates of hydrogen and methane formation.The rice husk SCWG process presents higher rates of carbon monoxide and carbon dioxide formation.Quite apparent visually, pressure increases tend to minimize the formation of hydrogen and carbon monoxide.At 1223 K and 31.19%wt of biomass in the process feed, the pressure variation from 200 to 300 bar minimizes the formation of hydrogen by 17.21% and by 16.92% for the formation of carbon monoxide.Applying the same verification to the formation of methane and carbon dioxide, an increase in the formation of these components of 7.83% and 1.43%, respectively, is noted.This result was predicted by Whitag et al. [38], who described that the increase in pressure disfavors the formation of products of interest during the process.This is justified by the fact that the increase in pressure disfavors the water-gas displacement reactions and the methanation reaction is favored following Le Chatelier's principle.Thus, hydrogen is largely consumed, forming methane and carbon dioxide.
In short, from the results reported in Figures 3 and 4, it is concluded that an increase in both temperature and biomass in the feed of the reaction process tends to increase the number of moles of hydrogen and carbon monoxide.Although this behavior is observed, it is important to highlight that, in terms of molar composition, the hydrogen fractions decrease as a function of increasing feed concentration [39].Furthermore, an increase in pressure tends to minimize the formation of these components.Higher rates of hydrogen For both conditions verified in Figure 4, the SCWG process of mustard husks presents higher rates of hydrogen and methane formation.The rice husk SCWG process presents higher rates of carbon monoxide and carbon dioxide formation.Quite apparent visually, pressure increases tend to minimize the formation of hydrogen and carbon monoxide.At 1223 K and 31.19%wt of biomass in the process feed, the pressure variation from 200 to 300 bar minimizes the formation of hydrogen by 17.21% and by 16.92% for the formation of carbon monoxide.Applying the same verification to the formation of methane and carbon dioxide, an increase in the formation of these components of 7.83% and 1.43%, respectively, is noted.This result was predicted by Whitag et al. [38], who described that the increase in pressure disfavors the formation of products of interest during the process.This is justified by the fact that the increase in pressure disfavors the water-gas displacement reactions and the methanation reaction is favored following Le Chatelier's principle.Thus, hydrogen is largely consumed, forming methane and carbon dioxide.
In short, from the results reported in Figures 3 and 4, it is concluded that an increase in both temperature and biomass in the feed of the reaction process tends to increase the number of moles of hydrogen and carbon monoxide.Although this behavior is observed, it is important to highlight that, in terms of molar composition, the hydrogen fractions decrease as a function of increasing feed concentration [39].Furthermore, an increase in pressure tends to minimize the formation of these components.Higher rates of hydrogen formation are observed for the SCWG process of mustard husks due to its higher ratio of H/C atoms; considering that this is the component of greatest interest, among the lignocellulosic residues verified, mustard husks would be more suitable due to their higher rates of hydrogen formation.
In addition to hydrogen, the SCWG process can be characterized by the production of synthesis gas (syngas), which is predominantly composed of H 2 and CO [40][41][42].An interesting parameter to consider when studying the potential for syngas formation is the relationship between the amounts of H 2 and CO (molar ratio H 2 /CO) [43].When the H 2 /CO molar ratio is close to one, the generated syngas is favorable for the synthesis of Eng 2024, 5 1105 methanol (CH 3 OH) and the production of light hydrocarbons such as methane (CH 4 ) and ethylene (C 2 H 4 ) using Fischer-Tropsch-type synthesis reactions.For H 2 /CO molar ratios close to two, the generated synthesis gas is considered ideal for the production of methanol (CH 3 OH) and dimethyl ether (DME), which are important as fuels and as intermediates in the chemical industry; when the H 2 ratio/CO is equal to three, the generated syngas is favorable to produce ammonia (NH 3 ) through the Haber-Bosch synthesis reaction [44].Figure 5 shows the behavior of the H 2 /CO molar ratio as a function of temperature and the amount of biomass in the process feed at 200 bar for both processes verified.
interesting parameter to consider when studying the potential for syngas formation is the relationship between the amounts of H2 and CO (molar ratio H2/CO) [43].When the H2/CO molar ratio is close to one, the generated syngas is favorable for the synthesis of methanol (CH3OH) and the production of light hydrocarbons such as methane (CH4) and ethylene (C2H4) using Fischer-Tropsch-type synthesis reactions.For H2/CO molar ratios close to two, the generated synthesis gas is considered ideal for the production of methanol (CH3OH) and dimethyl ether (DME), which are important as fuels and as intermediates in the chemical industry; when the H2 ratio/CO is equal to three, the generated syngas is favorable to produce ammonia (NH3) through the Haber-Bosch synthesis reaction [44].Figure 5 shows the behavior of the H2/CO molar ratio as a function of temperature and the amount of biomass in the process feed at 200 bar for both processes verified.
The results of the H2/CO molar ratios for both verified processes are presented in Figure 5 as a function of temperature and biomass composition in the process feed (%wt) at 200 bar.The results in Figure 5 indicate a significant difference in the behavior of the H2/CO ratio depending on the composition of the substrate used throughout the SCWG processes.The mustard husk SCWG process presents H2/CO ratios greater than two, indicating that this process may be more suitable for producing synthesis gas as a substrate for DME production processes.This result is similar to the SCWG process of cotton husks.The rice husk SCWG process presents higher rates of synthesis gas formation with H2/CO ratios close to one.A H2/CO ratio close to one is ideal for producing long-chain hydrocarbons such as paraffins, naphthas, and oils.This is because this balanced proportion of The results of the H 2 /CO molar ratios for both verified processes are presented in Figure 5 as a function of temperature and biomass composition in the process feed (%wt) at 200 bar.
The results in Figure 5 indicate a significant difference in the behavior of the H 2 /CO ratio depending on the composition of the substrate used throughout the SCWG processes.The mustard husk SCWG process presents H 2 /CO ratios greater than two, indicating that this process may be more suitable for producing synthesis gas as a substrate for DME production processes.This result is similar to the SCWG process of cotton husks.The rice husk SCWG process presents higher rates of synthesis gas formation with H 2 /CO ratios close to one.A H 2 /CO ratio close to one is ideal for producing long-chain hydrocarbons such as paraffins, naphthas, and oils.This is because this balanced proportion of hydrogen and carbon monoxide is necessary for the efficient synthesis of products through processes like the Fischer-Tropsch synthesis [45].
As observed, biomass processing using water as a reaction medium under supercritical conditions shows good hydrogen formation rates, and the H 2 :CO ratios under conditions that maximize the formation of these products allow their application as synthesis gas.Despite the good formation rates of the desired products, operating reactions under supercritical conditions involves various associated costs.Alternative routes for biomass processing, such as pyrolysis, are conducted under reduced temperature and pressure conditions; however, they result in high CO 2 formation and the production of large quantities of solid components [46].
Eng 2024, 5 1106 The different behaviors of the SCWG processes of the residues verified result from the different compositions of each substrate.Figure 6 shows the maximum formation of the majority of components formed throughout the SCWG processes as a function of the H/C and O/H ratios.The results presented correspond to conditions that maximize the formations of the respective verified components.Following what was presented in Figures 4 and 5, increases in the H/C ratio tend to maximize the formation of hydrogen and methane.Increases in the O/C ratio maximize the formation of carbon dioxide and carbon monoxide.However, this result is barely noticeable for the formation of carbon monoxide because, for the conditions that maximize the formation of this component, the differences between the quantities formed for the processes verified are minimal.Both results seen in Figure 6 make sense if analyzed by taking into account the main reactions throughout the biomass SCWG processes.
tions that maximize the formation of these products allow their application as synthesis gas.Despite the good formation rates of the desired products, operating reactions under supercritical conditions involves various associated costs.Alternative routes for biomass processing, such as pyrolysis, are conducted under reduced temperature and pressure conditions; however, they result in high CO2 formation and the production of large quantities of solid components [46].
The different behaviors of the SCWG processes of the residues verified result from the different compositions of each substrate.Figure 6 shows the maximum formation of the majority of components formed throughout the SCWG processes as a function of the H/C and O/H ratios.The results presented correspond to conditions that maximize the formations of the respective verified components.Following what was presented in Figures 4 and 5, increases in the H/C ratio tend to maximize the formation of hydrogen and methane.Increases in the O/C ratio maximize the formation of carbon dioxide and carbon monoxide.However, this result is barely noticeable for the formation of carbon monoxide because, for the conditions that maximize the formation of this component, the differences between the quantities formed for the processes verified are minimal.Both results seen in Figure 6 make sense if analyzed by taking into account the main reactions throughout the biomass SCWG processes.

Thermal Behavior of SCWG Processes of Lignocellulosic Waste
In addition to equilibrium compositions, the study of the thermal behavior of reaction systems is of fundamental importance for project development.To verify the equilibrium temperatures in non-isothermal systems, the entropy maximization methodology associated with the Peng-Robinson equation of state was used to calculate non-idealities.This methodology has already been used by Gomes et al. [6] for verifying the thermal behavior of reaction systems under supercritical conditions with satisfactory results validated with experimental data.
Figure 7 illustrates the thermal behavior of SCWG processes for lignocellulosic waste.The effects studied are: initial temperature (Figure 7a) with pressure at 220 bar and 10% wt biomass feed; pressure (Figure 7b) with initial temperature at 900 K and 10% wt biomass feed; and biomass composition (Figure 7c) with initial temperature at 900 K and pressure at 220 bar.
pressure at 220 bar.
From the results presented in Figure 7, it is clear that the initial temperature and the biomass composition in the feed of the reaction system have predominant effects on the behavior of the equilibrium temperature.This verification is in accordance with the results shown in Figure 3 and 4, considering that pressure has less significant effects on the development of the reactions.From the results presented in Figure 7, it is clear that the initial temperature and the biomass composition in the feed of the reaction system have predominant effects on the behavior of the equilibrium temperature.This verification is in accordance with the results shown in Figures 3 and 4, considering that pressure has less significant effects on the development of the reactions.
Checking the effect of the initial temperature on the behavior of the equilibrium temperature (Figure 7a), it is clear that, in general, the SCWG process of mustard husks presents higher equilibrium temperatures than the other processes.This result is justified by the fact that higher H/C ratios tend to favor methanation reactions, which are exothermic, thus increasing the equilibrium temperature of the reaction system.Similarly, the rice husk SCWG process presents lower values for equilibrium temperatures, since this substrate has the lowest H/C ratio (1.48) among the substrates studied.
For both cases, exothermic effects are predominant.However, it can be seen that the differences between the equilibrium temperatures and the initial temperature of the reaction system tend to decrease with increases in temperature at the beginning of the process, indicating that the reactions initially have an exothermic character that is minimized with an increase in the initial temperature of the reaction system.At 1200 K, the differences between the initial temperature and the equilibrium temperatures for both reaction processes are minimal, as can be confirmed in Table 3.At 1300 K, it is clear that the equilibrium temperatures become lower than the initial temperature, which indicates the endothermic effect becomes predominant.In addition to the effect of initial temperature, the results in Figure 7 indicate that pressure has a small, significant effect on the behavior of the equilibrium temperature.This result follows what was expected taking into account the behavior of the equilibrium compositions as a function of the system pressure.Other authors verified similar results when studying the effect of reaction system pressure on the thermal behavior of the process when conditioned in adiabatic reactors [6,11,33].

Conclusions
This study reveals the effectiveness of the proposed methodologies for evaluating the thermodynamic behavior of supercritical water gasification (SCWG) processes, both in validating the results and in analyzing the thermodynamic equilibrium and thermal behavior of the reaction systems.By utilizing more robust models such as the Peng-Robinson equation of state, it was possible to achieve a satisfactory correlation between the calculated and experimental data (R 2 > 0.99), highlighting the importance of considering gas non-idealities for more precise predictions.
The analysis of the thermodynamic behavior of the SCWG processes of lignocellulosic residues revealed consistent patterns in the formation of gaseous products such as hydrogen, methane, carbon monoxide, and carbon dioxide as a function of temperature, pressure, and biomass composition.
Significantly, biomass composition significantly influenced the composition of the formed products, with substrates like mustard husk exhibiting higher hydrogen and methane formation due to their higher H/C ratio.For the processes verified, the mustard husk SCWG process showed higher rates of hydrogen and methane formation, which is justified by the greater number of hydrogen atoms in its composition.Conversely, the rice SCWG process presents lower rates of hydrogen formation, which also presents higher rates of carbon monoxide and carbon dioxide formation due to its greater content of carbon atoms.The biomass of rice husks presents intermediate values with respect to the compositions of H and C, and for this reason it presents intermediate values for the compositions of the verified components (H 2 , CH 4 , CO and CO 2 ).
Moreover, the analysis of the H 2 /CO molar ratio indicated the potential of SCWG processes for synthesis gas production, with important implications for the production of chemicals such as methanol, dimethyl ether, and ammonia, depending on the temperature conditions and biomass composition.The SCWG process of lignocellulosic waste showed good rates of synthesis gas formation with H 2 /CO ratios between two and three, indicating that this can be directed to the production of ammonia and DME.The SCWG processes of rice and cotton husks also have H 2 /CO indices close to one under specific conditions of temperature, pressure and biomass composition, indicating that the syngas generated from this process can be directed to the production of methanol.
Lastly, the investigation of the thermal behavior of SCWG processes highlighted the importance of initial temperature and biomass composition in determining the equilibrium temperature of the system, with pressure exerting a less significant effect.These insights are crucial for the development and scaling of supercritical water gasification processes, underscoring the potential of utilizing lignocellulosic residues for the production of high-value-added products.

Patents
The results presented in this article were developed using the TeS-Thermodynamic Equilibrium Simulation software.This software was developed by the authors of this text and this article marks the first publication using this tool.The TeS was registered by the National Institute of Industrial Property with registration number BR512024000275-8.Campinas and the Federal University of Maranhão for their invaluable contributions to the personal and professional growth of countless people, as well as to all educators who actively promote the advancement of society.A.P. Mariano thanks Fundação de Amparo à Pesquisa do Estado de São Paulo (FAPESP) (grant number 23/01072-7).Finally, J.M. Santos Junior expresses his gratitude to Radix Engineering and Software for generously providing the time and essential tools needed to create these results.

Figure 1 .
Figure 1.Comparison between molar composition results at the thermodynamic equilibrium condition calculated by the Gibbs energy minimization methodology (Peng-Robinson and Ideal Gas) with experimental data reported by Chakinala et al. [31].

Figure 1 .
Figure 1.Comparison between molar composition results at the thermodynamic equilibrium condition calculated by the Gibbs energy minimization methodology (Peng-Robinson and Ideal Gas) with experimental data reported by Chakinala et al. [31].

Figure 2 .
Figure 2. Comparisons between data from Gomes et al. [6] and simulated data for product composition as a function of initial temperature, pressure at 250 bar and initial composition of Nannochloropsis sp.15% wt.

Figure 2 .
Figure 2. Comparisons between data from Gomes et al. [6] and simulated data for product composition as a function of initial temperature, pressure at 250 bar and initial composition of Nannochloropsis sp.15% wt.

Figure 3 .
Figure 3. Behavior of the equilibrium compositions of hydrogen (a), carbon monoxide (b), methane (c), and carbon dioxide (d) as a function of temperature and mass composition of biomass in the reaction process feed at 257.14 bar.

Figure 3 .
Figure 3. Behavior of the equilibrium compositions of hydrogen (a), carbon monoxide (b), methane (c), and carbon dioxide (d) as a function of temperature and mass composition of biomass in the reaction process feed at 257.14 bar.

Figure 4 .
Figure 4. Behavior of the equilibrium compositions of hydrogen (a), carbon monoxide (b), methane (c), and carbon dioxide (d) as a function of temperature and pressure with the biomass composition set at 31.19 %wt in the reaction system feed.

Figure 4 .
Figure 4. Behavior of the equilibrium compositions of hydrogen (a), carbon monoxide (b), methane (c), and carbon dioxide (d) as a function of temperature and pressure with the biomass composition set at 31.19 %wt in the reaction system feed.

Figure 5 .
Figure 5. Behavior of the H2/CO ratio as a function of temperature and biomass composition for the SCWG processes verified at 200 bar (a): mustard husks, (b): rice husks, (c): cotton husks.

Figure 5 .
Figure 5. Behavior of the H 2 /CO ratio as a function of temperature and biomass composition for the SCWG processes verified at 200 bar (a): mustard husks, (b): rice husks, (c): cotton husks.

Figure 6 .
Figure 6.Behavior of the maximum formation of the main products of the SCWG processes of the waste verified as a function of the H/C (a) and O/H ratios (b).

Figure 6 .
Figure 6.Behavior of the maximum formation of the main products of the SCWG processes of the waste verified as a function of the H/C (a) and O/H ratios (b).

Figure 7 .
Figure 7. Thermal behavior of reaction systems as a function of initial temperature (a), pressure (b), and initial biomass composition (c).

Figure 7 .
Figure 7. Thermal behavior of reaction systems as a function of initial temperature (a), pressure (b), and initial biomass composition (c).

Table 2 .
Mass composition of different types of biomass.

Table 3 .
Variation of the equilibrium temperature as a function of the initial temperature for the SCWG processes of lignocellulosic waste at 220 bar with biomass composition in the feed set at 10% wt.

Interest:
The authors declare no conflicts of interest.Parameters of the cubic equation of state M Constant for Kamath, Biegler, and Grossmann constraints σ k Slack variables for Kamath, Biegler, and Grossmann constraints T c,I Critical component temperature i P c,i Critical component pressure i w i Number of moles of component i in phase k; i = [1, 2, 3, . .., NC]; k = [v, l, s]