Next Article in Journal
Polish Farmers′ Perceptions of the Benefits and Risks of Investing in Biogas Plants and the Role of GISs in Site Selection
Previous Article in Journal
Energy Management of Industrial Energy Systems via Rolling Horizon and Hybrid Optimization: A Real-Plant Application in Germany
Previous Article in Special Issue
Biomass Valorization Recommender Tool Development
 
 
Font Type:
Arial Georgia Verdana
Font Size:
Aa Aa Aa
Line Spacing:
Column Width:
Background:
Article

Impact of Water Vapor on the Predictive Modeling of Full-Scale Indirectly Heated Biomass Torrefaction System Throughput Capacity

Perpetual Next, Zuidtoren, Taurus Avenue 3, 2132 LS Hoofddorp, The Netherlands
*
Author to whom correspondence should be addressed.
Energies 2025, 18(15), 3978; https://doi.org/10.3390/en18153978
Submission received: 28 May 2025 / Revised: 16 July 2025 / Accepted: 22 July 2025 / Published: 25 July 2025

Abstract

Biomass torrefaction must be self-sustaining and continuous to be commercially viable, eliminating dependence on additional fuels while achieving industrial-scale production. This study presents a predictive model of a full-scale continuous biomass torrefaction process that explicitly incorporates the radiation absorption properties of torrefaction gas, with a focus on water vapor. Previous research, primarily based on lab-scale batch processes, has not adequately addressed scale-up challenges or the dynamic evolution of torrefaction gas. Industrial insights from Perpetual Next confirm that water vapor significantly impacts reactor performance by absorbing heat and reducing radiative flux to the biomass. Simulations show that neglecting water vapor absorption in reactor design can lead to throughput deviations of 10–20%, affecting process stability and efficiency. Industrial-scale validation demonstrates that the model accurately predicts this effect, ensuring realistic energy demand and throughput expectations. By explicitly incorporating water vapor absorption into the radiation balance, the model provides a validated framework for optimizing reactor design and process scale-up. It demonstrates that failing to consider this effect can lead to operational instability and deviations from the intended torrefaction severity, ultimately affecting industrial-scale performance and self-sustaining operation.

1. Introduction

Biomass torrefaction is a thermochemical process that enhances biomass properties through heating to moderate temperatures (280–350 °C) in an inert or low-oxygen environment. This process produces torrefied biomass, a renewable, energy-dense, and hydrophobic feedstock that can contribute to defossilisation efforts across various industries [1]. Recent comprehensive reviews emphasize that continuous, industrial-scale torrefaction remains an active research frontier, with unresolved modeling and control challenges [2].
However, scaling torrefaction from laboratory or pilot-scale units to industrial capacity presents significant challenges, particularly when aiming for a self-sustaining operation [3]. A self-sustaining torrefaction process is one that requires no external fuel input during steady-state operation, encompassing the energy demands for both drying and torrefaction steps. First-principles energy-balance work has recently mapped the narrow autothermal envelopes for different biomasses, showing that small shifts in feed moisture or inert gas recycling can flip the net energy balance [4].
Perpetual Next has logged more than 10,000 h of continuous, self-sustaining torrefaction at its pilot plant in Derby (UK), and commercial plants in Dilsen-Stokkem (Belgium), and Vägari (Estonia) [5]. Operational data from these campaigns show that autothermal operation becomes particularly challenging whenever the incoming feedstock drifts outside the design envelope—for example, during unexpected increases in moisture or ash content [3]. Differences in moisture content and biomass type directly affect process efficiency and product consistency. Higher moisture content prolongs the drying phase, reducing the time available for torrefaction and consequently decreasing the release of torrefaction gases needed to sustain the process. Additionally, variations in biomass properties impact material handling and alter the composition and energy content of torrefaction gases. Therefore, for a given product quality and target yield (whether mass or energy-based), an optimal operating window must be identified—one where sufficient heat is generated to maintain self-sustaining operation while ensuring consistent biocarbon quality. Industrial-scale experience has also shown that these operating points are discrete rather than continuous, meaning process settings cannot be simply adjusted gradually to shift from one stable operating condition to another [6]. Given the high cost of a trial-and-error approach, there is a need for the development of a predictive model.
Existing torrefaction models in the literature often lack predictive capability, as most research has focused on laboratory-scale, batch processes with an emphasis on torrefaction kinetics [7,8,9]. Few studies have explored how these kinetics apply to continuous processes. A notable contribution from MIT provided a foundation for the kinetic and thermochemical modeling of torrefaction, where reaction kinetics are coupled with temperature [8,10,11]. Although originally developed for batch processes, these models can be adapted for continuous operations. However, applying these models to an industrial-scale, indirectly heated torrefaction system has revealed previously unaccounted effects, such as the greenhouse effect of water vapor. Underestimating this effect can lead to the overprediction of throughput and net calorific value while underestimating heat requirements.
To address these gaps, the authors have developed a first-principles-based model that incorporates the radiative absorption effects of water vapor, a major byproduct of torrefaction [1,7]. This study presents the development and validation of this model, demonstrating its accuracy in predicting key process parameters and capturing effects previously overlooked in the literature. By providing a more precise understanding of the energy balance and heat transfer dynamics in torrefaction, the model serves as a powerful tool for optimizing industrial-scale operations and ensuring self-sustaining performance.

2. Methodology

This section describes the methodology used to develop a predictive model for torrefaction in industrial-scale reactors. First, an overview of select reactor technologies is provided. Next, the design of the model system is explained, followed by a description of the mathematical model, including mass loss kinetics and heat transfer mechanisms. Finally, the implementation and validation approach is outlined, ensuring the model’s applicability to industrial-scale torrefaction.

2.1. Reactor Technologies

Perpetual Next owns and operates two distinct torrefaction reactor technologies [5]:
  • Rotary Drum Reactor —A cylindrical, rotating reactor in which biomass is continuously fed and heated indirectly by hot flue gas circulating through a jacket surrounding the drum. The drum is slightly inclined, allowing biomass particles to move downward due to gravity and the rotational motion. Inside the drum, internal flights facilitate mixing, ensuring uniform heat distribution and consistent torrefaction. This design enables extended residence times, making it suitable for achieving higher torrefaction severity.
  • Vibratory Bed Reactor—A reactor where biomass is transported through a vibrating bed, which is indirectly heated from above and below via a flue gas jacket. The vibration suspends the biomass above the bed, promoting mixing and enhancing heat transfer. The movement of biomass through the reactor is controlled by adjusting the vibration intensity and the reactor’s angle of vibration with respect to the normal (perpendicular direction), allowing precise regulation of residence time. Due to its shorter residence time, which is limited by the maximum size vibrating equipment, this configuration typically results in lower torrefaction severity when running at full capacity, compared to the rotary drum reactor.
Both reactors operate in a continuous mode and utilize indirect heating, where heat is transferred to the biomass primarily through radiation from the heated reactor surfaces. The key distinction between these technologies lies in their biomass handling and transport mechanisms, which influence residence time distribution and heat transfer efficiency. Data collected from these steady-state, continuous, industrial operations have been instrumental in the development and validation of the model. The next section discusses how both reactor technologies are considered during the development of the model.

2.2. Design

A common aspect of both reactor technologies is the torrefaction process itself; biomass travels through the reactor while being heated by contact with the steel surfaces. During this process, the biomass first undergoes drying, where moisture is evaporated, followed by torrefaction, during which thermal decomposition occurs, releasing torrefaction gases. At the reactor’s outlet, both the torrefied biomass and the torrefaction gas are extracted. The predictive model, therefore, requires an appropriate abstraction of the reactor geometry and a clear definition of the key operating parameters.

2.2.1. Reactor

The model aims to capture the torrefaction process and requires a simplification of the reactor geometry. The model adopts a parallel-plate representation, inspired by the vibratory bed reactor, where two parallel plates represent the heated reactor surfaces, with biomass suspended slightly above the bottom deck. This abstraction allows for a general approach while maintaining the essential physics of heat and mass transfer.
The main assumptions for this reactor setup include the following:
  • The contribution of side walls to heat transfer is negligible.
  • The steel temperature along the length of the reactor is provided as a boundary condition, effectively decoupling the flue gas side from the reactor side.
  • For the rotary drum reactor, the upper portion of the reactor is treated as a cavity, with the projected area of the cavity approximated as the top surface of the parallel plate [12]. The bottom arc of the drum is treated as the lower parallel plate. This assumption is reasonable when the solid fraction inside the reactor is low.
These assumptions are justified based on the understanding that radiation is the dominant heat transfer mechanism in indirectly heated systems. Convective heat transfer plays a minor role, primarily towards the end of the reactor when the production of torrefaction gases increases. By incorporating these considerations, the model effectively captures the primary heat and mass transfer phenomena occurring in both reactor types and the schematic is shown in Figure 1.

2.2.2. Process Parameter Design—Linking Model and Plant Data

Industrial operations produce hundreds of data streams each minute, but only a select few are both available online and have a significant impact on the torrefaction model. To keep the model practical and plant-relevant, the input vector is restricted to variables that meet those two criteria. In this study, the vibratory bed reactor uses alder and pine wood chips as baseline feedstocks, while the rotary drum reactor employs B-wood. The essential compositional parameters are listed in Table 1.
Primary measured inputs, residence time, feed-moisture content, mass-flow rate, average biomass composition, steel-wall temperature profile, and net calorific value, were selected based on online availability and the influence strength of model outputs.

Treatment of Secondary Variables

  • Flue gas circuit—assumed non-limiting because the jacket supplies heat rapidly enough to track wall set-points; tar fouling in downstream cold spots therefore lies outside the present scope.
  • Biomass elemental spread—day-to-day variation around the alder mean is < ± 2 wt% for C and H, smaller than the NCV change produced by the primary variables; this spread is folded into the NCV uncertainty band [3].
  • Particle size distribution—with d 50 10 mm, intra-particle conduction is not rate-limiting at the observed residence times; size variation is implicitly covered by the residence-time distribution.
  • Mass yield sampling error—plant mass yield deviates by 5 wt% from kinetic predictions, an effect that maps directly onto the NCV uncertainty already captured by biomass-composition spread.
Implications for Scale-Up
Sensitivity tests show that wall temperature, residence time, and feed moisture dominate torrefaction yield, whereas the excluded secondary factors shift the NCV by less than 0.5 MJ kg−1 across the industrial range. The chosen level of detail is therefore sufficient for reactor sizing and for defining an operating window, while limiting required inputs to variables routinely measured on site.

2.3. Model Framework

The model is a non-isothermal, steady-state plug flow representation of the torrefaction process, solving for both mass and energy balances. The calculations are performed in phases, ensuring an accurate representation of the interactions between biomass, torrefaction gas, and reactor walls. The approach follows the following three key steps, as illustrated in Figure 2:
  • Solid phase: The torrefaction kinetics are solved first to determine the mass loss of biomass and the amount of torrefaction gas produced. The energy balance is then applied to the solid phase to determine the biomass temperature, which in turn influences the kinetics. The coupling between heat transfer and reaction kinetics ensures an accurate representation of biomass decomposition.
  • Gas phase: No chemical reactions are assumed to occur in the gas phase, meaning only an energy balance is required to determine the gas-phase temperature. This implies that the ingress of oxygen at in- and outfeed of the reactor must be managed to be low in order to have consistency between model and production data, which is in agreement with the fundamental premise of safe torrefaction. The gas temperature is influenced by heat exchange with the biomass, reactor walls, and other process components.
  • Source term calculations: Since torrefaction gas, biomass, and reactor walls all participate in heat exchange, the model accounts for energy transfers at each control volume. The source terms for both mass and energy balances include contributions from reaction kinetics, radiative heat exchange, and convective heat transfer.

2.4. Model Equations

The governing transport equations for mass and energy, derived from the control volume in Figure 2, are given as follows. The mass balance for a component i is as follows:
d m i d x = r i · R T L ,
where m i is the mass flow rate and r i is the reaction rate of the component i. RT and L are the solid residence time and reactor length, respectively. The energy balances for the solid and gas phases are written as follows:
d ( m i H i ) s d x + Q i , s = 0
d ( m i H i ) g d x + Q i , g = 0
where H i represents the enthalphy of the component i, defined as follows:
H i = H f , i + T REF T C p , i d T
The components, reaction kinetics ( r i ) and the source terms ( Q i , s , Q i , g ) are discussed briefly in the subsequent sections.

2.4.1. Torrefaction Kinetics

The model applies the weight-loss kinetics developed by Prins et al. to describe torrefaction reactions [9]. Drying kinetics are taken from Bates and Ghoniem [11]. Bates and Ghoniem provided an approach to use the weight-loss kinetics in a transport equation suitable for batch processes [8]. The present model follows the same method, incorporating the transport equation formulated by Bates and Ghoniem into a continuous process [8].
The weight-loss kinetics follows a multi-step reaction scheme, where biomass decomposes into intermediate components before forming torrefaction gases. The reaction pathway is represented as follows:
Energies 18 03978 i001
where k i are the Arrhenius rate constants of the components i. A, B, and C are the solid components that are left after devolatilization; V1 and V2 are volatiles released from the decomposition of A and B, respectively, corresponding to hemi-cellulose and cellulose decomposition that happens during the torrefaction reaction. The sum of V1 and V2 makes the torrefaction gas, and the sum of A, B and C makes the torrefied biomass.
The method of Bates and Ghoniem for extracting kinetic parameters from TGA mass-loss curves was applied to the alder and pine profiles reported by Graham et al. [3]. Those experiments were carried out under a nitrogen atmosphere with a heating rate of 10 °C min−1 up to 900 °C, followed by a 10 min isothermal hold and baseline correction over 150–500 °C. The resulting mass-loss data (upto 450 °C) were then used to fit the kinetic model. The calibrated parameters accurately reproduce the mass yields observed at our vibratory bed and rotary drum plants, as shown in Figure 3, with a root-mean-square deviation of 3.5 wt %. Volatile-gas composition was measured in dedicated on-site sampling campaigns. Representative gas compositions are listed in Graham et al.’s Table 3 [3].

2.4.2. Heat Transfer

The source terms, Q i , s and Q i , g , represent the heat transfer rates between phases. In the torrefaction reactor, heat transfer occurs primarily through radiation and convection, while conduction is considered negligible due to the short contact time and contact surface between biomass particles and the reactor walls. Additionally, it is assumed that the particles are small enough for intra-particle heat transfer not to be a limiting factor. The model incorporates these mechanisms to ensure an accurate prediction of the temperature distribution within the system. The different forms of heat exchange terms are shown in Figure 2.
Radiative Heat Transfer is the dominant mode of heat transfer in indirectly heated torrefaction systems. The model treats this as a radiation exchange problem between parallel plates with a participating medium, where the biomass and steel surfaces are assumed to behave as gray bodies. For the rotary drum reactor, an effective emissivity is calculated for the steel to account for the cavity effect [12].
Water vapor is considered the primary radiative absorptive species, while CO2 absorption is neglected due to its minimal effect. Since water vapor absorbs and transmits radiation only at specific wavelengths, the transmittance must be considered as a function of the wavelength and thus as a function of wall temperature. To describe the spectral distribution of radiative energy, Planck’s law is used, which defines the spectral emissive power of a black body as follows [15]:
e λ ( T ) = 2 h c 2 λ 5 1 e h c λ k B T 1
where
  • e λ b is the spectral radiance of black body per unit wavelength ( W · m 3 · Sr 1 ).
  • h is Planck’s constant ( 6.626 × 10 34 J·s).
  • c is the speed of light in vacuum ( 3.00 × 10 8 m/s).
  • k B is the Boltzmann constant ( 1.381 × 10 23 J/K).
  • T is the absolute temperature in Kelvin.
  • λ is the wavelength of the emitted radiation.
Then the net radiative heat flux from the biomass and steel surfaces, Q b and Q S , are given as follows [16,17]:
Q b = 0 ε λ , b ε λ , s τ ¯ λ ( e λ , b e λ , s ) + ε λ , b ( 1 τ ¯ λ ) [ 1 + ( 1 ε λ , s ) τ ¯ λ ] ( e λ , b e λ , G ) 1 ( 1 ε λ , b ) ( 1 ε λ , s ) τ ¯ λ 2 d λ
Q s = 0 ε λ , b ε λ , s τ ¯ λ ( e λ , s e λ , b ) + ε λ , s ( 1 τ ¯ λ ) [ 1 + ( 1 ε λ , b ) τ ¯ λ ] ( e λ , s e λ , G ) 1 ( 1 ε λ , b ) ( 1 ε λ , s ) τ ¯ λ 2 d λ
where ϵ λ , i are the emissivities of biomass and steel as a function of wavelength and τ ¯ λ is the transmittance of the gas as function of wavelength. Since the biomass and steel are assumed to be gray bodies, they are constant. The transmittance as a function of wavelength is determined from the lookup tables published by Wyatt et al. [18]. Finally, the net radiative heat flux through the gas, Q g , is given as follows:
Q g = ( Q s + Q b ) .
Convective Heat Transfer is divided into free and forced convection, depending on the flow conditions. The heat transfer coefficients are determined using Nusselt number correlations, with the transition between free and forced convection governed by the Richardson number (Ri).
For free convection, the correlation proposed by Churchill and Chu is used [19]. For forced convection, correlations based on the Reynolds number are applied. Specifically,
  • For laminar flow, the correlation for flow over a flat plate, which is derived from Blasius’ solution is used [20].
  • For turbulent flow, the Gnielinski correlation is applied [21].
The shift between forced and free convection in the reactor is determined by the Richardson number, where if Ri < 16, the heat transfer coefficient is calculated based on forced convection. Then the heat transfer flux Q C is given as follows:
Q C , i = h i A Δ T
where h is the heat transfer coefficient, A is the surface area of heat exchange, and Δ T is the relevant temperature difference between the source and the sink.
The combined effects of radiation and convection define the energy exchange within the reactor, influencing both the biomass heating rate and the gas-phase temperature. These heat transfer mechanisms directly impact torrefaction kinetics by determining the local temperature profile inside the reactor.

2.4.3. Model Integration

The model solves the coupled mass- and energy-balance equations together with the drying and devolatilization kinetics at every axial node of the plug-flow reactor. This simultaneous approach yields the local gas and solid temperatures as well as the volatile release and mass yield profiles along the reactor length.
The solver requires five primary inputs—biomass elemental composition, steel-deck temperature profile, solids residence time, inlet moisture content, and biomass mass flow rate—while all other quantities (heat transfer coefficients, reaction enthalpies, gas-phase properties) are updated internally at each iteration. The resulting temperature fields and yield curves are carried forward to the Results section for a comparison with industrial plant data.

2.4.4. Key Modeling Assumptions

After detailing the reactor design, process parameters, and governing equations, the key simplifications that underpin the predictive model are summarized below.
Geometry-Related Assumptions
  • Both reactor types are represented as two infinite, parallel plates; side-wall heat losses are neglected.
  • In the rotary drum, the upper half of the shell is approximated as a radiative cavity whose projected area equals the top plate.
  • Solids advance as a steady plug flow; axial gas back-mixing and radial gradients are ignored.
Model-Related Assumptions
  • Biomass and steel surfaces behave as gray bodies with constant emissivity.
  • Particles are small enough that intra-particle conduction is not rate-limiting (lumped capacitance assumption).
  • The steel-wall temperature profile is imposed from plant data, decoupling the flue gas side from the solids side.
  • Moisture release and devolatilization are the only mass sources; no oxygen ingress or gas-phase chemical reactions occur.
  • Water vapor is treated as the sole radiatively participating species; CO2 absorption bands are neglected.
  • Multi-step weight-loss kinetics follow the Prins–Bates scheme with Arrhenius rate constants assumed independent of particle size and mineral content.
Together, these assumptions delineate the model’s validity envelope and highlight areas that would benefit from further plant data or refined sub-models. With this framework established, the next section presents the approach for the model calibration, validation, and analysis of industrial operating data.

2.4.5. Model Validation Approach

The developed model is solved numerically in MATLAB R2024a by iteratively solving the coupled mass and energy balance equations. The required inputs include material properties such as biomass composition, heat capacity, and emissivity. Operating conditions, including feed rate, moisture content, residence time, and reactor wall temperature, are also provided. Additionally, geometric parameters such as reactor length, width, and diameter are incorporated into the model.
Validation is conducted using operational data collected from Perpetual Next’s industrial torrefaction plants. For the vibratory bed reactor, a Monte Carlo analysis is performed to account for the variability in feedstock moisture content and process conditions, allowing for statistical verification of model predictions within an acceptable uncertainty range. The analysis consists of 1000 simulations, where key input parameters are randomly sampled from a defined distribution. The randomness reflects the natural process variations within the plant, while the distribution remains constrained by the plant’s control limits, ensuring that all simulations remain within the realistic operating range.
However, the same approach cannot be applied directly to the rotary drum reactor because the steel temperature is not measured directly. Instead, an approximate temperature was used based on data from a different plant to which Perpetual Next has licensed its technology and operates under similar conditions.

3. Results and Discussion

3.1. Model Validation

The model was validated using operational data from the following two large-scale torrefaction plants, each representing a different reactor technology: vibratory bed and rotary drum reactors.
The baseline feedstock for this study consisted of alder and pine chips with an as-received moisture content below 10 wt % entering the reactor. Net calorific value (NCV) was measured in real time with an online bomb calorimeter at 15-min intervals, while key process parameters—residence time, biomass feed rate, and steel-deck temperatures—were logged continuously. For the vibratory bed reactor, a six-month dataset covering stable operation from September 2023 to February 2024, operating at 2.5 t/h, was analyzed. Figure 4 compares the NCV distribution predicted by Monte-Carlo simulations with the distributions obtained from these plant data; the close agreement confirms that the model accurately captures the variability observed under industrial conditions.
For the rotary drum reactor, validation was performed using the average NCV values derived from operating parameters recorded during plant operation. Since the steel temperature is not directly measured, the model was used to estimate its value. To verify this calculation, steel temperature measurements from a similar plant operating under nearly identical conditions were used for comparison. The results showed that the measured steel temperature were within 5% of the model-predicted value, supporting the validity of the model’s heat transfer assumptions. Furthermore, Monte Carlo simulations of the rotary drum reactor produced an NCV spread that closely matches the measured spread, as shown in Table 2, reinforcing the model’s predictive capability.
The table below summarizes the measured (using bomb calorimeter) and model-predicted NCV values (using BOIE correlation) for both reactor types.
These results demonstrate that the model reliably predicts industrial-scale torrefaction behavior, making it a valuable tool for process optimization and scale-up applications.

3.2. Role of Water Vapor

The presence of water vapor in the torrefaction gas significantly influences heat transfer within the reactor. As a participating medium in radiative heat transfer, water vapor absorbs and re-emits radiation, reducing the net radiative heat flux reaching the biomass. Ignoring this effect in the model leads to an overestimation of the heat available for torrefaction, resulting in an artificially high prediction of net calorific value (NCV) and throughput capacity.
The influence of water vapor absorption is demonstrated in Figure 5. Figure 5 compares the predicted temperature profiles for two reactor configurations—vibratory bed (top row) and rotary drum (bottom row)—under otherwise identical operating conditions. Within each reactor type, the left panel includes radiative absorption and re-emission by water vapor, whereas the right panel omits this effect. The curves show the normalized temperatures of the steel wall (yellow), torrefaction gas (red) and biomass bed (blue) along the normalized reactor length, and the resulting net calorific value (NCV) is stated in each panel title.
For the vibratory bed reactor, the model predicts an NCV of 21 MJ/kg when water vapor absorption is included (Figure 5a), which aligns well with the experimental values. Without accounting for absorption, the predicted NCV increases to 25 MJ/kg (Figure 5b), exceeding observed plant data. Similarly, for the rotary drum reactor, the NCV is 27 MJ/kg with absorption (Figure 5c) but rises to 29 MJ/kg when absorption is ignored (Figure 5d). These differences highlight the importance of incorporating water vapor absorption in modeling to accurately represent heat transfer and reactor performance.
Additionally, the absorption effect can be seen in the gas-phase temperature profiles in Figure 5. In cases where water vapor absorption is included (Figure 5a,c), the gas temperatures are higher compared to the cases without absorption (Figure 5b,d). This indicates heat loss from the steel surfaces to the gas phase, reducing the energy available for torrefaction. In practice, this means that reactors operating with significant water vapor absorption will require a higher external heat duty to achieve the same torrefaction severity and maintain product quality.

3.3. Implications for Scale-Up

For a given torrefaction severity, accounting for water vapor absorption requires a higher energy input than simple design estimates would suggest. If the design is based on idealized heat transfer assumptions without considering the greenhouse effect of water vapor, the reactor will either produce a lower torrefaction severity than intended or require operation at a reduced throughput capacity to maintain the target product quality.
When keeping the calorific value (CV) of the torrefied biomass constant, throughput capacity can drop by 10–20%, depending on the reactor type and operating conditions. If, instead, the throughput is maintained, the produced torrefaction gas will have a lower calorific value, weakening the energy feedback loop required for self-sustaining operation. In extreme cases, this negative feedback can disrupt the energy balance, preventing the process from sustaining itself.
In either case, the process will have a narrower operating range than designed, making it more sensitive to fluctuations in moisture content and feedstock properties. This increases the challenge of reaching a stable operation, as variations in feed conditions could more easily push the process outside the optimal window, requiring tighter control strategies to maintain performance.
These findings emphasize the importance of incorporating water vapor absorption effects into the scale-up process to avoid overestimating throughput or underestimating thermal demand, ensuring robust and efficient reactor operation at an industrial scale.

4. Conclusions

A robust first-principles model has been developed for indirectly heated, continuous torrefaction reactors, explicitly incorporating water vapor absorption in the radiation balance. The model’s predictions align closely with measured industrial performance for both vibratory bed and rotary drum reactors, demonstrating its reliability for process analysis and optimization.
The key conclusions from this study are as follows:
  • Water vapor absorption significantly impacts heat transfer by reducing radiative heat flux to the biomass, influencing both energy balance and process stability.
  • Ignoring this effect leads to overestimated throughput and underestimated heat demand, which can cause operational instability and deviations from the intended torrefaction severity.
  • The model provides a validated framework for optimizing reactor design and scale-up, ensuring more reliable process performance at an industrial scale.
Future work should extend the model to include the flue gas side for better integration with heat exchanger design and flue gas recirculation. These improvements will further strengthen the model’s role in guiding the design of commercially viable torrefaction systems, enabling self-sustaining operation at an industrial scale.

Author Contributions

Conceptualization, C.B. and M.D.; methodology, C.B., M.R. and M.D.; software, C.B.; validation, C.B., M.R. and M.D.; writing—original draft preparation, C.B.; writing—review and editing, M.D.; visualization, C.B.; supervision, M.D. All authors have read and agreed to the published version of the manuscript.

Funding

The research reported in this paper has been funded by Momentum Global Ventures, Amsterdam, The Netherlands.

Data Availability Statement

The datasets presented in this article are not readily available because of commercial sensitivity. The production data are the company’s confidential data and cannot be made public.

Acknowledgments

The authors are indebted to the very valuable discussions during the various stages of this work with Ruud van Ommen, Wiebren de Jong, and Koen Reimert, and to Andrus Ööpik, for plant quality data collection.

Conflicts of Interest

All authors were employed by the company Perpetual Next. The authors declare that the research was conducted in the absence of any commercial or financial relationships that could be construed as a potential conflict of interest. The funders had no role in the design of the study; in the collection, analyses, or interpretation of data; in the writing of the manuscript; or in the decision to publish the results.

References

  1. Shankar Tumuluru, J.; Sokhansanj, S.; Hess, J.R.; Wright, C.T.; Boardman, R.D. A review on biomass torrefaction process and product properties for energy applications. Ind. Biotechnol. 2011, 7, 384–401. [Google Scholar] [CrossRef]
  2. Javanmard, A.; Abdul Patah, M.F.; Zulhelmi, A.; Wan Daud, W.M.A. A comprehensive overview of the continuous torrefaction method: Operational characteristics, applications, and challenges. J. Energy Inst. 2023, 108, 101199. [Google Scholar] [CrossRef]
  3. Graham, S.; Jones, J.; Dekker, M. An integrated laboratory and industrial scale study of autothermal torrefaction of hardwood, softwood and Miscanthus. Biomass Bioenergy 2025, 195, 107723. [Google Scholar] [CrossRef]
  4. Yun, H.; Wang, Z.; Wang, R.; Bi, X.; Chen, W.H. Identification of Suitable Biomass Torrefaction Operation Envelops for Auto-Thermal Operation. Front. Energy Res. 2021, 9, 636938. [Google Scholar] [CrossRef]
  5. PerpetualNext. Divisions and Locations. Available online: https://perpetualnext.com/en/divisions/locations/ (accessed on 10 March 2025).
  6. Hazra, S.; Morampudi, P.; Prindle, J.C.; Fortela, D.L.B.; Hernandez, R.; Zappi, M.E.; Buchireddy, P. Torrefaction of Pine Using a Pilot-Scale Rotary Reactor: Experimentation, Kinetics, and Process Simulation Using Aspen Plus. Clean Technol. 2023, 5, 675–695. [Google Scholar] [CrossRef]
  7. Perera, S.M.; Wickramasinghe, C.; Samarasiri, B.; Narayana, M. Modeling of thermochemical conversion of waste biomass–a comprehensive review. Biofuel Res. J. 2021, 8, 1481–1528. [Google Scholar] [CrossRef]
  8. Bates, R.B.; Ghoniem, A.F. Biomass torrefaction: Modeling of reaction thermochemistry. Bioresour. Technol. 2013, 134, 331–340. [Google Scholar] [CrossRef] [PubMed]
  9. Prins, M.J.; Ptasinski, K.J.; Janssen, F.J. Torrefaction of wood: Part 1. Weight loss kinetics. J. Anal. Appl. Pyrolysis 2006, 77, 28–34. [Google Scholar] [CrossRef]
  10. Bates, R.B.; Ghoniem, A.F. Biomass torrefaction: Modeling of volatile and solid product evolution kinetics. Bioresour. Technol. 2012, 124, 460–469. [Google Scholar] [CrossRef] [PubMed]
  11. Bates, R.B.; Ghoniem, A.F. Modeling kinetics-transport interactions during biomass torrefaction: The effects of temperature, particle size, and moisture content. Fuel 2014, 137, 216–229. [Google Scholar] [CrossRef]
  12. Stephan, P.; Atlas, V.H. B1 Fundamentals of Heat Transfer’. VDI Heat Atlas 2010, 15, 15–30. [Google Scholar]
  13. EN ISO 16948:2015; Solid Biofuels—Determination of Total Content of Carbon, Hydrogen and Nitrogen. European Committee for Standardization: Brussels, Belgium, 2015.
  14. EN 14775:2009; Solid Biofuels—Determination of Ash Content. European Committee for Standardization: Brussels, Belgium, 2009.
  15. Planck, M. The Theory of Heat Radiation; P. Blakiston’s Son & Co.: Philadelphia, PA, USA, 1914. [Google Scholar]
  16. Siegel, R. Parallel Plates, Radiative Heat Transfer Between, 2010. Article Added: 7 September 2010, Last Modified: 24 May 2011. 2010. Available online: https://www.thermopedia.com/content/69/ (accessed on 10 March 2025).
  17. Howell, J.R.; Mengüç, M.P.; Daun, K.; Siegel, R. Thermal Radiation Heat Transfer; CRC Press: Boca Raton, FL, USA, 2020. [Google Scholar]
  18. Wyatt, P.J.; Stull, V.R.; Plass, G.N. The infrared transmittance of water vapor. Appl. Opt. 1964, 3, 229–241. [Google Scholar] [CrossRef]
  19. Churchill, S.W.; Chu, H.H.S. Correlating Equations for Laminar and Turbulent Free Convection from a Vertical Plate. Int. J. Heat Mass Transf. 1975, 18, 1323–1329. [Google Scholar] [CrossRef]
  20. Incropera, F.P.; DeWitt, D.P.; Bergman, T.L.; Lavine, A.S. Fundamentals of Heat and Mass Transfer; Wiley: New York, NY, USA, 1996; Volume 6. [Google Scholar]
  21. Gnielinski, V. New Equations for Heat and Mass Transfer in Turbulent Pipe and Channel Flow. Int. Chem. Eng. 1976, 16, 359–368. [Google Scholar]
Figure 1. Simplified schematic of the indirectly heated torrefaction reactors.
Figure 1. Simplified schematic of the indirectly heated torrefaction reactors.
Energies 18 03978 g001
Figure 2. Control volume schematic showing mass and energy flows between different phases in the process.
Figure 2. Control volume schematic showing mass and energy flows between different phases in the process.
Energies 18 03978 g002
Figure 3. Comparison of the kinetic model with experimental data on the mass yield of torrefied biomass at varying temperatures.
Figure 3. Comparison of the kinetic model with experimental data on the mass yield of torrefied biomass at varying temperatures.
Energies 18 03978 g003
Figure 4. Vibratory bed reactor: Torrefied biomass NCV measurements versus Monte Carlo NCV predictions.
Figure 4. Vibratory bed reactor: Torrefied biomass NCV measurements versus Monte Carlo NCV predictions.
Energies 18 03978 g004
Figure 5. Comparison of model predictions with and without water vapor absorption. (a) Vibratory bed reactor with water vapor absorption. (b) Vibratory bed reactor without water vapor absorption. (c) Rotary drum reactor with water vapor absorption. (d) Rotary drum reactor without water vapor absorption.
Figure 5. Comparison of model predictions with and without water vapor absorption. (a) Vibratory bed reactor with water vapor absorption. (b) Vibratory bed reactor without water vapor absorption. (c) Rotary drum reactor with water vapor absorption. (d) Rotary drum reactor without water vapor absorption.
Energies 18 03978 g005
Table 1. Ultimate-analysis inputs for model feedstocks (dry basis).
Table 1. Ultimate-analysis inputs for model feedstocks (dry basis).
ComponentVägari (Estonia, Vibratory Bed)Dilsen-Stokkem (Belgium, Rotary Drum)
C (%) 50 ± 0.3 48 ± 0.3
H (%) 6.0 ± 0.4 6.0 ± 0.4
O (%)4243
N (%) 0.30 ± 0.04 0.30 ± 0.04
S (%) 0.02 0.10
Cl (%) 0.01 0.01
Ash (%) 0.9 ± 0.2 2.7 ± 0.2
Notes: Standard deviations reflect analytical reproducibility (EN ISO 16948:2015 [13] for C, H, N; EN 14775:2009 [14] for ash). Values are rounded to one significant digit for values ≥10%, two digits for values <10%. For the full proximate, trace-metal, and calorific value, see Tables 1 and 2 (Graham et al. [3]).
Table 2. Comparison of measured and model-predicted NCV for industrial reactors.
Table 2. Comparison of measured and model-predicted NCV for industrial reactors.
Reactor TypeMeasured NCV (MJ/kg)Model NCV (MJ/kg)
Vibratory Bed21.5 ± 0.821.4 ± 1.5
Rotary Drum27.0 ± 1.526.8 ± 1.8
Disclaimer/Publisher’s Note: The statements, opinions and data contained in all publications are solely those of the individual author(s) and contributor(s) and not of MDPI and/or the editor(s). MDPI and/or the editor(s) disclaim responsibility for any injury to people or property resulting from any ideas, methods, instructions or products referred to in the content.

Share and Cite

MDPI and ACS Style

Bhatraju, C.; Russell, M.; Dekker, M. Impact of Water Vapor on the Predictive Modeling of Full-Scale Indirectly Heated Biomass Torrefaction System Throughput Capacity. Energies 2025, 18, 3978. https://doi.org/10.3390/en18153978

AMA Style

Bhatraju C, Russell M, Dekker M. Impact of Water Vapor on the Predictive Modeling of Full-Scale Indirectly Heated Biomass Torrefaction System Throughput Capacity. Energies. 2025; 18(15):3978. https://doi.org/10.3390/en18153978

Chicago/Turabian Style

Bhatraju, Chaitanya, Matthew Russell, and Martijn Dekker. 2025. "Impact of Water Vapor on the Predictive Modeling of Full-Scale Indirectly Heated Biomass Torrefaction System Throughput Capacity" Energies 18, no. 15: 3978. https://doi.org/10.3390/en18153978

APA Style

Bhatraju, C., Russell, M., & Dekker, M. (2025). Impact of Water Vapor on the Predictive Modeling of Full-Scale Indirectly Heated Biomass Torrefaction System Throughput Capacity. Energies, 18(15), 3978. https://doi.org/10.3390/en18153978

Note that from the first issue of 2016, this journal uses article numbers instead of page numbers. See further details here.

Article Metrics

Back to TopTop