Impact of Water Vapor on the Predictive Modeling of Full-Scale Indirectly Heated Biomass Torrefaction System Throughput Capacity
Abstract
1. Introduction
2. Methodology
2.1. Reactor Technologies
- 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.
2.2. Design
2.2.1. Reactor
- 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.
2.2.2. Process Parameter Design—Linking Model and Plant Data
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 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 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
2.3. Model Framework
- 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
2.4.1. Torrefaction Kinetics
2.4.2. Heat Transfer
- is the spectral radiance of black body per unit wavelength ().
- h is Planck’s constant ( J·s).
- c is the speed of light in vacuum ( m/s).
- is the Boltzmann constant ( J/K).
- T is the absolute temperature in Kelvin.
- is the wavelength of the emitted radiation.
- 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].
2.4.3. Model Integration
2.4.4. Key Modeling Assumptions
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.
2.4.5. Model Validation Approach
3. Results and Discussion
3.1. Model Validation
3.2. Role of Water Vapor
3.3. Implications for Scale-Up
4. Conclusions
- 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.
Author Contributions
Funding
Data Availability Statement
Acknowledgments
Conflicts of Interest
References
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Component | Vägari (Estonia, Vibratory Bed) | Dilsen-Stokkem (Belgium, Rotary Drum) |
---|---|---|
C (%) | ||
H (%) | ||
O (%) | 42 | 43 |
N (%) | ||
S (%) | ||
Cl (%) | ||
Ash (%) |
Reactor Type | Measured NCV (MJ/kg) | Model NCV (MJ/kg) |
---|---|---|
Vibratory Bed | 21.5 ± 0.8 | 21.4 ± 1.5 |
Rotary Drum | 27.0 ± 1.5 | 26.8 ± 1.8 |
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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
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 StyleBhatraju, 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 StyleBhatraju, 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