Multiphase modeling of anisotropic biomass particle pyrolysis accounting for particle deformation and coupled gas-phase dynamics

This paper presents a novel single-grid, Eulerian-VOF model within the open-source Basilisk framework that fully resolves coupled solid-gas dynamics and anisotropic particle deformation during biomass pyrolysis, demonstrating excellent agreement with experimental data while providing a robust tool for developing sustainable pyrolysis processes.

The Gist

The Big Picture: Cooking a Log Without a Recipe

Imagine you are trying to perfectly cook a log of wood in a fire to turn it into fuel (a process called pyrolysis). To do this well, you need to know exactly what is happening inside the log as it heats up.

For a long time, scientists had two separate ways of looking at this problem:

1. The "Inside" View: They looked at how the wood shrinks and changes inside, but they guessed how the hot air outside was touching it.
2. The "Outside" View: They looked at how the hot air moved around the log, but they treated the log like a static rock that never changed shape.

The problem is that wood isn't a rock. As it cooks, it shrinks, it gets spongy (porous), and the hot air rushing past it changes because the log's shape is changing. The old methods missed the conversation between the "inside" and the "outside."

The New Solution: A Single, Smart Camera

This paper introduces a new computer model that acts like a single, high-definition camera watching the whole scene at once. It doesn't guess how the air and wood interact; it calculates the exact dance between them.

Here is how the authors built this "camera":

1. The "Volume-of-Fluid" Trick (The Water Balloon Analogy)

Usually, computers struggle to track a moving boundary, like a shrinking balloon. This model uses a method called Volume-of-Fluid (VOF).

• The Analogy: Imagine a grid of tiny boxes covering your screen. Some boxes are filled with "wood," some with "air," and some are a mix. As the wood shrinks, the model simply updates the percentage of "wood" in each box. It tracks the edge of the wood as it moves, just like tracking the edge of a water balloon being squeezed.

2. The "Sponge" Effect (Porosity and Shrinkage)

Wood is like a sponge. When it heats up, two things happen simultaneously:

• The Sponge gets holes: The material inside breaks down, creating more empty space (porosity).
• The Sponge gets smaller: The whole log shrinks in size.

The authors created a special rule (a mathematical function they call Z) to decide how much of the reaction causes the wood to get holes versus how much causes it to shrink. It's like deciding if a melting ice cube is turning into a puddle (getting holes) or just getting smaller (shrinking). They found that the best results come from a mix of both.

3. The "Traffic Jam" (Gas Flow Inside)

As the wood cooks, it releases gases. These gases have to squeeze through the tiny holes inside the wood to get out.

• The Analogy: Imagine people trying to run out of a crowded stadium. If the stadium is wide open, they run fast. If the exits are narrow and crowded, they move slowly. The model uses Darcy-Forchheimer equations to calculate this "traffic jam" effect, ensuring the gas doesn't just magically appear outside but actually pushes its way through the wood's pores.

4. The "Wood Grain" (Anisotropy)

Wood is not the same in every direction. Heat travels faster along the grain (like running down a hallway) than across it (like running through a crowd).

• The Analogy: Think of a stack of papers. It's easy to slide a finger along the stack (fast), but hard to push through the stack (slow). The model accounts for this by making heat and gas flow faster in the direction of the wood fibers and slower across them.

What Did They Test?

The team tested their model against real-world experiments with wood particles ranging from small spheres to cylinders. They checked:

• Temperature: Does the model predict the wood getting hot at the right speed? (Yes, it matched well).
• Mass Loss: Does the model predict how much wood turns into gas vs. charcoal? (Yes, within a very small error margin).
• Shape Change: Does the model show the wood shrinking correctly? (Yes, though predicting the exact final shape is still a bit tricky, the general trend was correct).

The Bottom Line

This paper presents a new, unified tool that stops guessing how wood shrinks and how air moves around it. Instead, it simulates the entire process in one go.

• Why it matters: It helps engineers design better systems to turn wood into renewable energy.
• The Catch: The model is complex and requires a lot of computer power, but the authors have made their code open-source (free for anyone to use and improve).

In short, they built a digital twin of a burning piece of wood that understands both the inside and the outside, allowing scientists to see the "invisible" changes happening inside the wood as it turns into fuel.

Technical Summary

Technical Summary: Multiphase Modeling of Anisotropic Biomass Particle Pyrolysis

Problem Statement
Current numerical models for biomass particle pyrolysis typically suffer from a fundamental limitation: they focus either on the evolution of the solid particle (internal structure, shrinkage, porosity) or on the surrounding gas-phase dynamics, but rarely on the coupled interactions between the two. Existing approaches often rely on sub-grid-scale correlations to estimate heat and mass transfer coefficients at the particle boundary, assuming a stationary interface. This assumption simplifies model complexity but fails to capture the significant impact of particle diameter variation and interface movement on exchange rates, particularly for biomass which undergoes substantial morphological changes (shrinkage and porosity evolution) during conversion. Furthermore, the anisotropic nature of biomass properties, such as thermal conductivity, is often neglected in multidimensional frameworks that resolve the external flow.

Methodology
To address these limitations, the authors propose a unified, single-grid Eulerian model that fully resolves both the solid biomass particle and the surrounding gas phase without relying on sub-grid correlations. The core methodology includes:

• Volume-Of-Fluid (VOF) Approach: The two-phase system is tracked using a VOF method to resolve the sharp interface between the external gas and the biomass. The biomass is treated as a "pseudo-phase" containing a mixture of a solid matrix and internal gas within pores.
• Coupled Governing Equations: The model solves conservation equations for mass, momentum, energy, and chemical species for both the external environment and the internal pseudo-phase.
  • Momentum: Darcy–Forchheimer terms are incorporated into the Navier-Stokes equations to account for drag effects within the porous matrix.
  • Energy: A single energy equation is solved for the pseudo-phase assuming thermal equilibrium between the internal gas and solid. Anisotropic thermal conductivity is explicitly modeled.
  • Chemistry: Solid-phase pyrolysis reactions are modeled using a detailed kinetic mechanism (CRECK mechanism) managed via the OpenSMOKE++ library. Gas-phase reactions are neglected for the specific low-temperature pyrolysis conditions tested but are acknowledged as necessary for future combustion/gasification studies.
• Shrinkage and Porosity Coupling: A novel approach is introduced to couple biomass porosity evolution with particle shrinkage. The model introduces a function, $Z(x,t)$, which partitions the chemical reaction source term between volume reduction (shrinkage) and internal porosity changes. This function is solved alongside a potential flow approximation to determine the shrinking velocity of the porous matrix.
• Numerical Implementation: The model is implemented in the open-source Basilisk framework using a finite volume method with adaptive mesh refinement (quad/octree grid). A second-order approximate projection method solves the Navier-Stokes equations, while scalar transport (temperature, species) is handled via a two-field approach to minimize numerical diffusion across the interface.

Key Contributions

1. Unified Multiphase Framework: The work presents a model that resolves the gas-solid interface dynamically, eliminating the need for empirical heat and mass transfer correlations.
2. Anisotropic and Deformable Particle Modeling: The framework accounts for the anisotropic nature of biomass (direction-dependent thermal conductivity and permeability) and couples internal porosity changes with external particle shrinkage in a single multidimensional simulation.
3. Mass Conservation and Convergence: The model demonstrates mass conservation and numerical convergence. While the moving interface results in first-order convergence for mass conservation (due to non-divergence-free flows), stationary interfaces show second-order convergence.
4. Open-Source Availability: The code and simulation setups are made publicly available within the Basilisk framework to enhance reproducibility.

Results and Validation
The model was validated against extensive experimental data involving wood particles in the centimeter scale at operating temperatures between 400°C and 700°C.

• Isotropic Sphere (Imposed Temperature): The model accurately predicted temperature profiles (core, half-radius, surface) and the release rates of volatile species (CO, CO2, CH4, etc.) for a poplar wood sphere. It successfully captured endothermic decomposition peaks and exothermic char formation peaks.
• Wooden Sphere in Flow: Simulations of Schima superba wood spheres in a laminar hot nitrogen flow showed excellent agreement with experimental mass loss and core temperature profiles. The model correctly captured the temperature plateau caused by moisture evaporation (approx. 373 K) by implementing a reversible reaction mechanism for water desorption/resorption.
• Shrinkage Profiles: The model predicted shrinking trends with an average error of approximately 10% in the final particle shape. While the model captured the general trend of shape evolution, it highlighted that a deeper fundamental understanding of the internal structural evolution is still required to perfectly predict final shapes.
• Anisotropic Cylinder: For a beech wood cylinder in forced convection, the model successfully reproduced the "bone-like" deformation observed in experiments, where corners degrade faster than the center due to anisotropic heat transfer and boundary conditions. The calculated heat exchange coefficients (convection and radiation) aligned well with experimental estimates.

Significance and Claims
The authors claim that this work represents a step forward in aiding the development of sustainable pyrolysis processes by providing a more rigorous physical description of particle behavior. The model's ability to resolve the interface and internal dynamics without empirical correlations makes it a powerful tool for:

• Multi-scale Modeling: Serving as a sub-grid model generator to derive specific correlations for larger-scale reactor simulations (e.g., bubbling beds, auger reactors) where interface resolution is computationally prohibitive.
• Process Optimization: Predicting yields, degradation times, and temperature profiles under complex fluid dynamic conditions.
• Fundamental Insight: Providing insights into the interplay between porosity changes and volume shrinkage, which are difficult to measure experimentally.

The paper concludes modestly, noting that while the model captures main experimental trends, the precise functional form of the shrinkage-porosity coupling ($Z$) remains an area requiring further fundamental investigation. Future work is identified as necessary to extend the model to combustion and gasification conditions by incorporating gas-phase reactions and handling larger chemical mechanisms.