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https://github.com/wigging/low-order-particle

Low-Order Modeling of Internal Heat Transfer in Biomass Particle Pyrolysis
https://github.com/wigging/low-order-particle

biomass heat-transfer pyrolysis

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Low-Order Modeling of Internal Heat Transfer in Biomass Particle Pyrolysis

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README 

        
# Code for Low-Order Particle Modeling Paper



Python code and COMSOL data for the following paper:



Gavin Wiggins, Peter Ciesielski, and Stuart Daw. "Low-Order Modeling of

Internal Heat Transfer in Biomass Particle Pyrolysis." Energy & Fuels, 2016,

30(6), pp. 4960-4969.  

[available online](http://pubs.acs.org/doi/abs/10.1021/acs.energyfuels.6b00554)



Requirements: Python 3, Matplotlib, NumPy, SciPy



## Data



Data from the 3-D Comsol simulations is available in the **comsol** folder.

Data from the Sadhukhan 2009 paper is available in the **sadhukhan2009**

folder.



## Functions



Module files prepended with **func** contain functions for modeling heat

conduction within a woody biomass particle. Details about each function are

available in the comment within each module file.



**funcHeatCond.py**  

Functions for 1-D transient heat conduction within a solid sphere, cylinder, or

slab shape. Each function returns an array of temperatures from the center to

surface of the particle at each time step. Properties such as thermal

conductivity and heat capacity can be constant or vary with temperature and

moisture content. Assumes convection at surface, symmetry at center, no

radiation, and constant particle size.



**funcKinetics.py**  

Kinetic reactions for gas, tar, and char yields from biomass pyrolysis.

Parameters for pre-factors and activation energies from Sadhukhan 2009 paper.



**funcOther.py**  

Various functions used to model 1-D biomass particle pyrolysis. Calculate the

shell volumes that comprise a solid sphere. Calculate the volume average

temperature of the entire sphere. Calculate the Sauter diameter of a shape.

Calculate the dimensionless Biot and pyrolysis numbers.



**funcRoots.py , funcTheta.py , funcZeta.py**  

Functions for solving the 1-D analytical solution of the transient heat

conduction equation.



## Models



Various models were created to investigate internal heat transfer within a

solid woody biomass particle. See the comments in each file for detailed

documentation, alternatively an overview is provided below.



**oak-200-20000.py**  

Compare volume average temperature profiles from 1-D model and 3-D Comsol

simulation of white oak particles with Feret diameters DF = 200 um to 20 mm.

Surface area to volume diameter, Dsv, is used for the 1-D model.



**oak-200.py , oak-20000.py**  

Compare temperature profiles of 1-D and 3-D models for DF = 200 um and 20 mm

dry white oak particle. Heat capacity as function of temperature and constant

thermal conductivity. Different equivalent spherical diameters and

characteristic lengths implemented with 1-D model.



**oak-bipy.py**  

Compare Biot and pyrolysis numbers for dry white oak particles. Thermal

properties evaluated at 773 K and kinetic rate constant from Sadhukhan 2009

paper.



**oak-diff.py**

Calculate and compare difference between 3-D surface and center temperature

profiles.



**pine-200.py , pine-20000.py**  

Compare temperature profiles of 1-D and 3-D models for DF = 200 um and 20 mm

dry loblolly pine particle. Heat capacity as function of temperature and

constant thermal conductivity. Different equivalent spherical diameters and

characteristic lengths implemented with 1-D model.



**pine-5400.py**  

Surface, volume, and center temperatures from 1-D and 3-D models for DF = 5.4

mm dry loblolly pine particle. Heat capacity as function of temperature and

constant thermal conductivity. Dsv used as equivalent spherical diameter for

1-D model.



**sadhukhan2009.py**  

Compare 1-D transient heat conduction model to Sadhukhan 2009 Figure 2

cylinder.



**sphere-ana-num.py**  

Compare 1-D analytical sphere solution to 1-D numerical and 3-D Comsol

solutions for transient heat conduction in solid sphere with constant k and Cp.



**sphere-cube.py**  

Compare temperature profiles of 3-D cube and 3-D sphere in Comsol to 1-D cube

and 1-D sphere model. Compare 3-D cube and 3-D sphere Comsol temperature

profiles. Sphere and cube are volume equivalent where sphere diameter is 1 mm

and cube side is 0.806 mm.



**sphere-cyl-slab.py**  

Compare temperature profiles of 1-D solid sphere, cylinder, and cube shapes

that are volume equivalent. Note that due to surface area, sphere heats the

slowest compared to the cylinder and cube shapes.



## License



Files in this repository are available under the MIT license. See the LICENSE

file for more info.