What is Thiele Modulus?
The
Thiele modulus is a dimensionless number that characterizes the relationship between the chemical reaction rate and the diffusion rate in a porous catalyst. It is crucial in determining whether a reaction is limited by the rate of reaction or by diffusion.
L is the characteristic length of the catalyst particle.
D is the effective diffusivity of the reactant in the catalyst.
k is the reaction rate constant.
C₀ is the initial concentration of the reactant.
Interpreting Thiele Modulus
The value of the Thiele modulus can be interpreted as follows: ϕ > 1: The process is
diffusion-controlled. The diffusion rate is much slower than the reaction rate, meaning the reaction is hindered by the slow movement of reactants.
Applications in Reactor Design
The Thiele modulus is extensively used in
catalyst design and reactor engineering. By adjusting the particle size, porosity, and other factors, engineers can optimize the Thiele modulus to achieve the desired balance between reaction and diffusion rates. This is particularly important in
heterogeneous catalysis, where solid catalysts are used.
Example Calculation
Consider a spherical catalyst particle with a diameter of 0.1 cm, an effective diffusivity of 1×10⁻⁶ cm²/s, a reaction rate constant of 1×10⁻³ s⁻¹, and an initial reactant concentration of 1 mol/L.
First, calculate the characteristic length (L), which is the radius of the sphere:
L = 0.1 cm / 2 = 0.05 cm
Then, calculate the Thiele modulus:
ϕ = (0.05 / √(1×10⁻⁶)) * √(1×10⁻³ * 1) = 50
Since ϕ = 50 >> 1, the process is diffusion-controlled.Conclusion
The Thiele modulus is a vital parameter in catalysis, providing insights into the interplay between chemical reaction rates and mass transfer limitations within porous catalysts. Understanding and manipulating this parameter allows for the efficient design and optimization of catalytic processes, ensuring both high performance and economic viability.
