Thiele Modulus Calculator

✖Length of Catalyst Pore, often referred to as the "pore length," is a characteristic dimension of the internal structure of a catalyst.ⓘ Length of Catalyst Pore [L]			+10% -10%
✖Rate Constant is a fundamental parameter in chemical kinetics that quantifies the rate at which a chemical reaction occurs.ⓘ Rate Constant [k]			+10% -10%
✖Diffusion Coefficient is Diffusion of respective Fluid into the Stream, where the fluid is subjected to flow.ⓘ Diffusion Coefficient [D_f]			+10% -10%

✖Thiele Modulus is the parameter, which is used for Calculating Effectiveness Factor.ⓘ Thiele Modulus [M_T]

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Formula

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Thiele Modulus

Formula

`"M"_{"T"} = "L"*sqrt("k"/"D"_{"f"})`

Example

`"0.339974"="0.09m"*sqrt("12.5mol/m³*s"/"0.876m²/s")`

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Thiele Modulus Solution

STEP 0: Pre-Calculation Summary

Formula Used

Thiele Modulus = Length of Catalyst Pore*sqrt(Rate Constant/Diffusion Coefficient)
M_T = L*sqrt(k/D_f)
This formula uses 1 Functions, 4 Variables

Functions Used

sqrt - A square root function is a function that takes a non-negative number as an input and returns the square root of the given input number., sqrt(Number)

Variables Used

Thiele Modulus - Thiele Modulus is the parameter, which is used for Calculating Effectiveness Factor.
Length of Catalyst Pore - (Measured in Meter) - Length of Catalyst Pore, often referred to as the "pore length," is a characteristic dimension of the internal structure of a catalyst.
Rate Constant - (Measured in Mole per Cubic Meter Second) - Rate Constant is a fundamental parameter in chemical kinetics that quantifies the rate at which a chemical reaction occurs.
Diffusion Coefficient - (Measured in Square Meter Per Second) - Diffusion Coefficient is Diffusion of respective Fluid into the Stream, where the fluid is subjected to flow.

STEP 1: Convert Input(s) to Base Unit

Length of Catalyst Pore: 0.09 Meter --> 0.09 Meter No Conversion Required
Rate Constant: 12.5 Mole per Cubic Meter Second --> 12.5 Mole per Cubic Meter Second No Conversion Required
Diffusion Coefficient: 0.876 Square Meter Per Second --> 0.876 Square Meter Per Second No Conversion Required

STEP 2: Evaluate Formula

Substituting Input Values in Formula

M_T = L*sqrt(k/D_f) --> 0.09*sqrt(12.5/0.876)

Evaluating ... ...

M_T = 0.339973810433718

STEP 3: Convert Result to Output's Unit

0.339973810433718 --> No Conversion Required

FINAL ANSWER

0.339973810433718 ≈ 0.339974 <-- Thiele Modulus

(Calculation completed in 00.004 seconds)

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Created by Pavan Kumar

Anurag Group of Institutions (AGI), Hyderabad

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DJ Sanghvi College of Engineering (DJSCE), Mumbai

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Mass Transfer Coefficient of Fluid passing through Single Particle

Go Overall Gas Phase Mass Transfer Coefficient = (2+0.6*(((Density*Velocity in Tube*Diameter of Tube)/Dynamic Viscosity of Liquid)^(1/2))*((Dynamic Viscosity of Liquid/(Density*Diffusivity of Flow))^(1/3)))*(Diffusivity of Flow/Diameter of Tube)

Initial Reactant Concentration for Rxn Containing Batch of Catalysts and Batch of Gas at 1st Order

Go Initial Concentration of Reactant = Reactant Concentration*(exp((Reaction Rate based on Volume of Catalyst Pellets*Solid Fraction*Height of Catalyst Bed)/Superficial Gas Velocity))

Rate Constant for Mixed Flow Reactor with Weight of Catalyst

Go Rate Const. based on Weight of Catalyst = (Reactant Conversion*(1+Fractional Volume Change*Reactant Conversion))/((1-Reactant Conversion)*Space Time for Reaction for Weight of Catalyst)

Space Time of Mixed Flow Reactor with Weight of Catalyst

Go Space Time for Reaction for Weight of Catalyst = (Reactant Conversion*(1+Fractional Volume Change*Reactant Conversion))/((1-Reactant Conversion)*Rate Const. based on Weight of Catalyst)

Rate Constant for Mixed Flow Reactor with Volume of Catalyst

Go Rate Const. on Volume of Pellets = (Reactant Conversion*(1+Fractional Volume Change*Reactant Conversion))/((1-Reactant Conversion)*Space Time based on Volume of Catalyst)

Space Time of Mixed Flow Reactor with Volume of Catalyst

Go Space Time based on Volume of Catalyst = (Reactant Conversion*(1+Fractional Volume Change*Reactant Conversion))/((1-Reactant Conversion)*Rate Const. on Volume of Pellets)

Mass Transfer Coefficient of Fluid passing through Packed Bed of Particles

Go Overall Gas Phase Mass Transfer Coefficient = (2+1.8*((Reynolds Number)^(1/2)*(Schimdt Number)^(1/3)))*(Diffusivity of Flow/Diameter of Tube)

Rate of Reaction in Mixed Flow Reactor Containing Catalyst

Go Rate of Reaction on Weight of Catalyst Pellets = ((Molar Feed Rate of Reactant*Reactant Conversion)/Weight of Catalyst)

Thiele Modulus

Go Thiele Modulus = Length of Catalyst Pore*sqrt(Rate Constant/Diffusion Coefficient)

Effectiveness Factor at First Order

Go Effectiveness Factor = tanh(Thiele Modulus)/Thiele Modulus

Thiele Modulus Formula

Thiele Modulus = Length of Catalyst Pore*sqrt(Rate Constant/Diffusion Coefficient)
M_T = L*sqrt(k/D_f)

What is Diffusion Coefficient?

It is a fundamental parameter that describes the ease with which particles or molecules can move through a medium, typically a gas, liquid, or solid. The diffusion coefficient is crucial in understanding mass transport processes, and it plays a significant role in various scientific and engineering applications.

What are Solid Catalyzed Reactions?

Solid-catalyzed reactions refer to chemical reactions where a solid material, known as a catalyst, facilitates the transformation of reactants into products without itself undergoing any significant change in composition. The use of solid catalysts is widespread in various industrial processes and research applications.

How to Calculate Thiele Modulus?

Thiele Modulus calculator uses Thiele Modulus = Length of Catalyst Pore*sqrt(Rate Constant/Diffusion Coefficient) to calculate the Thiele Modulus, Thiele Modulus formula is defined as a dimensionless parameter used to characterize the effectiveness of a catalyst particle in terms of diffusional limitations. It is commonly employed in the context of heterogeneous catalysis, where a solid catalyst is involved in a chemical reaction, and reactants must diffuse through the catalyst particle to reach the active sites. Thiele Modulus is denoted by M_T symbol.

How to calculate Thiele Modulus using this online calculator? To use this online calculator for Thiele Modulus, enter Length of Catalyst Pore (L), Rate Constant (k) & Diffusion Coefficient (D_f) and hit the calculate button. Here is how the Thiele Modulus calculation can be explained with given input values -> 0.339974 = 0.09*sqrt(12.5/0.876).

FAQ

What is Thiele Modulus?

Thiele Modulus formula is defined as a dimensionless parameter used to characterize the effectiveness of a catalyst particle in terms of diffusional limitations. It is commonly employed in the context of heterogeneous catalysis, where a solid catalyst is involved in a chemical reaction, and reactants must diffuse through the catalyst particle to reach the active sites and is represented as M_T = L*sqrt(k/D_f) or Thiele Modulus = Length of Catalyst Pore*sqrt(Rate Constant/Diffusion Coefficient). Length of Catalyst Pore, often referred to as the "pore length," is a characteristic dimension of the internal structure of a catalyst, Rate Constant is a fundamental parameter in chemical kinetics that quantifies the rate at which a chemical reaction occurs & Diffusion Coefficient is Diffusion of respective Fluid into the Stream, where the fluid is subjected to flow.

How to calculate Thiele Modulus?

Thiele Modulus formula is defined as a dimensionless parameter used to characterize the effectiveness of a catalyst particle in terms of diffusional limitations. It is commonly employed in the context of heterogeneous catalysis, where a solid catalyst is involved in a chemical reaction, and reactants must diffuse through the catalyst particle to reach the active sites is calculated using Thiele Modulus = Length of Catalyst Pore*sqrt(Rate Constant/Diffusion Coefficient). To calculate Thiele Modulus, you need Length of Catalyst Pore (L), Rate Constant (k) & Diffusion Coefficient (D_f). With our tool, you need to enter the respective value for Length of Catalyst Pore, Rate Constant & Diffusion Coefficient and hit the calculate button. You can also select the units (if any) for Input(s) and the Output as well.

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