Effectiveness Factor at First Order Calculator

tanh - The hyperbolic tangent function (tanh) is a function that is defined as the ratio of the hyperbolic sine function (sinh) to the hyperbolic cosine function (cosh)., tanh(Number)

Variables Used

Effectiveness Factor - Effectiveness Factor is term used to measure the resistance to pore diffusion.
Thiele Modulus - Thiele Modulus is the parameter, which is used for Calculating Effectiveness Factor.

STEP 1: Convert Input(s) to Base Unit

Thiele Modulus: 0.34 --> No Conversion Required

STEP 2: Evaluate Formula

Substituting Input Values in Formula

ξ = tanh(M_T)/M_T --> tanh(0.34)/0.34

Evaluating ... ...

ξ = 0.963168808260898

STEP 3: Convert Result to Output's Unit

0.963168808260898 --> No Conversion Required

FINAL ANSWER

0.963168808260898 ≈ 0.963169 <-- Effectiveness Factor

(Calculation completed in 00.004 seconds)

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Created by Pavan Kumar

Anurag Group of Institutions (AGI), Hyderabad

Pavan Kumar has created this Calculator and 100+ more calculators!

Verified by Vaibhav Mishra

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

Effectiveness Factor at First Order Formula

Effectiveness Factor = tanh(Thiele Modulus)/Thiele Modulus
ξ = tanh(M_T)/M_T

What is Thiele Modulus?

The Thiele modulus is a dimensionless parameter used in the analysis of diffusion and reaction in porous catalyst particles. It provides a measure of the relative rates of diffusion and reaction within a catalyst particle and is particularly important in the study of heterogeneous catalysis.

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 Effectiveness Factor at First Order?

Effectiveness Factor at First Order calculator uses Effectiveness Factor = tanh(Thiele Modulus)/Thiele Modulus to calculate the Effectiveness Factor, The Effectiveness Factor at First Order formula is defined as Effectiveness of a First-Order Reaction on a Solid Catalyst can be expressed in terms of the Thiele modulus. The Thiele modulus is a dimensionless parameter that characterizes the Effectiveness of a Catalyst Particle in terms of Diffusional limitations. Effectiveness Factor is denoted by ξ symbol.

How to calculate Effectiveness Factor at First Order using this online calculator? To use this online calculator for Effectiveness Factor at First Order, enter Thiele Modulus (M_T) and hit the calculate button. Here is how the Effectiveness Factor at First Order calculation can be explained with given input values -> 0.963169 = tanh(0.34)/0.34.

FAQ

What is Effectiveness Factor at First Order?

The Effectiveness Factor at First Order formula is defined as Effectiveness of a First-Order Reaction on a Solid Catalyst can be expressed in terms of the Thiele modulus. The Thiele modulus is a dimensionless parameter that characterizes the Effectiveness of a Catalyst Particle in terms of Diffusional limitations and is represented as ξ = tanh(M_T)/M_T or Effectiveness Factor = tanh(Thiele Modulus)/Thiele Modulus. Thiele Modulus is the parameter, which is used for Calculating Effectiveness Factor.

How to calculate Effectiveness Factor at First Order?

The Effectiveness Factor at First Order formula is defined as Effectiveness of a First-Order Reaction on a Solid Catalyst can be expressed in terms of the Thiele modulus. The Thiele modulus is a dimensionless parameter that characterizes the Effectiveness of a Catalyst Particle in terms of Diffusional limitations is calculated using Effectiveness Factor = tanh(Thiele Modulus)/Thiele Modulus. To calculate Effectiveness Factor at First Order, you need Thiele Modulus (M_T). With our tool, you need to enter the respective value for Thiele Modulus 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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