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Thiele Modulus for Deactivation Formula

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Thiele Modulus for Deactivation is the parameter, which is used for Calculating Effectiveness Factor. Check FAQs

M Td = L \cdot \sqrt{k''' \cdot \frac{a}{D e}}

M_Td - Thiele Modulus for Deactivation?L - Length of Catalyst Pore at Deactivation?k''' - Rate Const. on Volume of Pellets?a - Activity of Catalyst?D_e - Diffusion Coefficient at Deactivation?

Thiele Modulus for Deactivation Example

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Here is how the Thiele Modulus for Deactivation equation looks like with Values.

Here is how the Thiele Modulus for Deactivation equation looks like with Units.

Here is how the Thiele Modulus for Deactivation equation looks like.

0.0841 = 0.09 \cdot \sqrt{1.823 \cdot \frac{0.42}{0.876}}

0.0841 = 0.09m \cdot \sqrt{1.823s⁻¹ \cdot \frac{0.42}{0.876m²/s}}

0.0841 = 0.09 \cdot \sqrt{1.823 \cdot \frac{0.42}{0.876}}

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Thiele Modulus for Deactivation Solution

Follow our step by step solution on how to calculate Thiele Modulus for Deactivation?

FIRST Step Consider the formula

M Td = L \cdot \sqrt{k''' \cdot \frac{a}{D e}}

Next Step Substitute values of Variables

∴

M Td = 0.09m \cdot \sqrt{1.823s⁻¹ \cdot \frac{0.42}{0.876m²/s}}

Next Step Prepare to Evaluate

∴

M Td = 0.09 \cdot \sqrt{1.823 \cdot \frac{0.42}{0.876}}

Next Step Evaluate

∴

M Td = 0.0841411485345448

LAST Step Rounding Answer

∴

M Td = 0.0841

Thiele Modulus for Deactivation Formula Elements

Variables

Functions

Thiele Modulus for Deactivation

Thiele Modulus for Deactivation is the parameter, which is used for Calculating Effectiveness Factor.

Symbol: M_Td

Measurement: NAUnit: Unitless

Note: Value should be greater than 0.

Formulas to find Thiele Modulus for Deactivation

Length of Catalyst Pore at Deactivation

Length of Catalyst Pore at Deactivation, often referred to as the "pore length," is a characteristic dimension of the internal structure of a catalyst.

Symbol: L

Measurement: LengthUnit: m

Note: Value should be greater than 0.

Formulas to find Length of Catalyst Pore at Deactivation

Rate Const. on Volume of Pellets

The Rate Const. on Volume of Pellets is a specific form of expressing the rate constant in a catalytic reaction with respect to the Volume of the Catalyst Pellets.

Symbol: k'''

Measurement: First Order Reaction Rate ConstantUnit: s⁻¹

Note: Value should be greater than 0.

Formulas to find Rate Const. on Volume of Pellets

Activity of Catalyst

Activity of Catalyst refers to ratio between Ratio of Reactions before and after adding Catalyst Pellets.

Symbol: a

Measurement: NAUnit: Unitless

Note: Value can be positive or negative.

Formulas to find Activity of Catalyst

Diffusion Coefficient at Deactivation

Diffusion Coefficient at Deactivation is Diffusion of respective Fluid into the Stream, where the fluid is subjected to flow.

Symbol: D_e

Measurement: DiffusivityUnit: m²/s

Note: Value should be greater than 0.

Formulas to find Diffusion Coefficient at Deactivation

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.

Syntax: sqrt(Number)

Other formulas in Deactivating Catalysts category

Go Activity of Catalyst

a = - \frac{r' A}{- (r' A0)}

Go Weight of Catalyst in Batch Solids and Batch Fluids

W d = (\frac{V \cdot k d}{k'}) \cdot \exp (\ln (\ln (\frac{C A}{C A∞})) + k d \cdot t)

Go Deactivation Rate in Batch Solids and Mixed Constant Flow of Fluids

k d,MF = \frac{\ln (k' \cdot 𝛕 ') - \ln ((\frac{C A0}{C A}) - 1)}{t}

Go Deactivation rate for Batch Solids and Mixed Changing Flow of Fluids

k d,MF = \frac{\ln (𝛕 ') - \ln (\frac{C A0 - C A}{k' \cdot C A})}{t}

How to Evaluate Thiele Modulus for Deactivation?

Thiele Modulus for Deactivation evaluator uses Thiele Modulus for Deactivation = Length of Catalyst Pore at Deactivation*sqrt(Rate Const. on Volume of Pellets*Activity of Catalyst/Diffusion Coefficient at Deactivation) to evaluate the Thiele Modulus for Deactivation, The Thiele Modulus for Deactivation formula is defined as Thiele Modulus Calculated when Strong Diffusional Resistance Influences Reaction during Catalyst Deactivation, which can affect both the rate of internal diffusion and the rate of reaction. Thiele Modulus for Deactivation is denoted by M_Td symbol.

How to evaluate Thiele Modulus for Deactivation using this online evaluator? To use this online evaluator for Thiele Modulus for Deactivation, enter Length of Catalyst Pore at Deactivation (L), Rate Const. on Volume of Pellets (k'''), Activity of Catalyst (a) & Diffusion Coefficient at Deactivation (D_e) and hit the calculate button.

FAQs on Thiele Modulus for Deactivation

What is the formula to find Thiele Modulus for Deactivation?

The formula of Thiele Modulus for Deactivation is expressed as Thiele Modulus for Deactivation = Length of Catalyst Pore at Deactivation*sqrt(Rate Const. on Volume of Pellets*Activity of Catalyst/Diffusion Coefficient at Deactivation). Here is an example- 0.084141 = 0.09*sqrt(1.823*0.42/0.876).

How to calculate Thiele Modulus for Deactivation?

With Length of Catalyst Pore at Deactivation (L), Rate Const. on Volume of Pellets (k'''), Activity of Catalyst (a) & Diffusion Coefficient at Deactivation (D_e) we can find Thiele Modulus for Deactivation using the formula - Thiele Modulus for Deactivation = Length of Catalyst Pore at Deactivation*sqrt(Rate Const. on Volume of Pellets*Activity of Catalyst/Diffusion Coefficient at Deactivation). This formula also uses Square Root (sqrt) function(s).

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Thiele Modulus for Deactivation Formula

Thiele Modulus for Deactivation Example

Thiele Modulus for Deactivation Solution

Thiele Modulus for Deactivation Formula Elements

Other formulas in Deactivating Catalysts category

How to Evaluate Thiele Modulus for Deactivation?

FAQs on Thiele Modulus for Deactivation

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