Thiele Modulus for Deactivation Calculator

✖Length of Catalyst Pore at Deactivation, often referred to as the "pore length," is a characteristic dimension of the internal structure of a catalyst.ⓘ Length of Catalyst Pore at Deactivation [L]			+10% -10%
✖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.ⓘ Rate Const. on Volume of Pellets [k''']			+10% -10%
✖Activity of Catalyst refers to ratio between Ratio of Reactions before and after adding Catalyst Pellets.ⓘ Activity of Catalyst [a]			+10% -10%
✖Diffusion Coefficient at Deactivation is Diffusion of respective Fluid into the Stream, where the fluid is subjected to flow.ⓘ Diffusion Coefficient at Deactivation [D_e]			+10% -10%

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

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Thiele Modulus for Deactivation

Formula

`"M"_{"Td"} = "L"*sqrt("k'''"*"a"/"D"_{"e"})`

Example

`"0.084141"="0.09m"*sqrt("1.823s⁻¹"*"0.42"/"0.876m²/s")`

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Thiele Modulus for Deactivation Solution

STEP 0: Pre-Calculation Summary

Formula Used

Thiele Modulus for Deactivation = Length of Catalyst Pore at Deactivation*sqrt(Rate Const. on Volume of Pellets*Activity of Catalyst/Diffusion Coefficient at Deactivation)
M_Td = L*sqrt(k'''*a/D_e)
This formula uses 1 Functions, 5 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 for Deactivation - Thiele Modulus for Deactivation is the parameter, which is used for Calculating Effectiveness Factor.
Length of Catalyst Pore at Deactivation - (Measured in Meter) - Length of Catalyst Pore at Deactivation, often referred to as the "pore length," is a characteristic dimension of the internal structure of a catalyst.
Rate Const. on Volume of Pellets - (Measured in 1 Per Second) - 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.
Activity of Catalyst - Activity of Catalyst refers to ratio between Ratio of Reactions before and after adding Catalyst Pellets.
Diffusion Coefficient at Deactivation - (Measured in Square Meter Per Second) - Diffusion Coefficient at Deactivation 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 at Deactivation: 0.09 Meter --> 0.09 Meter No Conversion Required
Rate Const. on Volume of Pellets: 1.823 1 Per Second --> 1.823 1 Per Second No Conversion Required
Activity of Catalyst: 0.42 --> No Conversion Required
Diffusion Coefficient at Deactivation: 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_Td = L*sqrt(k'''*a/D_e) --> 0.09*sqrt(1.823*0.42/0.876)

Evaluating ... ...

M_Td = 0.0841411485345448

STEP 3: Convert Result to Output's Unit

0.0841411485345448 --> No Conversion Required

FINAL ANSWER

0.0841411485345448 ≈ 0.084141 <-- Thiele Modulus for Deactivation

(Calculation completed in 00.004 seconds)

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< 15 Deactivating Catalysts Calculators

Rate Constant based on Weight of Catalyst in Batch Solids and Batch Fluids

Go Rate Constant based on Weight of Catalyst = ((Volume of Reactor*Rate of Deactivation)/Weight of Catalyst in Deactivation of Catalyst)*exp(ln(ln(Reactant Concentration/Concentration at Infinite Time))+Rate of Deactivation*Time Interval)

Weight of Catalyst in Batch Solids and Batch Fluids

Go Weight of Catalyst in Deactivation of Catalyst = ((Volume of Reactor*Rate of Deactivation)/Rate Constant based on Weight of Catalyst)*exp(ln(ln(Reactant Concentration/Concentration at Infinite Time))+Rate of Deactivation*Time Interval)

Volume of Reactor for Batch Solids and Batch Fluids

Go Volume of Reactor = (Rate Constant based on Weight of Catalyst*Weight of Catalyst in Deactivation of Catalyst)/(exp(ln(ln(Reactant Concentration/Concentration at Infinite Time))+Rate of Deactivation*Time Interval)*Rate of Deactivation)

Initial Reactant Concentration of Reactant for Strong Pore Resistance in Catalyst Deactivation

Go Initial Conc. for 1st Order Catalyzed Reactions = Reactant Concentration for Strong Pore Diffusion*exp(((Rate Constant based on Weight of Catalyst*Space Time for 1st Order Catalyzed Reactions)/Thiele Modulus for Deactivation without a)*exp((-Rate of Deactivation*Time Interval)/2))

Deactivation rate for Batch Solids and Mixed Changing Flow of Fluids

Go Rate of Deactivation for Mixed Flow = (ln(Space Time for 1st Order Catalyzed Reactions)-ln((Initial Conc. for 1st Order Catalyzed Reactions-Reactant Concentration)/(Rate Constant based on Weight of Catalyst*Reactant Concentration)))/Time Interval

Rate Constant based on Weight of Catalyst in Batch Solids and Mixed Changing Flow of Fluids

Go Rate Constant based on Weight of Catalyst = (Initial Conc. for 1st Order Catalyzed Reactions-Reactant Concentration)/(Reactant Concentration*exp(ln(Space Time for 1st Order Catalyzed Reactions)-Rate of Deactivation for Mixed Flow*Time Interval))

Rate Constant based on Weight of Catalyst in Batch Solids and Plug Changing Flow of Fluids

Go Rate Constant based on Weight of Catalyst = ln(Initial Conc. for 1st Order Catalyzed Reactions/Reactant Concentration)*(1/exp((ln(Space Time for 1st Order Catalyzed Reactions)-Rate of Deactivation for Plug Flow*Time Interval)))

Deactivation Rate for Batch Solids and Plug Changing Flow of Fluids

Go Rate of Deactivation for Plug Flow = (ln(Space Time for 1st Order Catalyzed Reactions)-ln((1/Rate Constant based on Weight of Catalyst)*ln(Initial Conc. for 1st Order Catalyzed Reactions/Reactant Concentration)))/Time Interval

Deactivation rate for Batch Solids and Plug Constant Flow of Fluids

Go Rate of Deactivation for Plug Flow = (ln(Rate Constant based on Weight of Catalyst*Space Time for 1st Order Catalyzed Reactions)-ln(ln(Initial Conc. for 1st Order Catalyzed Reactions/Reactant Concentration)))/Time Interval

Rate Constant based on Weight of Catalyst in Batch Solids and Plug Constant Flow of Fluids

Go Rate Constant based on Weight of Catalyst = exp(ln(ln(Initial Conc. for 1st Order Catalyzed Reactions/Reactant Concentration))+Rate of Deactivation for Plug Flow*Time Interval)/Space Time for 1st Order Catalyzed Reactions

Initial Reactant Concentration of Reactant for No Pore Resistance in Catalyst Deactivation

Go Initial Conc. for 1st Order Catalyzed Reactions = Reactant Concentration for No Pore Diffusion*exp(Rate Constant based on Weight of Catalyst*Space Time for 1st Order Catalyzed Reactions*exp(-Rate of Deactivation*Time Interval))

Deactivation Rate in Batch Solids and Mixed Constant Flow of Fluids

Go Rate of Deactivation for Mixed Flow = (ln(Rate Constant based on Weight of Catalyst*Space Time for 1st Order Catalyzed Reactions)-ln((Initial Conc. for 1st Order Catalyzed Reactions/Reactant Concentration)-1))/Time Interval

Rate Constant based on Weight of Catalyst in Batch Solids and Mixed Constant Flow of Fluids

Go Rate Constant based on Weight of Catalyst = exp(ln((Initial Conc. for 1st Order Catalyzed Reactions/Reactant Concentration)-1)+Rate of Deactivation for Mixed Flow*Time Interval)/Space Time for 1st Order Catalyzed Reactions

Thiele Modulus for Deactivation

Go Thiele Modulus for Deactivation = Length of Catalyst Pore at Deactivation*sqrt(Rate Const. on Volume of Pellets*Activity of Catalyst/Diffusion Coefficient at Deactivation)

Activity of Catalyst

Go Activity of Catalyst = -(Rate at which Pellet converts Reactant A)/-(Rate of Reaction of A with a Fresh Pellet)

Thiele Modulus for Deactivation 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)
M_Td = L*sqrt(k'''*a/D_e)

What is Strong Diffusional Resistance?

Strong Diffusional Resistance in the context of catalysis refers to a situation where the movement of reactants or products through a medium, such as a catalyst or a reaction mixture, is significantly hindered by diffusion.

What is Deactivation of Catalyst?

Catalyst deactivation refers to a gradual loss of catalytic activity over time, leading to a decline in the catalyst's effectiveness in promoting a chemical reaction. This phenomenon can occur due to various factors, and understanding the mechanisms of catalyst deactivation is crucial for optimizing and extending the lifespan of catalysts in industrial processes.

How to Calculate Thiele Modulus for Deactivation?

Thiele Modulus for Deactivation calculator 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 calculate 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 calculate Thiele Modulus for Deactivation using this online calculator? To use this online calculator 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. Here is how the Thiele Modulus for Deactivation calculation can be explained with given input values -> 0.084141 = 0.09*sqrt(1.823*0.42/0.876).

FAQ

What is 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 and is represented as M_Td = L*sqrt(k'''*a/D_e) or Thiele Modulus for Deactivation = Length of Catalyst Pore at Deactivation*sqrt(Rate Const. on Volume of Pellets*Activity of Catalyst/Diffusion Coefficient 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, 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, Activity of Catalyst refers to ratio between Ratio of Reactions before and after adding Catalyst Pellets & Diffusion Coefficient at Deactivation is Diffusion of respective Fluid into the Stream, where the fluid is subjected to flow.

How to calculate 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 is calculated using 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 calculate Thiele Modulus for Deactivation, you need Length of Catalyst Pore at Deactivation (L), Rate Const. on Volume of Pellets (k'''), Activity of Catalyst (a) & Diffusion Coefficient at Deactivation (D_e). With our tool, you need to enter the respective value for Length of Catalyst Pore at Deactivation, Rate Const. on Volume of Pellets, Activity of Catalyst & Diffusion Coefficient at Deactivation 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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