Mass Transfer Coefficient for Batch Leaching Calculator

✖The Volume of Leaching Solution is the volume of complete solution i.e. solute plus solvent for Leaching.ⓘ Volume of Leaching Solution [V_Leaching]			+10% -10%
✖The Area of Leaching is the are of contact available for leaching mass transfer, i.e. the surface area of the solids in contact with the solvent liquid.ⓘ Area of Leaching [A]			+10% -10%
✖The Time of Batch Leaching is the time the solid and the solvent is kept into contact (mixed together) in Batch Leaching Operation.ⓘ Time of Batch Leaching [t]			+10% -10%
✖The Concentration of Saturated Solution with Solute is the concentration of the saturated solution in contact with the solute particles for batch leaching process.ⓘ Concentration of Saturated Solution with Solute [C_S]			+10% -10%
✖The Concentration of Solute in Bulk Solution at Time t is the solute concentration in bulk of solution at time t of the batch leaching process.ⓘ Concentration of Solute in Bulk Solution at Time t [C]			+10% -10%

✖The Mass Transfer Coefficient for Batch Leaching is the coefficient that accounts for driving force for mass transfer in the liquid phase.ⓘ Mass Transfer Coefficient for Batch Leaching [K_L]

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Formula

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Mass Transfer Coefficient for Batch Leaching

Formula

`"K"_{"L"} = (-"V"_{"Leaching"}/("A"*"t"))*ln((("C"_{"S"}-"C")/"C"_{"S"}))`

Example

`"0.015872mol/s*m²"=(-"2.48m³"/("0.154m²"*"600s"))*ln((("56kg/m³"-"25kg/m³")/"56kg/m³"))`

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Mass Transfer Coefficient for Batch Leaching Solution

STEP 0: Pre-Calculation Summary

Formula Used

Mass Transfer Coefficient for Batch Leaching = (-Volume of Leaching Solution/(Area of Leaching*Time of Batch Leaching))*ln(((Concentration of Saturated Solution with Solute-Concentration of Solute in Bulk Solution at Time t)/Concentration of Saturated Solution with Solute))
K_L = (-V_Leaching/(A*t))*ln(((C_S-C)/C_S))
This formula uses 1 Functions, 6 Variables

Functions Used

ln - The natural logarithm, also known as the logarithm to the base e, is the inverse function of the natural exponential function., ln(Number)

Variables Used

Mass Transfer Coefficient for Batch Leaching - (Measured in Mole per Second Square Meter) - The Mass Transfer Coefficient for Batch Leaching is the coefficient that accounts for driving force for mass transfer in the liquid phase.
Volume of Leaching Solution - (Measured in Cubic Meter) - The Volume of Leaching Solution is the volume of complete solution i.e. solute plus solvent for Leaching.
Area of Leaching - (Measured in Square Meter) - The Area of Leaching is the are of contact available for leaching mass transfer, i.e. the surface area of the solids in contact with the solvent liquid.
Time of Batch Leaching - (Measured in Second) - The Time of Batch Leaching is the time the solid and the solvent is kept into contact (mixed together) in Batch Leaching Operation.
Concentration of Saturated Solution with Solute - (Measured in Kilogram per Cubic Meter) - The Concentration of Saturated Solution with Solute is the concentration of the saturated solution in contact with the solute particles for batch leaching process.
Concentration of Solute in Bulk Solution at Time t - (Measured in Kilogram per Cubic Meter) - The Concentration of Solute in Bulk Solution at Time t is the solute concentration in bulk of solution at time t of the batch leaching process.

STEP 1: Convert Input(s) to Base Unit

Volume of Leaching Solution: 2.48 Cubic Meter --> 2.48 Cubic Meter No Conversion Required
Area of Leaching: 0.154 Square Meter --> 0.154 Square Meter No Conversion Required
Time of Batch Leaching: 600 Second --> 600 Second No Conversion Required
Concentration of Saturated Solution with Solute: 56 Kilogram per Cubic Meter --> 56 Kilogram per Cubic Meter No Conversion Required
Concentration of Solute in Bulk Solution at Time t: 25 Kilogram per Cubic Meter --> 25 Kilogram per Cubic Meter No Conversion Required

STEP 2: Evaluate Formula

Substituting Input Values in Formula

K_L = (-V_Leaching/(A*t))*ln(((C_S-C)/C_S)) --> (-2.48/(0.154*600))*ln(((56-25)/56))

Evaluating ... ...

K_L = 0.0158721204101732

STEP 3: Convert Result to Output's Unit

0.0158721204101732 Mole per Second Square Meter --> No Conversion Required

FINAL ANSWER

0.0158721204101732 ≈ 0.015872 Mole per Second Square Meter <-- Mass Transfer Coefficient for Batch Leaching

(Calculation completed in 00.004 seconds)

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Mass Transfer Coefficient for Batch Leaching

Go Mass Transfer Coefficient for Batch Leaching = (-Volume of Leaching Solution/(Area of Leaching*Time of Batch Leaching))*ln(((Concentration of Saturated Solution with Solute-Concentration of Solute in Bulk Solution at Time t)/Concentration of Saturated Solution with Solute))

Area of Contact for Batch Leaching Operation

Go Area of Leaching = (-Volume of Leaching Solution/(Mass Transfer Coefficient for Batch Leaching*Time of Batch Leaching))*ln(((Concentration of Saturated Solution with Solute-Concentration of Solute in Bulk Solution at Time t)/Concentration of Saturated Solution with Solute))

Time of Batch Leaching Operation

Go Time of Batch Leaching = (-Volume of Leaching Solution/(Area of Leaching*Mass Transfer Coefficient for Batch Leaching))*ln(((Concentration of Saturated Solution with Solute-Concentration of Solute in Bulk Solution at Time t)/Concentration of Saturated Solution with Solute))

Volume of Leaching Solution in Batch Leaching

Go Volume of Leaching Solution = (-Mass Transfer Coefficient for Batch Leaching*Area of Leaching*Time of Batch Leaching)/ln(((Concentration of Saturated Solution with Solute-Concentration of Solute in Bulk Solution at Time t)/Concentration of Saturated Solution with Solute))

Concentration of Saturated Solution in Contact with Solid in Batch Leaching

Go Concentration of Saturated Solution with Solute = Concentration of Solute in Bulk Solution at Time t/(1-exp((-Mass Transfer Coefficient for Batch Leaching*Area of Leaching*Time of Batch Leaching)/Volume of Leaching Solution))

Concentration of Solute in Bulk Solution at Time t for Batch Leaching

Go Concentration of Solute in Bulk Solution at Time t = Concentration of Saturated Solution with Solute*(1-exp((-Mass Transfer Coefficient for Batch Leaching*Area of Leaching*Time of Batch Leaching)/Volume of Leaching Solution))

Mass Transfer Coefficient for Batch Leaching Formula

What is Batch Leaching Test?

The Batch Leaching test estimates how readily solute particles mobilize out of the solid material if the material comes into contact with the solvent. The test involves placing a given mass of the solid sample in a container with a specific volume of a liquid solvent (leaching solution). The mixture is agitated for a specific amount of time. Afterwards, the mixture is filtered and the liquid (the leachate) is analyzed for contaminants. Batch Leaching is a two-step process, 1. Contacting solvent and solid to effect a transfer of a solute (leaching). 2. The separation of the solution from the remaining solid (washing).

What is Leaching Operation?

Leaching is a mass transfer operation in which we have a solid material which either contains components which are valuable to us or components which are considered an impurity of the solid, no matter what the case, such components are called solute. We take a liquid which is called a solvent and contact it intimately with the solid in order to extract the solute from the solid and bring it into the liquid thus effecting a separation. Leaching is a solid-liquid extraction process. The process of leaching generally concerns with processes where the solid is inert and contains soluble solute which is extracted from the inert solid with the help of chemical reaction; for example, the leaching of valuable metals from waste materials by using sulphuric acid. The process of leaching is extremely common in metallurgical industries.

How to Calculate Mass Transfer Coefficient for Batch Leaching?

Mass Transfer Coefficient for Batch Leaching calculator uses Mass Transfer Coefficient for Batch Leaching = (-Volume of Leaching Solution/(Area of Leaching*Time of Batch Leaching))*ln(((Concentration of Saturated Solution with Solute-Concentration of Solute in Bulk Solution at Time t)/Concentration of Saturated Solution with Solute)) to calculate the Mass Transfer Coefficient for Batch Leaching, The Mass Transfer Coefficient for Batch Leaching formula is defined as the Mass Transfer coefficient for the driving force in a Batch Leaching Operation. This value can be used for scale-up or design of continuous systems. Mass Transfer Coefficient for Batch Leaching is denoted by K_L symbol.

How to calculate Mass Transfer Coefficient for Batch Leaching using this online calculator? To use this online calculator for Mass Transfer Coefficient for Batch Leaching, enter Volume of Leaching Solution (V_Leaching), Area of Leaching (A), Time of Batch Leaching (t), Concentration of Saturated Solution with Solute (C_S) & Concentration of Solute in Bulk Solution at Time t (C) and hit the calculate button. Here is how the Mass Transfer Coefficient for Batch Leaching calculation can be explained with given input values -> 0.015872 = (-2.48/(0.154*600))*ln(((56-25)/56)).

FAQ

What is Mass Transfer Coefficient for Batch Leaching?

The Mass Transfer Coefficient for Batch Leaching formula is defined as the Mass Transfer coefficient for the driving force in a Batch Leaching Operation. This value can be used for scale-up or design of continuous systems and is represented as K_L = (-V_Leaching/(A*t))*ln(((C_S-C)/C_S)) or Mass Transfer Coefficient for Batch Leaching = (-Volume of Leaching Solution/(Area of Leaching*Time of Batch Leaching))*ln(((Concentration of Saturated Solution with Solute-Concentration of Solute in Bulk Solution at Time t)/Concentration of Saturated Solution with Solute)). The Volume of Leaching Solution is the volume of complete solution i.e. solute plus solvent for Leaching, The Area of Leaching is the are of contact available for leaching mass transfer, i.e. the surface area of the solids in contact with the solvent liquid, The Time of Batch Leaching is the time the solid and the solvent is kept into contact (mixed together) in Batch Leaching Operation, The Concentration of Saturated Solution with Solute is the concentration of the saturated solution in contact with the solute particles for batch leaching process & The Concentration of Solute in Bulk Solution at Time t is the solute concentration in bulk of solution at time t of the batch leaching process.

How to calculate Mass Transfer Coefficient for Batch Leaching?

The Mass Transfer Coefficient for Batch Leaching formula is defined as the Mass Transfer coefficient for the driving force in a Batch Leaching Operation. This value can be used for scale-up or design of continuous systems is calculated using Mass Transfer Coefficient for Batch Leaching = (-Volume of Leaching Solution/(Area of Leaching*Time of Batch Leaching))*ln(((Concentration of Saturated Solution with Solute-Concentration of Solute in Bulk Solution at Time t)/Concentration of Saturated Solution with Solute)). To calculate Mass Transfer Coefficient for Batch Leaching, you need Volume of Leaching Solution (V_Leaching), Area of Leaching (A), Time of Batch Leaching (t), Concentration of Saturated Solution with Solute (C_S) & Concentration of Solute in Bulk Solution at Time t (C). With our tool, you need to enter the respective value for Volume of Leaching Solution, Area of Leaching, Time of Batch Leaching, Concentration of Saturated Solution with Solute & Concentration of Solute in Bulk Solution at Time t 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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