Time of Batch Leaching Operation 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 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]			+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 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 Operation [t]

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Formula

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Time of Batch Leaching Operation

Formula

t = (- \frac{V Leaching}{A \cdot K L}) \cdot \ln ((\frac{C S - C}{C S}))

Example

647.8416 s = (- \frac{2.48 m³}{0.154 m² \cdot 0.0147 mol/s*m²}) \cdot \ln ((\frac{56 kg/m³ - 25 kg/m³}{56 kg/m³}))

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Time of Batch Leaching Operation Solution

STEP 0: Pre-Calculation Summary

Formula Used

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))
t = (-V_Leaching/(A*K_L))*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

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.
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.
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.
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
Mass Transfer Coefficient for Batch Leaching: 0.0147 Mole per Second Square Meter --> 0.0147 Mole per Second Square Meter 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

t = (-V_Leaching/(A*K_L))*ln(((C_S-C)/C_S)) --> (-2.48/(0.154*0.0147))*ln(((56-25)/56))

Evaluating ... ...

t = 647.841649394826

STEP 3: Convert Result to Output's Unit

647.841649394826 Second --> No Conversion Required

FINAL ANSWER

647.841649394826 ≈ 647.8416 Second <-- Time of Batch Leaching

(Calculation completed in 00.004 seconds)

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Created by Vaibhav Mishra

DJ Sanghvi College of Engineering (DJSCE), Mumbai

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< Operation Calculators

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))

< Important Formulas in Solid Liquid Extraction Calculators

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

Volume of Leaching Solution in Batch Leaching

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

Time of Batch Leaching Operation 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 Time of Batch Leaching Operation?

Time of Batch Leaching Operation calculator uses 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)) to calculate the Time of Batch Leaching, The Time of Batch Leaching Operation formula is defined as the Time of contact between the solid particles and the solvent in the batch leaching operation, also commonly considered as the time of agitation of the solution. Time of Batch Leaching is denoted by t symbol.

How to calculate Time of Batch Leaching Operation using this online calculator? To use this online calculator for Time of Batch Leaching Operation, enter Volume of Leaching Solution (V_Leaching), Area of Leaching (A), Mass Transfer Coefficient for Batch Leaching (K_L), 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 Time of Batch Leaching Operation calculation can be explained with given input values -> 647.8416 = (-2.48/(0.154*0.0147))*ln(((56-25)/56)).

FAQ

What is Time of Batch Leaching Operation?

The Time of Batch Leaching Operation formula is defined as the Time of contact between the solid particles and the solvent in the batch leaching operation, also commonly considered as the time of agitation of the solution and is represented as t = (-V_Leaching/(A*K_L))*ln(((C_S-C)/C_S)) or 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)). 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 Mass Transfer Coefficient for Batch Leaching is the coefficient that accounts for driving force for mass transfer in the liquid phase, 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 Time of Batch Leaching Operation?

The Time of Batch Leaching Operation formula is defined as the Time of contact between the solid particles and the solvent in the batch leaching operation, also commonly considered as the time of agitation of the solution is calculated using 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)). To calculate Time of Batch Leaching Operation, you need Volume of Leaching Solution (V_Leaching), Area of Leaching (A), Mass Transfer Coefficient for Batch Leaching (K_L), 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, Mass Transfer Coefficient for 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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