Number of Stages based on Solvent Decanted Calculator

✖The Fraction of Solute Remaining in Solid is the fraction of the solute that is present in the solid after washing in ratio to the initial solute mass.ⓘ Fraction of Solute Remaining in Solid [θ_N]			+10% -10%
✖The Amount of Solvent Decanted is the amount of solvent that is decanted from the solid in washing stage.ⓘ Amount of Solvent Decanted [b]			+10% -10%
✖The Amount of Solvent Remaining is the amount of solvent that is remaining in the solid in washing stage.ⓘ Amount of Solvent Remaining [a]			+10% -10%

✖The Number of Washings in Batch Leaching is the number of washings required after batch leaching operation.ⓘ Number of Stages based on Solvent Decanted [N_Washing]

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Number of Stages based on Solvent Decanted Solution

STEP 0: Pre-Calculation Summary

Formula Used

Number of Washings in Batch Leaching = (ln(1/Fraction of Solute Remaining in Solid)/ln(1+(Amount of Solvent Decanted/Amount of Solvent Remaining)))
N_Washing = (ln(1/θ_N)/ln(1+(b/a)))
This formula uses 1 Functions, 4 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

Number of Washings in Batch Leaching - The Number of Washings in Batch Leaching is the number of washings required after batch leaching operation.
Fraction of Solute Remaining in Solid - The Fraction of Solute Remaining in Solid is the fraction of the solute that is present in the solid after washing in ratio to the initial solute mass.
Amount of Solvent Decanted - (Measured in Kilogram) - The Amount of Solvent Decanted is the amount of solvent that is decanted from the solid in washing stage.
Amount of Solvent Remaining - (Measured in Kilogram) - The Amount of Solvent Remaining is the amount of solvent that is remaining in the solid in washing stage.

STEP 1: Convert Input(s) to Base Unit

Fraction of Solute Remaining in Solid: 0.001 --> No Conversion Required
Amount of Solvent Decanted: 30 Kilogram --> 30 Kilogram No Conversion Required
Amount of Solvent Remaining: 10.5 Kilogram --> 10.5 Kilogram No Conversion Required

STEP 2: Evaluate Formula

Substituting Input Values in Formula

N_Washing = (ln(1/θ_N)/ln(1+(b/a))) --> (ln(1/0.001)/ln(1+(30/10.5)))

Evaluating ... ...

N_Washing = 5.11713353936311

STEP 3: Convert Result to Output's Unit

5.11713353936311 --> No Conversion Required

FINAL ANSWER

5.11713353936311 ≈ 5.117134 <-- Number of Washings in Batch Leaching

(Calculation completed in 00.004 seconds)

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Home » Engineering » Chemical Engineering » Mass Transfer Operations » Solid Liquid Extraction » Batch Leaching » Washing » Number of Stages based on Solvent Decanted

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Created by Vaibhav Mishra

DJ Sanghvi College of Engineering (DJSCE), Mumbai

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< Washing Calculators

Number of Stages for Leaching based on Fraction Solute Retained and Beta Value

LaTeX Go Number of Washings in Batch Leaching = (ln(1/Fraction of Solute Remaining in Solid)/ln(1+Solvent Decanted per Solvent Remaining in Solid))

Beta Value based on Number of Stages and Fraction of Solute

LaTeX Go Solvent Decanted per Solvent Remaining in Solid = ((1/Fraction of Solute Remaining in Solid)^(1/Number of Washings in Batch Leaching))-1

Fraction of Solute Remaining based on Beta Value

LaTeX Go Fraction of Solute Remaining in Solid = (1/((1+Solvent Decanted per Solvent Remaining in Solid)^Number of Washings in Batch Leaching))

Beta Value based on Ratio of Solvent

LaTeX Go Solvent Decanted per Solvent Remaining in Solid = Amount of Solvent Decanted/Amount of Solvent Remaining

< Important Formulas in Solid Liquid Extraction Calculators

Area of Contact for Batch Leaching Operation

LaTeX 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

LaTeX 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

LaTeX 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 Solute in Bulk Solution at Time t for Batch Leaching

LaTeX 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))

Number of Stages based on Solvent Decanted Formula

LaTeX Go

Number of Washings in Batch Leaching = (ln(1/Fraction of Solute Remaining in Solid)/ln(1+(Amount of Solvent Decanted/Amount of Solvent Remaining)))
N_Washing = (ln(1/θ_N)/ln(1+(b/a)))

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 Number of Stages based on Solvent Decanted?

Number of Stages based on Solvent Decanted calculator uses Number of Washings in Batch Leaching = (ln(1/Fraction of Solute Remaining in Solid)/ln(1+(Amount of Solvent Decanted/Amount of Solvent Remaining))) to calculate the Number of Washings in Batch Leaching, The Number of Stages based on Solvent Decanted formula is defined as the number of washing in batch leaching operation to attain the Fractional Solute remaining in the solid based on the amount of solvent decanted. Number of Washings in Batch Leaching is denoted by N_Washing symbol.

How to calculate Number of Stages based on Solvent Decanted using this online calculator? To use this online calculator for Number of Stages based on Solvent Decanted, enter Fraction of Solute Remaining in Solid (θ_N), Amount of Solvent Decanted (b) & Amount of Solvent Remaining (a) and hit the calculate button. Here is how the Number of Stages based on Solvent Decanted calculation can be explained with given input values -> 5.117134 = (ln(1/0.001)/ln(1+(30/10.5))).

FAQ

What is Number of Stages based on Solvent Decanted?

The Number of Stages based on Solvent Decanted formula is defined as the number of washing in batch leaching operation to attain the Fractional Solute remaining in the solid based on the amount of solvent decanted and is represented as N_Washing = (ln(1/θ_N)/ln(1+(b/a))) or Number of Washings in Batch Leaching = (ln(1/Fraction of Solute Remaining in Solid)/ln(1+(Amount of Solvent Decanted/Amount of Solvent Remaining))). The Fraction of Solute Remaining in Solid is the fraction of the solute that is present in the solid after washing in ratio to the initial solute mass, The Amount of Solvent Decanted is the amount of solvent that is decanted from the solid in washing stage & The Amount of Solvent Remaining is the amount of solvent that is remaining in the solid in washing stage.

How to calculate Number of Stages based on Solvent Decanted?

The Number of Stages based on Solvent Decanted formula is defined as the number of washing in batch leaching operation to attain the Fractional Solute remaining in the solid based on the amount of solvent decanted is calculated using Number of Washings in Batch Leaching = (ln(1/Fraction of Solute Remaining in Solid)/ln(1+(Amount of Solvent Decanted/Amount of Solvent Remaining))). To calculate Number of Stages based on Solvent Decanted, you need Fraction of Solute Remaining in Solid (θ_N), Amount of Solvent Decanted (b) & Amount of Solvent Remaining (a). With our tool, you need to enter the respective value for Fraction of Solute Remaining in Solid, Amount of Solvent Decanted & Amount of Solvent Remaining and hit the calculate button. You can also select the units (if any) for Input(s) and the Output as well.

How many ways are there to calculate Number of Washings in Batch Leaching?

In this formula, Number of Washings in Batch Leaching uses Fraction of Solute Remaining in Solid, Amount of Solvent Decanted & Amount of Solvent Remaining. We can use 3 other way(s) to calculate the same, which is/are as follows -

Number of Washings in Batch Leaching = (ln(1/Fraction of Solute Remaining in Solid)/ln(1+Solvent Decanted per Solvent Remaining in Solid))
Number of Washings in Batch Leaching = (ln(Original Weight of Solute in Solid/Weight of Solute remaining in Solid after Washing)/ln(1+Solvent Decanted per Solvent Remaining in Solid))
Number of Washings in Batch Leaching = (ln(Original Weight of Solute in Solid/Weight of Solute remaining in Solid after Washing)/ln(1+Solvent Decanted per Solvent Remaining in Solid))

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