Solute Underflow Leaving Column based on Ratio of Overflow to Underflow Calculator

✖The Amount of Solute in Underflow entering column is the amount of the solute entering in the Underflow of the continuous leaching operation.ⓘ Amount of Solute in Underflow Entering Column [S₀]			+10% -10%
✖The Ratio of Discharge in Overflow to Underflow is the ratio of the solution, solvent or solute discharge in the overflow to that in the underflow.ⓘ Ratio of Discharge in Overflow to Underflow [R]			+10% -10%
✖The Number of Equilibrium Stages in Leaching is the Number of mass transfer stages in leaching operation required to attain a specified level of solid concentration.ⓘ Number of Equilibrium Stages in Leaching [N]			+10% -10%

✖The Amount of Solute in Underflow leaving column is the amount of the solute leaving in the Underflow of the continuous leaching operation.ⓘ Solute Underflow Leaving Column based on Ratio of Overflow to Underflow [S_N]

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Formula

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Solute Underflow Leaving Column based on Ratio of Overflow to Underflow

Formula

`"S"_{"N"} = ("S"_{"0"}*("R"-1))/(("R"^("N"+1))-1)`

Example

`"1.854794kg/s"=("9.85kg/s"*("1.35"-1))/((("1.35")^("2.5"+1))-1)`

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Solute Underflow Leaving Column based on Ratio of Overflow to Underflow Solution

STEP 0: Pre-Calculation Summary

Formula Used

Amount of Solute in Underflow Leaving Column = (Amount of Solute in Underflow Entering Column*(Ratio of Discharge in Overflow to Underflow-1))/((Ratio of Discharge in Overflow to Underflow^(Number of Equilibrium Stages in Leaching+1))-1)
S_N = (S₀*(R-1))/((R^(N+1))-1)
This formula uses 4 Variables

Variables Used

Amount of Solute in Underflow Leaving Column - (Measured in Kilogram per Second) - The Amount of Solute in Underflow leaving column is the amount of the solute leaving in the Underflow of the continuous leaching operation.
Amount of Solute in Underflow Entering Column - (Measured in Kilogram per Second) - The Amount of Solute in Underflow entering column is the amount of the solute entering in the Underflow of the continuous leaching operation.
Ratio of Discharge in Overflow to Underflow - The Ratio of Discharge in Overflow to Underflow is the ratio of the solution, solvent or solute discharge in the overflow to that in the underflow.
Number of Equilibrium Stages in Leaching - The Number of Equilibrium Stages in Leaching is the Number of mass transfer stages in leaching operation required to attain a specified level of solid concentration.

STEP 1: Convert Input(s) to Base Unit

Amount of Solute in Underflow Entering Column: 9.85 Kilogram per Second --> 9.85 Kilogram per Second No Conversion Required
Ratio of Discharge in Overflow to Underflow: 1.35 --> No Conversion Required
Number of Equilibrium Stages in Leaching: 2.5 --> No Conversion Required

STEP 2: Evaluate Formula

Substituting Input Values in Formula

S_N = (S₀*(R-1))/((R^(N+1))-1) --> (9.85*(1.35-1))/((1.35^(2.5+1))-1)

Evaluating ... ...

S_N = 1.85479355739541

STEP 3: Convert Result to Output's Unit

1.85479355739541 Kilogram per Second --> No Conversion Required

FINAL ANSWER

1.85479355739541 ≈ 1.854794 Kilogram per Second <-- Amount of Solute in Underflow Leaving Column

(Calculation completed in 00.004 seconds)

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Home » Engineering » Chemical Engineering » Mass Transfer Operations » Solid-Liquid Extraction » Counter Current Continuous Leaching for Constant Overflow (Pure Solvent) » Solute Underflow Leaving Column based on Ratio of Overflow to Underflow

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< 25 Counter Current Continuous Leaching for Constant Overflow (Pure Solvent) Calculators

Number of Equilibirum Leaching Stages based on Solute Underflow

Go Number of Equilibrium Stages in Leaching = (log10(1+((Amount of Solute in Underflow Entering Column*(Ratio of Discharge in Overflow to Underflow-1))/Amount of Solute in Underflow Leaving Column)))/(log10(Ratio of Discharge in Overflow to Underflow))-1

Solute Underflow Entering Column based on Ratio of Overflow to Underflow

Go Amount of Solute in Underflow Entering Column = (Amount of Solute in Underflow Leaving Column*((Ratio of Discharge in Overflow to Underflow^(Number of Equilibrium Stages in Leaching+1))-1))/(Ratio of Discharge in Overflow to Underflow-1)

Solute Underflow Leaving Column based on Ratio of Overflow to Underflow

Go Amount of Solute in Underflow Leaving Column = (Amount of Solute in Underflow Entering Column*(Ratio of Discharge in Overflow to Underflow-1))/((Ratio of Discharge in Overflow to Underflow^(Number of Equilibrium Stages in Leaching+1))-1)

Number of Equilibrium Leaching Stages based on Recovery of Solute

Go Number of Equilibrium Stages in Leaching = (log10(1+(Ratio of Discharge in Overflow to Underflow-1)/(1-Recovery of Solute in Leaching Column)))/(log10(Ratio of Discharge in Overflow to Underflow))-1

Number of Equilibirum Leaching Stages based on Fractional Solute Discharge

Go Number of Equilibrium Stages in Leaching = (log10(1+(Ratio of Discharge in Overflow to Underflow-1)/Fractional Solute Discharge))/(log10(Ratio of Discharge in Overflow to Underflow))-1

Solute Discharged in Underflow based on Ratio of Overflow to Underflow and Solution Discharged

Go Amount of Solute Discharge in Underflow = Amount of Solution Discharge in Underflow-((Amount of Solution Discharge in Overflow-Amount of Solute Discharge in Overflow)/Ratio of Discharge in Overflow to Underflow)

Solution Discharged in Underflow based on Ratio of Overflow to Underflow and Solute Discharged

Go Amount of Solution Discharge in Underflow = Amount of Solute Discharge in Underflow+((Amount of Solution Discharge in Overflow-Amount of Solute Discharge in Overflow)/Ratio of Discharge in Overflow to Underflow)

Ratio of Solvent Discharged in Underflow to Overflow

Go Ratio of Discharge in Overflow to Underflow = (Amount of Solution Discharge in Overflow-Amount of Solute Discharge in Overflow)/(Amount of Solution Discharge in Underflow-Amount of Solute Discharge in Underflow)

Solution Discharged in Overflow based on Ratio of Overflow to Underflow and Solute Discharged

Go Amount of Solution Discharge in Overflow = Amount of Solute Discharge in Overflow+Ratio of Discharge in Overflow to Underflow*(Amount of Solution Discharge in Underflow-Amount of Solute Discharge in Underflow)

Solute Discharged in Overflow based on Ratio of Overflow to Underflow and Solution Discharged

Go Amount of Solute Discharge in Overflow = Amount of Solution Discharge in Overflow-Ratio of Discharge in Overflow to Underflow*(Amount of Solution Discharge in Underflow-Amount of Solute Discharge in Underflow)

Fractional Solute Discharge based on Ratio of Overflow to Underflow

Go Fractional Solute Discharge = (Ratio of Discharge in Overflow to Underflow-1)/((Ratio of Discharge in Overflow to Underflow^(Number of Equilibrium Stages in Leaching+1))-1)

Solute Underflow Entering Column based on Recovery of Solute

Go Amount of Solute in Underflow Entering Column = Amount of Solute in Underflow Leaving Column/(1-Recovery of Solute in Leaching Column)

Solute Underflow Leaving Column based on Recovery of Solute

Go Amount of Solute in Underflow Leaving Column = Amount of Solute in Underflow Entering Column*(1-Recovery of Solute in Leaching Column)

Recovery of Solute based on Solute Underflow

Go Recovery of Solute in Leaching Column = 1-(Amount of Solute in Underflow Leaving Column/Amount of Solute in Underflow Entering Column)

Solution Discharged in Underflow based on Ratio of Overflow to Underflow

Go Amount of Solution Discharge in Underflow = Amount of Solution Discharge in Overflow/Ratio of Discharge in Overflow to Underflow

Solution Discharged in Overflow based on Ratio of Overflow to Underflow

Go Amount of Solution Discharge in Overflow = Ratio of Discharge in Overflow to Underflow*Amount of Solution Discharge in Underflow

Ratio of Solution Discharged in Overflow to Underflow

Go Ratio of Discharge in Overflow to Underflow = Amount of Solution Discharge in Overflow/Amount of Solution Discharge in Underflow

Solute Discharged in Underflow based on Ratio of Overflow to Underflow

Go Amount of Solute Discharge in Underflow = Amount of Solute Discharge in Overflow/Ratio of Discharge in Overflow to Underflow

Solute Discharged in Overflow based on Ratio of Overflow to Underflow

Go Amount of Solute Discharge in Overflow = Ratio of Discharge in Overflow to Underflow*Amount of Solute Discharge in Underflow

Ratio of Solute Discharged in Underflow to Overflow

Go Ratio of Discharge in Overflow to Underflow = Amount of Solute Discharge in Overflow/Amount of Solute Discharge in Underflow

Solute Underflow Entering Column based on Fractional Solute Discharge

Go Amount of Solute in Underflow Entering Column = Amount of Solute in Underflow Leaving Column/Fractional Solute Discharge

Solute Underflow Leaving Column based on Fractional Solute Discharge

Go Amount of Solute in Underflow Leaving Column = Amount of Solute in Underflow Entering Column*Fractional Solute Discharge

Fractional Solute Discharge Ratio based on Solute Underflow

Go Fractional Solute Discharge = Amount of Solute in Underflow Leaving Column/Amount of Solute in Underflow Entering Column

Recovery of Solute based on Fractional Solute Discharge

Go Recovery of Solute in Leaching Column = 1-Fractional Solute Discharge

Fractional Solute Discharge based on Recovery of Solute

Go Fractional Solute Discharge = 1-Recovery of Solute in Leaching Column

< 25 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

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 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))

Number of Equilibrium Leaching Stages based on Recovery of Solute

Number of Equilibirum Leaching Stages based on Fractional Solute Discharge

Go Number of Equilibrium Stages in Leaching = (log10(1+(Ratio of Discharge in Overflow to Underflow-1)/Fractional Solute Discharge))/(log10(Ratio of Discharge in Overflow to Underflow))-1

Number of Stages based on Original Weight of Solute

Go 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))

Solute Discharged in Underflow based on Ratio of Overflow to Underflow and Solution Discharged

Ratio of Solvent Discharged in Underflow to Overflow

Solute Discharged in Overflow based on Ratio of Overflow to Underflow and Solution Discharged

Solvent Remaining based on Original Weight of Solute and Number of Stages

Go Amount of Solvent Remaining = Amount of Solvent Decanted/(((Original Weight of Solute in Solid/Weight of Solute remaining in Solid after Washing)^(1/Number of Washings in Batch Leaching))-1)

Solvent Decanted based on Original Weight of Solute and Number of Stages

Go Amount of Solvent Decanted = Amount of Solvent Remaining*(((Original Weight of Solute in Solid/Weight of Solute remaining in Solid after Washing)^(1/Number of Washings in Batch Leaching))-1)

Original Weight of Solute based on Number of Stages and Amount of Solvent Decanted

Go Original Weight of Solute in Solid = Weight of Solute remaining in Solid after Washing*((1+(Amount of Solvent Decanted/Amount of Solvent Remaining))^Number of Washings in Batch Leaching)

Weight of Solute remaining based on Number of Stages and Amount of Solvent Decanted

Go Weight of Solute remaining in Solid after Washing = Original Weight of Solute in Solid/((1+Amount of Solvent Decanted/Amount of Solvent Remaining)^Number of Washings in Batch Leaching)

Number of Stages based on Solvent Decanted

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)))

Fractional Solute Discharge based on Ratio of Overflow to Underflow

Go Fractional Solute Discharge = (Ratio of Discharge in Overflow to Underflow-1)/((Ratio of Discharge in Overflow to Underflow^(Number of Equilibrium Stages in Leaching+1))-1)

Fraction of Solute remaining based on Solvent Decanted

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

Recovery of Solute based on Solute Underflow

Go Recovery of Solute in Leaching Column = 1-(Amount of Solute in Underflow Leaving Column/Amount of Solute in Underflow Entering Column)

Ratio of Solution Discharged in Overflow to Underflow

Go Ratio of Discharge in Overflow to Underflow = Amount of Solution Discharge in Overflow/Amount of Solution Discharge in Underflow

Ratio of Solute Discharged in Underflow to Overflow

Go Ratio of Discharge in Overflow to Underflow = Amount of Solute Discharge in Overflow/Amount of Solute Discharge in Underflow

Fraction of Solute as Ratio of Solute

Go Fraction of Solute Remaining in Solid = Weight of Solute remaining in Solid after Washing/Original Weight of Solute in Solid

Fractional Solute Discharge Ratio based on Solute Underflow

Go Fractional Solute Discharge = Amount of Solute in Underflow Leaving Column/Amount of Solute in Underflow Entering Column

Beta Value based on Ratio of Solvent

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

Fractional Solute Discharge based on Recovery of Solute

Go Fractional Solute Discharge = 1-Recovery of Solute in Leaching Column

Recovery of Solute based on Fractional Solute Discharge

Go Recovery of Solute in Leaching Column = 1-Fractional Solute Discharge

Solute Underflow Leaving Column based on Ratio of Overflow to Underflow Formula

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.

What are the Factors affecting Solvent Selection in Leaching Process?

Solubility of the target substance: The solvent should be able to dissolve the target substance to an acceptable extent. Chemical compatibility: The solvent should be chemically compatible with the target substance and not cause any adverse chemical reactions. Toxicity: The solvent should be safe for the environment and not pose any health risks to workers handling it. Cost: The cost of the solvent should be economically viable and not be too expensive. Recovery: The solvent should be recoverable and reusable. Boiling point: The boiling point of the solvent should be appropriate for the temperature range used in the process. Specific gravity: The specific gravity of the solvent should be suitable for the separation process. Viscosity: The viscosity of the solvent should be appropriate for efficient mixing and separation. Regulatory compliance: The solvent should comply with the relevant environmental regulations.

How to Calculate Solute Underflow Leaving Column based on Ratio of Overflow to Underflow?

Solute Underflow Leaving Column based on Ratio of Overflow to Underflow calculator uses Amount of Solute in Underflow Leaving Column = (Amount of Solute in Underflow Entering Column*(Ratio of Discharge in Overflow to Underflow-1))/((Ratio of Discharge in Overflow to Underflow^(Number of Equilibrium Stages in Leaching+1))-1) to calculate the Amount of Solute in Underflow Leaving Column, The Solute Underflow Leaving Column based on Ratio of Overflow to Underflow formula is defined as Solute underflow i.e. solute with solid leaving the column calculated based on Ratio of Underflow to Overflow and Number of Equilibrum Stages. Amount of Solute in Underflow Leaving Column is denoted by S_N symbol.

How to calculate Solute Underflow Leaving Column based on Ratio of Overflow to Underflow using this online calculator? To use this online calculator for Solute Underflow Leaving Column based on Ratio of Overflow to Underflow, enter Amount of Solute in Underflow Entering Column (S₀), Ratio of Discharge in Overflow to Underflow (R) & Number of Equilibrium Stages in Leaching (N) and hit the calculate button. Here is how the Solute Underflow Leaving Column based on Ratio of Overflow to Underflow calculation can be explained with given input values -> 1.854794 = (9.85*(1.35-1))/((1.35^(2.5+1))-1).

FAQ

What is Solute Underflow Leaving Column based on Ratio of Overflow to Underflow?

The Solute Underflow Leaving Column based on Ratio of Overflow to Underflow formula is defined as Solute underflow i.e. solute with solid leaving the column calculated based on Ratio of Underflow to Overflow and Number of Equilibrum Stages and is represented as S_N = (S₀*(R-1))/((R^(N+1))-1) or Amount of Solute in Underflow Leaving Column = (Amount of Solute in Underflow Entering Column*(Ratio of Discharge in Overflow to Underflow-1))/((Ratio of Discharge in Overflow to Underflow^(Number of Equilibrium Stages in Leaching+1))-1). The Amount of Solute in Underflow entering column is the amount of the solute entering in the Underflow of the continuous leaching operation, The Ratio of Discharge in Overflow to Underflow is the ratio of the solution, solvent or solute discharge in the overflow to that in the underflow & The Number of Equilibrium Stages in Leaching is the Number of mass transfer stages in leaching operation required to attain a specified level of solid concentration.

How to calculate Solute Underflow Leaving Column based on Ratio of Overflow to Underflow?

The Solute Underflow Leaving Column based on Ratio of Overflow to Underflow formula is defined as Solute underflow i.e. solute with solid leaving the column calculated based on Ratio of Underflow to Overflow and Number of Equilibrum Stages is calculated using Amount of Solute in Underflow Leaving Column = (Amount of Solute in Underflow Entering Column*(Ratio of Discharge in Overflow to Underflow-1))/((Ratio of Discharge in Overflow to Underflow^(Number of Equilibrium Stages in Leaching+1))-1). To calculate Solute Underflow Leaving Column based on Ratio of Overflow to Underflow, you need Amount of Solute in Underflow Entering Column (S₀), Ratio of Discharge in Overflow to Underflow (R) & Number of Equilibrium Stages in Leaching (N). With our tool, you need to enter the respective value for Amount of Solute in Underflow Entering Column, Ratio of Discharge in Overflow to Underflow & Number of Equilibrium Stages in Leaching 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 Amount of Solute in Underflow Leaving Column?

In this formula, Amount of Solute in Underflow Leaving Column uses Amount of Solute in Underflow Entering Column, Ratio of Discharge in Overflow to Underflow & Number of Equilibrium Stages in Leaching. We can use 3 other way(s) to calculate the same, which is/are as follows -

Amount of Solute in Underflow Leaving Column = Amount of Solute in Underflow Entering Column*Fractional Solute Discharge
Amount of Solute in Underflow Leaving Column = Amount of Solute in Underflow Entering Column*(1-Recovery of Solute in Leaching Column)
Amount of Solute in Underflow Leaving Column = Amount of Solute in Underflow Entering Column*(1-Recovery of Solute in Leaching Column)

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