Liquid-Liquid Extraction and Ternary Phase Equilibria

Why this unit matters

Liquid-liquid extraction distributes a solute between partially immiscible liquid phases. It is useful when relative volatility is low, boiling would damage the product, or a selective solvent provides an economical alternative. A partition coefficient alone does not establish phase disengagement or solvent recovery.

Real extraction designs require ternary liquid-liquid equilibrium data, tie lines, mixing and settling behavior, and consideration of emulsions. Countercurrent operations can substantially reduce solvent demand compared with a single crosscurrent contact.

Four lessons

• [Lesson 7.1: Distribution coefficients](../lessons/u07-l01.html)
• [Lesson 7.2: Ternary phase diagrams](../lessons/u07-l02.html)
• [Lesson 7.3: Multistage extraction](../lessons/u07-l03.html)
• [Lesson 7.4: Extraction contactors](../lessons/u07-l04.html)

Integration and modeling challenge

Build a balance diagram for a process in this unit, list the specified and unknown variables, and decide whether equilibrium, capacity, mass-transfer rate or dynamics limits the result. Solve a base case and two independently chosen disturbances. Include a unit table and one measured or reference property that could falsify the model. Record the critical operating constraint that would prevent an unreviewed classroom design from being built.

Engineering review prompts

• Which performance variables represent product quality, recovery, consumption and safety, and which are merely convenient intermediate calculations?
• What information is missing from the simplified analysis that would be needed in a hazard review or engineering procurement document?
• Can an alternative separation configuration lower energy consumption at the cost of higher solvent makeup, pressure drop or maintenance?
• If a separator meets equilibrium purity in a diagram but not in operation, what measurements discriminate insufficient stages from hydraulic or analyzer problems?

Instructor note

Successful work shows traceable calculations and clearly communicates the validity of assumptions. A complete case study should be reproducible from the given data and should not hide convergence failures or infeasible conditions. If a proposed design is infeasible, recognizing and explaining that infeasibility is a technically correct outcome.

Applied project 7: Liquid extraction

Deliverable

Prepare a ten-page preliminary engineering note for a separation process with a 100 kmol/h feed and at least two specified product qualities. You may change the illustrative feed quantities where the selected operation requires a solvent or additional phase. Present a process flow diagram, component balance table, energy or solvent-use estimate, model comparison, sensitivity plot and recommendation with a clearly labeled uncertainty range.

Process-specific work

Liquid-liquid extraction distributes a solute between partially immiscible liquid phases. It is useful when relative volatility is low, boiling would damage the product, or a selective solvent provides an economical alternative. A partition coefficient alone does not establish phase disengagement or solvent recovery.

Real extraction designs require ternary liquid-liquid equilibrium data, tie lines, mixing and settling behavior, and consideration of emulsions. Countercurrent operations can substantially reduce solvent demand compared with a single crosscurrent contact.

The scope of the report must include all four topics in this unit: Distribution coefficients, Ternary phase diagrams, Multistage extraction, Extraction contactors. The first analysis should be an analytic or graphical approximation. The second should be an independently formulated balance or numeric calculation. These cannot simply be two screenshots of the same routine.

Scenarios

Design point: Adopt a declared separation target and calculate the minimum feasible separation under the selected assumptions. High-load case: Increase the feed throughput by 30% and examine hydraulic or solvent constraints. Feed-quality disturbance: Change the critical component feed fraction by 10 percentage points, and verify that all product streams can remain nonnegative. Utility disturbance: Reduce the available heat or solvent by 20% and determine whether the target remains feasible. Do not extrapolate the simplified model through a phase transition or into a known invalid operating region.

Acceptance checklist

A satisfactory report identifies one physically infeasible case, includes closure of every component balance, presents at least two plausible competing designs, and explains the major limitation of the selected model. Include one risk associated with equipment safety and one risk involving waste or utility use. The result is a classroom design exercise, not a code-compliant plant design.

Unit 7 assessment — Liquid extraction

Problem 1: Distribution coefficients

Analytical prompt. For dilute extraction, fraction remaining=1/(1+D*S/F). Calculate or justify the consequence using the stated relation and a clearly declared consistent basis.

Numerical check. With D=3 and S/F=0.5, remaining fraction=0.40 and extracted fraction=0.60. Recreate this check, then change one input by 15% and calculate the sensitivity.

Conceptual discrimination. D may vary with loading and may not reflect high-concentration tie lines.

Practical investigation. Compare residual solute after a single extraction for several solvent-to-feed ratios and distribution coefficients.

Answer guidance. State the governing equation and the numeric result from the given base case. The changed-input result depends on the parameter selected. A complete answer must include a physical-unit check and explicitly identify tie-line slopes, emulsion formation and varying solvent compositions complicate real systems, especially for concentrated feeds.

Problem 2: Ternary phase diagrams

Analytical prompt. Ternary composition coordinates obey xA+xB+xC=1. Calculate or justify the consequence using the stated relation and a clearly declared consistent basis.

Numerical check. A mixture at (0.15,0.35,0.50) is normalized; (0.20,0.40,0.50) is not. Recreate this check, then change one input by 15% and calculate the sensitivity.

Conceptual discrimination. A ternary plot requires experimentally grounded binodals and tie lines.

Practical investigation. Sketch a simple ternary composition triangle and test whether three mole fractions always sum to one.

Answer guidance. State the governing equation and the numeric result from the given base case. The changed-input result depends on the parameter selected. A complete answer must include a physical-unit check and explicitly identify a single fixed distribution coefficient cannot reproduce the geometry of nonideal ternary phase envelopes.

Problem 3: Multistage extraction

Analytical prompt. Crosscurrent extraction: fraction remaining after N equal fresh-solvent stages=(1+D*S/F)^(-N). Calculate or justify the consequence using the stated relation and a clearly declared consistent basis.

Numerical check. With D=2, S/F=0.5 per stage and N=3, fraction remaining=1/8. Recreate this check, then change one input by 15% and calculate the sensitivity.

Conceptual discrimination. S is solvent amount per stage; total solvent is N*S.

Practical investigation. Calculate x_N/x_0=(1+D S/F)^{-N} with explicit constant phase-flow assumptions and inspect its diminishing returns.

Answer guidance. State the governing equation and the numeric result from the given base case. The changed-input result depends on the parameter selected. A complete answer must include a physical-unit check and explicitly identify assuming perfectly fresh solvent at every stage overestimates removal if solvent recycle is loaded or phase disengagement is incomplete.

Problem 4: Extraction contactors

Analytical prompt. Illustrative approach to equilibrium 1-exp(-t/tau). Calculate or justify the consequence using the stated relation and a clearly declared consistent basis.

Numerical check. At residence t=2*tau, approach≈86.5%. Recreate this check, then change one input by 15% and calculate the sensitivity.

Conceptual discrimination. An empirical contact-time constant is not intrinsic solvent equilibrium.

Practical investigation. Investigate residence-time and separation-factor sensitivity with an illustrative first-order contact model.

Answer guidance. State the governing equation and the numeric result from the given base case. The changed-input result depends on the parameter selected. A complete answer must include a physical-unit check and explicitly identify a high calculated equilibrium recovery is unhelpful if entrained solvent contaminates the product or downstream equipment.

Laboratory manual — Separation Processes I

Purpose and safety

All eighteen browser models are educational sensitivity tools. No real mixture property package, mechanical design correlation, relief-system calculation, or material compatibility analysis is supplied. Do not use them to size, operate or approve a chemical plant. The most important skill is recognizing when a displayed simplified result is infeasible or based on assumptions outside its domain. Equilibrium and hydraulic models in this book are not coupled to industrial design codes.

How to use an experiment

Begin with the baseline, record all input units, and independently compute the displayed result. Before changing a parameter, predict the response direction and the expected limiting case. Alter one parameter at a time and export the resulting curve to CSV. State whether a trend is a direct mathematical property of the model or a defensible prediction for real equipment. The answer is often different: constant relative volatility, fixed liquid flow and fixed heat capacity frequently fail outside narrow ranges.

Grading rubric

• Model statement and control volume: 20%.
• Correct baseline result and independent numerical check: 20%.
• Interpretation of response curve and asymptotes: 20%.
• Assumptions, dimensional consistency and infeasibility handling: 25%.
• Clear exported evidence, written conclusion and reproducibility: 15%.

Experiments

Laboratory 01: Relative-volatility equilibrium

Open: [Interactive model 01](labs/lab-01.html). Relation: y = αx/[1+(α−1)x]. Model limitation: Ideal binary constant-alpha VLE; sweep liquid composition and relative volatility; an azeotrope is not represented.

Method: Record the baseline result. Increase the first parameter in three steps and construct a response table. Identify the coefficient most likely to require measurement or a reliable property database. Calculate the result again by hand for one selected case; report both values without hiding rounding. Deliberately set a limiting parameter near its allowed boundary and explain what changes physically and what merely changes algebraically. Export the curve and annotate the units of both axes.

Investigation question: Does the response follow a conservation constraint, a phase-equilibrium relation, a hydraulic capacity relation, or an illustrative surrogate? State which missing physical mechanism would most likely dominate in a real equipment design.

Laboratory 02: Separation balance and recovery

Open: [Interactive model 02](labs/lab-02.html). Relation: D=F(z−xB)/(xD−xB); B=F−D. Model limitation: Steady binary component balances; disallows negative product flows and invalid ordering.

Method: Record the baseline result. Increase the first parameter in three steps and construct a response table. Identify the coefficient most likely to require measurement or a reliable property database. Calculate the result again by hand for one selected case; report both values without hiding rounding. Deliberately set a limiting parameter near its allowed boundary and explain what changes physically and what merely changes algebraically. Export the curve and annotate the units of both axes.

Investigation question: Does the response follow a conservation constraint, a phase-equilibrium relation, a hydraulic capacity relation, or an illustrative surrogate? State which missing physical mechanism would most likely dominate in a real equipment design.

Laboratory 03: Binary isothermal flash

Open: [Interactive model 03](labs/lab-03.html). Relation: Σ zᵢ(Kᵢ−1)/[1+β(Kᵢ−1)] = 0. Model limitation: Fixed equilibrium K-values, ideal material balance, no energy closure; no two-phase root is reported as single phase.

Method: Record the baseline result. Increase the first parameter in three steps and construct a response table. Identify the coefficient most likely to require measurement or a reliable property database. Calculate the result again by hand for one selected case; report both values without hiding rounding. Deliberately set a limiting parameter near its allowed boundary and explain what changes physically and what merely changes algebraically. Export the curve and annotate the units of both axes.

Investigation question: Does the response follow a conservation constraint, a phase-equilibrium relation, a hydraulic capacity relation, or an illustrative surrogate? State which missing physical mechanism would most likely dominate in a real equipment design.

Laboratory 04: Multicomponent flash

Open: [Interactive model 04](labs/lab-04.html). Relation: Rachford–Rice 3-component root and component reconstruction. Model limitation: Three hypothetical species, K2=1.10; component 3 fraction=1−z1−z2, enforced nonnegative; no energy balance.

Method: Record the baseline result. Increase the first parameter in three steps and construct a response table. Identify the coefficient most likely to require measurement or a reliable property database. Calculate the result again by hand for one selected case; report both values without hiding rounding. Deliberately set a limiting parameter near its allowed boundary and explain what changes physically and what merely changes algebraically. Export the curve and annotate the units of both axes.

Investigation question: Does the response follow a conservation constraint, a phase-equilibrium relation, a hydraulic capacity relation, or an illustrative surrogate? State which missing physical mechanism would most likely dominate in a real equipment design.

Laboratory 05: Flash latent-heat screen

Open: [Interactive model 05](labs/lab-05.html). Relation: β≈q/λ, clipped at 0≤β≤1. Model limitation: Constant latent heat and neglected sensible effects; this is a screening energy fraction, not a coupled thermodynamic flash.

Method: Record the baseline result. Increase the first parameter in three steps and construct a response table. Identify the coefficient most likely to require measurement or a reliable property database. Calculate the result again by hand for one selected case; report both values without hiding rounding. Deliberately set a limiting parameter near its allowed boundary and explain what changes physically and what merely changes algebraically. Export the curve and annotate the units of both axes.

Investigation question: Does the response follow a conservation constraint, a phase-equilibrium relation, a hydraulic capacity relation, or an illustrative surrogate? State which missing physical mechanism would most likely dominate in a real equipment design.

Laboratory 06: Rectifying operating line

Open: [Interactive model 06](labs/lab-06.html). Relation: y=R/(R+1)x+xD/(R+1). Model limitation: Constant molar overflow in the rectifying section; x-y plot is a mass-balance relation, not phase equilibrium.

Method: Record the baseline result. Increase the first parameter in three steps and construct a response table. Identify the coefficient most likely to require measurement or a reliable property database. Calculate the result again by hand for one selected case; report both values without hiding rounding. Deliberately set a limiting parameter near its allowed boundary and explain what changes physically and what merely changes algebraically. Export the curve and annotate the units of both axes.

Investigation question: Does the response follow a conservation constraint, a phase-equilibrium relation, a hydraulic capacity relation, or an illustrative surrogate? State which missing physical mechanism would most likely dominate in a real equipment design.

Laboratory 07: McCabe–Thiele stage stepping

Open: [Interactive model 07](labs/lab-07.html). Relation: Graphical equilibrium stepping to xB using two operating lines. Model limitation: Constant molar overflow, constant alpha and saturated-liquid feed q=1. Stage count includes modeled reboiler contact; condenser convention is explicit.

Method: Record the baseline result. Increase the first parameter in three steps and construct a response table. Identify the coefficient most likely to require measurement or a reliable property database. Calculate the result again by hand for one selected case; report both values without hiding rounding. Deliberately set a limiting parameter near its allowed boundary and explain what changes physically and what merely changes algebraically. Export the curve and annotate the units of both axes.

Investigation question: Does the response follow a conservation constraint, a phase-equilibrium relation, a hydraulic capacity relation, or an illustrative surrogate? State which missing physical mechanism would most likely dominate in a real equipment design.

Laboratory 08: Fenske minimum stages

Open: [Interactive model 08](labs/lab-08.html). Relation: Nmin=ln[(xD/(1−xD))((1−xB)/xB)]/ln(α). Model limitation: Binary constant-alpha total-reflux minimum-stage estimate; not a finite-reflux actual tray count.

Method: Record the baseline result. Increase the first parameter in three steps and construct a response table. Identify the coefficient most likely to require measurement or a reliable property database. Calculate the result again by hand for one selected case; report both values without hiding rounding. Deliberately set a limiting parameter near its allowed boundary and explain what changes physically and what merely changes algebraically. Export the curve and annotate the units of both axes.

Investigation question: Does the response follow a conservation constraint, a phase-equilibrium relation, a hydraulic capacity relation, or an illustrative surrogate? State which missing physical mechanism would most likely dominate in a real equipment design.

Laboratory 09: Tray capacity screening

Open: [Interactive model 09](labs/lab-09.html). Relation: % flood=100 V/Vmax. Model limitation: Simplified velocity ratio; no vendor geometry, foaming, surface tension, downcomer or entrainment correlation.

Method: Record the baseline result. Increase the first parameter in three steps and construct a response table. Identify the coefficient most likely to require measurement or a reliable property database. Calculate the result again by hand for one selected case; report both values without hiding rounding. Deliberately set a limiting parameter near its allowed boundary and explain what changes physically and what merely changes algebraically. Export the curve and annotate the units of both axes.

Investigation question: Does the response follow a conservation constraint, a phase-equilibrium relation, a hydraulic capacity relation, or an illustrative surrogate? State which missing physical mechanism would most likely dominate in a real equipment design.

Laboratory 10: Packed column height

Open: [Interactive model 10](labs/lab-10.html). Relation: H=N·HETP. Model limitation: Height equivalent to a theoretical plate is assumed constant, excluding distributors and end effects.

Method: Record the baseline result. Increase the first parameter in three steps and construct a response table. Identify the coefficient most likely to require measurement or a reliable property database. Calculate the result again by hand for one selected case; report both values without hiding rounding. Deliberately set a limiting parameter near its allowed boundary and explain what changes physically and what merely changes algebraically. Export the curve and annotate the units of both axes.

Investigation question: Does the response follow a conservation constraint, a phase-equilibrium relation, a hydraulic capacity relation, or an illustrative surrogate? State which missing physical mechanism would most likely dominate in a real equipment design.

Laboratory 11: Column pressure loss

Open: [Interactive model 11](labs/lab-11.html). Relation: ΔP=kQ². Model limitation: Quadratic pressure-drop sensitivity is only a screening model within a single turbulent-flow regime.

Method: Record the baseline result. Increase the first parameter in three steps and construct a response table. Identify the coefficient most likely to require measurement or a reliable property database. Calculate the result again by hand for one selected case; report both values without hiding rounding. Deliberately set a limiting parameter near its allowed boundary and explain what changes physically and what merely changes algebraically. Export the curve and annotate the units of both axes.

Investigation question: Does the response follow a conservation constraint, a phase-equilibrium relation, a hydraulic capacity relation, or an illustrative surrogate? State which missing physical mechanism would most likely dominate in a real equipment design.

Laboratory 12: Tray efficiency uncertainty

Open: [Interactive model 12](labs/lab-12.html). Relation: Nactual=ceil(N/E). Model limitation: Overall efficiency screening only; actual and Murphree efficiencies are not interchangeable.

Method: Record the baseline result. Increase the first parameter in three steps and construct a response table. Identify the coefficient most likely to require measurement or a reliable property database. Calculate the result again by hand for one selected case; report both values without hiding rounding. Deliberately set a limiting parameter near its allowed boundary and explain what changes physically and what merely changes algebraically. Export the curve and annotate the units of both axes.

Investigation question: Does the response follow a conservation constraint, a phase-equilibrium relation, a hydraulic capacity relation, or an illustrative surrogate? State which missing physical mechanism would most likely dominate in a real equipment design.

Laboratory 13: Gas absorber transfer units

Open: [Interactive model 13](labs/lab-13.html). Relation: yout=yin exp(−NTU). Model limitation: Constant overall driving force surrogate; outlet/inlet ratio exp(-NTU) does not resolve a true equilibrium pinch.

Method: Record the baseline result. Increase the first parameter in three steps and construct a response table. Identify the coefficient most likely to require measurement or a reliable property database. Calculate the result again by hand for one selected case; report both values without hiding rounding. Deliberately set a limiting parameter near its allowed boundary and explain what changes physically and what merely changes algebraically. Export the curve and annotate the units of both axes.

Investigation question: Does the response follow a conservation constraint, a phase-equilibrium relation, a hydraulic capacity relation, or an illustrative surrogate? State which missing physical mechanism would most likely dominate in a real equipment design.

Laboratory 14: Solvent regeneration inventory

Open: [Interactive model 14](labs/lab-14.html). Relation: Makeup=L×loss%; residual contaminant fraction≈1−regeneration efficiency. Model limitation: Makeup covers single-pass physical losses; regeneration-removal slider only illustrates a separate residual-contaminant indicator.

Method: Record the baseline result. Increase the first parameter in three steps and construct a response table. Identify the coefficient most likely to require measurement or a reliable property database. Calculate the result again by hand for one selected case; report both values without hiding rounding. Deliberately set a limiting parameter near its allowed boundary and explain what changes physically and what merely changes algebraically. Export the curve and annotate the units of both axes.

Investigation question: Does the response follow a conservation constraint, a phase-equilibrium relation, a hydraulic capacity relation, or an illustrative surrogate? State which missing physical mechanism would most likely dominate in a real equipment design.

Laboratory 15: Single-stage liquid extraction

Open: [Interactive model 15](labs/lab-15.html). Relation: Fraction remaining=1/(1+D×S/F). Model limitation: Dilute solute, immiscible carrier phases, constant distribution coefficient and equal concentration basis.

Method: Record the baseline result. Increase the first parameter in three steps and construct a response table. Identify the coefficient most likely to require measurement or a reliable property database. Calculate the result again by hand for one selected case; report both values without hiding rounding. Deliberately set a limiting parameter near its allowed boundary and explain what changes physically and what merely changes algebraically. Export the curve and annotate the units of both axes.

Investigation question: Does the response follow a conservation constraint, a phase-equilibrium relation, a hydraulic capacity relation, or an illustrative surrogate? State which missing physical mechanism would most likely dominate in a real equipment design.

Laboratory 16: Crosscurrent extraction stages

Open: [Interactive model 16](labs/lab-16.html). Relation: xN/x0=(1+D×S/F)^(−N). Model limitation: Identical fresh-solvent contacts, constant phase flows, equilibrium each stage; total solvent = N×S.

Method: Record the baseline result. Increase the first parameter in three steps and construct a response table. Identify the coefficient most likely to require measurement or a reliable property database. Calculate the result again by hand for one selected case; report both values without hiding rounding. Deliberately set a limiting parameter near its allowed boundary and explain what changes physically and what merely changes algebraically. Export the curve and annotate the units of both axes.

Investigation question: Does the response follow a conservation constraint, a phase-equilibrium relation, a hydraulic capacity relation, or an illustrative surrogate? State which missing physical mechanism would most likely dominate in a real equipment design.

Laboratory 17: Heat-integration duty screen

Open: [Interactive model 17](labs/lab-17.html). Relation: Saved annual heat = Q×save×hours (MWh/year). Model limitation: Gross hot-utility duty savings only; ignores utility temperature, capital cost, pressure drops and control costs.

Method: Record the baseline result. Increase the first parameter in three steps and construct a response table. Identify the coefficient most likely to require measurement or a reliable property database. Calculate the result again by hand for one selected case; report both values without hiding rounding. Deliberately set a limiting parameter near its allowed boundary and explain what changes physically and what merely changes algebraically. Export the curve and annotate the units of both axes.

Investigation question: Does the response follow a conservation constraint, a phase-equilibrium relation, a hydraulic capacity relation, or an illustrative surrogate? State which missing physical mechanism would most likely dominate in a real equipment design.

Laboratory 18: Column dynamic response

Open: [Interactive model 18](labs/lab-18.html). Relation: Δx(t)=gain[1−exp(−t/τ)]. Model limitation: Single first-order surrogate without dead time, coupling, material inventory or saturation; illustrative only.

Method: Record the baseline result. Increase the first parameter in three steps and construct a response table. Identify the coefficient most likely to require measurement or a reliable property database. Calculate the result again by hand for one selected case; report both values without hiding rounding. Deliberately set a limiting parameter near its allowed boundary and explain what changes physically and what merely changes algebraically. Export the curve and annotate the units of both axes.

Investigation question: Does the response follow a conservation constraint, a phase-equilibrium relation, a hydraulic capacity relation, or an illustrative surrogate? State which missing physical mechanism would most likely dominate in a real equipment design.