O/A Ratio Solvent Extraction: Calculation Guide

Last updated: 2026-10-21

For most copper circuits, O/A ratio solvent extraction design practice places the extraction duty between 1:1 and 1.5:1 by volume. In the worked example below, 200 m³/h of PLS at 4.0 g/L Cu needs an extraction O/A of about 1.07:1 to reach 91.3% copper recovery with a 10 vol% oxime organic, while a strip O/A near 1.4:1 follows directly from the electrowinning copper balance.

If you are new to the unit operation itself, start with our liquid–liquid separation pillar, then return here for the numbers.

Key Takeaways

• The O/A ratio is volumetric organic flow divided by volumetric aqueous flow, defined per stage and per circuit.
• In copper SX, extraction O/A typically runs 1:1 to 1.5:1; strip O/A is usually higher and set by the EW balance.
• The McCabe–Thiele operating line slope equals the aqueous-to-organic flow ratio, A/O = 1/(O/A).
• Too low an O/A overloads the organic; too high an O/A inflates organic inventory and entrainment losses.
• Verify every design O/A with isotherm and miniplant test work before fixing mixer-settler geometry.

O/A Ratio Solvent Extraction: Definition and Core Formula

The O/A ratio is a volumetric flow ratio that compares the organic-phase flow rate to the aqueous-phase flow rate at any given point in a solvent extraction circuit. It is a dimensionless design and operating parameter that determines how much copper (or other metal) each cubic metre of organic must carry, and it is a lever that sets the slope of the operating line on a McCabe–Thiele diagram. In practice, it is also a control variable that operators adjust — usually via the organic or aqueous flow pumps — when tenors drift away from design.

Solvent Extraction, step by step

The core formula is simple:

O/A = Q_org ÷ Q_aq

where Q_org is the volumetric flow of the organic phase and Q_aq is the volumetric flow of the aqueous phase, both measured at operating temperature. Three points of definition matter for engineers:

1. Per stage versus per circuit. Each mixer in a mixer-settler train has its own O/A ratio — the ratio of flows actually entering that mixer. The circuit-level O/A is the ratio of total fresh organic recycle flow to total PLS feed flow. In a series extraction train without aqueous split, these coincide closely for extraction; with aqueous splits (common in scrub and wash stages) they diverge substantially.
2. Volumetric, not mass basis. Organic phases in copper SX (kerosene diluent plus oxime extractant) have specific gravities around 0.80–0.85, while PLS sits near 1.03–1.10. A 1:1 volumetric O/A is therefore roughly a 0.76:1 mass ratio. Always convert consistently.
3. Per-pass versus cumulative. The O/A ratio governs per-pass behaviour: how much metal transfers per contact. Total metal recovery across the circuit is the product of per-stage efficiencies, which is why stage count and O/A must be designed together.

Everything downstream — mixer sizing, settler area, organic inventory, entrainment behaviour — flows from this single ratio.

Why the O/A Ratio Matters: Operating Lines, Continuity, and Entrainment

Operating line slope. On the extraction McCabe–Thiele diagram, where the y-axis is copper loading in the organic (g/L) and the x-axis is copper tenor in the aqueous (g/L), the operating line passes through the stage end points with slope equal to the aqueous-to-organic flow ratio: slope = A/O = 1/(O/A). With an O/A of 1.07:1, the operating line slope is 0.93 — nearly a 45° line. Drop the O/A to 0.8:1 and the slope steepens to 1.25, which forces each stage to swing the organic loading further and can push the operating line into the isotherm, choking off driving force. Raise the O/A and the line flattens, giving generous driving force but demanding more organic flow and inventory. The interplay between operating line and isotherm is exactly what our McCabe–Thiele and isotherm resource walks through graphically.

Phase continuity. The O/A ratio strongly influences which phase becomes continuous in the mixer. When organic is the majority phase (high O/A), the mix box naturally tends toward organic-continuous operation, producing aqueous droplets dispersed in organic. When aqueous dominates, aqueous-continuous operation follows. Continuity affects droplet size, mass-transfer coefficient, settling behaviour, and — critically for copper EW — which phase carries entrainment into the next circuit step. Continuity is discussed in depth in a dedicated section below.

Entrainment behaviour. O/A also sets the absolute flows through the mixer and settler, and entrainment losses scale with interfacial area generated and settling difficulty. Running an unnecessarily high extraction O/A means pumping and shearing more organic per tonne of copper, which typically raises organic-in-aqueous entrainment — organic losses that end up in the raffinate pond — and increases aqueous-in-organic carryover into strip, which transports chloride and other impurities toward the EW tankhouse.

Acid transport in strip. Extraction of Cu²⁺ by an oxime (LIX 984N-class or Acorga-class reagent) releases H⁺ into the raffinate; strip with spent electrolyte (~150–180 g/L H₂SO₄ in copper EW circuits) reverses the reaction. The strip O/A determines how much copper is transferred per pass and therefore how much the electrolyte copper tenor and free acid change between spent and advance electrolyte. A poorly chosen strip O/A either starves the EW section of tenor build-up or swings electrolyte conditions hard enough to disturb copper cathode quality.

Typical O/A Ranges by Circuit Duty

All values below are typical industry starting points for design discussion — every one of them must be verified by isotherm and miniplant test work for your specific liquor and reagent. They are broadly consistent with copper SX practice described in Davenport et al. and the Handbook of Solvent Extraction. See our copper SX–EW application page for circuit context.

Note the pattern in O/A ratio solvent extraction practice: duties where the organic must give up its tenor quickly into a limited aqueous flow run at higher O/A than extraction duties. The worked example below shows why.

How Do You Calculate the O/A Ratio? A Six-Step Worked Example

The example below is illustrative only; verify all numbers with isotherm and miniplant test work on your actual PLS and reagent. Any competent mixer-settler design study starts from exactly this calculation.

Example duty (all assumptions stated):

• PLS flow: 200 m³/h at 4.0 g/L Cu
• Target raffinate: 0.35 g/L Cu
• Organic: 10 vol% oxime extractant in kerosene diluent (LIX 984N-class), realistic maximum loading ≈ 4.5–5.0 g/L Cu at this strength (rule of thumb: 1 vol% oxime ≈ 0.4–0.5 g/L Cu capacity — confirm by isotherm)
• Spent electrolyte available for strip: 150 m³/h at 35 g/L Cu
• Two extraction stages, one strip stage, well-mixed stage efficiency assumed

Step-by-step:

1. Define the extraction duty. Copper to be removed per hour equals PLS flow times the tenor drop: 200 m³/h × (4.0 − 0.35) g/L = 200 × 3.65 = 730 kg/h Cu. As a check on recovery: (4.0 − 0.35) ÷ 4.0 = 91.25% ≈ 91.3% extraction.
2. Set the achievable loading swing (Δloading). At 10 vol% oxime, maximum capacity is roughly 4.0–5.0 g/L Cu. Design the loaded organic conservatively at 4.2 g/L Cu — about 93% of a 4.5 g/L nominal ceiling — to preserve mass-transfer driving force in the final stage. Stripped organic returning from strip typically retains 0.6–1.0 g/L Cu; assume 0.8 g/L. Δloading = 4.2 − 0.8 = 3.4 g/L Cu.
3. Compute the required organic flow. The organic must absorb 730 kg/h at a swing of 3.4 g/L per m³: organic flow = 730 ÷ 3.4 = 214.7 ≈ 215 m³/h. Sanity check against capacity: 215 m³/h × 4.2 g/L = 903 kg/h of loading capacity versus 730 kg/h duty — the organic never actually tops out, which is the point of the 93% margin.
4. Compute the extraction O/A ratio. O/A = 215 ÷ 200 = 1.07:1. This sits comfortably inside the typical 1:1 to 1.5:1 copper SX band. At this ratio the McCabe–Thiele operating line slope is A/O = 200/215 = 0.93.
5. Check the strip O/A against the EW copper balance. Strip must remove the same 730 kg/h from the organic. With 150 m³/h of spent electrolyte: strip O/A = 215 ÷ 150 = 1.43 ≈ 1.4:1, and the electrolyte copper rise is 730 ÷ 150 = 4.9 g/L, taking spent at 35 g/L Cu to an advance electrolyte of ~40 g/L Cu — a healthy, conventional EW operating window. What if you want a stronger spent electrolyte (higher free acid) or a higher advance tenor? Raise the strip O/A by cutting electrolyte flow: at 2:1 (organic 215 ÷ aqueous 107.5), the tenor rise becomes 730 ÷ 107.5 = 6.8 g/L, pushing advance electrolyte to ~42 g/L — check tankhouse stability and, more critically, confirm strip-stage disengagement, because high-O/A strip mixers running organic-continuous with hot, strong acid demand good phase-boundary control.
6. Cross-check against the isotherm and stage count. Plot the operating line (slope 0.93, anchored at raffinate 0.35 g/L and loaded organic 4.2 g/L) against your measured isotherm. Two extraction stages are adequate only if each stage can swing the loads shown in the next section with realistic stage efficiency (85–95% typical for copper oxime systems). If the second stage’s driving force collapses on the diagram, add a third stage or raise the O/A slightly and accept more organic inventory.

The logic chain — duty, swing, organic flow, O/A, strip check, isotherm check — is the same whether the plant treats 20 m³/h or 2,000 m³/h. For broader reading on SX calculation resources, browse our resource library.

What Does a Two-Stage Extraction Balance Look Like?

Splitting the 730 kg/h duty across two stages makes the per-stage O/A tangible. With 215 m³/h of organic against 200 m³/h of PLS in each stage (no splits), each stage’s organic loading swing equals its copper pickup divided by 215 m³/h. The table below continues the illustrative example.

The arithmetic closes: 500 + 230 = 730 kg/h, and 3.13 + 1.07 = 4.20 g/L loaded organic, matching Steps 2–3. Notice the stage-by-stage O/A is 215/200 = 1.07:1 in both stages — the circuit number and the stage number coincide because there are no aqueous splits. Note also that real stage efficiencies of 85–95% shift these end points; our stage efficiency resource explains how to derate the ideal McCabe–Thiele steps.

How Does the O/A Ratio Set the McCabe–Thiele Operating Line?

To make the slope relationship explicit: on the standard extraction diagram (organic loading y versus aqueous tenor x), the operating line equation is

y = y_return + (A/O) × (x_feed − x)

With y_return = 0.8 g/L (stripped organic), A/O = 200/215 = 0.93, and x_feed = 4.0 g/L, the line runs from (0.35, 4.2) at the rich end to (4.0, 0.8) at the lean end. Check the rich end: 0.8 + 0.93 × (4.0 − 0.35) = 0.8 + 0.93 × 3.65 = 0.8 + 3.39 = 4.19 ≈ 4.2 g/L. ✓ The line closes on the design end points because the O/A was derived from the duty — a useful self-check whenever someone hands you an operating line and an O/A that do not quite agree.

Why does this matter for design decisions? In O/A ratio solvent extraction, the gap between the operating line and the equilibrium isotherm at each stage is the mass-transfer driving force. A high O/A flattens the line, widening the gap everywhere but demanding more organic; a low O/A steepens it until, at some critical slope, the line touches the isotherm and an additional stage cannot help — pinch. The only fixes at pinch are more stages with intervening O/A changes, higher reagent concentration (raising the isotherm), or accepting a weaker raffinate. This is the core trade-off our McCabe–Thiele isotherm guide works through with interactive plots.

In O/A ratio solvent extraction design reviews, we recommend checking three slope scenarios — design, +15%, and −15% O/A — before freezing mixer volumes, because reagent assay drift and PLS tenor swings move the real operating line throughout the plant’s life.

Which O/A Ratio Should You Choose? A Sensitivity View

Holding the duty fixed (730 kg/h, 200 m³/h PLS) and varying only the organic flow shows the trade-off between recovery, organic inventory, and strip behaviour. Raffinate values below are illustrative readings from a typical oxime isotherm shape — your isotherm will differ.

Three lessons stand out. First, the recovery curve flattens hard above the design point: buying a further 1.7 percentage points of recovery costs 26% more organic circulating, with proportional capital in pumps, mixers, and settler area, plus higher solvent inventory carrying cost. Second, below the design point the required Δloading (4.06 g/L at 0.90:1) exceeds what a 10 vol% oxime can reliably deliver at good kinetics, and raffinate Cu deteriorates rapidly — the 81.3% row is effectively a failing circuit. Third, every change in extraction O/A propagates to strip O/A and the EW tenor balance, so the sensitivity check must be run on the full circuit, not the extraction battery alone.

What Happens When the O/A Ratio Drifts? Symptoms and Remediation

Operators rarely see “O/A drift” directly; they see its symptoms. In O/A ratio solvent extraction circuits, four signatures recur:

• Loaded organic tenor drift. Loaded organic climbing above ~4.4–4.5 g/L Cu in this example suggests organic flow is low relative to duty (O/A falling) or reagent strength has faded — the organic is being pushed toward its ceiling.
• Raffinate Cu creeping. Raffinate rising from 0.35 toward 0.6–0.8 g/L over weeks, with no PLS change, usually means stage driving force is eroding — again a falling effective O/A, failing stage efficiency, or reagent degradation.
• Phase continuity inversion. A mixer designed aqueous-continuous running organic-continuous (or vice versa) shows up as changed settling times, a rising or falling interfacial “rag layer,” and altered entrainment patterns.
• Entrainment spikes. Sudden increases in organic-in-raffinate or aqueous-in-loaded-organic often accompany O/A excursions because total flow through the mixer and settler velocity both change. Crud accumulation amplifies the effect — see our crud treatment guide and entrainment control resource.

When any of these appear, work the following sequence:

1. Verify flows at the battery limits. Recalibrate the organic and PLS flowmeters; an O/A error is very often an instrument error. Confirm density-corrected volumetric readings.
2. Sample and run the mass balance. Measure PLS, raffinate, loaded organic, and stripped organic tenors over one full shift; compute the actual Cu pickup per m³ of organic and compare with the design 3.4 g/L swing.
3. Restore the design O/A. If the balance shows organic flow 10% below design, correct the pump or the split first before touching reagent dosing.
4. Check reagent concentration. If tenor problems persist at correct O/A, run oxime assay; a drop from 10 vol% to 9 vol% cuts nominal capacity by roughly 0.45 g/L Cu in this example.
5. Correct continuity deliberately. If a mix box has inverted, restore the intended continuity by adjusting that stage’s O/A or agitator speed in small increments while watching disengagement.
6. Treat the crud layer. If entrainment remains high after O/A and continuity corrections, schedule crud removal and review our crud treatment procedures before resorting to chemical additives.

Which Phase Should Be Continuous — and How Does the O/A Ratio Decide?

Phase continuity — which phase forms the continuous matrix and which is dispersed as droplets — is one of the most consequential choices in SX design, and the O/A ratio is its primary lever. In aqueous-continuous operation, organic droplets are dispersed in a water-phase matrix: mass transfer of Cu²⁺ from aqueous into organic droplets is generally favourable for extraction kinetics, and organic entrainment in the raffinate tends to be lower per unit interfacial area. In organic-continuous operation, aqueous droplets are sheared into the organic bulk, which is the usual preference in strip stages contacting hot, strongly acidic electrolyte — it limits the volume of highly acidic aqueous dispersed in the mixer and reduces acid-in-organic carryover.

The natural tendency follows the majority phase: run the mixer at an O/A well above 1:1 and organic-continuous behaviour dominates; run well below and aqueous-continuous takes over. Around 1:1, continuity becomes sensitive to agitator speed, baffle design, and even transient flow changes — one reason designers often deliberately offset the design O/A from unity or force continuity with internal recycle. The consequences for entrainment are asymmetric and matter commercially: organic lost in raffinate is solvent inventory walking to the pond, while aqueous carried in loaded organic transports chloride into strip and then into the EW tankhouse, where chloride above even ~30 mg/L in electrolyte can affect cathode quality.

Hardware choice interacts with O/A too. Conventional mixer-settlers tolerate a wide O/A envelope and make continuity adjustments straightforward; centrifugal extractors handle high-intensity, small-footprint duties and very short phase ratios but demand tighter control because their residence time leaves less margin for disengagement errors. In both cases, the design O/A, the chosen continuity, and the agitator duty point should be locked together during pilot work, not improvised at commissioning.

Frequently Asked Questions About O/A Ratio Solvent Extraction

Below are the questions process engineers ask most often about O/A ratio solvent extraction design, with quantified answers drawn from the worked example above.

Mixer-Settler Settler Area and Mixer Volume Calculator: selection rules

What is a good O/A ratio for copper extraction?
For copper oxime SX, extraction O/A ratios of 1:1 to 1.5:1 are typical, with many large circuits landing near 1.0–1.1:1 — the worked example resolves to 1.07:1. The “good” value is whichever meets your raffinate target with two or three stages, keeps loaded organic at ~90–95% of isotherm capacity, and minimises organic inventory. Verify with an isotherm test before fixing it.

Why is strip O/A higher than extraction O/A in copper SX?
Strip concentrates copper into a smaller aqueous flow so the electrolyte tenor rises enough to feed EW economically. In the example, strip O/A is 215/150 = 1.4:1, lifting electrolyte from 35 to ~40 g/L Cu. The strip O/A is not free choice — it is dictated by the electrowinning copper balance and the tenor differential your tankhouse can tolerate.

Does a higher O/A ratio always mean better extraction?
No. Recovery gains show diminishing returns: in the sensitivity table, raising O/A from 1.07:1 to 1.35:1 improves recovery only from 91.3% to ~93.0% while organic inventory rises 26%. Meanwhile, very high O/A increases organic losses to entrainment and strip O/A moves away from the EW balance. There is an economic optimum, not a maximum.

How does the O/A ratio affect mixer sizing?
Total flow through a mixer equals organic plus aqueous: at 1.07:1 with 200 m³/h PLS, that is 415 m³/h. At a typical 2.5–3 minute extraction residence time, each mix box needs roughly 415 × 3 ÷ 60 ≈ 21 m³ of working volume (illustrative). A 30% higher O/A inflates mixer volume, agitator power, and settler area proportionally.

Can the O/A ratio cause phase continuity inversion?
Yes. Continuity tends to follow the majority phase: O/A well above 1:1 favours organic-continuous, well below favours aqueous-continuous. Near 1:1 the mix box can flip during flow transients, upsetting droplet size and entrainment. Designers offset the O/A from unity or force continuity with recycle to keep a stable margin.

Does O/A mean volume ratio or mass ratio?
Volumetric, always, in SX practice. Organic at ~0.82 specific gravity and PLS at ~1.05 mean a 1.07:1 volumetric O/A is only about 0.83:1 by mass. Mixing the two bases introduces errors of roughly 25–30%, which is enough to hide a genuine tenor problem — so state the basis on every flowsheet and datasheet.

How should I verify a calculated O/A ratio before detailed design?
Run batch isotherms on your actual PLS to confirm capacity per vol% oxime (expect ~0.4–0.5 g/L Cu per vol%), then continuous miniplant runs to confirm kinetics, stage efficiency, and entrainment at the candidate O/A. Only pilot-scale data validates the 3.4 g/L loading swing and 1.07:1 ratio used in this example for your liquor chemistry.

Conclusion

The O/A ratio solvent extraction calculation is ultimately four divisions strung together with one judgement call: duty divided by loading swing gives organic flow, organic flow divided by PLS flow gives the extraction O/A (1.07:1 in our example), and the same organic flow against the electrolyte balance gives strip O/A (1.4:1) — but the judgement call, choosing a loading swing that respects the isotherm, is where plants are won or lost. Every number here is illustrative; the sequence is not. If you are sizing or debottlenecking a circuit, our pilot testing service can generate the isotherm and miniplant data that turn these formulas into bankable mixer-settler dimensions.

D2EHPA vs Cyanex 272 in practice

References

1. Davenport, W.G.L., King, M.J., Schlesinger, M.E., Biswas, A.K., Extractive Metallurgy of Copper, 5th ed., Elsevier, 2011.
2. Lo, T.C., Baird, M.H.I., Hanson, C. (eds.), Handbook of Solvent Extraction, Wiley, 1983.
3. Kordosky, G.A., “Copper recovery using leach/solvent extraction/electrowinning technology: forty years of innovation, 22.5 million tonnes of copper annually,” JOM, 2002.
4. Rydberg, J., Cox, M., Musikas, C., Choppin, G.R. (eds.), Solvent Extraction Principles and Practice, Marcel Dekker / CRC Press.
5. U.S. Geological Survey, Mineral Commodity Summaries — Copper.
6. Hydrometallurgy (journal) — review literature on copper solvent extraction reagents and circuit design, general.

Changelog

• 2026-10-21 — First published.