Hand-considered hypotheses, 4101–4200
Extractive metallurgy: leaching, solvent extraction, electrowinning, pyrometallurgy, impurity control and process solution chemistry
Written one at a time, not composed. Each entry is given its own logical form, printed above it, and no form is reused in this hundred; the point of printing them is that a reader can check the variety is structural rather than only topical. None has been tested. Any number followed by “(estimate)” is an order-of-magnitude expectation, not a measurement; nothing here is a datum, and no citation is implied.
Leaching chemistry
Misattribution
H4101. Chalcopyrite's slow dissolution in ferric sulfate is almost always charged to the sulfur-rich layer that coats the grain, yet at process temperatures the rate tracks the ferric-to-ferrous ratio in the boundary layer far more closely than it tracks the layer's thickness. If that is right, the layer records the local oxidant demand rather than causing the slowdown. Hold total iron and layer thickness fixed while changing the ferric fraction at constant ionic strength, and the rate should move as much as it does over a comparable temperature interval.
Hidden reservoir
H4102. Acid demand measured in a short bottle-roll test leaves out the protons that clay and iron oxyhydroxide surfaces adsorb and release over weeks, so a heap's true acid consumption is set by a reservoir the test never fills. Washing the residue with several bed volumes between stages releases that stored acid and exposes the short test as a lower bound. If the reservoir is real, its size should scale with the gangue's cation-exchange capacity and not with its carbonate content.
Stepwise threshold
H4103. Recovery against redox potential for a mixed sulfide feed is not the smooth curve usually drawn but a staircase, each step marking the potential at which a particular mineral's surface becomes conductive enough to accept charge from the oxidant. If the steps are mineral-defined they should appear at the same potentials with ferric ion and with dissolved oxygen as oxidants, and their width should scale with grain size. A potential sweep on one polished specimen, with the solution analysed at each hold, separates a mineral property from a cell artefact.
Solubility inversion
H4104. Raising an atmospheric leach above roughly 60 °C (estimate) can lower the net copper rate, because the gaseous oxidant's solubility falls faster than the surface reaction accelerates. The crossover should vanish when ferric ion replaces oxygen as the oxidant, since only the gaseous route loses concentration on heating. Run the same ore in an open vessel and a sealed autoclave at matched temperatures: the open-vessel rate should peak, and the sealed one should keep climbing.
Wetted-area identity
H4105. Leach rates that differ severalfold between a stirred reactor and a column are read as a scale effect, but they may be one intrinsic rate multiplied by the wetted fraction of the surface. Normalise by dye-covered area on sectioned grains and the rates coincide, with the normalised rate independent of agitation. A column run with a surfactant that lowers the contact angle tests this without changing the ore at all.
Moving-boundary bound
H4106. Acid cannot reach a sulfide surface faster than the neutralisation front in the surrounding gangue advances, so the leach rate is bounded by the gangue's acid capacity per unit volume rather than by the mineral's own kinetics. Double the valuable mineral's surface area at constant gangue, and the rate does not move. Leaching a dilute and a rich sample of one gangue at equal acid supply is the direct test.
Couple reversal
H4107. In an ore carrying pyrite and chalcopyrite the galvanic couple can reverse direction when the pulp's potential crosses the two minerals' rest potentials, so the same pair protects chalcopyrite at low potential and accelerates it at high potential. A sign change in the couple current, measured between electrodes of the pure minerals in the same pulp, is the signature to look for. Sweeping the pulp potential while logging that current locates the reversal without any need to model the surface.
State memory
H4108. A washed and dried residue leaches differently from one kept wet, because drying converts metastable iron hydroxy sulfate into a phase that redissolves more slowly, and the difference survives re-slurrying. Drying temperature sets its size, and a residue dried under nitrogen shows none of it. Splitting one residue into wet, air-dried and freeze-dried portions and leaching each identically isolates it.
Wetting artefact
H4109. An induction period before a sulfide starts to leach is read as nucleation of a product layer, but on hydrophobic surfaces it is the time needed for solution to displace air from crevices. If so its length scales with the square of the crevice depth and ignores oxidant concentration, which no nucleation model allows. Vacuum-impregnating one sample and leaching it beside an air-dried twin settles the question in a day.
Tenor ceiling
H4110. No sulfate leach at atmospheric pressure can raise dissolved copper above the solubility of the least soluble copper phase the liquor is saturated with, so a high-tenor campaign must change the iron chemistry rather than add more acid. Temperature and sulfate activity move the ceiling; feed grade does not. A series at fixed acidity and rising total sulfate shows whether tenor follows the phase boundary or the acid dose.
Leaching at process scale
Residence-time distribution
H4111. A heap's recovery is predicted from bottle-roll kinetics scaled by a mean residence time, but the solution in a heap has a distribution wide enough that a small fraction leaves within hours while another fraction stays for months. Recovery is then set by the fraction of flow whose residence time exceeds the kinetic threshold, not by the mean. A tracer test with two tracers of different diffusion coefficients would show whether the spread is hydrodynamic or diffusive.
Channelling
H4112. Most of the solution in an unsaturated heap travels through a small part of the cross-section, and that part is fixed by the competition between gravity and capillarity at the lift height rather than by the ore's average permeability. Raise the lift at constant ore and flow, and the active fraction ought to shrink. Dye tracing on a large column at two lift heights would settle the point.
Scale argument
H4113. Agglomerate size sets the leach time because intraparticle diffusion scales with the agglomerate radius while interparticle flow scales with its permeability, and the two optima point in opposite directions. Their product gives an optimum agglomerate size that moves with the ore's clay content. Leaching agglomerates of three sizes at one flow and one acid strength should show a maximum, not a monotonic trend.
Evaporative concentration
H4114. In an arid heap, evaporation concentrates the applied acid in the upper lifts, so the ore there meets a higher acidity and a higher ferric activity than the irrigation solution carries, and part of the apparent acid consumption is really a water-balance term. Net evaporation sets its size, and covering the surface removes it. Two identical columns, one shaded and one exposed, with water addition matched to hold the same solution inventory, separate them.
Two-length-scale competition
H4115. The leach rate of a porous particle is reagent-limited at the surface and diffusion-limited inside, and the crossover is set by the Thiele modulus, which for a heap agglomerate is large enough that the observed rate barely depends on the intrinsic kinetics. The practical consequence is that a mineralogical change can be invisible until the agglomerates are made smaller. Leaching coarse and fine agglomerates of one ore at a single acid activity shows which regime the plant is in.
Diffusive starvation
H4116. The oxidant concentration at a mineral surface in a heap can fall well below the bulk value by a factor set by the consumption rate over the mass-transfer coefficient, so the ORP of the effluent is not the ORP at the reaction site. At fixed flow, the gap widens with the ore's sulfide content. A voltammetric microelectrode buried at two depths in a column, rather than effluent sampling, measures the gap directly.
Wetting hysteresis
H4117. Solution drains from a heap more slowly than the wetting front advanced, because the contact angle differs between advancing and receding fronts, so the retained inventory depends on irrigation history and not only on the ore's moisture characteristic. Drain-down after a long irrigation differs from drain-down after a short one, and that difference is the hysteresis. Identical columns irrigated for different durations, then drained on the same schedule, isolate it.
Permeability feedback
H4118. Leaching dissolves and reprecipitates material in the pore space, so permeability is a function of reaction extent rather than a fixed ore property, and it can fall as the leach proceeds even while the ore's mass falls. The feedback flattens the flow-versus-time curve in a way compaction alone cannot. Differential pressure across a column, logged against recovery, shows whether the flow decline tracks chemical extent.
Aeration-heat attribution
H4119. A sulfide heap's temperature rise is credited to pyrite oxidation because pyrite is the most abundant sulfide, but the reaction that actually heats the heap is the oxidation of the ferrous iron the leaching generates, which happens wherever the solution is aerated rather than where the pyrite sits. The hot zone then follows the air path, not the sulfide distribution. Temperature and oxygen profiles measured together in a column test which one the heat follows.
Gypsum ceiling
H4120. Once a liquor is saturated in gypsum, more acid does not raise the leach rate, because calcium activity is pinned by the solid and the added acid is spent on exchange rather than on the mineral. The plateau sits at a sulfate concentration independent of the copper grade. Adding calcium-free sulfate at fixed acidity distinguishes a calcium-activity ceiling from an ionic-strength effect.
Solvent extraction: the organic phase
Activity-concentration gap
H4121. Distribution ratios measured in synthetic single-metal solutions are treated as concentration ratios, but at plant ionic strengths the activity coefficients of extractant and complex shift enough that a ratio measured in pure sulfate can misstate a plant liquor by tens of per cent (estimate). The discrepancy tracks ionic strength rather than metal concentration. Measure one organic against a dilution series of plant liquor and of synthetic matrix at matched metal activity, and the two isotherms should separate.
Speciation blind spot
H4122. A circuit can appear to lose selectivity when the feed carries a ligand that complexes the impurity more strongly than the target, because the impurity's free-ion concentration falls and its extraction is suppressed rather than the extractant changing. Dilute at constant pH and the effect vanishes, since the complex dissociates. Extraction isotherms at two total impurity levels but one free-ion level, set by a competing ligand, test it.
Usable loading limit
H4123. Maximum loading of a hydroxyoxime is quoted as a stoichiometric ratio, but in practice the ceiling is set by the loaded organic's viscosity, which rises steeply before the stoichiometric limit and slows disengagement to a crawl. The usable ceiling therefore depends on temperature and diluent, not only on extractant molarity, and loading one organic to successively higher copper levels while timing phase separation at each point locates it.
Aggregation excess
H4124. An aldoxime can carry more copper per molecule than its nominal stoichiometry if the complex aggregates in the organic phase, and the extra capacity should appear as a change in slope of the loading isotherm rather than as a new species. At fixed loading, aggregation changes the organic's viscosity. Loading isotherms at two extractant molarities, normalised by that molarity, collapse only if a single stoichiometric complex forms.
Synergistic excess
H4125. Adding a synergist to a ketoxime raises the extraction coefficient, but beyond roughly one synergist per extractant molecule (estimate) the mixture can also extract acid, and stripping becomes harder rather than easier. Contact with a high-acidity feed leaves more acid in the loaded organic if the excess is real. Titrating the loaded organic for acid across a series of synergist ratios shows whether the benefit reverses.
Selectivity inversion
H4126. Two metals separated by a hydroxyoxime at ambient temperature can reverse their extraction order near 40–50 °C (estimate) if their extraction enthalpies differ in sign, so a circuit designed cool can lose selectivity when the plant runs warm. Isotherms at three temperatures give the inversion temperature without assuming a mechanism. Running one mixer-settler at two temperatures and analysing both phases shows whether the separation factor crosses unity.
Local pH
H4127. The pH that governs extraction is the interfacial one, which can differ from bulk by more than a pH unit (estimate) when proton release outruns diffusion, so a circuit can be selective in a beaker and unselective in a mixer. Mix harder and the difference grows, until interfacial area rather than diffusion limits the flux. Measuring extraction rate and interfacial pH with a microelectrode at two mixing speeds tests the claim.
Complexation switch
H4128. An impurity that an oxime ignores at low chloride can become extractable once chloride is high enough to form a neutral chloro-complex, so the organic's selectivity depends on the circuit's chloride balance rather than on the extractant. A step in the impurity's distribution ratio marks the switch, at a chloride activity set by the complex's formation constant. Isotherms across a chloride series at fixed pH and ionic strength locate the step.
Diluent effect
H4129. Changing diluent from aliphatic to aromatic changes the extractant's activity in the organic phase, so an isotherm measured in fresh kerosene does not transfer to a plant using recycled diluent of different aromatic content. Solubility parameter sets its size, and the isotherm's slope rather than its intercept carries the change. One aqueous feed against three diluents of known aromaticity, at fixed extractant molarity, tests the scaling.
Interfacial film
H4130. Ferric ion adsorbed at the interface can hydrolyse there and form a film invisible in either bulk phase, changing interfacial tension and slowing mass transfer, so an organic's performance decays before any chemical degradation is detectable. A dilute acid wash removes the film, and it re-forms faster at higher ferric loading. Interfacial tension and mass-transfer coefficient followed through a loading cycle, with and without an interstage wash, would expose the film.
Solvent extraction: hydraulics and decay
Emulsion inversion
H4131. A mixer-settler running organic-continuous can invert to aqueous-continuous after a shift in phase ratio or solids content, and the inversion is hysteretic: restoring the ratio does not restore the dispersion. A discontinuity in both the settling curve and the mixer's power draw is what hysteresis looks like. Sweeping phase ratio upward and then downward while logging both maps the loop.
Reservoir effect
H4132. Crud is treated as a nuisance stream to be removed, but it also accumulates extractant and metal and releases them slowly, so a circuit's inventory can drift while its mass balance appears to close. Slow metal release from crud into clean organic is the reservoir at work. Contacting a weighed crud sample with fresh organic over several days, with periodic analysis, measures the release.
Sampling bias
H4133. Aqueous entrainment in stripped organic is measured on a grab sample, but the sample can carry more entrainment than the stream because the sampling point sits where the dispersion is still coalescing. Draw the sample from a quiescent line further downstream and the bias shrinks. Sampling one stream at three distances from the settler, with a coalescing filter inserted in one line, exposes it.
Accounting error
H4134. Stage efficiency in a mixer-settler is computed as the approach to equilibrium in the mix, but much of the apparent shortfall can be entrainment returning aqueous to the wrong stage, which is a flowsheet error rather than a kinetic one. Then the shortfall follows the O/A ratio and not the mixing time. Measuring stage efficiency at two ratios and two mixing times separates the contributions.
Phase-ratio constraint
H4135. A circuit's throughput is often limited not by mixer residence time but by the settler's dispersion band at the required phase ratio, and the band height scales with the flux of the dispersed phase rather than with total flow. Invert the dispersion at the same total flow, and the constraint lifts. Band height against flux, measured for both dispersion types, maps the real limit.
Regime break
H4136. When the extractant is surface-active, initial extraction is set by interfacial area, but once the interface is saturated the rate is set by desorption of the complex, and the two regimes depend differently on mixing power. The log-rate against log-power curve breaks where the regime changes. Initial rates at six mixing speeds, with drop-size-derived interfacial area at each, locate the break.
Autocatalysis
H4137. Oxime hydrolysis produces a ketone and a hydroxylamine, and the products can shift interfacial pH enough to catalyse further hydrolysis, so degradation accelerates with age instead of staying first-order. Degradation plotted against cumulative contact time curves upward if the products catalyse. Accelerated ageing at two temperatures, with instantaneous rate measured at intervals, tests the shape.
Poisoning threshold
H4138. An organic can tolerate a strongly bound impurity up to a point without losing capacity, because the impurity occupies sites off the main extraction path, and capacity falls steeply only beyond that point. A plateau, then a drop, is the shape the capacity-versus-impurity curve takes. Loading a series to different impurity levels and then measuring target capacity maps it.
Steady-state penalty
H4139. Regenerating a loaded organic with stronger acid improves stripping immediately but increases acid co-extraction in the next cycle, so the steady-state benefit can be negative even when every single test looks better. Only after several cycles does the penalty surface. Ten consecutive load-strip cycles at two strip acidities, with net acid transfer measured each cycle, would reveal the penalty.
Recycle enrichment
H4140. In a circuit that recycles strip liquor to extraction, an impurity whose distribution ratio sits just below the extraction threshold can still accumulate to a high steady state, because the recycle multiplies a small extraction. The steady state is slow to arrive and follows the bleed ratio, not the extractant concentration. A staged run with an impurity spike, continued until the concentration plateaus, tests whether it follows the recycle ratio.
Electrowinning: current and cathode
Average-of-a-curve error
H4141. Tankhouse current efficiency is reported as one number, but it is an average over cathodes whose local current densities differ through busbar contact resistance, and efficiency is a concave function of current density, so the average efficiency is lower than the efficiency at the average current density. The gap grows with the spread of contact resistances. Clamp-metering individual cathode currents and comparing the arithmetic mean with the mass-balance efficiency would show the concavity.
Charge-balance closure
H4142. An electrowinning circuit's acid balance is closed by assuming one mole of acid per mole of copper, but oxygen evolution and ferrous oxidation change the balance without depositing metal, so the acid-to-copper ratio is a diagnostic of parasitic current rather than a check on Faraday's law. Add ferrous ion and the ratio rises; passivate an anode and it falls. Acid and copper measured across one cell at two ferrous levels test the relationship.
Inference from thickness
H4143. Current distribution on a cathode is inferred from deposit thickness, but thickness is also shaped by the additive's levelling action, so a thick edge can be a low-additive effect rather than a high-current effect. Change the additive concentration at constant total current and the inference fails. Comparing a thickness map with a segmented-cathode current map at two additive levels shows which explanation holds.
Shunt leakage
H4144. In a tankhouse with cells in series, part of the current bypasses each cell through the electrolyte manifold and the floor, and the loss is invisible because it is distributed. It shows as a difference between rectifier current and the sum of cell currents, growing with cell count and with the conductivity of spillage. Magnetic sensing on each busbar, compared with rectifier output, exposes the difference.
Low-potential passivation
H4145. A lead anode's post-interruption voltage is governed by how long its potential sat in the lead sulfate stability field, where a resistive film grows, and not by the high-potential corrosion the tankhouse usually watches. The film's resistance should scale with interruption time and recover as lead dioxide re-forms, with chloride shortening the recovery by stabilising soluble lead. Interrupting current for controlled intervals and logging the restart voltage at two chloride levels maps the transition.
Autocatalytic growth
H4146. Nodules grow because they sit at locally higher current density, and that higher density is itself caused by the nodule's protrusion into the boundary layer, so growth is autocatalytic and the final size distribution is set by initial roughness. Periodic current reversal, or a particle blocking the nodule tip, should interrupt it, and starting cathodes at controlled roughness while following the size distribution over time tests the feedback.
Co-deposition threshold
H4147. Antimony or bismuth is not co-deposited below a threshold in the electrolyte, but above it the impurity forms a layer that changes cathode morphology, after which deposition becomes self-sustaining. Cathode potential and mass transfer set the threshold; total impurity concentration alone does not. A Hull cell at a grid of impurity concentrations and current densities maps the boundary between smooth and nodular deposits.
Split sink budget
H4148. Glue and other levelling additives are consumed both by incorporation into the deposit and by degradation at the anode, and the two sinks scale differently with current density, so additive concentration cannot be inferred from deposit appearance. Incorporation scales with cathode current while anodic degradation scales with anode current, so their ratio moves when anode area moves. Decay measured in cells with two anode-to-cathode area ratios separates the sinks.
Bubble resistance
H4149. Oxygen bubbles at the anode change local conductivity and mass transfer, and their effect on cell voltage is usually folded into a lumped bubble resistance that is not constant but depends on current density and electrode spacing. Interrupt the current and the resistance falls, recovering with a time constant set by bubble rise velocity. High-speed cell-voltage logging after a current step separates the bubble term from the ohmic one.
Energy optimum
H4150. A cell's energy per tonne passes through a minimum with temperature, because raising temperature lowers voltage while lowering current efficiency through the ferric-ferrous shuttle, so neither the coldest nor the hottest operation is best. Iron concentration and current density move the optimum. A cell run at four temperatures and two iron levels, with both voltage and efficiency measured, maps it.
Solution chemistry and precipitation
Junction-potential bias
H4151. pH measured in a process stream with a glass electrode includes a liquid-junction potential whose size changes with ionic strength, and that change can exceed the pH difference the control loop is trying to hold. Change the reference filling solution and the bias shifts even though the sample's hydrogen activity is fixed. Two reference electrolytes of different ionic mobility, against one sample, expose the junction term.
Ionic-strength effect
H4152. An equilibrium constant measured at low ionic strength does not transfer to the ionic strengths of plant liquors, and the error is a function of composition rather than a constant offset, so the predicted direction of an impurity's response can reverse. A specific-ion interaction model fitted to the major ions makes the correction predictable. A precipitation boundary measured at two ionic strengths at the same free ion separates activity from equilibrium.
Hydrolysis threshold
H4153. Many metals begin to hydrolyse at a pH that shifts with temperature and total concentration, so in a circuit with a temperature gradient precipitation can start in a cool pipe rather than in the reactor designed for it. Read pressure drop or filter load rather than the reactor's pH probe: the step is there. pH and turbidity logged at three points along a cooling line show where precipitation actually begins.
Precipitation window
H4154. A metal may precipitate as a pure hydroxide only over a window of pH, staying dissolved below it and coprecipitating with an impurity above it, so a hydroxide step has an upper limit as well as a lower one. Above the window, impurity content in the solid rises with pH. Precipitating across a pH series and analysing solid and solution for the impurity maps the window.
Supersaturation memory
H4155. The supersaturation at which a salt crystallises depends on solution history, so two batches of identical composition can precipitate at different pH if one has been through a precipitation before. Seed with the same solid and the effect vanishes, the seed's surface area setting the residual supersaturation. Splitting one batch into seeded and unseeded portions at identical composition tests the memory.
Ageing reversal
H4156. An amorphous precipitate that ages into a crystalline one becomes less soluble, but its capacity to scavenge an impurity falls as its surface area drops, so an ageing step that improves the metal balance can release the impurity back into solution. The impurity's concentration falls, then rises, as ageing proceeds. Measuring metal and impurity together through an ageing series gives the crossover.
Competitive adsorption
H4157. When two metals compete for the same sites on a resin, the one with higher affinity can displace the other even at lower concentration, so a column's capacity for the target is set by a trace impurity's affinity rather than by its concentration. The target elutes ahead of the impurity, a chromatographic front that records the displacement. Loading a mixture and analysing the effluent time series tests whether displacement occurs.
Buffer capacity
H4158. A ferric-ferrous solution resists redox change, and the capacity is proportional to the product of the two species' concentrations over their sum, so adding oxidant to a ferrous-rich liquor changes potential far less than expected. ORP control turns sluggish exactly when the leach is most active. Titrating with oxidant while logging ORP at two iron ratios gives the buffer capacity directly.
Boundary crossing
H4159. A leach poised near a redox boundary can cross it when pH moves, so the same solution can dissolve a mineral at one pH and precipitate it at another with no change in oxidant supply. At constant ORP with drifting pH, the metal's concentration reverses direction at the crossing. Holding ORP with an oxidant controller while letting pH drift at a set rate tests whether precipitation is a boundary effect.
Crossover maximum
H4160. At low temperature a leach can be thermodynamically favourable but kinetically frozen, and at high temperature fast but limited by product solubility, so recovery against temperature has a maximum that implies no change of mechanism. Leaching across a temperature series while removing product by ion exchange tests whether the maximum moves with oxidant concentration and disappears when product is removed continuously.
Pyrometallurgy: slag, matte, metal
Mechanical partition term
H4161. The distribution of a minor element between slag and metal is measured in equilibrium experiments and then applied to a furnace, but an industrial slag carries suspended matte droplets, so the apparent coefficient includes a mechanical term. Slag viscosity and settling time set that term; oxygen potential does not. Analysing filtered and unfiltered slag fractions at the same oxygen potential separates the two.
Partition plateau
H4162. The partition coefficient of a valuable metal between slag and matte has a ceiling set by the availability of its dissolved species in the slag, not by matte grade, so raising grade past a point stops improving recovery and starts raising slag losses. Recovery against grade flattens at the ceiling. Slag-matte pairs sampled across a range of grades test whether the curve plateaus.
Activity-coefficient trap
H4163. An equilibrium constant for a slag reaction is often used with concentrations in place of activities, and the error is not constant because activity coefficients change with basicity and with the ferric-ferrous ratio. The error peaks where the slag's composition crosses a phase boundary. Comparing apparent constants at two basicities and one oxygen potential exposes the coefficient's effect.
Concentration-scale illusion
H4164. Replacing weight per cent with mole fraction changes the apparent effect of an additive on slag viscosity, and a model fitted in weight per cent can predict the wrong direction when the additive's molecular weight differs from the slag's average. Heavy-oxide additions carry the largest error. Refitting one viscosity dataset in both scales and comparing predictions at an untested composition tests the sensitivity.
Standard-state shift
H4165. A calculation using pure-substance standard states for a slag component can predict a different reaction direction than one using the component's actual standard state in the slag, especially for minor components whose activity coefficients are far from unity. At one temperature, the predicted equilibrium changes sign between the two conventions. Calculating one reaction both ways and comparing with a measured equilibrium would decide between the conventions.
Boundary-layer control
H4166. Volatilisation of a metal from a melt is modelled as first-order loss, but the rate is controlled by mass transfer through the gas boundary layer, so loss should scale with gas flow and surface area rather than with metal concentration. Once the interfacial reaction is fast the rate becomes concentration-independent. Loss measured at two gas flows and two surface areas, at one concentration, identifies the control regime.
Condensation accounting
H4167. Dust leaving a furnace carries a disproportionate share of volatile elements, usually attributed to entrainment of fines, but much of it can be vapour condensing onto dust surfaces downstream. Cool the gas against a clean surface instead, and the condensed fraction comes off there. Sampling at two points in the off-gas train with a cooled probe between them separates entrainment from condensation.
Coupled operating window
H4168. Matte grade and slag magnetite are treated as independent operating variables, but they are coupled through oxygen potential and silica activity, so raising grade raises magnetite unless silica is raised too. In the grade-magnetite plane the coupling draws a boundary that cannot be crossed without a phase change. Operating at two silica levels and mapping the accessible region tests it.
Wear feedback
H4169. Refractory wear is attributed to chemical attack, but wear changes the furnace's heat balance, which changes slag temperature and viscosity, which changes the wear rate, so the process contains a feedback loop that can accelerate wear. Wear rate then correlates with thermal history, not only with slag composition. Wear and heat balance logged together over a campaign test whether the loop is real.
Runaway gain
H4170. An exothermic smelting reaction can run away when feed reactivity rises, because heat release raises temperature, which raises rate, and the control loop's response is slower than the thermal time constant. A rise in off-gas temperature, unexplained by feed rate, precedes the runaway. A step change in the feed's sulfide content at fixed oxygen supply measures the loop gain.
Furnaces, beds and heat
Closure-term audit
H4171. A roasting furnace's heat balance is closed by adjusting an unmeasured loss, and that adjustment can absorb a real chemical effect such as oxidation of sulfide the assay missed. The closure term is largest exactly where the feed's sulfur analysis is least certain. Comparing the closure term with assay uncertainty across campaigns shows whether it is a loss or a residual.
Hot-spot migration
H4172. In a packed bed of sulfide concentrate the reaction zone can localise because product formation changes the bed's permeability, so gas bypasses the hot zone and reaction migrates elsewhere. The hot spot should move when gas flow is reversed, tracking the gas rather than the solids, and temperature mapping in a bed run in two directions tests which it follows.
Self-reinforcing channelling
H4173. Gas flowing through a pellet bed follows the largest voids, and the resulting local reaction shrinks pellets and opens those paths further, so channelling is self-reinforcing rather than a fixed property of the bed. The spread of local conversion widens with time instead of staying constant. Post-mortem sectioning of a partially roasted bed, compared with pressure-drop history, would show whether the spread widened.
Cooling segregation
H4174. Slow cooling of a matte or slag segregates a minor element into the last liquid, so its concentration in the product depends on cooling rate even when the equilibrium partition is fixed. Across a sectioned ingot the gradient scales with the square root of cooling time. Sectioning slowly cooled and quenched ingots and analysing across the section would expose the segregation.
Stratification
H4175. A molten slag can stratify into two layers of different composition when silica activity crosses a boundary, and the stratification is invisible in a single sample taken from the top. The layers differ in viscosity, so tapping behaviour changes before the analysis does. Sampling at two heights during tapping and measuring viscosity at each would show two layers if they exist.
Quench artefact
H4176. The oxygen potential of a slag is read from the ferric-ferrous ratio of a cooled sample, but that ratio keeps changing during cooling, so the analysed value records the cooling path rather than the furnace. The artefact grows with sample size and vanishes on a quenched thin film. Splitting one slag stream into a thick slow-cooled button and a splashed thin film and analysing both would measure the artefact.
Le Chatelier reversal
H4177. A flux is expected to lower a slag's liquidus, but if it raises the activity of a component already at its solubility limit, the addition can raise the liquidus instead. The reversal sits at the flux composition where a new phase becomes saturated. Liquidus measured across a flux series, with the phase assemblage identified at each point, locates the reversal.
Non-monotonic optimum
H4178. The rate of a solid-state roasting reaction can peak with temperature because the reactant's surface area sinters before the intrinsic rate rises enough to compensate, so the optimum temperature depends on the particle's thermal history rather than on activation energy alone. A pre-calcined feed shifts the optimum downward. Roasting a series at several temperatures with two pre-treatments tests the shift.
Dead-zone periodicity
H4179. A continuous furnace's dead zone can accumulate a low-melting phase and release it later as a surge, so product composition can show periodic excursions that no feed variation explains. Dead-zone volume over throughput sets the period, and emptying the furnace ends it. Running at two throughputs and comparing excursion periods tests the dead-zone explanation.
Autothermal threshold
H4180. A sulfide roaster or smelter becomes autothermal only above a feed sulfur content set by heat losses and off-gas volume rather than by reaction enthalpy alone. Recycling off-gas lowers the threshold by cutting the heat that leaves in the gas. Two campaigns with and without recycle test the threshold's dependence.
Impurity control and bleed
Closed-loop accumulation
H4181. Where a circuit recycles strip liquor or spent electrolyte, an impurity that is only partly rejected accumulates until rejection equals input, and the steady-state concentration is set by the bleed ratio rather than by the feed concentration. Accumulation is slow, showing up as gradual drift in cathode quality rather than as a step. Spiking the feed with a tracer impurity and following it over many residence times tests the steady state.
Bleed optimum
H4182. Raising the bleed lowers impurity concentrations but also lowers valuable-metal recovery, so there is an optimum bleed set by the impurity's rejection mechanism and by the metal's value. A dedicated rejection step moves the optimum away from the bleed-only value. Comparing net circuit value at three bleed rates with constant impurity input tests the optimum.
Split-ratio invariance
H4183. An impurity's concentration in a recycled stream can be independent of how the recycle is split between two unit operations, because the split changes its residence time and its rejection in compensating ways. Push one operation to saturation and the invariance breaks. Testing the circuit at two splits, with one operation near its limit each time, separates the regimes.
Masking
H4184. An impurity can sit above its specification without causing a defect because another impurity masks it, so tightening one limit without regard to the other can make the product worse. In the two-impurity plane the boundary is diagonal, not two independent limits. Depositing cathodes across a grid of the two concentrations tests whether the boundary is diagonal.
Interference
H4185. A method used to control an impurity can read high because a second element interferes, and the resulting over-addition of reagent can do more damage than the impurity itself. Hold the first element fixed, change the second, and watch the bias move. A set of spiked samples analysed with and without a separation step measures the bias.
Common-mode cancellation
H4186. Two measurements sharing a sample line and a reference electrode share a common drift, so their difference cancels it, and a stable but badly calibrated pair can control a process better than a calibrated but drifting one. The cancellation fails when the error is not common, for instance when one measurement includes a filtration step. Two instrument pairs, one sharing a line and one not, compared as controllers, are the comparison to run.
Polarisation scaling
H4187. In a membrane used to recover acid, the scaling that limits flux can form because concentration polarisation raises local supersaturation at the surface while the bulk remains undersaturated. Scaling begins well below bulk saturation and shifts with cross-flow velocity. Flux measured at two velocities and two bulk concentrations locates the polarisation effect.
Steric fouling
H4188. An ion-exchange resin loses capacity because a foulant blocks pore mouths rather than because it occupies functional sites, so a solvent wash that removes no metal can still restore capacity. The capacity loss should be larger for the target than for a smaller ion of the same charge, and comparing the uptake of two ions of different hydrated radius on a fouled resin tests whether the block is steric.
Two-name identity
H4189. Organic and biological fouling of a resin or membrane may be one deposit seen at two scales, since both are polysaccharide-rich films forming at the same hydrodynamic conditions. If they are one phenomenon, a shear step moves both identically. A laboratory biofilm and a plant foulant compared under the same shear and cleaning sequence test the identity.
Partition-loss maximum
H4190. An extractant can be lost to the aqueous phase not by solubility but by partitioning into a third phase at the interface, so the loss peaks where that phase is most stable rather than where temperature is highest. Reagent consumption peaks at a particular phase ratio. Measuring extractant in the aqueous phase across a phase-ratio series tests the maximum.
Control, analysis and closure
Aliasing
H4191. A process controlled by a titrator that samples every half hour can look stable while the underlying concentration oscillates near twice the sampling interval, because the controller sees only an aliased slow wave. Halve the interval and the oscillation disappears; double it and a different apparent period appears. High-frequency logging alongside normal control tests the aliasing.
Delay-limited stability
H4192. An acid-addition loop can go unstable not because its gain is too high but because the pH electrode's response carries a delay the tuning does not include, so stability depends on electrode age. A new electrode brings instability that the old one, at the same tuning, does not. Swapping electrodes without touching the controller tests the delay's role.
Effective dead time
H4193. A control loop's dead time is estimated from a step test, but in a circuit with recycle the effective dead time is longer than the physical transport time because the recycle returns a delayed disturbance. Effective dead time scales with recycle ratio. Step responses measured at two recycle ratios test the scaling.
Setpoint cycling
H4194. A pH controller can hold its setpoint while the actual pH cycles between two values, because reagent addition causes a local precipitation that redissolves only at a lower pH. Its period is set by precipitation kinetics, and diluting the reagent ends it; high-frequency pH logging during constant setpoint control is the test.
Path dependence
H4195. A leach's final composition can depend on the order reagents are added even at the same final pH and ORP, because the intermediate phases that form are not reversible. At identical final solution composition the residue mineralogy differs. Two leaches with acid and oxidant added in opposite orders, taken to the same endpoint, would reveal the path.
Slope error
H4196. A calibration built on synthetic standards can fail on plant liquor because the matrix changes the calibration's slope, not its intercept, so a single-point check passes while high readings drift. The bias depends on concentration and is zero at the check point. A dilution series of plant liquor against a synthetic calibration, at matched analyte activity, exposes the slope error.
Unsampled stream
H4197. A circuit's mass balance is closed by adjusting the feed assay, and the adjustment can hide a real loss to a stream that is never sampled, such as dust or crud. The closure error tracks that stream's flow, not the feed's grade. Comparing closure errors across campaigns with different dust flows tests the hidden stream.
Surface-to-volume scaling
H4198. An impurity's transfer rate is estimated from a laboratory rate constant and a plant residence time, but the product can be wrong by an order of magnitude (estimate) because the laboratory rate was measured at a much higher surface-to-volume ratio. The discrepancy scales with the ratio of the two surface-to-volume ratios. Running one reaction at two such ratios tests the scaling.
Composite averaging
H4199. Impurity control can be adequate on average and inadequate during the excursions that matter, because sampling frequency is matched to the mean rather than to the variance, so a plant can pass every composite and still make off-spec product. Only high-frequency samples show the excursions. Comparing composite and high-frequency analyses over the same period tests whether composites hide them.
One-stage impossibility
H4200. No single precipitation step can separate two metals whose hydroxide solubility products differ by less than the ratio of their concentrations, so a flowsheet claiming one-step removal of a minor impurity from a major metal at a high ratio depends on coprecipitation that will fail at scale. The impurity fraction in the solid then comes out independent of pH. Precipitating across a pH series at high major-to-minor ratio tests whether one step suffices.
Status
100 entries, 100 distinct forms. The forms fall into loose families rather than a grid: attribution and identity 15; bound and ceiling 10; inversion and reversal 7; threshold and onset 10; artefact and measurement 21; scale, transport and coupling 13; accumulation and feedback 10; control and optimisation 8; memory and path dependence 5; impossibility 1. The distribution was not fixed in advance and is uneven by design.
These are hypotheses about process-scale extractive metallurgy, written to be checkable with plant or pilot equipment rather than to be complete. None has been tested; the value of a list like this is the experiment it suggests, and that value is separate from whether the suggestion survives.
Incoprea Research · hand-considered hypotheses 4101–4200 · 3 November 2026 · ~/Desktop/Nov3/