Hand-considered hypotheses, 2701–2800

Chemical reactors and process safety; written one at a time. Each entry carries a different logical form — misattributed cause, hidden term, identity, bound, threshold, reversal, count, artefact that mimics an effect, scale argument, inverted practice, selection effect, unit trap, derived quantity, and forms of their own — and the form is printed with the entry so that structural repetition is visible rather than hidden. None has been tested. Every number that appears is a statement about an estimate, not a datum from a source; no citation is offered because none was consulted.

Mixing and feed dispersion

Misattribution
H2701. The blend time of a stirred tank is read from the disappearance of colour, but in liquids above roughly 100 mPa·s the last colourless patch vanishes by molecular diffusion through striations rather than by bulk circulation, so the number returned is a diffusion time wearing a mixing time's name (the 100 mPa·s figure is an estimate, not a measurement). Two indicators of different molecular diffusivity, at identical impeller speed and viscosity, separate the two: if the measured times differ by the ratio of diffusivities, bulk blending was already finished.
Count
H2702. Feed-point splits exhaust their usefulness quickly: a reactor with N feed points has at most N−1 independent split ratios that can change selectivity, because total feed is fixed by throughput and the splits must sum to one; an optimisation reporting N independent feed parameters is trading them against each other. Perturbing all N splits in one designed experiment and taking the singular values of the response matrix gives the rank directly.
Artefact mimicking effect
H2703. Selectivity that looks micromixing-limited in a pilot reactor is often the analytical quench finishing the reaction after the sample leaves, not the reactor finishing it. The same reactor run with two quench chemistries at equal conversion gives different selectivities if the quench is the cause, and an in-line stopped-flow quench compared with a grab sample settles it.
Null claim
H2704. At matched local energy dissipation and matched feed position, impeller type has no measurable effect on the selectivity of a fast second-order reaction; the differences reported between impellers are differences in where the feed lands relative to the blades. Two geometrically different impellers run at equal dissipation with the feed at the same dimensionless radius should return a null, and if they do not, the matched quantity was not the one that matters.
Threshold
H2705. Below a critical ratio of feed-jet momentum to bulk circulation momentum the plume does not reach the impeller and is consumed where it enters; above it the plume is captured and the local excess collapses. A ladder of feed rates at constant vessel flow, with a conductivity probe at the impeller, should show a step rather than a slope.
Inversion of standard practice
H2706. Slow addition is assumed to lower the local concentration of the limiting reagent, but below a certain rate the plume becomes lazy: it is no longer entrained by the bulk circulation and sits as a stratified layer, so local excess rises again as dosing slows. Three dosing rates spanning two decades, with local sampling near the feed point, should show a minimum rather than a monotone fall.
Reversal
H2707. Beyond the rate at which the impeller is flooded by gas, faster stirring can lower the gas-liquid mass transfer coefficient, because the cavities behind the blades coalesce into slugs that bypass the bulk instead of dispersing into small bubbles. A power ladder at fixed gas rate, with void-fraction probes at two heights, locates the maximum and shows whether it moves with the sparger's open area.
Hidden term
H2708. Every blend-time measurement contains the tracer's own injection time, and for a dip-tube injector that term is not negligible when agitation is high. Injecting the same volume through three nozzle diameters at constant impeller speed gives the injector's contribution as the intercept of measured time against nozzle size.
Threshold
H2709. Floating solids are drawn under only above an impeller speed set by the surface renewal at the vortex, and the transition is sharp because a particle that is wetted once tends to stay wetted. A speed ladder with a settling-trap count at the surface, run at two particle contact angles, should put the threshold where the wetting time equals the vortex residence time.
Selection effect
H2710. Published blend times are selected by method: only runs in which the endpoint was visible get reported, and invisible endpoints are recorded as limits and later dropped from correlations. Recovering the censored runs, or repeating one geometry with a quantitative endpoint, should shift the fitted exponent rather than the constant.
Unit trap
H2711. Tracer concentrations quoted in parts per million by mass and by volume differ by the tracer solution's density, which for concentrated salt solutions is several percent, so a correlation fitted across laboratories can carry a systematic offset that looks like a geometry effect. Recomputing every point as mole fraction from the stated recipe is the check, and it must use the injected solution's density, not the vessel contents'.
Identity
H2712. At a single operating point the mesomixing limit and the micromixing limit produce the same selectivity against feed rate, so a fitted micromixing time is an identity of the model chosen rather than of the chemistry. Changing the feed pipe diameter at constant feed rate moves mesomixing without moving micromixing, and the two must then separate.
Bound
H2713. Bounded by the local stoichiometric ratio at the plume, the selectivity gain available from redistributing feed does not grow with the number of feed points: once the plume's local ratio sits at the optimum for the wanted product, adding points buys nothing. A feed-split ladder taken past the point of no improvement, with local composition measured at the plume, shows the ceiling.
Scale argument
H2714. The excess temperature and concentration in a feed plume scale with the plume's surface-to-volume ratio, so a geometrically similar scale-up at constant power density lengthens the plume faster than it widens it, and the large unit's plume is thin relative to its own circulation. Two sizes with matched power density and matched feed velocity ratio, probed along the plume axis, test whether the excess is conserved.
Degeneracy
H2715. Fitting the same outlet selectivity across a fourfold range of feed rate, a two-zone and a three-zone mixing model both succeed, because the third zone's volume can be absorbed into the second zone's exchange rate. Varying the feed position, which the two models weight differently, breaks the degeneracy only if the third zone is real.
Memory claim
H2716. A loop reactor's outlet tail does not remember the loop's length after a few circulations, since each pass multiplies the variance by the same factor; the late-time slope is set by the loop's internal mixing, not by its residence time. Two loops of different length but matched mixing intensity, tracer injected at the pump suction, should give the same late slope.
Conservation argument
H2717. Ninety-five percent tracer recovery is the threshold below which a dead-volume claim is unsupported, because missing tracer and a dead zone are indistinguishable in the balance. Weighing the recovered tracer, rather than integrating the tail, turns the ambiguity into a number.
Identity
H2718. Blend times quoted at 95 percent and at 99 percent of homogeneity differ by a fixed factor only when the decay is exponential, and in vessels with a persistent dead zone the ratio between them drifts with impeller speed. Reporting both endpoints for one vessel at three speeds shows whether the ratio is constant, and a ratio that moves is evidence of a slow zone rather than of slower mixing.

Heat removal

Bound
H2719. Whatever surface is installed, heat removal per unit volume of a stirred reactor is capped by the coolant's permitted temperature rise times its flow, divided by the vessel volume; beyond that cap, extra area only lowers the wall temperature. Running at constant coolant flow while doubling the area should show no duty gain once the coolant leaves at the cap, and it is the outlet temperature, not the duty, that reveals it.
Hidden term
H2720. Averaged over a strongly non-uniform field, a jacket-side coefficient derived from an overall balance hides the region opposite the inlet nozzle, which sees a local velocity several times the jacket mean. Local flux gauges at four angular positions on one jacket expose a spread that does not shrink when the vessel is mixed harder, because the non-uniformity lives in the jacket.
Reversal
H2721. Lowering the jacket temperature does not always lower the hottest metal temperature: when the process side can crystallize or freeze at the wall, the layer that grows adds resistance faster than the extra driving force it buys, and the peak moves up. A jacket-temperature sweep with simultaneous wall-layer thickness measurement locates the turning point, which should move with the process-side water content.
Conservation argument
H2722. The energy balance of a reactor fed with concentrated reagent does not close unless the heat of dilution is carried, and for strong acids and bases that term can be a large fraction of the reaction enthalpy, absorbed silently into a fitted coefficient. Repeating the run with pre-diluted feed, or with a non-reacting surrogate of matched heat capacity, isolates the term.
Threshold
H2723. Film boiling begins at a wall superheat that falls as the local liquid velocity rises, because the departing bubble is swept away before it can coalesce into a vapour blanket, so the threshold is a property of the flow rather than of the surface alone. A heated section at constant flux, with velocity raised in steps and wall temperature logged, should show where the slope of the boiling curve changes.
Count
H2724. Two fouling resistances are all that duty data can identify separately on a two-stream exchanger, because only their sum enters the overall coefficient; cleaning one side is required to break the degeneracy. A table listing four resistances for a single exchanger is listing assumptions, and the test is to clean one side and watch which numbers move.
Unit trap
H2725. Older plant balances mix kilocalories and kilojoules, and the 4.184 factor is close enough to the scatter of a poorly instrumented exchanger that the error survives review; it appears as a coefficient roughly four times too large. Recomputing one exchanger's duty in both unit systems, from raw flows and temperatures, flags it without a new experiment.
Identity
H2726. In plant records fouling resistance and percentage of design coefficient lost are the same number only while the clean-side film dominates; once the tube-side film becomes the smaller of the two, the records diverge by the ratio of the films. Re-measuring the same exchanger at two flow rates without cleaning shows which regime the record sits in.
Scale argument
H2727. Area per unit volume shrinks as a vessel grows, because area rises with the square of length while volume rises with its cube; a tenfold increase in diameter therefore leaves roughly a tenth of the original area per unit volume (an estimate from geometry alone, not a measurement), and the same coolant rise demands a disproportionately larger external exchanger. Two sizes run at matched conversion and matched wall temperature, rather than matched jacket temperature, make the comparison honest.
Selection effect
H2728. Fouling data are selected by survival: exchangers that fouled catastrophically were redesigned or replaced and never entered the long-run record, so the surviving population is the tolerant one. Comparing a site that kept its failures in the record with one that removed them, for the same duty and the same water, should shift the apparent distribution without changing the water.
Derived quantity
H2729. Derived from two films, a wall and two fouling layers, an overall heat-transfer coefficient is nonetheless reported and used as if it were a material property; a change in it cannot be attributed without an independent measurement of one film. Varying the shell-side flow alone at fixed duty, and watching which of the two films moves, is the cheapest attribution test.
No-go claim
H2730. No pair of jacket inlet and outlet temperatures can give the wall temperature without the film split, because any two films summing to the same overall resistance fit the same data. A thermocouple embedded in the wall, or a heat-flux gauge, is required; without one, the wall temperature in a report is a model output.
Hysteresis claim
H2731. On a fouled surface the boiling curve follows different paths when flux is raised and when it is lowered, and the loop's width measures how much of the surface stays wetted at the lower flux. Stepping the flux up and down in one sequence, logging wall temperature at each step, gives the loop, and a clean surface should give a narrower one.
Artefact mimicking effect
H2732. A thermocouple whose sheath conducts along its length reads a temperature between the fluid and the wall, and the error grows with immersion, so a film resistance inferred from it can be the probe's own conductance. Two probes of different sheath diameter at one location, or one probe at two immersions, separate them.
Covariance argument
H2733. The correlation between a reactor's heat-transfer coefficient and its production rate is partly manufactured, since both follow the feed rate the operator chose, and the regression is fitting the schedule. Running the same duty at two feed rates by changing the coolant, and holding conversion, decouples them.
Inversion of standard practice
H2734. Sizing a jacket around the worst credible coefficient is the conventional move, but in reactors whose hot spot sits at the feed plume the peak temperature is set by how fast the feed disperses, and a jacket sized for the worst case leaves the plume untouched. The same jacket run at two feed dispersion qualities, at equal duty, shows which of the two governs the peak.
Threshold
H2735. Particulate fouling on a coolant side stops accumulating above a wall shear at which deposition and removal rates cross, and that threshold is largely independent of particle concentration above a few parts per million. A velocity ladder at fixed concentration, weighing the deposit rather than measuring duty, gives the crossing; duty alone confuses the threshold with the induction period.
Bound
H2736. Whatever the process side asks for, a jacket's removable flux is bounded by the coolant's nucleate boiling limit at the jacket's own pressure, and that bound falls sharply as the jacket runs nearer its boiling point. Raising process temperature while holding jacket pressure should show a duty ceiling that moves with jacket pressure, not with process temperature.

Residence-time distribution and flow

No-go claim
H2737. One tracer at one outlet cannot separate a bypass from a dead zone of the same volume, since both remove the same first moment; the two are indistinguishable in any single response. A second injection point, or a tracer excluded from the dead zone by its size, is needed before either can be asserted.
Unit trap
H2738. Space time quoted per unit catalyst mass and per unit reactor volume differ by the bed's bulk density, which varies by a factor of two or three between fills of the same nominal catalyst, so cross-paper comparisons can be out by that factor. Recomputing both from the reported bed mass is the test, and the disagreement usually vanishes once it is done.
Misattribution
H2739. An axial dispersion coefficient fitted from a single probe contains the probe's own response time, and for a fast tracer that term can dominate the fit at high flow. Two probes of different response time at the same axial position give the probe's contribution as the difference between the fits.
Count
H2740. Only the first two moments of an outlet curve are reliably identifiable when the record is truncated at three residence times, because the second moment is dominated by the tail that was cut off. Extending the record by a decade of time should change the fitted second moment more than the fitted first, and if it does not, the tail was noise.
Threshold
H2741. The apparent slope of an outlet curve's tail is set by the detector's limit of detection once concentration falls below it, and that slope is systematically shallower than the true one because the last points are noise around zero. Spiking the outlet with a known low concentration during the tail, or switching to a more sensitive detector mid-run, tests whether the fitted tail is real.
Reversal
H2742. Adding recycle narrows the outlet's concentration distribution while broadening the distribution of times spent at temperature, because a molecule that recycles passes the hot zone repeatedly. Two reactors with equal outlet variance but different recycle ratios, using a temperature-history tracer, show the divergence, which matters whenever conversion depends on exposure rather than on outlet concentration.
Hidden term
H2743. Every measured mean residence time includes the inlet manifold and distributor, and in small pilot units that volume can reach a tenth of the vessel, appearing as a systematic excess over volume divided by flow. Filling the manifold with a known displacement body, or tracer-testing it separately at its own inlet, removes the term.
Scale argument
H2744. The width of an outlet distribution from a tubular unit is set by the number of effective mixing cells, which for a fixed length-to-diameter ratio does not change with scale; the absolute spread therefore grows with the square root of the cell count while the relative spread falls. Two geometrically similar units, tracer-tested at the same residence time, should share a normalised variance if cell count is the invariant.
Identity
H2745. Indistinguishable in their first two moments, a two-tank-in-series model and a dispersion model with matched variance cannot be chosen between by fitting one outlet curve. Discrimination needs the third moment, or the response to a step, where the two differ in shape.
Selection effect
H2746. Published residence-time distributions come disproportionately from columns and vessels that behaved well, because a distribution with a large unexplained tail is usually written up as an apparatus fault rather than as a result. Comparing a laboratory's full archive with its published subset, for one packing, shows how much tail the selection removed.
Derived quantity
H2747. Measured to a few percent each, a volume and a flow give a space time that, in a vessel with a headspace, takes the nominal capacity rather than the liquid actually present, so the bias is systematic and one-signed. Weighing the liquid inventory, or integrating inlet flow over a batch, converts it into a known correction.
Null claim
H2748. Above four baffles of standard width, adding more has no measurable effect on the outlet distribution of a single-phase tank, because the mean flow is already axisymmetric. Two tanks with four and eight baffles, tracer-tested at the same impeller speed, should return the same normalised variance, and a difference would point to a wall effect rather than to baffling.
Bound
H2749. The variance of an outlet distribution cannot fall below a floor set by the outlet's own geometry: a side nozzle draws from a region whose residence times differ by the nozzle diameter divided by the through-flow velocity. Moving the outlet from centre to wall at the same flow should change the floor without changing bulk mixing.
Artefact mimicking effect
H2750. A conductivity probe's finite response time adds an exponential tail to every measured curve, and at high flow that tail can outlast the vessel's own. A probe of twice the response time at the same location doubles the artefact and leaves the vessel unchanged, which is the test.
Conservation argument
H2751. Fixed by volume and flow, the mean residence time is not a free parameter, so a fitted flow model that reproduces the curve but violates the mean is wrong regardless of fit quality. Constraining the fit to the measured mean and refitting shows how much of the apparent structure was absorbing the mismatch.
Hysteresis claim
H2752. In a trayed column with a downcomer, the froth-to-emulsion transition sits at different liquid rates depending on whether the liquid rate is being raised or lowered, and the gap between the two branches is a measure of the downcomer's inventory rather than of the tray's capacity. Stepping the liquid rate through the transition slowly at fixed gas rate gives the gap, and stepping faster should narrow it if inventory is the cause.

Scale-up

Inversion of standard practice
H2753. Constant power per unit volume is the standard scale-up rule, but for reactions whose selectivity is decided before the feed plume disperses the invariant that matters is the ratio of circulation time to plume dispersion time, which constant power density does not hold. A two-scale pair with equal power density but different circulation times, at fixed chemistry, tests whether the rule or the ratio predicts the selectivity.
Scale argument
H2754. Heat removal per unit volume falls with the inverse of linear size, so a large vessel's jacket is a smaller fraction of its heat-generation capacity than a small one's, and the shortfall shows up as a higher operating temperature rather than as a failure. Two geometrically similar vessels at matched power per volume but different sizes, run under the same feed, diverge in the slope of temperature against conversion.
Threshold
H2755. Buoyant motion inside the jacket, rather than forced motion, sets the wall temperature distribution once jacket flow falls below the crossover where buoyant and forced velocities are equal (an estimate, since neither is measured directly in plant). A jacket-flow ladder at constant duty, with wall thermocouples at top and bottom, shows the distribution becoming uniform.
Inversion of standard practice
H2756. Fit kinetics first and correct for mixing afterwards is the standard order, but when the pilot's fitted constant already carries a transport step the correction must be subtracted rather than added, and the usual procedure doubles the error. Running the pilot at three impeller speeds with everything else fixed reveals whether the fitted constant carries transport, before any correction is applied.
Bound
H2757. Impeller tip speed has an upper bound set by the onset of gas cavities that change the power draw, and past it added power no longer improves dispersion; the bound moves with gas rate, so a single number quoted for an impeller belongs to one gas rate. A tip-speed ladder at three gas rates, with power measured by torque rather than by motor current, shows the family of bounds.
Identity
H2758. Two vessels are called geometrically similar when every length ratio matches, yet the quantities that govern selectivity and heat removal are ratios of times, which geometric similarity does not preserve; the term is an identity of shape mistaken for an identity of behaviour. Two vessels with matched length ratios but different sizes, run at the same feed rate per unit volume, show whether shape alone carried the behaviour.
Count
H2759. Velocity ratio, time ratio and temperature-rise ratio cannot all be held across a scale change, because holding the first two fixes the third through the heat balance, so at most two of the three can be matched. A scale-up claiming all three was matched is either not reporting the third or has changed the chemistry along with the geometry.
Selection effect
H2760. Scale-up rules are validated on reactions that survived scale-up, and a rule that failed is rarely published as a failure, so the surviving set is biased toward chemistry that was not mixing-sensitive. Applying a published rule to a deliberately fast reaction and reporting the miss is the only way to see the bias.
Covariance argument
H2761. Gassed power draw and gas holdup co-vary with gas rate, so a regression of mass transfer against power draw alone credits power with what belongs to holdup. Holding holdup fixed by pre-dispersing the gas, or measuring both independently, separates the two coefficients.
Unit trap
H2762. Specific power quoted per cubic metre of ungassed liquid and per cubic metre of gassed dispersion differ by the holdup, which can be a third of the volume at high gas rate, so two vendors' numbers can differ by that factor with no disagreement about the machine. Recomputing both on one basis, from the reported holdup, is the check.
Reversal
H2763. The laboratory reactor is assumed to be the better-mixed one, but at matched power per unit volume its circulation time is shorter while its feed plume is also shorter-lived, so the local excess at the feed can be higher in the small unit. Local probes at the feed point in both sizes, at matched power density, test whether the small unit is worse at the only place that matters.
No-go claim
H2764. No single small-scale experiment can reproduce both the plume's local excess and the bulk's circulation pattern, because the two are governed by ratios that scale differently, and a pilot can match one or the other. Running the pilot twice, once matching plume velocity and once matching circulation time, and comparing the two selectivities, shows which ratio the chemistry reads.

Fouling

Threshold
H2765. Soft deposits stop consolidating below a wall shear set by the deposit's yield stress, and above it consolidation proceeds at a rate nearly independent of shear. Bracketing the threshold by running one foulant at three velocities and measuring the deposit's shear strength, rather than its mass, avoids confusing the threshold with the induction period.
Selection effect
H2766. Compiled fouling factors come from exchangers that were cleaned, and cleaning is scheduled when duty becomes intolerable, so the record's tail is truncated by maintenance policy rather than by physical law. Two sites with different cleaning thresholds, same duty and same water, should show different apparent distributions over the same underlying deposit.
Covariance argument
H2767. Fouling rate and fluid velocity correlate partly because both are set by the pump curve and the valve position the operator chose, not because one causes the other. Throttling to one flow from two pump speeds, or running one loop with a control valve and another with a variable-speed drive, decouples them.
Misattribution
H2768. Rising pressure drop across a fixed bed is often booked to coking, but in beds containing fines the first rise comes from rearrangement, with fines migrating into the void space at constant coke level. A bed pre-compacted to its settled voidage, run beside an untreated bed under the same feed, separates rearrangement from deposition.
Hidden term
H2769. Every fouling resistance calculated from an overall coefficient contains the wall's own conduction resistance, and the thickness used is the nominal one rather than the measured one after years of corrosion or relining. Ultrasonic thickness at the same spots where the thermocouples sit turns the hidden term into a known one.
Hysteresis claim
H2770. A deposit's removal threshold is higher than its formation threshold, so a surface that has fouled will not clean itself at the velocity that kept it clean when new; the gap between the two thresholds is the ageing of the deposit. A clean and a pre-fouled section run side by side at one velocity show the gap directly.
Bound
H2771. Fouling resistance approaches an asymptote set by the balance of deposition and removal, not by the deposit's ultimate thickness, so a curve that looks asymptotic may still be rising below the instrument's resolution. Following one exchanger for three times its apparent asymptote, with a direct deposit measurement at the end, distinguishes a true asymptote from a slow rise.
Scale argument
H2772. Resistance per unit mass of a deposit depends on its porosity, and porosity depends on how fast the layer formed, so a laboratory deposit grown quickly is more insulating per gram than a plant deposit grown slowly. Deposits formed at two rates on one surface, with porosity inferred from weight and thickness together, show whether resistance tracks mass or structure.
Reversal
H2773. Polishing a surface can accelerate fouling early on, because a rough surface retains a stagnant sublayer that keeps particles from adhering while a smooth one brings them into contact; the reversal is temporary and fades once a monolayer forms. Two sections, one polished and one grit-blasted, weighed at intervals over the first hundred hours, show whether the early advantage reverses.
Count
H2774. At most two fouling mechanisms can be identified from one duty-against-time curve, because particulate, crystallization and reaction fouling all produce curves differing only in curvature of the same order. Varying wall temperature independently of bulk velocity supplies a second axis, and the mechanisms separate along it.
Identity
H2775. In maintenance records the induction period and the cleaning interval are often the same number, because the exchanger is cleaned when duty falls rather than when deposit begins, so the record reports policy and not chemistry. A site that cleans on a fixed calendar, regardless of duty, gives the true induction period by contrast.
Derived quantity
H2776. Subtracting a clean coefficient that was itself measured once, often on another day and at another flow, is how a fouling factor is derived, so the fouling number inherits the clean measurement's error entirely. Re-measuring the clean coefficient immediately before and after a fouling run bounds the inherited error.
Null claim
H2777. Coated surfaces foul as fast as bare ones in the long run: a coating meant to resist fouling has no effect on asymptotic resistance once a deposit thicker than the coating's roughness has formed, because the deposit then fouls itself. Coated and uncoated sections run past their asymptotes, with adhesion measured at the end, test whether the coating acts on nucleation only.
Artefact mimicking effect
H2778. Lasting only as long as the heat-flux gauge's drift, an apparent induction period can be an instrument property rather than a surface one. Running the same foulant at a higher heat flux, which lifts the signal above the drift sooner, should shorten the apparent induction period without changing the deposit.

Two-phase and gas-liquid reactors

Hysteresis claim
H2779. The gas rate at which a packed column floods differs going up and coming down, and the loop's width measures how long the liquid film takes to reorganise rather than the packing's capacity. Cycling gas rate slowly through the transition at fixed liquid rate gives the width, and cycling faster should shrink it.
Degeneracy
H2780. Fitting a Langmuir-type rate expression and a power law to the same conversion series in a gas-liquid reactor succeeds equally well, because over the explored range both collapse onto the same function of outlet concentration. Changing interfacial area at fixed bulk concentration, by changing bubble size, breaks the degeneracy: only a genuinely interfacial step responds.
Percolation argument
H2781. Distributor open area affects the mass-transfer coefficient only above a superficial gas velocity at which bubble coalescence becomes connected across the column; below it the hole pattern is erased within the first metre of liquid. Two distributors of different open area, run through the same velocity ladder, should converge at low velocity and separate at high.
Reversal
H2782. Raising pressure in a bubble column raises holdup, which at fixed liquid feed shortens the liquid residence time; past the point where the solubility gain is smaller than the residence-time loss, overall conversion falls as pressure rises. A pressure ladder at constant liquid feed and constant catalyst inventory finds the turning point, which should move with liquid rate.
Bound
H2783. Conversion per pass in a gas-liquid reactor is bounded by gas solubility at the reactor's coldest point whenever a cold zone can hold dissolved gas unreacted, not by the catalyst's turnover rate. Imposing a deliberate cold spot and measuring outlet conversion tests whether the bound moves with the cold spot's temperature.
Misattribution
H2784. Behaviour labelled mass-transfer limited in a gas-liquid reactor is sometimes heat-transfer limited, since one interfacial area serves both and the thermal driving force is small; the two are indistinguishable in a conversion-only experiment. A run at the same conversion but with the liquid's thermal conductivity raised a few percent separates them.
Scale argument
H2785. Gas holdup in a bubble column rises with column diameter up to a point and then becomes independent of it, because wall-influenced coalescence suppression matters only while the wall's influence reaches across the column. Two diameters at one superficial velocity, with holdup from a pressure difference, show where the curves merge.
Identity
H2786. Slip velocity and holdup carry the same information in a single steady experiment at known gas and liquid rates, so reporting both as independent measurements doubles the apparent evidence. A transient experiment, where holdup lags the rates, is the only way to separate them.
Count
H2787. Two bubble size classes reproduce a column's axial holdup profile within the uncertainty of a pressure-difference measurement, and a third class improves the fit to that profile without improving prediction at a new velocity. Fitting both to one profile and testing each against a second velocity shows whether the extra class earns its parameter.
Selection effect
H2788. Published bubble-column data come mostly from columns with well-designed distributors, because a poor distributor is diagnosed and replaced before anything is written, so the surviving set understates sensitivity to gas entry. Comparing a laboratory's full commissioning archive with its published subset, for one column, gives the size of the removal.
Unit trap
H2789. Superficial velocity based on the empty column and on the two-phase dispersion differ by the holdup, which at high gas rate can be a third of the volume, so two reports can disagree by that factor while describing the same experiment. Recomputing both from the reported holdup and column area is the check.
Conservation argument
H2790. Ignoring dissolved gas, a gas balance around a gas-liquid reactor undercounts consumption by the amount held in the liquid leaving, and at high pressure that inventory can be a substantial fraction of one pass. Depressurising the outlet liquid and measuring the released gas closes the balance.
Null claim
H2791. Above the velocity at which the flow becomes fully developed, sparger type has no measurable effect on the mass-transfer coefficient, because the initial bubble size is forgotten within a few column diameters. Two spargers of different hole size, run at the same high velocity with holdup measured at two heights, should return a null.
Artefact mimicking effect
H2792. Reported liquid entrainment from a two-phase reactor is sometimes reflux from the sampling line, which cools and condenses vapour the reactor never entrained. A heated sampling line, or two line lengths at the same take-off point, separates the line's contribution from the reactor's.

Safety mechanisms, physical

Threshold
H2793. Minimum ignition energy of a dust falls steeply as particle size decreases only until the size approaches the flame's quench distance, below which further grinding no longer lowers it; the plateau is the kinetic limit and the steep part is a heat-loss effect. Sieved fractions of one material, dispersed at equal energy, show where the plateau begins, and it should move with dispersing pressure if the steep part is an artefact of agglomeration.
Reversal
H2794. Grinding a dust finer can make it harder to ignite in a given apparatus, because the finer powder agglomerates and the effective particle size in the cloud rises; the reversal shows as a minimum in ignition energy against sieve size when the cloud is dispersed gently. Dispersing with higher shear should move the minimum toward finer sieves if agglomeration is the cause.
Selection effect
H2795. Reported reactor incidents are selected by reporting threshold, and small releases are under-reported in proportion to their size, so the apparent size distribution is steeper than the real one. Two jurisdictions with different thresholds, for one industry and the same years, isolate the effect from the process.
Misattribution
H2796. Chatter of a relief valve is usually attributed to a set pressure too close to the operating pressure, but in many installations the instability is acoustic: the inlet line's quarter-wave resonance couples to the disc's motion at a frequency set by the line's length. Changing the inlet line's length slightly, without touching the set pressure, moves the chatter frequency if the line is the cause.
Bound
H2797. Adiabatic at constant volume, a confined deflagration's peak pressure is capped by the mixture's own pressure ratio, which depends on composition and initial state rather than on vessel size or ignition location; the observed peak lies below it, and the deficit measures heat loss and incomplete combustion. Igniting the same mixture at the centre and at the wall of one vessel, and comparing peaks, gives that deficit directly.
Hidden term
H2798. Charge measured on a filter housing includes charge generated upstream in the pipe, and the pipe's contribution can dominate at low flow, so the filter is credited with a generation rate that belongs to the line. Measuring charge at two points along the pipe at one flow gives the line's contribution as the difference.
Identity
H2799. Upper and lower flammability limits measured in a vertical tube differ according to whether the flame runs upward or downward, yet the two are often quoted as properties of the mixture; the difference is buoyancy acting on the flame during the test. Measuring one mixture in both directions at several tube diameters, and extrapolating to zero diameter, separates mixture property from apparatus.
No-go claim
H2800. No inerting test in a small vessel predicts the oxygen threshold of a large one when the small vessel's mixing time is comparable to the flame's residence time, because the threshold depends on local oxygen at the ignition point rather than on the mean. Two vessels of different size with matched mean oxygen but different mixing times, ignited at one location, would show thresholds that fail to agree.

Status and plan

100 of the series. The list is organised by unit operation rather than by hazard, because the mechanisms run across both: a residence-time argument appears in heat removal and a fouling argument appears in mass transfer, and separating them by topic would have hidden that.

What the hundred have in common is only a shape of reasoning — a quantity is claimed to be something other than what it is called, and a measurement is named that would settle it. None has been tested; several would be cheap to test and at least one, H2786, would retire a habit of reporting two numbers that are one number.

Incoprea Research · hand-considered hypotheses 2701–2800 · chemical reactors and process safety · 3 November 2026 · ~/Desktop/Nov3/