AqueousHydrogenSulfideOxidationKinetics implements the simplified correlation published by Millero, Hubinger, Fernandez, and Garnett (1987), doi:10.1021/es00159a003, for loss of total dissolved sulfide in air-saturated water, seawater, and NaCl solutions:

\[-\frac{d[\mathrm{H_2S}]_T}{dt} = k[\mathrm{O_2}][\mathrm{H_2S}]_T,\] \[\log_{10} k = 10.50 + 0.16\,\mathrm{pH} - \frac{3000}{T} + 0.44\sqrt{I}.\]

The original source reports k on a kg-water mol-1 h-1 basis. Temperature is in K and ionic strength is supplied on the mol/kg-water scale. The implementation reproduces the source coefficient 0.44. A later review by Luther et al. (2011) transcribes 0.49 in its summary equation; that secondary value is not used.

Evidence and validity boundary

The simplified source equation is accepted only inside its published range:

Every numerical input must be finite. A temperature, pH, or ionic strength outside these limits throws an IllegalArgumentException instead of extrapolating. The source reports a standard deviation of 0.18 in log10(k). secondOrderRateConstantRange(...) returns the corresponding multiplicative interval, using a factor of 10^0.18 = 1.51356. This interval is fit scatter, not complete predictive uncertainty.

The source also reports nominal half-times at 298.15 K and pH 8 of 50 +/- 16 h in water and 26 +/- 9 h in seawater. These observations are contextual checks, not independent validation data, because they were used in developing the same source analysis.

Constant-oxygen screening

The caller must establish an air-saturated dissolved-oxygen molality independently. pseudoFirstOrderRateConstant(...) calculates k[O2] and screenAirSaturatedExposure(...) applies the exact constant-oxygen solution:

\[f_{\mathrm{remaining}} = \exp(-k[\mathrm{O_2}]t).\]

For the illustrative inputs 298.15 K, pH 8, ionic strength 0.723 mol/kg water, and dissolved oxygen 250 micromol/kg water, the correlation gives k = 123.6175 kg water/(mol h) and a nominal half-life of 22.4288 h. The oxygen value is an example input, not a new solubility correlation or a source benchmark.

The analytical update is deterministic, gives exactly one remaining fraction at zero time, remains bounded from zero to one, and avoids timestep error. It reports total-sulfide loss only. It does not assign products or consume oxygen, because the source correlation does not supply a complete product stoichiometry for that purpose.

Residence-time range

screenResidenceTimeRange(...) compares a caller-provided aqueous residence time with the Millero pseudo-first-order chemical time over the published fit-scatter interval:

$ \tau = \frac{1}{k[\mathrm{O_2}]}, \qquad \mathrm{Da} = \frac{t_{\mathrm{res}}}{\tau} = k[\mathrm{O_2}]t_{\mathrm{res}}. $

The immutable result reports lower, nominal, and upper pseudo-first-order rates, chemical times, Damkohler numbers, and remaining fractions. Lower and upper refer to the source’s one-standard-deviation log10(k) fit interval. At the illustrative nominal half-life of 22.4288 h, the nominal Damkohler number is ln(2) and the nominal remaining fraction is exactly 0.5; the lower-rate result retains more sulfide and the upper-rate result retains less.

A zero residence time is an exact identity. Increasing residence time monotonically reduces every reported remaining fraction. Non-finite inputs or any multiplication/reciprocal overflow fail closed. The method deliberately reports continuous Damkohler evidence and does not add categorical reaction/transport thresholds. A caller may compare this diagnostic with an independently established transport time, but that does not constitute a pipeline source-term coupling or high-pressure qualification.

Target-time inversion

timeToRemainingFractionRange(...) inverts the same constant-oxygen first-order solution for a requested remaining-total-sulfide fraction f:

$ E_{\mathrm{required}} = -\ln f, \qquad t_{\mathrm{required}} = \frac{-\ln f}{k[\mathrm{O_2}]}. $

The immutable result reports the target fraction, required dimensionless exposure, lower/nominal/ upper pseudo-first-order rates, and the shortest, nominal, and longest required times. The shortest time uses the upper fit-scatter rate; the longest uses the lower rate. For the illustrative state above, a target fraction of 0.5 reproduces the nominal half-life of 22.4288 h. Substituting each reported time and its corresponding rate back into exp(-k[O2]t) recovers the requested fraction.

A target fraction of exactly one returns zero required exposure and zero time. The valid target interval is (0, 1]; exact zero is rejected because the first-order model approaches zero only as time tends to infinity. Stricter targets require monotonically longer times. Non-finite inputs, underflowed rates, or a required-time overflow fail closed.

This inverse calculation is a screening diagnostic, not an equipment-sizing guarantee. It retains the same air-saturated constant-oxygen, atmospheric-pressure, fit-scatter, and unidentified-product limitations. It does not establish a pipeline residence time, mass-transfer rate, or high-pressure reaction extent.

Piecewise exposure trajectory

AqueousHydrogenSulfideOxidationTrajectory.advance(...) propagates the same correlation through a non-empty ordered list of constant-state segments. For segment i, it computes

$ E_i = k_i[\mathrm{O_2}]i\Delta t_i, \qquad [\mathrm{H_2S}]{T,n} = [\mathrm{H_2S}]{T,0} \exp\left(-\sum{i=1}^{n}E_i\right). $

This analytical composition of exponentials has no numerical timestep error. Segment splitting at an unchanged state therefore leaves the result invariant. The implementation preserves source order and reports each segment’s second-order rate, pseudo-first-order rate, individual exposure, and cumulative exposure for audit. Zero-duration segments are accepted as exact identity steps.

Initial total sulfide must be within the source experiment interval of 20–30 micromol/kg water. Every segment independently applies the temperature, pH, ionic-strength, and caller-supplied air-saturated-O2 gates above. A pressure value is deliberately not part of the segment contract.

The reported 0.18 scatter in log10(k) is propagated as one common multiplicative correlation envelope across the trajectory. The result reports nominal, lower-rate, and upper-rate cumulative exposures and final molalities. Treating this as one systematic envelope avoids implying that successive segments contain independent experimental errors. It remains fit scatter rather than a complete uncertainty model.

The trajectory reports total-sulfide inventory closure as initial minus final minus reacted molality. It retains the same constant-oxygen and unidentified-product boundary as the single-state screen. Within this first-order screening model, only cumulative exposure controls the final fraction; the ordered diagnostics do not introduce path-dependent chemistry.

Per-segment inventory evidence

Each immutable SegmentResult also exposes inlet, outlet, and reacted total-sulfide molality for the lower-rate, nominal, and upper-rate paths. For each path r and segment i,

$ c_{r,i,\mathrm{out}} = c_0\exp(-E_{r,i,\mathrm{cumulative}}), \qquad c_{r,i,\mathrm{reacted}} = c_{r,i,\mathrm{in}}-c_{r,i,\mathrm{out}}. $

The first inlet equals the supplied initial total-sulfide molality. Every later inlet is exactly the preceding segment outlet, so each segment closes as inlet = outlet + reacted and the reacted increments telescope to the trajectory’s initial-minus-final inventory. A zero-duration segment has identical inlet and outlet and reports zero reaction. Splitting an unchanged segment preserves both final inventory and the sum of reacted increments.

At every segment outlet, the lower-rate path retains the most total sulfide and the upper-rate path retains the least. Over the complete shared trajectory, those paths respectively give the least and most total reacted sulfide. A single segment’s reacted increment need not follow that ordering after different prior depletion. These values are analytical bookkeeping for total dissolved sulfide under the same constant-oxygen assumption. They do not define oxygen consumption, sulfur products, stoichiometric source terms, or a pipeline control-volume coupling.

Endpoint loss-rate evidence

Each segment also reports the instantaneous total-sulfide loss rate at its inlet and outlet for the lower-rate, nominal, and upper-rate paths:

$ r_{r,i,\mathrm{in}} = k_{r,i}[\mathrm{O_2}]i c{r,i,\mathrm{in}}, \qquad r_{r,i,\mathrm{out}} = k_{r,i}[\mathrm{O_2}]i c{r,i,\mathrm{out}}. $

The rate unit is mol total sulfide/(kg water h). The local retention factor is

$ R_{r,i}=\exp\left(-k_{r,i}[\mathrm{O_2}]i\Delta t_i\right), \qquad c{r,i,\mathrm{out}}=c_{r,i,\mathrm{in}}R_{r,i}. $

For a positive-duration segment, the outlet loss rate cannot exceed its inlet loss rate. A zero-duration segment gives exactly R = 1 and equal endpoint rates. Multiplying local retention factors across unchanged-state segment subdivisions recovers the unsplit retention and final inventory.

These endpoint rates are differential screening evidence evaluated under the source’s constant-oxygen assumption. By themselves they are not a time-averaged control-volume source, a conversion to molar flow, oxygen consumption, or product stoichiometry.

Segment-mean loss-rate evidence

For each lower-rate, nominal, and upper-rate path, SegmentResult also exposes the analytical mean total-sulfide loss rate over the segment. For positive duration,

$ \overline{r}{r,i} =\frac{c{r,i,\mathrm{in}}-c_{r,i,\mathrm{out}}}{\Delta t_i} =\frac{c_{r,i,\mathrm{reacted}}}{\Delta t_i}. $

Its unit is mol total sulfide/(kg water h). Because the differential rate decays monotonically within a constant-state segment, the mean is bounded by the endpoint rates:

$ r_{r,i,\mathrm{out}}\leq\overline{r}{r,i}\leq r{r,i,\mathrm{in}}. $

Multiplying the mean by segment duration exactly recovers the reacted molality. For a zero-duration segment the quotient would be undefined, so the API returns its exact continuous limit k[O2] c_in; this equals both endpoint rates and remains finite. For an unchanged-state segment split into subsegments, duration-weighted mean rates recover the unsplit reacted inventory and unsplit mean rate.

This is a time average on a molality basis, not yet a volumetric or molar-flow control-volume source. Creating a pipeline source term requires separately qualified water inventory, phase transfer, oxygen consumption, reaction products, energy, pressure, and numerical coupling.

Explicit water-inventory projection

AqueousHydrogenSulfideOxidationWaterInventoryProjection.project(...) converts one immutable segment result from the molality basis to dimensional total-sulfide loss evidence using a caller-supplied liquid-water inventory m_w in kg:

$ \dot n_{r,i}=\overline{r}{r,i}m_w, \qquad n{r,i,\mathrm{reacted}}=c_{r,i,\mathrm{reacted}}m_w. $

The immutable result reports lower-rate, nominal, and upper-rate mean loss in mol/h and mol/s, together with reacted total sulfide in mol. The water inventory must be finite and strictly positive. For positive segment duration, each path closes exactly as

$ \dot n_{r,i}\Delta t_i=n_{r,i,\mathrm{reacted}}. $

At zero duration, reacted amount is exactly zero while the mean-loss output preserves the existing finite differential limit. Dimensional values scale linearly with water inventory. If an unchanged state is subdivided while the same water inventory is used for each subsegment, the reacted-mole increments sum to the unsplit result.

The supplied water inventory is explicit evidence, not a holdup or free-water prediction. This projection is an unsigned total-sulfide loss potential, not a component source applied to a control volume. It does not infer water dropout, consume O2, assign products or selectivity, calculate reaction heat, pressure or phase transfer, mutate pipeline/transient state, or update sulfur deposition and wall inventories. Those steps require separately qualified inputs and must compose with the existing pipeline and sulfur-deposition implementations.

Constant-water trajectory projection

The overloaded AqueousHydrogenSulfideOxidationWaterInventoryProjection.project(...) applies one caller-supplied constant liquid-water inventory to a complete immutable trajectory. It preserves the source order and returns every existing per-segment dimensional projection together with cumulative lower-rate, nominal, and upper-rate reacted total-sulfide amounts.

For each fit-scatter path r, the segment increments telescope at constant water inventory:

$ n_{r,\mathrm{reacted}} = \sum_i n_{r,i,\mathrm{reacted}} = m_w(c_0-c_{r,n,\mathrm{out}}). $

The result exposes the difference between the summed increments and this endpoint identity as a closure residual in mol. A one-segment trajectory exactly reuses the existing segment projection, an unchanged-state subdivision preserves cumulative reacted moles, and a trajectory containing only a zero-duration segment reports exactly zero reaction. The segment list is defensively immutable. A null trajectory, non-finite or non-positive inventory, numerical underflow, or non-finite accumulation fails closed.

The constant inventory is an explicit caller assumption; it is not a calculated pipeline holdup, water-dropout history, or moving material-parcel model. The cumulative amounts remain unsigned total-sulfide-loss evidence. They do not consume O2, assign sulfur products, calculate heat or phase transfer, create signed component sources, mutate pipeline/transient state, or update S8, FeS, wall, or sulfur-deposition inventories.

Product-agnostic sulfur-equivalent budget

The segment and constant-water trajectory results also expose the sulfur-element mass equivalent of the qualified total-sulfide loss. One mole of total sulfide contains one mole of sulfur atoms, so the conversion is

$ \dot m_{S,\mathrm{equiv},r,i} =\dot n_{r,i}M_S, \qquad m_{S,\mathrm{equiv},r,i} =n_{r,i,\mathrm{reacted}}M_S. $

where M_S = 0.032065 kg/mol reuses IronSulfideWallInventory.SULFUR_MOLAR_MASS_KG_PER_MOL. Segment results report lower-rate, nominal, and upper-rate mean sulfur-equivalent loss in kg/h and kg/s, plus reacted sulfur-equivalent mass in kg. The trajectory result reports cumulative reacted sulfur-equivalent mass and the corresponding mass-basis closure residual for every fit-scatter path.

For positive duration, the mass-rate integral closes exactly:

$ \dot m_{S,\mathrm{equiv},r,i}\Delta t_i =m_{S,\mathrm{equiv},r,i}. $

Zero duration gives exactly zero reacted sulfur-equivalent mass while preserving the finite analytical mean-rate limit. The segment sums telescope to the trajectory cumulative mass, unchanged-state subdivision is invariant, and all values scale linearly with the caller-supplied water inventory. Non-finite or unrepresentable derived mass fails closed.

This is a sulfur-atom conservation view, not an elemental-sulfur or S8 yield. It does not identify S8, sulfate, thiosulfate, polysulfides, FeS, or any other product; prescribe selectivity or oxygen demand; calculate reaction heat; or update a stream, wall, deposit, filter, or pipeline state. Product and deposition calculations require separately qualified stoichiometry and selectivity and must compose with the existing sulfur analyser, wall inventory, oxidation source, solid flash, and filter implementations.

Explicit elemental-sulfur allocation boundary

AqueousHydrogenSulfideOxidationElementalSulfurAllocation.allocate(...) creates an immutable, non-mutating accounting receipt between one qualified segment sulfur-equivalent budget and a caller-defined elemental-sulfur scenario. The caller must supply both an allocation fraction f_ES in [0, 1] and a non-blank allocation-basis identifier. The identifier records which external basis the caller used; its presence does not qualify that basis or turn the fraction into a measured product yield.

For each lower-rate, nominal, and upper-rate fit path, the receipt applies the same explicit fraction to mass rate and mass:

$ \dot m_{S,\mathrm{allocated}}=f_{ES}\dot m_{S,\mathrm{equiv}}, \qquad \dot m_{S,\mathrm{unallocated}}=\dot m_{S,\mathrm{equiv}}-\dot m_{S,\mathrm{allocated}}, $

$ m_{S,\mathrm{allocated}}=f_{ES}m_{S,\mathrm{equiv}}, \qquad m_{S,\mathrm{unallocated}}=m_{S,\mathrm{equiv}}-m_{S,\mathrm{allocated}}. $

The result exposes the source sulfur-equivalent budget, allocated elemental-sulfur scenario, unallocated sulfur-equivalent remainder, and closure residual on both rate and mass bases. Zero allocation leaves the complete source budget unallocated; full allocation leaves an exact zero remainder. Values scale linearly with the explicit water inventory, and summing receipts from an unchanged-state segment subdivision reproduces the unsplit allocated mass. Missing or invalid inputs, numerical overflow, and positive products that underflow to zero fail closed.

Downstream code may consume an allocated elemental-sulfur field once and must carry the unallocated remainder separately. It must not apply both the original source budget and the unallocated remainder as products, because that would double count sulfur. The receipt itself does not create S8 molecular amounts, supply a default fraction, select products, qualify stoichiometry or selectivity, consume O2, calculate heat, speciation, pressure, phase transfer or water holdup, create a signed source, execute a solid flash, or mutate a stream, wall, deposit, filter, corrosion, process, transient, or pipeline state.

Explicit mass-based S8 transfer receipt

AqueousHydrogenSulfideOxidationS8Transfer.create(...) selects exactly one lower-rate, nominal, or upper-rate path from an existing elemental-sulfur allocation and creates an immutable transfer receipt for NeqSim’s existing S8 component path. The caller must explicitly supply the fit path, a product-identity basis identifier, and a downstream idempotency key. The allocation-basis identifier and source-segment metadata are preserved.

The receipt copies the selected path on a mass basis without an additional conversion:

$ \dot m_{S8,\mathrm{transfer}}=\dot m_{S,\mathrm{allocated}}, \qquad m_{S8,\mathrm{transfer}}=m_{S,\mathrm{allocated}}. $

It also carries the source sulfur-equivalent budget, unallocated remainder, and existing rate- and mass-basis closure residuals. This exact kg/h and kg passthrough deliberately avoids calculating S8 moles or introducing another molecular-weight constant. Zero allocation gives an exact zero transfer, full allocation leaves an exact zero remainder, and the inherited fit-path ordering, water-inventory scaling, and unchanged-state segment-split mass sums are preserved.

The product-identity identifier records why the caller selected the S8 representation; it does not qualify that choice as a measured product distribution. The idempotency key is a hook for a downstream accounting ledger, not an in-memory consumption lock. A consumer must apply the transferred mass only once under that key and carry the unallocated sulfur-equivalent remainder separately. It must not also apply the original allocation or source budget as product.

This is the narrow mass-unit seam toward the existing SulfurDepositionAnalyser, TP-solid-flash, and SulfurFilter path. The receipt does not add S8 to a stream, run equilibrium or a solid flash, predict saturation, precipitation, deposition, capture or corrosion, consume O2, calculate heat, speciation, phase transfer or water holdup, or mutate any stream, wall, filter, process, transient, or pipeline state. Those operations remain separate and require independently qualified product identity and application evidence.

Piecewise target crossing

AqueousHydrogenSulfideOxidationTrajectory.timeToRemainingFractionRange(...) locates where a requested remaining-total-sulfide fraction is first reached inside a finite ordered segment list. It reuses the segment rates and the same required exposure as the single-state inverse:

$E_{\mathrm{target}}=-\ln f.$

For each lower, nominal, and upper fit-scatter path, cumulative exposure is summed through complete segments. Inside the crossing segment, the remaining exposure is divided by that segment’s pseudo-first-order rate. The immutable result reports:

The upper-rate path gives the shortest time and the lower-rate path gives the longest. A target fraction of one crosses at exact time zero in segment zero. An unchanged-state segment split cannot change any reported crossing time. Substituting each result back into the corresponding piecewise cumulative exposure recovers -ln(f).

The target interval remains (0, 1]. Every lower, nominal, and upper path must reach the target within the supplied finite trajectory. If even the slow lower-rate path does not reach it, the method throws an IllegalArgumentException; it does not extend the final state, extrapolate a residence time, or return infinity.

This diagnostic identifies a crossing within caller-defined aqueous screening segments. It does not locate a position in a pipeline, calculate flow residence time, size equipment, or couple the reaction to phase behavior, mass transfer, oxygen depletion, or a transient solver.

Absolute reacted-moles target crossing

AqueousHydrogenSulfideOxidationWaterInventoryProjection.timeToReactedMolesRange(...) converts a requested reacted total-sulfide amount to the remaining fraction required by the existing piecewise target-crossing calculation. With initial molality c_0, constant water inventory m_w, and requested reacted amount n_target,

$ n_0=c_0m_w, \qquad f_{\mathrm{target}}=\frac{n_0-n_{\mathrm{target}}}{n_0}. $

The immutable result records the input molality and water inventory, initial and target amounts, the corresponding remaining amount and fraction, and the existing shortest, nominal, and longest crossing times and segment indices. Reacting half of the initial dimensional inventory therefore maps exactly to a remaining fraction of 0.5; at the illustrative reference state the nominal time is 22.4288 h.

Forward evaluation at each reported fit-scatter crossing recovers the requested reacted amount. Larger targets require longer times. Scaling both the constant water inventory and reacted-moles target by the same factor leaves the target fraction and crossing times unchanged. Unchanged-state segment subdivision preserves elapsed times while the reported source-order crossing index follows the supplied segmentation. A target of exactly zero crosses at time zero.

The target must be finite, non-negative, and strictly less than the initial dimensional total-sulfide inventory; equality would require infinite time in this first-order model. Inputs that cannot represent a positive target change at the current floating-point scale fail closed. Every fit-scatter path must reach the target within the supplied finite trajectory.

This method dimensionalizes an analytical screening target only. The constant water inventory remains caller-supplied and is not a calculated holdup. The output is not a residence-time design, pipeline position, signed H2S source, oxygen demand, product yield, or deposition prediction.

Absolute remaining-moles target crossing

AqueousHydrogenSulfideOxidationWaterInventoryProjection.timeToRemainingMolesRange(...) converts a requested absolute remaining total-sulfide inventory to the fraction required by the existing piecewise target-crossing calculation. With initial molality c_0, constant water inventory m_w, and requested remaining amount n_remaining,target,

$ n_0=c_0m_w, \qquad f_{\mathrm{target}}=\frac{n_{\mathrm{remaining,target}}}{n_0}, \qquad n_{\mathrm{reacted,target}}=n_0-n_{\mathrm{remaining,target}}. $

The immutable result records the input molality and water inventory, initial, remaining, and complementary reacted amounts, the target fraction, and the existing shortest, nominal, and longest crossing times and segment indices. A remaining target equal to half the initial inventory maps exactly to a fraction of 0.5; at the illustrative reference state the nominal crossing is 22.4288 h. It agrees exactly with the reacted-moles inverse when the two dimensional targets are complements.

Forward evaluation at each reported fit-scatter crossing recovers the requested remaining amount. A smaller remaining target requires a longer time. Scaling both the constant water inventory and remaining-moles target by the same factor leaves the target fraction and crossing times unchanged. Unchanged-state segment subdivision preserves elapsed times while the source-order crossing index continues to describe the supplied segmentation. A target equal to the initial inventory crosses at exact time zero.

The target must be finite, strictly positive, and no greater than the initial dimensional inventory; exact zero is unreachable in finite time for this first-order model. Non-finite, numerically underflowing, overflowing, unrepresentable, or unreachable inputs fail closed. Every lower, nominal, and upper fit-scatter path must reach a non-identity target within the supplied finite trajectory.

This method is an absolute inventory-threshold screen, not a water-holdup calculation, residence- time design, pipeline position, signed H2S source, oxygen demand, product yield, or deposition prediction. The water inventory remains an explicit constant caller input.

Scientific stop boundary

This capability does not:

Electrolyte pH/speciation remains owned by issue #3144. TP flash, dynamics, pipeline coupling, and MCP publication remain coordinated with #2937, #2911, the pipeline roadmap, and #3153. Applying this atmospheric aqueous correlation to a Northern-Lights-type high-pressure CO2 pipeline requires separate phase, pressure, mass-transfer, and composition evidence.