Drybench Bioreactor.

What the app shows, how it works and how it was built, in the words of its own write-up, followed by the parameter defaults and the data sources with their licences.

What it does

Pick a preset (E. coli fed-batch, S. cerevisiae glucose-limited fed-batch, Pichia AOX1 on methanol, a chemostat, or a custom run that starts from E. coli's values) and the app simulates biomass, substrate, product, volume, the feed and dissolved oxygen against time, with the oxygen uptake and transfer rates, CO₂ evolution, the respiratory quotient and the exhaust gas. It says when dissolved oxygen would run out in the simulated vessel and, within the agitation, gas-flow and oxygen-enrichment limits you enter, what would rescue it: raise the agitation, then the gas flow, then the inlet's oxygen, and last cap the feed, each step the smallest on its grid that holds the setpoint to the end of the run. The rescue ignores cooling capacity, and says so wherever it is shown.

Bring your own vessel with a measured kLa, or your kLa readings at several agitation rates; or compute kLa from Van 't Riet's correlation with its range stated. Every preset value shows where it comes from and its reported range, and a value with no measured source is labelled illustrative. The pump sheet gives the rate to set for each interval of the feed, ready to print. A run is a link: the preset by id and version, and only the parameters you changed, so a teaching link gives the same run next year. Lecturer mode hides the results until a prediction is entered.

How it works

The model is the uptake-first unstructured one: Monod substrate limitation (Haldane and Andrews' substrate inhibition for methanol), Pirt's maintenance, Luedeking and Piret's product terms drawing on the same substrate budget as growth, the oxygen term multiplied with the substrate term (a model choice), and the balances with volume change for batch, fed-batch and chemostat runs. Oxygen and CO₂ come from carbon and degree-of-reduction balances with ammonium as the nitrogen source. Dissolved oxygen follows its own balance, dC/dt = kLa(C* − C) − OUR + (Fin/V)(Cfeed − C), with C* from the exhaust gas, starting at saturation with the inlet gas; the solubility is Benson and Krause's as the USGS documents it.

The equations are stiff (the substrate's time constant can be under a second while growth runs over hours), so they are solved by the modified Rosenbrock formula of Shampine and Reichelt 1997 with an analytic Jacobian, error control and located events, in a Web Worker, never on the page's own thread. Every switch (the feed starting, the cap, the substrate running out, dissolved oxygen crossing the setpoint) is located by the solver on its continuous extension, so a short excursion cannot fall between output points. Flags mark where a run leaves the biology the model covers, or where an input or correlation is outside its fitted range, as numbered notes on the chart, the table, the tiles and every export.

How it is checked

The engine is compared with an independent solver run offline: SciPy's Radau method at a relative tolerance of 1e-9, through pipeline/bioreactor-simulator/reference.py, on 33 scenarios across batch, fed-batch (exponential and constant feeds, a cap, a stop), chemostat steady states, steps and washout, oxygen-limited runs at kLa 50, 200 and 1,000 per hour, a kLa step from 20 to 40 per hour, planted short excursions, and each preset's published run. Closed forms check the chemostat's steady state and a batch run; the carbon and electron balances close at the end of every run. The right-hand sides agree with the oracle's to within 1e-12 relative. Each preset version keeps golden runs, so a model change that moves a published run beyond the stated tolerance fails the build.

The state variables are checked against an independent solver; the derived oxygen and CO₂ rates are compared with published measurements (listed on the verification page); there is no other comparison with process data. The wording stays draft until an independent reviewer with bioprocess experience signs the equations, the presets and the fixtures (Q-19).

Equations

Growth (Monod, or Haldane and Andrews with Ki)

f(S) = S/(Ks + S + S²/Ki); f(C) = C/(Ko + C), multiplied (a model choice)

Uptake and maintenance (Pirt)

qS = (μmax/Y + ms)·f(S)·f(C); μ = (μmax + Y·ms)·f(S)·f(C) − Y·ms where positive

Product (Luedeking and Piret)

qP = α·μ + β, from the same budget as growth: μ + qP = Y·max(0, qS − ms)

Balances with volume change

dX/dt = μX − (F/V)X; dS/dt = −qS·X + (F/V)(Sf − S); dP/dt = qP·X − (F/V)P; dV/dt = F (a chemostat draws off F = D·V)

Dissolved oxygen

dC/dt = kLa(C* − C) − OUR + (Fin/V)(Cfeed − C), C* from the exhaust gas; OUR from the degree-of-reduction balance, CER from the carbon balance, RQ = CER/OUR

kLa

kLa = a·(Pg/V)^b·vs^c (Van 't Riet), Pg from Hughmark's ratio; or your value, scaled by the same exponents; or your readings, log-log

Choices stated

Ks acts on uptake

Literature growth-fitted Ks is used as an uptake parameter: an explicit modelling choice, not an equivalent growth-Monod parameter. In the product-free, fully oxygenated Monod limit, growth half-saturation is Ks × (1 + 2Yms/μmax), with factors 1.092 for E. coli and 1.025 for yeast. Methanol inhibition and product allocation require the full model; no universal scalar conversion or preset refit is claimed.

Growth stops below maintenance

Growth is (μmax + Y·ms)·f(S)·f(C) − Y·ms where positive: Pirt's form while cells grow. Below uptake equal to maintenance nothing grows and nothing decays; death and endogenous decay are not modelled. The switches between growing, product only and maintenance only are located by the solver as events.

The product

Off by default (α and β zero). When on, it draws on the same substrate budget as growth and uses biomass-equivalent carbon fraction, degree of reduction and substrate yield. Chemically different products can distort OUR, CER and RQ; these outputs are approximate when product is enabled. Every product output reads "with your α and β; not a titre forecast".

Oxygen and CO₂

From the carbon and degree-of-reduction balances with ammonium as the nitrogen source, converting dry weight to C-mol through the measured carbon fraction. CER is the CO₂ produced; dissolved CO₂ and bicarbonate are not modelled.

C* and the exhaust gas

Air saturation by Benson and Krause as the USGS documents them, for 0 to 40 °C and 0.5 to 1.1 atm; a pressure from 1.1 to 3 atm runs and is flagged extrapolated, outside 0.5 to 3 atm or 0 to 40 °C a run is refused. C* in the vessel follows the exhaust gas's oxygen fraction, from the gas balance on the inlet at the vessel's temperature and pressure, the gas phase taken at steady state.

kLa

By its source: your value, at the setup's agitation, gas flow and starting volume, scaled to other settings by Van 't Riet's exponents with Hughmark's gassed-power ratio, so the power number cancels; your readings at several rpm, interpolated log-log and extended beyond them with a flag; or Van 't Riet's correlation with Hughmark's gassed power, a Rushton turbine's power number of 5 and two impellers summed (empirical correlation; Np = 5 and additive impeller power are nominal geometry assumptions). kLa is taken at the volume where the aeration is set and held.

Gas-flow basis

Choose actual reactor conditions or specified reference temperature and absolute pressure. Qactual = Qreference × Preference/P × Tkelvin/Treference. This preserves molar supply and supplies actual velocity to power and kLa calculations. Vvm is normalised by current liquid volume, so molar flow rises during feeding; kLa remains held between aeration changes. The ideal dry-gas convention excludes line humidification, head and salinity effects.

The feed

Constant, or exponential at a set growth rate from a rate designed to hold it (paying for maintenance, the product and the residual substrate), held at the pump's limit once reached, stopping at its set time or when the vessel reaches its working volume. The pump sheet gives each interval's rate as the law's average over it, so the volumes add up.

The rescue

When dissolved oxygen first falls below the setpoint (excursions under 3 minutes not counted), the cascade raises the agitation, then the gas flow, then the inlet's oxygen fraction, each the smallest step on its grid (10 rpm, 0.05 vvm, 1 percentage point) that holds the setpoint to the end of the run, found by bisection, within the limits you enter; at a limit the next lever takes over, and last, in a fed-batch run, the feed's growth rate is capped (steps of 0.005 per hour). It ignores cooling capacity, vessel pressure and gas-safety limits.

The solver

Shampine and Reichelt's modified Rosenbrock (W-) formula with its continuous extension, an analytic Jacobian checked against finite differences, a relative tolerance of 1e-7 with an absolute tolerance per state, and every switch, trigger and time event located on the continuous extension. A run that reaches 40,000 steps stops with the time it reached; a run is never clamped silently.

Flags

A run carries numbered notes where it leaves the biology the model covers: S. cerevisiae's uptake at 95 percent or more of its respiratory maximum, E. coli's glucose uptake at or above 0.8 g per g dry weight per hour (Vemuri et al. 2006, MG1655), and oxygen demand beyond what the vessel can transfer; and where an input or correlation is outside its fitted range. Each flag's code and rule version travel in every export.

Data sources, licences and versions

Times on screen are local time with the UTC offset; times in exports are UTC. Dates with no time are shown at the precision the source gave them.

The Export menu offers the time series of the runs on screen as CSV (every computed point, the units in the headers, the flags in force at each time, the data's origin and the product's basis, with the provenance file and a README whose first lines are the flag notes), the pump sheet as CSV in mL/h and mL, the chart as SVG or PNG with the flag notes in the caption strip, the printed bench sheet on A4 (the setup, the vessel's limits, the rescue, the chart, the pump sheet, the method block and the verification log) and the method paragraph as text. Copy link carries the preset by id and version and the parameters you changed, never results; a run you keep is stored in this browser.

Release gate: before the app leaves the preview, its exports and printed reports will carry the data versions, parameters, limits and a timestamp needed to reproduce a result, as the regulatory position says. This section will describe each format as it ships.

Each module below is a set of automated tests in the app's source code, with the expected results written into the tests. They check the app's logic against recorded inputs and stored reference records; none of them calls a live service.

src/lib/hosts/fixtures.test.ts

Every one of the 33 scenarios in pipeline/bioreactor-simulator/fixtures/scenarios.json against the engine: each point within the larger of 1e-5 of its value, a time shift of max(1e-4 h, 1e-5 of the elapsed time) times its slope, and its floor; inside the window after a change of aeration or feed, the series computed from dissolved oxygen on value alone; events within 1e-3 h; the growth switches, triggers and events; the carbon and electron balances within 0.5 percent; the closed forms, the oxygen solubility against the USGS DOTABLES program's own output, the exhaust-gas balance, the kLa correlation and the scale-up rules; the files' hashes against manifest.json. The oracle is SciPy 1.17.0's Radau, run offline by reference.py at a relative tolerance of 1e-9.

src/lib/hosts/model.test.ts and src/lib/fit/ode.test.ts

The right-hand sides against the oracle's at 13 states within 1e-12 relative; the Jacobian against central differences; one step and the linear solve against NumPy and LAPACK; fixed-step RK4's failure at kLa 1,000 per hour kept as a regression test; step-count ceilings per scenario.

src/lib/hosts/golden.test.ts

The 12 golden runs (each preset's default run and one with three changes, the E. coli rescue and the yeast page's chemostat link), written once per published preset version, within each point within the larger of the golden tolerance (1e-4 of the value; DO 0.01 percent of air saturation; OUR, OTR and CER 0.01 mmol/L/h; RQ 0.001), a time shift of max(1e-3 h, 1e-4 of the elapsed time) times its slope, and its floor: a change that moves a published run fails until the golden runs are re-recorded under a new preset version (a changed value) or a new model version (a changed equation), the earlier ones kept as superseded.

src/lib/hosts/presets.test.ts

Every preset value has its source with the table or page and a reported range, or is labelled; illustrative values pass the tenfold test (headline outputs unchanged at the precision shown); the matched yield and maintenance pairs; each preset's default run.

src/lib/hosts/setup.test.ts and rescue.test.ts

The link grammar's round trip and refusals; kLa by each source, exact at the setup's own settings; the rescue never exceeds a limit and takes the smallest holding step on each grid.

Draft until the independent bioprocess reviewer signs the equations, the presets and the fixtures (Q-19).

Release gate: before the app leaves the preview, each release will publish a verification dataset with expected outputs on this page, so you can run your own checks.

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