{ "about": { "what": "(b) Integrated carbon and electron closure of the allocation with a product whose composition differs from biomass, including feed and outflow", "oracle": "scipy.integrate.solve_ivp, Radau, rtol 1e-10 with per-state absolute tolerances, piecewise between time events (the feed's start and stop) and the state events where the regime switches (G, P, M; solve_ivp's event finder), sampled every half hour from the dense output; BDF at the same tolerances as the cross-check. A solver written for this fixture: dissolved oxygen dynamic with C* stated (no gas phase, which carries no carbon or electrons into the closure)", "states": "X, S, P, V, DO, then cumulative CO2 (mol), O2 (mol), substrate fed (g), carbon washed out (mol C) and electrons washed out (mol)", "closure": "carbon: |(C-mol in the vessel at 0 + substrate fed/MSc) − (C-mol in the broth + CO2 + washed out)| / in; electrons: the same with γ per C-mol and 4 per O2 taken up; the worst over the output times and every switch", "feasibility": "each case's yields judged by the bounds of (a) first; an infeasible case is refused without integrating; a feasible case keeps qCO2 and qO2 non-negative at every output time and on both sides of every switch (at a bound, at or above −1e-12 × γS·qS,max/(4·MSc))", "chemostat": "the product-bearing chemostat's end state against Q = D/Yxs + (αD + β)/Yps + ms, S* from qS(S*) = Q with fO from the oracle's DO, X* = D(Sf − S*)/Q, P* = (αD + β)X*/D", "negativeControls": [ "an infeasible yield, refused before integration", "the product booked as biomass in the accounting while MPc ≠ MXc, which must fail to close" ], "tolerance": { "closureRelative": 1e-07, "bdfFractionOfPeak": 1e-06, "chemostatRelative": 1e-06, "negativeClosureAbove": 0.001, "atBoundFloor": "-1e-12 × γS·qS,max/(4·MSc)" }, "versions": { "python": "3.12.14", "scipy": "1.17.0", "numpy": "2.3.5" }, "version": "0.15.0", "recordedOn": "2026-10-31", "script": "pipeline/bioreactor-simulator/reference-product-composition.py", "generatorSha256": "81421db2e2689f1562f85f8a17b17b14ad71cee17f2eaf981fa1acacc40930f9", "python": "3.12.14", "specification": "docs/design/bioreactor-product-composition.md", "ruling": [ "docs/board/memos/2026-10-24-cso-bioreactor-stage.md", "docs/board/memos/2026-10-31-cso-bioreactor-br8-allocation.md" ] }, "cases": [ { "id": "batch-lactate", "description": "Batch growth on glucose with a lactate product (γP = γS, carbon as the substrate's)", "mode": "batch", "kinetics": { 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0.00223139945417, "to": 0.00223139945742 } } ], "regimes": [ "G", "M" ], "endState": { "X": 3.2141713971666737, "S": -8.874351615746872e-15, "P": 1.9046968879133868, "V": 6.0, "DO": 6.7 }, "qsScale": 0.05060217652637555, "worstCarbonClosure": 1.32e-15, "worstElectronClosure": 1.54e-15, "minQCO2": 0.0, "minQO2": 0.0, "rows": [ { "t": 0.0, "X": 0.1, "S": 10.0, "P": 0.0, "V": 6.0, "DO": 6.7, "regime": "G", "mu": 0.46553036566, "qP": 0.28276518283, "qCO2": 0.0218287755223, "qO2": 0.0210483115969, "carbonClosure": 0.0, "electronClosure": 0.0 }, { "t": 0.5, "X": 0.126205724528, "S": 9.91614709882, "P": 0.0159177420517, "V": 6.0, "DO": 6.66601014751, "regime": "G", "mu": 0.465470992724, "qP": 0.282735496362, "qCO2": 0.0218262997047, "qO2": 0.0210459353183, "carbonClosure": 8.79e-16, "electronClosure": 8.78e-16 }, { "t": 1.0, "X": 0.159276203895, "S": 9.810327777, "P": 0.0360054917171, "V": 6.0, "DO": 6.65710662832, "regime": "G", "mu": 0.465433521071, "qP": 0.282716760536, "qCO2": 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"worstFractionOfPeak": 3.82e-09, "bySeries": { "X": 3.64e-09, "S": 3.68e-09, "P": 3.82e-09, "V": 0.0, "DO": 6.87e-10 }, "switchesEqual": true, "within": true } }, { "id": "negative-control-infeasible-yield", "description": "Negative control: a palmitic-acid product (γP 5.75) at Yps 0.6, above its carbon and electron bounds on glucose. Refused by the yield bounds before anything is integrated", "mode": "batch", "kinetics": { "muMax": 0.61, "Ks": 0.05, "Ki": null, "Yxs": 0.42, "ms": 0.067, "Ko": 0.1, "substrate": "glucose", "biomassCarbon": 0.4738, "biomassGamma": 4.17, "alpha": 2.0, "beta": 0.2, "product": { "formula": "C16H32O2", "Yps": 0.6 } }, "initial": { "X": 0.1, "S": 10.0, "V": 6.0 }, "oxygen": { "kLa": 2500.0, "Cstar": 6.7 }, "horizon": 14.0, "feasible": false, "refused": "yield-infeasible", "exceeds": [ "product-carbon", "product-electron" ], "integrated": false }, { "id": "negative-control-product-booked-as-biomass", "of": "batch-ethanol-like", "description": "Negative control: the ethanol-like case with the rates as specified but the product counted with biomass carbon and electrons in the accounting (model 2's bookkeeping); it must fail to close", "integrated": true, "worstCarbonClosure": 0.00932, "worstElectronClosure": 0.0564, "failsToClose": true } ] }