Industry: Biotech Product: ModelRisk Application: Bioreactor Design
A monoclonal-antibody process that produces 5.06 g/L on the bench is signed off for a 2,000 L production vessel on exactly that number. The deterministic plug-in — nominal viable-cell integral times nominal cell-specific productivity — says the campaign clears its 4.0 g/L release spec with room to spare. Then the first commercial campaign runs, and nearly a third of batches come back below spec. The number was never wrong; it was just one point in a distribution the design review never drew.
A biopharma manufacturer rebuilt the scale-up case in ModelRisk before committing the capital. The question was not "what titer does the process make" but "what is the distribution of harvest titer at 2,000 L, and how often does a batch fall through the 4.0 g/L floor once oxygen transfer, seed-train quality and cell-line variability all move at once." The simulation's first output is the headline the bench number hides: a titer distribution that straddles the spec rather than clearing it.
The deterministic plug-in lands at 5.06 g/L before the oxygen-transfer de-rate, and a nominal-case 4.57 g/L after it. But the simulated mean is 4.72 g/L with a P10 of 3.33 and a P90 of 6.41 — and 30.9% of batches finish below the 4.0 g/L spec floor. A facility planned against the point estimate is planning against a release rate it will never see.
Harvest titer is the product of three things that each carry real variability, and one scale-up penalty that the bench never sees:
Each of 200,000 simulated batches draws one value of each input and computes titer as IVCC × qP de-rated by the oxygen supply-to-demand ratio. The mean of that distribution sits below the deterministic plug-in because the de-rate bites hardest in the very batches where biomass is highest.
Because the de-rate is driven by kLa, the vessel's oxygen-transfer capacity directly buys batch-success probability. Sweeping the design kLa shows the trade clearly:
At the baseline vessel (kLa mode 230 1/h), 76% of batches meet spec — 37 of the 48-batch annual campaign. An upgraded impeller-and-sparger package (kLa mode 280) lifts that to 76%+, and across the full campaign the upgrade returns roughly 3 extra in-spec batches per year. At GBP 1.85M gross value per in-spec 2,000 L batch, that is about GBP 5M a year — the kind of number that decides whether a capital upgrade clears its hurdle rate.
Ranking the inputs by their P10-to-P90 swing on mean titer shows where the spread is born:
Cell-specific productivity (qP) and run quality dominate, each moving mean titer by roughly ±1.1 g/L across their plausible range; the viable-cell integral is second-tier at about ±0.5 g/L. Oxygen transfer kLa moves the mean by ±0.3 g/L — smaller than the biology, but unlike the biology it is something engineering can buy outright. The tornado tells the team that media and seed-train control attack the largest variance, while the kLa upgrade is the cleanest lever they fully own.
The per-batch failure probability compounds into the metric the plant actually plans on — in-spec batches delivered per campaign:
The baseline vessel delivers a mean of 33.6 in-spec batches (P10 of 29) against a 48-batch campaign; the upgraded oxygen-transfer package raises that to a mean of 36.3 (P10 of 32). The probability of delivering at least 36 in-spec batches rises from 29% to 61% — a capacity-planning swing that a single titer number cannot express.
A bench titer is a measurement; a scale-up commitment is a distribution. The ModelRisk model replaces "5 g/L, ships fine" with "4.72 g/L mean, 31% of batches below spec, and GBP 5M a year recoverable by buying oxygen transfer" — a set of numbers the design review can actually act on.