Batch Reactor (marimo notebook)

A self-contained walkthrough of Sobol global sensitivity analysis on a batch reactor running a first-order liquid-phase reaction $A\to B$. The rate constant $k(T,\mathrm{pH})$ combines an Arrhenius temperature dependence with a Hill-type pH saturation curve, and the inlet concentration $C_{A,0}$ feeds the mass balance directly. The mechanistic model is treated as already fitted — the example focuses on variance attribution, not estimation.

The notebook source lives at examples/batch_reactor_gsa.py. Run it interactively with uv run marimo edit examples/batch_reactor_gsa.py, or read the rendered output below.

What this example covers

• A three-input Sobol problem ($C_{A,0}$, $T$, $\mathrm{pH}$) defined with gsax.Problem.from_dict(...) and uniform marginals.
• A closed-form batch reactor start-up trajectory used as the model — the kind of cheap surrogate you would plug a fitted mechanistic predictor into.
• A single gsax.analyze(..., num_resamples=200, key=...) call to obtain $S_1$, $S_T$, $S_{ij}$ along with bootstrap 95 % confidence intervals.
• Three plots that read the indices off: steady-state bar chart with CI error bars, time-resolved $S_1(t)$ and $S_T(t)$ with shaded bootstrap envelopes, and a pairwise $S_{ij}$ heatmap.

See also

• Bootstrap Confidence Intervals for the bare-API version of the same bootstrap workflow on the Ishigami benchmark.
• Multi-Output & Time-Series for the shape rules used here when the output is (N, T, K).