V-RX-02 — zero-order decay (exact burnout time)

Tags: kinetics, reaction_order, isothermal

References:

• Khawam & Flanagan (2006), J. Phys. Chem. B 110:17315

Problem statement

Khawam & Flanagan (2006) exact isothermal integrations (FDS verifies its part_baking_soda case against the same forms). Sub-cases:

a) n = 0 — linear decay, exact finite burnout time. Compared only up to 0.9·tb with the depletion limiter DISABLED: the solver clamps ξ ≥ 0 inside ξⁿ, so at ξ = 0 the n = 0 rate stays A and would integrate ξ negative (kinetics.jl `fastpow`). b) n = 2 — ThermaKin's second-order case as single-reactant n = 2: ξ = ξ₀/(1 + ξ₀kt). c) n = 2/3 — contracting-sphere R3 model with FDS's NaHCO₃ parameters Apub = 3.4e11 1/s, E = 103 kJ/mol at T = 450 K; the marker is m^(1/3) linear in t. d) n = 0 with the limiter ENABLED (default) — non-negativity guard: run to 2× burnout and require 0 ≤ ξ ≤ limiter threshold at the end. This is the case the limiter exists for.

UNIT CONVERSION (pitfall): solver rate is A·e^(−E/RT)·ξⁿ with ξ in kg/m³; published constants for normalized m = ξ/ξ₀ convert as Aours = kpub·ξ₀^(1−n) (see exact/kinetics.jl header). Applied below for sub-case c.

V-RX-02a — zero-order decay (exact burnout time)

Quantities of interest (n = 1)

Solver configuration

V-RX-02b — second-order decay (ThermaKin C+C analog)

Quantities of interest (n = 1)

Solver configuration

V-RX-02c — contracting-sphere R3 decay (FDS NaHCO₃, 450 K)

Quantities of interest (n = 1)

Comparison with other codes

The same case was solved with FDS 6.11.0 at 0D particle; decks, outputs, and run provenance are committed under test/verification/reference/. Each code's error against the same exact solution is drawn below on a log scale, muted gray behind this solver's series — the signed linear-scale panel above shows where the error lives, this one compares magnitudes across codes.

Wall times at every ladder rung against the reference runs. Resolutions and simulated spans differ where noted (details in reference/timings.csv), so cross-code timings are indicative rather than a controlled benchmark; rungs at a matched resolution are directly comparable.

Solution overlays including the other codes' points: xihistoriesvs_codes.

Solver configuration

V-RX-02d — zero-order decay, depletion limiter ON (guard)

limiter roll-off characterization

Quantities of interest (n = 1)

Solver configuration