V-RX-03 — competing parallel reactions with yield splits

Tags: kinetics, parallel_reactions, stoichiometry, energy

References:

• FDS Verification Guide matl_e_cons (energy-superposition analog)
• standard parallel first-order kinetics (exact)

Problem statement

Two reactions consume the same reactant A with different product splits and different heats of reaction (FDS matl_e_cons analog). Exact solution:

ξA = ξ₀·e^(−(k₁+k₂)t); converted mass splits k₁:k₂, scaled by yields: ξB = νB·(k₁/k)·(ξ₀−ξA), ξC = νC·(k₂/k)·(ξ₀−ξA), ξG = (γB·k₁ + γC·k₂)/k·(ξ₀−ξ_A), k = k₁+k₂, γ = gas yields

Verifies stoichiometric bookkeeping (two-product yields) and heat-release superposition. E = 0 keeps rates exactly T-independent, so the reaction heats (h₁ endothermic, h₂ exothermic — h > 0 endothermic in THIS code, opposite to Gpyro/ThermaKin/FDS) perturb only the temperature, not the species solution.

Heat-release superposition target: a single cell pinned by Dirichlet faces satisfies the DISCRETE quasi-steady balance exactly:

2·kcell·(Tbc − Tc)/(Δz/2) = −Q̇·Δz ⇒ Tc − Tbc = Q̇·Δz²/(4·kcell)

with Q̇ = −(h₁k₁ + h₂k₂)·ξ_A(t) the net volumetric source. Quasi-steady is valid because the cell diffusion time Δz²/α = 0.02 s ≪ 1/(k₁+k₂) = 2.2 s. The gas is retained (default ImpermeableBC, no Darcy/Fickian transport), so the system is closed and Σξ = ξ₀ throughout.

Quantities of interest (n = 1)

Solver configuration