Supercritical hydrogen-yielding cracking of hydrocarbon feedstocks: variational thermodynamics, critical regimes, and the Gusev exergetic invariant

Supercritical hydrogen-yielding cracking of heavy hydrocarbon feedstocks exhibits universal critical regimes that fundamentally determine hydrogen production efficiency. A variational thermodynamic model is developed to describe these transitions. The model is based on the minimization of thermodynamic irreversibilities and leads to the Euler-Lagrange equation, from which the Gusev Exergetic Invariant emerges in its canonical form:

This invariant governs the transition between Low-H₂, Plateau, and High-H₂ regimes. The hydrogen-yield parameter acts as an order parameter, while the functional of irreversibilities becomes equivalent to a Landau-Ginzburg functional. Critical exponents β = 1/2, γ = 1, δ = 3 are derived and shown to be universal. A renormalization-group (RG) structure is established, revealing a critical fixed point corresponding to the plateau regime. The theory provides  a unified framework for optimizing hydrogen production in supercritical cracking reactors.

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