Industrial catalyst particles are often non-spherical, but resolved calculations of diffusion and reaction are too expensive for repeated use in reactor-scale simulations. This paper derives a contour-averaged one-dimensional particle model by averaging the multidimensional diffusion equation over level sets of a scalar coordinate s ( x ). Particle geometry is retained through the differential volume A ( s ) = d V / d s and metric factor γ ( s ) = 〈 | ∇ s | 2 〉 s . The methodology is demonstrated for one specific geometry, a hollow cylinder, comparing distance, Poisson, and principal-eigenfunction coordinates. The reduced models accurately reproduce two-dimensional reference calculations for transient diffusion, first-order effectiveness factors, and five-species steam methane reforming with Langmuir–Hinshelwood–Hougen–Watson kinetics and multicomponent transport up to the full dusty-gas model. Contour diagnostics expose the remaining local closure error. The closure proves robust and general: it applies unchanged across a wide range of diffusion models and across convex and concave particle shapes in two and three dimensions. Results for a large collection of shapes are provided as supplementary material. The accompanying open-source implementation constructs the reduced model for any shape specified by a signed-distance function and user-defined kinetics and diffusion models. Once A ( s ) and γ ( s ) have been precomputed, only a one-dimensional problem must be solved, providing a practical geometry-aware particle closure for reactor models.

