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Multiscale catalyst model for ammonia synthesis: coupling kinetics, diffusion and deactivation

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Abstract

This study introduces a multiscale model for ammonia synthesis catalysts that integrates intrinsic kinetics, intraparticle diffusion, and deactivation mechanisms, specifically water vapor self-poisoning and long-term aging. Extending the Temkin-Pyzhev kinetic framework, the model incorporates a size-dependent self-poisoning coefficient (γ(dp)), a time-dependent aging factor (af(t)), and a Thiele modulus-based effectiveness factor (η). Calibrated with experimental data, it accurately predicts nitrogen consumption rates (rN2) for catalyst particle sizes ranging from 0.6 to 9.0 mm and operational lifetimes of 2 to 5 years, with errors as low as 0.8% for larger particles. Unlike traditional models, this approach quantifies reduction-induced deactivation, which significantly impacts larger particles by markedly reducing activity. Implemented in MATLAB, the model provides a predictive tool for optimizing catalyst design and reactor performance under industrial conditions. By linking microkinetic, transport, and deactivation phenomena, this work enhances the efficiency and longevity of ammonia synthesis processes, both traditional and novel.

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Data availability

The author declares that the data supporting the findings of this study are available within the paper and its supplementary information files. Should any raw data files be needed in another format they are available from the corresponding author upon reasonable request. Source data are provided with this paper.

Abbreviations

CFD:

Computational fluid dynamic

A :

Pre-exponential factor, h−1

a i :

Activity, i = N2, H2, NH3

af(t) :

Time-dependent aging factor, dimensionless

C SM :

Stefan-Maxwell correction, dimensionless

D e :

Effective diffusivity, m2/h

dp :

Particle diameter, mm

E a :

Activation energy, J/mol

f i :

Fugacity, i = N2, H2, NH3

f i * :

Fugacity at reference state, i = N2, H2, NH3

k :

Rate constant, h−1

K a :

Equilibrium constant, dimensionless

P :

Pressure, atm

R :

Universal gas constant, J/mol/K

R p :

Pellet radius, m

r NH3 :

Intrinsic rate of ammonia formation, mol/m3s

r N2 :

Intrinsic rate of nitrogen consumption, mol/m3s

t :

Time, years

T :

Thermodynamic temperature, Kelvins

x :

Fractional conversion of N2,

α :

Constant

ε:

Catalyst porosity, dimensionless

γ(dp) :

Size-dependent self-poisoning coefficient, dimensionless

ϕ :

Thiele modulus, dimensionless

\(\Phi\) :

Fugacity coefficient, i = N2, H2, NH3

η :

Effectiveness factor, dimensionless

τ :

Tortuosity (labyrinth) factor, dimensionless

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Funding

The author has no relevant financial or non-financial interests to disclose. The author certifies that he has no affiliations with or involvement in any organization or entity with any financial interest or non-financial interest in the subject matter or materials discussed in this manuscript. The author has no financial or proprietary interests in any material discussed in this article.

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  1. KBR Inc. International Consulting, Dubai, UAE

    Nenad Zecevic

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  1. Nenad Zecevic
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Nenad Zecevic conceptualized the framework, performed the analysis, and wrote the manuscript.

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Correspondence to Nenad Zecevic.

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Zecevic, N. Multiscale catalyst model for ammonia synthesis: coupling kinetics, diffusion and deactivation. Reac Kinet Mech Cat 138, 3645–3664 (2025). https://doi.org/10.1007/s11144-025-02947-4

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