Modeling and Simulation of Nitrogen Generation by Pressure Swing Adsorption for Power-to-Ammonia

John B. J{\o}rgensen; Lorenz T. Biegler; Marcus J. Schytt

arxiv: 2604.09053 · v1 · pith:ZKVLSYRWnew · submitted 2026-04-10 · 💻 cs.CE · cs.NA· math.DS· math.NA

Modeling and Simulation of Nitrogen Generation by Pressure Swing Adsorption for Power-to-Ammonia

Marcus J. Schytt , Lorenz T. Biegler , John B. J{\o}rgensen This is my paper

Pith reviewed 2026-05-10 17:18 UTC · model grok-4.3

classification 💻 cs.CE cs.NAmath.DSmath.NA

keywords pressure swing adsorptionnitrogen generationpower-to-ammoniadynamic modelingcyclic steady statefinite volume discretizationair separation

0 comments

The pith

A first-principles dynamic model establishes an extensible basis for simulating and optimizing pressure swing adsorption for nitrogen generation.

A machine-rendered reading of the paper's core claim, the machinery that carries it, and where it could break.

The paper develops a dynamic one-dimensional model for a PSA superstructure to generate nitrogen from air for use in power-to-ammonia systems. It formulates the process with multicomponent mass, energy, and momentum balances coupled to adsorption kinetics on carbon molecular sieves, using consistent thermodynamics. The PDAE system is discretized by finite volumes, integrated with implicit Runge-Kutta methods, and solved for cyclic steady states via shooting techniques in an efficient Julia implementation. Demonstrations on a two-bed cycle compare discretization choices, solution methods, and ideal versus real gas effects on purity and recovery. This open framework matters for advancing decentralized, flexible air separation where closed-source models prevail.

Core claim

The proposed framework establishes an extensible basis for PSA simulation and optimization by providing a first-principles, dynamic, one-dimensional model formulated with thermodynamically consistent equations of state, coupling multicomponent balances with kinetically limited adsorption, semi-discretized using finite volume methods, integrated with diagonally implicit Runge-Kutta methods, and solved for cyclic steady states via shooting-based methods.

What carries the argument

The one-dimensional PSA superstructure model consisting of coupled PDAEs for mass, energy, and momentum transport with adsorption kinetics, solved to cyclic steady state.

If this is right

The model permits quantitative assessment of how spatial and temporal discretization affect simulation accuracy and efficiency.
Predicted nitrogen purity and recovery differ under ideal gas versus real-gas thermodynamic assumptions.
Shooting methods provide an effective way to reach cyclic steady states for repeated cycle simulations.
The Julia implementation with analytical derivatives and sparse solvers supports extension to optimization problems.

Where Pith is reading between the lines

These are editorial extensions of the paper, not claims the author makes directly.

Linking this PSA model to variable renewable power inputs could help design responsive P2A plants.
Adding experimental calibration data would strengthen the model's predictive power for industrial applications.
The approach could be adapted to simulate PSA for other gas separations or adsorbents in energy systems.

Load-bearing premise

The kinetically limited adsorption kinetics, one-dimensional flow assumptions, and numerical methods for cyclic steady state accurately represent real industrial PSA units.

What would settle it

Experimental measurements of nitrogen purity and recovery from a laboratory or industrial two-bed PSA air separation unit under known operating conditions could be compared directly to the model's predictions.

Figures

Figures reproduced from arXiv: 2604.09053 by John B. J{\o}rgensen, Lorenz T. Biegler, Marcus J. Schytt.

**Figure 1.** Figure 1: Diagram of the two-bed PSA superstructure. PSA SUPERSTRUCTURE The PSA process is simulated by periodically sequencing a set of operating steps (pressurization, adsorption, blowdown, desorption, purge, and pressure equalization) across multiple adsorption beds. In a conventional two-bed PSA configuration, the operating steps are symmetric and may be divided into two complementary half-cycles: an adsorpt… view at source ↗

**Figure 2.** Figure 2: Diagram of the 8-step PSA cycle [PITH_FULL_IMAGE:figures/full_fig_p007_2.png] view at source ↗

**Figure 3.** Figure 3: Fraction profiles throughout the 8-step PSA cycle at CSS (top: mobile, bottom: stationary) [PITH_FULL_IMAGE:figures/full_fig_p008_3.png] view at source ↗

read the original abstract

Power-to-ammonia (P2A) provides a carbon-free alternative to conventional ammonia production by replacing fossil-based feedstocks with electrolytic hydrogen and nitrogen from air separation. For decentralized P2A systems, pressure swing adsorption (PSA) offers a flexible alternative to cryogenic air separation. However, its industrial implementations are largely proprietary, and open, first-principles models capable of simulating its cyclic, nonlinear transport are scarce in literature. This work presents a first-principles, dynamic, one-dimensional model of a PSA superstructure for nitrogen generation, formulated with thermodynamically consistent equations of state, coupling multicomponent mass, energy, and momentum balances with kinetically limited adsorption on carbon molecular sieves. The resulting system of partial differential-algebraic equations (PDAEs) is semi-discretized using the finite volume method, integrated using diagonally implicit Runge-Kutta methods, and cyclic steady states (CSS) are computed via shooting-based solution methods. The framework is implemented in Julia, combining analytical derivatives with automatic differentiation and utilizing sparse linear algebra for efficient solution of the arising large nonlinear systems. The framework is demonstrated on a two-bed PSA cycle for air separation, comparing spatial and temporal discretization strategies, CSS solution methods, and the effects of ideal versus real-gas thermodynamics on predicted nitrogen purity and recovery. The proposed framework establishes an extensible basis for PSA simulation and optimization.

Editorial analysis

A structured set of objections, weighed in public.

Desk editor's note, referee report, simulated authors' rebuttal, and a circularity audit. Tearing a paper down is the easy half of reading it; the pith above is the substance, this is the friction.

Desk Editor's Note private letter to a colleague

This paper supplies a practical open Julia implementation of a first-principles 1D PSA nitrogen model with solid numerical comparisons, but stops short of any experimental checks.

read the letter

The core contribution is an open, first-principles dynamic model for pressure swing adsorption nitrogen generation aimed at decentralized power-to-ammonia. It fills a stated gap by giving a full PDAE formulation, finite-volume discretization, DIRK integration, and shooting method for cyclic steady state, all coded in Julia with automatic differentiation and sparse solvers. The demonstration on a two-bed air-separation cycle includes direct comparisons of spatial and temporal grids, solver choices, and ideal versus real-gas thermodynamics on purity and recovery. That package of details is what makes the work usable right away for people who need a starting simulation platform rather than another closed proprietary tool. The equations follow standard multicomponent balances with kinetically limited adsorption on carbon molecular sieves and consistent equations of state, so the setup itself is thermodynamically coherent and the numerical approach is conventional but well executed. The code choices for efficiency are sensible and documented. The main limitation is the complete absence of experimental validation. No measured purity, recovery, or breakthrough curves are shown, so it is impossible to judge how well the 1D assumptions and chosen kinetics reproduce real industrial behavior. The paper's own claim is modest—it only says the framework forms an extensible basis for simulation and optimization—so the missing validation does not break the stated contribution, but it does limit immediate use for design or scale-up. Readers who already work with PSA models or need an open Julia code base for P2A process studies will get the most out of it. Modelers looking for a reproducible starting point with method comparisons will find it worthwhile. I would send this to peer review. The implementation and numerical work are concrete enough to merit referee attention, even though revisions will probably request at least some benchmark data or sensitivity checks against literature measurements.

Referee Report

0 major / 3 minor

Summary. The manuscript presents a first-principles dynamic one-dimensional model for pressure swing adsorption (PSA) in nitrogen generation for power-to-ammonia applications. The model consists of thermodynamically consistent PDAEs coupling multicomponent mass, energy, and momentum balances with kinetically limited adsorption kinetics on carbon molecular sieves. The PDAEs are semi-discretized using the finite volume method, time-integrated with diagonally implicit Runge-Kutta schemes, and cyclic steady states are computed using shooting methods. The implementation in Julia utilizes automatic differentiation and sparse linear algebra. The framework is demonstrated through simulations of a two-bed air separation PSA cycle, with comparisons of spatial and temporal discretizations, CSS solution methods, and ideal versus real-gas thermodynamics on nitrogen purity and recovery. The central claim is that this provides an extensible basis for PSA simulation and optimization.

Significance. This work provides an open, reproducible computational framework for modeling PSA processes, which is significant given the proprietary nature of industrial PSA implementations and the need for flexible air separation in decentralized power-to-ammonia systems. The use of first-principles balances, advanced numerical methods (FVM, DIRK, shooting for CSS), and modern software tools (Julia with AD) allows for efficient simulation and potential optimization. The comparisons between discretization strategies and thermodynamic models offer insights into modeling choices. If the implementation is as described, it can serve as a foundation for further research in carbon-free ammonia production.

minor comments (3)

[Abstract] Abstract: the description of the demonstration cycle would be strengthened by briefly noting the specific PSA steps (pressurization, adsorption, blowdown, purge) employed in the two-bed example.
[Results] Results section (around discretization comparisons): the reported differences in purity and recovery between ideal-gas and real-gas cases should be accompanied by the actual numerical values (e.g., % purity, % recovery) rather than qualitative statements only.
[Numerical Methods] Implementation description: while the combination of analytical derivatives, AD, and sparse solvers is noted, a short statement on the observed wall-clock times or iteration counts for reaching CSS would help readers assess practical efficiency.

Simulated Author's Rebuttal

0 responses · 0 unresolved

We thank the referee for their positive assessment of the manuscript, including the recognition of its significance for open PSA modeling in power-to-ammonia systems and the recommendation for minor revision. No specific major comments were raised in the report.

Circularity Check

0 steps flagged

No significant circularity in derivation chain

full rationale

The paper constructs a first-principles PDAE model from multicomponent mass/energy/momentum balances with kinetically limited adsorption on carbon molecular sieves, using standard finite-volume semi-discretization, DIRK integration, and shooting-based CSS computation. The Julia implementation with AD and sparse solvers is presented directly; the two-bed air-separation demonstration compares discretization strategies, CSS methods, and ideal vs. real-gas thermodynamics as direct model outputs. No load-bearing steps reduce by construction to fitted inputs, self-citations, or ansatzes; the extensible-basis claim follows from the explicit construction without circular reduction.

Axiom & Free-Parameter Ledger

0 free parameters · 2 axioms · 0 invented entities

The framework rests on standard physical balances and numerical techniques; no new free parameters or invented entities are introduced in the abstract description.

axioms (2)

standard math Thermodynamically consistent equations of state for real-gas behavior
Invoked for coupling with mass, energy, and momentum balances in the PDAE system.
domain assumption Kinetically limited adsorption on carbon molecular sieves
Core assumption for the multicomponent adsorption dynamics in the nitrogen generation model.

pith-pipeline@v0.9.0 · 5554 in / 1274 out tokens · 58557 ms · 2026-05-10T17:18:06.218289+00:00 · methodology

discussion (0)

Reference graph

Works this paper leans on

6 extracted references · 6 canonical work pages

[1]

Clean Ammonia Roadmap

Noordende HV, Tubben G, Rouwenhorst KH, Fruytier M. Clean Ammonia Roadmap. ISPT (2024)

work page 2024
[2]

Pressure swing adsorption processes to purify oxygen using a carbon molecular sieve

Jee JG, Kim MB, Lee CH. Pressure swing adsorption processes to purify oxygen using a carbon molecular sieve. Chem. Eng. Sci. 60:869- 882 (2005)

work page 2005
[3]

Large-scale optimization strategies for pressure swing adsorption cycle synthesis

Dowling AW, Vetukuri SRR, Biegler LT. Large-scale optimization strategies for pressure swing adsorption cycle synthesis. AIChE J. 58:3777-3791 (2012)

work page 2012
[4]

Numerical Methods for Conservation Laws

Hesthaven JS. Numerical Methods for Conservation Laws. SIAM (2018)

work page 2018
[5]

Diagonally Implicit Runge-Kutta Methods for Ordinary Differential Equations: A Review

Kennedy CA, Carpenter MH. Diagonally Implicit Runge-Kutta Methods for Ordinary Differential Equations: A Review. NASA (2016)

work page 2016
[6]

Clapeyron.jl: An extensible, open-source fluid thermodynamics toolkit

Walker PJ, Yew HW, Riedemann A. Clapeyron.jl: An extensible, open-source fluid thermodynamics toolkit. Ind. Eng. Chem. Res. 61:6010-6027 (2022). © 2026 by the authors. Licensed to PSEcommunity.org and PSE Press. This is an open access article under the creative com- mons CC-BY-SA licensing terms. Credit must be given to creator and adaptations must be sha...

work page 2022

[1] [1]

Clean Ammonia Roadmap

Noordende HV, Tubben G, Rouwenhorst KH, Fruytier M. Clean Ammonia Roadmap. ISPT (2024)

work page 2024

[2] [2]

Pressure swing adsorption processes to purify oxygen using a carbon molecular sieve

Jee JG, Kim MB, Lee CH. Pressure swing adsorption processes to purify oxygen using a carbon molecular sieve. Chem. Eng. Sci. 60:869- 882 (2005)

work page 2005

[3] [3]

Large-scale optimization strategies for pressure swing adsorption cycle synthesis

Dowling AW, Vetukuri SRR, Biegler LT. Large-scale optimization strategies for pressure swing adsorption cycle synthesis. AIChE J. 58:3777-3791 (2012)

work page 2012

[4] [4]

Numerical Methods for Conservation Laws

Hesthaven JS. Numerical Methods for Conservation Laws. SIAM (2018)

work page 2018

[5] [5]

Diagonally Implicit Runge-Kutta Methods for Ordinary Differential Equations: A Review

Kennedy CA, Carpenter MH. Diagonally Implicit Runge-Kutta Methods for Ordinary Differential Equations: A Review. NASA (2016)

work page 2016

[6] [6]

Clapeyron.jl: An extensible, open-source fluid thermodynamics toolkit

Walker PJ, Yew HW, Riedemann A. Clapeyron.jl: An extensible, open-source fluid thermodynamics toolkit. Ind. Eng. Chem. Res. 61:6010-6027 (2022). © 2026 by the authors. Licensed to PSEcommunity.org and PSE Press. This is an open access article under the creative com- mons CC-BY-SA licensing terms. Credit must be given to creator and adaptations must be sha...

work page 2022