RePlaChem: Plasma Mechanism Reduction Tool

• The paper introduces RePlaChem, an open-source Fortran 90 library that automates the reduction of detailed plasma chemical mechanisms via DRGEP.
• It processes ZDPlasKin formatted mechanisms with simulation-derived reaction rates, using Dijkstra’s algorithm to generate a skeletal mechanism for direct reuse.
• The analysis demonstrates significant simulation speedups with controlled error metrics, while noting sensitivity to operating conditions and target species selection.

Searching arXiv for the RePlaChem paper and closely related mechanism-reduction work to ground the article in current literature. RePlaChem is an open-source Fortran 90 library for dimensionality reduction of plasma chemical mechanisms. It takes a detailed plasma chemical mechanism in ZDPlasKin format together with simulation-derived reaction rates, applies Directed Relation Graph with Error Propagation (DRGEP), and automatically generates a skeletal chemical mechanism that is again written in ZDPlasKin format, enabling direct reuse in solvers such as ZDPlasKin. Its stated purposes are to automate the reduction of large plasma mechanisms, accelerate otherwise computationally expensive numerical simulations, and provide an analysis tool for identifying dominant species and associated reactions under user-selected targets and operating conditions (Nikolaou et al., 6 Jul 2025).

1. Scope and problem setting

RePlaChem is tailored to plasma chemical kinetics, where detailed mechanisms often contain tens to hundreds of species and hundreds to thousands of reactions. In the description associated with the software, solving such stiff ODE systems typically requires very small time steps because of widely differing time scales among electrons, ions, radicals, neutrals, and excited states. The stated motivation is therefore species reduction: CPU cost is noted to scale roughly with the square of the number of species, so reducing the species count is a primary lever for tractability.

The library is organized around a detailed-to-skeletal transformation. The detailed mechanism is preserved as an explicit subset mechanism rather than being replaced by a black-box surrogate. In that sense, RePlaChem is species-oriented rather than purely reaction-lumping. The skeletal mechanism retains the same functional form as the original and can be passed back to the same plasma-chemistry workflow.

The software is also positioned as a gap-filling tool. The description states that there are many plasma solvers but almost no open, automated reduction libraries that produce mechanisms in formats used in the plasma community. A plausible implication is that RePlaChem is intended not only as a reduction backend but also as interoperability infrastructure for existing plasma-kinetics workflows.

2. Mechanism representation, required inputs, and generated outputs

RePlaChem reads a detailed plasma chemical mechanism in ZDPlasKin text format. The mechanism contains the full list of species, including ground-state species, ions, radicals, excited states, vibrational states, and electrons, together with the full list of reactions written as forward reactions; reverse reactions must be explicitly provided. The generic reaction form is

$$R_i : \sum_{j=1}^{N_s} \nu'_{ij} M_j \Rightarrow \sum_{j=1}^{N_s} \nu''_{ij} M_j .$$

The required inputs comprise three components. First, the mechanism file itself, for example detailedChemistry.txt. Second, time-resolved reaction-rate data $\dot{w}_i(t)$ for each reaction and plasma state, generated by solving a canonical problem such as a 0D pulsed discharge using ZDPlasKin. These rates are written in a specific binary Fortran format expected by RePlaChem. The provided helper module pcmo.f90, located in the utils/ directory, is intended to be included into the ZDPlasKin main.f90 so that rates are written in the correct format. Third, a reduction control file specifies the name of the detailed mechanism, the number of reaction-rate datasets and data points, the target species indices, and the acceptance thresholds for each target.

The output is a skeletal chemical mechanism in ZDPlasKin format. The skeletal species set $S^{\text{skel}}$ is a subset of the original species, and the skeletal reaction set $R^{\text{skel}}$ contains only reactions whose participants all belong to $S^{\text{skel}}$:

$$R^{\text{skel}} = \left\{ R_i \;\middle|\; M_{ij} \in S^{\text{skel}} \ \forall j \in \{1,\dots,N_s^i\} \right\}.$$

RePlaChem also produces an output directory containing the new mechanism file, a log of the reduction process, and a summary.txt file. According to the software description, summary.txt reports the number of species and reactions before and after reduction and, for each target, the dependency set size and a ranking of species by importance through the Overall Interaction Coefficient (OIC).

3. DRGEP formulation and reduction criterion

The reduction engine is DRGEP, a graph-based method originally developed for combustion and atmospheric chemistry and adapted here to plasma mechanisms. RePlaChem itself does not integrate ODEs; instead, it consumes reaction rates produced by a canonical solver. For each reaction $i$, the reaction rate is

$$\dot{w}_i = k_i \prod_{j=1}^{N_s} [M_j]^{\nu'_{ij}},$$

where $k_i$ is the forward rate coefficient and $[M_j]$ is the concentration of species $\dot{w}_i(t)$0. The net production rate of a target species $\dot{w}_i(t)$1 from reaction $\dot{w}_i(t)$2 is

$\dot{w}_i(t)$3

Total production and consumption rates are then defined as

$\dot{w}_i(t)$4

The modified Direct Interaction Coefficient (DIC) between target species $\dot{w}_i(t)$5 and another species $\dot{w}_i(t)$6 is

$\dot{w}_i(t)$7

with $\dot{w}_i(t)$8 if species $\dot{w}_i(t)$9 appears in reaction $S^{\text{skel}}$0 and $S^{\text{skel}}$1 otherwise. The description states that $S^{\text{skel}}$2, that larger $S^{\text{skel}}$3 indicates greater importance of $S^{\text{skel}}$4 for the production or consumption of $S^{\text{skel}}$5, and that RePlaChem uses the maximum DIC over all datasets to remain conservative.

Influence propagation is then handled through reaction chains. For a path

$S^{\text{skel}}$6

the Path Interaction Coefficient (PIC) is

$S^{\text{skel}}$7

and the Overall Interaction Coefficient (OIC) is the maximum over all paths,

$S^{\text{skel}}$8

The description states that RePlaChem uses Dijkstra’s algorithm to identify this strongest path in the weighted directed graph. Given an acceptance threshold $S^{\text{skel}}$9, the dependency set for target $R^{\text{skel}}$0 is

$R^{\text{skel}}$1

For multiple targets, the skeletal species set is the union of the dependency sets,

$R^{\text{skel}}$2

The threshold controls aggressiveness directly: higher $R^{\text{skel}}$3 yields fewer retained species and a smaller mechanism, with larger potential error; lower $R^{\text{skel}}$4 yields a more conservative reduction.

4. Software implementation and workflow with ZDPlasKin

The implementation is in Fortran 90 and has no external dependencies. It is organized into modules that parse the ZDPlasKin mechanism, load reaction-rate data, compute DICs, PICs, and OICs using Dijkstra’s algorithm, build dependency sets, construct the skeletal mechanism, and write output files and summaries (Nikolaou et al., 6 Jul 2025).

The operational workflow is explicitly solver-coupled. A canonical ZDPlasKin simulation is first run with the detailed mechanism. In that simulation, the user includes pcmo.f90 into main.f90 so that the time loop writes the reaction rates $R^{\text{skel}}$5 to the binary format expected by RePlaChem. RePlaChem is then run on the detailed mechanism, the rate data, and the control file. The generated skeletal mechanism can replace detailedChemistry.txt in the original ZDPlasKin project, after which simulations are rerun with the reduced chemistry.

User-visible configuration is limited to a small set of controls: the mechanism filename, the number of reaction-rate datasets, the number of data points, the list of target species indices, and the acceptance threshold for each target species. This suggests that the library’s interface is intentionally narrow, with most of the methodological complexity concentrated in the DRGEP machinery rather than in runtime configuration.

The associated repository is given as https://github.com/znikolaou/RePlaChem.git. The description further states that the examples/ directory contains a full working example, example reaction-rate data binary files, and an example control file, and presents the command form ./RePlaChem < control.in as an example of invocation.

5. Methane–hydrogen plasma validation case

The validation case is a methane–hydrogen plasma chemical mechanism with 77 species and 4404 reactions, described as representative of nanosecond pulsed discharge plasmas used for methane reforming. The canonical model is a 0D constant-volume reactor implemented in ZDPlasKin. The nanosecond power pulse has peak power density $R^{\text{skel}}$6 and pulse width $R^{\text{skel}}$7. The initial conditions are electron density $R^{\text{skel}}$8, gas temperature $R^{\text{skel}}$9, and pressure $S^{\text{skel}}$0.

The model accounts for electron-impact ionization, dissociation, excitation, heavy-particle chemistry, gas heating, and heat exchange with the environment. The species balance is written as

$S^{\text{skel}}$1

the reduced electric field is given through the Joule relation

$S^{\text{skel}}$2

and the gas temperature follows the energy balance

$S^{\text{skel}}$3

with

$S^{\text{skel}}$4

The 77 species comprise 18 charged species, 19 excited molecules, and 40 radicals and stable molecules. The reduction uses 738 time points from the nanosecond pulsed discharge simulation. The targets are 9 species: $S^{\text{skel}}$5, $S^{\text{skel}}$6, $S^{\text{skel}}$7, $S^{\text{skel}}$8, and $S^{\text{skel}}$9, while the threshold $$R^{\text{skel}} = \left\{ R_i \;\middle|\; M_{ij} \in S^{\text{skel}} \ \forall j \in \{1,\dots,N_s^i\} \right\}.$$0 is scanned from 0 to 0.8 to generate a family of skeletal mechanisms (Nikolaou et al., 6 Jul 2025).

6. Error metrics, reduction outcomes, interpretation, and limitations

Accuracy is assessed through the local error for a target species $$R^{\text{skel}} = \left\{ R_i \;\middle|\; M_{ij} \in S^{\text{skel}} \ \forall j \in \{1,\dots,N_s^i\} \right\}.$$1,

$$R^{\text{skel}} = \left\{ R_i \;\middle|\; M_{ij} \in S^{\text{skel}} \ \forall j \in \{1,\dots,N_s^i\} \right\}.$$2

and the mean maximum error over targets,

$$R^{\text{skel}} = \left\{ R_i \;\middle|\; M_{ij} \in S^{\text{skel}} \ \forall j \in \{1,\dots,N_s^i\} \right\}.$$3

The reported trend is monotonic in the expected direction: as the acceptance threshold increases, the numbers of species and reactions decrease, while $$R^{\text{skel}} = \left\{ R_i \;\middle|\; M_{ij} \in S^{\text{skel}} \ \forall j \in \{1,\dots,N_s^i\} \right\}.$$4 increases. A reduced mechanism with about 32 species and 838 reactions achieves a species reduction factor of approximately 2.4 from 77, a reaction reduction factor of approximately 5.3 from 4404, and $$R^{\text{skel}} = \left\{ R_i \;\middle|\; M_{ij} \in S^{\text{skel}} \ \forall j \in \{1,\dots,N_s^i\} \right\}.$$5. A second reduced mechanism with 20 species and 442 reactions yields $$R^{\text{skel}} = \left\{ R_i \;\middle|\; M_{ij} \in S^{\text{skel}} \ \forall j \in \{1,\dots,N_s^i\} \right\}.$$6.

The two explicit skeletal mechanisms are denoted Skeletal A and Skeletal B. Skeletal A contains 32 species and 838 reactions with $$R^{\text{skel}} = \left\{ R_i \;\middle|\; M_{ij} \in S^{\text{skel}} \ \forall j \in \{1,\dots,N_s^i\} \right\}.$$7. Its retained species include electrons, major neutral fragments, major C$$R^{\text{skel}} = \left\{ R_i \;\middle|\; M_{ij} \in S^{\text{skel}} \ \forall j \in \{1,\dots,N_s^i\} \right\}.$$8 hydrocarbons, selected C$$R^{\text{skel}} = \left\{ R_i \;\middle|\; M_{ij} \in S^{\text{skel}} \ \forall j \in \{1,\dots,N_s^i\} \right\}.$$9/C$i$0 intermediates, key ions, and vibrationally excited states $i$1 and $i$2. Skeletal B contains 20 species and 442 reactions with $i$3, retaining a narrower set and dropping various C$i$4 ions and heavier hydrocarbons that are described as important mainly in later afterglow stages. The associated performance figures are a speedup factor of approximately 2.0 for Skeletal A and approximately 3.1 for Skeletal B.

The analysis functionality is emphasized alongside reduction. For the electron target, the dominant species ranking begins with $i$5 and then $i$6. For acceptance threshold $i$7, 29 species are retained for the electron target, down to $i$8. The description interprets this as showing that dominant pathways for electron dynamics proceed through electron–cation chemistry, while dominant heavy-particle pathways for methane conversion involve $i$9, $$\dot{w}_i = k_i \prod_{j=1}^{N_s} [M_j]^{\nu'_{ij}},$$0, $$\dot{w}_i = k_i \prod_{j=1}^{N_s} [M_j]^{\nu'_{ij}},$$1, and certain C$$\dot{w}_i = k_i \prod_{j=1}^{N_s} [M_j]^{\nu'_{ij}},$$2/C$$\dot{w}_i = k_i \prod_{j=1}^{N_s} [M_j]^{\nu'_{ij}},$$3 intermediates. It also notes that vibrationally excited states remain crucial across reduced sets.

The stated limitations are conditional dependence on operating conditions, dependence on the target set, and the fact that the principal error metric directly controls only target-species number densities. The method is described as general for any plasma mechanism expressible in ZDPlasKin format, but optimality can degrade if operating conditions are changed strongly, which motivates using multiple datasets or regenerating the skeletal mechanism. In relation to other approaches, the description places DRGEP alongside sensitivity analysis, QSSA, CSP, ILDM, PCA-based reductions, and reaction pathway analysis, while emphasizing that RePlaChem produces a directly usable subset mechanism in a plasma-community format.