Reaction kinetic model set library construction method taking CPD base as core layer mechanism

Abstract

The invention provides a reaction kinetic model set library construction method taking a CPD base as a core layer mechanism. The method comprises the steps of experimental data collection and preprocessing, core layer mechanism standardization, expansion layer fuel specificity mechanism and model integration and verification. According to the method, based on a hierarchical architecture of a core layer (CPD mechanism) and an extension layer (target fuel sub-mechanism), high precision and universality of the model are realized by integrating a pyrolysis oxidation experiment and quantum chemistry calculation. The method can predict the pyrolysis behavior of the fuel under multiple working conditions, clarify the generation mechanism of polycyclic aromatic hydrocarbons (PAHs), and provide a high-precision and extensible digital tool basis for aviation fuel design, pollutant control and combustion optimization.

Description

Technical Field

[0001] The present invention relates to the technical field of fuel reaction kinetics modeling, in particular to a method for constructing a reaction kinetics model library with a CPD-based core layer mechanism. Background Art

[0002] With the transformation of energy structure and stricter environmental protection regulations, the need to develop efficient and clean combustion technologies and accurately predict fuel reaction behaviors is becoming increasingly urgent. As the core tool for revealing the microscopic mechanisms of complex processes such as combustion and pyrolysis, the construction method of reaction kinetic models directly affects the optimization of combustion efficiency, pollutant control and the reliability of new fuel design. As a core component in the pyrolysis and oxidation process of condensed-ring fuels, 1,3-cyclopentadiene (CPD) has always been a research focus in the field of combustion chemistry. The conjugated double bond system in its molecular structure confers special reaction activity: on the one hand, it is the main intermediate generated by the pyrolysis of biomass fuels (such as lignin derivatives) and high-density cyclic hydrocarbon fuels (such as norbornane), and it dominates the fuel consumption path through free radical chain reactions; on the other hand, as a key precursor for the formation of polycyclic aromatic hydrocarbons (PAHs), the cyclization and fusion behavior of CPD is directly related to the nucleation and growth process of soot particles. However, traditional kinetic model construction methods face severe challenges in the characterization of CPD-related pathways:

[0003] The limitations of single mechanism models are prominent. Existing models are mostly developed for specific fuels (such as n-heptane and toluene), and it is difficult to uniformly describe the common CPD generation mechanism in biomass-derived mixtures or synthetic high-energy fuels (such as the significant difference between the oxygen addition ring opening of benzene and the rearrangement path of furan fuels). This leads to excessive errors in the prediction of CPD dynamic concentrations, which in turn affects the reliability of the PAHs generation path. In addition, multi-scale parameter integration is difficult. The microscopic parameters of quantum chemical calculations (such as the CPD generation energy barrier) lack a systematic correlation with macroscopic experimental data (such as laminar flame speed). Traditional single-scale optimization algorithms rely too much on empirical fitting and sacrifice physical interpretability. The above problems have seriously restricted the analysis of soot generation mechanisms and the development of clean combustion technologies. It is urgent to achieve multi-scale collaborative optimization and modular architecture innovation through the construction of a model library with CPD as the core mechanism, providing a technical foundation for high-precision digital tools. Summary of the Invention

[0004] The purpose of the present invention is to provide a method for constructing a collection of reaction kinetic model libraries with CPD as the core layer mechanism. By modularly integrating the core reaction pathways of CPD generation and consumption and combining it with a multi-scale kinetic parameter optimization algorithm, it achieves systematic simulation and prediction of the reaction networks of complex fuel systems (such as biomass-derived compounds, synthetic high-energy fuels, etc.).

[0005] In order to achieve the above-mentioned object of the invention, the present invention adopts a technical solution specifically as follows: the present invention provides a method for constructing a reaction kinetic model library with CPD as the core layer mechanism, comprising the following steps:

[0006] A modular hierarchical architecture is adopted to achieve mechanism universality expansion through a multi-scale parameter fusion algorithm of quantum chemical calculations and experimental data, which is characterized by including the following steps:

[0007] Step 1: Collect pyrolysis and oxidation experimental data of CPD precursor fuel under a wide range of operating conditions, including temperature, pressure, residence time, fuel conversion rate, C0-C5 small molecule products, and PAHs concentration distribution information, and perform data collation and normalization;

[0008] Step 2: Focusing on the CPD oxidation and pyrolysis reactions, we obtained the thermodynamic and kinetic parameters of key elementary reactions through quantum chemical calculations. Combining literature data with experimental verification, we constructed a CPD core sub-mechanism library covering the formation of C0-C5 small molecules and C6-C15 aromatics.

[0009] Step 3: Based on the core layer mechanism, the initial decomposition paths of different CPD precursor fuels are targeted, and fuel-specific sub-mechanisms are established through quantum chemical calculations, experimental data optimization, and mechanism reuse rules;

[0010] Step 4: Integrate the core layer mechanism and fuel-specific sub-mechanisms according to a modular architecture to form a model collection library, and verify and optimize the model through wide-operating experimental data, including sensitivity analysis and key reaction path adjustment, to improve prediction accuracy and generalization ability.

[0011] Preferably, the CPD precursor fuel includes benzene, norbornane and furan compounds.

[0012] Preferably, step 2 specifically includes:

[0013] (1) With CPD as the core, atmospheric pressure oxidation data were obtained through jet stirred reactor experiments, and pyrolysis product distribution was collected through wide-pressure flow tube experiments;

[0014] (2) Using quantum chemical calculations to obtain the key reaction paths of CPD;

[0015] (3) Based on quantum chemical calculations and experimental verification, a CPD sub-mechanism library covering the generation of C0-C5 small molecules and C6-C15 aromatic hydrocarbons was formed by integrating literature data.

[0016] Preferably, in step 3, the development of the fuel-specific sub-mechanism includes:

[0017] (1) Reveal the initial decomposition path of fuel through flow tube reactor experiments;

[0018] (2) Using quantum chemical calculations to obtain the dissociation energy of each fuel bond and the potential energy surface of free radical generation;

[0019] (3) Bimolecular reactions with clear potential barriers were calculated using traditional transition state theory (TST), and the pressure-dependent rate constants of barrier-free dissociation reactions were calculated using the RRKM-ME method;

[0020] (4) The core mechanism is directly called for the common pathway, and the specific pathway is modeled separately; the common pathway includes the generation of polycyclic aromatic hydrocarbons starting from CPD and its free radicals, and the specific pathway includes the initial ring opening, dehydrogenation, isomerization, and hydrogen extraction reactions of the fuel.

[0021] Preferably, in step three, the mechanism reuse rule is: when the fuel sub-mechanism involves intermediate products and free radicals that overlap with species in the core mechanism reaction path, directly call the parameters of the species in the core layer mechanism; and model the specific pathway separately.

[0022] Preferably, in step 4, the modular architecture uses the CPD core sub-mechanism as a unified bottom layer, links each fuel sub-mechanism as an extension layer, and implements hierarchical calling rules through Chemkin-Pro software, giving priority to reusing the core layer reaction path.

[0023] Preferably, in step 4, the experiment includes comparing the simulation results with the experimental product concentrations in various pyrolysis reactors such as flow tubes, shock tubes and jet stirred reactors, using sensitivity analysis to identify key reaction paths, and reducing the deviation between experimental data and simulation values by adjusting the pre-exponential factors of key chemical reactions.

[0024] Preferably, the hierarchical calling rules further include automatically matching the extended layer sub-mechanism based on the fuel type, and identifying the contribution rate of the CPD and CPDyl complex to the formation of polycyclic aromatic hydrocarbons through sensitivity analysis.

[0025] Beneficial Effects: The present invention constructs a collection of reaction kinetic models with CPD as the core mechanism. This collection has the following advantages and effects:

[0026] (1) High accuracy: This method uses a modular architecture and multi-scale parameter fusion algorithm, combined with quantum chemical calculations and experimental data, to accurately describe the pyrolysis behavior of fuels under different working conditions;

[0027] (2) Wide range of applications: This method adopts a hierarchical architecture of core layer + extension layer to realize the modular design of the model. The core layer mechanism uniformly describes the common reaction pathways of multiple fuels, and the extension layer separately models the fuel-specific pathways. The CPD core mechanism in the model collection library covers a variety of experimental devices and working conditions under normal pressure and high pressure conditions, which can meet the diverse needs in practical applications;

[0028] (3) Easy to use: The model collection library is stored and managed in a structured form, which is convenient for quick search and call in practical applications, thus improving work efficiency;

[0029] (4) Generalization capability: Through modular design, the CPD core mechanism serves as a unified bottom layer, linking each fuel sub-mechanism as an extension layer, reducing the workload of repeated modeling. The CPD core layer uniformly describes the commonalities of multi-fuel reactions, reducing the need for separate modeling for each fuel, and improving the generalization capability of the model. BRIEF DESCRIPTION OF THE DRAWINGS

[0030] The accompanying drawings are used to provide further understanding of the present invention and constitute a part of the specification. They are used to explain the present invention together with the embodiments of the present invention and do not constitute a limitation of the present invention.

[0031] Figure 1 An expanded relationship diagram of the core mechanism and fuel sub-mechanisms provided for this embodiment;

[0032] Figure 2 The reaction network diagram of the generation and consumption pathways of CPD in the precursor fuel;

[0033] Figure 3 Comparison curve between simulation and experiment for the mole fraction of CPD and PAHs generated in 2,5-dimethylfuran fuel (DMF);

[0034] Figure 4 Comparison graph between simulation and experiment for the mole fractions of CPD and PAHs generated in benzene fuel (PhH);

[0035] Figure 5 Comparison curve between simulation and experiment for the mole fractions of CPD and PAHs generated in norbornane fuel (NBA). DETAILED DESCRIPTION

[0036] In order to make the purpose, technical solutions and advantages of the present invention more clearly understood, the present invention will be further described in detail below in conjunction with the accompanying drawings and embodiments. Of course, the specific embodiments described herein are only used to explain the present invention and are not intended to limit the present invention.

[0037] Example 1: Taking the biomass-derived fuel 2,5-dimethylfuran (DMF) as an example to construct a CPD core model library, a method for constructing a reaction kinetic model library with CPD as the core layer mechanism is provided, and the specific steps are as follows:

[0038] Step 1: Experimental data collection: Collect pyrolysis data of 2,5-dimethylfuran on a flow tube experimental platform, with pressures of 30 and 760 Torr, temperatures of 500-1500 K, and residence times of 0.4-31.3 s.

[0039] Step 2: Core mechanism call:

[0040] As an aromatic hydrocarbon precursor, the pyrolysis of CPD drives the aromatization process through a free radical chain reaction network. Figure 2 As shown, the cycloaddition reaction initiated by resonance-stabilized CPDyl as a precursor is the main source of these PAHs. The thermal oxidation model of CPD is a secondary reaction mechanism of DMF, so the CPD sub-mechanism and its key aromatic hydrocarbon generation pathway (e.g., CPDyl→naphthalene) are reused.

[0041] Step 3: Target fuel sub-mechanism expansion:

[0042] The thermal decomposition pathway of 2,5-dimethylfuran (DMF) is mainly controlled by unimolecular decomposition reactions and free radical attack reactions. Here we focus on the formation pathway of its key product 1,3-cyclopentadiene (CPD) and the subsequent reaction network. Figure 2 As shown in the figure, there are two competing pathways for the ring-opening isomerization of DMF at high temperature: one is the formation of a 1,3-pentadiene radical intermediate via α-cleavage of the CO bond, followed by intramolecular cyclization to form CPD; the other is the formation of a phenol intermediate via 1,5-hydrogen migration, which is dominant at lower temperatures (<1000K);

[0043] At the density functional theory level of B3LYP / 6-311++G(d,p), the species involved in the above DMF pathway were subjected to geometry optimization, vibrational frequency calculation, and zero-point vibrational energy correction to obtain thermodynamic properties and reaction potential energy surfaces.

[0044] The single-point energies of the species involved were further obtained using a high-precision theoretical method (CCSD(T) / cc-pVTZ) for the calculation of their reaction rate constants;

[0045] Based on the results of quantum chemical calculations, the rate constant of the H-abstraction reaction was obtained using traditional transition state theory (TST) combined with Eckart tunneling correction.

[0046] The microcanonical rate constants for the barrier-free dissociation reaction rely on theoretically calculated equilibrium constants and the high-pressure limit (HPL) rate constants for the association reaction, which are derived using the inverse Laplace transform (ILT) in the MESMER code.

[0047] During the calculation, argon was selected as the bath gas, and the interaction between the reactants and the bath gas Ar was modeled by the Lennard-Jones (LJ) potential. The LJ parameters of Ar were estimated to be σ = 3.465 =, ε = 113.5 K, DMF σ = 5.943 =, ε = 445.1 K, and the collision energy transfer was treated using a single-parameter exponential decline model: < ΔE下 >=300(T / 300) 0.85 ;

[0048] The transport data were estimated using the Benson group summation method with the RMG program.

[0049] Step 4: Simulation and verification:

[0050] The simulation study was carried out using the PFR module in Chemkin-Pro software. Some simulation results are shown in the figure below. Figure 3 As shown, the main reaction pathways for the decomposition of DMF at 30 and 760 Torr were found to be very similar.

[0051] like Figure 2 It shows that the R1C6H7O radical is completely consumed by the ring-opening reaction to generate the R2C6H7O radical. The R2C6H7O radical further undergoes an intramolecular 1,5-hydrogen transfer reaction to generate the R3C6H7O radical. The R3C6H7O radical can undergo two branched isomerization pathways to generate R4C6H7O and R5C6H7O radicals, of which the pathway to generate R4C6H7O is dominant at both 30Torr and 760Torr. The R4C6H7O radical has three decomposition pathways, ultimately generating phenol (C6H5OH) and cyclopentadiene (C5H6). The simulation results of their mole fractions are consistent with the experimental results as shown in Figure 2. Figure 3 As shown in Figure 2, it can be seen that under the two pressure conditions, the simulation results are consistent with the experimental results.

[0052] In addition to the decomposition products, the experimental and simulation results for a series of aromatic hydrocarbons are also consistent, including benzene (C6H6), toluene (C6H5CH3), styrene (C6H5C2H3), indene (C9H8), naphthalene (C 10 H8). Based on reaction rate analysis (ROP): Under 30Torr and 760Torr conditions, the formation of benzene (C6H6) is mainly controlled by the H atom substitution reaction of C6H5OH and the self-reaction of C3H3 free radicals. The formation of toluene (C6H5CH3) is mainly controlled by the CH3 free radical substitution of C6H5OH and the C3H3+C4H6 reaction at both pressures. The concentration of styrene (C6H5C2H3) is second only to benzene and toluene, and its dominant pathway is: C5H5+C3H3 combination reaction. The formation of indene (C9H8) is mainly controlled by the C5H5+C5H6 reaction. Naphthalene (C 10 The formation of H8) depends on C5H5 self-association.

[0053] Example 2: Taking aromatic fuel benzene (C6H6) as an example to construct a CPD core model collection library, the specific steps are:

[0054] Step 1: Experimental data collection;

[0055] Experimental data on the oxidation of benzene (C6H6) in a jet stirred reactor (JSR) were collected. The experimental conditions were pressure: 1 atm, temperature: 900-1350 K, residence time: 0.07 s, and equivalence ratio: 1.0.

[0056] Step 2: core mechanism call;

[0057] Figure 2 The reaction network analysis showed that there are two main pathways for benzene to generate CPD. One is the same pathway as DMF, which is obtained from phenol, and the other is obtained from CPDyl. Therefore, the rate constants of these two pathways and the thermal oxidation mechanism of CPD are reused.

[0058] Step 3: Target fuel sub-mechanism expansion;

[0059] Density functional theory (DFT) at the B3LYP / 6-311++G(d,p) level of theory was used to perform single-reference calculations of the stationary point structures, vibrational frequencies, and zero-point energies (ZPEs) on the C₆H₅O₂ potential energy surface (PES). All optimized local minima exhibited no imaginary frequencies, while the transition state (TS) stationary point exhibited only a single imaginary frequency. The reaction pathway was verified using intrinsic reaction coordinate calculations.

[0060] The microcanonical rate constants of each transition state were calculated based on the RRKM theory. For bimolecular reactions with well-defined potential barriers, conventional transition state theory (TST) was used. The density of states of the TS was treated using a rigid rotor resonator approximation, the partition function was treated using a hindered rotor approximation for the inner rotor, and the tunneling effect was corrected using the Eckart correction.

[0061] The temperature-pressure dependent rate constants were evaluated using a one-dimensional master equation (ME) method, with parameters taken from studies on the C6H5C2H2 / Ar system.

[0062] Thermodynamic and transport data were estimated using the Benson group addition method with the RMG program.

[0063] Step 4: Simulation and verification;

[0064] The simulation study was carried out using the PSR module in Chemkin-Pro software. The simulation results showed that the benzene oxidation model extended on the basis of the CPD model can well capture the generation trend of CPD and major products within the error range, such as Figure 4 shown.

[0065] In oxidative and flame atmospheres, benzene is consumed primarily through hydrogen abstraction reactions induced by free radicals such as H, OH, O, CH3, and HO2. Under the conditions of jet stirred reactor oxidation, benzene is consumed primarily through hydrogen abstraction reactions induced by OH.

[0066] In addition to hydrogen abstraction reactions, benzene can also undergo other types of bimolecular reactions with O, OH, etc. Figure 2 It can be seen that the oxygen addition reaction of benzene mainly produces phenol (C6H5OH) and C5H6 + CO. Experimental and theoretical calculation studies have shown that under conditions below 500K, the main product of the oxygen addition reaction is C6H5OH, while under conditions above 700K, C6H5OH and CPD are the main products of the oxygen addition reaction.

[0067] Example 3: Taking the polycyclic alkane fuel norbornane (NBA) as an example, a CPD core model library is constructed. The specific method is as follows:

[0068] Step 1: Experimental data collection;

[0069] The experimental data of the pyrolysis of norbornane (NBA) in a flow tube experimental platform were collected under the following experimental conditions: pressure: 30 Torr, temperature: 973~1373K.

[0070] Step 2: core mechanism call;

[0071] Reaction pathway analysis showed that Figure 2 The main decomposition pathways of NBA include H-abstraction reactions at the six-membered ring site and C-C bond dissociation to form a branched five-membered ring diradical. At the same time, there are multiple pathways for the formation of CPD, which can be obtained by cyclopentenyl radical dehydrogenation and ethylcyclopentenyl deethylation. These multiple reaction channels make CPD the main pyrolysis product of norbornane. The CPD pyrolysis-oxidation model, as a secondary reaction mechanism, can be regarded as a "bridge" connecting the two. Therefore, the CPD sub-mechanism and its key aromatic hydrocarbon generation pathways (such as CPDyl→naphthalene) are reused.

[0072] Step 3: Target fuel sub-mechanism expansion;

[0073] Based on the structural similarity analogy method, an analogy method was used to obtain the rate constant of the initial pyrolysis path of norbornane;

[0074] Thermodynamic and transport parameters were obtained from RMG.

[0075] The core mechanisms of CPD oxidation and pyrolysis were integrated to extract common pathways, and specific pathways were supplemented based on literature data.

[0076] Step 4: Simulation and verification;

[0077] The pyrolysis of norbornane in a convection tube reactor was simulated using the plug flow reactor PFR module in Chemkin-Pro. The measured experimental temperature curve was used as input parameters to predict the production of 1,3-cyclopentadiene (CPD), benzene (C6H6) and 1,3-cyclohexadiene (C6H8). The simulation results show that ( Figure 5 ), the model can well reproduce the pyrolysis reactivity under the same working conditions.

[0078] Most benzene is formed by the β-scission reaction of a cyclohexenyl radical (cC6H7), involving the cleavage of a C-H single bond. CH3-4-cC6H9 and PXCH2-4-cC6H9 are the primary precursors of CH3-5-SAXcC6H8, the latter of which is completely converted to CH3-5-cC6H7-13 via H-atom abstraction. Furthermore, 1,3-cyclohexadiene is primarily formed from CH3-4-cC6H9. At elevated temperatures, the majority of benzene forms from the reaction of two propargyl radicals (C3H3), a reaction widely considered essential for benzene formation.

[0079] In summary, the present invention constructs a modular architecture based on the core layer mechanism of cyclopentadiene (CPD), innovatively integrates quantum chemical calculations with multi-condition experimental data, develops common cross-fuel modeling technologies, and integrates a model library that can be arbitrarily controlled and expanded. This significantly improves the accuracy and efficiency of combustion simulations and provides a standardized and scalable intelligent analysis platform for the study of hydrocarbon fuel combustion mechanisms.

[0080] The above embodiments are only preferred implementations of the present invention, and the protection scope of the present invention is not limited to the above embodiments. All design ideas based on the modular mechanism framework with CPD as the core and multi-source data fusion fall within the protection scope of the present invention.

[0081] It should be noted that for those skilled in the art, without departing from the core layer mechanism constraints and multi-scale parameter optimization principles proposed in the present invention, equivalent technical changes such as improvements in feature extraction methods for specific fuel types, adjustments to the machine learning model architecture, etc. should all be regarded as within the scope of protection of the present invention.

Claims

1. A method for constructing a reaction kinetic model library with CPD as the core mechanism, using a modular hierarchical architecture, and achieving mechanism universality expansion through a multi-scale parameter fusion algorithm of quantum chemical calculations and experimental data. The characteristics are: The following steps are involved: Step 1: Collect pyrolysis and oxidation experimental data of CPD precursor fuel under a wide range of operating conditions, including temperature, pressure, residence time, fuel conversion rate, C0-C5 small molecule products, and PAHs concentration distribution information, and perform data collation and normalization; Step 2: Focusing on the CPD oxidation and pyrolysis reactions, we obtained the thermodynamic and kinetic parameters of key elementary reactions through quantum chemical calculations. Combining literature data with experimental verification, we constructed a CPD core sub-mechanism library covering the formation of C0-C5 small molecules and C6-C15 aromatics. Step 3: Based on the core layer mechanism, the initial decomposition paths of different CPD precursor fuels are targeted, and fuel-specific sub-mechanisms are established through quantum chemical calculations, experimental data optimization, and mechanism reuse rules; Step 4: Integrate the core layer mechanism and fuel-specific sub-mechanisms according to a modular architecture to form a model collection library, and verify and optimize the model through wide-operating experimental data, including sensitivity analysis and key reaction path adjustment, to improve prediction accuracy and generalization ability.

2. The construction method according to claim 1, characterized in that The CPD precursor fuel includes benzene, norbornane and furan compounds.

3. The construction method according to any one of claims 1 to 2, characterized in that Step 2 specifically includes: (1) With CPD as the core, atmospheric pressure oxidation data were obtained through jet stirred reactor experiments, and pyrolysis product distribution was collected through wide-pressure flow tube experiments; (2) Using quantum chemical calculations to obtain the key reaction paths of CPD; (3) Based on quantum chemical calculations and experimental verification, a CPD sub-mechanism library covering the generation of C0-C5 small molecules and C6-C15 aromatic hydrocarbons was formed by integrating literature data.

4. The construction method according to any one of claims 1 to 3, characterized in that In step three, the development of fuel-specific sub-mechanisms includes: (1) Reveal the initial decomposition path of fuel through experiments; (2) Using quantum chemical calculations to obtain the dissociation energy of each fuel bond and the potential energy surface of free radical generation; (3) Bimolecular reactions with clear potential barriers were calculated using traditional transition state theory (TST), and the pressure-dependent rate constants of barrier-free dissociation reactions were calculated using the RRKM-ME method. (4) The core mechanism is directly invoked for the common pathway, and the specific pathway is modeled separately; the common pathway includes the generation of polycyclic aromatic hydrocarbons starting from CPD and its free radicals, and the specific pathway includes the initial ring opening, dehydrogenation, isomerization and hydrogen extraction reactions of the fuel.

5. The construction method according to any one of claims 1 to 4, characterized in that In step three, the mechanism reuse rule is: when the fuel sub-mechanism involves intermediate products and free radicals that overlap with the species in the core mechanism reaction path, directly call the parameters of the species in the core layer mechanism; and model the specific pathway separately.

6. The construction method according to any one of claims 1 to 5, characterized in that: In step 4, the modular architecture uses the CPD core sub-mechanism as a unified bottom layer, links each fuel sub-mechanism as an extension layer, and implements hierarchical calling rules through existing software, giving priority to reusing the core layer reaction path.

7. The construction method according to any one of claims 1 to 6, characterized in that: In step 4, the experiment includes comparing the simulation results with the experimental product concentrations in a flow tube, a shock tube, and a jet stirred reactor, using sensitivity analysis to identify key reaction paths, and reducing the deviation between the experimental data and the simulation values by adjusting the pre-exponential factors of key chemical reactions.

8. The construction method according to claim 6, characterized in that: The hierarchical calling rules also include automatically matching the extended layer sub-mechanism based on the fuel type, and identifying the contribution rate of CPD and CPDyl complexes to the generation of polycyclic aromatic hydrocarbons through sensitivity analysis.

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