Reactive Flow Model Research Articles

Reversible Molten Catalytic Methane Cracking Applied to Commercial Solar-Thermal Receivers

When driven by sunlight, molten catalytic methane cracking can produce clean hydrogen fuel from natural gas without greenhouse emissions. To design solar methane crackers, a canonical plug flow reactor model was developed that spanned industrially relevant temperatures and pressures (1150–1350 Kelvin and 2–200 atmospheres). This model was then validated against published methane cracking data and used to screen power tower and beam-down reactor designs based on “Solar Two,” a renewables technology demonstrator from the 1990s. Overall, catalytic molten methane cracking is likely feasible in commercial beam-down solar reactors, but not power towers. The best beam-down reactor design was 9% efficient in the capture of sunlight as fungible hydrogen fuel, which approaches photovoltaic efficiencies. Conversely, the best discovered tower methane cracker was only 1.7% efficient. Thus, a beam-down reactor is likely tractable for solar methane cracking, whereas power tower configurations appear infeasible. However, the best simulated commercial reactors were heat transfer limited, not reaction limited. Efficiencies could be higher if heat bottlenecks are removed from solar methane cracker designs. This work sets benchmark conditions and performance for future solar reactor improvement via design innovation and multiphysics simulation.

Introduction to special issue on advances in multi-phase fluid and multi-scale particulate reactive flow modeling and simulation for petroleum engineering applications

Introduction to special issue on advances in multi-phase fluid and multi-scale particulate reactive flow modeling and simulation for petroleum engineering applications

Modeling the CO2 capture and in situ conversion to CH4 on dual function Ru-Na2CO3/Al2O3 catalyst

Abstract A dynamic kinetic model is proposed to describe the CO2 adsorption and in situ hydrogenation to CH4 on a 4%Ru-10%Na2CO3/Al2O3 catalyst. One dimensional isothermal heterogeneous plug flow reactor model with axial dispersion is considered. The reaction network and kinetic equations are deduced from experimental data analysis. The molecular modeling includes competitive adsorption of CO2 and H2O on same adsorption site. During CO2 storage period, CO2 is adsorbed onto Na2O species to form Na2CO3. Alternatively, CO2 can be also adsorbed onto NaOH species releasing H2O to the gas phase, which can further be adsorbed onto free adsorption sites located downstream. It was needed to consider formation of unstable bicarbonates to fit the experimental data. During CO2 hydrogenation step, adsorbed carbonates are decomposed, promoted by the presence of H2. CH4 is then formed through the Sabatier’s reaction and the as-formed H2O interacts with regenerated adsorption sites. Temporal evolution of CO2, CH4 and H2O during CO2 storage and hydrogenation cycles is accurately predicted by the model, for a wide range of reactant concentrations and temperature (250−400 °C), gaining understanding on mechanisms and dynamics of the process on dual function materials.

A review of recent developments and future prospects in gasification systems and their modeling

Gasification is receiving a renaissance in response to global warming mitigation. Total gasification installation, construction and planning energy capacity has increased from 42 GWth to 400 GWth between 1999 and 2020. One of the drivers of gasification technologies that has influenced their increase is their capability to accommodate low-value feedstock and organic wastes. Another driving factor is the technology prospect for enhanced power efficiency and environmental performance when used in Integration Combined Cycle (IGCC) with carbon capture. Although gasification has been at the forefront of many studies, it is missing comprehensiveness and organization of the vast information in the literature. There are more than 600,000 studies that focus on gasification and they are mostly very chaotic for their usage for further research development and policy decision making. For instance, the field of modeling and simulation of reactive flow has expanded and high fidelity analyses have been utilized in addressing gasification challenges significantly. Moreover, there had been new developments in areas such as plasma gasification, supercritical water gasification, small scale gasification systems developments, co-gasification and coupling of gasification with other technologies such as anaerobic digestion. Hence, in this work we present a systematic organization of the reported findings, recent developments and future prospects. Recent developments on feed material characteristics of different fuels utilized for gasification in order to evaluate their potential is reported herein. In addition, literature survey of gasification processes, classifications of gasification and influence of process parameters and technologies were also reported. The effect of different parameters like pressure, catalyst, and temperature on the gasification efficiency and gas composition were extracted and presented. At the end, some areas that have witnessed recent progress were highlighted and future prospects in this continually growing thermochemical conversion field was presented.

An explicit reduced-order model of Cu-Zeolite SCR catalyst for embedding in ECM

A piecewise analytical solution is developed as part of an explicit reduced-order model for a state-of-the-art Cu-SSZ-13 SCR catalyst in the degreened state (550 °C-4 h). Simplifying the species, coverage and energy balance equations by treating the monolithic catalyst as an array of CSTRs in series, along with additional approximations based on intrinsic catalyst behavior allow for the decoupling of the conservation equations. This yields analytical solutions for all relevant catalyst states and outputs, which can be integrated using a simple fixed step explicit Euler scheme. The reduced-order model utilizes the same reaction kinetics as the high-fidelity 1D plug flow reactor model, developed using NH3-temperature programmed desorption (TPD) and 4-step [40] reactor data on the degreened catalyst. SCR kinetics are modeled here using a global single-site approach, accounting for ammonia (NH3) and ammonium nitrate (AN) dynamics. Washcoat diffusion is considered using the overall mass transfer approach [39], and in the case of SCR catalysts, we demonstrate the applicability of the asymptotic internal Sherwood number for realistic reaction rates and washcoat diffusivities. Model results show the ability of the piecewise analytical solution to produce nearly identical results as the high-fidelity model, which in turn is validated with experimental reactor data. The reduced-order model is also translated to a full-size catalyst under transient engine drive cycle conditions. SCR outlet temperature, NH3 and AN coverage, along with outlet NOx and N2O slip predictions are in line with the high-fidelity model and experimental measurements. The simplified model presented here is generally applicable to all single-layer monolithic catalysts utilizing linear reaction rate expressions for solved species. This model allows for the tracking of catalyst states (such as NH3 coverage) and outputs (such as NOx) onboard the engine control module (ECM), enabling the development of model-based estimators and control strategies necessary to meet the upcoming emission and durability requirements.

Transported PDF modeling of compressible turbulent reactive flows by using the Eulerian Monte Carlo fields method

Although the transported probability density function (PDF) method has been developed for decades, its application has been mainly focused on the low-Mach number flow problems. This work extends the transported PDF method to compressible flow problems. The Eulerian Monte Carlo fields (EMCF) solution method is employed to solve the transported PDF equation for compressible flow problems. A pseudo stagnation enthalpy is introduced and its stochastic partial differential equation is derived to ensure total energy conservation numerically. A new mixing model called interaction by partial exchange with mean (IPEM) is introduced to expand the available choices of mixing models for the EMCF method. The consistency of the EMCF method is examined for solving the transported PDF equation. Numerical implementation details are discussed, such as the density coupling between the compressible flow solver and the EMCF solver, discretization schemes for the mixing terms and the stochastic terms. The implemented compressible flow solver coupled with the EMCF solver is verified and validated in a series of test cases with increasing level of complexity, ranging from a statistically one-dimensional turbulent mixing layer to a self-excited resonance model rocket combustor. It is observed that in general with the increase of compressibility, there is an increase in the sensitivity of the modeling results to the different models and algorithms. This makes it necessary to develop a thorough understanding of the model sensitivity in order to develop a robust and accurate simulation solver for highly compressible turbulent reactive flows. The thermo-acoustic instability inside the model rocket combustor case is captured reasonably, which demonstrates the overall capability of the developed compressible turbulent combustion solver based on the transported PDF method.

Operator inference for non-intrusive model reduction of systems with non-polynomial nonlinear terms

This work presents a non-intrusive model reduction method to learn low-dimensional models of dynamical systems with non-polynomial nonlinear terms that are spatially local and that are given in analytic form. In contrast to state-of-the-art model reduction methods that are intrusive and thus require full knowledge of the governing equations and the operators of a full model of the discretized dynamical system, the proposed approach requires only the non-polynomial terms in analytic form and learns the rest of the dynamics from snapshots computed with a potentially black-box full-model solver. The proposed method learns operators for the linear and polynomially nonlinear dynamics via a least-squares problem, where the given non-polynomial terms are incorporated on the right-hand side. The least-squares problem is linear and thus can be solved efficiently in practice. The proposed method is demonstrated on three problems governed by partial differential equations, namely the diffusion–reaction Chafee–Infante model, a tubular reactor model for reactive flows, and a batch-chromatography model that describes a chemical separation process. The numerical results provide evidence that the proposed approach learns reduced models that achieve comparable accuracy as models constructed with state-of-the-art intrusive model reduction methods that require full knowledge of the governing equations.

Hot-spot initiated burn waves in heterogeneous-explosive detonation reaction zones: Mixed-mode reaction and the reactive-thermal wave model

Heterogeneous detonation reaction spreads from sufficiently supercritical hot spots as burn waves, the growth and coalescence of which controls the bulk reaction rate. The statistical hot spot model formally homogenizes these effects, giving a rate term that depends on the number density of supercritical hot spots, η, and the burn wave speed, V. In order to completely specify statistical-hot-spot-based reaction rate laws for use in reactive flow models, one must obtain realistic expressions for η and V. The focus of this paper is upon the burn-wave structure and its speed, V. Specifically, a physically-based, temperature-dependent reactive-thermal wave prescription is developed which, when suitably nondimensionalized, depends on a single parameter, α. Numerical simulations show that α characterizes the reaction morphology. Specifically, α controls important elements of the degree-of-heterogeneity in mixed-mode reaction—transitional behavior that may lie anywhere between homogeneous and heterogeneous limiting cases. The model also yields an analytic, physical-properties-based formula for V. This expression enables the development of a new class of Arrhenius-based, formally-homogenized, mixed-mode-reaction-aware reaction rate law.

Ignition and growth modeling of shock initiation using embedded particle velocity gauges in the plastic bonded explosive LX-14

ABSTRACT Recently Vandersall et al. [1] reported a series of shock initiation experiments using embedded manganin pressure gauges in the plastic bonded explosive (PBX) LX-14 (95.5% HMX and 4.5% Estane by weight) plus Ignition and Growth (I & G) simulations of all the gauge records. Jones et al. [2] reported a study of LX-14 using embedded particle velocity gauges in a similar shock strength range. It is prudent to test the ability of a reactive flow model to predict both types of gauge results. The I & G LX-14 model parameters based on the pressure records are compared to five sets of particle velocity gauge records. Excellent agreement was obtained with all five particle velocity experiments, implying that the two types of gauges yield equivalent results and that either technique can be used with the I & G model.

Oxidation Kinetics of Magnesium‐Manganese Oxides for High‐Temperature Thermochemical Energy Storage

In this article, the high‐temperature (≥1000 °C) oxidation kinetics of porous magnesium‐manganese oxide structures considered for large‐scale thermochemical energy storage are determined. For this analysis, oxides with Mn/Mg molar ratios of 2/3, 1/1, and 2/1 are synthesized via solid‐state reaction and crushed to a powder with particle sizes ranging from 125 to 180 μm. The powder is thermally reduced at 1500 °C inside a heated alumina tube under argon flow. Subsequently, the resulting porous bed is oxidized at temperatures between 1000 and 1500 °C with an oxygen to argon molar ratio of 1:4 (leading to an oxygen partial pressure of 0.2 atm). An Arrhenius‐type kinetic rate law is derived using the theory of internal oxidation assuming spherical particles. Subsequently, the kinetic rate law parameters are identified by comparing measured oxygen flow at the reactor outlet to the oxygen output computed using a 1D plug flow reactor model incorporating the postulated kinetic model. Results indicate that the derived bulk kinetic rate law describes the measured oxidation kinetics well and is suited for designing thermochemical energy storage modules based on magnesium‐manganese oxides.

An efficient symmetric finite volume element method for second-order variable coefficient parabolic integro-differential equations

This paper is devoted to develop a symmetric finite volume element (FVE) method to solve second-order variable coefficient parabolic integro-differential equations, arising in modeling of nonlocal reactive flows in porous media. Based on barycenter dual mesh, one semi-discrete and two fully discrete backward Euler and Crank–Nicolson symmetric FVE schemes are presented. Then, the optimal order error estimates in $$L^{2}$$ -norm are derived for the semi-discrete and two fully discrete schemes. Numerical experiments are performed to examine the convergence rate and verify the effectiveness and usefulness of the new numerical schemes.

Stimulating tariff formation models for reactive power flows and electricity quality control

It is shown that up to the present time, an effective, operating, efficient model of reactive power flow and power quality control has not been created in Russia. It is necessary to sharpen attention to the problem. It is necessary to analyze the state of the problem. To try to find out the reasons. Give suggestions. Involve specialists in its discussion. The main reason for the lack of a workable model is legal barriers to its implementation in practice. The criterion for legitimacy of application of incentive tariffs in the form of discounts (surcharges) may be equality of income of the energy supplying organization from application of economically justified tariff and income from application of incentive tariff. Known proposals in the form of mathematical expressions for calculation of discounts (surcharges) to the tariff require changes to existing regulatory and legal documents, which are not related to the methods of calculation of surcharges (discounts). What complicates the process of their implementation. The proposed model of formation of the incentive tariff with the use of a single approach to calculation of discounts (surcharges) both in case of power quality and in case of consumption of reactive power, does not require changes in the documents not related to the methods of calculation of discounts (surcharges) and differs in compliance with the criterion of legitimacy of their application.

Thermodynamically Consistent Detonation Model for Solid Explosives

An improved reactive flow model with thermodynamic consistency is proposed to deal with the detonation hydrodynamics of solid explosives. Based on the assumption that the chemical mixture composed of solid-phase reactants and gas-phase products can arrive at mechanical equilibrium, but cannot arrive at thermal equilibrium, the solid-phase reactants and gas-phase products may possess one pressure and one velocity, but two temperatures or internal energies. With the help of the energy conservation of the mixture and pressure equivalence between the constituents, the conservation equation of internal energy and the evolution equations of the volume fraction for the solid-phase reactants and of pressure for the chemical mixture are derived. Thus, the full governing equations of the proposed detonation model include the conservation equations of mass, momentum, and total energy, and the evolution equation of pressure for the chemical mixture, and the conservation equations of mass and internal energy, and the evolution equation of the volume fraction for the solid-phase reactants. The theoretical analysis shows that there exists a distinct discrepancy between the proposed model and the Zel’dovich–Neumann–Doring detonation model for the steady structure of the detonation wave. The numerical simulation results of typical detonation problems show that the important characteristics of detonation flows can be well captured and also demonstrate that the proposed detonation model of solid explosives is reasonable.

Multiscale modeling of transients in the shock-induced detonation of heterogeneous energetic solid fuels

We pursued a quantitative comparison of the continuum and mesoscale simulations of metal particle reactions in a condensed explosive. The continuum or homogeneous approximation assumed a single combustible mixture; contrastingly, in the present heterogeneous treatment of a mixture, aluminum and 1,3,5,7-tetranitro-1,3,5,7-tetrazocane were considered independent reactive granules of micron size with binder being inert material with strength. Both simulations similarly estimated the steady detonation velocity and peak pressure, while the early flame acceleration transients, marked by a complex flow structure behind the flame front, were observed only in the mesoscale simulation. The precise multi-interface processing techniques, combined with granule-level reactive flow models developed in this study, are deemed applicable to general heterogeneous solid fuel combustion studies related to granules of various size, shape, and reactivity.

Nucleation and crystal growth kinetic parameter optimization of a continuous Poiseuille flow struvite crystallizer using a discretized population balance and dynamic fluid model

Struvite crystallization is an important process in recovering phosphorus from waste streams, but kinetic parameters involve significant uncertainty. In this research a model is developed which includes population balance, fluid flow equations, and kinetic relations. Power law rate coefficients for struvite nucleation (knuc=7.509×107L-1.min-1) and growth (kg=16.72μm.min-1) are optimised by combining a Poiseuille flow reactor model (PFR) and experimental data for phosphorus concentration and particle size distribution (PSD) at the reactor outlet. Nucleation and crystal growth rates were optimized using both filtered and sonicated PSD samples. The model incorporated three key aspects: non-ideal thermodynamics; Poiseuille fluid flow (including advection, diffusion and reaction); and a discretized population balance model (PBM). Sensitivity analysis using deltas (min/max) showed diffusion effects to be negligible and indicated that power law rate constants for both nucleation and growth were more influential on PSD and phosphorus concentration than the associated rate orders. Optimized parameters agreed reasonably well with a previous study conducted by our group under different conditions, using a different model, providing confidence in results. The optimized nucleation rate, knuc, was only 12% lower than that found using a similar model for a seeded system, where secondary nucleation is dominant. Additionally, a primary nucleation model provided a poor fit to experimental data. These two factors indicate that secondary nucleation is an influential mechanism. A 2nd order growth model provided a better fit to data than a previously suggested 5th order growth model. The optimized growth rate coefficient, kg, was higher than in any previous studies, an effect attributed to sonication, which eliminated aggregates.

Experimental analysis and compartmental modeling of the residence time distribution in DN6 and DN15 continuous oscillatory baffled crystallizer (COBC) systems

Compartment models (CMs) are widely used to capture typical hydrodynamic features of systems, generally having low computational cost. The main building blocks of the CMs are the continuous stirred tank reactor and plug flow reactor models. In this study, the hydrodynamics of two laboratory scale continuously oscillated baffled crystallizer systems were investigated: the commercially available DN15 and a scaled down version known as the DN6. CM structures were identified based on residence time distribution (RTD) measurements by direct fitting method for both the DN6 and DN15 systems, which showed superior performance compared to the traditional tank in series CM structure determination. To attain a more accurate CM calibration, the piston and pump flowrates obtained by the typical peristaltic pump configurations were thoroughly analyzed.The investigations revealed that the behavior of the systems varies based on the oscillation amplitudes and frequencies, so the number of compartments required for an adequate model was identified based on measurement with different amplitudes and frequencies. It is shown that adaptive tank in series CMs are needed to capture the measured RTD characteristics over a broad piston operation range. Not only the RTD curves but the calculated compartment numbers follow similar trends in DN6 and DN15. This enabled the generalization of the CM structure for the DN6 and DN15 systems.

Process-based upscaling of reactive flow in geological formations

Recently, there is an increased interest in reactive flow in porous media, in groundwater, agricultural and fuel recovery applications. Reactive flow modeling involves vastly different reaction rates, i.e., differing by many orders of magnitude. Solving the ensuing model equations can be computationally intensive. Categorizing reactions according to their speeds makes it possible to greatly simplify the relevant model equations. Indeed some reactions proceed so slow that they can be disregarded. Other reactions occur so fast that they are well described by thermodynamic equilibrium in the time and spatial region of interest. At intermediate rates kinetics needs to be taken into account. In this paper, we categorize selected reactions as slow, fast or intermediate. We model 2D radially symmetric reactive flow with a reaction-convection-diffusion equation. We show that we can subdivide the PeDaII phasespace in three regions. Region I (slow reaction); reaction can be ignored, region II (intermediate reaction); initially kinetics need to be taken into account, region III (fast reaction); all reaction takes places in a very narrow region around the injection point. We investigate these aspects for a few specific examples. We compute the location in phase space of a few selected minerals depending on salinity and temperature. We note that the conditions, e.g., salinity and temperature may be essential for assigning the reaction to the correct region in phase space. The methodology described can be applied to any mineral precipitation/decomposition problem and consequently greatly simplifies reactive flow modeling in porous media.

Selective conversion of CO2 to methanol over intermetallic Ga-Ni catalyst: Microkinetic modeling

The conversion of CO2 from industrial effluent flue gas streams into methanol will not only help in mitigating global warming but also provide a clean source of alternate energy. In this study, the microkinetic model for methanol synthesis from CO2/H2 on supported intermetallic Ga3Ni5 catalyst based on the single-site mechanism is presented. The reaction route (RR) analysis was used to develop a rate expression without any presumption of the most abundant reactive intermediate (MARI) and rate-determining steps (rds). The silica-supported Ga3Ni5 catalyst was prepared through co-precipitation method and characterized by various techniques. The developed kinetic model was tested, and its parameters were estimated with the experimental data obtained over the lab synthesized catalyst. From the results obtained, it was found that the hydrogenation of formate intermediate is the rds and surface adsorbed CO2 and H-atom were MARI of the system. Based on rds and MARI, the final kinetic expression was tested against experimental data for a wide range of temperatures. The calculated data from the kinetic expression was found to fit the experimental results well, thereby validating the kinetic parameters and reaction mechanism proposed in this study. In addition, based on a plug flow reactor model, the kinetic parameters predicted the theoretical CO2 conversion at high temperatures, thus, demonstrating the robustness of the rate expression and accuracy of kinetic parameters proposed in this study.

Diffuse interface modelling of reactive multi-phase flows applied to a sub-critical cryogenic jet

In order to simulate cryogenic H2−O2 jets under subcritical condition, a numerical model is constructed to solve compressible reactive multi-component flows which involve complex multi-physics processes such as moving material interfaces, shock waves, phase transition and combustion. The liquid and reactive gaseous mixture are described by a homogeneous mixture model with diffusion transport for heat, momentum and species. A hybrid thermodynamic closure strategy is proposed to construct an equation of state (EOS) for the mixture. The phase transition process is modeled by a recent fast relaxation method which gradually reaches the thermo-chemical equilibrium without iterative process. A simplified transport model is also implemented to ensure the accurate behavior in the limit of pure fluids and maintain computational efficiency. Last, a 12-step chemistry model is included to account for hydrogen combustion. Then the developed numerical model is solved with the finite volume method where a low dissipation AUSM (advection upstream splitting method) Riemann solver is extended for multi-component flows. A homogeneous reconstruction strategy compatible with the homogeneous mixture model is adopted to prevent numerical oscillations across material interfaces.Having included these elements, the model is validated on a number of canonical configurations, first for multiphase flows, and second for reactive flows. These tests allow recovery of the expected behavior in both the multiphase and reactive limits, and the model capability is further demonstrated on a 2D burning cryogenic H2−O2 jet, in a configuration reminiscent of rocket engine ignition.

Autoignition of an n-heptane jet in a confined turbulent hot coflow of air

The autoignition of a continuous, single jet of pure liquid n-heptane injected concentrically and axisymmetrically from a water-cooled circular nozzle into a confined turbulent hot coflow (CTHC) of air at atmospheric pressure has been investigated experimentally at air temperatures up to 1150 K and velocities up to 40 m/s. The aim of this work was to examine the emergence of liquid-fuel autoignition in the presence of flow, mixture and phase inhomogeneities, to which end, the velocity, temperature and fuel-droplet fields inside the CTHC reactor were characterized in a series of dedicated measurement campaigns. Distinct phenomena were identified concerning the emergence of various regimes: no autoignition, random spots, and continuous flame. In the random spots regime, autoignition appeared in the form of well-defined, discrete localized spots occurring randomly within the reactor, similar to observations in a similar apparatus with gaseous fuels (Markides, 2005; Markides and Mastorakos, 2005, 2011; Markides et al., 2007). High-speed optical measurements of these random spots were made from which the autoignition locations/lengths were measured, and then used to infer average autoignition delay, or residence, times from injection based on the bulk air velocity. An increase in the air temperature moved the region of autoigniting spots closer to the injector nozzle, thus decreasing the autoignition length and also decreasing the autoignition delay time. Generally, autoignition moved downstream with increasing bulk air velocity, but the delay times decreased contrary to the aforementioned earlier work with pre-vaporized n-heptane in this geometry. Of interest is the finding that at the highest investigated air velocities, the autoignition length decreased as the air velocity increased, which again deviates from the same earlier work with vaporized n-heptane. Furthermore, higher liquid injection velocities also resulted in increased autoignition lengths and times. The results from this work suggest that the turbulent inhomogeneous autoignition of liquid fuels cannot be directly predicted from chemical delay times of equivalent homogeneous systems, or even from knowledge of the turbulent inhomogeneous autoignition of single-phase (gaseous) fuels in the same reactor system (flow geometry, fuel, conditions, etc.), and that the effects of evaporation and turbulent mixing must be accounted for. The data can assist the development of advanced turbulent and multiphase reacting flow models.