Reaction Rate Equation Research Articles

Ammonia converter Simulation and Optimization Based on an Innovative Correlation for (KP) Prediction

In this paper, the simulation and optimization of an industrial ammonia synthesis reactor is illustrated. The converter under study is of a vertical design, equipped with three radial-flow catalyst beds with inter-stage cooling and two quenching points. For building the model, a modified kinetic equation of ammonia synthesis reaction, based on Temkin- Pyzhev equation and an innovative correlation for (KP) prediction, was developed in suitable form for the implementation in Aspen HYSYS plug flow reactor using the spreadsheet embedded in the software with the introduction of some invented simulation techniques. A new parameter, which is a function of (T, P and α), was introduced into the reaction rate equation to account for the variation of KP with pressure. The simulation model is able to describe the converter behavior with acceptable accuracy. A case study was done, using Aspen HYSYS Optimizer, illustrated the optimum reactor temperature profile, after 12 years of operation, to achieve maximum production. The result predicts an increase of 8 tons ammonia per day accompanied with an increase of steam production of 12 tons per day.

Validation of a Fixed Bed Reactor Model for Dimethyl Ether Synthesis Using Pilot-Scale Plant Data

The one-dimensional (1D) mathematical model of fixed bed reactor was developed for dimethyl ether (DME) synthesis at pilot-scale (capacity: 25–28 Nm3/h of syngas). The reaction rate, heat, and mass transfer equations were correlated with the effectiveness factor. The simulation results, including the temperature profile, CO conversion, DME selectivity, and DME yield of the outlet, were validated with experimental data. The average error ratios were below 9.3%, 8.1%, 7.8%, and 3.5% for the temperature of the reactor, CO conversion, DME selectivity, and DME yield, respectively. The sensitivity analysis of flow rate, feed pressure, H2:CO ratio, and CO2 mole fraction was investigated to demonstrate the applicability of this model.

Simple microwave pyrolysis kinetics of lignocellulosic biomass (oil palm shell) with activated carbon and palm oil fuel ash catalysts

Abstract The important parameters characterizing microwave pyrolysis kinetics, namely the activation energy (E a) and the rate constant pre-exponential factor (A), were investigated for oil palm shell mixed with activated carbon and palm oil fuel ash as microwave absorbers, using simple lab-scale equipment. These parameters were estimated for the Kissinger model. The estimates for E a ranged within 31.55–58.04 kJ mol−1 and for A within 6.40E0–6.84E+1 s−1, in good agreement with prior studies that employed standard techniques: Thermogravimetric Analysis (TGA) and Differential Scanning Calorimetry (DSC). The E a and A were used with the Arrhenius reaction rate equation, solved by the 4th order Runge-Kutta method. The statistical parameters coefficient of determination (R 2) and root mean square error (RMSE) were used to verify the good fit of simulation to the experimental results. The best fit had R 2 = 0.900 and RMSE = 4.438, respectively, for MW pyrolysis at power 440 W for OPS with AC as MW absorber.

Comparison of kinetics and thermochemical energy storage capacities of strontium oxide, calcium oxide, and magnesium oxide during carbonation reaction

In this work kinetics of carbonation reaction of strontium oxide was investigated using the well-known random pore model. This non-catalytic gas-solid reaction can be utilized both for carbon capture and storage (CCS) and thermochemical energy storage (TCES) applications. In order to obtain kinetic parameters and reaction rate equation, a set of experiments ranging from 800 °C to 950 °C in temperature and 5 to 40 vol% in concentration of CO2 were conducted. It was concluded that fractional function describes the concentration dependency of reaction rate very well. The activation energy of this reaction was calculated to be about 64 kJ/mol and the best exponential function indicating temperature dependency of CO2 diffusivity through the product layer was also estimated. Furthermore, it was attempted to depict the importance of this reaction for CCS and TCES purposes. This goal was achieved by comparing our results with those of around 50 similar researches carried on MgO, CaO, and SrO-based sorbents. Comparison was done using six screening criteria; i.e. CO2 uptake, CO2 uptake rate, conversion, conversion rate, thermal energy, and thermal power.

Shear Reaction of Explosives and Propellants

When loaded by weak impact, both explosives and propellants undergo shear reaction. Out shear reaction hydro-reactive model (TDSR) is similar to our old surface burn hydro-reactive model (TDRR), except for the reaction rate equation. We perform tests and computer simulations of shear reaction in both explosives and propellants. For explosives we use the well-known Steven test but with different diagnostics (back surface velocity histories). For propellants we use a new test configuration. In both cases we run our TDSR simulations and are able to get a reasonable reproduction of test results.

Kinetic Study on CO-Selective Methanation over Nickel-Based Catalysts for Deep Removal of CO from Hydrogen-Rich Reformate

The CO-selective methanation process is considered as a promising CO removal process for compact fuel processors producing hydrogen, since the process selectively converts the trace of CO in the hydrogen-rich gas into methane without additional reactants. Two different types of efficient nickel-based catalysts, showing high activity and selectivity to the CO methanation reaction, were developed in our previous works; therefore, the kinetic models of the reactions over these nickel-based catalysts have been investigated adopting the mechanistic kinetic models based on the Langmuir chemisorption theory. In the methanation process, the product species can react with the reactant and also affect the adsorption/desorption of the molecules at the active sites. Thus, the kinetic parameter study should be carried out by global optimization handling all the rate equations for the plausible reactions at once. To estimate the kinetic parameters, an effective optimization algorithm combining both heuristic and deterministic methods is used due to the large solution space and the nonlinearity of the objective function. As a result, 14 kinetic parameters for each catalyst have been determined and the parameter sets for the catalysts have been compared to understand the catalytic characteristics.

Vanillin hydrodeoxygenation kinetics on takovite derived NiAlOx mixed oxides

Vanillin, a representative moiety of lignin, having three different oxygenated groups, was used as a model molecule on catalytic hydrodeoxygenation (HDO). The transformation of vanillin was carried out at in a batch reactor at 413–573 K, 1.2 MPa of H2 and using a takovite-derived, reduced NiAlOx mixed oxide. The concentration of the reaction products, as well as vanillin conversion, was measured by gas-chromatography. After identifying the products, a reaction network scheme was proposed in order to calculate the reaction rates by assuming a pseudo-first order. Then, from an ordinary differential equations system for each species of each reaction network, the concentration value evolution was calculated using Runge Kutta- Butcher 5th order method. For each concentration experimental data in the reaction mixture a minimum-square adjustment with Levenberg-Marquardt minimization was used. The experimental data were fitted by a FORTRAN (“mIKC”) code, which numerically solved the differential equations system until obtaining the ones in this work. A very good fitting between experimental data and the calculated ones using the proposed reaction rate equations validated the reaction scheme. Reaction temperature plays a crucial role when aiming to obtain fully deoxygenated products, e.g. hydrocarbons like cyclohexane and methyl cyclohexane, 553 K being the ideal one.

Study on the mechanism of Al-Si alloy preparation via aluminothermic reduction–molten salt electrolysis in KF–AlF3 molten salt

In this study, Al–Si alloy, a precursor of the solar-grade silicon, was prepared via the aluminothermic reduction–molten salt electrolysis of SiO2 in KF–AlF3 molten salt by employing liquid aluminum as the working cathode. The reaction mechanism of the aluminothermic reduction of SiO2 in KF–AlF3 molten salt at 750 °C was determined by thermogravimetry–differential scanning calorimetry. The reaction rate equation for the aluminothermic reduction of SiO2 in KF–AlF3 molten salt was:dαdt=7.156×1024e−4.688×105RT(1−α)1.734. In 49.4 wt% KF–47.6 wt% AlF3–3 wt% SiO2 molten salt at 750 °C, the Si content in the Al–Si alloy obtained by the aluminothermic reduction–molten salt electrolysis of SiO2 was 24.53 wt%. Compared with solely aluminothermic reduction of SiO2, the current efficiency in the process of the aluminothermic reduction–molten salt electrolysis of SiO2 was evaluated. The results reveal that the Al–Si alloy is predominantly prepared in the aluminothermic reduction step, while supplemented by electrolysis. The calculated Faradic current efficiency of the proposed aluminothermic reduction–molten salt electrolysis process was 28.4%.

Kinetic modeling of aquathermolysis for upgrading of heavy oils

The growing energy demand and reduction of conventional oil reservoirs have prompted the investigation of technologies to recover unconventional heavy oils. Steam injection is the most widely used thermal method for heavy oil recovery. However, this process presents some challenges due to the high viscosity and content of heavy components such as resins and asphaltenes in this type of oil. Additionally, the mechanisms of the different chemical reactions that take place during steam injection are not fully understood. Aquathermolysis is another approach that can be used not only for heavy oil recovery but also for heavy oil upgrading. An analysis and discussion of the kinetic models focused on the aquathermolysis reaction reported up to date is performed. Different aspects of reaction mechanisms, operating conditions, reaction rate equations, kinetic parameter values, and catalytic decay terms are reviewed. It has been concluded that kinetic modeling studies for aquathermolysis are scarce in the literature and that the reported models are simple in nature, which indicates the need for more research in this area for proper evaluation of technologies for in situ upgrading of heavy oils, either catalytic or non-catalytic.

Thermogravimetric analysis of co-combustion between municipal sewage sludge and coal slime: Combustion characteristics, interaction and kinetics

Based on the physical and chemical properties of municipal sewage sludge (SS) and coal slime (CS), the combustion behaviors of SS, CS and their blends were investigated by the thermogravimetric analyzer. The interaction between SS and CS was evaluated, and the combustion reaction rate equations were obtained. The results suggest that during the co-combustion, SS could improve the ignition performance, while CS could enhance the activity in the high temperature zone and improve the slagging characteristics. There was the most significant interaction in 550–600℃, which had a positive effect on the entire combustion process, and the synergy reached its peak when the CS ratio was 40% with synergy index SI=1.53. The combustion of the blend was a multi-step process, which conformed to the nth-order model, and the addition of CS could reduce the apparent activation energy of SS during the entire combustion process.

Modeling Initiation and Detonation of Complex Explosive Formulations

Since 1980 we’ve developed and used our reactive flow model TDRR (= reactant Temperature Dependent Reaction Rate). TDRR makes it possible to calculate initiation and detonation of a single component explosive. It includes EOSs (Equations of State) for the reactant and products, and a reaction rate equation for the transition from reactant to products. As the EOSs and the reaction rate are calibrated for a certain formulation, say HV5 (95% HMX+5% Viton), it’s not possible to use them for a different formulation of the same materials, say HV15. Here we expand TDRR to handle general formulations with any number of components (explosives, binders and products). We call our expanded model TDRRF (F for Formulation). We first write down the model equations and then use them with two computed examples: 1) HVx and BFx formulations (x=explosive mass ratio, H=HMX, V=Viton, B=TATB, F=kelF) and 2) BHx formulations (x=B mass ratio).

Modeling of Impact Energy Release of PTFE/Al Reactive Material

Many scholars have used experimental research methods to conduct extensive research on the impact energy release behavior of Polytetrafluoroethylene(PTFE)/Al reactive materials. However, in numerical simulation, PTFE/Al still lacks the calculation parameters of impact energy release behavior. In order to obtain the simulation parameters of PTFE/Al impact ignition, the Hill mixture law was used to calculate the material parameters of PTFE/Al (mass ratio 73.5/26.5), and according to the Hugoniot curve of PTFE/Al and the γ state equation, the JWL equation of state of a PTFE/Al unreacted substance and reaction product was fitted with a genetic algorithm. According to the PTFE/Al impact energy release experiment, the parameters of the PTFE/Al chemical kinetic equation were determined, and the parameters of the trinomial reaction rate equation were fitted. The obtained parameters were used in the simulation calculation in LS-dyna to predict the damage of the aluminum target plate under the impact of the PTFE/Al reactive fragments.

Shock initiation performance of NTO-based polymer bonded explosive

3-nitro-1,2,4-tri-azol-5-one (NTO) is a high energy insensitive explosive. To study the shock initiation process of NTO-based polymer bonded explosive JEOL-1 (32%octahydro-1,3,5,7-tetranitro-1,3,5,7-tetrazocine (HMX), 32% NTO, 28% Al and 8% binder system), the cylinder test, the gap experiments and numerical simulation were carried out. Firstly, we got the detonation velocity (7746 m/s) and the parameters of Jones-Wilkins-Lee (JWL) equation of state (EOS) for detonation product by cylinder test and numerical simulation. Secondly, the Hugoniot curve of unreacted explosive for JEOL-1 was obtained calculating the data of pressure and time at different Lagrangian positions. Then the JWL EOS of unreacted explosive was obtained by utilizing the Hugoniot curve as the reference curve. Finally, we got the pressure growth history of JEOL-1 under shock wave stimulation and the parameters of the ignition and growth reaction rate equation were obtained by the pressure-time curves measured by the shock-initiation gap experiment and numerical simulation. The determined trinomial ignition and growth model (IG model) parameters can be applied to subsequently simulation analysis and design of insensitive ammunition with NTO-based polymer bonded explosive.

Catalytic Ozonation of Toluene over Acidic Surface Transformed Natural Zeolite: A Dual-Site Reaction Mechanism and Kinetic Approach

Volatile organic compounds (VOCs) are responsible for damage to health due to their carcinogenic effects. Catalytic ozonation using zeolite appears as a valuable process to eliminate VOCs from industrial emissions at room temperature. For full-scale application of this new abatement technology, an intrinsic reaction rate equation is needed for an effective process design and scale-up. Results obtained here provide a mechanistic approach during the initial stage of catalytic ozonation of toluene using an acidic surface transformed natural zeolite. In particular, the contribution of Lewis and Brønsted acid sites on the surface reaction mechanism and overall kinetic rate are identified through experimental data. The least-squares non-linear regression method allows the rate-determining step to be established, following a Langmuir–Hinshelwood surface reaction approximation. Experimental evidence suggest that ozone is adsorbed and decomposed at Lewis acid sites, forming active atomic oxygen that leads to the oxidation of adsorbed toluene at Brønsted acid sites.

Synthesis of Ni-B/Hydroxyapatite by Electrochemical Method and Its Application as Catalyst on NaBH<sub>4</sub> Hydrolysis

The result of burning hydrogen which is environmentally friendly makes hydrogen as a very attractive fuel. Hydrogen storage is interesting research material. One alternative to hydrogen storage is a metal-hydride as NaBH4. In this paper, the catalyst for hydrogen production from storage, namely The result of burning hydrogen, which is environmentally friendly, makes hydrogen a desirable fuel. Hydrogen storage is exciting research material. One alternative to hydrogen storage is a metal-hydride as NaBH4. In this paper, the catalyst for hydrogen production from storage, namely NaBH4, was synthesized by electrochemical. Ni-B catalyst with hydroxyapatite as catalyst support was prepared by electrochemical. Ni-B/HA catalyst was synthesized at various current densities (namely 67, 133, and 200 mA/cm2) and various electrolysis times (namely 30, 60, and 90 minutes). The resulting catalysts were analyzed by XRD and used as the catalyst for hydrogen production from the hydrolysis reaction of NaBH4. The fastest hydrogen production was obtained using a catalyst generated at 133 mA/cm2 and an electrolysis time of 60 minutes. The reaction rate equation for the hydrolysis of NaBH4 has a first-order reaction to the concentration of NaBH4. The resulting reaction rate constant ranged from 233.33 mL/g/min to 861.11 mL/g/min. The relationship between reaction temperature and reaction rate constant can be expressed by the equation k = 2.2x106exp (5534/T).

Determination of Rate Equation for the Electrochemical Hydrogenation and Hydrogenolysis of Furfural in Acidic Media over Copper

The use of electricity from renewable sources allows for carbon neutral electrochemical processes to be operated. One example process is that of the electrochemical hydrogenation and hydrogenolysis of furfural (FF) to furfuryl alcohol (FA) and 2-methylfuran (MF). FA is used as a reactant in making furanic polymers for molds and castings, and MF has been identified as a high octane fuel. The electrochemical reactions of FF to FA and MF occur in parallel in acidic conditions on Cu catalysts. In this work we investigated the reaction mechanism by proposing a set of elementary steps, deriving the corresponding rate equation, and fitting it to the data. A Langmuirian trend was seen in the production rate vs FF concentration data.Experimentation was done using a catholyte that contained 0.1 or 0.5 M H2SO4 with a concentration of FF between 10 and 120 mM. The potential was first varied in pH 0 with 100 mM FF to determine the Tafel slope and exchange current densities, as well as the range of potential where the reaction is not mass transfer limited. The Tafel region of the system was found to be between -517 mV and -572 mV. To determine the effect of concentration of FF, the applied potential was set to -560 mV vs RHE, where the system is limited by kinetics and not mass transfer. The reaction rates to desired products were found to change from positive order to zero order with respect to FF concentration, showing a Langmuirian trend. It was found that the plateau in the reaction rate was 50% and 58% lower for MF and FA species respectively when the pH was changed from 0 to 1. The reaction rate equation was determined to be the equation that best fit the data across both pH levels.

Time evolution calculation of muon catalysed fusion: Emission of recycling muons from a two-layer hydrogen film

Recycling muon having approximately 10 keV kinetic energy produced in a muon catalysed fusion (μCF) cycle is expected to be a source of negative muon beam with high-spatial/time coherence. We report a time evolution calculation of μCF cycle with a particular focus on the emission of recycling muons from a hydrogen film target. Rate equations for the μCF reactions are solved using the 4th-order Runge-Kutta method. Considering a two-layer solid hydrogen film target composed of 1 mm hydrogen-deuterium layer and 2 µm deuterium-tritium layer, we have numerically simulated the time evolution of the muonic states and their populations in these layers. The muon atomic and molecular processes in the layers are solved simultaneously by introducing a probability of muonic deuterium atoms traveling between the layers via the Ramsauer-Townsend effect. The use of T2 amplifies the recycling muon emission. A weak dependence of the emission fraction of the recycling muons on the T2 concentration is predicted, which can be utilized to minimize the usage of tritium.

Kinetics of the homogenous diazotization of p-nitroaniline with nitrous acid solution using stopped-flow technique

Diazotization is common in the fine chemical industry however its kinetics study is rare. In this work, the stopped-flow technique was adopted to study the kinetic parameters of the diazotization reaction between p-nitroaniline and nitrous acid. The results revealed that the p-nitroaniline diazotization is a second-order reaction with excessive hydrochloric acid, and the reaction rate equation with a pre-exponential factor and activation energy of 6.95 × 108 L·mol−1·s−1 and 37.79 kJ·mol−1 respectively was obtained according to Arrhenius equation. In addition, the kinetic model was established, the correlated values of k1 matched well with the experimental values with an AAD of 7.1%. This work provides theoretical data and guidance for its process optimization.

Learning heterogenous reaction rates from stochastic simulations.

Reaction rate equations are ordinary differential equations that are frequently used to describe deterministic chemical kinetics at the macroscopic scale. At the microscopic scale, the chemical kinetics is stochastic and can be captured by complex dynamical systems reproducing spatial movements of molecules and their collisions. Such molecular dynamics systems may implicitly capture intricate phenomena that affect reaction rates but are not accounted for in the macroscopic models. In this work we present a data assimilation procedure for learning nonhomogeneous kinetic parameters from molecular simulations with many simultaneously reacting species. The learned parameters can then be plugged into the deterministic reaction rate equations to predict long time evolution of the macroscopic system. In this way, our procedure discovers an effective differential equation for reaction kinetics. To demonstrate the procedure, we upscale the kinetics of a molecular system that forms a complex covalently bonded network severely interfering with the reaction rates. Incidentally, we report that the kinetic parameters of this system feature peculiar time and temperature dependences, whereas the probability of a network strand to close a cycle follows a universal distribution.

Upscaling bimolecular reactive transport in highly heterogeneous porous media with the LAgrangian Transport Eulerian Reaction Spatial (LATERS) Markov model

The LAgrangian Transport Eulerian Reaction Spatial (LATERS) Markov model was developed to predict upscaled bimolecular reactive transport in a flow around an array of solid cylinders. This method combines the stochastic Lagrangian Spatial Markov model (SMM) to predict transport and a volume averaged reaction rate equation to predict reactions of the form $$A+B\rightarrow \emptyset$$ . Here, we extend the LATERS Markov model to upscale bimolecular reactive transport in a Darcy flow through an idealized heterogeneous porous medium. In agreement with previous literature, the accuracy of the prediction is a function of the Damkohler (Da) numbers, i.e., high Da are more challenging because of incomplete mixing. It was found that a key component which must be incorporated into the upscaled model in these high Da systems is the idea that nearby A and B particles should be more likely to react than those that are farther apart. This is here achieved by appropriately reducing the resolution of the spatial grid employed to resolve the reactive process.