Acid-rock reaction kinetics in a two-scale model based on reaction order correction

The reaction order plays a crucial role in evaluating the response rate of acid-rock.However,the conventional two-scale model typically assumes that the reaction order is constant as one,which can lead to significant deviations from reality.To address this issue,this study proposes a novel multi-order dynamic model for acid-rock reaction by combining rotating disk experimental data with theoretical derivation.Through numerical simulations,this model allows for the investigation of the impact of acidification conditions on different orders of reaction,thereby providing valuable insights for on-site construction.The analysis reveals that higher response orders require higher optimal acid liquid flow rates,and lower optimal H+diffusion coefficients,and demonstrate no significant correlation with acid concentration.Consequently,it is recommended to increase the displacement and use high-viscosity acid for reservoirs with high calcite content,while reducing the displacement and using low-viscosity acid for reservoirs with high dolomite content.

NATURAL PRODUCTS SYNTHESIS BY RETRO-DIELS-ALDER REACTION Ⅱ~1 ASYMMETRIC SYNTHESIS OF (+) AND (-) 5-OXO-ENDO-TRICYCLO [5.2.1.0.^(2, 6)] DECA-3, 8-DIENE 1 BY ENZYME-CATALYZED REACTION

Asymmetric syntheses of both enantiomerically pure (+) and (-) 5-oxo-endo-tricyclo [5.2.1.0.^(2,6)] deca-3, 8-diene 1 was described. The key step is the use of enzyme-catalyzed hydrolysis of meso-diacetate 5.

AUTO-DARBOUX TRANSFORMATION AND EXACT SOLUTIONS OF THE BRUSSELATOR REACTION DIFFUSION MODEL

Firstly, using the improved homogeneous balance method, an auto-Darboux transformation (ADT) for the Brusselator reaction diffusion model is found. Based on the ADT, several exact solutions are obtained which contain some authors' results known. Secondly, by using a series of transformations, the model is reduced into a nonlinear reaction diffusion equation and then through using sine-cosine method, more exact solutions are found which contain soliton solutions.

Study on reaction characteristics of phenolic hydroxyl in coal by using the model compound during direct coal liquefaction

The reaction characteristics of phenolic hydroxyl group were studied under the conditions of direct coal liquefaction. 2-naphthol was used as a coal model compound in this study. Under the conditions of with and without catalysts, a series of experiments were conducted at different temperatures, pressures and reaction time. Gas chromatography-mass spectrometry and gas chromatography were used to identify and quantify the reactants and products respectively. The conversion of 2-naphthol rises with the increase of reaction temperature, initial pressure and catalyst amount. The results indicated that tem- perature had a significant effect on 2-naphthol conversion, which promoted the dehydroxylation reaction. However, initial pressure had an important influence on the hydrogenation of 2-naphthol and naphthalene. The iron catalyst plays a significant role of cracking instead of hydrogenation. It is concluded that the harsh reaction conditions of high temperature, high pressure, and more catalyst are conducive to promoting dehydroxylation of 2-naphthol. The reaction mechanism was put forward based the experimental results, in which 2-tetralone was an intermediate.

Exploring the contribution of oxygen reduction reaction to Mg corrosion by modeling assisted local analysis

Oxygen reduction reaction(ORR)has been disclosed in recent studies as a significant secondary cathodic process during magnesium corrosion.This work elaborates on the contribution of ORR to the total corrosion process of pure Mg at different impurity levels in NaCl electrolyte with the assistance of local techniques.A finite element based numerical model taking into account the contribution of ORR during the corrosion of the Mg test materials has been designed in this study considering the local oxygen concentration.Respective computational simulations were calibrated based on the experimental data and evaluated accordingly.Finally,the simultaneous monitoring of local concentration of H_(2) and O_(2),and the combined modeling study reveal the relation between ORR and hydrogen evolution reaction.

Empirical correction of kinetic model for polymer thermal reaction process based on first order reaction kinetics

Based on the theory of first-order reaction kinetics,a thermal reaction kinetic model in integral form has been derive.To make the model more applicable,the effects of time and the conversion degree on the reaction rate parameters were considered.Two types of undetermined functions were used to compensate for the intrinsic variation of the reaction rate,and two types of correction methods are provided.The model was explained and verified using published experimental data of different polymer thermal reaction systems,and its effectiveness and wide adaptability were confirmed.For the given kinetic model,only one parameter needs to be determined.The proposed empirical model is expected to be used in the numerical simulation of polymer thermal reaction process.

KINETIC MODEL FOR DIFFUSION-CONTROLLED INTERMOLECULAR REACTION OF HOMOGENOUS POLYMER UNDER STEADY SHEAR

The kinetic model for diffusion-controlled intermolecular reaction of homogenous polymer under steady shear was theoretically studied. The classic formalism and the concept of conformation ellipsoids were integrated to get a new equation, which directly correlates the rate constant with shear rate. It was found that the rate constant is not monotonic with shear rate. The scale of rate constant is N^-1.5 （N is the length of chains）, which is in consistent with de Gennes＇s result.

A Theoretical Study on Nonadiabatic Trapping Models of the Reaction NH+H←→N+H_2

The properties of nonadiabatic trapping models of the reaction NH+H -N+H, are investigated in a collinear model as \veil as a non-collinear thermal reaction on the basis of theintrinsic reaction coordinate (IRC) intbrmation obtained by ah initio calculations at QCISD/631 IG** ie\el. Using the unitied statistical theory fornonadiabatic trapping models. the thermal rateconstants over the temperature range of 2000-3000K are computed which are in excellent agreementwith the experiment results.

Subdomain Model for Predicting Armature Reaction Field of Dual-Stator Consequent-Pole PM Machines Accounting for Tooth-Tips

This paper presents an exact analytical subdomain model of dual-stator consequent-pole permanent-magnet(DSCPPM)machines accounting for tooth-tips,which can accurately predict the armature reaction field distribution in DSCPPM machines.In the proposed subdomain model,the field domain is composed of four types of sub-regions,viz.magnets,outer/inner air gaps,slots and slot openings.The analytical expressions of vector potential in each sub-region are determined by boundary and interface conditions.In comparison to the analytically predicted results,the corresponding flux density field distributions computed by finite element(FE)method are analyzed,which confirms the excellent accuracy of the developed subdomain model.

Elastodynamic modeling and joint reaction prediction for 3-PRS PKM

To gain a thorough understanding of the load state of parallel kinematic machines(PKMs), a methodology of elastodynamic modeling and joint reaction prediction is proposed. For this purpose, a Sprint Z3 model is used as a case study to illustrate the process of joint reaction analysis. The substructure synthesis method is applied to deriving an analytical elastodynamic model for the 3-PRS PKM device, in which the compliances of limbs and joints are considered. Each limb assembly is modeled as a spatial beam with non-uniform cross-section supported by lumped virtual springs at the centers of revolute and spherical joints. By introducing the deformation compatibility conditions between the limbs and the platform, the governing equations of motion of the system are obtained. After degenerating the governing equations into quasi-static equations, the effects of the gravity on system deflections and joint reactions are investigated with the purpose of providing useful information for the kinematic calibration and component strength calculations as well as structural optimizations of the 3-PRS PKM module. The simulation results indicate that the elastic deformation of the moving platform in the direction of gravity caused by gravity is quite large and cannot be ignored. Meanwhile, the distributions of joint reactions are axisymmetric and position-dependent. It is worthy to note that the proposed elastodynamic modeling method combines the benefits of accuracy of finite element method and concision of analytical method so that it can be used to predict the stiffness characteristics and joint reactions of a PKM throughout its entire workspace in a quick and accurate manner. Moreover, the present model can also be easily applied to evaluating the overall rigidity performance as well as statics of other PKMs with high efficiency after minor modifications.

CFD modeling of reaction and mass transfer through a single pellet: Catalytic oxidative coupling of methane

In this study a mathematical model of a small scale single pellet for the oxidative coupling of methane（OCM）over titanite pervoskite is developed.The method is based on a computational fluid dynamics（CFD）code which known as Fluent may be adopted to model the reactions that take place inside the porous catalyst pellet.The steady state single pellet model is coupled with a kinetic model and the intra-pellet concentration profiles of species are provided.Subsequent to achieving this goal,a nonlinear reaction network consisting of nine catalytic reactions and one gas phase reaction as an external program is successfully implemented to CFD-code as a reaction term in solving the equations.This study is based on the experimental design which is conducted in a differential reactor with a Sn/BaTiO3 catalyst（7-8 mesh） at atmospheric pressure,GHSV of 12000 h-1,ratio of methane to oxygen of 2,and three different temperatures of 1023,1048 and 1073 K.The modeling results such as selectivity and conversion at the pellet exit are in good agreement with the experimental data.Therefore,it is suggested that to achieve high yield in OCM process the modeling of the single pellet should be considered as the heart of catalytic fixed bed reactor.

Theoretical uncertainties of(d,^(3)He)and(^(3)He,d)reactions owing to the uncertainties of optical model potentials

The theoretical uncertainties of single proton transfer cross sections of the(^(3)He,d)and(d,^(3)He)reactions,owing to the uncertainties of the entrance-and exit-channel optical model potentials,are examined with the^(30)Si(^(3)He,d)^(31)P,^(13)B(d,^(3)He)^(12)Be,and^(34)S(^(3)He,d)^(35)Cl reactions at incident energies of 25,46,and 25 MeV,respectively,within the framework of the distorted wave Born approximation.The differential cross sections at the first peaks in the angular distributions of these reactions are found to have uncertainties of approximately 5%,owing to the uncertainties in the optical model potentials from 20,000 calculations of randomly sampled parameters.This amount of uncertainty is found to be nearly independent of the angular momentum transfer and the target masses within the studied range of incident energies.Uncertainties in the single proton spectroscopic factors obtained by matching the theoretical and experimental cross sections at different scattering angles are also discussed.

A modified model for isothermal homogeneous and heterogeneous reactions in the boundary-layer flow of a nanofluid

The homogeneous and heterogeneous reactions in the boundary-layer of a flat surface are considered. The autocatalysts are assumed to be of regular sizes, while the solution is a dilute nanofluid. The heat release due to the chemical reactions is taken into account. The Buongiorno’s model is used to describe the behaviors of this reaction system. This configuration makes the current model be different from all previous publications. Multiple solutions are given numerically to the rescaled nonlinear system, whose stability is verified. The results show that the strength coefficients of the homogeneous and heterogeneous reactions are key factors to cause the appearance of the multiple solutions in the distribution of the chemical reactions. Nanofluids enhance the diffusion of heat and help maintain the stability of chemical reactions.

Free radical reaction model for n-pentane pyrolysis

A mathematical mechanism of the n-pentane pyrolysis process based on free radical reaction model was presented.The kinetic parameters of n-pentane pyrolysis are obtained by quantum chemistry and the reaction network is established. The solution of the stiff ordinary differential equations in the n-pentane pyrolysis model is completed by semi implicit Eular algorithm. Then the pyrolysis mechanism based on free radical reaction model is built,and the computational efficiency increases 10 times by algorithm optimization. The validity of this model and its solution method is confirmed by the experimental results of n-pentane pyrolysis.

Shape Evolution of the Compound Nucleus in the Superheavy Element Synthesis Reaction via the BUU Model

By taking the BUU model, we simulate the superheavy element synthesis reaction. With the rotation effect being included in the BUU model, the effect of the non-centrality of the reaction ^48Ca＋^238U→^286 112 is studied. It is shown that the promising impact parameter in the synthesis process can be released from zero to a value little smaller than the radius of the smaller nucleus involved in the reaction. Meanwhile, the compound nucleus may involve rich shape phases.

Adsorption of Pentachlorophenol onto Oxide and Clay Minerals: Surface Reaction Model and Environmental Implications

The adsorption of pentachlorophenol （PCP） onto quartz, kaolinite, illite, montmorillonite and iron oxides has been investigated by batch equilibrium techniques. The pH-dependent isotherms are curves with peak values, the position of which is at about pH = 5-6 depending on the mineral species. Based on distribution of both speciation of surface hydroxyls on minerals and PCP in solution a surface reaction model involving surface complexation and surface electrostatic attraction is presented to fit the pH-dependent isotherms, and both reaction constants are calculated. The results show that on quartz and phyllosilicate minerals the predominant adsorption reaction is surface complexation, meanwhile both of surface electrostatic attraction and surface complexation are involved on the iron oxide minerals. The reaction constants of surface electrostatic adsorption are usually one to three orders in magnitude, larger than that of surface complexation. The concentration-dependent isotherms can be well fitted by Langmnir equation with the correlation coefficient R〉0.93 for kaolinite and iron oxides. The maximum adsorption is found in the order： hematite 〉 lepidocrocite 〉 goethite 〉 kaolinite 〉 quartz 〉 montmorillonite ≈ illite, which can be interpreted by consideration of both reaction mechanism and surface hydroxyl density. The significant adsorption of PCP onto mineral surfaces suggests that clay and iron oxide minerals will play an important role as HIOCs are adsorbed in laterite or latertoid soil, which is widespread in South China.

A New Geochemical Reaction Model for Groundwater Systems

Through a survey of the literature on geology, hydrogeology and hydrogeochemistry, this paper presents a hydrogeochemical model for the groundwater system in a dross-dumping area of the Shandong Aluminium Plant. It is considered that the groundwater-bearing medium is a mineral aggregate and that the interactions between groundwater and the groundwater-bearing medium can be described as a series of geochemical reactions. On that basis, the principle of minimum energy and the equations of mass balance, electron balance and electric neutrality are applied to construct a linear programming mathematical model for the calculation of mass transfer between water and rock with the simplex method.

Numerical Modelling and Simulation of Chemical Reactions in a Nano-Pulse Discharged Bubble for Water Treatment

A zero-dimensional model to simulate a nano-pulse-discharged bubble in water was developed. The model consists of gas and liquid phases corresponding to the inside and outside of the bubble, respectively. The diffusions of chemical species from the gas to the liquid phase through the bubble interface was also investigated. The initial gas is Ar, but includes a little H20 and 02 in the bubble. The time evolution of the OH concentration in the liquid phase was mainly investigated as an important species for water treatment. It was shown that OH was generated in the bubble and then diffused into the liquid. With the application of a continuous nano-pulse discharge, more OH radicals were generated as the frequency increased at a low voltage for a given power consumption.

OPERATOR-SPLITTING GALERKIN METHOD FOR ONE KIND OF OIN REACTION MODEL FOR THE POLLUTION IN GROUNDWATER

The operator-splitting methods for the mathematic model of one kind of oin reactions for the problem of groundwater are considered.Optimal error estimates in L 2 and H 1 norm are obtained for the approximation solution.

Numerical Simulation on Gas-Solid Two-Phase Turbulent Flow in FCC Riser Reactors(Ⅰ) Turbulent Gas-Solid Flow-Reaction Model

Gas-solid two-phase turbulent flows,mass transfer,heat transfer and catalytic cracking reactions areknown to exert interrelated influences in commercial fluid catalytic cracking(FCC)riser reactors.In the presentpaper,a three-dimensional turbulent gas-solid two-phase flow-reaction model for FCC riser reactors was devel-oped.The model took into account the gas-solid two-phase turbulent flows,inter-phase heat transfer,masstransfer,catalytic cracking reactions and their interrelated influence.The k-V-k_P two-phase turbulence modelwas employed and modified for the two-phase turbulent flow patterns with relatively high particle concentration.Boundary conditions for the flow-reaction model were given.Related numerical algorithm was formed and a nu-merical code was drawn up.Numerical modeling for commercial FCC riser reactors could be carried out with thepresented model.