Effective Reaction Rate Research Articles

Filtered reaction rate and interphase mass transfer models in reactive gas‐solid flows

AbstractThis work pursues the closure for the effective reaction rate based on fine‐grid two‐fluid model (TFM) simulations in reactive gas‐solid flows. It is found that the mesoscale mechanism in the solid‐catalyzed reaction is constrained by the kinetic regime (KR) and the external mass transfer‐controlled regimes (EMTR). Thus, a filtered reaction rate model ηsubgrid considered two different regimes is proposed. The mesoscale effectiveness factor proposed in previous work is adopted in KR. A filtered interphase mass transfer model QM, which is constructed by analogy to the interphase heat transfer model, is used in EMTR. ηsubgrid shows a good predictability in two regimes via a priori test. The fidelity of ηsubgrid is also assessed via a filtered TFM simulation. The results indicate that the simulations incorporating corrections for the drag force and reaction rate yield better agreement with the fine‐grid simulations for both mass fraction and reaction rate profiles.

Upscaling the reaction rates in porous media from pore- to Darcy-scale

Modeling and prediction of reactive transport in porous media are challenging due to the complexity of the characterization of reactions across spatial and time scales. The application of reaction rates obtained from batch experiments to porous media is not valid because it disregards the influences of flow pathways, distribution of residence time, transport limitations within the porous media, as well as neglecting the impact of surface mineralogy heterogeneity. In this study, we presented how the pore-scale modeling can help to improve the Darcy-scale simulations. First, the reactive transport was simulated in a pore-network model and was validated against the experiments. Then, the pore-network results were averaged to obtain the effective reaction rates as a function of pore velocity, the inlet concentration, and the resident concentration. The upscaled function was incorporated into the Darcy-scale model and showed a significant improvement in predicting the concentration profiles. Notably, the use of batch reaction rates in the Darcy model (ADRE-batch) led to significant underestimation, up to 93%, of the required pore volume injection for complete contaminant removal from the simulation domain.

Quantum information scrambling and chemical reactions

The ultimate regularity of quantum mechanics creates a tension with the assumption of classical chaos used in many of our pictures of chemical reaction dynamics. Out-of-time-order correlators (OTOCs) provide a quantum analog to the Lyapunov exponents that characterize classical chaotic motion. Maldacena, Shenker, and Stanford have suggested a fundamental quantum bound for the rate of information scrambling, which resembles a limit suggested by Herzfeld for chemical reaction rates. Here, we use OTOCs to study model reactions based on a double-well reaction coordinate coupled to anharmonic oscillators or to a continuum oscillator bath. Upon cooling, as one enters the tunneling regime where the reaction rate does not strongly depend on temperature, the quantum Lyapunov exponent can approach the scrambling bound and the effective reaction rate obtained from a population correlation function can approach the Herzfeld limit on reaction rates: Tunneling increases scrambling by expanding the state space available to the system. The coupling of a dissipative continuum bath to the reaction coordinate reduces the scrambling rate obtained from the early-time OTOC, thus making the scrambling bound harder to reach, in the same way that friction is known to lower the temperature at which thermally activated barrier crossing goes over to the low-temperature activationless tunneling regime. Thus, chemical reactions entering the tunneling regime can be information scramblers as powerful as the black holes to which the quantum Lyapunov exponent bound has usually been applied.

Transition path theory for diffusive search with stochastic resetting

Many chemical reactions can be formulated in terms of particle diffusion in a complex energy landscape. Transition path theory (TPT) is a theoretical framework for describing the direct (reaction) pathways from reactant to product states within this energy landscape, and calculating the effective reaction rate. It is now the standard method for analyzing rare events between long lived states. In this paper, we consider a completely different application of TPT, namely, a dual-aspect diffusive search process in which a particle alternates between collecting cargo from a source domain A and then delivering it to a target domain B. The rate of resource accumulation at the target, k AB , is determined by the statistics of direct (reactive or transport) paths from A to B. Rather than considering diffusion in a complex energy landscape, we focus on pure diffusion with stochastic resetting. Resetting introduces two non-trivial problems in the application of TPT. First, the process is not time-reversal invariant, which is reflected by the fact that there exists a unique non-equilibrium stationary state (NESS). Second, calculating k AB involves determining the total probability flux of direct transport paths across a dividing surface S between A and B. This requires taking into account discontinuous jumps across S due to resetting. We derive a general expression for k AB and show that it is independent of the choice of dividing surface. Finally, using the example of diffusion in a finite interval, we show that there exists an optimal resetting rate at which k AB is maximized. We explore how this feature depends on model parameters.

Modulating Internal Coordination Configurations for High‐Density Atomic Antimony toward Advanced Fast‐Charging Sodium‐Ion Batteries

AbstractFast‐charging ability of sodium‐ion batteries (SIBs) is mainly determined by a highly effective redox reaction rate. However, traditional metal@carbon composites rarely achieve atom‐level dispersion at high density, resulting in poor reaction rates. Herein, supported by the introduction of carbon vacancies, abundant C─S/C─O chemical bonds are successfully established in a carbon carrier. Then, plenty of Sb single atoms (Sb SA/PC) are first anchored with a high loading of 31.4 wt%, achieving a high yield of 210.56 g per batch. Benefiting from dense Sb─O─C/Sb─S─C interfacial chemical bonds, Sb─S2O coordination configurations are firmly confined in the interior of carbon. Surprisingly, the conductivity of Sb SA/PC‐2 is approximately 2.2 × 107 times greater than that of pristine Sb2S3. Consequently, Sb SA/PC‐2 exhibits ultrahigh fast‐charging capability (201.7 mAh g−1 at 20.0 A g−1) and ultralong cycling life (364.4 mAh g−1 at 5.0 A g−1 after 5000 cycles). Theoretical calculations reveal that the fast‐charging capability can be attributed to the low migration barrier and increased number of active sites. Moreover, owing to the structural integrity of Sb single atoms, phase separation is effectively inhibited. This work is anticipated to open an avenue toward designing advanced electrode materials for ultrafast‐charging SIBs.

Influence of temperature on the chemical evolution and desorption of pure CO ices irradiated by cosmic-rays analogues

ABSTRACT Carbon monoxide (CO) plays a vital role in interstellar chemistry, existing abundantly in both gaseous and frozen environments. Understanding the radiation-driven chemistry of CO-rich ices is crucial for comprehending the formation and desorption of C-bearing molecules in the interstellar medium (ISM), particularly considering the potential impact of temperature on these processes. We report experimental data on irradiation processing of pure CO ice by cosmic ray analogues (95.2 MeV 136Xe23+ ions) at temperatures of 10, 15, and 20 K, in the IGLIAS set-up coupled to the IRRSUD beamline at GANIL (Caen, France). The evolution of the irradiated frozen samples was monitored by infrared spectroscopy. The computational PROCODA code allows us to quantify the chemical evolution of the samples, determining effective reaction rates coefficients (ERCs), molecular abundances at the chemical equilibrium (CE) phase, and desorption processes. The model integrated 18 chemical species – 8 observed (CO, CO2, C3, O3, C2O, C3O, C3O2, and C5O3) and 10 non-observed but predicted (C, O, C2, O2, CO3, C4O, C5O, C2O2, C2O3, C4O2) – linked via 156 reactions. Our findings reveal temperature-driven influences on molecular abundances at chemical equilibrium, desorption yields and rates, and ERC values. Certain reaction routes exhibit distinct thermochemical behaviours of gas- and ice-phase reactions which may be attributed to the presence of neighbouring molecules within the ice matrix. This study provides pivotal insights into the chemical evolution of CO-enriched ice under irradiation, impacting solid-state astrochemistry, clarifying molecular abundances, and advancing our understanding of ISM chemistry and temperature effects on ionized radiation-processed frozen ices.

Analytic prediction of the effective reaction rate for methane cracking in molten catalysts: Transition from kinetics-dominated to diffusion-limited regimes

Molten catalytic media are increasingly attracting interest as a suitable reaction environment where cracking of hydrocarbons and separation of the solid carbon product can be achieved simultaneously, ideally avoiding catalyst regeneration. In conditions relevant to industrial production, multiscale approaches are needed to predict the reactor performance, where the macroscopic dynamics of two-phase flow is combined with the evolution of the reaction inside individual bubbles. We here develop a thermodynamically-consistent, analytically solvable model for predicting the effective reaction rate resulting from the interplay between diffusive transport within the bubble and the surface reaction at the gas/liquid interface. The analytical solution is based on a spectral (eigenvalue/eigenfunction) expansion of the concentration profiles. We show how in practically affordable conditions, the effective characteristic time of the reaction can be estimated based only on the dominant eigenvalue of the diffusion-reaction problem. The closed-form knowledge of the dominant eigenvalue provides key insight in establishing the range of existence of diffusion-limited, mixed, and kinetics-controlled regimes. Based on the limiting solutions of the model, an approximate model for the conversion, yielding the explicit dependence of conversion on the equilibrium, kinetics and transport parameters is derived. The approach proposed is validated by comparing its predictions with the solution of the fully-coupled mass/momentum local balance equations obtained through a finite-element commercial solver enforced on a moving boundary domain to account for the bubble expansion due to the increasing number of moles in the gas phase.

Mental model of the influence of reactant properties on reaction rate

Reaction rate is still considered difficult by students because it contains abstract concepts and mathematical equations, so students' mental models are not complete. To connect the three levels of representation in the process of addressing chemical problems, learning has to employ mental models as a whole. Therefore, this study aims to obtain students' mental models regarding the influence of reactants properties on reaction rates. This research uses a qualitative descriptive method with the Mental Model Diagnostic Test-Interview About Event (MMDT-IAE) instrument. Based on the research results, there are two types of mental models, namely Partial Understanding (PU) and Partial Understanding with Certain Misconceptions (PU/SM). The effect of surface area on reaction rate, students 1, 2, 3, 4, 6, and 7 answered correctly but could not connect the three levels of representation, while student 5 could not explain the relationship between effective collisions and reaction rate. The influence of structure on reaction rates, students 1, 2, 3, 4, and 7 can answer structure, reactivity and collision theory, while student 5 cannot explain collision theory. Students 1, 4, and 7 can answer all the probing questions but cannot connect the three levels to the influence of ionization energy on the reaction rate. The conclusion of this research is that students' mental models regarding the influence of reactant properties are not complete and there are students who experience misconceptions. The implications of this research are as a basis for teachers to design appropriate learning strategies.

Modeling the chemical evolution and kinetics of pure H2O Ices under various types of radiation employing the PROCODA code

Water is one of the most abundant molecules in space, especially in cold environments, where it is the main constituting of astrophysical ices. The space ionizing radiation affects these ices and induces chemical changes, including desorption to gas-phase, which increase the complexity of the interstellar medium. In this work, we employed the PROCODA code to investigate the behavior of several pure water ices under different type of ionizing radiation such as UV, X-rays, electrons and cosmic rays analogues. Here, we employ molecular column densities from laboratory and solved a set of coupled chemical reactions to calculated effective reaction rates (ERCs) and characterize the chemical equilibrium of water ices under high radiation fluences. Briefly, we monitored the evolution of nine species (including the observed ones H2O, H2O2, and O3, and the predicted ones H, O, H2, OH, O2, and HO2). A discussion on the branching ratio for the considered reactions with the type of ionizing radiation is provided. Among the results, we observed that approximately 63% of the modeled molecules quantified at chemical equilibrium were non-observed species in the X-rays experiment, highlighting the importance of this work in providing insights into the processes that occur on the surface of icy interstellar grains exposed to cosmic radiation, including the formation and destruction of water ice. Accurate modeling of these processes can lead to a better understanding of the chemical evolution of interstellar and circumstellar environments, as well as offer insight into the formation and composition of celestial objects such as comets.

State-specific slip boundary conditions in non-equilibrium gas flows: Theoretical models and their assessment

In this study, we develop and assess a new approach to modeling slip boundary conditions in gas mixtures with coupled state-to-state vibrational-chemical kinetics and surface physical and chemical processes: adsorption, desorption, vibrational energy transitions, and chemical reactions. Expressions for velocity slip, temperature jump, and mass fluxes of species are derived on the basis of the advanced kinetic boundary condition taking into account gain and loss of particles in surface processes; theoretical expressions for the mass fluxes obtained in the frame of various approaches are compared. The developed model is implemented to the fluid-dynamic solver for modeling dynamics and state-to-state air kinetics in the boundary layer near stagnation point. Several test cases corresponding to a various degree of gas rarefaction are considered. Recombination probabilities and effective reaction rates are calculated and compared to recent molecular-dynamic simulations; the proposed model yields the best agreement for the recombination rate coefficient. It is shown that temperature jump significantly affects fluid-dynamic parameters and surface heat flux; the role of heterogeneous reactions on the silica surface is weaker. In the surface heating, there is a competition between these two effects: whereas the temperature jump reduces the wall heat flux, surface reactions cause its increase, but to a lesser extent. It is concluded that the model proposed in this study describes self-consistently detailed vibrational kinetics, rarefaction effects, and surface reactions and can be applied both in continuum and slip flow regimes.

Understanding the Molecular Kinetics and Chemical Equilibrium Phase of Frozen CO during Bombardment by Cosmic Rays by Employing the PROCODA Code

Within the cold regions of space, ices that are enriched with carbon monoxide (CO) molecules are exposed to ionizing radiation, which triggers new reactions and desorption processes. Laboratory studies on astrochemical ices employing different projectiles have revealed the appearance of several new species. In this study, we employed the upgraded PROCODA code, which involves a calculation phase utilizing thermochemistry data, to map the chemical evolution of pure CO ice irradiated by cosmic-ray analogs. In the model, we have considered 18 different chemical species (six observed: CO, CO2, C3, O3, C2O, and C5O3; 12 unobserved: C, O, C2, O2, CO3, C3O, C4O, C5O, C2O2, C2O3, C3O2, and C4O2) coupled at 156 reaction routes. Our best-fit model provides effective reaction rates (effective rate constants, (ERCs)), branching ratios for reactions within reaction groups, several desorption parameters, and the characterization of molecular abundances at the chemical equilibrium (CE) phase. The most abundant species within the ice at the CE phase were atomic oxygen (68.2%) and atomic carbon (18.2%), followed by CO (11.8%) and CO2 (1.6%). The averaged modeled desorption yield and rate were 1.3e5 molecules ion−1 and 7.4e13 molecules s−1, respectively, while the average value of ERCs in the radiation-induced dissociation reactions was 2.4e-1 s−1 and for the bimolecular reactions it was 4.4e-24 cm3 molecule−1 s−1. We believe that the current kinetics study can be used in future astrochemical models to better understand the chemical evolution of embedded species within astrophysical ices under the presence of an ionizing radiation field.

Gas Phase Reaction of Ketene with H2S in Troposphere: Catalytic Effects of Water and Ammonia

Background: Additions of water monomer (H2O) to simplest ketene, i.e., H2C=C=O (mentioned as ketene, henceforth) in the Earth's atmosphere results in the formation of acetic acid. However, this reaction is not feasible under tropospheric conditions due to the high reaction barrier amounting to nearly 40 kcal mol-1. A Significant reduction of the barrier height (below 20 kcal mol-1) is achieved upon addition of another H2O molecule as a catalyst. It is worth mentioning that like H2O and ammonia (NH3), H2S could also play an important role in the “loss mechanism” of various atmospherically important species such as ketones and aldehydes. Aims: This study aims to get insight into the energetics and kinetics of a reaction between ketene and H2S in the troposphere which has not been done before. Objective: Due to close similarity of H2O and H2S, studying the sulfolysis reaction between ketene and H2S could provide some interesting insights into the nature of various hydrogen bonded complexes of ketene as well as the impact on the products formed under the atmospheric conditions. Methods: The water and ammonia catalyzed gas-phase addition reactions of ketene with H2S has been investigated using CCSD(T)-F12a/cc-pVTZ-F12a//M06-2X/6-311++G** level of theory. In this study, rate constants for all possible reaction channels are calculated using transition state theory. Results: It is found that, under tropospheric conditions at 298 K and 1 atm, the rates via catalyzed reaction channels are significantly faster than those via uncatalyzed reactions. Between the two catalysts, ammonia acts as far better catalyst than water for this reaction. However, since the concentration of water is significantly larger than ammonia, the effective rate of water catalyzed reaction becomes higher than that of ammonia catalyzed reaction. Combustion is a major source of ketene in atmosphere. Under combustion conditions such as in the presence of air and at or above ignition temperature, the ammonia catalyzed channel is faster below 1500 K, while the uncatalyzed reaction channel becomes faster above that temperature. Conclusion: Results from the present study show that the barrier for thioacetic acid formation through uncatalyzed sulfolysis of ketene via faster C=O addition pathway is substantially high as 40.6 kcal mol-1. The barrier height of the two transition states TS1 and TS2 are 19.7 and 13.8 kcal mol-1 for water catalyzed reaction and 14.4 and 7.2 kcal mol-1 for ammonia catalyzed reaction. Thus, ammonia has appreciably lowered the barrier height compared to water as catalyst. It has been observed that the hydrolysis reaction is more probable than the sulfolysis reaction under atmospheric conditions in the troposphere, but the ammonia catalysed sulfolysis is the fastest one at 298 K. The effective rate constant of the water catalysed hydrolysis reaction is found to be more than the ammonia catalysed reaction due to the higher monomer concentration of water than ammonia. Ammonia catalyzed reaction rate increases monotonously with increasing temperature. Further rate coefficient for uncatalyzed reaction is found to be dominant under combustion conditions, i.e., above 1500 K.

Molecular data needs for advanced collisional-radiative modelling for hydrogen plasmas

Population models for molecular hydrogen (H2) are applicable in various fields of plasma physics and particularly in fusion research: they are necessary for the evaluation of plasma diagnostics (e.g. optical emission spectroscopy) or can be used to evaluate effective reaction rates for molecular processes (e.g. molecular-assisted recombination in divertor plasmas). The accuracy and completeness of population models for molecular hydrogen is strongly linked to the accuracy and availability of molecular reaction data. While there are recently huge improvements in the field of electron impact cross sections, the shortfalls regarding input data availability persist in the area of collisions between heavy particles and H2. An overview of the status of population models for H and H2 based on the Yacora solver is given. The data needs for collisional-radiative modelling are demonstrated by means of three examples comprising different detail levels, namely a purely electronic collisional-radiative model for the singlet system of H2, a corona model for the Fulcher-α band and a vibrationally resolved collisional-radiative model for the electronic ground state X1 of H2.Graphical abstractElectronic energy level diagram of the hydrogen molecule delimiting the population models discussed in this work

Effective parameters for biogeochemical reaction rates in heterogeneous porous media

Biogeochemical reactions are the key processes that control the cycle and transformation of subsurface materials. However, biogeochemical reaction rates vary with observation scales. Such scaling effect are usually addressed with effective parameters, but it remains unclear how to estimate these effective parameters. In this work, we summarized those main factors that may affect the estimation of effective parameters, and discussed the variation of effective parameters under different combinations of factors in numerical simulations. The results indicate that the substrate sources strongly affect the estimation of the effective parameters. In scenarios with identical substrate sources, the effective parameters differ little from the intrinsic parameters, and thus the macroscopic effective biogeochemical reaction rate can be directly estimated from the volume-averaged concentrations of reactants. However, in scenarios with different substrate sources, the mean-field rates usually overestimate the macroscopic effective rates, and the extent of such overestimation diminishes with increasing flow velocity (or with decreasing Da). The above results provide meaningful insights into the estimation of macroscopic effective biogeochemical reaction rates in a variety of natural or artificial scenarios. We also decomposed the effective parameters to explain the above results. It is suggested that the homogeneous distribution of electron donors, electron acceptors and microorganisms, as well as their positive spatial correlation with each other, are the main reasons for the diminished scaling effect of biogeochemical reactions.

Insight into the action mechanism of ammonia in one-pot synthesis of hermetic Al@Ag core–shell particles via deposition model

In this study, Al@Ag particles with hermetic silver shell were successfully prepared by a facile one-pot electroless plating method and the effect of NH3·H2O in reaction process was investigated. The result shows that the concentration ratio of NH3·H2O to Ag+ from 18:1–55:1 triggers a continuous transition of the silver coating from raspberry-like granule to hermetic and then loose. This transition is mainly dependent on the suppression of Ag deposition as increasing NH3·H2O concentration. It was confirmed using silver deposition kinetic and electrochemistry tests. Based on these experimental results, a deposition model was proposed to quantify the specific behavior of NH3·H2O in inhibiting Ag deposition from the perspective of interfacial reaction between active center and [Ag(NH3)2]+. The deposition model was fitted well with experimental results and the effective chemical reaction rate (keff) at solid-liquid interface were calculated, which is the critical factor affecting nucleation and coating quality. As CNH3·H2O:CAg+= 48:1, keff is 0.0117 mol L−1 min−1, a compact core-shell Al@Ag particle is realized and the resistivity as low as 1.21 × 10−4 Ω·cm even with Ag content is 15.61 wt%. This work revealed the dual role of NH3·H2O in complexing Ag+ and regulating keff to control silver grain size and distribution.

Modeling Catalyzed Reactions on Metal-Doped Amorphous Silicates: The Case of Niobium-Catalyzed Ethylene Epoxidation

Metal-doped amorphous silicates are promising materials for heterogeneous catalysis because they are easy to make and their properties can be tuned for specific reactions. However, the amorphous nature of the surface makes the characterization difficult, and improvements are based on a trial and error approach. Density functional theory simulations can in principle provide direct structure–property relations, but the sampling of the active site configuration space is not possible via brute force. In this contribution, we use the Nb-catalyzed epoxidation of ethylene as a test reaction to analyze various aspects of the modeling that need to be taken into account for simulations of effective reaction rates. We show that each site can host a variety of transition state structures that represent the same reaction event, but that can differ considerably in reaction barrier. Furthermore, many different sites need to be sampled. We then use machine learning to identify the most important descriptors of the bare active site that correlate directly with the energy barrier. Although our test set is too small for quantitative predictions of reaction rates, we discuss what the important features of a very active site are that can drive the kinetics in the real material.

Particle-scale and sub-grid drag models coupled CFD for simulating the CO methanation in a CFB riser

The diffusion and chemical reactions inside the catalyst particles and the heterogeneous flow structure in the computational cells are key factors to affect the accuracy of the coarse-grid simulation in circulating fluidized bed (CFB) methanation reactors. In this work, a particle-scale model is developed to calculate the effective reaction rate considering the transient diffusion and chemical reactions in the particle scale, i.e., the scale of the single catalyst particle. A modified sub-grid drag model is proposed to consider the effects of the meso-scale and chemical reactions on the heterogeneous gas-solid interaction, where the meso-scale is between the single particle and the whole reactor and featured with the particle cluster. Subsequently, a coupled model is developed by integrating the particle-scale and modified sub-grid drag models into CFD. Moreover, the coupled model is validated to achieve accurate predictions on the CO methanation process in a CFB riser. Notably, the coupled model can be performed with a coarse grid (∼58 times particle diameter) and a large time step (0.005 s) to accelerate the simulation. By simply changing the reaction kinetics, different gas-solid catalytic reaction systems can be simulated by using the coupled model.

Novel 3D analysis of reduction behavior of single iron-oxide particle in CO-CO2 gas atmosphere

The production of steel, which is achieved by the reduction of iron ores mainly through indirect reduction reactions in a blast furnace, is gradually increasing worldwide. Because the reducing gas diffuses three-dimensionally, irregular particle shapes influence the reduction through differences in the diffusion length. The analysis of actual irregularly shaped iron-ore particles using existing models is difficult because they are primarily effective for 1D systems. Therefore, a novel reduction model based on the 3D diffusion equation that accommodates irregular particle shapes and 3D systems was developed in this study. The established model was validated by reproducing experimental conditions and comparing the quantified effective diffusivity and chemical reaction rate constant using the shrinking core model. In addition, the model was used to investigate the reducing behavior of an actual sintered-ore particle and the effects of particle sphericity and macro pore content. The sintered-ore particle had a higher reduction rate than that of a spherical equivalent with the same volume because sections of the surface with shorter diffusion lengths facilitated the gas diffusion. Additionally, the particle sphericity was determined to be inversely proportional to the reduction rate because the rate of gas diffusion into the particle depended on the diffusion length. With respect to porous particles, the gas was found to readily diffuse into the particles through pores, leading to a higher reduction rate for higher pore numbers. Overall, the gas diffusion was confirmed to drive the reduction reaction.

Fictitious neutron sinks to trace radiative s-process nucleosynthesis

Context. Asymptotic giant branch (AGB) stars are strong producers of s-process elements, which are synthesized by successive slow neutron captures on elements heavier than iron. The nucleosynthesis calculation involves solving large nuclear networks with hundreds of nuclei, which in a stellar evolution code can greatly extend the computational time. However, the s-process is often measured using a handful of elements located on the neutron magic shells and grouped into tracers called ls, hs, and vhs. Aims. We propose a fictitious network that approximates the production of ls, hs, and vhs species at a minimal computational expense. The network is specifically designed for the radiative s-process in AGB stars. It is an alternative to methods using large networks that can be used as a fast exploratory tool to trace the production of s-elements. Methods. The fictitious network was constructed by assembling species with Z ≥ 18 into seven fictitious particles whose abundances and reaction rates model the effective properties of the corresponding groups. The effective reaction rates were tabulated as a function of neutron density and number of neutrons captured per initial heavy seed (Ncapt) using single-zone nucleosynthesis calculations. The accuracy of our network was tested by comparing the abundances obtained with the fictitious and large networks during the radiative burning of 13C during the interpulse period of a 2 M⊙, [Fe/H] = −2 star. Results. The fictitious network reliably reproduces the abundances of ls, hs, and vhs species during the radiative s-process. The accuracy of the method increases with the strength of the nucleosynthesis as measured by Ncapt, but diminishes when the nuclear distribution is different from the initial distribution. This network is well suited to follow the s-process nucleosynthesis in low-mass AGB stars where neutrons are mainly produced below the envelope by the 13C(α, n) reaction.

Digital Core Analysis as an Efficient Tool for Acid Treatment Optimization

Digital rock workflow for acid treatment optimization is developed. It includes construction of a digital rock model based on X-ray microtomography, running a set of multiscale digital experiments and a number of acid flooding experiments on rock samples for the model tuning. Here, we present results of application of the developed workflow for Austin chalk rock treatment by hydrochloric acid on core samples of 8 mm in diameter. Pore-scale simulations were performed using high-resolution 3D microCT models to determine the dependencies of rock permeability, active surface area and effective reaction rate on actual porosity. These properties were used to populate the laboratory-size core models, and Darcy-scale numerical approach was applied to simulate the dissolution at different injection rates. The core-scale simulations demonstrated inhomogeneous character of dissolution process leading to wormhole development in a certain range of injection rates. In parallel to numerical simulations, laboratory experiments on the same rock samples were performed at flow rates close to the optimal regimes followed by microCT imaging of wormhole structures. This information was then used to tune the model parameters. After that, the dependencies of the number of pore volumes injected until the breakthrough (PVBT) on the injection rate were obtained numerically for all the cores considered.