Kinetic Expression Research Articles

Dissolution of Lithium Contained in Lepidolite Using Ascorbic Acid: Kinetic and Modeling Analysis

In this work, a kinetic study and modeling of the decomposition of a rock sample in an ascorbic acid medium with a high content of lepidolite phase were carried out, the results of which are of great importance due to the sample’s high lithium (Li) content. The rock sample was characterized by X-ray diffraction (XRD), inductively coupled plasma atomic emission spectroscopy (ICP-AES) and X-ray photoelectron spectroscopy (XPS), and the mineral species detected in the sample were lepidolite, at 65.3%, quartz, at 30.6%, and muscovite, at 4.1%, with a quantitative chemical analysis indicating the presence of elements such as Li, Si, K, Na, O, Al and, to a lesser extent, Fe and Ti; this highlights that the Li content present in the sample was 3.38%. Lithium was the element with which the chemical analysis of the kinetics was performed, resulting in decomposition curves comprising the induction period, progressive conversion and stabilization; this highlighted that the reaction progressed during the first two periods, obtaining a reaction order (n) of 0.4307 for the induction period and an activation energy (Ea) of 48.58 kJ mol−1, followed by a progressive conversion period with n = 0.309 and Ea = 25.161 kJ mol−1. This suggested a mixed control regime present in the lower temperature ranges, with a transition from chemical control to transport control present at high temperatures, with the study of the nature of the reaction and the concentration effect showing that chemical control predominates. The kinetic parameters and kinetic expressions for both periods were obtained, with the modeling showing that the calculated and experimental data do not present a major discrepancy.

Electrical Double Layer Spillover Drives Coupled Electron- and Phase-Transfer Reactions at Electrode/Toluene/Water Three-Phase Interfaces.

A mechanism for the concerted pathway of coupled electron- and phase-transfer reactions (CEPhT) is proposed. CEPhT at three-phase interfaces formed by a solid electrode, an insulating organic solvent, and an aqueous electrolyte is driven by electric double layer (EDL) spillover, with significant electrostatic potential gradients extending a few nanometers into the insulating phase. This EDL spillover phenomenon is studied using scanning electrochemical cell microscopy to interrogate the oxidation of ferrocene in toluene to ferrocenium in water, (Fc)tol → (Fc+)aq + e-. Finite element method simulations of the electrostatic potential distribution and species concentration profiles enable the calculation of complete i-E curves that incorporate mass transport, electron transfer, phase transfer, and the EDL structure. Simulated and experimental i-E traces show good agreement in the current magnitude and the effect of the supporting electrolyte, identifying an unexpected dependence of overall reaction kinetics on the concentration of the supporting electrolyte in the aqueous phase due to EDL spillover. An interfacial toluene/water mixing region generates a unique electrochemical microenvironment where concerted electron transfer and solvent shell replacement facilitate CEPhT. Kinetic expressions for concerted and sequential CEPhT mechanisms highlight the role of this interfacial environment in controlling the rate of CEPhT. These combined experimental and simulated results are the first to support a concerted mechanism for CEPhT where (Fc)tol is transported to the interfacial mixing region at the three-phase interface, where it undergoes oxidation and phase transfer. EDL spillover can be leveraged for engineering sample geometries and electrostatic microenvironments to drive electrochemical reactivity in classically forbidden regions, e.g., insulating solvents and gases.

Performance of a RuCs/MgO catalyst coated on additive manufactured support structures via electrophoretic deposition for ammonia synthesis

This work investigates the electrophoretic deposition of a catalytic coating on so-called fluid guiding elements (FGE) with a ruthenium-based catalyst for use in ammonia synthesis reactors. FGE are additive manufactured metallic pipe inserts that have shown to enhance the heat transfer compared to empty pipes by dividing the fluid flow and alternately guiding the partial flows to the wall. Consequently, they could improve the performance of temperature sensitive structured catalytic systems. To be able to demonstrate the degree of process intensification, the required steps to enable the deposition of a reference catalyst for ammonia synthesis are developed. Further, the distribution of catalytically active compounds is characterized. The catalytic activity is assessed in a plug flow reactor under pressures up to 5MPa and compared against a fixed bed from the same batch. The expected activity from the reference catalyst is calculated by a kinetic rate expression. The coating process does not affect catalytic activity, but a steady deactivation and high sensitivity to feed gas impurities are observed. Possible mechanisms for the deactivation are examined and discussed.

Highly Stable Ni-B/Honeycomb-Structural Al2O3 Catalysts for Dry Reforming of Methane.

Two-component catalysts have garnered significant attention in the field of catalysis due to their ability to inhibit Ni sintering. In the present work, honeycomb-structuralstructured Al2O3-supported Ni and B were prepared to enhance coke tolerance during dry reforming of methane (DRM). Transmission electron microscopy (TEM) results revealed that the average particle sizes on Ni/Al2O3 and Ni-0.16B/Al2O3 were 7.6 nm and 4.2 nm, respectively, indicating that B can effectively inhibit Ni sintering. After a 100-hour reaction, the conversion of CH4 and CO2 on Ni/Al2O3 decreased by approximately 5 %, whereas on Ni-0.16B/Al2O3, there was no significant decrease in CH4 and CO2 conversion, with values of approximately 81.6 % and 87.2 %, respectively. In situ DRIFT spectra demonstrated that Ni-0.16B/Al2O3 enhanced the activation of CO2, thus improving the catalyst's stability. A Langmuir-Hinshelwood-Hougen-Watson (LHHW) model was developed for intrinsic kinetics, and the resulting kinetic expressions were well-fitted fit to the experimental data, with R2 values exceeding 0.9. ActivationThe activation energies were also calculated. The outstanding stability of Ni-0.16B/Al2O3 can be attributed to its stable honeycomb structure and B's ability to significantly inhibit Ni sintering, reduce catalyst particle size, and enhance coke tolerance.

The Effect of External Magnetic Field on Electron Scale Kelvin–Helmholtz Instability

We use particle-in-cell, fully electromagnetic, plasma kinetic simulation to study the effect of external magnetic field on electron scale Kelvin–Helmholtz instability (ESKHI). The results are applicable to collisionless plasmas when, e.g., solar wind interacts with planetary magnetospheres or a magnetic field is generated in AGN jets. We find that as in the case of magnetohydrodynamic (MHD) KHI, in the kinetic regime, the presence of an external magnetic field reduces the growth rate of the instability. In the MHD case, there is a known threshold magnetic field for KHI stabilization, while for ESKHI this is to be analytically determined. Without a kinetic analytical expression, we use several numerical simulation runs to establish an empirical dependence of ESKHI growth rate, Γ(B 0)ω pe, on the strength of the applied external magnetic field. We find the best fit is hyperbolic, Γ(B0)ωpe=Γ0ωpe/(A+BB¯0) , where Γ0 is the ESKHI growth rate without an external magnetic field and B¯0=B0/BMHD is the ratio of external and two-fluid MHD stability threshold magnetic field, derived here. An analytical theory to back up this growth rate dependence on the external magnetic field is needed. The results suggest that in astrophysical settings where a strong magnetic field pre-exists, the generation of an additional magnetic field by the ESKHI is suppressed, which implies that nature provides a “safety valve”—natural protection not to “over-generate” magnetic field by the ESKHI mechanism. Remarkably, we find that our two-fluid MHD threshold magnetic field is the same (up to a factor γ0 ) as the DC saturation magnetic field, previously predicted by fully kinetic theory.

The technological prospects of repurposing methane steam reformers into ammonia crackers for decarbonized H2 production

The decarbonization of hydrogen production can be accelerated by repurposing existing methane steam reformers into ammonia crackers. Through kinetic modeling, reactor optimization, and process integration, we demonstrated the viability of repurposing industrial reformers into NH3 crackers using a Co-Ba-Ce extrudate catalyst. First, we combined an improved kinetic rate expression, validated through experiments, with a high-fidelity 2-D model to optimize the operation of a multi-tubular reactor with a fixed capacity of 7000 Nm3 h−1. Subsequently, we used heat integration techniques to integrate the reactor with supplementary and separation units. We proved the process energy efficiency to be 65.7% before heat integration and 75.3% for the integrated plant. The integrated, optimized plant results demonstrated the necessity of implementing an adiabatic pre-cracker, an element typically omitted in catalytic NH3 decomposition techno-economic models. Our findings underscore the importance of real-world constraints and operational aspects in designing and optimizing NH3 conversion processes.

Electrochemical–Mechanical Coupling Is Essential to Predict Solid-Electrolyte Fracture during Li-Metal Plating

Lithium propagation through the solid electrolyte is a main failure mechanism for the all-solid-state lithium-anode battery. Preceding the lithium penetration is a crack formation, i.e., fracture, in the solid electrolyte, providing a passage for lithium to preferentially grow during plating [1,2], due to the field-enhancement effect at the lithium tip [3]. Therefore, it is vital to understand both the crack initiation and lithium propagation for the prediction of the system behaviors, as well as the optimization of the interfacial design. Mathematical modeling is a key tool for the fundamental understanding of the undergoing physical processes.There are several solid-electrolyte fracture models in the literature, but they often treat none or a limited amount of the electrochemical–mechanical couplings. This is despite the fact that high stack pressure, as well as the stress build-up at the lithium/electrolyte interface, necessitate the consideration of stress in the thermodynamic, kinetic, and transport constitutive and governing equations. In particular, the Butler–Volmer equation (or alternative interfacial kinetic expression) must be modified to take into account the stress effects on the reaction kinetics. Furthermore, the incorporation of an appropriate lithium mechanical constitutive behavior is equally important for an accurate depiction of the system behaviors.Consequently, we aim to build a model that brings together (1) rigorous electrochemical–mechanical couplings and (2) appropriate lithium properties at the battery-application length scale to study the crack initiation during battery operation. It features an isolated Gaussian-curved lithium peak in perfect contact with the lithium-lanthanum-zirconium-oxide (LLZO) solid electrolyte. LLZO is treated as an elastic solid, while lithium is modeled as a non-Newtonian fluid. The pseudo-viscosity of lithium is carefully extracted from Haslam et al.’s thin-film compression experiment [4] using the force–displacement relationship in the squeeze-flow experiment. Current flow in the LLZO is treated with Ohm’s law, and the model is solved for a steady-state application of current.Preliminary results show that electrochemical–mechanical couplings strongly influence the model outputs. The stress distribution is intimately intertwined with the interfacial current distribution, which dictates the fracture initiation. Other key sensitivities include the constitutive model for the lithium metal and the asperity geometry. We also aim to present model parameter values that produce an experimentally observed fracture current density of around 1 mA/cm2.

The role of cyclodextrins in the acceleration of the reaction rate in a biphasic hydroformylations

Water based biphasic hydroformylation assisted by cyclodextrins is known for enhanced reaction rates in comparison to the non-assisted biphasic hydroformylation. In this paper, the liquid–liquid interface of the hydroformylation of 1–octene, enhanced by randomly methylated-β cyclodextrins (RAME-β cyclodextrins), was examined for the first time using an in-situ image-based boroscopic technology. This technique enables the observation of the liquid–liquid interfacial area (aLL) during the reaction and under reaction conditions, facilitating an explicit analysis of the droplet population.In this study defined mixtures of the reaction components with RAME-β cyclodextrins increased the aLL by 84 %. A kinetic study showed that RAME-β cyclodextrins reduce the rate limiting effect of the nonanal concentration in the two phasic water/octene system on the interphase. The kinetic expression shows consequently higher reaction rates for this three-phase conversion, leading to a 387 % increase in aldehyde yield. When comparing four different amounts of RAME-β cyclodextrins (nCD:nRh(acac)(CO)2 = 0 / 12:1 / 24:1 / 50:1), we observed a decreasing dependency of the reaction rates on the conversion progress and therefore on the nonanal formation for higher cyclodextrin concentrations. A recovery test of the aqueous phase involving nonanal and 1-octene reveals a drastically increased concentration of 1029 % 1-octene (coctene = 1.08 10-3 mg mg−1) and 13676 % nonanal (cnonanal = 14.41 10–3 mg mg−1) after the addition of 0.002 mol RAME–β cyclodextrins. These findings affirm that RAME-β cyclodextrins primarily remove nonanal from the interfacial region while facilitating an increased availability of 1-octene for the surface bound reaction.

An Application of DC Motor Modelled Classical Sliding Mode Control with Moving Sliding Surface to Rotary Inverted Pendulum System

The rotary inverted pendulum system (RIP), which is highly favored in control applications, is examined in this work. By determining the coordinates of the Rip elements' centers of gravity, the system's total kinetic and potential energies were determined. The kinetic and potential energy expressions were used to generate the Lagrangian function. Expressions providing the system's equations of motion were discovered by taking the Lagrangian approach into consideration. The motor's equations, which will initiate the system, have also been considered. Through the use of state variables and a Matlab program, the system's pendulum angle was managed by using a moving sliding surface and the traditional sliding mode control technique. Based on the dynamics, the slip surface's slope was computed. The sliding surface's slope was computed based on the system's dynamics. The genetic algorithm was utilized to determine the ideal values for the coefficients employed in the control structure. The findings showed that the inaccuracy was roughly zero and that the pendulum angle took around 1.5 seconds to reach the intended reference value. Furthermore, it noted that the motor torque and current values are 12 Nm and 2.5 amps, respectively. The findings show that the motor values are reasonably similar to the values seen in real-world applications. Control in real-time applications won't be an issue if the motor is chosen based on these values

Kinetic Model Implementation of Fluidized Bed Devolatilization

Computational modeling is a powerful tool for studying and investigating the behavior of fluidized bed gasifiers and the modeling of the initial devolatilization step is necessary to provide a reliable description of the whole process involving the feedstock decomposition and the subsequent gasification reaction. In this work, a bench-scale fluidized bed reactor was used to examine the devolatilization of different carbonaceous materials within the temperature range from 650 to 850 °C. The experimental test campaign was used to derive the linear correlation factor to describe the devolatilization in terms of product distribution as a function of temperature and highlight the different behavior between lignocellulosic and plastic feedstocks. Furthermore, the experimental data were used to develop concise kinetic expressions able to fit the experimental devolatilization times ranging from 75 in the case of poplar at a lower temperature and 22 s for the Organic Fraction of Municipal Solid Waste (OFMSW) at a higher temperature. The obtained model produces a simple kinetic expression where the size of the particle is enclosed in the kinetic parameters. The kinetic model sided by the application of linear correlations describes the overall thermal decomposition in a fluidized bed, simplifying its modeling in commercial simulation software, even when particles are considered as point-like bodies.

PERSPECTIVE: Analysis of thixotropic timescale

Thixotropy is characterized by a time-dependent rise in viscosity under no or weak flow conditions and a decrease in viscosity over time when subjected to strong flow conditions. The characteristic timescale associated with the thixotropic phenomenon, particularly how the viscosity increases with time, has been termed the thixotropic timescale. Several approaches have been suggested in the literature for estimating the thixotropic timescale. The most prominent approach, however, infers it from a specific form of a kinetic expression for structure parameter evolution. In this paper, we study the various kinds of structural kinetic models. By carefully analyzing the same, we propose a parameter for the thixotropic timescale associated with the most generic form of kinetic expression for structure parameter evolution. We observe that increasing the thixotropic timescale weakens the thixotropic character of a system when the viscosity of the structural kinetic model continuously increases over time and eventually diverges under quiescent conditions. We also propose a new phenomenological measure of the thixotropic timescale: τthix=(dlnη/dt)−1, where η is viscosity and t is time. The proposed definition allows a straightforward and unique way to determine the thixotropic timescale through experiments and agrees well with the conventional notion of thixotropy.

Core–Shell catalyst particles for tandem catalysis: An experimental/numerical approach towards optimal design

Tandem catalysis is a promising approach to intensify chemical processes and increase their efficiency. On the other hand, the design of efficient, optimal and targeted tailored tandem catalysts is yet so challenging as the optimal catalyst loading is difficult to assess a priori. In this article, we present a concise route towards the design of optimal core–shell tandem catalyst particles on the example of coupled RWGS and FTS reactions for any specific spherical morphology. The route features five consecutive steps including: tandem system identification, catalyst synthesis, i.e. mono- and tandem-functional, catalyst characterization and initial performance test, kinetic modeling with parameter estimation if necessary, and optimal design of catalysts. The initial step features thermodynamic equilibrium calculations for RWGS and FTS showing a common operational window. Then, Pt and Co are selected as active metals and the formulation of the tandem catalyst is designed. For the second step, the synthesis route for the tandem catalyst Pt,CeO2@SiO2-Co, and the mono-functional catalysts, Pt@SiO2 and CeO2@SiO2-Co are presented. For the third step, all catalysts were tested for CO2 hydrogenation as an exemplary tandem process. A reduced transport model from literature was adjusted for RWGS and FTS reactions with kinetic expression from literature to enable numerical optimization. The kinetic parameters are estimated based on the performance tests of the mono-functional reference materials, i.e. Pt@SiO2 for RWGS and CeO2@SiO2-Co for FTS. The model is validated by cross comparison to the data from the tandem reaction setup. In the fifth step, the model was used for the numerical optimization of the catalyst loading on core and shell leading to the identification of the optimal design, resulting in a significant increase of C2+ Yield.

Elucidating solvent effects on lipase-catalyzed peroxyacid synthesis through activity-based kinetics and molecular dynamics.

Peroxyacid synthesis is the first step in Prilezhaev epoxidation, which is an industrial method to form epoxides. Motivated by the development of a kinetic model as a tool for solvent selection, the effect of solvent type and acid chain length on the lipase-catalyzed peroxyacid synthesis was studied. A thermodynamic activity-based ping-pong kinetic expression was successfully applied to predict the effect of the reagent loadings in hexane. The activity-based reaction quotients provided a prediction of solvent-independent equilibrium constants. However, this strategy did not achieve satisfactory estimations of initial rates in solvents of higher polarity. The lack of compliance with some assumptions of this methodology could be confirmed through molecular dynamics calculations i.e. independent solvation energies and lack of solvent interaction with the active site. A novel approach is proposed combining the activity-based kinetic expression and the free binding energy of the solvent with the active site to predict kinetics upon solvent change. Di-isopropyl ether generated a strong interaction with the enzyme's active site, which was detrimental to kinetics. On the other hand, toluene or limonene gave moderate interaction with the active site rendering improved catalytic yield compared with less polar solvents, a finding sharpened when peroctanoic acid was produced.

Revealing novel and conservative T-cell epitopes with MHC B2 restriction on H9N2 avian influenza virus (AIV)

B2 haplotype major histocompatibility complex (MHC) has been extensively reported to confer resistance to various avian diseases. But its peptide-binding motif is unknown, and the presenting peptide is rarely identified. Here, we identified its peptide-binding motif (X-A/V/I/L/P/S/G-X-X-X-X-X-X-V/I/L) invitro using Random Peptide Library-based MHC I LC-MS/MS analysis. To further clarify the structure basis of motif, we determined the crystal structure of the BF2∗02:01-PB2552-560 complex at 1.9Å resolution. We found that BF2∗02:01 had a relatively wide antigen-binding groove, and the structural characterization of pockets was consistent with the characterization of peptide-binding motif. The wider features of the peptide-binding motif and increased number of peptides bound by BF2∗02:01 than BF2∗04:01 might resolve the puzzles for the presence of potential H9N2 resistance in B2 chickens. Afterward, we explored the H9N2 avian influenza virus (AIV)-induced cellular immune response in B2 haplotype chickens invivo. We found that ratio of CD8+ T cell and kinetic expression of cytotoxicity genes including Granzyme K, interferon-γ, NK lysin, and poly-(ADP-ribose) polymerase in peripheral blood mononuclear cells were significantly increased in defending against H9N2 AIV infection. Especially, we selected 425 epitopes as candidate epitopes based on the peptide-binding motif and further identified four CD8+ T-cell epitopes on H9N2 AIV including NS198-106, PB2552-560, NP182-190, and NP455-463 via ELI-spot interferon-γ detections after stimulating memory lymphocytes with peptides. More importantly, these epitopes were found to be conserved in H7N9 AIV and H9N2 AIV. These findings provide direction for developing effective T cell epitope vaccines using well-conserved internal viral antigens in chickens.

Methane Combustion Kinetics over Palladium-Based Catalysts: Review and Modelling Guidelines

Fugitive methane emissions account for a significant proportion of greenhouse gas emissions, and their elimination by catalytic combustion is a relatively easy way to reduce global warming. New and novel reactor designs are being considered for this purpose, but their correct and efficient design requires kinetic rate expressions. This paper provides a comprehensive review of the current state of the art regarding kinetic models for precious metal catalysts used for the catalytic combustion of lean methane mixtures. The primary emphasis is on relatively low-temperature operation at atmospheric pressure, conditions that are prevalent in the catalytic destruction of low concentrations of methane in emission streams. In addition to a comprehensive literature search, we illustrate a detailed example of the methodology required to determine an appropriate kinetic model and the constants therein. From the wide body of literature, it is seen that the development of a kinetic model is not necessarily a trivial matter, and it is difficult to generalize. The model, especially the dependence on the water concentration, is a function of not only the active ingredients but also the nature of the support. Kinetic modelling is performed for six catalysts, one commercial and five that were manufactured in our laboratory, for illustration purposes.

Kinetic study of Fe & Co perovskite catalyst in Fischer–Tropsch synthesis

The investigation of the reaction's kinetics is one of the most crucial aspects of the design of a commercial process. The current research investigates the kinetics of Fischer–Tropsch synthesis using a perovskite catalyst. The LaFe0.7 Co0.3 O3 perovskite catalyst was prepared via the thermal sol–gel technique and characterized using BET, XRD, SEM, and H2-TPR techniques. According to operating conditions (e.g. H2/CO: 1–2, pressure: 10–20 barg, temperature: 240–300 °C, and GHSV: 3000 1/h), Fischer–Tropsch reaction kinetics (CO conversion) were carried out in a fixed-bed reactor. Using the framework of Langmuir–Hinshelwood–Hougen–Watson (LHHW) theories, 18 kinetic expressions for CO conversion were derived, and all were fitted to experimental data one by one to determine the optimum condition. The correlation was derived from experimental data and well-fitted using LHHW form (according to the enol mechanism, carbon monoxide and dissociated hydrogen atoms are adsorbed and reacted on the surface of the catalyst) −rCO = kpbCOPCO(bH2PH2)0.5/(1 + bCOPCO + (bH2PH2)0.5)2. Finally, the activation energy of the optimum kinetic model was determined with respect to the Arrhenius equation under various operating conditions. The activation energy of perovskite catalyst is about 106.25 kJ/mol at temperatures 240–300 °C, pressures 10–20 barg, and H2/CO ratios 1–2, which is lower than other types of catalyst. Therefore, the catalyst was activated at a high temperature and demonstrated stable performance without any temperature runaway and coking issues.

Kinetics of CO2 hydrogenation to methanol over CuO/ZnO/ZrO2 catalyst: Comparison of the differential and integral methods of kinetic analysis

AbstractThe experimental data over CuO/ZnO/ZrO2 catalyst for a wide range of operating conditions were used to develop the kinetics of the reaction CO2 hydrogenation to methanol. Three kinetic models such as the power law model, the Graaf kinetic model, and the Park kinetic model were tested against the experimental data. Both the mechanistic models have been developed based on the Langmuir‐Hinshelwood‐Hougen‐Watson approach and are specific only to the methanol synthesis from CO/CO2 hydrogenation. In an attempt to reduce the number of parameters in the two models, the abridged forms of these models were also tried. Overall, 25 kinetic rate equations were tested and the best‐fit kinetic rate expression with optimized parameters was worked out. Both the integral and differential methods of kinetic analysis were employed and their efficacy in finding the best‐fit expression was compared. The MATLAB built‐in function fminsearch was employed to perform the regression of the data. The Graaf model in its parent form, but with the new optimized values of the parameters, was found to be the best‐fit rate model. The Graaf kinetics, with re‐estimated parameters, could be helpful in designing and simulating a methanol synthesis reactor operating on CO2 and H2 feed and utilizing a CuO/ZnO/ZrO2 catalyst.

A Study on the Pyrolysis Behavior and Product Evolution of Typical Wood Biomass to Hydrogen-Rich Gas Catalyzed by the Ni-Fe/HZSM-5 Catalyst

The thermo-chemical conversion of biomass wastes is a practical approach for the value-added reclamation of bioenergy in large quantities, and pyrolysis plays a core role in this process. In this work, poplar (PR) and cedar (CR) were used as staple wood biomasses to investigate the apparent kinetics of TG/DTG at different heating rates. Secondly, miscellaneous wood chips (MWC), in which PR and CR were mixed in equal proportion, were subjected to comprehensive investigations on their pyrolysis behavior and product evolution in a fixed bed reactor with pyrolysis temperature, catalyst, and the flow rate H2O steam as influencing factors. The results demonstrated that both PR and CR underwent three consecutive pyrolysis stages, the TG/DTG curves shifted to higher temperatures, and the peak temperature intervals also enhanced as the heating rate increased. The kinetic compensation effect expression and apparent reaction kinetic model of CR and PR pyrolysis were obtained based on the law of mass action and the Arrhenius equation; the reaction kinetic parameter averages of Ea and A of its were almost the same, which were about 72.38 kJ/mol and 72.36 kJ/mol and 1147.11 min−1 and 1144.39 min−1, respectively. The high temperature was beneficial for the promotion of the pyrolysis of biomass, increased pyrolysis gas yield, and reduced tar yield. This process was strengthened in the presence of the catalyst, thus significantly increasing the yield of hydrogen-rich gas to 117.9 mL/g-biomass. It was observed that H2O steam was the most effective activator for providing a hydrogen source for the whole reaction process, promoted the reaction to proceed in the opposite direction of H2O steam participation, and was beneficial to the production of H2 and other hydrocarbons. In particular, when the flow rate of H2O steam was 1 mL/min, the gas yield and hydrogen conversion were 76.94% and 15.90%, and the H2/CO was 2.07. The yields of H2, CO, and CO2 in the gas formation were significantly increased to 107.35 mL/g-biomass, 53.70 mL/g-biomass, and 99.31 mL/g-biomass, respectively. Therefore, H2 was the most dominant species among gas products, followed by C-O bond-containing species, which provides a method for the production of hydrogen-rich gas and also provides ideas for compensating or partially replacing the fossil raw material for hydrogen production.

Limitations and generalizations of the first order kinetics reaction expression for modeling diffusion-driven exchange: Implications on NMR exchange measurements.

The study and modeling of water exchange in complex media using different applications of diffusion and relaxation magnetic resonance (MR) have been of interest in recent years. Most models attempt to describe this process using a first order kinetics expression, which is appropriate to describe chemical exchange; however, it may not be suitable to describe diffusion-driven exchange since it has no direct relationship to diffusion dynamics of water molecules. In this paper, these limitations are addressed through a more general exchange expression that does consider such important properties. This exchange fraction expression features a multi-exponential recovery at short times and a mono-exponential decay at long times, both of which are not captured by the first order kinetics expression. Furthermore, simplified exchange expressions containing partial information of the analyzed system's diffusion and relaxation processes and geometry are proposed, which can potentially be employed in already established estimation protocols. Finally, exchange fractions estimated from simulated MR data and derived here were compared, showing qualitative similarities but quantitative differences, suggesting that the features of the derived exchange fraction in this paper can be partially recovered by employing an existing estimation framework.

Data‐driven identification of crystallization kinetics

AbstractA novel data‐driven methodology is presented for developing mathematical models for crystallization processes. The data‐driven approach is based on the sparse identification of nonlinear dynamics (SINDy) method, which iterates between a partial least‐squares fit and a sparsity‐promoting step leading to the discovery of sparse interpretable models. The performance of the SINDy methodology is characterized for the identification of crystallization kinetics in a mixed tank operated in a continuous mode, the isothermal crystallization of lysozyme in a batch stirred tank and cooling crystallization of paracetamol. The SINDy method is robust against noise. Good agreement is obtained between the data‐driven model and the data obtained from crystallization experiments. The presented data‐driven approach can be attractive for modeling industrial crystallization processes where process analytical technology tools are available for the measurement of process variables but functional forms of kinetic expressions are unknown.