Multireaction Systems Research Articles

Temperature-dependent oxidation kinetics and mechanical properties degradation of Cf/ZrB2-SiC composites

The oxidation kinetics and microstructures evolution of Cf/ZrB2-SiC composites are investigated by experimental characterizations. An empirical model containing multi-reaction systems is further established for predicting the specimen mass evolution during isothermal oxidantion. Based on the morphological observations and in-situ tensile responses, three oxidation mechanisms of carbon phase controlled by reaction and diffusion kinetic are categorized as uniform, non-uniform and superficial oxidation. The relationship between fracture modes and internal fibers microstructures indicates that the structural origin of the fracture mode transition is the toughening mechanism transition of fibers on the ceramics matrix induced by oxidative damage.

Mechanistic and modeling insights into the immobilization of Cd and organic carbon during abiotic transformation of ferrihydrite induced by Fe(II)

Iron (Fe) oxides and fulvic acid (FA) are the key components affecting the fate of cadmium (Cd) in soil. The presence of FA influences Fe mineral transformation, and FA may complicate phase transformation and dynamic behavior of Cd. How varying Fe minerals and FA affect Cd immobilization during the ferrihydrite transformation induced by various Fe(II) concentrations, however, is still lack of quantitative understanding. In this study, we built a model for Cd species quantification during phase transformation based on mechanistic insights obtained from batch experiments. Spectroscopic analysis showed that Fe(II) concentrations affected secondary Fe minerals formation under the condition of co-existence of Cd and FA, and ultimately changed the distribution of Cd and FA. Microscopic analysis revealed that besides surface adsorption, part of Cd was sequestrated by magnetite, whereas FA was able to diffuse into lepidocrocite defects. The model revealed that adsorbed Cd was mainly controlled by FA and ferrihydrite, and direct complexation of Cd by FA had a strong impact on the continuous change in Cd at lower Fe(II) concentration. The results contribute to an in-depth understanding of the mobility of Cd in the environment and provide a method for quantifying the dynamic behavior of heavy metals in multi-reactant systems.

Determination of kinetic constants by using transient temperature data from continuous stirred tank reactors

Mathematical modelling of transient states of continuous stirred tank reactors was considered for the case of homogeneous liquid-phase reactions. A simple and very precise kinetic measurement strategy was proposed: registration of the reactor temperature during the start-up of the reaction process. The dynamic reactor model consisted of mass and energy balances written in dimensionless forms to enable general conclusions and easy computer implementation. Model simulations were carried out by using a numerical solver for stiff differential equations and a reaction invariant was revealed by theoretical analysis. A series of transient laboratory-scale experiments for a strongly exothermic reaction, a reaction between sodium thiosulphate and hydrogen peroxide was conducted and the kinetic parameters, the pre-exponential factors and activation energies were estimated. The data fitting was further improved by incorporating the decomposition of hydrogen peroxide as a side reaction. The estimated kinetic parameters were investigated further by sensitivity analysis and Markov-Chain-Monte-Carlo-Method (MCMC) to confirm their reliability. The proposed method is applicable for relatively simple systems with a measurable heat effect. For complex multireaction systems the method should be completed with chemical analysis.

Selectivity engineering with Single Feed Hybrid Reactive Distillation Configurations: Complex reaction schemes with inerts and inert forming azeotropes

Hybrid Reactive Distillation Configurations (HRDCs), with single feed/multi-side draws having both reactive and non-reactive sections, can be effectively used to get the desired selectivity in multi-reaction systems. Our previous research (Hasan et al., 2013a,b, 2014, 2015; Singh et al., 2018, 2019, 2021) was focused on finding designs of hybrid RD columns of desired selectivity for complex reaction schemes without inerts. In the present work, we extend the approach to cover a wider range of multi-reaction schemes and include systems with inerts present in feed as well as inert forming multi-azeotropes in the column. Using the concepts of attainable region and graphical simulation approach, we developed algorithms that are capable of finding at least one feasible design of hybrid RD configuration successfully that give the desired selectivity in the systems under study. Further, the effect of inert percentage in feed and volatility of inert on the design of hybrid RD columns is also investigated. The developed methodology allows us to find the maximum allowable percentage of inerts in feed to obtain a feasible design of hybrid RD column. The methodologies developed here are applicable to any number of inerts present in the feed, any number of total components, inerts of any volatility, inerts forming multi-azeotropes with any of the reactant, product/desired product. However, they are limited to single feed configurations and to the multi-reaction schemes with a maximum of three products undergoing further side reactions wherein the reactant(s) is/are of intermediate volatility.

Ingeniously designed Ni-Mo-S/ZnIn2S4 composite for multi-photocatalytic reaction systems

Molybdenum disulfide (MoS 2 ) with low cost, high activity and high earth abundance has been found to be a promising catalyst for the hydrogen evolution reaction (HER), but its catalytic activity is considerably limited due to its inert basal planes. Here, through the combination of theory and experiment, we propose that doping Ni in MoS 2 as catalyst can make it have excellent catalytic activity in different reaction systems. In the EY/TEOA system, the maximum hydrogen production rate of EY/Ni-Mo-S is 2.72 times higher than that of pure EY, which confirms the strong hydrogen evolution activity of Ni-Mo-S nanosheets as catalysts. In the lactic acid and Na 2 S/Na 2 SO 3 systems, when Ni-Mo-S is used as co-catalyst to compound with ZnIn 2 S 4 (termed as Ni-Mo-S/ZnIn 2 S 4 ), the maximum hydrogen evolution rates in the two systems are 5.28 and 2.33 times higher than those of pure ZnIn 2 S 4 , respectively. The difference in HER enhancement is because different systems lead to different sources of protons, thus affecting hydrogen evolution activity. Theoretically, we further demonstrate that the Ni-Mo-S nanosheets have a narrower band gap than MoS 2 , which is conducive to the rapid transfer of charge carriers and thus result in multi-photocatalytic reaction systems with excellent activity. The proposed atomic doping strategy provides a simple and promising approach for the design of photocatalysts with high activity and stability in multi-reaction systems. In this paper, doping Ni in MoS 2 as catalyst can make it have excellent catalytic activity in different reaction systems. It has been proved that Ni-Mo-S nanosheet has strong hydrogen evolution activity as catalyst by combining theory and experiment.

Numerical simulations of dead zone formation in the catalytic flow-through membrane reactor

The use of catalytic membranes in chemical reactor engineering has significantly improved the reactor performance. Therefore, mathematical modelling and numerical simulations of catalytic membrane reactors are important for optimal parameter design increasing the selectivity and yield of certain products in chemical reactions. In this paper, the mathematical model of the flow-through catalytic membrane reactor is based on coupled nonlinear convection-diffusion-reaction equations with temperature-dependent reaction rate constants. The series reactions in the reactor are characterized by the power-law kinetics of fractional order which until now has been rarely investigated in the literature. Under specific reaction and process conditions the reactant can be depleted and a dead-zone can be formed in the membrane reactor. The numerical simulation of this phenomenon requires special solvers. The key idea of this work is to construct an appropriate time-marching scheme for solving the steady-state model equations. The effects of parameters such as reaction order, Peclet number, and Thiele modulus on solution profiles and formation of dead-zones are studied numerically. The simulation results show how these parameters influence the appearance and size of the dead zone for the non-isothermal multi-reaction systems.

Stochastic self-tuning hybrid algorithm for reaction-diffusion systems.

Many biochemical phenomena involve reactants with vastly different concentrations, some of which are amenable to continuum-level descriptions, while the others are not. We present a hybrid self-tuning algorithm to model such systems. The method combines microscopic (Brownian) dynamics for diffusion with mesoscopic (Gillespie-type) methods for reactions and remains efficient in a wide range of regimes and scenarios with large variations of concentrations. Its accuracy, robustness, and versatility are balanced by redefining propensities and optimizing the mesh size and time step. We use a bimolecular reaction to demonstrate the potential of our method in a broad spectrum of scenarios: from almost completely reaction-dominated systems to cases where reactions rarely occur or take place very slowly. The simulation results show that the number of particles present in the system does not degrade the performance of our method. This makes it an accurate and computationally efficient tool to model complex multireaction systems.

Theory-Based Development of Performance Metrics for Comparing Multireactant Enzymes

The kcat/KM ratio holds substantial significance as a comparative figure of merit in the evaluation of enzymes with uni-molecular mechanisms. However, its applicability in the evaluation of multi-reactant systems is frequently not justified. Here, we derive figures of merit for multi-reactant enzyme mechanisms based on the stabilization of the transition states and the kinetic Haldane equilibrium relationships. For most bi-molecular reactions, the ratio of kcat/KiaKb (where Kia is the dissociation constant of A and Kb is the Michaelis constant of B) is best suited for comparing enzyme performance, especially at non-saturating reactant concentrations. The value of this parameter for assessing the performance of a series of oxidoreductase mutants is demonstrated. Figures of merit for other common enzymatic mechanisms are derived, which enable a theory-based approach for comparing steady-state catalytic performances of enzymes with multiple reactants.

Enhanced Energy Savings from Simultaneous Triple Esterification of C4–C6 Alcohols in a Single Reactive Distillation Column

This paper introduces multiple esterification reactions of three alcohols occurring in a single reactive distillation (RD) column and reports significant energy savings by combining three reactions in the single unit. To realize a feasible integration of the three reactions, the removal of the common water product from the unstable heterogeneous azeotrope should be possible through liquid–liquid decantation in the eight-component system. For this multireaction system, only the direct sequence can produce three esters with a purity higher than 99.0 mol % due to the behavior of liquid–liquid phase equilibrium. We demonstrate an economic evaluation of the direct sequence of a single RD column simultaneously producing the three esters by comparing the direct sequence with the two parallel RD sequences in the same design basis. The total annual cost of the triple esterification direct sequence is reduced by 21.3–25.2% compared to that of the parallel esterification system.

Selectivity Engineering with Hybrid Reactive Distillation Column: Mixtures Containing Inerts and Multi-Azeotropes

Reactive Distillation (RD) which combines reaction and distillation can be effectively used to get desired selectivities in multi-reaction systems. In case of azeotropic systems, nonideal vapor-liquid equilibrium and distillation boundaries are responsible for the contraction of the feasible reactive stage composition region required for the design of hybrid RD column. In the present study, we show that if the mixture contains inert as well then this feasible reactive stage composition region reduced further and thereby decreases the feasible design options of desired selectivity in multireaction systems. Therefore, an attempt is made here, to developed a conceptual design algorithm which is based on combined graphical-simulation approach and attainable region concepts. The developed methodology successfully finds at least one feasible design of hybrid RD column to give desired selectivity. Method gives excellent starting values for rigorous simulations suited to industrial applications.

Physical modeling of the laboratory-scale packed bed reactor for partial gas-phase oxidation of alcohol using gold nanoparticles as the heterogeneous catalyst

Packed bed reactors are often used for catalyst screening studies due to their simple construction and ease of operation. The use of gold nanoparticles for partial oxidation reactions of alcohols has arisen interest of the scientific community. A model was generated to explain the experimentally observed reactor behavior (conversion of alcohol, yields of products) in the alcohol oxidation over gold nanoparticles. The model for this gas-phase heterogeneously catalyzed multi-reaction system consisted of the dynamic mass and energy balances and Langmuir–Hinshelwood–Hougen–Watson, Mars van Krevelen or Power law expressions for the reaction kinetics. Fluid flow was described with convection and dispersion terms. A semi-empirical pressure drop correlation was used. This resulted in a rapidly running model by reducing the problem size significantly. Powerful gPROMS Modelbuilder software was used as the model development, simulation and parameter estimation platform. The primary task was to punctually define and solve the complete set of equations (Partial Differential Equations (PDEs) together with algebraic equations). The modeling effort focused on the selection of the complete set of equations to adjust the degrees of freedom 0 and on the simultaneous solution of the whole set. Numerical method of lines was applied to convert the partial differential equations to ordinary ones. All reactions were assumed to take place on evenly distributed active sites of the porous catalyst particles. The dynamic mass balances consisting of internal diffusion and surface reaction within the porous particles were solved simultaneously with the mass and energy balances of the whole reactor. The axial and radial concentration and temperature profiles inside the reactor and the concentration profiles within the particles were then obtained results. Starting from experiments performed at T=125–250°C, p=1atm and superficial gas velocity of 0.03m/s, a parameter estimation analysis was conducted. After the parameter estimation, the calculated alcohol conversion and yields of the main products (acetaldehyde and acetic acid) followed relatively closely the experimentally observed ones. The estimated parameters were the rate constants and the activation energies and the adsorption parameters (with LHHW kinetics, Mars van Krevelen kinetics) and reaction orders of oxygen (Power law kinetics). Simulation studies were done to show how feed temperature and catalyst loading influenced the results and how the Peclet number reflected on obtained results.

Harnessing the Combined Power of Theoretical and Experimental Data through Multiscale Informatics

ABSTRACTMonumental, recent and rapidly continuing, improvements in the capabilities of ab initio theoretical kinetics calculations provides reason to believe that progress in the field of chemical kinetics can be accelerated through a corresponding evolution of the role of theory in kinetic modeling and its relationship with experiment. The present article reviews and provides additional demonstrations of the unique advantages that arise when theoretical and experimental data across multiple scales are considered on equal footing, including the relevant uncertainties of both, within a single mathematical framework. Namely, the multiscale informatics framework simultaneously integrates information from a wide variety of sources and scales: ab initio electronic structure calculations of molecular properties, rate constant determinations for individual reactions, and measured global observables of multireaction systems. The resulting model representation consists of a set of theoretical kinetics parameters (with constrained uncertainties) that are related through elementary kinetics models to rate constants (with propagated uncertainties) that in turn are related through physical models to global observables (with propagated uncertainties). An overview of the approach and typical implementation is provided along with a brief discussion of the major uncertainties (parametric and structural) in theoretical kinetics calculations, kinetic models for complex chemical mechanisms, and physical models for experiments. Higher levels of automation in all aspects, including closed‐loop autonomous mixed‐experimental‐and‐computational model improvement, are advocated for facilitating scalability of the approach to larger systems with reasonable human effort and computational cost. The unique advantages of combining theoretical and experimental data across multiple scales are illustrated through a series of examples. Previous results demonstrating the utility of simultaneous interpretation of theoretical and experimental data for assessing consistency in complex systems and for reliable, physics‐based extrapolation of limited data are briefly summarized. New results are presented to demonstrate the high predictive accuracy of multiscale informed models for both small (molecular properties) and large (global observables) scales. These new results provide examples where the optimization yields physically realistic parameter adjustments and where physical model uncertainties in experiments are larger than kinetic model uncertainties. New results are also presented to demonstrate the utility of the multiscale informatics approach for design of experiments and theoretical calculations, accounting for both theoretical and experimental existing knowledge as well as relevant parametric and structural uncertainties in interpreting potential new data. These new results provide examples where neglecting structural uncertainties in design of experiments results in failure to identify the most worthwhile experiment. Further progress in the chemical kinetics field (particularly at the intersection of theory, kinetic modeling, and experiment) would benefit from increased attention to understanding parametric and structural uncertainties for all three—the uncertainty magnitude and cross‐correlations among model parameters as well as limitations of the model structures themselves.

Thermodynamic Equilibrium Analysis of Propane Dehydrogenation with Carbon Dioxide and Side Reactions

A thermodynamic analysis of propane dehydrogenation with carbon dioxide was performed using constrained Gibbs free energy minimization method. Different reaction networks corresponding to different catalytic systems, including non-redox and redox oxide catalysts, were simulated. The influences of CO2/C3H8 molar ratio (1–10), temperature (700–1000 K), and pressure (0.5–5 bar) on equilibrium conversion and product composition were studied. In the presence of CO2 with a molar ratio of CO2/C3H8 = 1, the temperature of dehydrogenation can be 30 K lower than that of dehydrogenation in the presence of steam (H2O/C3H8 = 1) and about 50 K lower than that of simple dehydrogenation without dilution to achieve 60% propane conversion. It was found that the occurrence of dry reforming of propane and coke-forming side reactions could strongly impact the equilibrium product composition of the multireaction system and, therefore, these reactions should be kinetically controlled. Comparison of the simulated reactant conversions with those reported in the literatures revealed that the experimental conversion levels of propane are far below the corresponding equilibrium values due to rapid catalyst deactivation by coke, implying that research efforts should be directed toward formulation of more active and selective catalysts.

Selectivity engineering with single feed multi-side draw hybrid reactive distillation columns

In multireaction systems reactive distillation (RD) not only increases the reactant conversion and purity but also proves very helpful to achieve the selectivity of the desired product. Designing a reactive distillation column for a multicomponent multireaction system is a challenging task, especially when the reactant is intermediate boiling or saddle in the residue curve map of the mixture. In the previous work (Hasan et al., 2014), we introduced simple hybrid RD column and hybrid RD column with single side draw to obtain a desired selectivity in single reactant multireaction schemes. In this work, we extend the approach further to include multi-side draw hybrid RD configuration and present, a new synthesis and design methodology. The developed algorithm is a combination of geometric method and simulation based design. We determine a surface of reactive stage compositions (SRSCs) such that if the reaction takes place at any of the compositions that belongs to SRSCs then the desired selectivity is ensured. Further, we also show that a single feed multi-side draw hybrid RD configuration is capable to give a desired selectivity in multi-reactant multireaction schemes wherein, both the reactants are saddle in the corresponding residue curve map. This is illustrated using an industrially relevant example of transesterification of dimethyl carbonate with ethanol to achieve the desired selectivity toward ethyl methyl carbonate. The results provide a good starting point for rigorous simulation. The algorithm presented here is applicable to any number of components and can be directly applied to even multi azeotropic systems as well. Though at this stage its applicability is restricted to the single feed configurations, we believe that the developed approach can be conveniently extended to multi-feed configurations with appropriate modifications.

Spontaneity and Equilibrium II: Multireaction Systems

The thermodynamic criteria for spontaneity and equilibrium in multireaction systems are developed and discussed. When N reactions are occurring simultaneously, it is shown that G and A will depend upon N independent reaction coordinates, ξα (α = 1,2, ..., N), in addition to T and p for G or T and V for A. The general criteria for spontaneity and equilibrium are the same as those for a single-reaction system, dG ≤ 0 (T and p constant) or dA ≤ 0 (T and V constant). However, dG and dA are now the sum of N terms. It is shown that this sum has the form dG = dA = ∑α=1N Δrμα dξα, where Δrμα is the reaction chemical potential for reaction α, (∂G/∂ξα)T,p,ξj. Consequently, the result that dG < 0 at a particular composition provides no information about which of the N reactions are proceeding spontaneously and which are nonspontaneous. At most compositions, there exist an infinite number of both spontaneous and nonspontaneous pathways for the system. Equilibrium in a multireaction system exists at a single compositi...

Selectivity engineering with single-feed hybrid reactive distillation columns

Reactive distillation (RD) can be advantageously used to improve the selectivity of the desired product in the multi-reaction system. Process synthesis and design of RD systems to attain the desired selectivity is a challenging task. Our previous work in this field (e.g. Amte et al., 2011, 2012) was restricted to fully reactive RD models and their networks. In this work, we examine the potential of a hybrid reactive distillation column, with both reactive and non-reactive sections, through an example of a single reactant complex reaction scheme (e.g. van de Vusse reaction) in which reactant is intermediate boiling. An algorithm for conceptual design of such columns is presented. It is based on the boundary value method (BVM) that utilizes the concept of operation leaves of rectifying and stripping sections; the overlap of which indicates the potential feasible split. Based on the desired selectivity, we determine the locus of reactive stage compositions in the RD column. Its intersections with the non-reactive stage composition lines (SCL) allow rapid screening of feasible designs of hybrid reactive distillation (HRD) columns. The approach generates multiple designs and allows one to compare them in terms of energy and catalyst requirement. The proposed method is applicable to single reactant single-feed hybrid columns, and because of its graphical representation, it cannot be directly used for systems with a large number of components. More work is therefore necessary to extend this approach to the multi-reactant double-feed hybrid configurations.

Optimization based conceptual design of reactive distillation for selectivity engineering

Reactive distillation can be effectively used to enhance the selectivity of the desired product in a multi-reaction system. Due to complex interaction of reactions and distillation, identification of an appropriate reactive distillation configuration for the known performance targets has been a challenge. The objective of this contribution is to present an MINLP optimization technique that would assist one to identify a suitable configuration for selectivity maximization at conceptual design level. An illustrative example of industrially important reaction of dimerization of isobutene for maximizing the selectivity toward di-isobutene is considered. The results of the optimization are found to be in agreement with those obtained by performing independent simulation using ASPEN PLUS simulator. Thus, the work highlights the potential of an optimization based tool for conceptual design of reactive distillation that involves complex reaction systems.

Shortcut design of reactive distillation columns

Shortcut design methods can be valuable tools for rapid screening of different separation process alternatives to assess feasibility and determine minimum energy demand. This work presents a variant of the feed angle method (Kraemer et al., 2011), which applies to single- and double-feed reactive distillation columns. The proposed method relies on pinch point analysis and determines the minimum energy demand from the calculation of a tray at the feed pinch. It is fully algorithmic and insensitive to impurities in product specifications. Its validity and performance is illustrated by a variety of case studies covering multi-component and multi-reaction systems, mixtures with potential liquid–liquid phase split, and double-feed columns. The results show that the method is sufficiently accurate and computationally efficient, even for highly non-ideal systems and complex configurations.

Attainable region of reactive distillation—Part IV: Inclusion of multistage units for complex reaction schemes

Reactive distillation (RD) can be advantageously used to improve selectivity of the desired product in a multi-reaction system. Because of the complexity in vapor liquid equilibrium and reaction kinetics, the design methodology is not straightforward and one has to adopt conceptual design and synthesis methods to arrive at the appropriate RD configuration. This paper is continuation of our earlier work (Amte et al., 2011), aimed at extending the concept of attainable region to a larger family of reactors that includes different reactive distillation units. In this work, we incorporate multistage reactive rectification and reactive stripping models with total reflux and total reboil, respectively. We further define the respective vectors, which justify the need of the corresponding units in the RD network. The van de Vusse schemes with both non-azeotropic and azeotropic vapor−liquid equilibria are considered and the attainable regions are constructed. Explanation is provided based on the visualization of selectivity lines in the composition space. In all the cases studied here, the feasible region is significantly broader than the one realized for the network of only conventional reactors.

Feasibility of Batch Reactive Distillation with Equilibrium‐Limited Consecutive Reactions in Rectifier, Stripper, or Middle‐Vessel Column

A general overall feasibility methodology of batch reactive distillation of multireaction systems is developed to study all the possible configurations of batch reactive distillation. The general model equations are derived for multireaction system with any number of chemical equilibrium‐limited reactions and for any number of components. The present methodology is demonstrated with the detailed study of the transesterification of dimethyl carbonate in two reversible cascade reactions in batch reactive distillation process. Pure methanol is produced as distillate, and pure diethyl carbonate is produced at the bottom simultaneously in middle‐vessel column; in each section, continuous feeding of ethanol is necessary. The results of feasibility study are successfully validated by rigorous simulations.