Unknown Kinetic Parameters Research Articles

Dimensionality reduction enabled efficient kinetic parameters estimation and process optimization during continuous flow synthesis of ibuprofen

Complex reaction networks with multiple components and unknown kinetic parameters are commonly encountered in the process of reaction kinetic and reactor modeling. In this study, a dimensionality reduction strategy is used to effectively solve complex reaction kinetics-reactor coupled model. Ten unknown kinetic parameters from the synthesis of ibuprofen are identified based on genetic algorithm, which employs the elite and adaptation strategies. A convergence region is determined to compromise the accuracy and stability of the solutions. The statistical analyses are performed to clarify the reliability of the estimated parameters, which are also validated by the experimental data. Dynamic analyses show that only 1.2 times of the average residence time is required to make the flow-reaction process reach steady state. The sensitivity analyses help bridge the gap between the yield of ibuprofen and operating conditions. The proposed method can provide general guidelines for kinetic parameters estimation and optimization in similar systems.

Genuine differential voltammetry

A novel form of differential voltammetry is proposed, developed through the implicit anodic and cathodic current components of the experimentally accessible conventional net current measured in a voltammetric experiment. By employing basic mathematical modelling of an electrode reaction of a dissolved redox couple at a conventional, macroscopic electrode within the framework of the Butler-Volmer electrode kinetic model, the implicit anodic and cathodic current components of the net conventional current are clearly defined and can be estimated. Consequently, a novel form of differential current, calculated as the difference between anodic and cathodic implicit current components associated with a single potential of the voltammetric experiment, can be established. This differential current demonstrates remarkable characteristics in terms of electrode kinetics and analytical performance, particularly in cases involving fast, seemingly electrochemically reversible electrode processes. It holds promise to be analytically superior to the best-known differential voltammetric techniques so far (e.g., square-wave voltammetry), as well as provides a means for estimating the rate constants of very fast, apparently reversible electrode processes at macroscopic electrodes under mild experimental conditions (i.e., studied at slow potential scan rates). The practical implication of the novel methodology is significant: a simple linear sweep voltammogram of a quasi-reversible electrode reaction with unknown electrode kinetic parameters can be readily transformed into the novel type of differential voltammogram through a convolution procedure of the conventional net current, paving a new way for studying electrode processes by voltammetry.

An optimization-free Fisher information driven approach for online design of experiments

Developing mathematical models used to elucidate reaction kinetics plays a crucial role in the design, control, and optimization of chemical processes. One of the most challenging tasks in kinetic model identification is the precise estimation of unknown kinetic model parameters. This challenge can be effectively addressed through the application of Model-Based Design of Experiments (MBDoE) techniques, which enable the design of experiments facilitating precise model parameter estimation with minimal runs and analytical resources. Nevertheless, MBDoE techniques rely on an optimization procedure that is susceptible to parametric uncertainty, making the design procedure computationally intensive and prone to issues of local optimality. MBDoE techniques are also employed in online procedures to expedite the identification of kinetic models in autonomous platforms. As a result, ensuring rapid convergence becomes imperative to mitigate numerical issues during operational processes. In this paper a Fisher Information Matrix Driven (FIMD) approach is introduced to tackle these challenges. The methodology integrates a sampling-based experimental design approach with experiment ranking based on FIM to select the most informative experiment at each iteration. The effectiveness of the proposed design methodology is examined and discussed via two different case studies of increasing complexity: a fed-batch reactor in which the fermentation of baker’s yeast is carried out and a nucleophilic aromatic substitution in a flow reactor system.

Impact of Composition Ratio on the Expansion Behavior of Polyurethane Grout.

Different formulations of foaming polyurethane grout offer controlled expansion rates. This is crucial for precision in filling voids without exerting excessive pressure on surrounding structures, which could potentially cause damage. This study focuses on the impact of composition on the expansion performance of tailor-made polyurethane grouting materials. Initially, multiple unknown chemical reaction kinetic parameters were identified by combining free expansion tests, which involved measuring density and temperature changes, with the particle swarm optimization algorithm. A numerical simulation, integrating chemical kinetic models and fluid flow equations, was established to replicate the free expansion process of polyurethane grout in a cup, aligning with our experimental results. Subsequently, we analyzed the polymerization process of polyurethane grout with varying compositions to determine the effect of composition ratios on grout expansion. Our findings reveal that the expansion ratio of foaming polyurethane is predominantly influenced by the concentrations of physical and chemical foaming agents, followed by isocyanate concentration. Polyol, in contrast, exerts a relatively minor influence. Furthermore, the solubility of the physical foaming agent in the grout determines both its maximum allowable concentration and its maximum contribution to volume increase. This study provides valuable insights for the design and selection of polyurethane grout components tailored to diverse applications.

Artificial Intelligence for Electrochemical Prediction and Optimization of Direct Carbon Fuel Cells Fueled with Biochar

At present, direct carbon fuel cells constitute an emerging energy technology that electrochemically converts solid carbon to electricity with high efficiency. The recent trend of DCFCs fueled with biochar from biomass carbonization as green fuel has reinforced the environmental benefits of DCFCs as a clean and sustainable technology. However, there remain new challenges related to some complex unknown kinetic parameters, X=(αa,αc,σg,i0,a,i0,c,ilO2,ilCO2,c,ilCO2,a,ilCO), of the electrochemical conversion of biochar in DCFCs and there is a need for intelligent techniques for prediction and optimization, refering to the available experimental data. The differential evolution (DE) algorithm, which ranked as one of the top performers in optimization competitions with competitive accuracy and convergence speed, was used here for providing the optimized values of these parameters by minimizing the root mean squared errors (RMSE). The proposed technique was then applied to DCFCs fueled by activated pure carbon (APC) using CO2 and CO/CO2 electrochemical models with RMSE around 10−2 and 10−3, respectively. Then, the CO/CO2 model was applied to a DCFC fueled with almond shell biochar (ASB), which displayed a slight increase in RMSE (of the order of 10−2) due to the complex porous structure of ASB and the content of additional chemical elements that affect the electrochemistry of the DCFC and are not considered in the model.

A kinetic study on oxygen redox reaction of a double-perovskite reversible oxygen electrode— Part II: Modelling analysis

Mixed ionic and electronic conductor double perovskites are very promising oxygen electrode materials for solid oxide cell technology. However, understanding their specific kinetic mechanism is a fundamental preliminary step towards detecting the best reachable performance, optimising the operation conditions and the electrode architecture. Indeed, the contributions of different rate-determining steps can vary as a function of the working point. In this framework, after a detailed experimental campaign devoted to the study of SmBa0.8Ca0.2Co2O5+δ (SBCCO) oxygen electrode behaviour, the authors propose a theoretical analysis of oxygen reduction and oxygen evolution reaction paths that couples a preliminary study through equivalent circuit analysis with a physics-based model to predict the operation of SBCCO as a reversible oxygen electrode. Following a semi-empirical approach, the kinetics formulation was derived from thermodynamics and electrochemistry fundamental principles and was tuned on electrochemical impedance spectroscopy (EIS) spectra in order to retrieve the unknown kinetic parameters. The successful cross-checking of the simulated results with the experimental data obtained by direct current measurements validated the proposed model, here applicable in further works on full cells to simulate the SBCCO oxygen reversible electrode performance.

A volatile fatty acids adaptive observer-based hierarchical optimal controller design to maximum gas production of two-stage anaerobic digestion process

Volatile fatty acids (VFA), which influence the stability and gas production, are important state variables in anaerobic digestion (AD) process. Three main components of VFA can indicate the metabolic state of AD internal environment and be considered as a better basis for AD monitoring strategies. A VFA adaptive observer (VFA-AO) is proposed to estimate unknown gas production kinetic parameters and unmeasurable states simultaneously, including the concentration of three main components of VFA. Otherwise, using the estimated information, a VFA-AO-based hierarchical optimal controller (VFA-AO-based HOC) is designed to maximize gas production rates of AD. The proposed controller is compared with two existing control algorithms. Simulation results show that, despite the concentration of pollutants in the inlet fluctuates, VFA-AO achieves a reliable states and kinetic parameters estimation, and VFA-AO-based HOC maximizes gas production.

Moisture swing frequency response method for characterization of ion-transport kinetics of CO2 adsorption

Direct air capture of CO2 (DAC) sufficiently mitigates atmospheric CO2 to prevent the impacts of global warming of 1.5 °C above preindustrial levels. To overcome the challenges of the kinetics of sorbent under the ultra-low partial pressure (40 Pa) of DAC, the underlying mechanisms need to be constructed for better designs, simulations, and developments of the separation processes of carbon dioxide. Herein, a transient model based on the diffusion-reaction of ions at the molecular scale is developed for the moisture swing adsorption (MSA) process, disclosing the mechanism of mass transfer of multi-ions of sorbents. To compare the model with the experiment quantitatively, Fourier-transformed moisture-swing frequency response is applied to accurately measure the H2OCO2 concentration response, ensuring a systematic approach for unknown kinetic parameters for the model. The results reveal that the gradient of water vapor causes a counter gradient of CO2 concentration, generating the spontaneous transportation of CO2 of the MSA membrane from one side to another. Specifically, the diffusion coefficient of HCO3− drives the CO2 adsorption process predominantly, where the diffusion coefficient of HCO3− increases about ten times, leading to a nearly 12 times enhanced CO2 separation rate accordingly. Notably, CO2 adsorption kinetics can be stimulated by controlling specific ion conductivity in the moisture swing sorbent. With the enhancement of adsorption kinetics and low capital cost, the progress of CO2 mitigation using Moisture Swing Adsorption can be achieved for direct air capture of CO2.

Parameter Identification in Metabolic Reaction Networks by Means of Multiple Steady-State Measurements

In this work, we investigate some theoretical aspects related to the estimation approach proposed by Liebermeister and Klipp, 2006, in which general rate laws, derived from standardized enzymatic mechanisms, are exploited to kinetically describe the fluxes of a metabolic reaction network, and multiple metabolic steady-state measurements are exploited to estimate the unknown kinetic parameters. Further mathematical details are deeply investigated, and necessary conditions on the amount of information required to solve the identification problem are given. Moreover, theoretical results for the parameter identifiability are provided, and symmetrical and modular properties of the proposed approach are highlighted when the global identification problem is decoupled into smaller and simpler identification problems related to the single reactions of the network. Among the advantages of the proposed innovative approach are (i) non-restrictive conditions to guarantee the solvability of the parameter estimation problem, (ii) the unburden of the usual computational complexity for such identification problems, and (iii) the ease of obtaining the required number of measurements, which are actually steady-state data, experimentally easier to obtain with respect to the time-dependent ones. A simple example concludes the paper, highlighting the mentioned advantages of the method and the implementation of the related theoretical result.

Effect of Synthesis Method on Reaction Mechanism for Hydrogen Evolution over CuxOy/TiO2 Photocatalysts: A Kinetic Analysis.

The existing literature survey reports rare and conflicting studies on the effect of the preparation method of metal-based semiconductor photocatalysts on structural/morphological features, electronic properties, and kinetics regulating the photocatalytic H2 generation reaction. In this investigation, we compare the different copper/titania-based photocatalysts for H2 generation synthesized via distinct methods (i.e., photodeposition and impregnation). Our study aims to establish a stringent correlation between physicochemical/electronic properties and photocatalytic performances for H2 generation based on material characterization and kinetic modeling of the experimental outcomes. Estimating unknown kinetic parameters, such as charge recombination rate and quantum yield, suggests a mechanism regulating charge carrier lifetime depending on copper distribution on the TiO2 surface. We demonstrate that H2 generation photoefficiency recorded over impregnated CuxOy/TiO2 is related to an even distribution of Cu(0)/Cu(I) on TiO2, and the formation of an Ohmic junction concertedly extended charge carrier lifetime and separation. The outcomes of the kinetic analysis and the related modeling investigation underpin photocatalyst physicochemical and electronic properties. Overall, the present study lays the groundwork for the future design of metal-based semiconductor photocatalysts with high photoefficiencies for H2 evolution.

A novel green approach for silver recovery from chloride leaching solutions through photodeposition on zinc oxide

Silver is extensively used in electronics, industrial catalysis, and biomedical sector owing to its enhanced physicochemical properties. E-waste recycling may contribute significantly to enhance silver recovery in the view of a circular economy and limit the depletion of mineral sources. In this scenario, hydrometallurgical routes represent the most widely used techniques for silver extraction/recovery and require strong acidic solutions, high temperatures, and multiple operating units. An alternative sustainable route for silver recovery from leaching solutions used for silver extraction in industrial applications is herein proposed for the first time. The novel green process of silver recovery is based on the UV/vis light-driven photocatalytic deposition of pure metallic silver over low-cost and non-toxic ZnO photocatalyst. In the second step, ZnO is dissolved by slight acidification and pure metallic silver is easily recovered. Low environmental impact, mild operating conditions, and economic viability are among the major perks of the new silver recovery process developed.In the view of a full-scale implementation, several operating conditions of the recovery process (i.e., photocatalyst load, starting silver concentration, type of hole scavenger and irradiation) were thoroughly investigated. A mathematical model capable of describing the system behaviour under different operating conditions was also developed and allowed to estimate unknown kinetic parameters for the Ag-photodeposition process.

Multiscale modeling of collective cell migration elucidates the mechanism underlying tumor–stromal interactions in different spatiotemporal scales

Metastasis is the pathogenic spread of cancer cells from a primary tumor to a secondary site which happens at the late stages of cancer. It is caused by a variety of biological, chemical, and physical processes, such as molecular interactions, intercellular communications, and tissue-level activities. Complex interactions of cancer cells with their microenvironment components such as cancer associated fibroblasts (CAFs) and extracellular matrix (ECM) cause them to adopt an invasive phenotype that promotes tumor growth and migration. This paper presents a multiscale model for integrating a wide range of time and space interactions at the molecular, cellular, and tissue levels in a three-dimensional domain. The modeling procedure starts with presenting nonlinear dynamics of cancer cells and CAFs using ordinary differential equations based on TGFβ, CXCL12, and LIF signaling pathways. Unknown kinetic parameters in these models are estimated using hybrid unscented Kalman filter and the models are validated using experimental data. Then, the principal role of CAFs on metastasis is revealed by spatial–temporal modeling of circulating signals throughout the TME. At this stage, the model has evolved into a coupled ODE–PDE system that is capable of determining cancer cells’ status in one of the quiescent, proliferating or migratory conditions due to certain metastasis factors and ECM characteristics. At the tissue level, we consider a force-based framework to model the cancer cell proliferation and migration as the final step towards cancer cell metastasis. The ability of the multiscale model to depict cancer cells’ behavior in different levels of modeling is confirmed by comparing its outputs with the results of RT PCR and wound scratch assay techniques. Performance evaluation of the model indicates that the proposed multiscale model can pave the way for improving the efficiency of therapeutic methods in metastasis prevention.

Safety-Critical Model-Free Control for Multi-Target Tracking of USVs with Collision Avoidance

Dear editor, This letter addresses the multi-target tracking of underactuated unmanned surface vehicles (USVs) subject to multiple stationary/moving obstacles. The kinetic model parameters of each USV are totally unknown. A safety-critical model-free control method is proposed for tracking multiple targets with a collision-free containment formation. Specifically, a distributed containment extended state observer (DCESO) is designed to estimate the convex hull spanned by the multiple targets. At the kinematic level, a collision-free kinematic guidance law is presented using a control barrier function (CBF) and an extended state observer for each follower USV. At the kinetic level, a model-free position tracking control law by using an adaptive ESO (AESO) is presented for each follower USV. By the designed safety-critical model-free control method, cooperative tracking of multiple targets under multiple stationary/moving obstacles can be achieved using completely unknown kinetic model parameters. Simulations are provided to illustrate the efficacy of the proposed safety-critical model-free control method for a fleet of USVs.

Mechanistic modelling of solar disinfection (SODIS) kinetics of Escherichia coli, enhanced with H2O2 – part 1: The dark side of peroxide

The present bi-partite work describes the development and validation of a mechanistic kinetic model of SODIS E. coli inactivation, enhanced with H2O2. In this first part, the mechanism of the baseline dark phenomena is modelled. A mechanistic model involving E. coli cellular respiration, inactivation due to HO· and O2·- radicals, and bacterial thermal inactivation, was developed using a series-event model based on the accumulation of damage and cell recovery corrected with the Arrhenius equation for inclusion of the thermal events. The contribution of external H2O2 was included in the internal H2O2 balance, while the balance of extracellular H2O2 considered the consumption caused by its self-decomposition, interactions with cells’ membrane, and organic matter from dead cells. Specifically, the kinetic parameters of the external H2O2 sinks, the oxidation reaction of intracellular Fenton, and bacterial thermal inactivation were independently estimated by model regression from experimental data of E. coli inactivation and H2O2 consumption at different controlled conditions of temperature and initial H2O2 concentration. We complemented the values of the kinetic constants available in the literature with the unknown kinetic parameters estimated from experiemetnal and literature data. The missing kinetic parameters were successfully validated (bacteria error = 4.5%, H2O2 error = 12.9%). This kinetic model helps to understand the intracellular mechanisms and the contributions of each source of inactivation, with the role of radicals’ damage being most important at temperatures below 40 °C, and the thermal inactivation for temperatures above this value.

Modelling and parameter identification for a two-stage fractional dynamical system in microbial batch process

In this paper, we consider mathematical modelling and parameter identification problem in bioconversion of glycerol to 1,3-propanediol by Klebsiella pneumoniae. In view of the dynamic behavior with memory and heredity and experimental results in batch culture, a two-stage fractional dynamical system with unknown fractional orders and unknown kinetic parameters is proposed to describe the fermentation process. For this system, some important properties of the solution are discussed. Then, taking the weighted least-squares error between the computational values and the experimental data as the performance index, a parameter identification model subject to continuous state inequality constraints is presented. An exact penalty method is introduced to transform the parameter identification problem into the one only with box constraints. On this basis, we develop a parallel Particle Swarm Optimization algorithm to find the optimal fractional orders and kinetic parameters. Finally, numerical results show that the model can reasonably describe the batch fermentation process, as well as the effectiveness of the developed algorithm. Keywords: fractional dynamical system, parameter identification, parallel optimization,

Robust optimal control for a batch nonlinear enzyme-catalytic switched time-delayed process with noisy output measurements

In this paper, we consider a nonlinear switched time-delayed (NSTD) system with an unknown time-varying function describing the batch culture. The output measurements are noisy. According to the actual fermentation process, this time-varying function appears in the form of a piecewise-linear function with unknown kinetic parameters and switching times. The quantitative definition of biological robustness is given to overcome the difficulty of accurately measuring intracellular material concentrations. Our main goal is to estimate these unknown quantities by using noisy output measurements and biological robustness. This estimation problem is formulated as a robust optimal control problem (ROCP) governed by the NSTD system subject to continuous state inequality constraints. The ROCP is approximated as a sequence of nonlinear programming subproblems by using some techniques. Due to the highly complex nature of these subproblems, we propose a hybrid parallel algorithm, based on Nelder–Mead method, simulated annealing and the gradients of the constraint functions, for solving these subproblems. The paper concludes with simulation results.

Development of a cloud SaaS service for a comprehensive research of polymerization processes

The article is devoted to the description of the network architecture of the developed cloud SaaS service for the implementation of a comprehensive study of polymerization processes. The main problem of using local software systems for such tasks is briefly voiced. The main methods and mathematical approaches that allow solving the direct problem of predicting the main molecular characteristics of the produced polymer product for various loading modes of the reaction system and the inverse problem of identifying some of the unknown kinetic parameters are considered. Methods and approaches to the development of algorithms and software are considered separately. As part of the cloud service being developed, a three-tier architecture for accessing data and computing resources is described in detail, the main tasks of each level and the advantages of using this approach are described. The hardware and system requirements for the computing nodes of the developed network application have been written out.

Combination of PAT and mechanistic modeling tools in a fully continuous powder to granule line: Rapid and deep process understanding

Comprehensive understanding of an integrated continuous pharmaceutical technology was achieved in this study by a combining design of experiments and mechanistic modeling-based simulations. The powder to granule line consisted of twin-screw wet granulation, vibrational fluid-bed drying and milling. A Partial Least Squares (PLS) regression model was built using Near-infrared (NIR) spectroscopy for the real-time monitoring of the product moisture content after the milling step. A split-plot full factorial experimental design was set up and executed to help the understanding of the relationships between the moisture content and process parameters. Furthermore, a mechanistic model was built, involving heat transfer between the drying air and the solid material. The unknown kinetic model parameters were estimated using the results of the experimental study resulting in good calibration and validation performance. The simulations not only reinforced the experimental observations but also paves the way for model-based process monitoring and optimal control.

Growth laws and invariants from ribosome biogenesis in lower Eukarya

Eukarya and Bacteria are the most evolutionarily distant domains of life, which is reflected by differences in their cellular structure and physiology. For example, Eukarya feature membrane-bound organelles such as nuclei and mitochondria, whereas Bacteria have none. The greater complexity of Eukarya renders them difficult to study from both an experimental and theoretical perspective. However, encouraged by a recent experimental result showing that budding yeast (a unicellular eukaryote) obeys the same proportionality between ribosomal proteome fractions and cellular growth rates as Bacteria, we derive a set of relations describing eukaryotic growth from first principles of ribosome biogenesis. We recover the observed ribosomal protein proportionality, and then continue to obtain two growth-laws for the number of RNA polymerases synthesizing ribosomal RNA per ribosome in the cell. These growth-laws, in turn, reveal two invariants of eukaryotic growth, i.e. quantities predicted to be conserved by Eukarya regardless of growth conditions. The invariants, which are the first of their kind for Eukarya, clarify the coordination of transcription and translation kinetics as required by ribosome biogenesis, and link these kinetic parameters to cellular physiology. We demonstrate application of the relations to the yeast S. cerevisiae and find the predictions to be in good agreement with currently available data. We then outline methods to quantitatively deduce several unknown kinetic and physiological parameters. The analysis is not specific to S. cerevisiae and can be extended to other lower (unicellular) Eukarya when data become available. The relations may also have relevance to certain cancer cells which, like bacteria and yeast, exhibit rapid cell proliferation and ribosome biogenesis.

Modelling and optimal state-delay control in microbial batch process

In this paper, we consider optimal control problem involving a time-varying state-delay system arising in 1,3-propanediol microbial batch process. The dynamic system in this problem includes unknown time-varying delay function and unknown kinetic parameters. To optimally determine the unknown delay function and unknown kinetic parameters in the system, the weighted least-squares error between the computed values and experimental data is minimized subject to path constraints. By parameterizing the delay function with piecewise quadratic basis functions, the optimal state-delay control problem is approximated by a sequence of parameter optimization problems. Furthermore, an exact penalty method is utilized to transform these parameter optimization problems into the ones only with box constraints. On this basis, a modified differential evolution algorithm is developed to solve the resulting optimization problems. Finally, numerical results are presented to verify the effectiveness of the developed solution approach.