A joint model-based experimental design approach for the identification of kinetic models in continuous flow laboratory reactors

Conducting new experiments for biomass gasifiers is expensive and time consuming. Therefore, it is important to select conditions for new experiments so maximum information is obtained. In this study, sequential Bayesian model-based design of experiments (MBDoE) is used to design new experimental runs for a heat-integrated biomass downdraft gasifier. This MBDoE approach is valuable because it accounts for model structure, prior information about plausible parameter values, and previous experimental data in a relatively simple way. Operating conditions selected for each new run are biomass moisture content, water injection rate, and the desired energy demand from the downstream engine. Three types of MBDoE with different objective functions are considered: A-optimal, V-optimal, and a proposed new type of focused V-optimal design. A-optimal design is used to when the goal is to obtain improved parameter estimates, without specifying how the model will be used. Performing two new A-optimal runs reduced the standard deviations for model parameters by 18.4% on average compared to when only old data are available. The three most-improved parameter estimates are activation energies for char gasification reactions involving carbon dioxide, hydrogen, and steam, respectively. The focused V-optimal methodology results in greater improvements in prediction accuracy for tar concentration and outlet temperature, which are key model responses. Using two designed Vf-optimal runs reduces standard deviations for these variables by 59.4%, on average, compared to when only old data are available. New A-optimal and V-optimal runs lead to corresponding improvements of 30.7% and 50%, respectively.

A comprehensive framework for model evaluation and refinement using MBDoE estimability and structural identifiability: application to a crystallization process

The need for first principles based models for chemical and biological processes has led to the development of techniques for model-based design of experiments (MBDOE). These techniques help in speeding up the parameter estimation efforts and typically lead to improved parameter precision with a relatively short experimental campaign. In the case of complex kinetic networks involving parallel and/or consecutive reactions, correlation among model parameters makes the inverse problem of parameter estimation very difficult. It is therefore important to develop experimental design techniques that not only increase information content about the system to facilitate precise parameter estimation but also reduce the correlation among parameters. This article presents a multiobjective optimization (MOO) based framework for experimental design, where, in addition to the traditional objective of eliciting maximally informative data for parameter estimation, an explicit objective to reduce correlation among parameters is included. The proposed MOO based framework is tested on two case studies, and results are compared with the traditional alphabetical designs. The approach provides a pictorial representation of trade-off between system information and correlation among parameters in the form of Pareto-optimal front, which offers the experimentalist the freedom to choose experimental design(s) that are most suitable to implement on the experimental system and realize the benefits of such experiments.

Model-based experimental design and parameter estimation, coupled with in situ infrared and laser backscattering instrumentation, was applied to the cooling crystallization of a drug compound to construct a model for use in the design of an optimal operating procedure. Because the model was constructed completely from in situ sensor data, with no sampling procedures, the amount of pharmaceutical compound required for batch process development was significantly reduced. Modeling issues involving the selection of the expressions for the supersaturation and nucleation rate, as well as the electronics mode in the laser backscattering instrument, were explored. All but one of the kinetic parameters from the gray-box model constructed using laser backscattering data were close to the kinetic parameters for a first-principles model constructed from data from off-line particle size measurements. The model was used to design batch operating procedures to minimize nucleation and maximize the sharpness of the crystal size distribution. This appears to be the first time that the procedure of model-based experimental design, parameter estimation, model selection, and optimization has been applied to the crystallization of a pharmaceutical, as well as the first time that this procedure has been applied to a crystallization process that forms loosely bound aggregates.

Optimal design of infusion tests for the identification of physiological models of acquired von Willebrand syndrome

Nucleophilic aromatic substitutions (SNAr) are key chemical transformations in pharmaceutical and agrochemical synthesis, yet their complex mechanisms (concerted or two-step) complicate kinetic model identification. Accurate kinetic models for SNAr are essential for scale-up, optimization, and control of the reaction process, but conventional methods struggle with mechanism uncertainty driven by substrates, nucleophiles, and reaction conditions, with data collection being difficult due to its source-intensive nature. We address this using DoE-SINDy, a data-driven framework for generative modelling without complete theoretical understanding. A benchmark study on the SNAr reaction of 2,4-difluoronitrobenzene with morpholine in ethanol was conducted, incorporating parallel and consecutive side-product formation. Ground-truth kinetic models validated in prior studies were used to generate in-silico data under varying noise levels and sampling intervals. DoE-SINDy successfully identified the true kinetic model with minimal runs, quantifying the impact of key design factors such as inlet concentrations, residence time, sample size and experimental budget on model identification.

Disentangling model complexity in green roof hydrological analysis: A Bayesian perspective

Data Reconciliation in Reaction Systems using the Concept of Extents

Quantitative systems models have been increasingly used to accelerate the development of pharmaceutical processes that traditionally require time and resource-intensive experimental campaigns. However, despite the potential benefits of modelling in pharmaceutical process development, there is often a lack of confidence from stakeholders to adopt these approaches in a systematic way. This is particularly important in a highly regulated sector such as the pharmaceutical industry, where model uncertainty evaluation may have to be quantified and filed if model results are to be included as part of a regulatory submission. In this study, a systematic procedure is proposed, combining both standard techniques (e.g., global sensitivity analysis, model-based design of experiments) and new methods based on data analytics to assess model fidelity and to support practitioners in model usage for pharmaceutical development. A direct compression systems model for manufacturing oral solid dosage products is used as a case study. The systems model is comprised of the following sub-models: (1) Tablet press unit operation, (2) Tablet disintegration test unit, (3) In vitro dissolution test unit. The implementation of the methodology is critically discussed, showing the effectiveness of the approach and the benefits of the proposed techniques in (i) evaluating model fidelity as a result of uncertainty in parameter estimation, (ii) assessing whether it is necessary to estimate all systems model parameters in a statistically satisfactory way, and (iii) analyzing whether model calibration should be carried out on a unit basis or considering the overall system.

This model-based design of experiments (MBDOE) method determines the input magnitudes of an experimental stimuli to apply and the associated measurements that should be taken to optimally constrain the uncertain dynamics of a biological system under study. The ideal global solution for this experiment design problem is generally computationally intractable because of parametric uncertainties in the mathematical model of the biological system. Others have addressed this issue by limiting the solution to a local estimate of the model parameters. Here we present an approach that is independent of the local parameter constraint. This approach is made computationally efficient and tractable by the use of: (1) sparse grid interpolation that approximates the biological system dynamics, (2) representative parameters that uniformly represent the data-consistent dynamical space, and (3) probability weights of the represented experimentally distinguishable dynamics. Our approach identifies data-consistent representative parameters using sparse grid interpolants, constructs the optimal input sequence from a greedy search, and defines the associated optimal measurements using a scenario tree. We explore the optimality of this MBDOE algorithm using a 3-dimensional Hes1 model and a 19-dimensional T-cell receptor model. The 19-dimensional T-cell model also demonstrates the MBDOE algorithm’s scalability to higher dimensions. In both cases, the dynamical uncertainty region that bounds the trajectories of the target system states were reduced by as much as 86% and 99% respectively after completing the designed experiments in silico. Our results suggest that for resolving dynamical uncertainty, the ability to design an input sequence paired with its associated measurements is particularly important when limited by the number of measurements.

Flatness-Based Design of Experiments for Model Selection

A review on model-based design of experiments for parameter precision – Open challenges, trends and future perspectives

In this work, catalyst screening and reaction kinetic modeling are performed for two Ni-based and one Rh-based commercial catalysts for a reverse water gas shift (rWGS) reaction under atmospheric and 30 bara pressure. Ni-based catalysts displayed higher activity compared to Rh-based catalysts despite the severe initial deactivation Ni-based catalysts suffered, which increases catalyst selectivity toward CO formation. Ni/Al2O3 catalyst with lower Ni content (2 w-%) exhibited higher selectivity toward CO formation compared to the Ni/Al2O3 catalyst with higher Ni content (15 wt %). The Ni/Al2O3 (2 wt % of Ni) catalyst was further tested for kinetic modeling. Three kinetic models were developed based on reaction mechanisms and kinetic models obtained from other publications for rWGS/WGS, methanation, and methane steam reforming reactions based on different mechanistic approaches. The model based on mechanistic assumptions originally proposed by Xu and Froment was concluded to be the most suitable to describe the high temperature reaction system of the rWGS and methanation over supported nickel catalyst. On the basis of statistical analysis, the model proposed by Xu and Froment was also concluded to be the best for the catalyst and reaction system studied in this work.

We propose a robust way of achieving a well test interpretation by combining the sequential predictive probability method with an artificial neural network approach. The sequential predictive probability method considers all possible reservoir models and determines which candidate model or models best predict the well response. This method is dependent on obtaining good initial estimates for the parameters governing the candidate reservoir models, which is achieved by applying the artificial neural network approach. We use the neural network to identify the characteristic components of the pressure derivative curve corresponding to the flow regimes known to be in each candidate model. Reservoir parameters are then computed using the data in the identified range of the corresponding behavior. As a final step, the candidate models and their initial estimates are evaluated using the sequential probability method. The method discriminates between the candidate models and simultaneously performs nonlinear regression to compute the best estimates of reservoir parameters. The trained neural network was able to identify the characteristic components of the derivative curve in most cases. The algorithm written to interpret the neural network signals into flow regimes required special procedures to take care of the misclassification from the neural network. The initial estimates of reservoir parameters from the neural network were found to be reasonably close to the eventual estimates from the sequential predictive probability method.

Model-integrated process development demonstrated on the optimization of a robotic cation exchange step