Belmiro Duarte | Instituto Politécnico de Coimbra (original) (raw)

Papers by Belmiro Duarte

Computer-aided chemical engineering, 2017

Abstract This study addresses the glyceride transesterification (TE) kinetics, a crucial step in ... more Abstract This study addresses the glyceride transesterification (TE) kinetics, a crucial step in bio-diesel production from vegetable oils. To overcome common limitations of the existing kinetic models, a n th order reversible model with a broader domain of application is fitted to experimental data gathered from different authors. We consider the glyceride TE employing sodium methoxide (NaOCH 3 ), and use a general four-step model building approach, including (i) structural identifiability analysis; (ii) outlier detection using a robust M-estimator; (iii) parameter estimation (PE) and subsequent construction of the respective confidence intervals; and (iv) practical identifiability analysis. The results show that although the kinetic models with five (5P) and six (6P) parameters are structurally non-identifiable, the former (5P) can be shown to be practically identifiable and fit accurately the data, with an average relative deviation (ARD) of 6.5 %.

Industrial & Engineering Chemistry Research, Jun 6, 2018

This study addresses the glyceride transesterication (TE) kinetics, a crucial step in biodiesel p... more This study addresses the glyceride transesterication (TE) kinetics, a crucial step in biodiesel production from vegetable oils. A n th order reversible model is considered to describe the TE reaction rate, using experimental data gathered from dierent authors for a broad range of conditions. An incremental model-building strategy is used, consisting on the following sequence of steps: (a) structural identiability analysis; (b) outliers detection using a robust M-estimator; (c) parameter estimation and subsequent construction of the respective condence intervals; and (d) practical identiability analysis. The methodology is applied to the glyceride TE reaction with sodium methoxide as catalyst, using a data set comprising 144 points collected from literature, and comparing the results for a ve (5P) and a six (6P) parameters' model. Although the results show that both kinetic models are structurally non-identiable, the former is I Page 1 of 40 ACS Paragon Plus Environment Industrial & Engineering Chemistry Research practically identiable for the case study analyzed. Furthermore, the 5P model shows a good capability of explaining the data features, with an average relative deviation of 5.2% for the residuals. The methodology presented can be used to analyze general kinetic reactions when experimental data is available and plausible reaction mechanisms are known.

Journal of Multivariate Analysis, Mar 1, 2015

T-optimum designs for model discrimination are notoriously difficult to find because of the compu... more T-optimum designs for model discrimination are notoriously difficult to find because of the computational difficulty involved in solving an optimization problem that involves two layers of optimization. Only a handful of analytical T-optimal designs are available for the simplest problems; the rest in the literature are found using specialized numerical procedures for a specific problem. We propose a potentially more systematic and general way for finding T-optimal designs using a Semi-Infinite Programming (SIP) approach. The strategy requires that we first reformulate the original minimax or maximin optimization problem into an equivalent semi-infinite program and solve it using an exchange-based method where lower and upper bounds produced by solving the outer and the inner programs, are iterated to convergence. A global Nonlinear Programming (NLP) solver is used to handle the subproblems, thus finding the optimal design and the least favorable parametric configuration that minimizes the residual sum of squares from the alternative or test models. We also use a nonlinear program to check the global optimality of the SIP-generated design and automate the construction of globally optimal designs. The algorithm is successfully used to produce results that coincide with several T-optimal designs reported in the literature for various types of model discrimination problems with normally distributed errors. However, our method is more general, merely requiring that the parameters of the model be estimated by a numerical optimization.

Energy, Jun 1, 2017

Soybean is currently recognized as a high value crop, allowing the manufacture of a broad range o... more Soybean is currently recognized as a high value crop, allowing the manufacture of a broad range of products. This contribution investigates the synergies resulting from coupling the production of biodiesel with soybean processing facilities, defining the core structure of a soy-based biorefinery. Simulations in Aspen Plus ® were performed, employing a detailed modeling framework. A base case scenario was established, allowing a detailed economic assessment of the process, a profitability and risk analysis, as well as the identification of plant integration opportunities.

Journal of Statistical Computation and Simulation, Apr 10, 2022

Social Science Research Network, 2022

Contemporary clinical trials communications, Jun 1, 2023

Statistics and Computing, Oct 1, 2022

Computer-aided chemical engineering, 2023

Neste trabalho desenvolve-se uma «package» destinada à resolução de sistemas de Equações Diferenc... more Neste trabalho desenvolve-se uma «package» destinada à resolução de sistemas de Equações Diferenciais Parciais/Algébricas (EDP/As) evolutivas unidimensionais, baseada no Método dos Elementos Finitos Móveis (MEFM) utilizando polinómios cúbicos de Hermite como aproximações. O referido método, bem como as aproximações, foram escolhidos após testes comparativos utilizando códigos baseados em metodologias de grelha adaptativa e fixa, para além de outros espaços de funções base. Como critérios de escolha podem citar-se a robustez de cada um dos algoritmos implementados, o tempo de computação necessário e a generalização que cada um permite. O MEFM mostrou-se particularmente indicado para problemas que desenvolvem frentes abruptas e choques, onde as derivadas espaciais têm elevadas magnitudes. Utilizaram-se e testaram-se outros métodos tais como, Diferenças Finitas Fixas, Elementos Finitos Fixos com aproximações lineares e cúbicas de Hermite e Elementos Finitos Móveis baseados em linhas poligonais rectas. Fez-se um estudo comparado das metodologias de Malha Fixa e de Malha Adaptativa, tendo-se dado particular destaque ao MEFM, dada a sua escolha para a concepção do código generalizado. A referida «package» foi aplicada a Equações Diferenciais Parciais (EDPs) escalares e vectoriais e ainda a sistemas mistos de EDP/As (Equações Diferenciais Parciais/Algébricas). Foram, de igual modo, resolvidos, com êxito, modelos de frente de reacção que descrevem fenómenos reais. Foi formulada uma nova metodologia baseada no Método dos Multiplicadores de Lagrange para o tratamento sistemático de EDP/As, sendo as soluções obtidas pela minimização da norma quadrada sob as restrições decorrentes das Equações Algébricas. Desenvolveu-se um método baseado em critérios de minimização para o tratamento de condições fronteira. Foram também implementados algorítmos de estimativa do erro espacial e de refinamento de malha baseado neste indicador

Computer Aided Chemical Engineering, 2019

Operations Research for Health Care, 2018

Design strategies using Bayesian-Lot Quality Assurance Sampling (B-LQAS) monitoring plans for vac... more Design strategies using Bayesian-Lot Quality Assurance Sampling (B-LQAS) monitoring plans for vaccination coverage and disease eradication typically assume a model with prior information of the parameters. One of the goals B-LQAS plans is finding the minimum sample size so that the characteristics of the risk curve meet user-specified requirements; however, there is no systematic approach to find such optimal B-LQAS plans to date. This paper formulates the problem as a mixed integer linear program and uses a branch and cut method to find the solution. The method also works when we have a user-specified weight function to account for a different emphasis in the misclassification error rates and different priors. We apply our algorithm to construct a few B-LQAS plans for estimating vaccination coverage in a given population using different weighting functions, priors and target proportions of vaccination coverage/disease eradication and compare results with those obtained from current methods. Numerical results support that our proposed method is computationally efficient, produces more accurate estimates than those commonly used and the estimates are more robust to model assumptions. In practical applications, the B-LQAS plans incorporate prior information about the prevalence, thus allowing the governments implementing plans more adequate to the specificities of the communities.

Chemosphere, 2015

In this paper, rigorous data and adequate models about linear alkylbenzene sulfonate (LAS) adsorp... more In this paper, rigorous data and adequate models about linear alkylbenzene sulfonate (LAS) adsorption/desorption on agricultural soil are presented, contributing with a substantial improvement over available adsorption works. The kinetics of the adsorption/desorption phenomenon and the adsorption/desorption equilibrium isotherms were determined through batch studies for total LAS amount and also for each homologue series: C10, C11, C12 and C13. The proposed multiple pseudo-first order kinetic model provides the best fit to the kinetic data, indicating the presence of two adsorption/desorption processes in the general phenomenon. Equilibrium adsorption and desorption data have been properly fitted by a model consisting of a Langmuir plus quadratic term, which provides a good integrated description of the experimental data over a wide range of concentrations. At low concentrations, the Langmuir term explains the adsorption of LAS on soil sites which are highly selective of the n-alkyl groups and cover a very small fraction of the soil surface area, whereas the quadratic term describes adsorption on the much larger part of the soil surface and on LAS retained at moderate to high concentrations. Since adsorption/desorption phenomenon plays a major role in the LAS behavior in soils, relevant conclusions can be drawn from the obtained results.

Chemosphere, Jan 9, 2015

The behaviour of Linear Alkylbenzene Sulfonate (LAS) in agricultural soil is investigated in the ... more The behaviour of Linear Alkylbenzene Sulfonate (LAS) in agricultural soil is investigated in the laboratory using continuous-flow soil column studies in order to simultaneously analyze the three main underlying phenomena (adsorption/desorption, degradation and transport). The continuous-flow soil column experiments generated the breakthrough curves for each LAS homologue, C10, C11, C12 and C13, and by adding them up, for total LAS, from which the relevant retention, degradation and transport parameters could be estimated, after proposing adequate models. Several transport equations were considered, including the degradation of the sorbate in solution and its retention by soil, under equilibrium and non-equilibrium conditions between the sorbent and the sorbate. In general, the results obtained for the estimates of those parameters that were common to the various models studied (such as the isotherm slope, first order degradation rate coefficient and the hydrodynamic dispersion coeff...

Materials

The design of continuous thickeners and clarifiers is commonly based on the solid flux theory. Ba... more The design of continuous thickeners and clarifiers is commonly based on the solid flux theory. Batch sedimentation experiments conducted with solid concentrations still provide useful information for their application. The construction of models for the velocity of settling allows the estimation of the flux of solids throughout time, which can, in turn, be used to find the area of the units required to achieve a given solid concentration in the clarified stream. This paper addresses the numerical treatment of data obtained from batch sedimentation experiments of calcium carbonate particles. We propose a systematic framework to fit a model that is capable of representing the process features that involve (i) the numerical differentiation of data to generate initial estimates for the instantaneous velocity of settling; (ii) the integration of a differential equation to fit the model for the velocity of settling; and (iii) the assessment of the quality of the fit using common statistic...

Polymers

Companies regularly face market pressure to develop products faster but they also need to simulta... more Companies regularly face market pressure to develop products faster but they also need to simultaneously incorporate technological constraints, sustainability trends, and customer requirements into their designs, which requires the use of systematic procedures. Firms that exploit natural resources and convert them into high-value products are among them. However, the literature on the application of such systematic approaches to products of this type remains scarce, as they often requrire extensive experimental plans involving the testing and optimization of multiple formulations. Here, we propose a systematic approach to the design of pine-resin-in-water emulsions, which can be used to fabricate pressure-sensitive adhesives. The strategy is customer-centric in the sense that the customers’ specifications are integrated into the decision-making tool used to assess the quality of the formulations obtained through experiments. This tool uses loss functions to assess satisfaction with ...

Mathematics

The systematic design of exact optimal designs of experiments is typically challenging, as it res... more The systematic design of exact optimal designs of experiments is typically challenging, as it results in nonconvex optimization problems. The literature on the computation of model-based exact optimal designs of experiments via mathematical programming, when the covariates are categorical variables, is still scarce. We propose mixed-integer semidefinite programming formulations, to find exact D-, A- and I-optimal designs for linear models, and locally optimal designs for nonlinear models when the design domain is a finite set of points. The strategy requires: (i) the generation of a set of candidate treatments; (ii) the formulation of the optimal design problem as a mixed-integer semidefinite program; and (iii) its solution, employing appropriate solvers. For comparison, we use semidefinite programming-based formulations to find equivalent approximate optimal designs. We demonstrate the application of the algorithm with various models, considering both unconstrained and constrained ...

Mathematical Biosciences and Engineering

The modeling of polymeric reactions is a topic of large interest. The gelation reactions that may... more The modeling of polymeric reactions is a topic of large interest. The gelation reactions that may result from self-crosslinking or hybrid (agent based-) crosslinking are examples with interest specially in biomaterials applications. The composition of polymer entities during the reaction is hard to follow, and their concentration is not a good measure of the system dynamics. One alternative is monitoring the rheological behavior of the reacting mass, and relate the elastic modulus of the mixture with the rheological degree of conversion. In this paper we use rheological data to fit Malkin and Kulichikin (1996) [1] based models to describe the crosslinking of chitosan. First, the self-crosslinking of chitosan is considered. Then, the agent-based crosslinking reaction promoted by genipin is addressed. We use dynamical rheological data to fit the reaction models. The model fitting problem generated using Maximum Likelihood principle with heteroscedastic prediction error variance is for...

Computer Aided Chemical Engineering, 2016

Abstract This paper addresses the nitrogen oxides absorption process in nitric acid plants. A mec... more Abstract This paper addresses the nitrogen oxides absorption process in nitric acid plants. A mechanistic model is developed for this gas-liquid reactive absorption system, able to predict the unit behaviour and support its optimization during regular and transient operating regimes. A rigorous rate-based model was adopted, and a new modelling strategy is proposed to assure the compatibility of mass transfer limitations and equilibrium kinetics. The model has the form of a DAE system, and is solved with an algebraic solver combined with an integration algorithm. This study was focused on the analysis of the unit steady state. The acid strength through the whole column was analysed and a good agreement with industrial data is observed.