Leôncio Diógenes Tavares Câmara

An approach to parameters estimation of a chromatography model using a clustering genetic algorithm based inverse model

Genetic algorithms are tools for searching in complex spaces and they have been used successfully in the system identification solution that is an inverse problem. Chromatography models are represented by systems of partial differential equations with non-linear parameters which are, in general, difficult to estimate many times. In this work a genetic algorithm is used to solve the inverse problem of parameters estimation in a model of protein adsorption by batch chromatography process. Each population individual represents a supposed condition to the direct solution of the partial differential equation system, so the computation of the fitness can be time consuming if the population is large. To avoid this difficulty, the implemented genetic algorithm divides the population into clusters, whose representatives are evaluated, while the fitness of the remaining individuals is calculated in function of their distances from the representatives. Simulation and practical studies illustrate the computational time saving of the proposed genetic algorithm and show that it is an effective solution method for this type of application.

Uncertainty Quantification in Chromatography Process Identification Based on Markov Chain Monte Carlo

Modeling and simulation of chromatography systems leads to better understanding of the mass transfer mechanisms and operational conditions that can be used to improve molecular separation/purification. In this chapter, parameter uncertainty produced by the model and measurement errors in a front velocity chromatography model is quantified by means of a Bayesian method, the delayed rejection adaptive metropolis algorithm, which is a variant of the Markov Chain Monte Carlo (MCMC) method. The model is also evaluated for a random sample of parameters, being then determined the uncertainty in the prediction.

O novo modelo Front Velocity aplicado na modelagem da separação de enantiômeros via processo Leito Móvel Simulado

Devido as propriedades terapeuticas dos enantiomeros de um farmaco racemico, surge a necessidade de separa-los. Entre os processos utilizados para a separacao desse tipo de composto, o Leito Movel Simulado (LMS) tem recebido destaque, por ser um processo continuo e contracorrente que apresenta um grande eficiencia de separacao. Os farmacos racemicos em geral sao caros e por isso existe o interesse em evitar possiveis desperdicios ocasionados por uma operacao inadequada do equipamento utilizado na separacao. Para determinar os parâmetros de operacao do LMS e necessario predizer o transporte de massa que ocorre no interior das colunas cromatograficas que compoe o LMS. Atualmente os modelos usados na predicao do transporte de massa nesse tipo de processo sao compostos por sistemas de equacoes diferenciais parciais e apresentam um alto custo computacional, alem de que necessitam dado obtidos previamente atraves da realizacao de experimentos de equilibrio que sao interpretados por isotermas de adsorcao. Neste trabalho, para modelar processo de separacao em LMS a nova abordagem Front Velocity foi proposta. Esta e composta por equacoes diferenciais ordinarias e nao se utiliza de isotermas de adsorcao e consequentemente nao se faz necessario a realizacao de experimentos de equilibrio. Na cromatografia preparativa um experimento de pulso e conduzido, e do cromatograma resultante sa determinadas via aplicacao do problema inverso os parâmetros globais de transferencia de massa do modelo Front Velocity.. Na segunda etapa os parâmetros obtidos na caracterizacao da coluna cromatografica foram utilizados na simulacao do processo LMS, obtendo os perfis de separacao dos compostos da mistura estudada. Para a validacao da modelagem empregada, os resultados simulados foram comparados com dados experimentais da separacao dos enantiomeros do racemato Cetamina (Santos, et al., 2004) e tambem confrontados com as simulacoes obtidas a partir de modelos classicos. Os resultados obtidos mostraram que o modelo Front Velocity possui uma concordância razoavel com os dados experimentais em particular quando foi utilizada a cinetica de Langmuir como mecanismo de transferencia de massa. Da mesma forma mostrou perfis de separacao semelhantes aos obtidos pela modelagem classica usando apenas equacoes diferenciais ordinarias e exigindo um tempo de simulacao computacional aproximadamente vinte vezes menor.

Comparación de diferentes algoritmos metaheurísticos en la estimación de parámetros del modelo relacional general de cromatografía líquida en columna

Optimization, scaling and parameter estimation are inverse problems that appear in many biotechnological processes. In the solution of inverse problems, different techniques such as metaheuristics algorithms, have been used. These algorithms efficiently search for and find good solutions to a problem with a reasonable computational cost. In this pape, four well-known metaheuristic algorithms (Genetic Algorithm, Differential Evolution, Ant Colony Optimization and Particle Swarm Optimization) are applied to the problem of parameter estimation in the liquid chromatography separation process. The effectiveness of each method is analyzed and performance comparison based on different statistical criteria is made. The procedure allows to obtain estimated values close to the real parameters, with a good fit of the curves generated by the model to syntetically generated experimental data. The algorithm that performs better is Differential Evolution.

OXIDATIVE CRACKING OF LINEAR HYDROCARBONS AT LOW TEMPERATURES

This work describes the oxidative cracking of n-alkanes with molecular oxygen at low temperatures (below 473 K) in an autoclave reactor. An increase of the oxygen consumption rate with increasing hydrocarbon size was observed. Data for n-hexadecane indicate that oxidative cracking is an autocatalytic reaction. The oxidation rate increased with the progress of the reaction. Low molecular weight compounds were formed as the main products. CG and CG-MS analyses of the liquid products found homologous series of oxygen compounds (acids, ketones, and ethers) and short-chain n-alkanes. Our results strongly suggest that oxidative cracking can be employed for processing heavy materials such as polymers and petroleum residues.

Inverse Stochastic Routine Combined to a Stepwise Modeling Approach in the Chromatographic Column Characterization Applied to Simulated Moving Bed-SMB Separation of Verapamil Enantiomers

Simulated Moving Bed (SMB) chromatographic processes for the enantiomers separation of the drug verapamil were evaluated through stepwise modeling approach. Predictions of the model were compared to the dispersive equilibrium model in the simulation of continuous separation process and validated with data taken for both compounds in a SMB experimental set-up. An inverse problem tool was associated to the chromatographic columns aiming at their characterization through the global mass transfer parameters using only the experimental residence times of each enantiomer. According to the study conducted, the proposed approach was shown to be a tool with a good potential to predict the chromatographic behavior of a sample in a test pulse, as well as the simulation of separation of a compound in SMB equipment despite minor discrepancies presented in the first work cycles of the SMB. Moreover, the approach can be easily implemented and applied in the analysis of the process.

Accelerated Direct-Problem Solution: A Complementary Method for Computational Time Reduction

This paper presents a proposal designed to reduce the time required by the process to estimate the parameters of a system by accelerating the direct-problem solution as the slow phase in any estimation method. This proposal is considered a complement to existing procedures, such as the combination of different optimization methods for the purpose of reducing the number of calls to the objective function. The proposal consists of a procedure that helps study the relation between the direct-problem solution step and the time required for this solution, as well as the influence of the direct solution’s built-in error on the accuracy of the estimated parameters. Consequently, the extent in which the estimation process can be accelerated without impairing estimation accuracy can be determined. For the purpose of testing its viability, this proposal was applied to the estimation problem of the kinetic parameters of a chromatography column process, as modeled using the front-velocity method. The results from this test show that, by accelerating the direct-problem solution, the estimation time can be reduced significantly, without affecting the accuracy of the estimation.

Uma Versão Modificada do Método Evolução Diferencial para Estimativa de Parâmetros do Modelo de Difusão Anômala Assimétrica

No contexto de solucao de problemas inversos, formulados implicitamente, os metodos de otimizacao estocasticos desempenham um papel fundamental para a estimativa de parâmetros. Entre esses metodos, destaca-se o algoritmo Evolucao Diferencial (Differential Evolution – DE). Neste trabalho, e apresentada uma versao modificada deste metodo para estimar parâmetros de um novo modelo para o fenomeno de difusao anomala assimetrica. Os resultados apresentados neste trabalho indicam que com esta modificacao, e possivel diminuir o tempo de CPU atraves da reducao do numero de iteracoes empregando uma reducao do espaco de busca para cada incognita.

Uncertainty analysis in mass transfer parameter estimations for chromatographic separation of glucose and fructose

In this paper, a statistical approach for the analysis of the propagation of uncertainty is shown, in the estimate of the kinetic parameters of mass transference used to model a chromatographic column in Simulated Moving Bed. The modeling of the chromatography column was accomplished intervening the new approach front velocity. The analysis of how it is propagated the operational factors uncertainty involved in the process of chromatography toward the estimated parameters was carried out by the use of response surface methodology. Furthermore, chromatographic regions where factors cause bigger variation in the output and their respective patterns were determined. The analysis was applied to the separation process of glucose and fructose.

Front Velocity Modeling Approach to Column Chromatographic Characterization and Evaluation of Ketamine Enantiomers Separation with Simulated Moving Bed

Simulated Moving Bed (SMB) is an efficient compounds separation process that operates in a continuous regime and works in a countercurrent flow of solid phase. Among several applications, this process has excelled in petrochemical resolution and especially nowadays in the separation of enantiomers from racemic mixtures, which are considered difficult to separate. In this work, the new Front Velocity approach to model an SMB process was proposed. To describe the mass transfer that occurs in the chromatographic process, the front velocity approach considers that convection is the dominant phase in the solute transport along the chromatographic column. “Front Velocity” is a discrete model (steps) where flow rate determines the advancing of liquid phase through the column. The steps are advancing liquid phase and mass transfer between the liquid and solid phases, the latter in the same time interval. Thus, the experimental volumetric flow is used for discretization of the control volumes moving along the porous column with the same velocity as the liquid phase. The mass transfer was represented by two different kinetic mechanisms without (linear type) and with maximum adsorption capacity (Langmuir type). The proposed approach was studied theoretically and evaluated by comparison with experimental data of ketamine anesthetic separation in SMB. The results were also compared with the simulation model using dispersive equilibrium. In the chromatographic column characterization step the new approach was associated with R2W inverse tool to determine the lumped mass transfer parameters using only the experimental residence time of each enantiomer in the high performance liquid chromatography (HPLC) column. In the second step the mass transfer kinetic equations developed in the approach were applied in each column of the SMB process together with the values determined in the characterization of the chromatographic column, to perform the continuous separation process. The simulation results show good agreement between the modeling proposal and pulse experiments used to characterize the column in enantiomeric separation of ketamine over time. The simulations of the SMB separation show a discrepancy with the experimental data in the early cycles, but after these initial cycles, the model has good correlation with the experimental data. According to the study conducted the proposed approach proved to be a potential tool for prediction of the chromatographic behavior of a sample in a pulse experiment and to simulate the compounds separation in an SMB process despite small differences shown in the first SMB work cycles. Furthermore, the model equations can be easily implemented and applied in the analysis of the process, as it requires a small number of parameters and consists of ordinary differential equations.