Chemical Engineering Problems Research Articles

Dead-Core Solutions to Simple Catalytic Reaction Problems in Chemical Engineering

The catalytic chemical reaction is usually carried out in a pellet where the catalyst is distributed throughout its porous structure. The selectivity, yield and productivity of the catalytic reactor often depend on the rates of chemical reactions and the rates of diffusion of species involved in the reactions in the pellet porous space. In such systems, the fast reaction can lead to the consumption of reactants close to the external pellet surface and creation of the dead core where no reaction occurs. This will result in an inefficient use of expensive catalyst. In the discussed simplified diffusion-reaction problems a nonlinear reaction term is of power-law type with a small positive reaction exponent. Such reaction term represents the kinetics of catalytic reaction accompanied by a strong adsorption of the reactant. The ways to calculate the exact solutions possessing dead cores are presented. It was also proved analytically that the exact solution of the nonlinear two-point boundary value problem satisfies physical a-priori bounds. Furthermore, the approximate solutions were obtained using the orthogonal collocation method for pellets of planar, spherical and cylindrical geometries. Numerical results confirmed that the length of the dead core increases for the more active catalysts due to the larger values of the reaction rate constant. The dead core length also depends on the pellet geometry.

Local Convergence Balls for Nonlinear Problems with Multiplicity and Their Extension to Eighth-Order Convergence

The main contribution of this study is to present a new optimal eighth-order scheme for locating zeros with multiplicity m≥1. An extensive convergence analysis is presented with the main theorem in order to demonstrate the optimal eighth-order convergence of the proposed scheme. Moreover, a local convergence study for the optimal fourth-order method defined by the first two steps of the new method is presented, allowing us to obtain the radius of the local convergence ball. Finally, numerical tests on some real-life problems, such as a Van der Waals equation of state, a conversion chemical engineering problem, and two standard academic test problems, are presented, which confirm the theoretical results established in this paper and the efficiency of this proposed iterative method. We observed from the numerical experiments that our proposed iterative methods have good values for convergence radii. Further, they not only have faster convergence towards the desired zero of the involved function but also have both smaller residual error and a smaller difference between two consecutive iterations than current existing techniques.

Robust Nonlinear Partial Least Squares Regression Using the BACON Algorithm

Partial least squares regression (PLS regression) is used as an alternative for ordinary least squares regression in the presence of multicollinearity. This occurrence is common in chemical engineering problems. In addition to the linear form of PLS, there are other versions that are based on a nonlinear approach, such as the quadratic PLS (QPLS2). The difference between QPLS2 and the regular PLS algorithm is the use of quadratic regression instead of OLS regression in the calculations of latent variables. In this paper we propose a robust version of QPLS2 to overcome sensitivity to outliers using the Blocked Adaptive Computationally Efficient Outlier Nominators (BACON) algorithm. Our hybrid method is tested on both real and simulated data.

Application of Scilab/Xcos for process control applied to chemical engineering educational projects

AbstractThe study of process control applied to chemical engineering problems can be significantly improved by the use of simulation packages. However, it has been noted that few works have been focusing on elucidation of the use of open source packages for academic projects on process control. In fact, there is few online discussion groups aimed to the application of Xcos® package for chemical engineering projects. Given this, this work aims to apply the Xcos® for studying the implementation of the process control theory applied to chemical engineering projects, focusing on the development of control loops block diagrams, PID control tuning, and process response analysis. The purpose of the application is developing a virtual environment for academic discussion and repository of examples. The results of two benchmark case studies are illustrated, showing that the problems can be easily modified, allowing the student to solve other similar examples for future applications. For the first case, the settling time ranged from 24.067 to 72.492 min, while for the second case the stabilization time ranged from 5.301 to 20.904 min.The results evidence that the Xcos® software can be widely applied by the academic community, due to its simplicity and robustness in demonstrating the principal aspects of control theory.

Optimal Synthesis of Batch Water Networks Using Dynamic Programming

Water minimization in the process industry is becoming increasingly important due to increasingly stringent environmental legislation, especially for batch plants. This work proposes a dynamic programming (DP) method for the optimal design of water-using networks in batch plants. DP is a powerful framework for dealing with a large spectrum of multistage decision-making problems and has been applied in numerous chemical engineering problems. The proposed methodology is explained as follows. Firstly, based on the start time and end time of each operation, the whole process is divided into N stages. Secondly, the water requirement of water-using units in each stage is satisfied and the state of stored water and wastewater generation is determined. The backward procedure of DP is used to solve the DP problems. The target of freshwater consumption of the process and the optimal design of the water network are obtained simultaneously. In order to display the versatility of the proposed approach, four examples from literature are considered. Example 1 is a completely batch process with a fixed flowrate problem. Example 2 is a hybrid batch water system comprising various modes of operations and operating patterns. Example 3 is a fixed-mass load problem with a regeneration unit, while example 4 considers the batch water network design with multiple contaminants. The results obtained in this work were comparable with the results from literature, implying that it can be applicable to both mass transfer-based and non-mass transfer-based batch water networks.

Enhanced surrogate assisted framework for constrained global optimization of expensive black-box functions

An enhanced surrogate assisted framework, based on Probability of Improvement (PI) method, is proposed in this paper. We made some modifications to the original PI approach to enhance the performance of the modeling and optimization framework, leading to fewer rigorous simulations to find the optimal solution without loss of accuracy. We also extended the algorithm for handling general constraints using a fully probabilistic approach. The behavior of the proposed framework was investigated through a set of 9 Unconstrained Test Functions (UTF), 7 Constrained Optimization Problems (COP) and 3 Chemical Engineering Problems (CEP). The numerical results indicate that a lower number of rigorous model simulations were needed for optimizing UTF compared to the classic PI method and that the proposed framework was capable of achieving sustained near optimal solutions for COP and CEP. These results indicate that the proposed framework is suitable for solving computationally expensive constrained black-box optimization problems.

The Impact of Global Sensitivities and Design Measures in Model-Based Optimal Experimental Design

In the field of chemical engineering, mathematical models have been proven to be an indispensable tool for process analysis, process design, and condition monitoring. To gain the most benefit from model-based approaches, the implemented mathematical models have to be based on sound principles, and they need to be calibrated to the process under study with suitable model parameter estimates. Often, the model parameters identified by experimental data, however, pose severe uncertainties leading to incorrect or biased inferences. This applies in particular in the field of pharmaceutical manufacturing, where usually the measurement data are limited in quantity and quality when analyzing novel active pharmaceutical ingredients. Optimally designed experiments, in turn, aim to increase the quality of the gathered data in the most efficient way. Any improvement in data quality results in more precise parameter estimates and more reliable model candidates. The applied methods for parameter sensitivity analyses and design criteria are crucial for the effectiveness of the optimal experimental design. In this work, different design measures based on global parameter sensitivities are critically compared with state-of-the-art concepts that follow simplifying linearization principles. The efficient implementation of the proposed sensitivity measures is explicitly addressed to be applicable to complex chemical engineering problems of practical relevance. As a case study, the homogeneous synthesis of 3,4-dihydro-1H-1-benzazepine-2,5-dione, a scaffold for the preparation of various protein kinase inhibitors, is analyzed followed by a more complex model of biochemical reactions. In both studies, the model-based optimal experimental design benefits from global parameter sensitivities combined with proper design measures.

Applying Grid partitioning based Fuzzy inference system as novel algorithm to predict Asphaltene precipitation

ABSTRACTAsphaltene precipitation is one of challenging problems in petroleum and chemical engineering so the importance of investigation of Asphaltene precipitation is clear. The asphaltene deposition effects on wellbore plugging, wettability alteration and facility damages. In order to solve these problems, a novel investigation based on Grid partitioning based Fuzzy inference system algorithm to predict precipitated asphaltene in terms of dilution ratio, temperature and carbon number of precipitant was developed. The predicting algorithm performance was evaluated statistically and graphically. The coefficients of determination (R2) for training and testing phases 0.9973 and 0.9900 respectively which confirm the great accuracy and high potential of predicting algorithm for estimation of precipitated asphaltene so this algorithm can be used as high accurate and simple software for prediction of asphaltene behavior in crude oil.

Teaching-Learning-Based Optimization with Learning Enthusiasm Mechanism and Its Application in Chemical Engineering

Teaching-learning-based optimization (TLBO) is a population-based metaheuristic search algorithm inspired by the teaching and learning process in a classroom. It has been successfully applied to many scientific and engineering applications in the past few years. In the basic TLBO and most of its variants, all the learners have the same probability of getting knowledge from others. However, in the real world, learners are different, and each learner’s learning enthusiasm is not the same, resulting in different probabilities of acquiring knowledge. Motivated by this phenomenon, this study introduces a learning enthusiasm mechanism into the basic TLBO and proposes a learning enthusiasm based TLBO (LebTLBO). In the LebTLBO, learners with good grades have high learning enthusiasm, and they have large probabilities of acquiring knowledge from others; by contrast, learners with bad grades have low learning enthusiasm, and they have relative small probabilities of acquiring knowledge from others. In addition, a poor student tutoring phase is introduced to improve the quality of the poor learners. The proposed method is evaluated on the CEC2014 benchmark functions, and the computational results demonstrate that it offers promising results compared with other efficient TLBO and non-TLBO algorithms. Finally, LebTLBO is applied to solve three optimal control problems in chemical engineering, and the competitive results show its potential for real-world problems.

Programming skills in the industry 4.0: are chemical engineering students able to face new problems?

A reflection on teaching programming at undergraduate level using advanced tools is presented. Advanced digital tools and computational evolution have shaped different areas, such as industrial process, communications, education and innovation. New technologies, such as the Internet of Things-IoT, cloud computing and artificial intelligence, have boosted software development and computational skills in different areas. The chemical engineering knowledge acquired by senior students and programming skills can be integrated to develop computational tools, favoring chemical engineers to take advantage of new opportunities in digital area. Normally, programming courses are offered at the beginning of chemical engineering program, with examples not related to chemical engineering problems. To fill this gap, an elective discipline was created for final year undergraduate students in the Department of Chemical Engineering at University of São Paulo (Brazil). This paper discusses the main motivations for a new programming course, presents the structure of the course and shows some outcomes from a students' survey about what they have learned.

Rapid phase stability calculations in fluid flow simulation using simple discriminating functions

This paper presents a new phase stability method that is applicable when repeated phase behavior calculations are needed as it is the case with multiphase fluid flow compositional simulation in upstream petroleum engineering. Two discriminating functions act as classifiers in such a way that a positive value of one of the two functions determines the stability state of the mixture. The two functions are generated off line, prior to the simulation, and their expressions are very simple so that they can be evaluated rapidly in a non-iterative way for every discretization block and at each timestep during the simulation. The CPU time required for phase stability calculations is dramatically reduced while still obtaining correct classification results corresponding to the global minimum of the system Gibbs energy function. The method can be applied to any chemical engineering problem where the class of several objects needs to be determined repeatedly and quickly.

Application of Gaussian cubature to model two-dimensional population balances

Abstract In many systems of engineering interest the moment transformation of population balance is applied. One of the methods to solve the transformed population balance equations is the quadrature method of moments. It is based on the approximation of the density function in the source term by the Gaussian quadrature so that it preserves the moments of the original distribution. In this work we propose another method to be applied to the multivariate population problem in chemical engineering, namely a Gaussian cubature (GC) technique that applies linear programming for the approximation of the multivariate distribution. Examples of the application of the Gaussian cubature (GC) are presented for four processes typical for chemical engineering applications. The first and second ones are devoted to crystallization modeling with direction-dependent two-dimensional and three-dimensional growth rates, the third one represents drop dispersion accompanied by mass transfer in liquid-liquid dispersions and finally the fourth case regards the aggregation and sintering of particle populations.

Optimization of chemical engineering problems with EMSO software

AbstractEMSO software, a free tool for teaching and academic research, presents a favorable environment for simulation and optimization of chemical engineering problems. Although its use in research activities have been demonstrated in the literature, its application as a supporting tool for educational purposes in process systems engineering courses has not been evaluated. The objective of this paper is to demonstrate that this software is suitable as a tool for educational purposes in process systems engineering courses at undergraduate (complementary elective subject) and graduate levels. To accomplish this task, different cases studies, encompassing different sort of programming formulations, are proposed and solved with different solvers in EMSO.

Influence of randomization strategies and problem characteristics on the performance of Differential Search algorithm

In this work, the influence of different random number generators, problem dimensionality, and number of function evaluations on the optimization efficiency of Differential Search algorithm is presented in detail. Two types of random number generators were taken into account: discrete and continuous. Different combinations between the dimensionality property and the number of function evaluation setting were tested on: i) a set of benchmark functions from the CEC 2013 special session on real parameter optimization; and ii) 2 chemical engineering problems (optimal operation of an alkylation unit and heat exchanger network design). Also, a comparison with other optimizers was performed. It was found that, in similar conditions, the performance of the algorithm (in terms of the best solutions) varies substantially depending on the distribution used. In case of the benchmark problems, the best solutions were obtained for Binomial and Weibull distribution. For the separable functions is was observed that, indifferent of the distribution used, the algorithm was not able to find acceptable solution within the constraint represented by the number of function evaluations. In the case of the alkylation problem the best solutions were obtained by the Weibull distribution, the performance of the Differential Search algorithm being comparable to other optimizers such as Differential Evolution. In the case of the heat exchanger, three different distribution provided near optimal solutions (Binomial, ChiSquare and Weibull).

Experimental proof of the existence of mass‐transfer resistance during early stages of ethylene polymerization with silica supported metallocene/MAO catalysts

The size of a silica supported metallocene/MAO (methylaluminoxane) catalyst plays an important role in determining its productivity during ethylene polymerization. From a chemical engineering point of view, this size dependency of catalytic activity of supported metallocenes is mathematically connected with the different levels of mass‐transfer resistance in big and small catalyst particles but no experimental evidence has been provided to date. The results of this systematic experimental study clearly demonstrate that the intraparticle monomer diffusion resistance is high in bigger catalyst particles during initial instants of ethylene polymerization and diminishes with the polymer particle growth. Two different silica supported metallocene/MAO catalysts provided the same results while highlighting the fact that catalyst chemistry should be carefully considered while studying complex chemical engineering problems. © 2017 American Institute of Chemical Engineers AIChE J, 63: 4476–4490, 2017

Solution of six chemical engineering problems using the Chebyshev orthogonal collocation technique

AbstractThe Chebyshev orthogonal collocation is a powerful and accurate numerical technique, which is also relatively easy to implement using modern mathematical software (e.g., MATHEMATICA © and MATLAB ®). This technique allows the elucidation of engineering problems involving partial differentials equations or boundary value problems. Six chemical engineering problems concerning the transfer of momentum, heat, and mass, with varying degree of complexity, are elucidated. The results obtained using the subject numerical technique were systematically bench‐marked against the results derived from alternative approaches. Benchmarking indicates good agreement between the results, despite the simplicity of this technique. Thus, this technique has a great potential for the elucidation of problems, for which no known solutions exist.

An effective pseudospectral optimization approach with sparse variable time nodes for maximum production of chemical engineering problems

AbstractAn effective pseudospectral method is proposed for dynamic optimization problems, the aim of which is to maximize production of these problems in chemical engineering. Several variable time nodes are considered to be optimization variables in the whole time horizon to obtain a precise localization of the switching points of the optimal control profiles. To ensure accuracy, the intervals between the variable time nodes are further divided into multiple subintervals uniformly. Then the state and the control vector are all parameterized. To improve the efficiency, the sensitivities of the states with respect to the controls and the variable time nodes are derived from the solution of the discretized dynamic system. Three chemical dynamic optimization problems are tested as an illustration. The detailed comparisons between the proposed method and the methods reported in the literature are also carried out. The research results reveal the effectiveness of the proposed approach.

Improvement of Karush–Kuhn–Tucker conditions under uncertainties using robust decision making indexes

Almost all practical engineering problems work with uncertainties. Particularly, in chemical engineering problems, uncertainties in process models and measurements increase complexity on optimization modeling. In these cases, points are transformed in regions, and the point conditions need to be extended to its neighborhood. Extension and validation of Karush–Kuhn–Tucker (KKT) conditions under uncertainties scenarios are not trivial. In this paper, we propose two new conditions to improve robustness at second order KKT conditions.

Some novel and optimal families of King’s method with eighth and sixteenth-order of convergence

In this study, our principle aim is to provide some novel eighth and sixteenth-order families of King’s method for solving nonlinear equations which should be superior than the existing schemes of same order. The relevant optimal orders of the proposed families satisfy the classical Kung–Traub conjecture which was made in 1974. The derivations of the proposed schemes are based on the weight function and rational approximation approaches, respectively. In addition, convergence properties of the proposed families are fully investigated along with one lemma and two main theorems describing their order of convergence. We consider a concrete variety of real life problems e.g. the trajectory of an electron in the air gap between two parallel plates, chemical engineering problem, Van der Waal’s equation which explains the behavior of a real gas by introducing in the ideal gas equations and fractional conversion in a chemical reactor, in order to check the validity, applicability and effectiveness of our proposed methods. Further, it is found from the numerical results that our proposed methods perform better than the existing ones of the same order when the accuracy is checked in the multi precision digits.

An Adaptive Pseudospectral Method for Constrained Dynamic Optimization Problems in Chemical Engineering

AbstractAn adaptive pseudospectral method with two novel strategies is proposed to solve constrained dynamic optimization problems in chemical engineering. The first strategy is to introduce slope information in designing appropriate subintervals, so that the approach becomes more efficient to track the optimal control profiles. The second strategy is to redistribute the collocation points based on the approximation error, thus ensuring the accuracy of the method. Two constrained dynamic optimization problems with multiple control variables are tested as illustrations, and the proposed approach is compared with other methods. The research results reveal the effectiveness of the proposed method in improving the solution accuracy of dynamic optimization problems.