Optimization Strategies Based on Sequential Quadratic Programming Applied for a Fermentation Process for Butanol Production

In this work, the mathematical optimization of a continuous flash fermentation process for the production of biobutanol was studied. The process consists of three interconnected units, as follows: fermentor, cell-retention system (tangential microfiltration), and vacuum flash vessel (responsible for the continuous recovery of butanol from the broth). The objective of the optimization was to maximize butanol productivity for a desired substrate conversion. Two strategies were compared for the optimization of the process. In one of them, the process was represented by a deterministic model with kinetic parameters determined experimentally and, in the other, by a statistical model obtained using the factorial design technique combined with simulation. For both strategies, the problem was written as a nonlinear programming problem and was solved with the sequential quadratic programming technique. The results showed that despite the very similar solutions obtained with both strategies, the problems found with the strategy using the deterministic model, such as lack of convergence and high computational time, make the use of the optimization strategy with the statistical model, which showed to be robust and fast, more suitable for the flash fermentation process, being recommended for real-time applications coupling optimization and control.     

Optimisation-based simulation of a pressure swing adsorption process

In this paper, an optimisation-based approach is developed for the determination of the cyclic steady-sate (CSS) of a pressure swing adsorption process (PSA). It consists in treating the simulation problem as a single dynamic optimisation problem where the performance index is the CSS condition, the decision variables are the state variables at the start of the cycle and the constraints are given by the process model equations with associated initial conditions. The resulting optimisation problem is solved using a gradient-based non linear programming (NLP) method, e.g. SQP method, where the gradients are computed by means of four different methods: finite differences, numerical and analytical sensitivities and adjoint system methods.     

Constrained optimization of a preparative ion-exchange step for antibody purification

Today, the optimization of chromatographic separation is usually based on experimental work and rule of thumb. The process and analytical technology (PAT) initiative, of the US Food and Drug Administration, has provided the opportunity of using model-based approach when designing downstream processing of pharmaceutical substances. A nonlinear chromatography model was used in this study to optimize a preparative ion-exchange separation step involving two components. Separation was simulated with the general rate model employing Langmuir kinetics. Optimization was performed with an indirect method allowing constraints on the purity, thus avoiding sub-optimization, which can lead to noisy objective functions. The six decision variables used in the optimizations were flow rate, loading volume, initial salt concentration in the elution, final salt concentration in the linear elution gradient and the two cut points. A graphical representation of the effect of the decision variables on the objective function was used to verify that the optimization had converged to the true optimum. The optimal operating points, using productivity and yield separately as objective functions, were found and compared with the product of productivity and yield as objective function. The optimum obtained with this objective function had a lower productivity, than the productivity function, but much higher yield, which makes it a good substitute for a cost function.     

Prediction model for increasing propylene from FCC gasoline secondary reactions based on Levenberg–Marquardt algorithm coupled with support vector machines

Levenberg–Marquardt (LM) algorithm was adopted to optimize the multiple parameters of the support vector machines (SVM) model to overcome the difficulty in selecting the parameters of SVM and to fit relational expression of high nonlinearity. Strategy of dividing the training data into working data to train SVM and the testing data so as to avoid over‐fitting was performed. Comparison of the proposed LM/SVM method with three reported hybridized SVM approaches (GA/SVM, SM/SVM and SQP/SVM) was also carried out. The new method was applied in modelling for the prediction of propylene by secondary reactions of FCC gasoline. Best performance of LM/SVM employing polynomial kernel was demonstrated. Good agreement between predicted results and experimental data suggests that the LM/SVM method is successfully developed and the SVM model for increasing propylene is well established. Finally, sequential quadratic programming (SQP) algorithm was employed to optimize the operation conditions of FCC gasoline secondary reaction for maximizing the propylene yield. The obtained optimization conditions are consistent with experimental data and reported results, indicating that the optimization results are reliable. Copyright © 2010 John Wiley & Sons, Ltd.     

Water liquid-vapor equilibria predicted by refined ab initio derived potentials

Coexistence properties for water near the critical point using several ab initio models were calculated using grand canonical Monte Carlo simulations with multiple histogram reweighting techniques. These models, that have proved to yield a good reproduction of the water properties at ambient conditions, perform rather well, improving the performance of a previous ab initio model. It is also shown that bulk geometry and dipole values, predicted by the simulation, can be used and a good approximation obtained with a polarizable rigid water model but not when polarization is excluded.     

A Kinetic Study for the Noncatalytic Esterification of Palm Fatty Acid Distillate

In this work, the reaction scheme for the esterification of palm fatty acid distillate performed under the noncatalytic and high‐temperature condition (230–290°C) was investigated with a rigorous mathematical modeling. The esterification reaction was assumed to be the pseudo–homogeneous second‐order reversible reaction, and the mass transfer effectiveness factor (η) was introduced in the modeling framework to systematically and collectively consider both evaporation and reaction, which are simultaneously and competitively occurred in the liquid phase. The nonlinear programming problem was constructed with the objective function consisting of the errors between experimental data and the estimated values from the reaction model. The problem was solved by using the Nelder–Mead simplex algorithm to identify kinetic parameters, reaction rate constants, and mass transfer coefficients. The values of mass transfer coefficients were found to follow the Hertz–Knudsen relation and expressed as a function of reaction temperature. From the reaction rate constants obtained from the proposed kinetic models, the apparent activation energy was estimated to be 43.98 kJ/mol, which is lower than the value obtained from the reaction using heterogeneous catalysts. This low value indicates that reactants and products behave as an acid catalyst at relatively high operating temperature and constant pressure.     

Effect of detoxification of dilute-acid corn fiber hydrolysate on xylitol production

Four different detoxification methods were evaluated for the production of xylitol from corn fiber dilute-acid hydrolysate using Candida tropicalis. Although C. tropicalis could ferment the dilute partially neutralized hydrolysate to xylitol in low yields (0.1 g/g), it could not ferment the concentrated hydrolysate. Overliming, calcium hydroxide neutralization, neutralization combined with activated charcoal, and overliming combined with activated charcoal methods were used to improve the fermentation of the concentrated hydrolysates. The partial neutralization combined with activated charcoal treatment was the most effective method with respect to xylitol yield and productivity. The highest xylitol yield (0.4 g of xylitol/g of xylose) was obtained for the highest concentration of hydrolysate (three times the original) that had been treated with calcium hydroxide and activated charcoal. The corresponding productivity was 0.23 g/(L x h). Overliming caused reduction in xylitol yield.     

An efficient nonlinear programming strategy for PCA models with incomplete data sets

Processing plants can produce large amounts of data that process engineers use for analysis, monitoring, or control. Principal component analysis (PCA) is well suited to analyze large amounts of (possibly) correlated data, and for reducing the dimensionality of the variable space. Failing online sensors, lost historical data, or missing experiments can lead to data sets that have missing values where the current methods for obtaining the PCA model parameters may give questionable results due to the properties of the estimated parameters. This paper proposes a method based on nonlinear programming (NLP) techniques to obtain the parameters of PCA models in the presence of incomplete data sets. We show the relationship that exists between the nonlinear iterative partial least squares (NIPALS) algorithm and the optimality conditions of the squared residuals minimization problem, and how this leads to the modified NIPALS used for the missing value problem. Moreover, we compare the current NIPALS‐based methods with the proposed NLP with a simulation example and an industrial case study, and show how the latter is better suited when there are large amounts of missing values. The solutions obtained with the NLP and the iterative algorithm (IA) are very similar. However when using the NLP‐based method, the loadings and scores are guaranteed to be orthogonal, and the scores will have zero mean. The latter is emphasized in the industrial case study. Also, with the industrial data used here we are able to show that the models obtained with the NLP were easier to interpret. Moreover, when using the NLP many fewer iterations were required to obtain them. Copyright © 2010 John Wiley & Sons, Ltd.     

Improvement of the prediction ability of multivariate calibration by a method based on the combination of data fusion and least squares support vector machines

This paper suggests a novel method named DF-LS-SVM, which is based on least squares support vector machines (LS-SVM) regression combined with data fusion (DF) to enhance the ability to extract characteristic information and improve the quality of the regression. Simultaneous multicomponent determination of Fe(III), Co(II) and Cu(II) was conducted for the first time by using the proposed method. Data fusion is a technique that integrates information from disparate sources to produce a single model or decision. The LS-SVM technique allows for learning a high-dimensional feature with fewer training data, and reduces the computational complexity by only requiring the solution of a set of linear equations instead of a quadratic programming problem. Experimental results showed that the DF-LS-SVM method was successful for simultaneous multicomponent determination even when severe overlap of spectra existed. The DF-LS-SVM method is an attractive and promising hybrid approach that combines the best properties of the two techniques. The results obtained from an additional test case, simultaneous differential pulse voltammetric determination of o-nitrophenol, m-nitrophenol and p-nitrophenol, also demonstrated that the DF-LS-SVM method performed somewhat better than LS-SVM and PLS methods.     

A derivation of the master equation from path entropy maximization

The master equation and, more generally, Markov processes are routinely used as models for stochastic processes. They are often justified on the basis of randomization and coarse-graining assumptions. Here instead, we derive nth-order Markov processes and the master equation as unique solutions to an inverse problem. We find that when constraints are not enough to uniquely determine the stochastic model, an nth-order Markov process emerges as the unique maximum entropy solution to this otherwise underdetermined problem. This gives a rigorous alternative for justifying such models while providing a systematic recipe for generalizing widely accepted stochastic models usually assumed to follow from the first principles.     

Molecular dynamics simulations of liquid methanol and methanol-water mixtures with polarizable models

A polarizable model for simulation of liquid methanol, compatible with the COS/G2 water model, has been developed using the Charge-on-Spring (COS) technique. The model consists of three point charges, with one polarizable center on the oxygen atom. The Lennard-Jones parameters on the oxygen atom together with the molecular polarizability were varied to reproduce the experimental heat of vaporization and density of liquid methanol at ambient conditions. We examined the energies of various methanol dimers in the gas phase and compared them with values obtained from ab initio calculations. The model was then used to study the thermodynamic, dynamic, structural, and dielectric properties of liquid methanol as well as of a methanol-water mixture. A microscopic picture of the structure of pure liquid methanol and of the methanol-water mixture is provided. Good agreement was found between the results from our model simulations and available experimental and ab initio calculation data. In particular, the experimental dielectric permittivity of 32 could be reproduced, which had been shown to be difficult when using nonpolarizable models.     

Framework-based design of a new all-purpose molecular simulation application: the Adun simulator

Here we present Adun, a new molecular simulator that represents a paradigm shift in the way scientific programs are developed. The traditional algorithm centric methods of scientific programming can lead to major maintainability and productivity problems when developing large complex programs. These problems have long been recognized by computer scientists; however, the ideas and techniques developed to deal with them have not achieved widespread adoption in the scientific community. Adun is the result of the application of these ideas, including pervasive polymorphism, evolutionary frameworks, and refactoring, to the molecular simulation domain. The simulator itself is underpinned by the Adun Framework, which separates the structure of the program from any underlying algorithms, thus giving a completely reusable design. The aims are twofold. The first is to provide a platform for rapid development and implementation of different simulation types and algorithms. The second is to decrease the learning barrier for new developers by providing a rigorous and well-defined structure. We present some examples on the use of Adun by performing simple free-energy simulations for the adiabatic charging of a single ion, using both free-energy perturbation and the Bennett's method. We also illustrate the power of the design by detailing the ease with which ASEP/MD, an elaborated mean field QM/MM method originally written in FORTRAN 90, was implemented into Adun.     

Self-avoiding walks in slits and slabs with interactive walls

Self-avoiding walk models of a polymer confined between two parallel attractive walls in two and three dimensions (slits and slabs, respectively) have recently had a revival of interest. They were first studied as simple models of steric stabilisation and sensitised flocculation in colloids. The revival has been catalysed by new exact solution techniques, that have allowed the solution of directed walk models in two dimensions in full generality, and by new Monte Carlo techniques that have allowed the simulation of the full parameter space in the three-dimensional slab model. Additionally, rigorous techniques applied to the slab problem have also yielded new results. The contributions to the study of this problem that have been recently added include a novel phase diagram for the “infinite-slab” (when the walls are a macroscopic distance apart but both walls may still “see” the polymer) the delineation of the repulsive and attractive regimes of the parameter space, and a conjectured scaling theory for the problem in general dimensions.     

Simulation of aerated lagoon using artificial neural networks and multivariate regression techniques

The aim of this study was to develop an empirical model that provides accurate predictions of the biochemical oxygen demand of the output stream from the aerated lagoon at International Paper of Brazil, one of the major pulp and paper plants in Brazil. Predictive models were calculated from functional link neural networks (FLNNs), multiple linear regression, principal components regression, and partial least-squares regression (PLSR). Improvement in FLNN modeling capability was observed when the data were preprocessed using the PLSR technique. PLSR also proved to be a powerful linear regression technique for this problem, which presents operational data limitations.     

Ethanol production from jerusalem artichoke by inulinase and zymomonas mobilis

Ethanol production from Jerusalem artichoke was studied using inulinase and Z.mobilis by simultaneous saccharification and fermentation (SSF) process. The SSF process showed higher ethanol yield and productivity than the acid or enzymatic prehydrolyzed two-step process. The optimum temperature and inulinase concentration for SSF were 35°C and 0.25% (v/w, 4.4 units/g of sugar), respectively. In order to operate the SSF process in a continuous mode, inulinase and Z.mobilis cells were coimmobilized in alginate beads, using chitin as a matrix for enzyme immobilization. The maximum ethanol productivity of the continuous SSF process was 55.1 g/L/h, with 55% conversion yield. At the conversion yield of 90%, the productivity was 32.7 g/L/h. The continuous SSF system could be operated stably over 2 wk with an ethanol concentration of 48.6 g/L (95% of theoretical yield).     

Dynamic optimization of multicomponent batch distillation processes using continuous and discontinuous collocation polynomial policies

Optimization of batch distillation has been studied extensively over the last 30 years. Previously, the solution methods were basically derived or computed using short-cut models due to the lack of suitable computation techniques. In this study, a modified approach based on the work of Biegler and coworkers (L. T. Biegler, Comput.Chem.Eng., 8 (1984) 243; J. E. Cuthrell and L. T. Biegler, AIChE J., 8 (1987) 1257) was implemented to determine optimal constrained solutions for a ternary system with various objective functions, such as maximum product, minimum energy required and mininum end time, using a rigorous model. Unlike previous investigations, the optimal control solutions derived in this study were independent of the process model implemented. Therefore, no limitation on the distillation models exists, i.e. any rigorous model can be used to find solutions.The optimal control problem for the batch distillation of mixtures of benzene, toluene and o-xylene was solved. The solutions were assumed to be continuous or discontinuous polynomials. It was found that a discontinuous solution is superior to continuous results because of the discontinuous nature of the system itself.     

Optimization of injection‐molding process for mechanical properties of polypropylene components via a generalized regression neural network

This study analyzed contour distortions, wear and tensile properties of polypropylene (PP) components applied in the interior coffer of automobiles. A hybrid method integrating a trained generalized regression neural network (GRNN) and a sequential quadratic programming (SQP) method is proposed to determine an optimal parameter setting of the injection‐molding process. The specimens were prepared under different injection‐molding conditions by changing melting temperatures, injection speeds, and injection pressures. Average contour distortions at six critical locations, wear and tensile properties were selected as the quality targets. Sixteen experimental runs, based on a Taguchi orthogonal array table, were utilized to train the GRNN and then the SQP method was applied to search for an optimal setting. The trained GRNN was capable of predicting average contour distortions, wear and tensile properties at various injection‐molding conditions. In addition, the analysis of variance (ANOVA) was implemented to identify significant factors for the molding process and the proposed algorithm was compared with traditional schemes like the Taguchi method and the design of experiments (DOE) approach. Copyright © 2007 John Wiley & Sons, Ltd.     

Microscopic models for quantum mechanical calculations of chemical processes in solutions: LD/AMPAC and SCAAS/AMPAC calculations of solvation energies

Our previously developed approaches for integrating quantum mechanical molecular orbital methods with microscopic solvent models are refined and examined. These approaches consider the nonlinear solute–solvent coupling in a self-consistent way by incorporating the potential from the solvent dipoles in the solute Hamiltonian, while considering the polarization of the solvent by the potential from the solute charges. The solvent models used include the simplified Langevin Dipoles (LD) model and the much more expensive surface constrained All Atom Solvent (SCAAS) model, which is combined with a free energy pertubation (FEP) approach. Both methods are effectively integrated with the quantum mechanical AMPAC package and can be easily combined with other quantum mechanical programs. The advantages of the present approaches and their earlier versions over macroscopic reaction field models and supermolecular approaches are considered. A LD/MNDO study of solvated organic ions demonstrates that this model can yield reliable solvation energies, provided the quantum mechanical charges are scaled to have similar magnitudes to those obtained by high level ab initio methods. The incorporation of a field-dependent hydrophobic term in the LD free energy makes the present approach capable of evaluating the free energy of transfer of polar molecules from non polar solvents to aqueous solutions. The reliability of the LD approach is examined not only by evaluating a rather standard set of solvation energies of organic ions and polar molecules, but also by considering the stringent test case of sterically hindered hydrophobic ions. In this case, we compare the LD/MNDO solvation energies to the more rigorous FEP/SCAAS/MNDO solvation energies. Both methods are found to give similar results even in this challenging test case. The FEP/SCAAS/AMPAC method is incorporated into the current version of the program ENZYMIX. This option allows one to study chemical reactions in enzymes and in solutions using the MNDO and AM1 approximations. A special procedure that uses the EVB method as a reference potential for SCF MO calculations should help in improving the reliability of such studies.     

Controlled-Rate Thermal Desorptton

A new way of conducting thermal desorption experiments is described. The method consists in maintaining the desorption rate constant by a rigorous control of temperature. The equations for two models of constant rate desorption are described: from a surface with only one type of adsorption site, and with two different types. The technique is applied to two real systems and the kinetic parameters are determined. The results are compared with those obtained by using TPD. The main advantages are discussed and the methodology and modifications required for a TPD set-up to work at a constant desorption rate are described.