Fernando P. Bernardo

Quality costs and robustness criteria in chemical process design optimization

Abstract The identification and incorporation of quality costs and robustness criteria is becoming a critical issue while addressing chemical process design problems under uncertainty. This article presents a systematic design framework that includes Taguchi loss functions and other robustness criteria within a single-level stochastic optimization formulation, with expected values in the presence of uncertainty being estimated by an efficient cubature technique. The solution obtained defines an optimal design, together with a robust operating policy that maximizes average process performance. Two process engineering examples (synthesis and design of a separation system and design of a reactor and heat exchanger plant) illustrate the potential of the proposed design framework. Different quality cost models and robustness criteria are considered, and their influence in the nature and location of best designs systematically studied. This analysis reinforces the need for carefully considering/addressing process quality and robustness related criteria while performing chemical process plant design.

Robustness criteria in process design optimization under uncertainty

Abstract The incorporation of robustness criteria in process design under uncertainty is a key issue to derive optimal designs for quality. This article presents a systematic design framework for process quality that embeds Taguchis method within a stochastic optimization formulation. The problem is formulated as a single-level optimization problem with expected objective function values computed by an efficient cubature technique. The solution obtained determines an optimal design together with a robust operating policy that maximize average process performance. A process example of a reactor and heat exchanger is provided.

A theoretical model for transdermal drug delivery from emulsions and its dependence upon formulation

This article presents a theoretical model of transdermal drug delivery from an emulsion-type vehicle that addresses the vehicle heterogeneity and incorporates the prediction of drug transport parameters as function of the vehicle composition. The basic mass transfer model considers interfacial and diffusion resistances within the emulsion and partition/diffusion phenomena across two skin compartments in series. Drug transport parameters are predicted as follows: partition coefficients are derived from regular solutions theory, drug diffusivity in the continuous phase is computed from a free volume theory with segmental motion, and permeability of the surfactant layer around droplets is estimated based on a free surface area model. These relationships are incorporated within the basic mass transfer model, so that the overall model is able to predict temporal profiles of drug release from the vehicle and of drug concentration in plasma, as a function of vehicle composition. In this way, the proposed model provides a sound physicochemical basis to support the development of new formulations and the planning of experiments. A simulated case study regarding a nitroglycerin ointment is presented in detail, illustrating how thermodynamic and kinetic factors inherent to the emulsion vehicle can modulate drug release and subsequent systemic absorption.

A virtual platform to teach separation processes

In this article the Unit Operations and Separation Processes area of a virtual platform called LABVIRTUAL(http://labvirtual.eq.uc.pt) is presented aiming to support the autonomous study of undergraduate students engaged in a Chemical Engineering degree, especially in Portuguese‐speaking countries. The main features, subjects, computational applications, and examples in the platform are described, as well as a first assessment by the students.

Inclusion of information costs in process design optimization under uncertainty

Abstract Recent developments in process design have focused on establishing optimization-based approaches to support decision-making under uncertainty, but few efforts have been made to study and consider how information regarding this uncertainty affects optimal decision. In this paper we develop an optimal design framework that, besides integrating process profitability, robustness and quality issues, allows one to decide how much it is worth to spend in research and experimentation for selectively reducing parameter uncertainties and guiding R&D activities. The design problem is thus formulated as a stochastic optimization problem, whose objective function includes an information cost term, leading to the identification of optimal parameter uncertainty levels one should end up with, as well as the corresponding amounts to be spent in R&D. A case study comprising a reactor and heart exchanger system is introduced and provides an illustrative application for the suggested methodology.

Performance of cubature formulae in probabilistic model analysis and optimization

In probabilistic model analysis and optimization, expected values of a model output f ( x ) in face of continuous random inputs x are estimated through n -dimensional integrals, where n = d i m ( x ) . Cubature formulae are approximations of these integrals by a weighted sum of function evaluations at carefully chosen points. When each function evaluation corresponds to a heavy computational simulation, and particularly in optimization problems, one needs very efficient formulae with few integration points, even though only having modest accuracy. In this paper, we evaluate the performance of several cubature formulae with few points, including Smolyak type formulae, also known as sparse grid integration, and recently proposed thinned cubatures, constructed using orthogonal arrays. Tests are made for a wide family of smooth and non-oscillatory functions f ( x ) , possibly with significant anisotropy, and covering both normal and uniform input probability distributions. Two practical case studies are also presented, one of analysis of a large scale mass transfer model with uncertain parameters and a second one of optimal production planning under uncertain market conditions. Results clearly indicate that cubatures with large negative weights, including Smolyak type formulae, are not reliable, contrary to positive thinned cubatures that produce very reasonable estimates up to dimension 24. These thinned cubatures may also surpass quasi-Monte Carlo methods also up to dimension 24.

Integrated process and product design optimization: a cosmetic emulsion application

Abstract A simultaneous approach to address optimal product and process design is presented and applied to a cosmetic lotion case study. The problem formulation integrates product quality, as assessed by customers, a model predicting lotion viscosity as a function of its composition and a process model linking process design and operation with lotion composition and microstructure. The solution of such a problem identifies the optimal lotion composition together with the interrelated process optimal specifications. This integrated design approach is shown to provide better solutions than the ones obtained when product and process design problems are solved separately.

Value of information analysis in product/process design

Abstract We propose a generic optimisation-based formulation for the integrated design of chemical products and respective processes, driven by product quality factors, and incorporating both model and parameter uncertainties. Different problem levels are discriminated and the value of eliminating their associated uncertainties is also evaluated. This value of information analysis may greatly support product/process development, indicating priorities for further research. A cosmetic lotion case study illustrates the proposed methodology and concepts, with the prediction of aqueous phase viscosity being identified as the key aspect for further solution refinement.

Process Design Under Uncertainty: Robustness Criteria and Value of Information

In the last three decades, process design under uncertainty has evolved as an optimization-based tool to systematically handle uncertainty at an early design stage thus avoiding overdesign, underdesign or other suboptimal decisions. In this chapter, we address this issue presenting a generic framework to guide the decision-maker on the design problem definition that systematises several considerations and assumptions, namely regarding constraints violation, uncertainty classification and modelling, operating policy and decision-making criteria under uncertainty. This generic framework is then explored for handling process robustness and value of information features. A case study of a reactor and heat exchanger system illustrates the several presented formulations, namely optimal process design accounting for product quality and optimal R&D decisions in order to selectively reduce uncertainties.

Constrained Smoothing of Experimental Data in the Identification of Kinetic Models

Abstract In the context of the application of systematic methodologies for the incremental development of mechanistic kinetic models, various regularization techniques have been explored to allow the estimation of rate phenomena as the derivatives of sparse data sets. Through a combination of a numerical approach with aspects of qualitative analysis, this work proposes a novel method to obtain smoothed concentration profiles that allow their reliable differentiation. Two different case studies are considered to illustrate the performance of the method.