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Abstract This paper presents a model-based assessment of the thermochemical conversion of microalgal biomass into Fischer-Tropsch liquids, hydrogen and electricity through polygeneration. Two novel conceptual plants are investigated, which are both comprised of the same operation units (gasification, water-gas shift, Fischer-Tropsch synthesis, upgrading, separation, Rankine cycle and gas turbines) and mainly differ in the location of the water-gas-shift unit. Both plants are found to present a carbon efficiency greater than conventional biomass-to-liquid processes. The most profitable plants in terms of the saleable products yields ca. 0.23 m3 (1.4 bbl) of liquid transportation fuels (gasoline, kerosene and diesel), ca. 16 kg of hydrogen (716.8 scm), and ca. 1.55 × 109 J (430 kW·h) of electricity per 1000 kg of dried microalgae. The corresponding displaced fossil fuels could offset the carbon emissions by 0.56 kg of carbon dioxide for every kg of processed dried microalgae. Nevertheless, predicted break-even prices are lower than 40 USD per ton of dried microalgae in the base case scenario, which is at least 10 times cheaper than the current best scenario for microalgal biomass production. These low prices are a major impediment to the viability of these thermochemical polygeneration plants, albeit presenting a good potential toward cleaner liquid fuel production. Graphical abstract Image 1 Highlights • Novel conceptual routes for thermochemical conversion of microalgal biomass into products. • Model based techno-economic and environmental analysis using commercial process simulator. • Yield per ton of microalgae: 0.23 m3 of liquid fuels, 16 kg of hydrogen, and 430 kW·h of electricity. • Displaced fossil fuels to offset carbon emissions by 560 kg of carbon dioxide per ton of microalgae. • Break-even price for microalgae biomass is the major impediment to the economic competitiveness. [ABSTRACT FROM AUTHOR]

A methodology for combining multi-parametric programming and NCO tracking is presented in the case of linear dynamic systems. The resulting parametric controllers consist of (potentially nonlinear) feedback laws for tracking optimality conditions by exploiting the underlying optimal control switching structure. Compared to the classical multi-parametric MPC controller, this approach leads to a reduction in the number of critical regions. It calls for the solution of more difficult parametric optimization problems with linear differential equations embedded, whose critical regions are potentially nonconvex. Examples of constrained linear quadratic optimal control problems with parametric uncertainty are presented to illustrate the approach. [ABSTRACT FROM AUTHOR]

Abstract: This paper presents a discretize-then-relax methodology to compute convex/concave bounds for the solutions of a wide class of parametric nonlinear ODEs. The procedure builds upon interval methods for ODEs and uses the McCormick relaxation technique to propagate convex/concave bounds. At each integration step, a two-phase procedure is applied: a priori convex/concave bounds that are valid over the entire step are calculated in the first phase; then, pointwise-in-time convex/concave bounds at the end of the step are obtained in the second phase. An approach that refines the interval state bounds by considering subgradients and affine relaxations at a number of reference parameter values is also presented. The discretize-then-relax method is implemented in an object-oriented manner and is demonstrated using several numerical examples. [Copyright &y& Elsevier]

Abstract: This paper presents a methodology for the optimal design and operation of man-portable power generation devices based on fuel cells. To illustrate the methodology, we focus on a simple process that consists of a fuel processing reactor, a solid-oxide fuel cell (SOFC) and two burners in a stack. Hydrogen is produced from ammonia decomposition, while butane is catalytically oxidized to produce heat and maintain the stack at a sufficiently high temperature. First, a model is formulated for predicting the steady-state performance of the process, which relies on intermediate fidelity modeling assumptions. Subsequently, this model is used as a basis to study and determine the optimal design and operation of the overall system. The optimization problem is formulated so that the specific energy density of the fuels (ammonia and butane) is maximized, while meeting a specified power demand, maintaining the stack at its thermal equilibrium, and satisfying tight constraints in regard to the emission of both ammonia and nitric oxide gases. The effects of the operating temperature and nominal power demand on the performance of the system are analyzed thoroughly, with emphasis placed on several counter-intuitive results that provide insight into the design. Finally, a parametric study is presented, which considers the effect of uncertainties in the heat loss coefficients and the exchange current densities, as well as that of the electrolyte thickness, on the optimal design and operation of the process. [Copyright &y& Elsevier]

Over the past decade, membrane contactors (MBC) for CO 2 absorption have been widely recognized for their large intensification potential compared to conventional absorption towers. MBC technology uses microporous hollow-fiber membranes to enable effective gas and liquid mass transfer, without the two phases dispersing into each other. The main contribution of this paper is the development and verification of a predictive mathematical model of high-pressure MBC for natural gas sweetening applications, based on which model-based parametric analysis and optimization can be conducted. The model builds upon insight from previous modeling studies by combining 1-d and 2-d mass-balance equations to predict the CO 2 absorption flux, whereby the degree of membrane wetting itself is calculated from the knowledge of the membrane pore-size distribution. The predictive capability of the model is tested for both lab-scale and pilot-scale MBC modules, showing a close agreement of the predictions with measured CO 2 absorption fluxes at various gas and liquid flowrates, subject to a temperature correction to account for the heat of reaction in the liquid phase. The results of a model-based analysis confirm the advantages of pressurized MBC operation in terms of CO 2 removal efficiency. Finally, a comparison between vertical and horizontal modes of operation shows that the CO 2 removal efficiency in the latter can be vastly superior as it is not subject to the liquid static head and remediation strategies are discussed. [ABSTRACT FROM AUTHOR]

An algorithm is proposed for locating a feasible point satisfying the KKT conditions to a specified tolerance of feasible inequality-path-constrained dynamic programs (PCDP) within a finite number of iterations. The algorithm is based on iteratively approximating the PCDP by restricting the right-hand side of the path constraints and enforcing the path constraints at finitely many time points. The main contribution of this article is an adaptation of the semi-infinite program (SIP) algorithm proposed in Mitsos (2011) to PCDP. It is proved that the algorithm terminates finitely with a guaranteed feasible point which satisfies the first-order KKT conditions of the PCDP to a specified tolerance. The main assumptions are: (i) availability of a nonlinear program (NLP) local solver that generates a KKT point of the constructed approximation to PCDP at each iteration if this problem is indeed feasible; (ii) existence of a Slater point of the PCDP that also satisfies the first-order KKT conditions of the PCDP to a specified tolerance; (iii) all KKT multipliers are nonnegative and uniformly bounded with respect to all iterations. The performance of the algorithm is analyzed through two numerical case studies. [ABSTRACT FROM AUTHOR]

• Comparison of reformulated MIQCPs against original MIPOPs using the solvers GUROBI, BARON and SCIP. • Investigation of preprocessing strategies and redundant quadratic constraints on performance of MIQCP reformulation. • MIQCP reformulation engine implemented in the C++ library CANON. • Reformulated MIQCPs solved significantly faster with GUROBI than original MIPOPs with BARON or SCIP. • Several unsolved test instances from MINLPLib successfully solved to global optimality after MIQCP reformulation. This paper revisits the approach of transforming a mixed-integer polynomial program (MIPOP) into a mixed-integer quadratically-constrained program (MIQCP), in the light of recent progress in global solvers for this latter class of models. We automate this transformation in a new reformulation engine called CANON , alongside preprocessing strategies including local search and bounds tightening. We conduct comparative tests on a collection of 137 MIPOPs gathered from test libraries such as MINLPLib. The solver GUROBI gives the best performance on the reformulated MIQCPs and outperforms the generic global solvers BARON and SCIP. The MIQCP reformulation also improves the performance of SCIP compared to direct MIPOP solution, whereas the performance of BARON is comparable on the original MIPOPs and reformulated MIQCPs. Overall, these results establish the effectiveness of quadratic reformulation for MIPOP global optimization and support its integration into global solvers. [ABSTRACT FROM AUTHOR]

Highlights • Robust multi-parametric NCO-tracking controllers do not entail a discretization of the continuous-time dynamics. • The robust-counterpart multi-parametric dynamic optimization (mp-DO) problem retains the same complexity as nominal mp-DO. • Data classifiers based on deep learning can accurately describe the critical regions in (nominal or robust) mp-DO. • The methodology is demonstrated for a fluid catalytic cracking (FCC) unit and a chemical reactor cascade. Abstract This paper presents an extension of the recent multi-parametric (mp-)NCO-tracking methodology by Sun et al. [Comput. Chem. Eng. 92 (2016) 64–77] for the design of robust multi-parametric controllers for constrained continuous-time linear systems in the presence of uncertainty. We propose a robust-counterpart formulation and solution of multi-parametric dynamic optimization (mp-DO), whereby the constraints are backed-off based on a worst-case propagation of the uncertainty using either interval analysis or ellipsoidal calculus and an ancillary linear state feedback. We address the case of additive uncertainty, and we discuss approaches to dealing with multiplicative uncertainty that retain tractability of the mp-NCO-tracking design problem, subject to extra conservativeness. In order to assist with the implementation of these controllers, we also investigate the use of data classifiers based on deep learning for approximating the critical regions in continuous-time mp-DO problems, and subsequently searching for a critical region during on-line execution. We illustrate these developments with the case studies of a fluid catalytic cracking (FCC) unit and a chemical reactor cascade. [ABSTRACT FROM AUTHOR]

Highlights • The paper contributes set-membership regression (SMR), a new approach to nonlinear parameter estimation under measurement uncertainty. • Links between SMR and both guaranteed parameter estimation and classical statistical inference are investigated. • Several approaches to describing tight enclosures of the SMR regions using complete- search methods are developed. • Case studies are presented to illustrate various theoretical and computational aspects of SMR. Abstract This paper introduces set-membership nonlinear regression (SMR), a new approach to nonlinear regression under uncertainty. The problem is to determine the subregion in parameter space enclosing all (global) solutions to a nonlinear regression problem in the presence of bounded uncertainty on the observed variables. Our focus is on nonlinear algebraic models. We investigate the connections of SMR with (i) the classical statistical inference methods, and (ii) the usual set-membership estimation approach where the model predictions are constrained within bounded measurement errors. We also develop a computational framework to describe tight enclosures of the SMR regions using semi-infinite programming and complete-search methods, in the form of likelihood contour and polyhedral enclosures. The case study of a parameter estimation problem in microbial growth is presented to illustrate various theoretical and computational aspects of the SMR approach. [ABSTRACT FROM AUTHOR]

• Short-term planning of a full-scale integrated refinery-petrochemical complex under realistic scenarios. • Corresponding MIQCQP model consists of 7000 equations and 35,000 bilinear terms in the base-case scenario. • Lagrangean decomposition closes the optimality gap to below 4% in all investigated scenarios and within 1% in two scenarios. • Paves the way towards tractable global otpimization for large-scale planning problems in similar applications. We present an integrated methodology for optimal short-term planning of integrated refinery-petrochemical complexes (IRPCs) and demonstrate it on a full-scale industrial case study under four realistic planning scenarios. The large-scale mixed-integer quadratically constrained optimization models are amenable to a spatial Lagrangean decomposition through dividing the IRPC into multiple subsections, which comprise crude management, refinery, fuel blending, and petrochemical production. The decomposition algorithm creates virtual markets for trading crude blends and intermediate petrochemical streams within the IRPC and seeks an optimal tradeoff in such markets, with the Lagrange multipliers acting as transfer prices. The best results are obtained for decompositions with two or three subsections, achieving optimality gaps below 4% in all four planning scenarios. The Lagrangean decomposition provides tighter primal and dual bounds than the global solvers BARON and ANTIGONE, and it also improves the dual bounds computed using piecewise linear relaxation strategies. [ABSTRACT FROM AUTHOR]

This paper is concerned with tube-based model predictive control (MPC) for both linear and nonlinear, input-affine continuous-time dynamic systems that are affected by time-varying disturbances. We derive a min–max differential inequality describing the support function of positive robust forward invariant tubes, which can be used to construct a variety of tube-based model predictive controllers. These constructions are conservative, but computationally tractable and their complexity scales linearly with the length of the prediction horizon. In contrast to many existing tube-based MPC implementations, the proposed framework does not involve discretizing the control policy and, therefore, the conservatism of the predicted tube depends solely on the accuracy of the set parameterization. The proposed approach is then used to construct a robust MPC scheme based on tubes with ellipsoidal cross-sections. This ellipsoidal MPC scheme is based on solving an optimal control problem under linear matrix inequality constraints. We illustrate these results with the numerical case study of a spring–mass–damper system. [ABSTRACT FROM AUTHOR]

• Novel bi-objective formulation to mitigate non-informative experiments in model-based experimental design under uncertainty. • Conditional-value-at-risk is considered alongside the average information in a bi-objective optimization problem. • Discretization of experimental set combined with continuous-effort approximation yield convex optimization regardless of model structure. • Characterization of a Pareto-efficient frontier from which experimenters can choose depending on their attitude to risk. • Industrially relevant experiment design problems proven computationally tractable with the proposed methodology. A key challenge in maximizing the effectiveness of model-based design of experiments for calibrating nonlinear process models is the inaccurate prediction of information that is afforded by each new experiment. We present a novel methodology to exploit prior probability distributions of model parameter estimates in a bi-objective optimization formulation, where a conditional-value-at-risk criterion is considered alongside an average information criterion. We implement a tractable numerical approach that discretizes the experimental design space and leverages the concept of continuous-effort experimental designs in a convex optimization formulation. We demonstrate effectiveness and tractability through three case studies, including the design of dynamic experiments. In one case, the Pareto frontier comprises experimental campaigns that significantly increase the information content in the worst-case scenarios. In another case, the same campaign is proven to be optimal irrespective of the risk attitude. An open-source implementation of the methodology is made available in the Python software Pydex. [ABSTRACT FROM AUTHOR]

Integrated refinery-petrochemical facilities are complex systems that require advanced decision-support tools for optimal short-term planning of their operations. The problem can be formulated as a mixed-integer quadratically constrained quadratic program (MIQCQP), in which discrete decisions select operating modes for the process units, while the entire process network is represented by input-output relationships based on bilinear expressions describing yields and stream properties, pooling equations, fuels blending indices and cost indicators. We develop a novel decomposition-based algorithm for deterministic global optimization that divides the network into small clusters according to their functionality. Inside each cluster, we derive a mixed-integer linear programming (MILP) relaxation based on piecewise McCormick envelopes, dynamically partitioning the variables that belong to the cluster and reducing their domains through optimality-based bound tightening. Results for an industrial case study in Colombia show profit improvements above 10% and significantly reduced optimality gaps compared with the state-of-the-art global optimization solvers BARON and ANTIGONE. [ABSTRACT FROM AUTHOR]

• Modeling interdependency between production and investment decisions is critical. • Investment in anaerobic digestion for vinasse treatment is advisable. • Second-generation ethanol via hydrolysis of surplus bagasse is still uncompetitive. • Long-term electricity contracting could hedge the risks accrued from investment. The past decades have seen a diversification of the sugarcane industry with the emergence of new technology to produce bioenergy from by-product and waste process streams. Given Brazil's ambitious goal of reducing green-house gas emissions by over 40% below 2005 levels by 2030, it is of paramount importance to develop reliable decision-making systems in order to stimulate investment in these low-carbon technologies. This paper seeks to develop a more accurate optimization model to inform risk-conscious investment decisions for bioenergy generation capacity in sugarcane mills. The main objective is for the model to enable a better understanding of how Brazilian government policies, such as the electricity price in the regulated market, may impact these investments, by taking into account the uncertainty in sugar, ethanol and spot electricity markets and the interdependency between production and investment decisions in terms of saleable product mix. The proposed methodology combines portfolio optimization theory with superstructure process modeling and it relies on simple surrogates derived from a detailed sugarcane plant simulator to retain computational tractability and enable scenario analysis. The case study of an existing sugarcane plant is used to demonstrate the methodology and illustrate how the model can assist decision-makers. In all of the scenarios assessed, the model recommends investment in extra bioelectricity capacity via the anaerobic digestion of vinasse but advises against investment in second-generation ethanol production via the hydrolysis of surplus bagasse. Furthermore, the decision to upgrade the cogeneration system with a condensation turbine is highly sensitive to the electricity price practiced in the regulated market, capacity constraints on the sugar-ethanol mix, and the accepted level of risk. Another key insight drawn from the case study is that recent market conditions have favored a production focused on the sugar business, making it challenging for policy-makers to create attractive scenarios for biofuels. Long-term electricity contracting appears to be the main hedging strategy for de-risking other products and investments in the sugarcane business, provided it is priced adequately. [ABSTRACT FROM AUTHOR]