This thesis explores different paradigms for incorporating uncertainty with optimization frameworks for applications in chemical engineering and site-wide operations. First, we address the simulation optimization problem, which deals with the search for optimal input parameters to black-box stochastic simulations which are potentially expensive to evaluate. We include a comprehensive literature survey of the state-of-the-art in the area, propose a new provably convergent trust region-based algorithm, and discuss implementation details along with extensive computational experience, including examples for chemical engineering applications. Next, we look at the problem of long-term site-wide maintenance turnaround planning. Turnarounds involve the disruption of production for significant periods of time, and may incur enormous costs in terms of maintenance manpower as well as lost sales. The problem involves (1) the simulation of profit deterioration due to wear and tear followed by the determination of how frequently a particular turnaround should take place; and (2) the consideration of site network structure and turnaround frequencies to determine how turnarounds of different plants may be coordinated over a long-term horizon. We investigate two mixed-integer models, the first of which determines optimal frequencies of individual plant turnarounds, while the second considers maximizing long-term profit through coordination of turnarounds across the site. We then turn to more conventional methods of dealing with optimization under uncertainty, and make use of a combined robust optimization and stochastic programming approach to medium-term maintenance planning in integrated chemical sites. The nature of the uncertainty considered affects two aspects of maintenance planning, one of which is most suitably addressed through a robust optimization framework, while the other is better handled with stochastic programming models. In summary, we highlight the importance of considering uncertainty in optimization as well as the choice of approach or paradigm used through chemical engineering applications that span varied domains and time scales.

Sustainable approaches have been extensively proposed in product, process and system levels. However, a lack of applicable solutions for these methods is identified in the existing research. This research considers uncertainties affecting sustainable systems and comprehensively discusses the need for the optimal design in product and system levels under uncertainty. Based on the economic, social and environmental requirements of a sustainable product, and uncertainties in engineering systems, two innovative methods are proposed. The methods, including agent-based modeling (ABM) and Big Data, quantify effects of users’ preference changes as a significant uncertainty source in a product design process. The effect of quantified uncertainties on the product sustainability is then evaluated, and solutions to reduce the effects are developed. Through a novel control engineering method, uncertainties are modeled in the design process of a product. Using two mathematical models, the cost and environmental impacts in the design process are minimized under users’ preference changes. The models search for an optimal number of iterations in the design process to achieve a sustainable solution. The methods have been extended to model and optimize the sustainable system design under uncertainties. Design of Eco-Industrial Parks (EIPs) is a practical and scientific solution to achieve sustainable industries. To improve the feasibility of flow exchanges between industries in an EIP under several uncertainties, this research provides a perspective analysis for establishing flow exchanges between industries. The sources of uncertainties in the EIPs are then comprehensively studied, and research gaps are highlighted. Finally, models to optimize flow exchanges between industries are presented and the validity of models is evaluated using real data. A major is including all sustainability pillars in the proposed approach. The research addresses users’ preferences to highlight the role of individuals in the society. Moreover, the economic and environmental objective functions have been considered for optimal decision making in the design process. This research underlines the role of uncertainty studies in the sustainable system design. Multiple classifications, perspective analysis, and optimization objectives are presented to help decision makers with the optimal design of sustainable systems under uncertainties. / February 2017

A partnership between oilfield operators and the federal government in the coupled CO₂ enhanced oil recovery (EOR) and storage projects brings long-term benefits for both. We quantify the win-win condition for this partnership in terms of an optimum storage tax credit. We describe the field-scale design optimization of coupled CO₂-EOR and storage operations from the viewpoint of oilfield operators. We introduce a CO₂ market model and investigate two special CO₂ market problems, namely a fixed storage requirement and an integrated asset optimization. The first problem follows an environmental objective by giving priority to the storage element of CO₂-EOR and storage; the second prioritizes the oil recovery and relies on the principles of a free market where CO₂ is a commodity and the commitment to storage is made based on the economic benefits. We investigate the CO₂ market sustainability conditions and quantitatively derive them for the fixed storage requirement and integrated asset optimization problems. Ultimately, we quantify the impact of storage tax credit on the operator benefits, the federal government benefits, and the optimum economic storage capacity of an oilfield. CO₂ EOR-storage projects are long-term and capital-intensive and therefore vulnerable to the risks of the CO₂ market. Two important uncertain economic parameters are investigated, the oil price and the storage tax credit. The government plays an important role in reducing the CO₂ market risks because it has the leverage to regulate the storage tax credit. The stochastic optimization results show that a transparent storage tax credit reinforces the sustainability of the CO₂ market and helps both the government and the oilfield operators boost their long-term benefits. / text

One key outcome of this research is the design for a 3-D tractor-trailer base-drag reduction device that predicts a 41% reduction in wind-averaged drag coefficient at 57 mph (92 km/h) and that is relatively insensitive to uncertain wind speed and direction and uncertain deflection angles due to mounting accuracy and static aeroelastic loading; the best commercial device of non-optimized design achieves a 12% reduction at 65 mph. Another important outcome is the process by which the optimized design is obtained. That process includes verification and validation of the flow solver, a less complex but much broader 2-D pathfinder study, and the culminating 3-D aerodynamic shape optimization under uncertainty (OUU) study. To gain confidence in the accuracy and precision of a computational fluid dynamics (CFD) flow solver and its Reynolds-averaged Navier-Stokes (RANS) turbulence models, it is necessary to conduct code verification, solution verification, and model validation. These activities are accomplished using two commercial CFD solvers, Cobalt and RavenCFD, with four turbulence models: Spalart-Allmaras (S-A), S-A with rotation and curvature, Menter shear-stress transport (SST), and Wilcox 1998 k-ω. Model performance is evaluated for three low subsonic 2-D applications: turbulent flat plate, planar jet, and NACA 0012 airfoil at α = 0°. The S-A turbulence model is selected for the 2-D OUU study. In the 2-D study, a tractor-trailer base flap model is developed that includes six design variables with generous constraints; 400 design candidates are evaluated. The design optimization loop includes the effect of uncertain wind speed and direction, and post processing addresses several other uncertain effects on drag prediction. The study compares the efficiency and accuracy of two optimization algorithms, evolutionary algorithm (EA) and dividing rectangles (DIRECT), twelve surrogate models, six sampling methods, and surrogate-based global optimization (SBGO) methods. The DAKOTA optimization and uncertainty quantification framework is used to interface the RANS flow solver, grid generator, and optimization algorithm. The EA is determined to be more efficient in obtaining a design with significantly reduced drag (as opposed to more efficient in finding the true drag minimum), and total predictive uncertainty is estimated as ±11%. While the SBGO methods are more efficient than a traditional optimization algorithm, they are computationally inefficient due to their serial nature, as implemented in DAKOTA. Because the S-A model does well in 2-D but not in 3-D under these conditions, the SST turbulence model is selected for the 3-D OUU study that includes five design variables and evaluates a total of 130 design candidates. Again using the EA, the study propagates aleatory (wind speed and direction) and epistemic (perturbations in flap deflection angle) uncertainty within the optimization loop and post processes several other uncertain effects. For the best 3-D design, total predictive uncertainty is +15/-42%, due largely to using a relatively coarse (six million cell) grid. That is, the best design drag coefficient estimate is within 15 and 42% of the true value; however, its improvement relative to the no-flaps baseline is accurate within 3-9% uncertainty. / Ph. D.

Phenomenological material models such as Johnson-Cook plasticity are often used in finite element simulations of large deformation processes at different strain rates and temperatures. Since the material constants that appear in such models depend on the material, experimental data, fitting method, as well as the mathematical representation of strain rate and temperature effects, the predicted material behavior is subject to uncertainty. In this dissertation, evidence theory is used for modeling uncertainty in the material constants, which is represented by separate belief structures that are combined into a joint belief structure and propagated using impact loading simulation of structures. Yager’s rule is used for combining evidence obtained from more than one source. Uncertainty is quantified using belief, plausibility, and plausibility-decision functions. An evidence-based design optimization (EBDO) approach is presented where the nondeterministic response functions are expressed using evidential reasoning. The EBDO approach accommodates field material uncertainty in addition to the embedded uncertainty in the material constants. This approach is applied to EBDO of an externally stiffened circular tube under axial impact load with and without consideration of material field uncertainty caused by spatial variation of material uncertainties due to manufacturing effects. Surrogate models are developed for approximation of structural response functions and uncertainty propagation. The EBDO example problem is solved using genetic algorithms. The uncertainty modeling and EBDO results are presented and discussed.

[pt] A indústria do petróleo é uma das mais importantes e dinâmicas do Brasil. Em uma indústria naturalmente integrada como a petrolífera, é necessário um adequado planejamento estratégico da cadeia integrada de petróleo que contemple todos os seus processos, como a produção de petróleo, refino, distribuição e comercialização de derivados. Além disso, a indústria de petróleo está suscetível a diversas incertezas relacionadas a preço de petróleo e derivados, oferta de óleo bruto e demanda de produtos. Em face destas oportunidades e desafios, foi desenvolvido no âmbito desta dissertação um modelo de programação estocástica para o planejamento estratégico da cadeia de petróleo brasileira. O modelo contempla as refinarias e suas unidades de processos, as propriedades dos petróleos e derivados, a logística nacional e decisões de comercialização de petróleo e derivados, incluindo incertezas associadas a preço de mercado, produção de petróleo nacional e demanda interna de derivados. A partir do modelo estocástico foram formulados um modelo robusto e um modelo MinMax no intuito de comparar o desempenho e a qualidade da solução estocástica. Os modelos propostos foram aplicados a um exemplo real, com 17 refinarias e 3 centrais petroquímicas que processam 50 produtos intermediários, destinados a produção de 10 derivados associados à demanda nacional, 8 campos de exploração de petróleo, 14 produtores gás natural, 1 produtor de óleo vegetal, 13 terminais, 4 bases de distribuição e 278 arcos de transporte. Na análise de resultados foram utilizadas medidas como Valor Esperado da Informação Perfeita (EVPI) e Valor da Solução Estocástica (VSS). / [en] The oil industry is one of the most important and dynamic in Brazil. As the oil industry naturally integrated, we need an appropriate strategic planning to the oil supply chain that consider all its processes, such as oil production, refining, distribution and refined products marketing. Moreover, the oil industry is susceptible to various uncertainties regarding the oil and products price, crude oil supply and products demand. In light of these opportunities and challenges, it was developed in this dissertation a stochastic programming model for the strategic planning of the Brazilian oil supply chain. The model includes refineries and process units, oils and their products properties, logistics and national marketing decisions of oil and products, including uncertainties associated with market price, oil domestic production and refined products domestic demand. Based on the stochastic model a robust model and a MinMax model were formulated in order to compare the performance and quality of the stochastic solution. The proposed models were applied to a real example, with 17 refineries and 3 petrochemical power plants that process 50 intermediate products, intended to production of 10 final products associated to national demand, 8 oil fields, 14 natural gas producers, 1 vegetal oil producer, 13 terminals, 4 delivery points and 278 arches of transport. In the results analysis was used as measures the Expected Value of Perfect Information (EVPI) and the Value of the Stochastic Solution (VSS).

In view of the current situation of fluctuating high crude oil prices, it is now more important than ever for petroleum refineries to operate at an optimal level in the present dynamic global economy. Acknowledging the shortcomings of deterministic models, this work proposes a hybrid of stochastic programming formulations for an optimal midterm refinery planning that addresses three factors of uncertainties, namely price of crude oil and saleable products, product demand, and production yields. An explicit stochastic programming technique is utilized by employing compensating slack variables to account for violations of constraints in order to increase model tractability. Four approaches are considered to ensure both solution and model robustness: (1) the Markowitz???s mean???variance (MV) model to handle randomness in the objective coefficients of prices by minimizing variance of the expected value of the random coefficients; (2) the two-stage stochastic programming with fixed recourse approach via scenario analysis to model randomness in the right-hand side and left-hand side coefficients by minimizing the expected recourse penalty costs due to constraints??? violations; (3) incorporation of the MV model within the framework developed in Approach 2 to minimize both the expectation and variance of the recourse costs; and (4) reformulation of the model in Approach 3 by adopting mean-absolute deviation (MAD) as the risk metric imposed by the recourse costs for a novel application to the petroleum refining industry. A representative numerical example is illustrated with the resulting outcome of higher net profits and increased robustness in solutions proposed by the stochastic models.

The control and optimization of chemical plants is a major area of research as it has the potential to improve both economic output and plant safety. It is often prudent to separate control and optimization tasks of varying complexities and time scales, creating a hierarchical control structure. Within this structure, it is beneficial for one control layer to be able to account for the effects of other layers. A clear example of this, and the basis of this work, is closed-loop dynamic real-time optimization (CL-DRTO), in which an economic optimization method considers both the plant behavior and the effects of an underlying model predictive controller (MPC). This technique can be expanded on to allow its use and methods to be employed in a greater diversity of applications, particularly unstable and uncertain plant environments. First, this work seeks to improve on existing robust MPC techniques, which incorporate plant uncertainty via direct multi-scenario modelling, by also including future MPC behavior through the use of the CL modelling technique of CL-DRTO. This allows the CL robust MPC to account for how future MPC executions will be affected by uncertain plant behavior. Second, Lyapunov MPC (LMPC) is a generally nonconvex technique which focuses on effective control of plants which exhibit open-loop unstable behavior. A new convex LMPC formulation is presented here which can be readily embedded into a CL-DRTO scheme. Next, uncertainty handling is incorporated directly into a CL-DRTO via a robust multi-scenario method to allow for the economic optimization to take uncertain plant behavior into account while also modelling MPC behavior under plant uncertainty. Finally, the robust CL-DRTO method is computationally expensive, so a decomposition method which separates the robust CL-DRTO into its respective scenario subproblems is developed to improve computation time, especially for large optimization problems. / Thesis / Doctor of Philosophy (PhD) / It is common for control and optimization of chemical plants to be performed in a multi-layered hierarchy. The ability to predict the behavior of other layers or the future behavior of the same layer can improve overall plant performance. This thesis presents optimization and control frameworks which use this concept to more effectively control and economically optimize chemical plants which are subject to uncertain behavior or instability. The strategy is shown, in a series of simulated case studies, to effectively control chemical plants with uncertain behavior, control and optimize unstable plant systems, and economically optimize uncertain chemical plants. One of the drawbacks of these strategies is the relatively large computation time required to solve the optimization problems. Therefore, for uncertain systems, the problem is separated into smaller pieces which are then coordinated towards a single solution. This results in reduced computation time.

[pt] O presente trabalho tem como foco o estudo do Sistema Petrobras, no que tange o planejamento estratégico dos investimentos da Companhia, sob a ótica da cadeia integrada do petróleo. A partir de um dos modelos matemáticos mais utilizados (e há mais tempo) na empresa, diversas decisões estratégicas de suma importância são suportadas, de modo a maximizar seu resultado operacional ao longo de um horizonte de tempo da ordem de 10 (dez) anos. Com embasamento na literatura atual, evoluções são propostas e testadas no modelo matemático. Primeiramente são introduzidas técnicas de programação estocástica em dois estágios, onde as decisões de investimento são representadas por variáveis de primeiro estágio; e a operação de todo o sistema – desde o refino até a comercialização do petróleo e derivados, passando por toda a questão logística – passa a fazer parte do segundo estágio, após a realização / revelação dos parâmetros estocásticos. Em um segundo passo, técnicas de decomposição são aplicadas para contornar eventuais limitações geradas pelo grande porte atingido pelo modelo, que cresce proporcionalmente ao número de cenários envolvidos na otimização. Os resultados mostram que o modelo estocástico começa a esbarrar nestas limitações a partir da resolução de problemas com mais de 30 cenários. Por outro lado, apesar do tempo computacional consideravelmente maior, o modelo decomposto chegou a resolver até 80 cenários, nos testes realizados. / [en] This work focuses on the study of Petrobras, regarding the strategic planning of the Company s investments, from an integrated oil supply chain perspective. From one of the most widely used mathematical models in the Company, several strategic decisions of great importance are supported, so as to maximize its operating result over a time horizon of approximately 10 (ten) years. Based in current literature, developments are proposed and tested in the mathematical model. First, two-stage stochastic programming techniques are introduced, where investment decisions are represented by first-stage variables; and system s operation – from oil refining and sales to the entire logistics issue – by second-stage variables, after realization of the stochastic parameters. In a second step, decomposition techniques are applied to circumvent any large scale limitations. The results show that the stochastic model starts to reach these limitations in problems with 30 scenarios or more. On the other hand, despite the considerably greater computational time, the decomposed model was able to solve up to 80-scenarios problems, during the tests.

In view of the current situation of fluctuating high crude oil prices, it is now more important than ever for petroleum refineries to operate at an optimal level in the present dynamic global economy. Acknowledging the shortcomings of deterministic models, this work proposes a hybrid of stochastic programming formulations for an optimal midterm refinery planning that addresses three factors of uncertainties, namely price of crude oil and saleable products, product demand, and production yields. An explicit stochastic programming technique is utilized by employing compensating slack variables to account for violations of constraints in order to increase model tractability. Four approaches are considered to ensure both solution and model robustness: (1) the Markowitz’s mean–variance (MV) model to handle randomness in the objective coefficients of prices by minimizing variance of the expected value of the random coefficients; (2) the two-stage stochastic programming with fixed recourse approach via scenario analysis to model randomness in the right-hand side and left-hand side coefficients by minimizing the expected recourse penalty costs due to constraints’ violations; (3) incorporation of the MV model within the framework developed in Approach 2 to minimize both the expectation and variance of the recourse costs; and (4) reformulation of the model in Approach 3 by adopting mean-absolute deviation (MAD) as the risk metric imposed by the recourse costs for a novel application to the petroleum refining industry. A representative numerical example is illustrated with the resulting outcome of higher net profits and increased robustness in solutions proposed by the stochastic models.