No / Optimal design and operation of MSF desalination process is considered here using MINLP technique within gPROMS model builder 2.3.4. gPROMS provides an easy and flexible platform to build a process flowsheet graphically and the corresponding master model connecting automatically individual unit model equations during simulation and optimisation. For different freshwater demand throughout the year and with seasonal variation of seawater temperature, the total annualised cost of desalination is minimised. It is found that seasonal variation in seawater temperature results in significant variation in design and some of the operating parameters but with minimum variation in of process temperatures. The results also reveal the possibility of designing stand-alone flash stages which would offer flexible scheduling in terms of the connection of various units (to build up the process) and efficient maintenance of the units throughout the year as the weather condition changes. In addition, operation at low temperatures throughout the year will reduce design and operating costs in terms of low temperature materials of construction and reduced amount of anti-scaling and anti-corrosion agents.

Cette étude concerne l’optimisation multiobjectif de réseaux d’eau industriels via des techniques de programmation mathématique. Dans ce travail, un large éventail de cas est traité afin de proposer des solutions aux problèmes de réseaux les plus variés. Ainsi, les réseaux d’eau monopolluants sont abordés grâce à une programmation mathématique linéaire (MILP). Cette méthode est ensuite utilisée dans le cadre d’une prise en compte simultanée des réseaux d’eau et de chaleur. Lorsque le réseau fait intervenir plusieurs polluants, le problème doit être programmé de façon non linéaire (MINLP). L’optimisation multicritère de chaque réseau est basée sur la stratégie epsilon-contrainte développée à partir d’une méthode lexicographique. L’optimisation multiobjectif suivie d’une réflexion d’aide à la décision a permis d’améliorer les résultats antérieurs proposés dans la littérature de 2 à 10% en termes de consommation de coût et de 7 à 15% en ce qui concerne la dépense énergétique. Cette méthodologie est étendue à l’optimisation de parcs éco-industriels et permet ainsi d’opter pour une solution écologique et économique parmi un ensemble de configurations proposées. / This study presents a multiobjective optimization of industrial water networks through mathematical programming procedures. A large range of various examples are processed to propose several feasible solutions. An industrial network is composed of fixed numbers of process units and regenerations and contaminants. These units are characterized by a priori defined values: maximal inlet and outlet contaminant concentrations. The aim is both to determine which water flows circulate between units and to allocate them while several objectives are optimized. Fresh water flow-rate (F1), regenerated water flow-rate (F2),interconnexions number (F3), energy consumption (F4) and the number of heat exchangers (F5) are all minimized. This multiobjective optimization is based upon the epsilon-constraint strategy, which is developed from a lexicographic method that leads to Pareto fronts. Monocontaminant networks are addressed with a mixed linear mathematical programming (Mixed Integer Linear Programming, MILP) model, using an original formulation based on partial water flow-rates. The obtained results we obtained are in good agreement with the literature data and lead to the validation of the method. The set of potential network solutions is provided in the form of a Pareto front. An innovative strategy based on the GEC (global equivalent cost) leads to the choice of one network among these solutions and turns out to be more efficient for choosing a good network according to a practical point of view. If the industrial network deals with several contaminants, the formulation changes from MILP into MINLP (Mixed Integer Non Linear Programming). Thanks to the same strategy used for the monocontaminant problem, the networks obtained are topologically simpler than literature data and have the advantage of not involving very low flow-rates. A MILP model is performed in order to optimize heat and water networks. Among several examples, a real case of a paper mill plant is studied. This work leads to a significant improvement of previous solutions between 2 to 10% and 7 to 15% for cost and energy consumptions respectively. The methodology is then extended to the optimization of eco-industrial parks. Several configurations are studied regarding the place of regeneration units in the symbiosis. The best network is obtained when the regeneration is owned by each industry of the park and allows again of about 13% for each company. Finally, when heat is combined to water in the network of the ecopark, a gain of 11% is obtained compared to the case where the companies are considered individually.

Durant ces 40 dernières années, le gaz naturel a vu son utilisation augmenter jusqu’à constituer aujourd’hui la troisième ressource énergétique mondiale. Il est alors devenu nécessaire de l’acheminer sur des distances de plus en plus longues entre les lieux d’extraction et de consommation. Ce transport peut s’effectuer à l’état liquide par des méthaniers ou à l’état gazeux par le biais des réseaux de transport de gaz naturel composés de canalisations de grandes dimensions, tant en diamètre qu’en longueur. Cette thèse porte sur la modélisation et l’optimisation de la configuration des réseaux de transport de gaz naturel et sur l’application au cas du réseau principal de transport français qui présente plusieurs particularités. En effet, il s’agit d’un réseau de grandes dimensions, fortement maillé pour lequel plusieurs sources d’approvisionnement sont possibles pour desservir divers points de consommation. Il possède en outre, des stations d’interconnexion entre les canalisations. GRTgaz en est le gestionnaire. Ce travail concerne l’étude de la faisabilité de configurer le réseau de transport pour un scénario d’approvisionnement et de consommation. Le coeur de cette thèse porte sur le développement d’un modèle de réseau de transport de gaz et sur la détermination des flux et des configurations des stations d’interconnexion dans ce réseau à l’aide d’outils d’optimisation. L’une des innovations est la description et la modélisation des stations d’interconnexion, carrefours incontournables du réseau. Deux modèles sont ainsi proposés, faisant intervenir une formulation d’une part mixte non linéaire en nombres entiers et d’autre part, non linéaire continue. Leur efficacité en fonction de différents solveurs d’optimisation est ensuite discutée. Le choix de la meilleure formulation du problème de transport de gaz naturel a été étudié sur un ensemble de réseaux fictifs, mais représentatifs du réseau français. La meilleure stratégie, basée sur l’utilisation combinée d’une ormulation non linéaire continue, du choix de la pression comme variable et d’une initialisation par un sous-problème a ensuite été appliquée sur des instances de taille réelle. Les difficultés du passage à des instances réelles ont ensuite été résolues à l’aide de deux améliorations: d’une part, la mise à l’échelle des variables a permis de mieux conditionner le problème, puis d’autre part, une suite de relaxations a été employée afin de résoudre tous les cas réels. Les solutions sont finalement validées à l’aide de solutions métiers existantes. / In the past 40 years, the use of natural gas has grown , so that it became the third most commonly used fuel Its use requires infrastructure for its transport over large distances between the places of extraction and consumption. This transport can be carried out by liquid methane or a gaseous state through networks of natural gas transmission pipelines that are large in both diameter and length. This thesis focuses on the optimization of natural gas transmission networks and the application to the case of the main french transmission one which presents several peculiarities. Indeed, it is a highly meshed network in which multiple sources of supply are available to feed various points of consumption. This network also owns stations of interconnection between pipelines. In this context, GRTgazis the system operator on the French territory. This work concerns the study of the feasibility of scenarios for supply and consumption. The core of this thesis is the development of a model of a gas transmission network and the determination of ows using optimization tools. One innovative aspect deals with the description and modeling of interconnection stations, that are the main hubs of the network. Two models are proposed, either based on a mixed integer non-linear formulation or on nonlinear continuous one. Their eciencyunder dierent optimization solvers are discussed. The choice of the best formulation of the problem of transportation of natural gas has been studied on a set of network ctitious, but enough representative of the french network. The best strategy, based on a continuous non-linear formulation, involving the choice of pressure as a variable as well as a sub-problem for initialization purpose was then applied to instances of actual size. The diculties of the transition to real cases were then solved using two improvements: rst, variable scale which provided a better condition the problem, then a series of relaxation have been used to solve all real cases. The solutions are nally validated using existing business applications.

L'amélioration des systèmes énergétiques est considérée comme un levier technologique pour répondre aux défis liés à la croissance de la demande d’électricité et des émissions des gaz à effet de serre. Les futures centrales devraient présenter une intégration thermique plus flexible et des sources de chaleur mixtes possibles. Une des solutions fiables consiste à utiliser un cycle de Brayton au CO2 supercritique (CO2-SC), un tel cycle à haut rendement est théoriquement prometteur pour les applications nucléaires, fossiles et solaires thermiques. Un des principaux obstacles au déploiement du cycle de Brayton au CO2-SC est de justifier sa faisabilité, sa viabilité et son potentiel à l’échelle industrielle. Dans ce contexte deux axes de recherche ont été identifiées : • Une sélection rigoureuse de l’équation d’état qui permet de représenter les propriétés d’intérêt du CO2-SC. • Une nouvelle méthodologie pour l’optimisation des centrales électriques, permettant de sélectionner automatiquement le procédé optimal parmi une grande quantité de configurations possibles (dénomme superstructure). Les résultats de la première partie de cette thèse mettent en lumière que l’équation de SW est pertinente pour limiter l’impact de l’imprécision de l’équation d’état sur le dimensionnement du procédé. Dans cette thèse, un simulateur de procédé commercial, ProSimPlus a été combiné avec un solveur type évolutionnaire (MIDACO) afin d’effectuer des optimisations superstructure. Premièrement, le critère d’optimisation est de maximiser le rendement énergétique du procédé. Dans un deuxième temps, on cherche simultanément à minimiser les coûts du procédé. Pour ce faire, des fonctions de coût internes à EDF ont été utilisées afin de permettre l’estimation des coûts d'investissement (CAPEX), des dépenses opérationnelles (OPEX) et du coût actualisé de l'électricité (LCOE) / Efficiency enhancement in power plant can be seen as a key lever in front of increasing energy demand. Nowadays, both the attention and the emphasis are directed to reliable alternatives, i.e., enhancing the energy conversion systems. The supercritical CO2 (SC-CO2) Brayton cycle has recently emerged as a promising solution for high efficiency power production in nuclear, fossil-thermal and solar-thermal applications. Currently, studies on such a thermodynamic power cycle are directed towards the demonstration of its reliability and viability before the possible building of an industrial-scale unit. The objectives of this PhD can be divided in two main parts: • A rigorous selection procedure of an equation of state (EoS) for SC-CO2 which permits to assess influences of thermodynamic model on the performance and design of a SC-CO2 Brayton cycle. • A framework of optimization-based synthesis of energy systems which enables optimizing both system structure and the process parameters. The performed investigations demonstrate that the Span-Wagner EoS is recommended for evaluating the performances of a SC-CO2 Brayton cycle in order to avoid inaccurate predictions in terms of equipment sizing and optimization. By combining a commercial process simulator and an evolutionary algorithm (MIDACO), this dissertation has identified a global feasible optimum design –or at least competitive solutions– for a given process superstructure under different industrial constraints. The carried out optimization firstly base on cycle energy aspects, but the decision making for practical systems necessitates techno-economic optimizations. The establishment of associated techno-economic cost functions in the last part of this dissertation enables to assess the levelized cost of electricity (LCOE). The carried out multi-objective optimization reflects the trade-off between economic and energy criteria, but also reveal the potential of this technology in economic performance.

Due to legal, economic and socio-environmental factors, reverse logistics practices and extended producer responsibility have developed into a necessity in many countries. The end results and expectations may differ, but the motivation remains the same. Two significant components in a reverse logistics system -product recovery options and return channels - are the focus of this thesis. The two main issues examined are allocation of the returned products to recovery options, and selection of the collection methods for product returns. The initial segment of this thesis involves the formulation of a linear programming model to determine the optimal allocation of returned products differing in quality to specific recovery options. This model paves the way for a study on the effects of flexibility on product recovery allocation. A computational example utilising experimental data was presented to demonstrate the viability of the proposed model. The results revealed that in comparison to a fixed match between product qualities and recovery options, the product recovery operation appeared to be more profitable with a flexible allocation. The second segment of this thesis addresses the methods employed for the initial collection of returned products. A mixed integer nonlinear programming model was developed to facilitate the selection of optimal collection methods for these products. This integrated model takes three different initial collection methods into consideration. The model is used to solve an illustrative example optimally. However, as the complexity of the issue renders this process ineffective in the face of larger problems, the Lagrangian relaxation method was proposed to generate feasible solutions within reasonable computational times. This method was put to the test and the results were found to be encouraging.

The fast growing waste stream of electronic and other complex consumer products is making the bulk recycling problem an important environmental protection issue. These products must be recycled because they contain hazardous materials such as lead and mercury. The focus of this thesis is the development of systematic methods for designing systems to recover mixed plastics from electronic products such as computers and televisions. Bulk recycling systems are similar to other chemical engineering process systems. Therefore they can be synthesized and designed using some existing techniques that have been applied to distillation and reaction systems. However, the existence of various uncertainties from different sources, such as the variation of component fractions and product prices, makes it crucial to design a flexible and sustainable system, and is also a major challenge in this research. Another challenge is that plastics can be separated by different mechanisms based on different properties, but separating a mix of plastics often requires using a combination of different methods because they can have overlapping differentiating properties. Therefore many decisions are to be made including which methods to choose and how to connect them. To address the problem systematically, the design under uncertainty problem was formulated as a stochastic Mixed Integer Nonlinear Program (sMINLP). A Sample Average Approximation (SAA) method wrapped on the Outer Approximation method has been developed in this thesis to solve such problems efficiently. Therefore, large design under uncertainty problems can be solved without intractable computational difficulty. To allow making choices from separation methods by different mechanisms, this research modeled various plastics separation methods taking account of the distribution of particle properties and unified them using a canonical partition curve representation. Finally, an overall design method was proposed in this work to incorporate the design of size reduction units into the separation system. This research is the first formal development of a systematic method in this area to account for uncertainties and interactions between process steps.

This thesis considers three separate but connected problems regarding energy networks: the load flow problem, the optimal power flow problem, and the islanding problem. All three problems are non-convex non linear problems, and so have the potential of returning local solutions. The goal of this thesis is to find solution methods to each of these problems that will minimize the chances of returning a local solution. The thesis first considers the load ow problem and looks into a novel approach to solving load flows, the Holomorphic Embedding Load Flow Method (HELM). The current literature does not provide any HELM models that can accurately handle general power networks containing PV and PQ buses of realistic sizes. This thesis expands upon previous work to present models of HELM capable of solving general networks efficiently, with computational results for the standard IEEE test cases provided for comparison. The thesis next considers the optimal power flow problem, and creates a framework for a load flow-based OPF solver. The OPF solver is designed with incorporating HELM as the load flow solver in mind, and is tested on IEEE test cases to compare it with other available OPF solvers. The OPF solvers are also tested with modified test cases known to have local solutions to show how a LF-OPF solver using HELM is more likely to find the global optimal solution than the other available OPF solvers. The thesis finally investigates solving a full AC-islanding problem, which can be considered as an extension of the transmission switching problem, using a standard MINLP solver and comparing the results to solutions obtained from approximations to the AC problem. Analysing in detail the results of the AC-islanding problem, alterations are made to the standard MINLP solver to allow better results to be obtained, all the while considering the trade-off between results and elapsed time.

With increasing global energy consumption, stringent environmental protection legislation and safety regulations in industrialised nations, energy saving has been put under high priority. One of the most efficient ways of energy reduction is through heat transfer enhancement for additional heat recovery. Applying compact heat exchanger is one of the main strategies of heat transfer enhancement. However, the application of compact heat exchangers is prohibited by the lack of design methodology. Therefore, the aim of this research is to tackle the problem of developing optimisation methodologies of plate/plate-fin heat exchanger design. A mathematical model of plate-fin heat exchanger design is proposed to consider fin type selection with detailed geometry and imposed constraints simultaneously. The concept of mix-and-match fin type combinations is put forward to include all possible fin type combinations in a heat exchanger. The mixed integer nonlinear programming (MINLP) model can be converted to a nonlinear programming (NLP) model by employing continuous heat transfer and pressure drop correlations and considering the basic fin geometric parameters as continuous variables. The whole optimisation is based on volumetric minimisation or capital cost minimisation and completed by CONOPT solver in GAMS. Case studies are carried out to demonstrate the effectiveness and benefits of the new proposed methodology. For plate heat exchangers, the design methodology is developed on the basis of plate-fin heat exchanger methodology, and takes phase change, plate pattern selection, flow arrangement and pressure drop constraints simultaneously. The phase change problem is tackled by dividing the whole process into several subsections and considering constant physical properties in each subsection. The performances of various flow arrangements are evaluated by correction factors of logarithmic mean temperature difference. For two-phase conditions, the heat transfer and pressure drop performance are predicted by continuous two-phase Nusselt number and Fanning friction factor correlations to avoid the MINLP problem. The optimisation is solved by CONOPT solver as well. The feasibility and accuracy of the new proposed methodology is examined by case studies.

<div>Designing configurations for multicomponent distillation, a ubiquitous process in chemical and petrochemical industries, is often challenging. This is because, as the number of components increases, the number of admissible distillation configurations grows rapidly and these configurations vary substantially in their energy needs. Consequently, if a method could identify a few energy-efficient choices from this large set of alternatives, it would be extremely attractive to process designers. Towards this, we develop the first mixed-integer nonlinear programming (MINLP) based solution approach that successfully identifies the most energy-efficient distillation configuration for a given separation. Current sequence design strategies are largely heuristic. The rigorous approach presented here can help reduce the significant energy consumption and consequent greenhouse gas emissions by separation processes. </div><div> </div><div>In addition to the combinatorial complexity, the challenge in solving this problem arises from the nonconvex fractional terms contained in the governing equations. We make several advances to enable solution of these problems.</div><div><br></div><div>(1). We propose a novel search space formulation by embedding convex hulls of various important substructures. We prove that the resulting formulation dominates all the prior formulations in the literature.</div><div><br></div><div>(2). We derive valid cuts to the problem by exploiting the monotonic nature of the governing equations. </div><div><br></div><div>(3). We adapt the classical Reformulation-Linearization Technique (RLT) for fractional terms. Our RLT variant exploits the underlying mathematical structure of the governing equation, and yields a provably tighter convex relaxation.</div><div><br></div><div>(4). We construct the simultaneous hull of multiple nonlinear terms that are constrained over a polytope obtained by intersecting a hypercube with mass balance constraints. This yields a tighter convex relaxation than the conventional approach where the nonlinear terms are convexified individually over a box.</div><div><br></div><div>(5). A key challenge in constructing a valid convex relaxation has been that the denominator of certain fractions in the governing equation can approach arbitrarily close to zero. Using our RLT variant, we construct the first valid relaxation. </div><div><br></div><div>(6). We leverage powerful mixed-integer programming (MIP) solvers by implementing a discretization-based solution procedure with an adaptive partitioning scheme.</div><div><br></div><div>With extensive computational experiments, we demonstrate that the proposed approach outperforms the state-of-the-art in the literature. The formulation can be tailored to other objectives by appending the relevant constraints. Here, we present an extension that identifies the distillation configuration that has the highest thermodynamic efficiency. Finally, we illustrate the practicality of the developed approaches with case studies on crude fractionation and natural gas liquid recovery. </div>

Shale gas has emerged as a potential resource to transform the global energy market. Nevertheless, gas extraction from tight shale formations is only possible after horizontal drilling and hydraulic fracturing, which generally demand large amounts of water. Part of the ejected fracturing fluid returns to the surface as flowback water, containing a variety of pollutants. Thus, water reuse and water recycling technologies have received further interest for enhancing overall shale gas process efficiency and sustainability. Thereby, the objectives of this thesis are: - Develop mathematical models to treat flowback and produced water at various salinities and flow rates, decreasing the high environmental impact due to the freshwater withdrawal and wastewater generated during shale gas production at minimum cost. - Develop mathematical programming models for planning shale gas water management through the first stage of the well's life to promote the reuse of flowback water by optimizing simultaneously all operations belonging several wellpads. Within the first objective, we developed medium size generalized disjunctive-programming (GDP) models reformulated as mixed integer non-linear programming problems (MINLPs). First, we focused on flowback water pretreatment and later, in wastewater desalination treatment. Particularly, an emergent desalination technology, Membrane Distillation, has been studied. All mathematical models have been implemented using GAMS® software. First, we introduce a new optimization model for wastewater from shale gas production including a superstructure with several water pretreatment alternatives. The mathematical model is formulated via GDP to minimize the total annualized cost. Hence, the superstructure developed allows identifying the optimal pretreatment sequence with minimum cost, according to inlet water composition and wastewater desired destination (i.e., water reuse as fracking fluid or desalination in thermal or membrane techonologies). As each destination requires specific composition constraints, three case studies illustrate the applicability of the proposed approach. Additionally, four distinct flowback water compositions are evaluated for the different target conditions. The results highlight the ability of the developed model for the cost-effective water pretreatment system synthesis, by reaching the required water compositions for each specified destination. Regarding desalination technologies, a rigorous optimization model with energy recovery for the synthesis of multistage direct contact membrane distillation (DCMD) system has been developed. The mathematical model is focused on maximizing the total amount of water recovered. The outflow brine is fixed close to salt saturation conditions (300 g·kg-1) approaching zero liquid discharge (ZLD). A sensitivity analysis is performed to evaluate the system’s behavior under different uncertainty sources such as the heat source availability and inlet salinity conditions. The results emphasize the applicability of this promising technology, especially with low steam cost or waste heat, and reveal variable costs and system configurations depending on inlet conditions. Within the second objective, large-scale multi-period water management problems, and collaborative water management models have been studied. Thus, to address water planning decisions in shale gas operations, in a first stage a new non-convex MINLP optimization model is presented that explicitly takes into account the effect of high concentration of total dissolved solids (TDS) and its temporal variations in the impaired water. The model comprises different water management strategies: direct reuse, treatment or send to Class II disposal wells. The objective is to maximize the “sustainability profit” to find a compromise solution among the three pillars of sustainability: economic, environmental and social criteria. The solution determines freshwater consumption, flowback destination, the fracturing schedule, fracturing fluid composition and the number of tanks leased at each time period. Because of the rigorous determination of TDS in all water streams, the model is a nonconvex MINLP model that is tackled in two steps: first, an MILP model is solved on the basis of McCormick relaxations for the bilinear terms; next, the binary variables that determine the fracturing schedule are fixed, and a smaller MINLP is solved. Finally, several case studies based on Marcellus Shale Play are optimized to illustrate the effectiveness of the proposed formulation. Later, a simplified version of the shale gas water management model developed in the previous work has been used to study possible cooperative strategies among companies. This model allows increasing benefits and reduces costs and environmental impacts of water management in shale gas production. If different companies are working in the same shale zone and their shale pads are relatively close (under 50 km), they might adopt a cooperative strategy, which can offer economic and environmental advantages. The objective is to compute a distribution of whatever quantifiable unit among the stakeholders to achieve a stable agreement on cooperation among them. To allocate the cost, profit and/or environmental impact among stakeholders, the Core and Shapley value are applied. Finally, the impact of cooperation among companies is shown by two examples involving three and eight players, respectively. The results show that adopting cooperative strategies in shale water management, companies are allowed to improve their benefits and to enhance the sustainability of their operations. The results obtained in this thesis should help to make cost-effective and environmentally-friendly water management decisions in the eventual development of shale gas wells.