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A game theoretic framework for strategic refinery production planning is presented in which strategic planning problems are formulated as non-cooperative potential games whose solutions represent Nash equilibria. The potential game model takes the form of a nonconvex nonlinear program (NLP) or nonconvex mixed integer nonlinear program (MINLP). Tactical planning decisions are linked to strategic decision processes through a potential game structure derived from a Cournot oligopoly-form game in which multiple crude oil refineries supply several markets. The resulting production planning decisions are rational in a game theoretic sense and are robust to deviations in competitor strategies. These solutions are interpreted as mutual best responses yielding maximum profit in the competitive planning game. Case studies are presented which illustrate the utility of the game theoretic framework in the analysis of production planning problems in competitive scenarios, including competitor removal and capacity expansion. Natural Sciences and Engineering Research Council of Canada; Government of Ontario; McMaster Advanced Control Consortium

Industrial automation systems normally consist of four different hierarchy levels: planning, scheduling, real-time optimization, and control. At the planning level, the goal is to compute an optimal production plan that minimizes the production cost while meeting process constraints. The planning model is typically formulated as a mixed integer nonlinear programming (MINLP), which is hard to solve to global optimality due to nonconvexity and large dimensionality attributes. Uncertainty in component qualities in gasoline blending due to measurement errors and variation in upstream processes may lead to off-specification products which require re-blending. Uncertainty in product demands may lead to a suboptimal solution and fail in capturing some potential profit due to shortage in products supply. While incorporating process uncertainties is essential to reducing the production cost and increasing profitability, it comes with the disadvantage of increasing the complexity of the MINLP planning model. The key contribution in the planning level is to employ the inventory pinch decomposition method to consider uncertainty in components qualities and products demands to reduce the production cost and increase profitability of the gasoline blend application. At the control level, the goal is to ensure desired operation conditions by meeting process setpoints, ensure process safety, and avoid process failures. Model predictive control (MPC) is an advanced control strategy that utilizes a dynamic model of the process to predict future process dynamic behavior over a time horizon. The effectiveness of the MPC relies heavily on the availability of a reasonably accurate process model. The key contributions in the control level are: (1) investigate the use of different system identification methods for the purpose of developing a dynamic model for high-purity distillation column, which is a highly nonlinear process. (2) Develop a novel hybrid based MPC to improve the control of the column and achieve flooding-free control. Dissertation Doctor of Philosophy (PhD) The operation of a chemical process involves many decisions which are normally distributed into levels referred to as process automation hierarchy. The process automation hierarchy levels are planning, scheduling, real-time optimization, and control. This thesis addresses two of the levels in the process automation hierarchy, which are planning and control. At the planning level, the objective is to ensure optimal utilization of raw materials and equipment to reduce production cost. At the control level, the objective is to meet and follow process setpoints determined by the real-time optimization level. The main goals of the thesis are: (1) develop an efficient algorithm to solve a large-scale planning problem that incorporates uncertainties in components qualities and products demands to reduce the production cost and maximize profit for gasoline blending application. (2) Develop a novel hybrid-based model predictive control to improve the control strategy of an industrial distillation column that faces flooding issues.

Energy demand for buildings has been rising during recent years. Increasing building energy consumption has caused many energy-related problems and environmental issues. The on-site community energy system application is a promising way of providing energy for buildings. Community energy system usage reduces the primary energy consumption and environmental effects of greenhouse gas (GHG) emissions compared to the implementation of the stand-alone energy systems. Furthermore, due to the increase in electricity price and shortage of fossil fuel resources, renewable energies and energy storage technologies could be great alternative solutions to solve energy-related problems. Generally, the energy system might include various technologies such as internal combustion engine, heat recovery system, boiler, thermal storage tank, battery, absorption chiller, ground source heat pump, heating coil, electric chiller, solar photovoltaics (PV) and solar thermal collectors, and seasonal thermal energy storage. The economic, technical and environmental impacts of energy systems depend on the system design and operational strategy. The focus of this thesis is to propose unified frameworks, including the mathematical formulation of all of the components to determine the optimal energy system configuration, the optimal size of each component, and optimal operating strategy. The proposed methodologies address the problems related to the optimal design of the energy system for both deterministic and stochastic cases. By the use of the proposed frameworks, the design of the energy system is investigated for different specified levels of GHG emissions ratio, and the purpose is to minimize the annual total cost. To account for uncertainties and to reduce the computational times and maintain accuracy, a novel strategy is developed to produce scenarios for the stochastic problem. System design is carried out to minimize the annual total cost and conditional value at risk (CVaR) of emissions for the confidence level of 95%. The results demonstrate how the system size changes due to uncertainty and as a function of the operational GHG emissions ratio. It is shown that with the present-day technology (without solar technologies and seasonal storage), the lowest amount of GHG emissions ratio is 37%. This indicates the need for significant technological development to overcome that ratio to be 10% of stand-alone systems. This thesis introduces novel performance curves (NPC) for determining the optimal operation of the energy system. By the use of this approach, it is possible to identify the optimal operation of the energy system without solving complex optimization procedures. The application of the proposed NPC strategy is investigated for various case studies in different locations. The usage of the proposed strategy leads to the best-operating cost-saving and operational GHG savings when compared to other published approaches. It has shown that other strategies are special (not always optimal) cases of the NPC strategy. Based on the extensive literature review, it is found that it is exceptionally complicated to apply the previously proposed models of seasonal thermal energy storage in optimization software. Besides, the high computational time is required to obtain an optimum size and operation of storage from an optimization software. This thesis also proposes a new flexible semi-analytical, semi-numerical methodology to model the heat transfer process of the borehole thermal energy storage to solve the above challenges. The model increases the flexibility of the storage operation since the model can control the process of the storage by also deciding the appropriate storage zone for charging and discharging. Thesis Doctor of Engineering (DEng)

Ph. D. Thesis In order to compute more realistic production plans and schedules, techniques using nonlinear programming (NLP) and mixed-integer nonlinear programming (MINLP) have gathered a lot of attention from the industry and academy. Efficient solution of these problems to a proven ε-global optimality remains a challenge due to their combinatorial, nonconvex, and large dimensionality attributes. The key contributions of this work are: 1) the generalization of the inventory pinch decomposition method to scheduling problems, and 2) the development of a deterministic global optimization method. An inventory pinch is a point at which the cumulative total demand touches its corresponding concave envelope. The inventory pinch points delineate time intervals where a single fixed set of operating conditions is most likely to be feasible and close to the optimum. The inventory pinch method decomposes the original problem in three different levels. The first one deals with the nonlinearities, while subsequent levels involve only linear terms by fixing part of the solution from previous levels. In this heuristic method, infeasibilities (detected via positive value of slack variables) are eliminated by adding at the first level new period boundaries at the point in time where infeasibilities are detected. The global optimization algorithm presented in this work utilizes both piecewise McCormick (PMCR) and Normalized Multiparametric Disaggregation (NMDT), and employs a dynamic partitioning strategy to refine the estimates of the global optimum. Another key element is the parallelized bound tightening procedure. Case studies include gasoline blend planning and scheduling, and refinery planning. Both inventory pinch method and the global optimization algorithm show promising results and their performance is either better or on par with other published techniques and commercial solvers, as exhibited in a number of test cases solved during the course of this work. Thesis Doctor of Philosophy (PhD) Optimal planning and scheduling of production systems are two very important tasks in industrial practice. Their objective is to ensure optimal utilization of raw materials and equipment to reduce production costs. In order to compute realistic production plans and schedules, it is often necessary to replace simplified linear models with nonlinear ones including discrete decisions (e.g., “yes/no”, “on/off”). To compute a global optimal solution for this type of problems in reasonable time is a challenge due to their intrinsic nonlinear and combinatorial nature. The main goal of this thesis is the development of efficient algorithms to solve large-scale planning and scheduling problems. The key contributions of this work are the development of: i) a heuristic technique to compute near-optimal solutions rapidly, and ii) a deterministic global optimization algorithm. Both approaches showed results and performances better or equal to those obtained by commercial software and previously published methods.

This thesis presents frameworks for the optimal strategic production planning of petroleum refineries operating in competition in multiple markets. The game theoretic concept of the Cournot oligopoly is used as the basic competitive model, and the Nash equilibrium as the solution concept for the formulated problems, which are reformulated into potential games. Nonlinear programming potential game frameworks are developed for static and dynamic production planning problems, as well for mixed integer nonlinear expansion planning problems in which refiners have access to potential upgrades increasing their competitiveness. This latter model represents a novel problem in game theory as it contains both integer and continuous variables and thus must satisfy both discrete and continuous mathematical definitions of the Nash equilibrium. The concept of the mixed-integer game is introduced to explore this problem and the theoretical properties of the new class of games, for which conditions are identified defining when a class of two-player games will possess Nash equilibria in pure strategies, and conjectures offered regarding the properties of larger problems and the class as a whole. In all examples, petroleum refinery problems are solved to optimality (equilibrium) to illustrate the competitive utility of the mathematical frameworks. The primary benefit of such frameworks is the incorporation of the influence of market supply and demand on refinery profits, resulting in rational driving forces in the underlying production planning problems. These results are used to justify the development of frameworks for enterprise optimization as a means of decision making in competitive industries. Thesis Doctor of Philosophy (PhD) This thesis presents a mathematical framework in which refinery production planning problems are solved to optimal solutions in competing scenarios. Concepts from game theory are used to formulate these competitive problems into mathematical programs under single objective functions which coordinate the interests of the competing refiners. Several different cases are considered presenting refinery planning problems as static and dynamic programs in which decisions are time independent or dependent, respectively. A theoretical development is also presented in the concept of the mixed integer game, a game theoretic problem containing both continuous and discrete valued variables and which must satisfy both continuous and discrete definitions of Nash equilibrium. This latter development is used to examine refinery problems in which individual refiners have access to numerous unit upgrades which can potentially improve performance. The results are used to justify a game theoretic approach to enterprise optimization.

The objective of the hot rolling mill is to transform slabs of steel into thin strips which conform to specific dimensional and metallurgical customer requirements. High performance and flexibility in the operation is required due to strict customer demands, variable market conditions, and the drive for continuous improvement. Historically human schedulers have performed the scheduling and sequencing tasks, however it is not a reasonable expectation that they consider all the complex objectives required in optimal production of a hot mill. Therefore, there are significant opportunities for improvement in this area through the application of mathematical optimization models and solution algorithms. This work presents a set of models and a solution algorithm for optimal scheduling and sequencing of production within a hot rolling steel mill. The models and algorithms presented within this thesis are specifically developed for ArcelorMittal Dofasco’s Hot Strip Mill in Hamilton, Ontario, Canada. First, a graph theoretic representation of the production block is developed along with an asymmetric travelling salesman formulation of the sequencing problem. A slab transition cost function comprised of the hot rolling process objectives is formalized. The objective of the optimization is to generate a complete block sequence which minimizes the cost of transitions between slabs thus minimizing the overall cost of production. The Concorde exact solver is leveraged for the sequencing problem. Second, the scheduling of slabs from inventory into blocks is considered in addition to sequencing. A methodology for slab clustering is defined. The novel concept of width-groups is developed and a heuristic algorithm is devised to calculate an objective for the MILP slab scheduling model. The objective of the scheduling optimization is to construct a set of blocks which minimize deviation from the calculated width-group design. A revised sequencing model, updated to reflect the relaxations enabled by the width-group design, is formulated. Industrial production and offline trials show that the proposed scheduling-sequencing framework outperforms the human scheduler in all critical performance metrics for both scheduling and sequencing. A conservative estimate of the reoccurring monetary benefits available from use of the proposed scheduling-sequencing optimization framework is greater than $1.2M CAD per year. Thesis Master of Applied Science (MASc)

Distillation columns are primary equipment in petrochemical, gas plants and refineries. Distillation columns energy consumption is estimated to be 40% of the total plant energy consumption. Optimization of distillation columns has potential for saving large amount of energy and contributes to plant wide optimization. Currently rigorous tray to tray models are used to describe columns separation with high accuracy. Rigorous distillation models are being used as part of design, optimization and as a part of on-line real-time optimization applications. Due to large number of nonlinear equations, rigorous distillation models are not suitable for inclusion in optimization models of complex plants (e.g. refineries), since they would make the model too large. For this reason, current practice in plant-wide optimization for planning or for scheduling is to include simplified model. Accuracy of these simplified models is significantly lower than the accuracy of the rigorous models, thereby causing discrepancy between production planning and RTO decisions. This work describes reduced size hybrid model of distillation columns, suitable for use as stand-alone tool for individual column or as part of a complete plant model, either for RTO or for production planning. Hybrid models are comprised of first principles material and energy balances and empirical models describing separation in the column. Hybrid models can be used for production planning, scheduling and optimization. In addition this work describes inferential model development for estimating streams purity using real time data. Inferential model eliminates the need for Gas Chromatography GC analyzers and can be used for monitoring and control purposes. Predictions from the models are sufficiently accurate and small size of the models enable significant reduction in size of the total plant models. Thesis Master of Applied Science (MASc)

This work suggests a new multiple ejector refrigeration cycle operated by an NGL Recovery Plant's waste heat as a replacement to the mechanical compression refrigeration cycle. This will result in significant power reduction and CO2 emission reduction. Typical NGL plant compresses its feed to a high pressure (3040 kPa). The feed gas compressors’ discharge reaches approximately 150 OC. After that, the feed is cooled by three-stage propane vapour compression refrigeration cycle. This paper examines various options for thermal power cooling in such plants in order to eliminate part of the propane chilling system. Since most of the new plants are located in desert climates, typical designs based on absorption refrigeration are not very efficient. Design proposed in this work employs ejector refrigeration and it is based on 45 OC air as a cooling media (summer conditions in hot climates). Performance factor has been defined as the total cooling provided by the refrigeration system over the total cooling required in the 1st cooling stage of the NGL Recovery Plant. Cooling based on a single N-pentane ejector cycle with N-pentane has COP of 0.342 and performance factor (ƞ) of 0.842. Multistage ejector N-pentane refrigeration system has COP of 0.714 and performance factor (ƞ) of 1.053. For a typical 750 Million scf/d NGL plant, the new design saves $12 Millions in capital costs and $1.5 in annual electricity cost. Thesis Master of Applied Science (MASc)

Current gasoline blend planning practice is to optimize blend plans via discrete-time multi-period NLP or MINLP models and schedule blends via interactive simulation. Solutions of multi-period models using discrete-time representation typically have different blend recipes for each time period. In this work, the concept of an inventory pinch point is introduced and used it to construct a new decomposition of the multi-period MINLP problems: at the top level nonlinear blending problems for periods delimited by the inventory pinch points are solved to optimize multi-grade blend recipes; at the lower level a fine grid multi-period MILP model that uses optimal recipes from the top level is solved in order to determine how much to blend of each product in each fine grid period, subject to minimum threshold blend size. If MILP is infeasible, corresponding period between the pinch points is subdivided and recipes are re-optimized. Two algorithms at the top level are examined: a) multi-period nonlinear model (MPIP) and b) single-period non-linear model (SPIP). Case studies show that the MPIP algorithm produces solutions that have the same optimal value of the objective function as corresponding MINLP model, while the SPIP algorithm computes solutions that are most often within 0.01% of the solutions by MINLP. Both algorithms require substantially less computational effort than the corresponding MINLP model. Reduced number of blend recipes makes it easier for blend scheduler to create a schedule by interactive simulation. Master of Applied Science (MASc)

This work describes an architecture which enables experiments in optimization of networks that represent systems in diverse application domains, e.g. multi-product food production plants, gasoline blending and shipment, heat exchanger networks in refineries, etc. The prototype implementation is a web-based workbench (NOPT). Design of the workbench enables instantiation of different application domains via attributes describing entities (materials, energy) flowing through network arcs, and via node models relevant to the domain. From data describing the network attributes, NOPT generates a mathematical model described by a set of linear equations and provides a user with abilities to select appropriate solution algorithms. Multi-step composite algorithms, each solving a subnetwork or an entire network for specific time periods can be constructed with input from the user. Some of the steps in the algorithm can be non-linear procedures which compute specific model parameters. Hence, the architecture enables solution of bi linear systems of type “x*y” (e.g. energy balances) by first solving for “x’ (e.g. mass flows) from some other set of equations (e.g. mass balances) and then solve for “y” since “x’ is known. Current architecture of NOPT also supports the inclusion of external node models that helps user to import his customized node models into the workbench via the feature called User Node. Master of Computer Science (MCS)

In process industries, heat exchanger networks represent an important part of the plant structure. The purpose of the networks is to maximize heat recovery, thereby lowering the overall plant costs. Previously published research on heat exchanger networks deals with two categories: • Synthesis of heat exchanger networks with the goal of designing a structure that provides the lowest total (capital plus operating) costs. • Data reconciliation with the goal of establishing true performance of the network and identifying correct heat transfer coefficients for individual exchangers in the network. Since heat exchanger models are highly nonlinear due to presence of log mean temperature difference term, solution of the network models is not always guaranteed. Most of the published results have used some form of approximation of the log mean temperature difference term. The approximations have been designed to provide reasonable accuracy while providing better convergence properties. Nevertheless, these are approximations and lead to the results that are not quite accurate. The goal of this research is to develop heat exchanger network models and algorithms for design, monitoring and optimization that are easy to implement in engineering practice and have excellent convergence properties. Presented here is a new heat exchanger network simulation algorithm which solves rigorously heat exchanger network equations in three phases: Phase 1: Solve mass balance equations for the network, i.e. determine flows in all branches of the network. These equations are linear. • Phase 2: Compute heat exchanger heat transfer factor for each exchanger in the network. Computation of the factor for each heat exchanger employs current flows through the exchanger and values of the exchanger variables at some base operating conditions. • Phase 3: Compute all heat exchanger outlet temperatures, given temperatures of the inlet streams and the results from Phase 1 and Phase 2. The computation in this phase is also employing a set of linear equations, while retaining full rigorous of the heat transfer equations. Hence, we have successfully transformed solution of a heat exchanger network into multi-phase solutions of sets of linear equations. This approach is then used for HEN synthesis and data reconciliation of HENs. HEN synthesis has been extensively studied over years and significant progress has been achieved in the development of robust methods for design of cost-optimal networks but one of the relatively less addressed issues is to deign HENs based on standard or modular sizes of heat exchangers. The major complexities in HEN synthesis are handling the combinatorial nature of the problem and finding a feasible and optimum solution using simultaneous synthesis methods. In this research, HEN simulation algorithm combined with differential evolutionary optimization is used for design of HENs with modular sizes of heat exchangers. This approach is successfully applied to examples available in the literature. Previously published results have used heat exchangers that have been sized for a placement at a specific location in a heat exchanger network, thereby aiming to provide the lowest cost solution. The research presented here shows that equally good or better solutions can be obtained by using standard, modular sizes of the heat exchangers. The approach used in this work is more realistic, since in practice heat exchangers are available in standards sizes, not custom made (in other words, a heat exchanger typically would have a size of 50 or 100 sq ft, but not 49.8 or 101.9 sq ft as may be calculated by the methods published in the literature). Data reconciliation and parameter estimation is an important step in HEN performance monitoring. In the current research, the HEN simulation algorithm is extended to develop a framework for data reconciliation of HEN and to estimate the change in the overall heat transfer coefficient of heat exchangers. This methodology is successfully implemented on two case studies from the literature. Master of Applied Science (MASc)

Multi Time period Gasoline blending is an example of multipurpose production system that is designed to produce multiple products by switching from one product to another. Various factors such as demand for gasoline, availability of supply component, and blend recipes vary with time. Task of the gasoline blender is to decide how much of each product to produce at what point in time (lot sizing) and what should be the blend recipe in order to minimize overall cost (optimize the blend recipe) . The production plans need to account for set-up times between blends and to minimize switching between different product blends. Traditional optimization techniques provide a single optimal solution. This research is using evolutionary optimization algorithm called differential evolution to identify multiple solutions t hat all have the same total cost but offer the blend planner multiple choices in terms of how much of a given product to blend at what point in time. Master of Applied Science (MASc)