A Novel Back-Off Algorithm for the Integration Between Dynamic Optimization and Scheduling of Batch Processes Under Uncertainty

This thesis presents a decomposition algorithm for obtaining robust scheduling and control decisions. It iteratively solves scheduling and dynamic optimization problems while approximating stochastic uncertainty through back-off terms, calculated through dynamic simulations of the process. This algorithm is compared, both in solution quality and performance, against a fully-integrated MINLP

An Improved Robust Optimization Approach for Scheduling Under Uncertainty

In practice, the uncertainty in processing time data frequently affects the feasibility of optimal solution of the nominal production scheduling problem. Using the unit-specific event-based continuous time model for scheduling, we develop a novel multi-stage robust approach with corrective action to ensure robust feasibility of the worst case solution while reducing the conservatism arising from traditional robust optimization approaches. We quantify the probability of constraint satisfaction by using a priori and a posteriori probabilistic bounds for known and unknown uncertainty distributions, consequently, improving the objective value for a given risk scenario. Computational experiments on several examples were carried out to measure the effectiveness of the proposed method. For a given constraint satisfaction probability, the proposed method improves the objective value compared to the traditional robust optimization approaches

Integration of design and control for large-scale applications: a back-off approach

Design and control are two distinct aspects of a process that are inherently related though these aspects are often treated independently. Performing a sequential design and control strategy may lead to poor control performance or overly conservative and thus expensive designs. Unsatisfactory designs stem from neglecting the connection of choices made at the process design stage that affects the process dynamics. Integration of design and control introduces the opportunity to establish a transparent link between steady-state economics and dynamic performance at the early stages of the process design that enables the identification of reliable and optimal designs while ensuring feasible operation of the process under internal and external disruptions. The dynamic nature of the current global market drives industries to push their manufacturing strategies to the limits to achieve a sustainable and optimal operation. Hence, the integration of design and control plays a crucial role in constructing a sustainable process since it increases the short and long-term profits of industrial processes. Simultaneous process design and control often results in challenging computationally intensive and complex problems, which can be formulated conceptually as dynamic optimization problems. The size and complexity of the conceptual integrated problem impose a limitation on the potential solution strategies that could be implemented on large-scale industrial systems. Thus far, the implementation of integration of design and methodologies on large-scale applications is still challenging and remains as an open question. The back-off approach is one of the proposed methodologies that relies on steady-state economics to initiate the search for optimal and dynamically feasible process design. The idea of the surrogate model is combined with the back-off approach in the current research as the key technique to propose a practical and systematic method for the integration of design and control for large-scale applications. The back-off approach featured with power series expansions (PSEs) is developed and extended to achieve multiple goals. The proposed back-off method focuses on searching for the optimal design and control parameters by solving a set of optimization problems using PSE functions. The idea is to search for the optimal direction in the optimization variables by solving a series of bounded PSE-based optimization problems. The approach is a sequential approximate optimization method in which the system is evaluated around the worst-case variability expected in process outputs. Hence, using PSE functions instead of the actual nonlinear dynamic process model at each iteration step reduces the computational effort. The method mostly traces the closest feasible and near-optimal solution to the initial steady-state condition considering the worst-case scenario. The term near-optimal refers to the potential deviations from the original locally optimum due to the approximation techniques considered in this work. A trust-region method has been developed in this research to tackle simultaneous design and control of large-scale processes under uncertainty. In the initial version of the back-off approach proposed in this research, the search space region in the PSE-based optimization problem was specified a priori. Selecting a constant search space for the PSE functions may undermine the convergence of the methodology since the predictions of the PSEs highly depend on the nominal conditions used to develop the corresponding PSE functions. Thus, an adaptive search space for individual PSE-optimization problems at every iteration step is proposed. The concept has been designed in a way that certifies the competence of the PSE functions at each iteration and adapts the search space of the optimization as the iteration proceeds in the algorithm. Metrics for estimating the residuals such as the mean of squared errors (MSE) are employed to quantify the accuracy of the PSE approximations. Search space regions identified by this method specify the boundaries of the decision variables for the PSE-based optimization problems. Finding a proper search region is a challenging task since the nonlinearity of the system at different nominal conditions may vary significantly. The procedure moves towards a descent direction and at the convergence point, it can be shown that it satisfies first-order KKT conditions. The proposed methodology has been tested on different case studies involving different features. Initially, an existent wastewater treatment plant is considered as a primary medium-scale case study in the early stages of the development of the methodology. The wastewater treatment plant is also used to investigate the potential benefits and capabilities of a stochastic version of the back-off methodology. Furthermore, the results of the proposed methodology are compared to the formal integration approach in a dynamic programming framework for the medium-scale case study. The Tennessee Eastman (TE) process is selected as a large-scale case study to explore the potentials of the proposed method. The results of the proposed trust-region methodology have been compared to previously reported results in the literature for this plant. The results indicate that the proposed methodology leads to more economically attractive and reliable designs while maintaining the dynamic operability of the system in the presence of disturbances and uncertainty. Therefore, the proposed methodology shows a significant accomplishment in locating dynamically feasible and near-optimal design and operating conditions thus making it attractive for the simultaneous design and control of large-scale and highly nonlinear plants under uncertainty

Systems and control : 21th Benelux meeting, 2002, March 19-21, Veldhoven, The Netherlands

Book of abstract

Systematic approaches for synthesis, design and operation of biomass-based energy systems

A biomass-based energy system (BES) is a utility facility which produces cooling, heat and power simultaneously from biomass. By having a BES installed on-site, industrial processes can reduce energy costs by locally producing heat, cooling and power for process and work place requirements. However, several barriers have hindered development of BESs in the energy industry. These barriers include doubts over its operational uncertainties (e.g., seasonal biomass supply, equipment reliability, etc.), the misconception that generating energy from biomass is only a marginal business and the lack of successful cooperative partnerships within the industry. According to literature, such barriers are due to the lack of frameworks that address design aspects and demonstrate the economic viability of a BES. This thesis presents systematic approaches and frameworks to design a BES. These approaches emphasise on integrating synthesis, design and operation decision making for a BES during its preliminary design phase. Firstly, a systematic approach is presented to synthesise a BES considering seasonal variations in biomass supply and energy demand. In this approach, a multi-period optimisation model is formulated to perform technology and design capacity selection by considering seasonal variations in biomass supply and energy demand profiles. This approach is then extended to systematically allocate equipment redundancy within the BES in order to maintain a reliable supply of energy. In this approach, k-out-of-m system modelling and the principles of chance-constrained programming are integrated in a multi-period optimisation model to simultaneously screen technologies based on their respective equipment reliability, capital and operating costs. The model also determines equipment capacities, along with the total number of operating (and stand-by) equipment based on various anticipated scenarios in a computationally efficient manner. Following this, a systematic approach is developed to simultaneously screen, size and allocate redundancy within a BES considering its operational strategies (e.g., following electrical load or following thermal load). Subsequently, a systematic framework on Design Operability Analysis (DOA) is developed to analyse BES designs in instances of failure. This framework provides a stepwise procedure to evaluate proposed BES designs under scenarios of disruption and analyse their true feasible operating range. Knowledge of the feasible operating range enables designers to determine and validate if a BES design is capable of meeting its intended operations. Following this, a systematic Design Retrofit Analysis (DRA) framework is presented to debottleneck and retrofit existing BES designs in cases where energy demands are expected to vary in the future. The presented framework re-evaluates an existing BES design under disruption scenarios and determines its real-time feasible operating range. The real-time feasible operating range will allow designers to determine whether debottlenecking is required. If debottlenecking is required, the framework provides systematic debottlenecking and retrofit guidelines for BES designs. The design of a BES is then extended further to consider its interaction in an eco-industrial park (EIP). Since heat, cooling and power are essentially required in most industrial processes, a BES can be more economically attractive if synthesised for an EIP. As such, an optimisation-based negotiation framework is developed to analyse the potential cost savings allocation between participating plants in an EIP coalition. This framework combines the principles of rational allocation of benefits with the consideration of stability and robustness of an EIP coalition to changes in cost assumptions. Lastly, possible extensions and future opportunities for this research work are highlighted at the end of this thesis

A Polyhedral Study of Mixed 0-1 Set

We consider a variant of the well-known single node fixed charge network flow set with constant capacities. This set arises from the relaxation of more general mixed integer sets such as lot-sizing problems with multiple suppliers. We provide a complete polyhedral characterization of the convex hull of the given set

A Comprehensive Techno-Economic Framework for Shale Gas Exploitation and Distribution in the United States

Over the past years, shale gas has turned into one of the most significant sources of energy in the United States. Technological advancements have provided the energy industry with the necessary tools to allow the economic exploitation of an enormous volume of natural gas trapped in shale formations. This has boosted the domestic gas production and generated a boom in other sectors of the economy in the country. However, major challenges are involved in the development of shale gas resources. A drastic decline of wells’ productivity, the costs involved in the gas production and distribution facets, and the volatile behavior of the energy market represent some of the complexities faced by a gas operator. In this context, the utilization of a comprehensive frameworks to analyze and develop long-term strategies can represent a meaningful supporting tool for shale gas operators. The main objective of this research work is the development and implementation a novel techno-economic framework for the optimal exploitation and delivery of shale gas in the United States. The proposed framework is based on an interdisciplinary approach that combines data driven techniques, petroleum engineering practices, reservoir simulations and mathematical programming methods. Data analysis algorithms are implemented to guide the decision-making processes involved in the unconventional reservoir and define the predominant trends of certain exogenous parameters of the system. Petroleum engineering practices and reservoir simulation models are required for a realistic description of the formations and the proper definition of strategies to extract the gas from the shale rock. Finally, the mathematical programming is required for describing the surface facilities design and operations to ensure the allocation of the shale gas in the different commercialization points. The output of this framework will provide the optimal operations and infrastructure by maximizing the net present value (NPV). To demonstrate the efficacy of the proposed decision-making structure, a case study based on the liquid-rich region of the Marcellus play is considered in this work. The application of the proposed framework depicts the influence of reservoir complexities and external factors in establishing optimal strategic decisions for the exploitation, processing and allocation of shale gas. The coordination of the different facets including the drilling and completion activities and the design and operation of the surface facilities has a key role in maintaining the economy of a shale gas venture above its economic threshold