Among the options for industrial waste heat recovery and reuse which are currently discussed, heat pumping receives far less attention than other technologies (e.g. organic rankine cycles). This, in particular, can be linked to a lack of comprehensive methods for optimal design of industrial heat pump and refrigeration systems, which must take into account technical insights, mathematical principles and state-of-the-art features. Such methods could serve in a twofold manner: (1) in providing a foundation for analysis of heat pump economic and energetic saving potentials in different industries, and further (2) in giving directions for experimentalists and equipment manufacturers to adapt and develop heat pump equipment to better fit the process needs. This work presents a novel heat pump synthesis method embedded in a computational framework to provide a basis for such analysis. The superstructure-based approach is solved in a decomposition solution strategy based on mathematical programming. Heat pump features are incorporated in a comprehensive way while considering technical limitations and providing a set of solutions to allow expert-based decision making at the final stage. Benchmarking is completed by applying the method on a set of literature cases which yields improved-cost solutions between 5 and 30% compared to those reported previously. An extended version of one case is presented considering fluid selection, heat exchanger network (HEN) cost estimations, and technical constraints. The extended case highlights a trade-off between energy efficiency and system complexity expressed in number of compression stages, gas-and sub-cooling. This is especially evident when comparing the solutions with 3 and 5 compression stages causing an increase of the coefficient of performance (COP) from 2.9 to 3.1 at 3% increase in total annualized costs (TAC).

The large potential for waste resource and heat recovery in industry has been motivating research toward increasing efficiency. Process integration methods have proven to be effective tools in improving industrial sites while decreasing their resource and energy consumption; however, location aspects and their impact are generally overlooked. This paper presents a method based on process integration, which considers the location of plants. The impact of the locations is included within the mixed integer linear programming framework in the form of heat losses, temperature and pressure drop, and piping cost. The objective function is selected as minimisation of the total cost of the system excluding piping cost and -constraints are applied on the piping cost to systematically generate multiple solutions. The method is applied to a case study with industrial plants from different sectors. First, the interaction between two plants and their utility integration are illustrated, depending on the piping cost limit which results in the heat pump and boiler on one site being gradually replaced by excess heat recovered from the other plant. Then, the optimisation of the whole system is carried out, as a large-scale application. At low piping cost allowances, heat is shared through high pressure steam in above-ground pipes, while at higher piping cost limits the system switches toward lower pressure steam sharing in underground pipes. Compared to the business-as-usual operation of the sites, the optimal solution obtained with the proposed method leads to 20% reduction in the overall cost of the system, including the piping cost. Further reduction in the cost is possible using a state of the art method but the technical and economic feasibility is not guaranteed. Thus, the present work provides a tool to find optimal industrial symbiosis solutions under different investment limits on the infrastructure between plants.

This research presents a mathematical formulation for optimizing integration of complex industrial systems from the level of unit operations to processes, entire plants, and finally to considering industrial symbiosis opportunities between plants. The framework is constructed using mixed-integer linear programming (MILP) which exhibits rapid conversion and a global optimum with well-defined solution methods. The framework builds upon previous efforts in process integration and considers materials and energy with thermodynamic constraints imposed by formulating the heat cascade within the MILP. The model and method which form the fundamentals of process integration problems are presented, considering exchange restrictions and problem formulation across multiple timescales to provide flexibility in solving complex design, planning, and operational problems. The work provides the fundamental problem formulation, which has not been previously presented in a comprehensive way, to provide the basis for future work, where many process integration elements can be appended to the formulation. A case study is included to demonstrate the capabilities and results for a simple, fictional, example though the framework and method are broadly applicable across scale, time, and plant complexity.

Industries consume large quantities of energy and water in their processes which are often considered to be peripheral to the process operation. Energy is used to heat or cool water for process use; additionally, water is frequently used in production support or utility networks as steam or cooling water. This enunciates the interconnectedness of water and energy and illustrates the necessity of their simultaneous treatment to improve energy and resource efficiency in industrial processes. Since the seminal work of Savulescu and Smith in 1998 introducing a graphical approach, many authors have contributed to this field by proposing graphically-or optimization-based methodologies. The latter encourages development of mathematical superstructures encompassing all possible interconnections. While a large body of research has focused on improving the superstructure development, solution strategies to tackle such optimization problems have also received significant attention. The goal of the current article is to study the proposed methodologies with special focus on mathematical approaches, their key features and solution strategies. Following the convention of Jeżowski, solution strategies are categorized into: decomposition, sequential, simultaneous, meta-heuristics and a more novel strategy of relaxation/transformation. A detailed, feature-based review of all the main contributions has also been provided in two tables. Several gaps have been highlighted as future research directions.

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