Materials and Society: The Circular Economy (SAM13) Edited by Jean-Pierre Birat, Gael Fick, Mauro Chiappini, Valentina Colla, Andrea Declich, Barbara Fornai, Dominique Millet and Leiv Kolbeinsen REGULAR ARTICLE A quadratic programming model for the optimization of off-gas networks in integrated steelworks Alessandro Maddaloni, Ruben Matino, Ismael Matino, Stefano Dettori, Antonella Zaccara, and Valentina Colla * Scuola Superiore Sant’Anna, TeCIP Institute ICT-COISP, Pisa, Italy Received: 20 August 2019 / Accepted: 26 November 2019 Abstract. The European steel industry is constantly promoting developments, which can increase efficiency and lower the environmental impact of the steel production processes. In particular, a strong focus refers to the minimization of the energy consumption. This paper presents part of the work of the research project entitled “Optimization of the management of the process gas network within the integrated steelworks” (GASNET), which aims at developing a decision support system supporting energy managers and other concerned technical personnel in the implementation of an optimized off-gases management and exploitation considering environmental and economic objectives. A mathematical model of the network as a capacitated digraph with costs on arcs is proposed and an optimization problem is formulated. The objective of the optimization consists in minimizing the wastes of process gases and maximizing the incomes. Several production constraints need to be accounted. In particular, different types of gases are mixing in the same network. The constraints that model the mixing make the problem computationally difficult: it is a non-convex quadratically constrained quadratic program (QCQP). Two formulations of the problem are presented: the first one is a minimum cost flow problem, which is a linear program and is thus computationally fast to solve, but suitable only for a single gas network. The second formulation is a quadratically constrained quadratic program, which is slower, but covers more general cases, such as the ones, which are characterized by the interaction among multiple gas networks. A user- friendly graphical interface has been developed and tests over existing plant networks are performed and analyzed. 1 Introduction Steel production is among the largest energy-intensive industrial processes in the world, as well as one of the most important CO 2 emission sources. In particular, in the integrated steelworks, the blast furnace (BF) and the basic oxygen furnace (BOF) need 13-14 GJ/t of produced steel [1]. In addition, steel industry is responsible for about 4–5% of total world CO 2 emissions, as it is deeply dependent on fossil fuels [2,3]. Furthermore, energy cost represents about 20% of the total operation cost [4]. However, the major role of steel utilization in the modern society is undeniable. In order to improve energy saving and to reduce environmental impact and total operation cost, the optimal management of the energy resources produced inside the plant, such as off-gases, becomes decisive. The gases produced in the integrated steelworks contain significant amount of carbon monoxide and hydrogen and, for this reason, they represent a good replacement of natural gas (NG) in all the operation where heat, steam or electricity are required or need to be produced. Their use inside the steelmaking facilities is not new: they are directly reused in several unit operations for heating purposes or are exploited in boilers and in power plants, respectively, for steam and electricity productions. However, no optimization exists for such reuse and situations of overproduction or underproduction of gas can often occur. In the first case, the gasholders where the gas is stored become full and the excess gas is flared or the production is slowed down, in order to allow the decrease of the gasholder level. In the second case, NG is purchased in order to satisfy the demand of the different form of energy inside the plant. Consequently, these situations correspond to economic losses and increase of environmental impact. The off-gases produced during steel production are valuable by-products. Therefore, in literature different works can be found, which deals with the maximization of the use of such gases. Some of them refer to the increase of their reuse by producing chemical products; a complete review on this topic is provided in [5]. More specific studies can be found in [6] and in [7], respectively, for methanol * e-mail: v.colla@santannapisa.it Matériaux & Techniques 107, 502 (2019) © SCF, 2020 https://doi.org/10.1051/mattech/2019025 Matériaux & Techniques Available online at: www.mattech-journal.org