Special Issue on “Process Modeling in Pyrometallurgical Engineering”

This Special Issue on “Process Modeling in Pyrometallurgical Engineering” consists of 39 articles, including two review papers, and covers a wide range of topics related to process development and analysis based on modeling in ironmaking, steelmaking, flash smelting, casting, rolling operations, etc [...

Design of Small LNG Supply Chain by Multi-Period Optimization

A mathematical model for the design of small-scale supply chains for liquefied natural gas (LNG) has been developed. It considers the maritime delivery of LNG from supply ports to satellite terminals and land-based transports from the terminals to consumers on or off the coast. Both tactical and strategic aspects in the supply chain design are addressed by optimizing the maritime routing of a heterogeneous fleet of ships, truck connections, and the locations of the satellite terminals. The objective is to minimize the overall cost, including operation and investment costs for the selected time horizon. The model is expressed as a mixed-integer linear programming problem, applying a multi-period formulation to determine optimal storage sizes and inventory at the satellite terminals. Two case studies illustrate the model, where optimal LNG supply chains for a region with sparsely distributed island (without land transports) and a coastal region at a gulf (with both sea and land transports) are designed. The model is demonstrated to be a flexible tool suited for the initial design and feasibility analysis of small-scale LNG supply chains

Principal Component Analysis of Blast Furnace Drainage Patterns

Monitoring and control of the blast furnace hearth is critical to achieve the required production levels and adequate process operation, as well as to extend the campaign length. Because of the complexity of the draining, the outflows of iron and slag may progress in different ways during tapping in large blast furnaces. To categorize the hearth draining behavior, principal component analysis (PCA) was applied to two extensive sets of process data from an operating blast furnace with three tapholes in order to develop an interpretation of the outflow patterns. Representing the complex outflow patterns in low dimensions made it possible to study and illustrate the time evolution of the drainage, as well as to detect similarities and differences in the performance of the tapholes. The model was used to explain the observations of other variables and factors that are known to be affected by, or affect, the state of the hearth, such as stoppages, liquid levels, and tap duration

Numerical Analysis of Factors Affecting the Burden Surface and Porosity Distribution in the Upper Part of the Blast Furnace

A proper burden and porosity distribution of the bed in the upper shaft are important prerequisites for realizing a stable and efficient operation of the ironmaking blast furnace. The discrete element method was used to investigate the effects of the static friction coefficient between burden particles and shaft angle on the burden profile and porosity distribution in the bed formed by charging the burden with a bell-less charging equipment. The results indicate that a large static friction coefficient makes the particles stay closer to the impact point (i.e., where they fall) from the rotating chute. A large mixed region of the burden bed decreases the gas permeability, and an increase in the burden particle roughness will worsen this problem. The burden surface shape becomes flatter with an increase in the shaft angle. These findings explain the effect of particle properties and wall geometry on the inner structure of the burden bed

Estimation of the Blast Furnace Hearth State Using an Inverse-Problem-Based Wear Model

An undisturbed and well-controlled hearth state is an essential prerequisite for achieving a long campaign life and low production costs in an ironmaking blast furnace, because hearth wear and hot metal and slag drainage are crucial factors in its operation. With the objective to estimate the hearth state of the refractory of a three-taphole blast furnace, a wear model of the hearth erosion and skull formation was developed. The model is based on thermocouple readings in the hearth lining and solves an inverse heat conduction problem for a series of co-axial vertical slices, where the erosion and skull lines are optimized simultaneously. The model is optimized for fast computation by adopting a novel procedure featuring fixed mesh during the looping calculation. The results revealed that the hearth refractory showed an elephant-foot-shaped profile with excessive erosion in the hearth periphery, indicating that liquid flows are suppressed in the hearth bottom and that the permeability of the core of the deadman is low. These findings were further elaborated and confirmed by a comparison between the estimated hearth state and other key operation variables, including the coke rate, blast kinetic energy, and residual carbon appetite of the hot metal

A Model of Optimal Gas Supply to a Set of Distributed Consumers

A better design of gas supply chains may lead to a more efficient use of locally available resources, cost savings, higher energy efficiency and lower impact on the environment. In optimizing the supply chain of liquefied natural gas (LNG), compressed natural gas (CNG) or biogas for smaller regions, the task is to find the best supplier and the most efficient way to transport the gas to the customers to cover their demands, including the design of pipeline networks, truck transportation and storage systems. The analysis also has to consider supporting facilities, such as gasification units, truck loading lines and CNG tanking and filling stations. In this work a mathematical model of a gas supply chain is developed, where gas may be supplied by pipeline, as compressed gas in containers or as LNG by tank trucks, with the goal to find the solution that corresponds to lowest overall costs. In order to efficiently solve the combinatorial optimization problem, it is linearized and tacked by mixed integer linear programming. The resulting model is flexible and can easily be adapted to tackle local supply chain problems with multiple gas sources and distributed consumers of very different energy demands. The model is illustrated by applying it on a local gas distribution problem in western Finland. The dependence of the optimal supply chain on the conditions is demonstrated by a sensitivity analysis, which reveals how the model can be used to evaluate different aspects of the resulting supply chains