April 1999 By Susana Mondschein and Sara Pimentel Chile is the world's largest copper producer and exporter. In 1997 the country produced 3.4 million tons of copper, accounting for around 30 percent of the world's copper production. The State operates most of the smelters and refineries (smelters transform copper concentrate with approximately 30 percent copper into blister copper that is approximately 99 percent pure; see Box 1). Currently, the State owns five of the seven primary copper smelters, with a total smelting capacity of around 4.7 million tons of copper concentrates per year (see Box 2). Box 1: The Copper Production Process Copper is present in the earth's crust mainly in the form of sulfide ores, which are complex mixtures of sulfides of copper and iron, combined with compounds of other metals such as arsenic, zinc, silver, and gold. The copper concentration in an orebody is low; typically copper ores contain between 0.5 percent to 2 percent copper. In 1997, approximately 85 percent of the world's primary copper originated in sulfide ores, which are treated by pyrometallurgical techniques, starting with copper concentrates. The production process consists of the following steps: (a) concentration by froth flotation, and (b) smelting to produce blister copper (99 percent copper). The blister copper is finally fire and electro-refined to produce high-grade copper (refined copper or cathodes), which is suitable for fabrication and use. The method used to concentrate copper minerals is froth flotation, by which copper ores are attached to air bubbles rising through an aqueous pulp of ground ore. The "floated" minerals are held in a stable froth on top of the flotation cell from where they are mechanically removed to form the concentrate. Although the mineralogical composition of the concentrates depends directly on their origin, it is roughly a third copper a third sulfur, and a third iron. In the smelting step, by melting the concentrates in a furnace, and later treatment in converters, the sulfur, iron and other undesirable elements are removed from the concentrate to produce blister copper. Refining is the final phase for obtaining high-grade copper. Box 2: The International Copper Market Cathodes (refined copper), concentrates, and to a lesser extent, blister are the main copper products traded in the international market. Cathodes account for 61.6 percent of Chilean copper exports, followed by concentrates (33.6 percent) and blister (4.8 percent). The daily price for refined copper (cathodes) is determined through transactions made in the London Metal Exchange and in New York Commodity Exchange Inc. The price of the other products is calculated using cathode prices as a base and discounting the price of the additional processes that are required to refine the product until becoming a cathode. These discounts correspond to treatment charges (smelter) and refining charges (refinery). The treatment and refining charges vary in the international market according to available capacity of the smelters and refineries all over the world and the availability of copper concentrates in the market. The price of copper fluctuates considerably over time. At present, due to a slowdown of the principal economies of Asia, copper demand has decreased, resulting in a surplus at the cathodes market. For this reason the copper price is at 65 cents per pound, which is approximately half the price it commanded in January 1997. The smelting process generates gases, which contain sulfur dioxide, particulate matter and arsenic. These gases pollute the atmosphere unless they are treated in expensive abatement plants to eliminate their pollutants before they are released. Despite the significant growth of the copper industry in recent decades (from 0.8 million tons in 1975 to 3.4 million tons in 1996), the Chilean government only began to study the effects of the copper production process on the environment in the late 1980s. This concern led, in 1991, to new environmental regulations regarding sulfur dioxide and particulate matter emissions. New emission standards for arsenic will become effective shortly. Currently, the most important environmental challenge for the public mining industry is meeting the new environmental standards by solving the pollution problem in the copper smelters. Within the framework of Chilean air quality regulations, all of the state-owned smelters have submitted cleanup plans that will eventually ensure compliance with the new air quality standards. These plans involve the installation of efficient gas collection systems, electrostatic precipitators and sulfuric acid plants to reduce the amount of pollutants emitted into the atmosphere (see Box 3). Some of these plans are being implemented and have successfully completed some stages. However, each smelter developed its own cleanup plan independently, without considering its effects on the other smelters. For example, most mines rely too heavily on the smelter that is closest to the mine, thereby ignoring the possibility of processing some concentrates with high amounts of arsenic in smelters with better air dispersion conditions. Box 3: Main Pollution Abatement Equipment Electrostatic precipitators are commonly used to reduce the amount of particulate matter in the contaminant gases, with efficiencies higher than 90 percent. A significant amount of arsenic is attached to the particulate matter. Therefore, the abatement of particulate matter also reduces the amount of arsenic in the gases. Sulfur dioxide can be removed from the effluent gases as sulfuric acid, liquid sulfur dioxide or elemental sulfur, but the most common and efficient abatement technology is the production of sulfuric acid as a byproduct. Sulfuric acid is an important raw material to produce copper from oxide ores, and due to increasing production of this type of copper in the country, the demand for sulfuric acid is expected to increase significantly over the next years. The total expected cost of these plans is approximately $1.3 billion, most of it going to install sulfuric acid plants and electrostatic precipitators. Considering the importance of these investments required by the plans, the Chilean Copper Commission (COCHILCO), which is the institution charged with reviewing and approving investment projects in the state-owned mining companies, decided to develop a project which would rationalize the assignment of investment resources in the state-owned smelters. Moreover, this project could be used to evaluate the economic impact of some new environmental standards. COCHILCO's aim was to develop a conceptual framework for the integrated operation of all public-sector copper smelters, to study the sensitivity of the system to local changes and to determine the optimal investment policy. An integrated system of copper smelters implies: scale economies associated with the size of the facilities; redistribution of concentrates among smelters in order to minimize pollution (the sulfur and arsenic content of the concentrates vary according to origin); joint decisions by the smelters on the distribution of sulfuric acid to demand locations according to their distances; the effects on the acid price of sulfuric acid production. Consequently, a decision-support system was developed to help the State determine an efficient investment policy satisfying environmental regulations, while satisfying all operational constraints. After meetings with the engineers responsible for smelting operations, the experts on pollutant dispersion models, and representatives from companies which manufacture pollutant-abatement equipment and smelting technologies, a mathematical programming model was developed to solve this productive-environmental problem. The model maximizes the total discounted profit for the state-owned copper smelters. The Decision-Support System The decision-support system consists of two mathematical models: the smelters' model, which is a non-linear integer programming model that optimizes the smelters' operational and investment decisions; and the sulfuric acid market model, which is a network flow model to describe the economic behavior of the sulfuric acid market. These two models interact through the input that each receives from the other: The smelters' model optimizes, among other decisions, the sulfuric acid production levels considering the acid price determined by the sulfuric acid market model. On the other hand, the sulfuric acid equilibrium price is affected by the supply of sulfuric acid, which is partly determined by the sulfuric acid production at the state-owned smelters according to the smelters' model. An equilibrium solution is reached through an iterative procedure. The smelters' model maximizes the total expected profit from the state-owned copper smelters, discounted over the planning horizon, subject to technical, environmental and market constraints. Revenues accrue from the sales of concentrates, refined copper and sulfuric acid. Additional sources of income are obtained from smelting private concentrates and from the residual value of the smelters that would close down. The costs include copper and acid production, resizing the smelters, installation of electrostatic precipitators and sulfuric acid plants, and transportation of the concentrate from the treatment plants to the smelters. The main decisions are divided into investment and operational decisions. The investment decisions consider the time, place and dollar value of infrastructure investments (smelting capacity, electrostatic precipitators and sulfuric acid plants). The operational decisions are how much copper concentrate to export and how much to process domestically; how to distribute the concentrate to be processed within the country among the five state-owned smelters; how much sulfuric acid to produce; and the amount of pollutants to be emitted into the atmosphere. The model also considers the possibility of closing current smelters, either totally or partially, and of installing new smelters at new locations. The sulfuric acid market model applies the economic theory of spatial equilibrium, which considers a homogeneous good with high transportation costs that is sold, possibly at different prices, at various geographically separated locations. The spatial equilibrium problem has been widely studied in the economics literature. In particular, our model estimates the relevant regional supply and demand curves and applies the model developed by Samuelson [1952] to the Chilean case. The resulting model is a network flow model (see Box 4). Box 4: The Sulfuric Acid Market World production of sulfuric acid is approximately 150 million tons per year. Most of it comes from two main sources: sulfur toasting (approximately 80 percent) and effluent gases of copper smelters (about 20 percent). In recent years the importance of effluent gases has increased due to pollution control all over the world. The demand for sulfuric acid mainly comes from the industry that produces phosphated fertilizers for agriculture (around 70 percent) and the chemical and copper mining industries. Sulfuric acid is a highly corrosive and very dangerous product. Therefore, storage, handling and transportation costs are very high. This is the main factor that explains why the sulfuric acid market is mainly local. Less than 5 percent of the production is traded in the international market. Furthermore, most of this international trade is due to the excedents generated at the copper smelters, which are compelled to produce sulfuric acid that cannot be sold locally as a byproduct of the pollution control efforts. Currently, Chilean sulfuric acid production (2.6 millions tons per year) represents approximately 1.7 percent of the total world production. This production is consumed domestically, mainly in the leaching process to produce refined copper from oxide ores. However, as a result of new environmental regulations regarding the emission of sulfur into the atmosphere, Chilean production is expected to increase significantly over the next years, reaching in the year 2005 a total of around 6 million tons. This increase will have an important effect on the price of sulfuric acid in Latin America. The decision-support system was developed using GAMS. DICOPT was used to manage the master problem; CPLEX to solve the linear and integer programming problems; and CONOPT to solve the non-linear programming structures. A complete description of the decision support system can be found in Mondschein and Schilkrut [1997] and Caldentey and Mondschein [1998]. Main Implications The decision-support system is a new environmental management tool that has helped the government analyze its investments in pollution control in the state-owned copper smelters. It also is the first formal instrument developed to analyze the interrelationships among the decisions made by the smelters and the related subsystems (such as the sulfuric acid market and State-owned concentrate treatment plants). The integrated vision considered in the decision support system evaluates all feasible solutions, including alternatives that are difficult to visualize when smelters optimize operations independently. For example, we compare the total expected profit of the copper industry over a planning horizon of 10 years. Implementing the solutions proposed by our model and comparing them to the original cleanup plans, we observe an increase in profits of approximately $814 million (6 percent), which represents more than 1 percent of Chile's annual GDP. The substantial increase in profits is due to significant improvements in the allocation of concentrates among the smelters. Another important contribution of the model concerns investments in smelting capacity. The installation of a new smelter at a place with good conditions for dispersing air pollutants has been debated for a long time within the government. To date, no agreement has been reached. To aid the government in making this decision, our model includes the option of installing a new smelter within the 20-year planning horizon. The results, using the current operational, economical and environmental data, suggest that new investment is not convenient within the horizon. To the best of our knowledge, our model is the first to incorporate the behavior of the sulfuric acid market. Thus, the price of the sulfuric acid, which is an important factor in deciding when and where to build new acid plants (or expand existing plants), is determined endogenously and is not assumed exogenous, as in most models of this type. Our experience showed that even the experts in product trade do not have any formal tool to evaluate the impact of the expected increase in acid supply on its price and its distribution in the country. Knowing the future evolution of the price of sulfuric acid and where it will be produced helps anticipate future requirements of infrastructure (such as roads and ports). Additionally, the model can be used to estimate the cost of government policies and the impact of other exogenous factors, such as changes in the price of copper and the incorporation of new smelting technologies. It also can be used by the State to evaluate the economic impact of different environmental standards. For example, while preparing the Arsenic Emission Standard Draft, at the request of CONAMA (National Environmental Commission), the model was run to evaluate the economic impact of different levels of emissions at each smelter. Research Group This project was developed by a group of consultants commissioned by the Chilean Copper Commission jointly with National Environmental Commission (CONAMA), which provided the funds through a World Bank loan. The director of the project, developed in two phases between 1994 and 1997, was Susana Mondschein. Regina Massai and Sarita Pimentel from Cochilco, and Eduardo Engel and Ariel Schilkrut from the University of Chile were also part of the research team in the first phase of the project. In the second phase of the project, Regina Massai, Sarita Pimentel and Pedro Santic from Cochilco and René Caldentey and Eduardo Engel from the University of Chile participated in the project's development. We also thank many engineers from the state-owned smelters for their collaboration. References Mondschein, S. and Schilkrut, A. (1997), "Optimal Investment Policies for Pollution Control in the Copper Industry," Interfaces, Vol. 27, No. 6, November-December, pp. 69-87. Caldentey, R. and Mondschein, S. (1998), "Decision Support System for Pollution Control in the Copper Industry, Including a Model for the Sulfuric Acid Market," submitted to Operations Research. Samuelson, P. (1952), "Spatial Price Equilibrium and Linear Programming," The American Economic Review, Vol. 42, pp. 283-303. Susana Mondschein is on the faculty of the Department of Industrial Engineering, University of Chile; e-mail: smondsch@dii.uchile.cl. Sara Pimentel is a member of the Chilean Copper Commission; e-mail: spimente@cochilco.cl Table of Contents OR/MS Today Home Page OR/MS Today copyright © 1999 by the Institute for Operations Research and the Management Sciences. All rights reserved. Lionheart Publishing, Inc. 506 Roswell Street, Suite 220, Marietta, GA 30060, USA Phone: 770-431-0867 | Fax: 770-432-6969 E-mail: lpi@lionhrtpub.com URL: http://www.lionhrtpub.com Web Site © Copyright 1999 by Lionheart Publishing, Inc. All rights reserved.