Optimizing the Supply of Bulk Gases

This article is based on a talk given by Jon Jolliffe, Systems Manager of BOC Gases Europe to the Mathematical Programming Study Group.

Industrial Gases

BOC's main business is the supply of gases to industry. With the exception of carbon dioxide, which is obtained as a by-product of brewing, these gases are obtained from the air by fractional distillation at extremely low (cryogenic) temperatures.

Air consists of roughly 80% nitrogen, 20% oxygen, 1% argon and minuscule quantities of other gases. In addition there can be variable quantities of water vapour, carbon dioxide and pollutants.

The uses of industrial gases are myriad and reflect their physical and chemical properties. Because it is non-combustible, nitrogen is used for putting out mine fires. As it doesn't contain oxygen, it is used as a preservative: crisp bags are filled with it so that the crisps don't go soggy. In its liquid form it is intensely cold and so is used as a refrigerant.

Oxygen, on the other hand, promotes combustion and so is used in steelworks and chemical processes. It promotes microbial activity and so is used in sewage treatment as well as the more obvious areas of health care and breathing equipment. Argon is used in welding and to fill light bulbs.

Production and Distribution

Although air is all around us and is free, the process of separating it into its components is one where there are substantial economies of scale. Efficient plants may cost tens of millions of pounds and consume tens of MW of electricity. It thus makes sense to build a large plant and incur distribution costs rather than building a number of small plants near the customers.

Another reason why products need to be distributed is because individual customers do not want to buy nitrogen and oxygen in the roughly 3:1 ratio in which they are produced by an Air Separation Unit (ASU). A schematic of an ASU is shown at Figure 1.

Figure 1: Schematic of an Air Separation Unit

There are three ways of delivering industrial gases:

  • by pipeline to a neighbouring site (known as "tonnage");
  • in liquid form in bulk tankers;
  • as compressed gases in cylinders.

Only the largest customers, such as a steelworks or an oil refinery, have the demand which justifies BOC's building an ASU near to their site in order to supply gases by pipeline. BOC's business can be viewed as building tonnage plants to satisfy long-term contracts with the largest customers and then distributing and selling the surplus gases to other customers. For this reason its plants tend to be in the traditional areas of heavy industry with Fawley near Southampton the only plant in southern England. Each plant has its own fleet of vehicles to deliver the surplus gases to the other customers which it supplies.

In order for a customer to receive gases in liquid form from a bulk tanker, it must have suitable storage tanks and equipment (although these are usually supplied by BOC as part of its contract with the customer). It follows that it is the medium-to-large customers which receive gases from bulk tankers. Delivery is economic over long distances so customers all over the country can be satisfied. Some deliveries may also be made from a storage and trans-shipment depot such as Wolverhampton which has its own fleet of delivery vehicles.

Small customers buy their gases in cylinders. This is the least efficient form of distribution: the cylinders are enormously heavy compared with the weight of their contents. It is therefore only economic to distribute cylinders over short distances. When planning BOC's activities, it suffices therefore to aggregate such demand and include it as local market demand.

The Optimization Problem

The problem which BOC faces is to minimize the total variable costs of production and distribution while meeting demand as far as possible. This problem is most acute when BOC is negotiating a tonnage contract: how would a new ASU affect the existing pattern of production and distribution? What are the marginal costs and benefits?

To answer these and related questions, BOC has developed PANDA, (Production and Distribution Analysis). This is an LP-based model of BOC's production and distribution system. Because its primary focus is to support investment decisions, it works with average demands and is concerned only with distribution in bulk tankers. To keep matters simple, demand is aggregated into tanker loads and tankers are assumed to make straightforward out-and-return trips. The outcome from a run is a pattern of production and distribution rather than detailed logistics. BOC has separate systems for day-to-day activities including vehicle routing.

The PANDA Model

The main decision variables in the PANDA model are how much production there should be at each ASU and how the quantities of products not required by tonnage customers should be distributed. In principle, demands will be met from the nearest plant with spare production of that gas. In practice, matters are complicated by the varying efficiency of the plants. More modern ASUs are more efficient and so it can make sense to produce extra gas at such plants and incur greater distribution costs.

Although much of the production and distribution system can be represented faithfully by Linear Programming, there are some important exceptions. An ASU may consist of multiple columns (the main component, where the fractional distillation takes place), each of which is either on or off. If a column is on, there is some flexibility in flow rate and also some in the proportions of gases produced; typically these are expressed as operating modes, e.g. maximum argon mode; maximum oxygen mode. Of course, it is always possible to vary the proportions more by venting unwanted products to the air, but this is obviously wasteful.

Another series of decisions concerns the liquefiers. At one extreme a plant may have individual liquefiers for each gas, while at the other extreme nitrogen may be the only gas with a liquefier. In the latter case the other gases are liquefied in a heat exchanger which vaporises liquid nitrogen or other tonnage gases. Liquefiers are similar to fractionation columns in being either on or off, but they do not give rise to integer decisions in the same way. This is because it is practicable to run the liquefiers in "campaigns", running them for some days and then turning them off. The effort and costs associated with starting up a fractionation column make it undesirable to run them in campaigns.

A final area for decision-making lies in the use of electricity. Since privatisation, BOC has bought electricity at a flat rate price. Now this is changing to a block-structured tariff in which the price falls as more electricity is used. Modelling this requires the use of Integer Programming and is implemented using Special Ordered Sets.

Uses of PANDA

PANDA is primarily a tool to support senior management. It provides advice on the problems which they face: deciding where to site a new plant; determining its size; setting the production budget; negotiating large contracts. As such, the model has sophisticated data handling and reporting facilities so that it can be used in extensive "What if?" analyses. New plants can be configured along with changes to existing ones and changes to the demand and to the delivery systems.

The model was built in the mid-1980s when demand for liquid gases was increasing and new technology made it possible to build more efficient liquefiers. It was used to consider where and when to build these liquefiers and what size of liquefier to build.

When a new plant was built in Dublin, PANDA was used to determine its size and model the effects on the existing plants in Belfast and Cork.

More recently a number of large supply contracts in the North of England were up for renewal. These had been supplied by two production sites which were becoming outdated. Many possible solutions were considered and evaluated with PANDA. Eventually it was decided to build a new ASU at the Sheffield site, extend the pipeline system in the Sheffield area and close the other production site.

Finally, PANDA is used in the annual budget cycle to predict the production and distribution patterns. The marketing department estimates the demand for the forthcoming year and PANDA then assesses how that demand should be achieved and the costs involved.

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