Economy of Scale and the Six-Tenths Factor

When demand is high for commodity chemicals, advantage can be taken of the economy of scale. This principle holds as long as each major piece of equipment in the plant can be made larger as the production rate is increased. This makes possible a single-train plant, with no or few pieces of equipment duplicated. However, when the equipment size exceeds the maximum size that can be fabricated and shipped, then equipment must be duplicated and the economy of scale is lost because two or more trains of equipment are required. The economy of scale is embedded in the following relationship, which correlates the variation of cost with capacity  

This relationship has been foimd to give reasonable results for individual pieces of equipment and for entire plants. Although, as shown by Williams (1947a,b), the exponent, m, may vary from 0.48 to 0.87 for equipment and from 0.38 to 0.90 for plants, the average value is close to 0.60. Accordingly, Eq. (16.3) is referred to as the six-tenths rule. Thus, if the capacity is doubled, the 0.6 exponent gives only a 52% increase in cost. Equation (16.3) is used in conjunction with Eq. (16.2) to take cost data from an earlier year at a certain capacity and estimate the current cost at a different capacity. As an example, suppose the total depreciable capital investment for a plant to produce 1,250 tonnes/day (1 tonne = 1,000 kg) of ammonia 

As discussed below in Section 16.7, the Aspen Engineering Suite provides methods more accurate than the six-tenths factor method of Equation (16.3) for determining the effect of scale on capital cost. The Aspen methods apply engineering-based scale-up rules to each piece of process equipment and to buildings, site development, and other items of capital cost. 

Note that in several cases, the plants produce combined products. Both ethylene and propylene are produced from a naphtha cut obtained from the fractionation of crude oil. A combined ammonia-urea fertilizer plant is common. The electrolysis of a brine solution produces both chlorine and sodium hydroxide. Recent literature data are usually given for plant capacities in tonnes per year (1 tonne = 1,000 kg) or tons per day (1 ton = 2,000 lb) of product, but the capacity data in Table 16.8 are given in pounds of product per year. Also included in the table is the value of Q for use in the following modification of Eq. (16.3)  

Commodity Chemical(s) Production Rate(s) (Millions of Pounds/Year) Capital Investment Factor [C in Eq. (16.4) for 1995] 

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