Six-tenths rule

This is applicable for any given year of installation but does not correct for the differences in cost from year to year. This is conveniendy done as described in the section for year indices. Experience has indicated that this six-tenths rule is reasonably accurate for capacity scale-up of individual items of equipment. Thus, if the cost of one size of a piece of equipment is knotm, an estimating figure for one twice as large can be found by multiplying by (2)° . 

An analysis of equipment costs and capital investment for chemical plants (Wilson, 1947 Chilton, 1950 Vilbrandt and Dryden, 1959 Guthrie, 1970) showed that the six-tenths factor can be applied for a rough evaluation of the influence of equipment size on its cost. The six-tenths rule can be described as a power law expression ... 

The value of the index n is traditionally taken as 0.6 the well-known six-tenths rule. This value can be used to get a rough estimate of the capital cost if there are not sufficient data available to calculate the index for the particular process. Estrup (1972) gives a critical review of the six-tenths rule. Equation 6.2 is only an approximation, and if sufficient data are available the relationship is best represented on a log-log plot. Garrett (1989) has published capital cost-plant capacity curves for over 250 processes. 

ESTRUP, C. (1972) Brit. Chem. Eng. Proc. Tech. 17, 213. The history of the six-tenths rule in capital cost estimation. 

This result implies that/4 V273, a relationship close to the classical six-tenths rule used in cost estimating. From (e), Lopt = (4Vhr)1/3 this yields a rather surprising result, namely... 

It is, of course, also true that a plant of twice the output would probably cost significantly less than twice as much as the smaller one (a price factor of 20 6, if the six-tenths rule is used), and so would be more attractive financially - but the same questions have to be asked. 

Since the design/retrofit problem embeds batch plant scheduling, it systematically includes the determination of the production sequence and the equipment sizes based on a performance criterion. Equipment sizes are considered either as continuous variables or as discrete ones and so the problem can involve either discrete variables or a set of mixed ones. Most of the existing literature has focused on single objectives involving a cost criterion typically based on capital investment. This criterion is generally expressed as a non-linear function of the size of the equipment, following the six-tenths rule. 

Cost and space requirements are also important factors although few comparative up-to-date cost data are available. If the cost of a small crystallizer is known, however, a rough estimate of the cost of a larger one may be made by the six-tenths rule. 

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... 

Based on the demonstration, the cost to drill a well was assumed to be 5,000. To achieve the appropriate maximum groundwater extraction rate of 24 gpm, three recovery wells are required, resulting in a cost of approximately 15,(XX). A 5200 gallon, holding tank cost 5,000. Using the "six-tenths rule" to scale-up, the cost of a 10,0(X) gallon tank for a Ml-scale remediation was assumed to cost 7,400. Three tanks will be required, resulting in a cost of 22,200. A V2 horse-power pump cost 1,035 for the demonstration. A pump for each well would cost a total of 3,105. These additional costs amount to about 40,000. 

The value of the cost exponent, n, used in Equations 7.1 and 72, varies depending on the class of equipment being represented. See Table 7.3. The value of n for different items of equipment is often around 0.6. Replacing n in Equation 7.1 and/or 5.2 by 0.6 provides the relationship referred to as the six-tenths rule. A problem using the six-tenths rule is given in Exartple 7.3. 

Use the six-tenths rule to estimate the percentage increase in purchased cost when the capacity of a piece of equipment is doubled. 

Special care must be taken in using the six-tenths rule for a single piece of equipment. The cost exponent may vary considerably from 0.6, as illustrated in Example 7.4. The use of this rule for a total chemical process is more reliable and is discussed in Section 73. 

Conpare the error for the scale-up of a reciprocating conpressor by a factor of 5 using the six-tenths rule in place of the cost exponent given in Table 7.3. 

The six-tenths rule is more accurate in this application than it is for estimating the cost of a single piece of equipment. The increased accuracy results from the fact that multiple units are required in a processing plant. Some of the process units will have cost coefficients, n, less than 0.6. For this equipment the six-tenths rule overestimates the costs of these units. In a similar way, costs for process units having coefficients greater than 0.6 are underestimated. When the sum of the costs is determined, these differences tend to cancel each other out. 

Six-tenths rule, 183-184. 189-190 Skirts (elevated towers), 40-41 Smith, Karl, 919... 

The reason for this is that, when extrapolated to small production volumes of industrial processes, starting from a certain level, the so-called six-tenths rule, which relates the investment expenditures and production capacity as... 

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