### ESTIMATING COST MODELS: Power-Sizing Model.

*is usedto estimatethe costsof industrialplants and equipment.*

**power-sizing model**The model "scales up" or "scales down" known costs, thereby accounting for economies of scale that are common in industrial plant and equipment costs. Consider the cost to build a refinery.Wouldit cost twice as much to build the samefacility with double the capacity? It is unlikely. The power-sizing model uses the exponent (x), called the power-sizing exponent, to reflect economies of scale in the size or capacity:

where x is the power-sizing exponent, costs of A and B are at the same point in time (same dollar basis), and size or capacity is in the same physical units for both A and B.'

The power-sizing exponent (x) can be 1.0(indicating a linear cost-versus-size/capacity relationship) or greater than 1.0 (indicating diseconomies of scale), but it is usually less than 1.0 (indicating economies of scale). Generally the ratio should be less than 2, and it should never exceed 5.This model works best in a "middle" range-not very small or very large size.

Exponent values for plants and equipment of many types may be found in several sources, including industry reference books, research reports, and technical journals. Such exponent values may be found in Perry's Chemical Engineers' Handbook, Plant Design and Economics for Chemical Engineers, and Preliminary Plant Design in Chemical Engineering. Table 2-1 gives power sizing exponent values for several types of industrial

facilities and equipment. The exponent given applies only to equipment within the size range specified.

In Equation 2-3 equipment costs for both A and B occur at the same point in time. This equation is useful for scaling equipment costs but not for updating those costs. When the time of the desired cost estimate is different from the time in which the scaling occurs (per Equation 2-3) cost indexes accomplish the time updating. Thus, in cases like Example 2-8 involving both scaling and updating, we use the power sizing model together with.cost indexes.

**TABLE2-1**Example Power-Sizing Exponent Values

**EXAMPLE 2-8.**Based on her work in Example 2-7,Miriam has been asked to estimate the cost today of a 2500 ft^2

heat exchange system for the new plant being-analyzed.'She has the following data.

· Her company paid $50,000.0for a 1000 ft^2 heat exchanger 5 years ago.

· Heat exchangers within this range of capacity have a power sizing exponent (x) of .0.55.

· Five years ago the Heat Exchanger Cost Index (HECI) was 1306; it is 1487 today.

**SOLUTION.**Miriam will first use Equation 2-3 to scale up the cost of the 1000 ft^2 exchanger to one that is

2500 ft^2 using the 0.55 power-sizing exponent.

Miriam knows that the $82,8000 reflects only the scaling up of the cost of the 1000 ft^2 model

to a 2500 ft^2 model. Now she will use Equation 2-2 and the HECI data to estimate the cost of a

2500 ft^2 exchanger today. Miriam's cost estimate would be:

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