46 Purchased Equipment (PE) Cost

PE is the purchased price of equipment from a vendor (someone selling the equipment). It is one of the major factors in the TCI direct costs.

It includes the cost to build the equipment but does not include the cost associated with transportation of that equipment to the site, and installation, etc.

Many times we may estimate PE costs based on costs of PE from previous projects. We will usually use factors to adjust the cost for capacity or changes in prices over time.

Effect of Capacity

There are a variety of ways to adjust PE pricing to account for different equipment capacity (bigger or smaller equipment). The most common, simple relationship, and the one we’ll use in this class, is shown below:

[latex]\frac{C_{a}}{C_{b}}=\Big(\frac{A_{a}}{A_{b}}\Big)^n[/latex]

Where

[latex]C_{a}[/latex] – desired equipment cost

[latex]C_{b}[/latex] – base cost for known equipment

[latex]A_{a}[/latex] – desired capacity

[latex]A_{b}[/latex] – base capacity

[latex]n[/latex] – cost exponent (given for each type of equipment)

We can rearrange this equation and plot it in a linear form as well (many times you may see log-based plots comparing equipment capacity and cost):

[latex]ln(C_{a})=ln(K)+n ln(A_{a})[/latex]

Where

[latex]K=\frac{C_{b}}{A_{b}^n}[/latex]

If you are curious, we show how this equation is derived below:

Since [latex]C_{b}[/latex] and [latex]A_{b}[/latex] are known values for equipment, we can treat them as constants and take use [latex]K[/latex] to represent [latex]\frac{C_{b}}{A_{b}^n}[/latex], and take the ln of both sides of the equation.

\begin{align*}
\frac{C_{a}}{C_{b}}&=\Big(\frac{A_{a}}{A_{b}}\Big)^n\\
C_{a} & = \frac{C_{b}}{A_{b}^n}×A_{a}^n\\
C_{a} & = K × A_{a}^n \\
ln(C_{a}) &= ln(K) + n ln(A_{a}) \\
\end{align*}

Table 1: Examples of Cost Exponents for Process Equipment

Note: heat exchanger capacities are measured by the area of heat exchange, thus the unit is [latex]m^2[/latex].

Analogous exponent values are shown due to copyright considerations. You can find the updated values in Analysis, Synthesis and Design of Chemical Processes, fifth edition, Section 2, Chapter 7.2, Table 7.3.[latex]^{[1]}[/latex]

A general rule for cost exponents is called the six-tenths rule. This is a generalization that for many processes, the exponent will be close to six-tenth’s (0.60). You can see this applies better to certain equipment more than others based on the table above.

Effect of Time

As you may know, the value of money changes with time due to factors such as inflation. Cost indexes give us an estimate of what a common item costs at different points in time.

[latex]C_{2}=C_{1}\Big(\frac{I_{2}}{I_{1}}\Big)[/latex]

where

[latex]C_{1}[/latex] – known cost of equipment/plant at a known (past) time

[latex]C_{2}[/latex] – cost of equipment/plant at a time of interest

[latex]I_{1}[/latex] – the cost index at a known time

[latex]I_{2}[/latex] – the cost index at a time of interest

Table 2: Cost indexes for 1996-2020

Analogous time indexes are shown due to copyright considerations. You can find the updated values in Analysis, Synthesis and Design of Chemical Processes, fifth edition, Section 2, Chapter 7.2.2, Table 7.4.[latex]^{[1]}[/latex]

Marshall and Swift Equipment cost index and Chemical Engineering Plant Cost Index are two common types of cost indexes that we will use for this course.

Note the Marshall and Swift is used for equipment, whereas the plant cost index is for an overall plant cost including installation, piping, etc.