51 Practice Exercises

Multiple Choice Questions

Exercise: Equipment Prices with the Effect of Capacity and Time

Equipment Type Range of Correlation Capacity Units Cost Exponent (n)
Air compressor, multiple stages 1 -1500 [latex]kW[/latex] 0.85
Shell and tube heat exchanger stainless steel 1.9 – 1860 [latex]m^2[/latex] 0.60
Horizontal tank carbon steel 0.5-74 [latex]m^3[/latex] 0.30
centrifugal pump stainless steel 1-70 [latex]hp[/latex] 0.67
Crystalizer 0.2-3.8 [latex]m^3[/latex] 0.47
Year Marshall and Swift Equipment cost index Chemical Engineering Plant Cost Index
1996 211.7 154.7
2000 264.8 169.3
2004 301.7 186.3
2008 339.2 212.8
2012 391.5 227.8
2016 418.9 237.8
2020 458.3 258.8

In 2008, a carbon steel horizontal tank with a capacity of 26.5[latex]m^3[/latex] gallons costs $6700, then which of the following is the closest estimation to the cost of the same type of tank with a capacity of 50[latex]m^3[/latex] cost in 2020?






b) $10,100

We combine the effect of capacity and time by multiplying the two factors. For time, we use the Marshall and Swift Equipment cost index because we are interested in the cost of a piece of equipment.

C_{2} &=C_{1}×\Big(\frac{A_{a}}{A_{b}}\Big)^n×\Big(\frac{I_{2}}{I_{1}}\Big)\\
C_{2} & = $6700×\Big(\frac{50}{26.5}\Big)^{0.30}×\Big(\frac{458.3}{339.2}\Big)\\
C_{2} & ≈ $10,100

Exercise: Preliminary Estimation of Purchased Equipment Costs

Using the preliminary estimation of purchased equipment costs, estimate the price of a centrifugal compressor with the power of 400kW.

The value of a, b and n are shown as follows:

Equipment Units for Size, S S lower S upper a b n
centrifugal compressors driver power, kW 75 30,000 490,000 16,800 0.6

a) $1,100,000

b) $7,210,000

c) $490,000

d) the size of the equipment is out of the range for effective estimation


a) $1,100,000

The size of the compressor is 400kW, which is within the range of S lower and S upper, so we can eliminate choice d).
Then we can use the formula:

&≈ $1,100,000


Exercise: Calculating Depreciation

Equipment A Equipment B
Purchased Value $80,000 $100,000
Salvage Value $30,000 $40,000
Life of Equipment 5 years 10 years

Suppose we have 2 choices for a piece of equipment that serves the same purpose in our process, and we want to choose the equipment with the smallest depreciation, which one should we choose?

a) equipment A

b) equipment B

c)  they have the same depreciation value


b) equipment B

&\text{Depreciation of equipment A}\\
&=\frac{\text{purchased value}-\text{salvage value}}{\text{life of equipment }(n)}\\

&\text{Depreciation of equipment B}\\
&=\frac{\text{purchased value}-\text{salvage value}}{\text{life of equipment }(n)}\\


Long Answer Questions

Exercise: Estimating Project Cost Using the Lang Factor

Shown above is the block flow diagram of a carbon-capture process. The cost of equipment for each step is listed as follows:

Equipment Price
Absorber $80,000
Heat Exchanger $65,000
Stripper $50,000
5-stage Compression $120,000
Separator $30,000
Mixer $30,000


Type of Plant FCI TCI
solid processing plant 3.9 4.6
solid-fluid processing plant 4.1 4.9
fluid processing plant 4.8 5.7

All of the compounds are in liquid or vapour states. Estimate the TCI of the project.


Since all of the compounds are in liquid or vapour states, we take [latex]F_{lang}=5.7[/latex]

C_{TM}&=F_{lang} \sum_{i=1}^{n}C_{p,i}\\

Exercise: Calculating the number of Operating Labour

Shown below is a PFD of a catalytic reforming plant used in oil refineries to produce a high-octane gasoline component. Calculate the number of operators needed per shift for the process.

Image obtained from User: mbeychok via Wikimedia Commons / CC BY-SA 3.0

Note: Naphtha is a flammable liquid hydrocarbon mixture


From the labels, the process does not involve handling solids([latex]P=0[/latex]). And we can count that we have a total of 12 process steps that handle fluids without accounting for the number of pumps and vessels, shown in the diagram below:

So [latex]P=0\;;N_{np}=12[/latex]. Substitute this into the formula:

& = 3.008\\
& ≈ 4

The number of operating labour is rounded up to the nearest integer.


Exercise: Return on Investment

Suppose the estimation of the key manufacturing costs for our process are listed below:

[latex]FCI[/latex] $1,650,000
[latex]TCI[/latex] $2,000,000
[latex]C_{RM}[/latex] $600,000
[latex]C_{UT}[/latex] $280,000
[latex]C_{OL}[/latex] $320,000
[latex]C_{WT}[/latex] $500,000

a) Calculate the cost of manufacturing (do not include depreciation)

b) If the market price of the product is $500/tonne, how many tonnes of the product do we need to sell per year to get an ROI of 10%?









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Foundations of Chemical and Biological Engineering I Copyright © 2020 by Jonathan Verrett is licensed under a Creative Commons Attribution-ShareAlike 4.0 International License, except where otherwise noted.

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