1. Cost estimation model for PAN based carbon fiber manufacturing process
Amaninder Singh Gill1, Darian Visotsky1, Laine Mears2, Joshua D. Summers1
1 Department of Mechanical Engineering,
Clemson University,
Clemson, SC, USA
2 Department of Automotive Engineering,
Clemson University International Center for Automotive Research,
Greenville, SC, USA

2. Motivation Estimation for the Presentation
The worst slot to present in a conference (Harvard Business Review)
The worst time in the day (J Physiology & Pathophysiology keynote)

3. Motivation Why propose a cost model for Carbon Fiber Manufacturing?
Upcoming structural material in automotive and aerospace industry
Lightwieghting for CAFÉ compliance; CFRP BIW helps in weight reduction
Model how changes in manufacturing process affect the cost
Lack of analytical mass based models in the literature
Tune up manufacturing process to balance technical and economical aspects: maybe a small increase in technical properties requires a high increase in cost, and is not worth it

4. Methodology for Weight based CF cost model study
Study the manufacturing processes involved in the manufacturing of Carbon Fiber
Model each of the processes involved to account for the materials and energy consumption
Evaluate this consumption in term of market prices
Account for the price elasticity on the inputs
Compare with the actual cost (across three countries) and compare results

5. Carbon fiber manufacturing process
Precursor: Polyacrilonitrile (PAN). Used by 96% of global market [4]
Four stages: Oxidation, Carbonization, Surface treatment, and Sizing [1, 2]
Process yield η = 0.55 KgCF/KgPAN [1]
Carbon fiber with a carbon content of 93 to 95 % is obtained [1]
PAN spool
CF spool
CF manufacturing process
The functions that have been removed are low level functions that need to be considered in later stages of design

6. Carbon fiber manufacturing process
Figure adapted from Bunsell, 1997
Process stages
Oxidation: PAN fibers are heated up in an oven in presence of air. Incorporation of oxygen through a cyclization mechanism
Carbonization: Oxidized fiber are heated up in an inert atmosphere. Non carbon molecules are removed
Surface treatment: Fibers are pulled through an electrolytic bath. This roughens the surface and enhances the adhesion when used in CFRP
Sizing: A coating is applied to protect and lubricate the fibers for the ease of handling
We need to understand the process to model the variable costs on each of its stages

7. Cost model Weight based model, which output is the cost per Kg of CF
𝐶 𝑇 = 𝐶 𝐿 + 𝐶 𝑂 + 𝐶 𝐶 + 𝐶 𝑀 + 𝐶 𝐶𝑁 + 𝐶 𝐸
Weight based model, which output is the cost per Kg of CF
Fixed costs are constant regardless level of activity: cost of labor, overhead costs, capital cost [3]
Variable costs depend on level of activity: cost of materials, consumables, and energy [3]

8. 𝐶 𝐹 = 𝐶 𝐶 + 𝐶 𝐿 + 𝐶 𝑂 Cost model Calculation of fixed costs CF
Capital cost CC: Initial investment for setting up the facility. Includes buying real estate, building infrastructure and buying equipment
Labor cost CL: Wages being paid to employees directly involved in the production process
Overhead cost CO: Indirect costs such as engineers, managers, warehousing, utilities, legal fees, etc.
𝐶 𝐹 = 𝐶 𝐶 + 𝐶 𝐿 + 𝐶 𝑂

9. Cost model 𝐶 𝑉 = 𝐶 𝑀 + 𝐶 𝐶𝑁 + 𝐶 𝐸 Calculation of variable costs CV
Material cost CM: Incurred by precursor material. Is calculated for 1 Kg of CF, therefore is affected by process yield η
𝐶 𝑀 =Precursor cost per Kg∙Amount of precursor required
𝐶 𝑀 =Precursor Cost per Kg x Amount of Carbon Fiber Required Yield Percentage (η
Consumables cost CCN: Other materials required for process, calculated for each stage
Energy cost CE: Cost of energy directly involved in the process, calculated for each stage
𝐶 𝑉 = 𝐶 𝑀 + 𝐶 𝐶𝑁 + 𝐶 𝐸

10. Cost model
Calculation of consumables cost CCN and energy cost CE for each process stage
1- Oxidation
Energy to heat up PAN fibers
Country
CE,oxi (Cents)
U.S.A.
102
Germany
0.07
Japan
41.71
𝐻 𝑜𝑥𝑖 = 0 𝐻 𝑜𝑥𝑖 𝑑𝐻 = 1 𝜂 ∙ 𝑇 𝑖 𝑇 𝑓 𝐶 𝑝 𝑇 𝑑𝑇
𝐻 𝑜𝑥𝑖 =0.55∙ 𝐶 𝑝 𝑇 𝑑𝑇 = 𝑀𝐽 𝐾𝑔 𝐶𝐹
The corresponding cost results
𝐶 𝐸,𝑜𝑥𝑖 = 𝐻 𝑜𝑥𝑖 ∙𝐶𝑜𝑠𝑡 𝑝𝑒𝑟 𝑢𝑛𝑖𝑡 𝑜𝑓 𝑒𝑙𝑒𝑐𝑡𝑟𝑖𝑐𝑖𝑡𝑦

11. Cost model 2- Carbonization
Calculation of consumables cost CCN and energy cost CE for each process stage
2- Carbonization
An inert gas is utilized in this stage, and can be considered a consumable
𝐶 𝐶𝑁,𝑐𝑎𝑟𝑏 =Volume of inert gas ∙Cost per unit volume of gas
Energy to heat up oxidized fibers and the nitrogen
𝐻 𝑐𝑎𝑟𝑏,𝐶𝐹 = 𝐶 𝑝,𝐶𝐹 𝑇 𝑑𝑇 =1.91 𝑀𝐽 𝐾𝑔 𝐶𝐹
Country
CE,carb (cents)
U.S.A.
89.57
Germany
0.58
Japan
281.67
𝐻 𝑐𝑎𝑟𝑏, 𝑁 2 =1.39 𝑀𝐽 𝐾𝑔 𝐶𝐹
𝐻 𝑐𝑎𝑟𝑏
𝐻 𝑐𝑎𝑟𝑏 = 𝐻 𝑐𝑎𝑟𝑏,𝐶𝐹 + 𝐻 𝑐𝑎𝑟𝑏, 𝑁 2 =3.3 𝑀𝐽 𝐾𝑔 𝐶𝐹
𝐶 𝐸,𝑐𝑎𝑟𝑏 = 𝐻 𝑐𝑎𝑟𝑏 ∙𝐶𝑜𝑠𝑡 𝑝𝑒𝑟 𝑢𝑛𝑖𝑡 𝑜𝑓 𝑒𝑙𝑒𝑐𝑡𝑟𝑖𝑐𝑖𝑡𝑦
Variation of specific heat of different CF with temperature during carbonization [5]

12. Cost model 3- Surface treatment
Calculation of consumables cost CCN and energy cost CE for each process stage
3- Surface treatment
The electrolyte (Sulphuric Acid) utilized is a consumable (0.0001Kg for 1kg CF) [5]
𝐶 𝐶𝑁,𝑠𝑢𝑟𝑓 = 𝜆 𝑠𝑜𝑙 x 𝐶 𝑠𝑜𝑙 x Cost per unit volume of Sulphuric Acid
Country
CCN,surf ($)
U.S.A.
1.62
Germany
Japan
2.43
Addition yield in Kgsol/KgCF
Solution concentration in Kgacid/Kgsol
Electric energy for electrolytic treatment [5]
𝐻 𝑠𝑢𝑟𝑓 = 4Ω 𝜌𝜙
Ω = Energy for surface treatment parameter 
𝜌 = Density of the carbon Fiber
Φ = Diameter of Individual Fibers
Country
CE,surf (cents)
U.S.A.
1.35
Germany
0.027
Japan
6.2
𝐻 𝑠𝑢𝑟𝑓 =2 𝑉∙𝐴∙𝑚𝑖𝑛 𝑚 𝑠 𝑚𝑖𝑛 ∙ 𝐽 𝑠 𝑉∙𝐴 𝐾𝑔 𝑚 3 ∙6 𝜇𝑚 =0.05 𝑀𝐽 𝐾𝑔 𝐶𝐹
C E_𝑠𝑢𝑟𝑓 = 𝐻 𝑠𝑢𝑟𝑓 x Cost per unit Electricity

13. Cost model
Calculation of consumables cost CCN and energy cost CE for each process stage
4- Sizing
An epoxy resin is utilized for coating the fibers [5] kg f epoxy per Kg of CF
𝐶 𝐶𝑁,𝑠𝑖𝑧 = 𝜆 𝑒𝑚𝑢𝑙𝑠 ∙ Cost per unit volume of epoxy resin
Country
CCN,siz ($)
U.S.A.
0.19
Germany
0.18
Japan
0.15
𝜆 𝑒𝑚𝑢𝑙𝑠 = epoxy solution utilized per Kg of CF
Electric energy for drying processes
𝐻 𝑠𝑖𝑧,𝑝𝑟𝑒 = 𝑇 𝑖,𝑝𝑟𝑒 𝑇 𝑓,𝑝𝑟𝑒 𝐶 𝑝,𝐶𝐹 𝑇 𝑑𝑇
𝐻 𝑠𝑖𝑧
𝐻 𝑠𝑖𝑧,𝑝𝑜𝑠𝑡 = 𝑇 𝑖,𝑝𝑜𝑠𝑡 𝑇 𝑓,𝑝𝑜𝑠𝑡 𝐶 𝑝,𝐶𝐹 𝑇 𝑑𝑇
Country
CE,siz (cents)
U.S.A.
4.07
Germany
0.2
Japan
23.64
C E,siz = 𝐻 𝑠𝑖𝑧 x Cost per unit Electricity

14. A generic Marshallian Demand Curve [7]]
Price elasticity
The cost of materials, consumables and energy changes with the quantity of these goods being purchased
If these inputs are purchased en masse, they tend to get a lot cheaper
This effect can be seen for CF as well: price drops from $300/Kg for 1 ton/year to $15/Kg for 35 tons/year [6]
It can be modeled as
∈ = Elasticity of the Price
Q = Initial Quantity
P = Initial Price
𝑑𝑄/𝑄 = Change in Quantity
𝑑𝑃/𝑃 = Change in Price
∈ = 𝑑 𝑄 𝑄 𝑑 𝑃 𝑃
This model takes into account the price elasticity
A generic Marshallian Demand Curve [7]]

15. Validation of cost model (Fixed Cost)
The proposed model is tested to see how well it works in different situations
Three scenarios are proposed, for which the cost is known:
[8]
[9]
Some elements of the cost model are not considered because of unavailability of information. This is the case of capital cost
Fixed costs calculated initially for a metric ton [10, 11, 12]:

16. Validation of cost model (Variable Cost)
Materials cost [17]
Consumables and energy costs [13, 14, 15, 16]

17. Validation of cost model - Results
The obtained costs can be compared with actual cost for each one of the three cases analyzed:
Discrepancies can be attributed to
a) Lack of accurate data on industrial chemicals input
b) Difference in the process parameters
c) Choice of Reagent
d) Price Elasticity
The model is robust and can accommodate all factors related with cost. However, the lack of reliable data impede to perform more accurate analysis

18. Conclusions
A cost model for the PAN-based CF manufacturing process was developed
It was validated comparing results throughout three virtual manufacturing plants located in different countries (and continents)
Acceptable results were obtained (error 40%-60%), considering limitations due to the lack of information in public domain
The model is useful for analyzing the components of the final cost of CF, allowing to identify where to focus efforts
It is recommended to further develop cost models for CF, considering also new developing technologies, such as utilizing lignin as precursor [17]. They would be valuable tools for decision making
Future Work: Extend the cost model to incorporate physical properties in the calculation of the final cost

19. References
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20. Thank You !
Questions?