Section 6: Conclusions and Recommendations
A.2 Process Calculations
Calculations have corresponding spreadsheets in Appendix B.
ZnS Calculations ZnS mass feed rate
The required ZnS mass feed rate, to the R2R unit, can be determined based on the production rate, and cell width. The following assumptions were made for these calculations: a production rate of 100 ft/min and 20-inch wide solar cells. In addition, ZnS was assumed to have a density of 4.09 g/cm3 (CRC Handbook of Chemistry and Physics, 2011). Calculations for ZnO have similar theory behind them and are omitted due to the presence of this example. Process calculations for ZnO can be found in spreadsheet form in Appendix B.
Pyridine required
ZnS NCs were mixed with pyridine to form an ink solution for deposition onto the CIS absorber layer, via a R2R process. To determine the volume of required pyridine, a 1:10 molar ratio (ZnS: Pyridine) was assumed. For this calculation, a pyridine liquid density of 0.9819 kg/L was assumed (CRC Handbook of Chemistry and Physics, 2011).
68 ZnSO4 and Na2S required
A fast-precipitation reaction between ZnSO4 and Na2S produces ZnS:
ZnSO4 (aq.) +Na2S (aq.) →ZnS (s) + Na2SO4 (aq.)
Using the ZnS required mass feed and the reaction scheme above, the required ZnSO4 and Na2S mass feed rates can be calculated. For these calculations, 100% conversion was assumed due to a high reaction rate, kA=1.7*1023-6.2*1024L/ (mol*hr) (Sampaio et al., 2009).
ZnSO4:
=7.56 kg ZnSO4/day Na2S:
=3.65 kg Na2S/day
A mass balance can be performed around the ZnS reactor to calculate the exiting mass of Na2SO4.
Na2SO4: mNa2SO4 = (mZnSO4+mNa2S)-(mZnS)=(7.56 kg/day+3.65 kg/day)-(4.54 kg/day) =6.65 kg Na2SO4/day
Water for ZnS
Because ZnSO4 and Na2S are acquired in solid form can require in an aqueous medium, water is required to mix the reactants. The water required for the reaction can be determined based on the solubility of the reactants. For both reactants, it was assumed that the mass of the
69 reactants would be 10% less than the maximum solubility. Shown below is a sample example for the water required for Na2S.
ZnO Raw Materials Calculations ZnO
Production rate and dimensions: 100 ft/min of 20 inch reel Film Thickness: 50 nm
Density of ZnO= 5.606 g/cm^3= 5606 kg/m^3 Required feed of zinc acetate dihydrate:
Required feed of MEA:
MEA and zinc acetate dihydrate are fed in a 1:1 molar ratio
Required feed of 2-methoxy-ethanol
0.7 M ratio of zinc acetate dihydrate required
70 50% solvent recycling rate:
52 kg/ day of fresh 2-methoxyethanol is fed while 52 kg/day 2-methoxy will come from recycling.
ZnO:Ga
The calculations for ZnO:Ga are analogous to the calculations for ZnO, with the exception of the film thickness (300 nm) and the addition of the gallium dopant. Gallium will be doped at a 2 at.
% concentration, from the source Ga(NO3)3.
Production volume for ZnO:Ga= Production volume of ZnO* 300 nm/50 nm= 0.0000045 m3/min
Production rate= 0.0000045 m3/min*5600 kg/m3= 0.0252 kg/min ZnO:Ga = 3.1 *10-4 kmol/min ZnO: Ga
Gallium Doping Requirements:
Metal Contact Calculations
71 A gridded silver contact mesh will be deposited via a patterned roller with silver paste.
Calculations for CIS have similar theory behind them and are omitted due to the presence of this example. Process calculations for CIS can be found in spreadsheet form in Appendix B. The dimensions and cost calculations are as follow:
Vertical Lines
Horizontal Lines
The total cost of using this mass of silver is calculated:
72 Silicone Sealant Calculations
There will be a uniform layer of silicone sealant rolled onto the finished solar cell. The dimensions of this layer and resulting material use and costs are detailed below.
A quantity of 0.8226 kg/day is used in determining the approximate cost per day of sealing 300 ft/min of solar cells.
73 A.3 Equipment Calculations
Oven Reel
An example calculation for calculating oven real size based on sealant annealing times is provided. Given an output of 300 ft/min of PV film with an annealing time of 1 minute, optimal oven reel dimensions assumptions can be checked for feasibility. Determining the size of a roll and keeping it within the bounds of a standard sized oven is important to control equipment costs.
To accommodate the spacing of the metal contact grid, the circumference is chosen to be a multiple of 1 cm.
Based on the assumption of circumference and diameter, the number of circulations the film will make around the reel (1456) is negligible in the thickness it adds to the diameter of the roll and is thus unaccounted for in oven size determination.
Pumps and Electric Motors
The purchase cost for centrifugal pumps was calculated using Equation A.1 (Seider et al., 2009).
(A.1)
74 FT is the pump-type factor and FM is the material factor. The base cost is shown below in Equation A.2, where S is the size factor (Seider et al., 2009).
(A.2)
The size factor is determined using equation A.3, where Q is the flow rate in gallons per minute (GPM) and pump head (H) in feet (Seider et al., 2009).
(A.3)
The pump head is calculated by using Equation A.4, where ρ is the liquid density of the fluid (Seider et al., 2009).
(A.4)
The purchase cost for electric motors is calculated through Equation A.5 (Seider et al., 2009).
(A.5)
FT is the motor-type factor and CB is given in Equation A.6, where PC is the power consumption in horsepower (PC), which is given by Equation A.7 (Seider et al., 2009).
(A.6)
(A.7)
The pump brake horsepower, PB, is given by Equation A.8 (Seider et al., 2009).
(A.8)
The efficiency of the electric motor, ηM, is given by Equation A.9 (Seider et al., 2009).
(A.9) Example pump calculation for water
First, the pump head is calculated by finding the rise in pressure in the water. This pressure rise was determined based on a heuristic. Based on Seider et al., 2009, a pressure rises
75 requires a change of 2 psi for 100 ft of piping and a control valve pressure drop of at least 10 psi.
Therefore, it was assumed that the water would be pumped over, at most, 200 ft in the plant.
Based on a liquid density of 62.43 lb/ft3 for water at room temperature (298 K), Equation A.4 was applied to a calculate H.
Next, the size factor was calculated using Equation A.3. However, Equation A.3 is limited to flow rates of 50 gallons per minute and all water consumption requirements were restricted to less than 50 gallons per minute. Therefore, the calculated size factor was based on a flow rate of 50.0 gallons per minute.
= 8.80
The base cost is calculated using the size factor using Equation A.2.
Using the CB, the CP is calculated using Equation A.5. The FM is 1 and the FT is 1 using Table 22.20 and 22.21 from Seider et al., 2009.
The CBM is calculated using an FBM of 3.3 (Seider et al., 2009).
The CBM,motor of the electric motor needs to be added to the CBM,pump of the pump for the total CBM. The efficiency of the motor is calculated using Equation A.9 using a PB of 7.35 hp.
The power consumption is calculated using Equation A.7.
76 Using this PC, the CB is solved using Equation A.6.
The purchase cost is then calculated using Equation A.5 and an FT of 1 (Seider et al., 2009).
Once again, a FBM of 3.30 is used to calculate the CBM,motor.
Total CBM is the addition of both the pump and motor bare module costs.
All 17 pumps are calculated using this method yielding a total of $4,538,870 for all the pumps and their backups.
77
Appendix B: Spreadsheets See D2L for relevant spreadsheets.
78
79
Appendix C: Overall Mass Balance
Figure 4: Overall mass balance
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Appendix D: Web Printouts
Figure 5: CE Cost Index for February 2012
81 Figure 6: N2 pricing information
82
Appendix E: Logs
See D2L for meeting minutes.