We will now present a detailed cost analysis which explains why freeze drying allows considerable savings compared to supercritical drying, which is the only other drying method capable of yielding aerogel monoliths. The cost estimate refers to the production of insulation boards, 1ft2, 1 in. thick. This sample size was chosen because estimates exist for the production of this type of sample by supercritical drying [10]. The estimate is based on the criteria reported in Ref. [1] and can be broken down in energy costs, personnel costs, and financial costs. Using very conservative assumptions, we will show that freeze drying allows to save about 40% of the cost, compared to supercritical drying. The cost savings are due for the most part to the higher capacity and lower cost of a freeze dryer compared to a supercritical dryer. Note that the estimate scales with the thickness of the boards.
Mass of Silica and Solvent. For thermal insulation purposes, estimates by Pekala and Hrubesh [2] show that the optimal density of aerogels should be around 0.1 g/cm3. Thus, the polymer weight of a 1ft2, 1 in. thick panel (volume V = 2360 cm3) is 0.236 kg. To calculate the weight of the solvent, we assume a porosity Π around 90%, which is typical for aerogels. Using t-butanol as a solvent, (density d = 0.775 g/cm3), the weight of the solvent is V x d x Π = 1.646 kg.
Raw material costs. For t-butanol, bulk retail prices are of about $11/kg, and for isocyanates and polyols, about $3/kg. (bona fide quotes from Fisher Scientific for 1,000 kg batches. Higher amounts will command lower prices, so this has to be considered a conservative estimate). Assuming a 90% synthesis efficiency for the polymer and 10% solvent loss during freeze drying, the raw material costs are of CRaw = 0.236 x 3 /0.9 + 1.646 x 11 x 1 = $2.6/board.
Energy costs (refrigeration-sublimation-condensation-evacuation). We assume to freeze a board starting from 300C (slightly above the melting point of t-butanol) to -300C, which is the typical freezing temperature that we are using to freeze dry aerogel monoliths. This process will require cooling of the liquid from 30 to 240C (which is the freezing temperature of t-butanol), cooling of the solid from 24 to -300C and removal of the enthalpy of fusion of t-butanol (DHf = 6.7 kJ/mol). Using tabulated values [6] for the specific heats of liquid t-butanol (cp,l = 220 J/(mol K)), of solid t-butanol (cp,s= 146.11 J/(mol K)), of silica (cp = 1.8 J/(gram K)), the weight fractions as calculated above, the energy Ef to be removed during freezing is given by: Ef = m(butanol) x cp,l x (30 – 24) + m(butanol) x cp,s x (25+30) + m(butanol) x DHf + m(silica) x cp x (30+30) = 380 kJ/board. To this energy, one needs to add the energy necessary to condense the vapors. Assuming a condenser operating at -300C which cools t-butanol vapor at a temperature of 250C, and using the tabulated value of the enthalpy of vaporization (DHv = 51 kJ/mol), the condensation energy Ec is Ec = m(butanol) x cp,s x (25+30) + m(butanol) x DHv = 1398 kJ/board. Thus, the total energy to be provided by the refrigerator is Ef + Ec = 1778 kJ/board. For an ammonia refrigerator operating between +30 and -300C, typical coefficient of performance values are of 1.6, thus the total energy required for refrigeration is Er = 1111 kJ/board. Additional energy Eh is necessary to provide the heat of sublimation and to heat the board from -300C to room temperature (250C). Using the values for heat capacities and enthalpy of vaporization reported above, one obtains Eh = 1580 kJ/board. The energy required by the vacuum system is on the order of 0.36 kWh per kg of solvent [1]; thus, the energy consumption is 0.36 x 1.756 = 2132 kJ/board. It is customary to allow an increase to the utilities cost of 20% in order to cover thermal losses and other charges. With this 20% correction, the total energy required by the process is of (2132+1580+1111) x 1.2 = 5787 kJ/board. The median energy price in the US is 12c/kWh, therefore the total energy cost is CE = $0.2/board. This estimate is in line with data reported by manufacturers. For example, Cuddon, Inc. [7] reports an energy consumption of 2.2 kWh/kg for a 1500 kg ice capacity dryer. For a 1,500 kg batch producing 850 boards and an energy cost of $0.12/kWh, the energy cost would amount to $0.46/board. The difference between our estimate and the manufacturer's data is due to the different solvent. Industrial freeze drying is water-based, and water has a specific heat and sublimation enthalpy about 5 times higher than those of t-butanol. We not that this estimate is probably very conservative. In our experience, there is no need to refrigerate samples below 00C. We assumed to refrigerate to -30 0C, which increases costs by about 40%.
Capacity. A typical freeze dryer has a capacity of 1500 kg, which corresponds to the solvent contained in 850 boards. The cycle time for water is estimated to be around 15 hours [8], thus the hourly capacity of a dryer is 100 kg/hour, or 57 boards/hour. Assuming a 20 hours/day operating time and 250 days/year of operation, the yearly capacity of such a freeze dryer is 250 x 20 x (hourly capacity) = 2.85 x 105 boards/year. To minimize labor costs, a minimum of 3 dryers is required, see also below. Thus, the total plant capacity is 171 boards/hour, or 8.55 x 105 boards/year. We note that the plant capacity is likely to be about 10 times higher for t-butanol than for water. T-butanol has a pressure at the triple point which is about 100 times higher than water, and this translates in a sublimation rate 5 to 10 times higher than that of water [11,12]. Thus, the capacity of a t-butanol-based plant will be at least 5 times higher than that of a plant operating with water. This higher capacity will lower labor and financial costs also by about a factor 5. Since we are interested in a conservative estimate, use here capacities calculated for water sublimation.
Labor. We assume to have three technicians working on the process. One for chemical reparation and two for the freeze drying process, working in shifts. For this type of entry-level jobs, the average salary is y = $15/hour. The costs are estimated to increase to 2y per hour to over operating supplies, supervision, payroll overhead, plant overhead and process control. The average labor cost per kilogram ice is then ($2y)24/20 x (plant throughput per hour) [1]. Using the capacities reported in the previous section, we obtain a labor cost CL = $0.63/board.
Financial (fixed) costs. For freeze drying, typical assumptions are a depreciation of 7.5% per year and loan charges of 8% per year. Thus, the financial charges amount to $0.149 per $ borrowed [1]. The cost of one freeze dryer with a capacity of 1500 kg is $1.5M (installed) [9]. For 3 dryers, one would need a 4.5 M loan. One should also assume to borrow another $500k for the initial set-up, e.g., purchase of chemicals and other equipment. The total loan amount is then of $5M, which translates into $745k/year for financial charges. Yearly maintenance costs represent about 5% of the equipment cost [1], or about $250k/year. The total financial costs amount to CF =995k/year, or $1.16/board.
Total Cost. The total cost per board is the sum of the raw material costs CRaw, of the energy costs CE, of the labor costs CL and the financial costs CF:
C = Craw + CE + CL + CF = 2.6 + 0.2 + 0.63 + 1.16 = $4.6 for a 1” thick board.
Industrial scale up economical effect: According to Luna Innovations Incorporated (NASDAQ: LUNA) (see https://lunainc.com/advances-nanomanufacturing-scale-up-cost-control/) – the scale up processes and cost optimization using nano-manufacturing can yield cost savings between 70% and 80% for the final product.
In our cost saving calculations, we are considerably more conservative and we are assuming as follows:
Using the earlier formula, the above yields the total cost per board of:
C = Craw + CE + CL + CF = 1.82 + 0.2 + 0.32 + 0.93 = $3.27 for a 1” thick board.
Our estimate shows that freeze drying represents a saving of about 70% over conventional silica aerogel materials (~ $11 for a 1ft2 , 1" thick board [10]). The reason is mostly due to savings in financial costs. Conventionally, aerogels are produced by supercritical drying. This requires high pressure autoclaves, which increase cost because of the need of thick walls and because of liability issues.
[1] A.I. Liapis and R. Bruttini, Freeze Drying. In A. S. Mujumdar, editor Handbook of industrial drying, 4th edition, Chapter 11.
[2] L. W. Hrubesh, and R. W. Pekala, “Thermal properties of organic and inorganic aerogels”, J. Mater. Res. 9, 731-738 (1994).
[3] M. Bertino. L. S. White, “One-step synthesis, cross-linking and freeze drying of aerogels”, invention disclosure BER-15-018, filed Apr. 15, 2015 with VCU's Technology Transfer Office. Provisional patent application filed Aug. 1, 2016.
[4] K. Kanamori, M. Aizawa, K. Nakanishi, T. Hanada, “Elastic organic–inorganic hybrid aerogels and xerogels”, J Sol-Gel Sci Technol (2008) 48, 172–181 DOI: 10.1007/s10971-008-1756-6
[5] Not used.
[6] All data taken from NIST online database: webbook.nist.gov, last accessed March 1, 2017
[7] cuddonfreezedry.com, last accessed March 1, 2017.
[8] Estimates for capacity and drying times follow general guidelines reported by American Lyophilizer, Inc., see also freezedryer.com, last accessed March 1, 2017.
[9] Bona fide quote from Cuddon, Inc. Received Nov. 15, 2015.
[10] http://www.marketsandmarkets.com/Market-Reports/building-insulation-materials-market-510.html
[11] E. Degn Egeberg, J. Engell, “Freeze drying of silica gels prepared from siliciumethoxid”, Journal de Physique Colloques, 1989, 50 (C4), p.C4-23-C4-28. Doi: 10.1051/jphyscol:1989404.jpa-00229479
[12] M. Karel, In Glodblith, S.A., Rey, L. and Rothmayr, W.W. (Eds.): “Freeze drying and advanced food technology”. (Academic Press 1975) 177-202.
