### Memorandum

To: Docket EPA
- HQ
- OAR
- 2013
- 0748 From: Gerald Wozniak, Margaret Sheppard, and Dave Godwin

EPA/Stratospheric Protection Division Subject: Derivation of Charge Limits for Room Air Conditioners Date: May 2 7 , 2014 This document describes how EPA derived the refrigerant charge limits for room air conditioners and heat pumps proposed in “Protection of Stratospheric Ozone: Listing of Substitutes for Refrigeration and Air Conditioning and Revision of the Venting Prohibition for Certain Refrigerant Substitutes.” Source documents for calculations These charge limits are based upon calculations from formulas in Underwriters L aboratories (UL) standard 484, Room Air Conditioners . The formulas in Appendix F of the UL 484 standard in turn are based upon the international industry standard International Electrotechnical Commission ( IE C ) 60335
- 2
- 40 , “Particular Requirements for Electrical Heat Pumps, Air Conditioners and Dehumidifiers” (2005)
. Kataoka, et al. (2000) first derived these formulas and discussed their technical basis. These formulas are empirically derived, considering molecular mass, lower flammability limit, refrigerant dispersion, leak rates, and the dimensions of the space that refrigerant leaks into. These formulas also were proposed to the IEC SC 61D and International Organization for Standardization (I SO) TC86 SC1 WG1 joint working groups to assist in setting standards for using flammable refrigerants in air conditioning equipment and dehumidifiers (Kataoka et al., 2000). Formula used to establish limits The formula from appendix F of UL484 (section 1.6) , “Requirements for Charge Limits,” is for appliances with charge amounts m1 < M < m2 , where M is the refrigerant charge amount in appliance in kg, m1 is 4m 3 

### x the lower flammability limit (LFL) in kg/m 3 

### , and m2 is 26m 3 

### x LFL. The formula for the maximum allowable charge size is as follows:

### = 2 . 5 ( ) h √

Where, mmax 

### = the maximum allowable charge size allowed for the space, in kg, LF L = the lower flammability limit of the refrigerant in kg/m 3 

### , h 0 

### = the installation height of the indoor unit in m (0.6 m for an air conditioning (AC ) unit on the floor, 1.0 m for an AC unit in a window, 1.8 m for a wall
- mounted AC unit, and 2.2 m for a ceiling
- mounted AC unit) A = the area of the room, in m2 

### The formulas are based upon the conservative assumption that the ceiling of the room is 2.2 m ( 8 ft) high. The formulas are designed to prevent exceedance of 25% of the LFL. EPA used the following methodology to derive the maximum allowable charge limits by means of the aforementioned equation. This approach included examining the charge limit with respect to the LFLs of different refrigerants, while taking into consideration variables such as the installation height (h 0 

### ) of the AC unit and the area of the room
. Source of values in the formula for maximum allowable charge size Lower Flammability Limit (LFL) values EPA used the following information in calculating the lower flammability limit on the basis of mass per unit volume (kg/m 3 

### ), abbreviated LFLm 

### . Refrigerant designation IUPAC chemical

name or blend composition Molar mass (kg/kmol) LF Lm 

### in

kg/m 3 

### LF Lv 

### in %

v/v R
- 290 Propane 44.1 0.038 2.1% R
- 32 Difluoromethane 52 0.306 14.4% R
- 441A 290/600/600a/170

(60/30/5/5) 48.44 0.041 2.05% For R
- 290 and R
- 32, the LFLm 

### values are listed in Appendix B of UL 484. For R
- 441A, EPA used the LFL as a percentage of volume per volume from A.S. Trust & Holdings’ SNAP submission (2.05%) and calculated the LFLm 

### from the LFLv 

### using the following formula: LF Lm 

### = (MM/24.4) x LFLv 

### x 1000 Where, LF Lm 

### = lower flammability limit in kg/m 3 

### (0.041), MM = molecular mass in kg/mol (0.04844) , LF Lv 

### = lower flammability limit as a percentage volume (0.0205) , 24.4 = conversion factor, 1 mole of a gas per 24.4 liters at standard temperature (32oF, 0oC) and pressure (1 atmosphere, 101.325 kPa), based on the ideal gas law ,

### 1 000 = conversion factor, 1000 liters per m 3



### Installation Height (h0 

### ) values Appendix F in the UL484 standard sets four installation heights for a unit: 0.6 m for an AC unit on the floor, 1.0 m for an AC unit in a window, 1.8 m for a wall
- mounted AC unit, and 2.2 m for a ceiling
- mounted AC unit . In terms of determining if concentrations are small enough to remain below the LFL if the refrigerant is released, a greater compressor height h 0 

### corresponds with better mixing of the refrigerant throughout a room. For example, a release of refrigerant near the ceiling will be more thoroughl y mixed and there will be lower concentrations than if the same refrigerant charge is released close to the floor. EPA established the tables of proposed cha rge limits with h0 

### values that correspond to the following room air conditioner ty pes:
 

### h 0 

### =0.6 m: packaged terminal air conditioners (PTACs) , packaged terminal heat pumps (PTHPs) , and portable air conditioners (all units on or near floor)  

### h 0 

### = 1. 0 m : window AC units  

### h 0 

### = 1.8 m : wall
- mounted AC unit s  

### h 0 

### =2.2 m : ceiling
- mounted AC unit s

### Correlation of AC unit capacity and room area

After determining the LFLm 

### and installation heights the EPA used approximation of appropriate capacities for cooling a given area. Th e capacities for cooling a given area of a room is based upon the following table from EnergyStar 2014 : **Area To Be Cooled ( ft** **2** 

### ) **Capacity Needed (BTUs /** **hour) 100 up to 150**  5,000 **150 up to 250** 6,000 **250 up to 300** 7,000 **300 up to 350** 8,000 **350 up to 400** 9,000 **400 up to 450** 10,000 **450 up to 550** 12,000 **550 up to 700** 14,000 **700 up to 1,000** 18,000 **1,000 up to 1,200** 21,000 **1,200 up to 1,400** 23,000 **1,400 up to 1,500** 24,000 **1,500 up to 2,000** 30,000 **2,000 up to 2,500** 34,000 EPA used the correlations below in associating capacity with room area . We used a conversion factor of 0.092903 m2

### /ft2



### . EPA established the tables of proposed charge limits with respect to the minimum area required for a maximum charge that correspond to the room air conditioner ty

pe.

### Area To Be Cooled

range ( ft2 

### ) min ( ft2 

### ) max ( ft2 

### ) min (m2 

### ) max (m2 

### ) Capacity (BTU/hr) 100 up to 150 100 150 9. 3 13.9 5,000 150 up to 250 150 250 13.9 23.2 6,000 250 up to 300 250 300 23.2 27. 9 7,000 300 up to 350 300 350 27. 9 32.5 8,000 350 up to 400 350 400 32.5 37. 2 9,000 400 up to 450 400 450 37. 2 41.8 10,000 450 up to 550 450 550 41.8 51. 1 12,000 550 up to 700 550 700 51. 1 65.0 14,000 700 up to 1,000 700 1,000 65.0 92.9 18,000 1,000 up to 1,200 1000 1,200 92.9 111. 4 21,000 1,200 up to 1,400 1200 1,400 111. 5 130. 1 23,000 1,400 up to 1,500 1400 1,500 130. 1 139. 4 24,000 1,500 up to 2,000 1500 2,000 139. 4 185.8 30,000 2,000 up to 2,500 2000 2,500 185.8 232. 3 34,000
Sources of uncertainty in capacity value EPA’s Energy Star program website also suggests some adjustments to capacity to address additional factors that may increase or decrease cooling capacity needed for a room: o 

### If the room is heavil y shaded, reduce cap acity b y 10 percent. o 

### If the room is very

sunny, increase capacity b y 10 percent. o 

### If more than two people regularl y occup y the room, add 600 BTUs for each additional person. o 

### If the unit is used in a kitchen, increase capacity by 4,000 BTUs. The calculations used to derive the charge sizes in EPA’s proposed rule do not adjust for these additional factors.

### Proposed charge limits

Table A below illustrates the maximum design charge sizes (kg) for window air conditioners with an installation height equal to 1m for different cooling capacities
. Table B illustrates the maximum design charge sizes (kg) for PTACs, PTHPs and portable air conditioning units with an installation height equal to 0 .6 m. Table C illustrates the maximum design charge sizes (kg) for wall mounted AC units with an installation height equal to 1.8 m. Table D illustrates the maximum design charge sizes (kg) for ceiling
- mounted AC units with an installation height equal to 2.2m. These tables clearly indicate that charge sizes will slightly incre ase as a result of the installation height of the unit. For example , the charge size of 1.73 kg for R
- 32 in Table A (the lowest installation height) is much smaller than the charge size of 3.82 kg for R
- 32 in Table D (the highest installation height). Itis also important to note that these charge sizes were derived with respect to the minimum room area for a given capacity and thus these calculations are based on a conservative anal ys is . For example, if the maximum room area was considered , it would yield a slightly higher maximum design charge size. The UL standard indicates that the formula used above is for appliances with charge sizes in a given range of m1 and m2. As indicated on page 1 of this memo, m2 is 26 m 3 

### x LFL. Therefore, the calculations of allowable charge size, shown in Tables A through D, must be checked to ensure the values remain below m2
. Although this limit is not reached in Tables A and B, it is reached in Tables C and D ; those values are marked with an asterisk (*). Specificall y, these maximum charge limits will apply and supersede those in the T ables C and D :  In Table E , for R
- 32, for capacities >= 18,000 B TU/hr : 7.9 5 6 kg.  In Table E , for R
- 290 , for capacities = 34,000 B TU/hr : 0.9 88 kg.  In Table E , for R
- 441A , for capacities = 34,000 B TU/hr : 1.0 66 kg.  In Table F , for R
- 32, for capacities >= 12,000 B TU/hr : 7.9 5 6 kg.  In Table F , for R
- 290 , for capacities >= 24,000 B TU/hr : 0.9 88 kg.  In Table F , for R
- 441A , for capacities >= 23,000 B TU/hr : 1.0 66 kg. In corporating these results, Tables E and F present the maximum charge size limits for wall
mounted and ceiling
- mounted room air conditioners, respectivel y.

### The proposed charge limits are stated below in Tables A, B, E and F
. (Values published in the notice of proposed rulemaking are rounded to

the nearest tenth of a kilogram, rather than the nearest gram.) Table A
. Maximum Design Charge Sizes for Window Air Conditioners Refrigerant **Maximum design charge size (kg)** Associated cooling capacity (BTU/hr) 5,000 6,000 7,000 8,000 9,000 10,000 12,000 14,000 18,000 21,000 23,000 24,000 30,000 34,000 R
- 32 1.734 2.124 2.742 3.004 3.244 3.468 3.679 4.067 4.588 5.484 6.008 6.489 6.717 7.756 R
- 290 0.128 0.157 0.202 0.221 0.239 0.256 0.271 0.300 0.338 0.404 0.443 0.478 0.495 0.572 R
-441A 0.141 0.172 0.222 0.243 0.263 0.281 0.298 0.330 0.372 0.445 0.487 0.526 0.544 0.629 Note: For use with self

- contained air conditioning units or heat pumps with an evaporator at least 0.6 and no more than 1.0 m above the floor. (Assumes h0 =1.0 m) Cooling capacities between those in the table are to be linearly interpolated between the next smaller and larger capacities listed in the table.



### Table B. Maximum Design Charge Sizes for Packaged Terminal Air Conditioners, Packaged Terminal Heat Pumps, and Portable Air Conditioning Units Refrigerant **Maximum design charge size (kg)** Associated cooling capacity (BTU/hr) 5,000 6,000 7,000 8,000 9,000 10,000 12,000 14,000 18,000 21,000 23,000 24,000 30,000 34,000 R
- 32 1.041 1.274 1.645 1.802 1.947 2.081 2.207 2.440 2.753 3.290 3.605 3.893 4.030 4.653 R
- 290 0.077 0.094 0.121 0.133 0.144 0.153 0.163 0.180 0.203 0.243 0.266 0.287 0.297 0.343 R
-441A 0.084 0.103 0.133 0.146 0.158 0.169 0.179 0.198 0.223 0.267 0.292 0.316 0.327 0.377 Note: For use with self

- contained air conditioning units or heat pumps with an evaporator no more than 0.6 m above the floor. (Assumes h0 =0.6 m) Cooling capacities between those in the table are to be linearly interpolated between the next smaller and larger capacities listed in the table.

### Table C. Derived Maximum Design Charge Sizes for Wall
- Mounted AC Units

Refrigerant **Maximum design charge size (kg)** Associated cooling capacity (BTU/hr) 5,000 6,000 7,000 8,000 9,000 10,000 12,000 14,000 18,000 21,000 23,000 24,000 30,000 34,000 R
- 32 3.122 3.823 4.936 5.407 5.840 6.243 6.622 7.321 8.259 * 9.871 * 10.814 * 11.680 * 12.090 * 13.960 * R
- 290 0.230 0.282 0.364 0.399 0.431 0.460 0.488 0.540 0.609 0.728 0.797 0.861 0.891 1.029 * R
-441A 0.253 0.310 0.400 0.438 0.473 0.506 0.537 0.593 0.670 0.800 0.877 0.947 0.980 1.132 *

Note: For use with self

- contained air conditioners or heat pumps with an evaporator at least 1.0 and no more than 1.8 m above the floor. (Assumes h0=1.8 m) Cooling capacities between those in the table are to be linearly interpolated between the next smaller and larger capacities listed in the table. See Table E for maximum charge sizes for those above marked with an asterisk (*).



### Table D. Derived Maximum Design Charge Sizes for Ceil ing
- Mounted AC Units: Refrigerant **Maximum Design Charge Size (kg)**  Associated capacity (BTU/hr) 5,00 0 6,000 7,000 8,000 9,000 10,000 12,000 14,000 18,000 21,000 23,000 24,000 30,000 34,000 R
- 32 3.8 1

5 4.67 3 6.03 3 6.608 7.138 7.63 1 8.09 3 * 8.948 * 10.09 4 * 12.065

* 13.217

* 14.276

* 14.777

* 17.06 3 * R
- 290 0.28

1 0.34 4 0.44 5 0.4 87 0.5 26 0.56 3 0. 597 0.66 0 0.74 4 0.8 8 9 0.97 4 1.05 2 * 1.0 8 9 * 1.2 58 * R
-441A 0.30

9 0.3 79 0.4 8 9 0.5 36 0.5 79 0 .619 0.656 0.725 0.818 0.9 7 8 1.07 1 * 1.157 * 1. 198 * 1.38 3 * Note: For use with self

- contained air conditioners or heat pumps with an evaporator more than 1.8 m above the floor. (Assumes h0=2.2 m) Cooling capacities between those in the table are to be linearly interpolated between the next smaller and larger capacities listed in the table. See Table F for maximum charge sizes for those above marked with an asterisk (*).

### Table E . Maximum Design Charge Sizes for Wall
- Mounted AC Units

Refrigerant **Maximum design charge size (kg)** Associated cooling capacity (BTU/hr) 5,000 6,000 7,000 8,000 9,000 10,000 12,000 14,000 18,000 21,000 23,000 24,000 30,000 34,000 R
- 32 3.122 3.823 4.936 5.407 5.840 6.243 6.622 7.321 7.956 7.956 7.956 7.956 7.956 7.956 R
- 290 0.230 0.282 0.364 0.399 0.431 0.460 0.488 0.540 0.609 0.728 0.797 0.861 0.891 0 .9 88 R
-441A 0.253 0.310 0.400 0.438 0.473 0.506 0.537 0.593 0.670 0.800 0.877 0.947 0.980 1. 066

Note: For use with self

- contained air conditioners or heat pumps with an evaporator at least 1.0 and no more than 1.8 m above the floor. (Assumes h0=1.8 m) Cooling capacities between those in the table are to be linearly interpolated between the next smal ler and larger capacities listed in the table. 

### Table F . Maximum Design Charge Siz es for Ceiling
- Mounted AC Unit Refrigerant **Maximum Design Charge Size (kg)**  Associated capacity (BTU/hr) 5,000 6,000 7,000 8,000 9,000 10,000 12,000 14,000 18,000 21,000 23,000 24,000 30,000 34,000 R
- 32 3.8 15 4.67 3 6.03 3 6.608 7.138 7.63 1 7.956 7.956 7.956 7.956 7.956 7.956 7.956 7.956 R
- 290 0.28 1 0.34 4 0.44 5 0.4 87 0.5 26 0.56 3 0. 597 0.66 0 0.74 4 0.8 8 9 0.97 4 0 .9 88 0 .9 88 0 .9 88 R
-441A 0.309 0.3 79 0.4 8 9 0.5 36 0.5 79 0 .619 0.656 0.725 0.818 0.9 7 8 1. 066 1. 066 1. 066 1. 066 Note: For use with self

- contained air conditioners or heat pumps with an evaporator more than 1.8 m above the floor. (Assumes h0=2.2 m) Cooling capacities between those in the table are to be linearly interpolated between the next smaller and larger capacities listed in the table.

### Conversion to English units of measure For the readers’ information, we provide the same maximum design charge sizes as above converted to ounces, using the conversion factor 35.274 oz/kg. **Maximum Design Charge Sizes in**  **Ounces f**  **or Window Units Capacity (BTU/hr)**  **Refrigerant 5**  **,000 6**  **,000 7**  **,000 8**  **,000 9**  **,000 1**  **,000 0**  **12 ,000**  **14 ,000**  **18 ,000**  **21 ,000**  **23 ,000**  **24 ,000**  **3 ,000**  **0 34**  **,000** R
- 32 61 .17 74.92 96.72 105.96 114 .44 122 .35 129.77 143 .46 161.85 193 .45 211.91 228.89 236.92 273.57 R
- 290 4.51 5.52 7 .13 7.81 8 .44 9 .02 9.57 10.58 11.93 14 .26 15.62 16.87 17 .47 20 .17 R
-441A 5 .26 6 .45 8 .32 9 .12 9 .85 10 .53 11 .16 12 .34 13 .92 16 .64 18.23 19 .69 20.38 2 3.54 

### Maximum Design Charge Sizes **in Ounces**  

### for PTACs/PTHPs **Capacity (BTU/hr) Refrigerant**  **5 ,000**  **6 ,000**  **7 ,000**  **8 ,000**  **9 ,000**  **1 ,000**  **0 12**  **,000 14**  **,000 18**  **,000 21**  **,000 23**  **,000 24**  **,000 3**  **,000 0**  **34 ,000**  **R -**  **32** 36.70 44.95 58.03 63.57 68.67 73.41 77.86 86.08 97.11 116.07 127.15 137.33 142.15 164.14 **R -**  **290** 2.71 3.31 4.28 4.69 5.06 5.41 5.74 6.35 7.16 8.56 9.37 10.12 10.48 12.10 **R -**  **441A** 3.16 3.87 4.99 5.47 5.91 6.32 6.70 7.41 8.35 9.99 10.94 11.82 12.23 14.12

### Maximum Design Charge Sizes **in Ounces**  **for Wall** **- Mounted Units**  **Refrigerant** 

### Capacity (BTU/hr) **5 ,000**  **6 ,000**  **7 ,000**  **8 ,000**  **9 ,000**  **1 ,000**  **0 12**  **,000 14**  **,000 18**  **,000 21**  **,000 23**  **,000 24**  **,000 3**  **,000 0**  **34 ,000**  **R -**  **32** 110.11 134.86 174.10 190.72 206.00 220.22 233.58 258.23 280.64 280.64 280.64 280.64 280.64 280.64 **R -**  **290** 8.12 9.94 12.83 14.06 15.19 16.23 17.22 19.04 21.48 25.67 28.12 30.37 31.44 34.85 **R -**  **441A** 8.93 10.93 14.11 15.46 16.70 17.85 18.94 20.93 23.62 28.23 30.92 33.40 34.57 37.60 

### Maximum Design Charge Sizes **in Ounces**  **for Ceiling Mounted Units**  **Capacity (BTU/hr) Refrigerant**  **5 ,000**  **6 ,000**  **7 ,000**  **8 ,000**  **9 ,000**  **1 ,000**  **0 12**  **,000 14**  **,000 18**  **,000 21**  **,000 23**  **,000 24**  **,000 3**  **,000 0**  **34 ,000**  **R -**  **32** 134.58 164.83 212.79 233.10 251.78 269.16 280.64 280.64 280.64 280.64 280.64 280.64 280.64 280.64 **R -**  **290** 9.92 12.15 15.69 17.18 18.56 19.84 21.05 23.27 26.25 31.37 34.37 34.85 34.85 34.85 **R -**  **441A** 10.91 13.36 17.25 18.90 20.41 21.82 23.14 25.59 28.86 34.50 37.60 37.60 37.60 37.60

### References

Energy Star, “Properl y Sized Room Air Conditioners.” Available at http://www.energystar.gov/?c=roomac.pr_properl y_sized ; accessed May 8, 2014. IEC 60335
- 2
- 40, “Particular Requirements for Electrical Heat Pumps, Air Conditioners and Dehumidifiers
. ” 2005
. Kataoka, O., Yoshizawa, M. and Hirakawa, T. 2000. Allowable charge calculation method for flammable refrigerants. International Refrigeration and Air Conditioning Conference, Purdue University, West Lafayette IN , USA. 2000. Available online at http://docs. lib.purdue.edu/cgi/viewcontent.cgi?article=1505&context=iracc UL484, Room Air Conditioners. Appendix F, “Requirements for Charge Limits.” 8 th 

### Edition. August 2012.