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CHILLER SIZING Introduction After a technical review, a company has decided that a chiller is required for the molding operations. The next, more difficult, step is how much chiller is needed for my operations. • If they select too small a chiller, the undersized unit will never cool the processing equipment – creating bad parts. • They can choose too large a chiller, allowing for future expansion. However, the company could be paying for capacity that will never be used. Because of these issues, sizing a chiller to slightly exceed the capacity requirements is the most cost effective option. To facilitate this choice, we recommend the following calculations for providing data to the decision-making process. In addition, utilizing more than one formula to “cross-check” operations is recommended. Concepts and Definitions The first law of thermodynamics says that the total quantity of energy in the universe remains constant. This is the principle of the conservation of energy. This first principle considers heat and energy as two magnitudes of the same physical nature.1 Keeping the quantity of energy (heat) in our universe as a constant means: HEAT IN = HEAT OUT The HEAT IN part of the equation can come from a variety of sources, most commonly: Cartridge heaters Heater bands Circulators/hot water Plastic melt stream 1 J. DeRosnay (July 3, 1998): "Entropy and the Laws of Thermodynamics", in: F. Heylighen, C. Joslyn and V. Turchin (editors): Principia Cybernetica Web (Principia Cybernetica, Brussels), URL: http://pcp.lanl.gov/ENTRTHER.html . G.Hise, author January, 2007 J. Cavanaugh, editor CHILLER SIZING The HEAT OUT part of the equation is primarily a chiller. Some heat is lost by natural conditions such as being emitted into the ambient air. Systems where it is not desirable to lose heat (energy) to the surrounding air use some form of insulation. For the purposes of this training, the universe can be defined simply as a Plastic Processing Apparatus that has some form of heat source and is being cooled by an IMS Chiller. Here is a simple schematic: The arrow shows flow of the heat transfer fluid which is typically a mixture of ethylene glycol and water. Optimum heat transfer is commonly 25% glycol by volume. Propylene glycol can also be used. The Plastic Processing Apparatus can be any number of physical items. Some of the most common are: an injection mold an extrusion die an extrusion cooling tank To accurately size the chiller using the above definitions and principles, you can see that it is necessary to define (and ideally measure) all sources of heat going IN or OUT of the process. With this understanding, we can now discuss some common ways to approach chiller sizing. G.Hise, author January, 2007 J. Cavanaugh, editor CHILLER SIZING Chiller Sizing Method #1 Based on Resin usage. The IMS Company Catalog contains a formula that can be used to size a chiller on an injection molding process. The formula and description are as follows: Tonnage = A x ( B – C ) Removal Capacity where: A=Material Use in lbs./hr B=Temperature of Melt C=Temperature of part when it comes out of mold Removal Capacity=12,000 BTU/hr./ton removal capacity of chiller system set at 50˚F, which includes estimated radiation losses, etc. At 40˚F, use 8,000. At 30˚F, use 6,100. At 20˚F, use 5,800. Always round up. Example: 100 lbs./hr processes (not the machine rating) 450˚F melt temperature 150˚F part temperature when mold opens Tonnage = 100 x ( 450 – 150) = 100 x 300 12,000 12,000 = 30,000 / 12,000 = 2.5 Round up to the next size: 3 Ton Here is the process model that forms the basis of this sizing formula: Heat is transferred from the melt to the mold as it flows into and resides in the mold cavity. The formula assumes that this is the only transfer of heat out of the plastic and is the sole reason that the temperature of the part is less than the temperature of the melt. Heat is transferred from the mold to the cooling water that circulates from the chiller. The formula assumes that this is the only transfer of heat out of the mold. The calculated cooling capacity (chiller size in Tons) is the measure of the amount of heat given off to the mold by the plastic that must be carried away by the cooling water. Once back in the chiller, this heat is removed from the water, via a heat exchanger, and can re-circulate as chilled water. The large G.Hise, author January, 2007 J. Cavanaugh, editor CHILLER SIZING tank in the chiller acts as a reservoir to spread out the load on the refrigeration system (meaning the heat exchange in the chiller does not have to match the rate of heat exchange at the mold). For best results with this formula, these considerations must be evaluated: The process must be similar to the drawing above. Likely, this will be an injection molding process. You must know intended chilled water temperature set point that the molder will use because it greatly affects the formula (the Removal Capacity). The colder the water temperature that will be maintained, the larger the calculated chiller size will be. The temperature of the plastic part should be taken immediately when it falls from the mold. A delay allows the part to cool. This can actually cause the chiller sizing to be too high (the B-C number will be larger than actual). Chiller Sizing Method #2 Method to be used when replacing an existing cooling system. Anyone who has reviewed the chiller literature may have seen this general formula: BTU = Constant (weight of water) x GPM x Temperature Differential Example: 500 Constant (weight of water) x 10 GPM (gallons per minute) = 5000 x 12˚ temperature differential = 60,000 Required BTU/hr Divide by 12,000 (each 12,000 BTU requires 1 Ton of cooling) = 5 Ton Here is the schematic that applies to this formula. Notice this is the same basic drawing used to define our terms earlier in the article. This should give you a sense that this formula is much more general and universally applied than the previous published formulas. One fact should stand out and it is the primary reason why this formula cannot be used exclusively, that is, this formula depends upon the process already having circulating cooling water that can be measured. This may be a portable chiller, a central chiller, water from a well, water from a cooling tower, or any other source of cool water. If the process is new or for some other reason does not already have cooling going on, then some other formula must be used. G.Hise, author January, 2007 J. Cavanaugh, editor CHILLER SIZING If the cooling that you measured is adequate and represents the same job (heat removal) that you wish the new chiller (that you are sizing) to do, then you are done. Your answer is the required chiller size. Suppose a circulating cooling line is in place, but it is not adequate. For example, suppose you need the process cooled to 200˚F. Water from a cooling tower is flowing through the process and keeping it at 250˚F. Suppose that without the water from the cooling tower, the process is at 400˚F. Clearly, the existing cooling is providing some heat removal, however if you size the chiller to match that capacity, the chiller will be undersized. If this is an injection molding process, then the IMS formula may work, otherwise it is necessary to take a step back, define the process and take a more general approach explained below. Chiller Sizing Method #3 (THE GENERAL APPROACH) General method usable for any cooling application. Let’s start by saying that if sizing formulas #1 (IMS) and #2 (General) do not apply, then proceed with caution. IMS Technical Support can be contacted at 1-866-467-9001 and would be delighted to help you size the chiller appropriately. If you are not handing this off, then proceed as follows: ASK QUESTIONS There is much about the process that you will need to know. If you are speaking with someone at the process that cannot answer these questions, then ask them to please put you in contact with someone that can answer. An undersized chiller will fail and IMS will not cover the replacement cost if we are not given an opportunity to help size it properly. WRITE DOWN EVERYTHING There will be many numbers to remember. By making good notes, you can be sure that everything is defined. MAKE A SKETCH OF THE PROCESS IF NECESSARY A diagram, such as those shown in this paper, that show all HEAT IN and HEAT OUT of the process, is critical. You can represent the process as a block. Whether the process is an injection mold, an extrusion die, or anything else does not change the need to identify anything that is adding heat (heaters, hot plastic, etc.) and anything else taking heat away (ambient air, cooling water, etc.). IDENTIFY THE PROCESS DETAILS While it was acceptable to show the process as a block in the above sketch, there may still be a need to define it. If it is a mold, then you commonly need to know overall dimensions and the material from which it is constructed. The same thing applies to an extrusion die. If the process is a cooling tank on an extrusion line, then the tank dimensions are needed along with the water volume, flow in, and flow out. If any heaters are present, you need wattages. Once the process is defined, and all HEAT IN and HEAT OUT are measured or calculated, then the chiller can be sized. Following are some examples of actual chiller sizing. In these cases, as with almost all chiller sizing, the calculated chiller size based upon heat removal needs was larger than originally anticipated. Resist the temptation to size a chiller by looking at list prices in the catalog and comparing it to the budget. Although budgets are a reality, a chiller that is too small can inhibit your process and waste your capital investment. You are making your recommendation based on actual calculated need and have science on your side. G.Hise, author January, 2007 J. Cavanaugh, editor CHILLER SIZING Following are three examples showing a variety of approaches: Example A is injection molding of coat hangers. The chiller cools the injection mold each cycle. Example B is an extrusion line. A spray tank is used to cool extruded pipe. The chiller supplies the spray tank with cool water. Example C is vertical molding using a tank of chilled water to keep the mold cool. The chiller keeps the cooling tank at a constant temperature. EXAMPLE A: Chiller Sizing – General Approach Heat Removal Formula (this is a general formula and is not specific to plastics) BTU = WT X CP X ∆T where, WT = weight of material to be cooled per hour (lbs.) CP = specific heat of material (BTU/lb.-°F) ∆T = temperature decrease (°F) Customer Provided Information 12 cavities, each one hanger of 27.36 grams, one runner is 6.66 grams. So each mold cycle is (12 x 27.36) + 6.66 = 334.98 grams 334.98 grams x 0.002205 pounds/gram = .74 pounds of plastic per cycle Each cycle is 15 seconds. There are 3600 seconds in an hour. So, 15 seconds is 3600/15 = 240 cycles per hour. 0.74 lbs./cycle x 240 cycle/hour = 177.6 pounds/hour = WT One plastic used is polystyrene. Polystyrene has a specific heat in the range of 0.299-0.406 BTU/lb.-°F Let’s use the center of the range. CP = 0.35 BTU/lb.-°F The material enters at 500-600 °F . The mold temperature is 120 °F. Using a melt temperature for polystyrene of 360-530°F, we can estimate ∆T = 530 – 360 = 170 °F Calculation Getting back to the formula: BTU = 177.6 x 0.35 x 170 = 10,567.2 = 0.88 Ton This number does not contain any error for heating of the cooling water due to summer ambient temperatures, friction from flowing through the plumbing, or any variations in material temperature, weight, or specific heat. Generally accepted practice is to allow 20% margin of error to account for these factors which are difficult to measure. Adding a 20% cushion to the above heat removal calculation would yield a chiller size of 1 Ton for each press running this process. G.Hise, author January, 2007 J. Cavanaugh, editor CHILLER SIZING EXAMPLE B: Chiller Sizing – General Approach PROCESS INFORMATION ON THE SIZER incoming water temp: 65°F water temp upon exit: 70.5°F spray nozzles in use: 140 max water flow each nozzle: 1.35 gal/min incoming water pipe: qty.2 – 1.5 inch lines length of cooling chamber: 240 inches schedule 40 PVC pipe, 4.25OD, 4.00 ID (also run schedule 80) processing speed: 2000 pounds/hr melt temp: 320°F die temp: 380°F pipe temp upon exiting the die: 360°F pipe temp upon exiting the cooling chamber: 113°F specific heat of plasticized PVC: 0.30 density: 87.4 pounds/foot3 thermal conductivity: 1.11 BTU-in/hr-ft2-°F CHILLER REQUIREMENTS 45-50°F water out 50-60°F tower water coming in 480VAC incoming power air-cooled optional filter on incoming water CHILLER SIZING CALCULATION kW = [WT X CP X ∆T] / [3412 X H] where WT = weight of material to be cooled (lbs.) CP = specific heat ∆T = temperature decrease (°F) H = cooling time (hours) Using one cooling chamber length of material: WT = 240 in X π X [(4.25in)2 – (4in)2] X 87.4 lbs/ft3 X 1ft3/1728 in3 = 78.65 lbs (78.65 lbs) / (240 in) = 0.3277 lb/in (2000 lb/hr) X (1in / 0.3277 lb) = 6102.65 in/hr H=(240 in) / (6102.65 in/hr) = 0.0393 hr ∆T = 360°F - 113°F = 247°F CP = 0.30 So, kW = (78.65 x 0.30 x 247) / (3412 x 0.0393) = 43.46 kW 43.46kW x 3414.99 BTU/hr-kW = 148,415 BTU/hr (148,415 BTU/hr) / (12,000 BTU/hr/ton) = 12.4 Ton closest size is 15 ton. Recommend 15 Ton Chiller. G.Hise, author January, 2007 J. Cavanaugh, editor CHILLER SIZING Suppose you cannot afford a 15 Ton chiller. To get the chilling requirements down to 10 Ton, the next smaller size and price point, you could slow down the processing speed, hurting production and cutting profits, or not cool the pipe down as much provided you can still hold the dimensional tolerances and handle it. Better yet, you can use the full 15 Ton chiller, speed up the line, thereby increasing production and profits and making the chiller a great return on investment. EXAMPLE C: Chiller Sizing – General Approach Following is two sizing calculations for the same process. The calculated sizes are similar, but not identical. The second approach is the IMS formula. Neither of these calculations is exact, but this allows you to see how they compare in their approximations. Ultimately, use the larger of the two. Chiller Sizing – Method One (based upon cooling water information) For Water in Tanks: kW = Volume (gal) x ∆T (°F) 325 x Heat-Up Time (hrs) Given: Tank = 20 gallons ∆T = 130°F - 80°F = 50°F Heat-Up Time = 1 hour kW = (20 x 50) / (325 x 1) = 3.08 kW Converting kW to BTU/hr: 3080 W x 3.4129 = 10,512 BTU/hr 10,512 BTU/hr / 12,000 BTU/hr/ton = 0.876 Ton Closest Chiller Size is 1-Ton Chiller Chiller Sizing – Method Two (based upon processed plastic information) Tonnage = A x (B – C) Removal Capacity Where: A = material usage (lbs/hr) B = temperature of the melt (°F) C = temperature of the part after cooling (°F) Removal Capacity = 12,000 BTU/hr/ton with chiller set at 50°F (use 8,000 if set at 40°F) Given: A = 40 lbs/hr polyethylene B = 400°F tool temp; close to melt temp C = 80°F; part near ambient for ease of handling G.Hise, author January, 2007 J. Cavanaugh, editor CHILLER SIZING Tonnage = 40 x (400 – 80) = 1.07 Ton 12,000 Closest Chiller Size is 1½-Ton Chiller G.Hise, author January, 2007 J. Cavanaugh, editor