Heat Exchanger Example: Heating Water with Steam using a Modulating Control Valve HEAT EXCHANGER FORMULAS & EXAMPLE
B) What is the mean temperature difference ( ΔT M ) between the steam and the water being heated? From the HX formula we can see that in order to determine the size of the HX required to heat the water, we must first know the steam temperature (which is directly related to steam pressure) in the HX during the period of maximum demand. The steam pressure in the HX is dependent on the pressure drop across the control valve. For optimal control in heating applications, it is typical to target a 50% pressure drop across the valve at the maximum steam load. Therefore, at full load, the pressure drop across the control valve is 50 PSIG and the steam pressure supplied to the heat exchanger is also 50 PSIG. As the steam (primary fluid) passes thru the heat exchanger, it transfers its latent heat energy to the water (secondary fluid) and condenses without a change in temperature. Therefore, the condensate leaving the heat exchanger is at the same temperature as the steam entering. From the saturated steam table, the steam temperature ( T S ) of 50 PSIG saturated steam is 298°F. The water inlet temperature ( T i ) is 50°F and the water outlet temperature ( T o ) is 140°F. We now have enough information to calculate the mean temperature difference between the steam (primary fluid) and water (secondary fluid). Formula 3 is used to calculate the mean temperature difference ( Δ T M ) which is the average of the temperature differences at both ends of the HX: ΔT M = (T S - T o ) + (T S - T i ) = (298 - 140) + (298 - 50) = 158 + 248 = 406 = 203°F 2 2 2 2 C) What is the Overall heat transfer coefficient (U) of the heat exchanger? The U value of the HX depends on several factors, including type of HX, the quality of the steam used, if any fouling is expected, if the flow of water is turbulent or laminar, and the material of construction. The higher the U value, the better the heat transfer, and the smaller the HX needs to be. Typical U values range from 120 for a stainless steel HX to over 200 for copper. For this example, a Stainless Steel HX was selected for longevity purposes and so a U value of 120 will be used to determine the HX size. D) What is the minimum heat transfer surface area (A) of the heat exchanger that can meet the design heat load? The size of a HX is dependent on the steam pressure inside its shell. The higher the steam pressure, the smaller the HX for a given heat load. 50 PSIG was chosen because the supply pressure is 100 PSIG and this gives a 50% pressure drop across the control valve, as previously discussed. If a lower steam pressure is used, this would require a larger HX, and vice versa. In a heat exchanger, the mean heat transfer rate is proportional to the mean temperature difference between the two fluids, as given by Formula 1 . Rearranging this equation gives Formula 2 , where E has been replaced by E D , the design heat load. Using Formula 2 and the mean temperature difference determined above, gives the heat transfer surface area: 120 Btu/(hr-ft 2 -°F) x 203°F Therefore, for a perfectly sized heat exchanger, the heat transfer area of the tube is 185 square feet. In practice, the heat exchanger is usually oversized by at least 15% to account for fouling of the heating surfaces over time or to allow for an increase in the maximum heat load. A = E D = 4,500,000 Btu/hr = 185 ft 2 U Δ T M
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