HEAT EXCHANGER FORMULAS & EXAMPLE Heat Exchanger Example: Heating Water with Steam using a Modulating Control Valve
Basic overview of system: A shell and tube heat exchanger ( HX ) is used to heat 100 GPM of water from 50°F to 140°F using saturated steam at 100 PSIG to the inlet side of the control valve. A modulating control valve, in conjunction with a temperature sensor and electronic controller, is used to regulate the flow of steam into the HX. At the design load of 100 GPM, the valve will supply the HX with 50 PSIG steam. At times of lower demand, the flow rate of water can be reduced to a minimum of 25 GPM. The HX is constructed with stainless steel and has an overall heat transfer coefficient of 120 Btu/(hr-ft 2 -°F). The condensate produced from the condensing steam in the HX will drain thru a float-type steam trap located directly below the exchanger outlet and into a condensate return line with total back pressure of 10 PSIG.
OBJECTIVES: (see Figure 18) 1) Select an appropriately sized HX that will effectively heat water from an estimated start temperature of 50°F to a final temperature of 140°F. The system must operate effectively in the flow rate range of 25 GPM to 100 GPM. 2) Select the appropriately sized Control Valve to effectively deliver steam to the HX. 3) Select the appropriately sized Steam Trap for draining condensate from the HX. The selection is based on steam pressure and condensate load in the HX. 4) Discuss advantages of using a Pumping Trap so the steam system can operate in vacuum during low demand, why a pumping trap may be a necessity if the condensate return line has back pressure or the condensate must be lifted after the HX, and how to select the proper size Pumping Trap.
Heat Exchanger System with Steam Trap at Maximum Load
Figure 18:
Control Valve
100 psig
Vacuum Breaker
Air Vent
50 psig
STEAM
Steam
Temp Sensor
Heat Exchanger
F&T Steam Trap
Hot Water Outlet
Cold Water Inlet
Condensate
HEAT EXCHANGER SIZING The basic formula describing the heat transfer in a heat exchanger is E = U x A x Δ T M , where E (Btu/hr) is the average heat transfer rate, U is the overall heat transfer coefficient, A (ft 2 ) is the heat transfer surface area (size) of the HX and Δ T M is the average temperature difference between the steam and water being heated. A) What is the design heat load (E D ) for this application? The first step in sizing a HX is to calculate the maximum heat load (Btu/hr) required to heat the water. The design heat load ( E D ) of the heat exchanger is the maximum heat load that needs to be transferred by the steam to the water based on the given conditions. The maximum heat load occurs at the maximum water flow, which is 100 GPM. Using Formula 5 : E D = Q w x 500 x C p x Δ T w
= 100 GPM x 500 lbs/hr x 1.0 Btu/(lb-˚F) x (140˚F – 50˚F) 1 GPM
= 50,000 lbs/hr x 1.0 Btu/(lb-˚F) x 90˚F
= 4,500,000 Btu/hr
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