A thermal process within a facility rejects 10,000 lbm/hr of hot water (T_out = 190°F). An energy audit of the facility revealed that instead of using an open water system, which feeds fresh cold water (T_in = 55°F) to the boiler, a closed-loop water system can be set up (with a total cost of $90,000) to reuse the hot water wasted by the facility at the end of the thermal process, as depicted in the sketch below. Determine the simple payback period for the closed-loop installation if the cost of fuel is $6/MMBtu and the boiler efficiency is 80 percent. Assume that the facility is operated 4,000 hours per year.

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Tin = 55F Boiler Facility . Closed loop system SOLUTION First the annual fuel savings is estimated based on the energy saved by using water at Tout = 190F rather than Tin = 55F: Tout = 190F mcp (Tout-Tin) (10,000 lbm/hr) x (1.0 Btu/hr-F)[(190-55) F] AQ 0.80 nb = 1687 x 106 Btu/hr Then, the total fuel cost savings during one year can be estimated as: AE = AQXN X Cost = 1.687 MMBtu/hr x 4,000hr / year x $6/MMBtu = $40,500/year