Same as Problem 9.1. If the life of the cogeneration system is 40 years, provide the optimal size of the cogeneration system for the hospital when the average interest rate is 8 percent and the inflation rate is 4 percent.

Problem 9.1

Provide a simple payback analysis for implementing a cogeneration system in a hospital. Assume the following characteristics for the cogeneration system:

• Fuel input rate: 8,000 Btu/kWh

• Heat recovery rate: 4,800 Btu/kWh

• Maintenance cost: $0.02/kWh

• Maximum electrical output: 200 kW, 300 kW, 400 kW, 500 kW, 600 kW, 700 kW, or 800 kW

• Installed equipment cost: $700/kW, $1,000/kW, or $1,500/kW Table 9.8 summarizes the energy usage and cost of the hospital. Assume that the boiler(s) efficiency is 75 percent. The heating value of diesel fuel is 140,000 Btu/gallon. Present the results in one graph: the payback period versus the equipment cost for various equipment sizes.

Table 9.8

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TABLE 9.8 Monthly Energy Demands and Costs for a Hospital Utility Summary Month January February March April May June July August September October November December Total (kWh) 226,400 273,600 280,800 228,000 246,000 301,200 346,800 403,200 303,600 276,000 272,400 276,000 3,434,000 Electricity (kW) 546 572 564 526 692 884 1,040 944 860 872 662 524 2,7020 28,949 25,251 28,755 36,604 45,031 46,374 36,541 33,559 28,042 25,041 393,215 Fuel Oil (Gallon) 20,659 20,555 16,713 10,235 12,193 12,352 20,604 17,276 10,457 10,890 13,478 17,661 183,073 ($) 14,911 12,639 9,670 4,742 5,347 9,001 3,122 5,711 3,762 3,726 5,255 7,808 85,694