Provide a simple payback period analysis for implementing a cogeneration system to be installed in a hospital. Use the following characteristics for the cogeneration system: • Fuel input rate: 10,000 Btu/kWh • Heat recovery rate: 5,500 Btu/kWh

Question

Provide a simple payback period analysis for implementing a cogeneration system to be installed in a hospital. Use the following characteristics for the cogeneration system:
• Fuel input rate: 10,000 Btu/kWh
• Heat recovery rate: 5,500 Btu/kWh
• Maintenance cost: $0.02/ kWh
• Maximum electrical output: 200 kW or 300 kW
• Installed equipment cost: $1000/kW
Table 13.10 summarizes the energy usage and cost of the hospital. Assume that the boiler(s) efficiency is 70 percent. For this analysis, assume also that the cogeneration system requires diesel fuel only (the other option is dual fuel). Assume the heating value of diesel fuel is 140,000 Btu/ gal.

Utility Summary
Fuel Oil		Electricity
($)	(Gallon)	($)	(kW)	(kWh)	Month
14,911	20,659	2,7020	546	226,400	January
12,639	20,555	28,949	572	273,600	February
9,670	16,713	31,048	564	280,800	March
4,742	10,235	25,251	526	228,000	April
5,347	12,193	28,755	692	246,000	May
9,001	12,352	36,604	884	301,200	June
3,122	20,604	45,031	1,040	346,800	July
5,711	17,276	46,374	944	403,200	August
3,762	10,457	36,541	860	303,600	September
3,726	10,890	33,559	872	276,000	October
5,255	13,478	28,042	662	272,400	November
7,808	17,661	25,041	524	276,000	December
85,694	183,073	393,215		3,434,000	Total

Accepted Answer

For each month, the energy cost incurred with a cogeneration system is calculated using a stepby-step procedure based on Eqs. (13.3) and (13.4). Table 13.11 summarizes the results of the stepby-step analysis performed for the month of January. Table 13.12 provides the results for all the months with the payback period for each cogeneration size. In this example, the smaller cogeneration system (200 kW) is more cost-effective because there is no option to sell excess generated power to the utility. However, a detailed economic analysis should be carried out to optimize the size of the cogeneration system.

[latex]kWh_{cogen}=Min{24.N_{d}.kW_{cogen};kWh_{actual}}[/latex] (13.3)

[latex]TE_{cogen}=Min{24.N_{d}.kW_{cogen};TE_{actual}}[/latex] (13.4)

TABLE 13.11 Details of Step-by-Step Analysis Performed for the Month of January in Example 13.3

System 300 kW	Cogeneration 200 kW	Energy/Cost Requirements
226,400	226,400	Electrical energy requirements (kWh)
2,024	2,024	Thermal energy requirements (MMBtu)
223,400	148,808	Cogenerated electrical energy, [latex]kWh_{cogen}[/latex] (kWh)
1,228	808	Cogenerated thermal energy, [latex]TE_{cogen}[/latex] (MMBtu)
3,000	77,600	Electrical energy to be purchased from utility (kWh)
796	1,206	Thermal energy to be directly generated (MMBtu)
15,957	10,628	Fuel use for cogeneration (gal)
5,686	8,614	Fuel energy for direct generation of thermal energy (gal)
21,643	19,242	Total fuel use requirements (gal)
557	9,258	Cost of utility electrical energy ($)
15,627	13,893	Cost of fuel ($)
4,468	2,976	Cost of maintenance ($)
20,450	26,127	Total cost ($)

TABLE 13.12 Cogeneration Cost Savings and Payback Periods

300 Cogen Cost, Cogen ($/month)	200 Cogen E Cost ($/month)	Output(kW) Conventional E cost ($/month)
20,450	26,127	41,931
27,687	28,920	41,588
21,753	27,108	40,718
14,813	14,527	29,993
14,121	20,178	34,102
26,034	31,658	45,605
24,142	32,167	49,153
31,536	37,815	52,085
20,414	26,388	40,303
16,339	22,687	37,285
16,512	21,581	33,297
17,892	22,097	32,849
251,692	311,251	478,909	Total ($)
300,000	200,000	0	Equipment cost ($)
1.32	1.19	_	Payback period (yr)

Question 13.3: Provide a simple payback period analysis for implementing a ...

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