Examples

Economics and EROEI for Conservation and Solar Power

Systems

Simplified Energy and Cost Analysis

For Low Flow Shower Heads Typical household can save 40% per

shower, or 9 gallons. Assume water temperature in is 70° F and heated to 120 ° F.

Energy Saved Per Day

If cost is 8.3¢/kWh, yearly savings are

Or $33/year

gal

lb

Btu

kWh

Flb

BtuFgal 3.8

3413

11)70120(9

kWhcyeardaysdaykWh 3.83601.1

daykWhESAVED 1.1

Cost of shower head ≈$15, replaced by homeowner at no cost

$ payback is

Cost of Saved Energy=

This is less than 1/10th the electricity

moyearmoYEAR

5.51233

15$$

TC

C

SAVED 0

kWh

C

yryrday

daykWh

C 05.0103601.1

1500

Cost of Conservation Example

Replace a standard A Lamp with a CFL Lamp.

A Lamp uses 75 Watts, $0.50CFL Lamp uses 20 Watts, $15Price of Electricity 8.4¢/kWhA Lamp life 8 months (2/3 yr)CFL Lamp life 10 years

Cost Difference in 10 years is:

50.7$8/1205.015$ monthlifemonth

Reduction in Energy Cost per year if lamp operates 3hr/day on 1,100hr/yr

yrkWWhr /1.5$/$084.055100,1

Reduction in equipment cost

Payback time

yr/75.0$yr/5.2$85.5/5.14$

Cost of Energy (simple)Energy Savings

Cost

Levelized cost (CCE)Effective discount rate, i =3%Life Time, t =10 yr

CRF

CCE

hrkWhrW /61100,155

kWcyrkW

yr/2.1

/61

/$75.0

tii )1(1 117.003.1103.0 10

kWhckWh 4.161117.05.7$

Parabolic Collector Analysis

Economics and Energy return oninvestment

Energy investment is equal to

The energy return is

EROEI is

Energy recovery is 1.5 years for a life of 15 years the EROEI is 10:1

yrBtu

yrBtu/%5.67100

1043.5

/1066.39

9

Btu91043.5

3 66 10 9. B tu yr

CO2 Generation

To compare the production of CO2 from the combustion of fossil fuels with the CO2 production from solar energy conversion systems, we will calculate the amount of CO2 that is added to the atmosphere per unit of energy produced by each system. We will illustrate the calculation procedure first for a fossil energy system using coal as fuel.

The basic stoichiometric equation for the combustion of coal is

energy released To calculate the amount of CO2 produced

per unit of energy generated we need to know the energy released per unit of carbon, i.e., the heating value, and the percent carbon content of coal.

C O C O 2 2

Both heating value and carbon content vary slightly among the types of coal used in the U.S.A. We will demonstrate the methodology using bituminous type coal which is plentiful and widely used for power generation. We are given a heating value of 29MJ/kg of coal and a carbon content of 40% by weight for bituminous coal.

With the data given, assuming complete combustion, one can obtain that the combustion of 1 kg of coal with 0.4 kg of carbon having a molecular weight of 12 yields 1.47 kg of CO2 while releasing 29 MJ of thermal energy.

If the conversion efficiency of the heat of combustion to useful energy is 70% we find that coal-fired energy systems will generate 0.0016 moles of CO2 per kJ of useful heat delivered