Applications of Available-Energy Accounting

10 Applications of Available-Energy Accounting

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WILLIAM J. W E P F E R 1 Professional Engineering Consultants, 3915 N. Lake Drive, Milwaukee, WI 53211

This paper surveys the results of three practical applications of available-energy costing as well as some of the accompanying methodology. To i l l u s t r a t e the use of available-energy accounting in the costing of system products, the results of a study made for a firm (a paper manufacturer) co-generating shaft power (and electricity) as well as low-pressure process steam for different end-uses is shown. Comparison with the firm's previous costing of excess e l e c t r i c i t y emphasizes the crucial importance of second-law methods. I t should be mentioned that these same techniques can be applied to any system with multiple products, for examples: (i) co-generation systems having hot-water, compressed a i r or refrigeration outputs in addition to steam and shaft power; and, (ii) process industries like petroleum refining engaged in the production of many products. The application of available-energy costing to f a c i l i t i e s operation is illustrated with an example from the electric u t i l i t y industry--namely that of feedwater heater maintenance and replacement. Here available-energy costing holds the key to determining when the heater should be replaced altogether, after successively plugging leaky tubes. The f i n a l example applies available-energy costing to an optimal design problem—the economic sizing of steam piping and insulation. I t is only through the available-energy concept that the relative dissipations due to pipe f r i c t i o n and heat transfer can accurately be assessed. In turn, the true costs of these dissipations can then be weighted against the capital costs of piping and insulation. Results of Costing Co-generated Steam and Shaft Power Co-generation is a v i t a l element in the paper industry because paper production requires large quantities of low-pressure 1

Current address: Professional Engineering Consultants, Milwaukee, WI 53211.

0-8412-0541-8/80/47-122-161$06.50/0 © 1980 American Chemical Society Gaggioli; Thermodynamics: Second Law Analysis ACS Symposium Series; American Chemical Society: Washington, DC, 1980.


162

THERMODYNAMICS: SECOND LAW ANALYSIS

steam and mechanical shaft power. The following results, taken from a case study in the paper industry (1), were obtained by applying the available-energy costing methodology described in the preceding paper by Reistad and Gaggioli (2) to three representative co-generating power plants. These results are contained in Table I and on Figures 1-3. Figure 1 is a simplified schematic diagram of a co-generation system typical of systems b u i l t twenty years ago. (In fact, this system will be designated as the 1960 system.) The diagram shows the average annual available-energy flows and consumptions as well as the unit costs of process steam and e l e c t r i c i t y outputs. The incentive for improving energy conversion systems is generally economic. The capital cost to improve a system must result in a savings which is greater. The 1960 system was b u i l t in a time when fuel was inexpensive and there was l i t t l e or no incentive to build e f f i c i e n t systems. The overall second-law e f f i c i e n cy of 28% is indicative of this fact. The so-called 1976 system is shown in Figure 2. This system u t i l i z e s a coal-fired boiler to generate 600 p s i steam. The increase in overall efficiency to 33% is primarily due to the elimination of the large heat transfer consumptions associated with the low-pressure boiler in the 1960 system. The paper company, contemplating the addition of a paper machine to increase their production, sought to expand their co-generating capacity. The 1980 system, as illustrated in Figure 3, has been proposed as the typical means of supplying the required steam and shaft work. (See reference (_3) for other more economic alternatives.) In the 1980 system, steam would be produced at 1250 p s i . Under these conditions, the temperature difference between the combustion products and the steam is significantly reduced, and the consumption of available energy that drives the heat transfer is decreased to 23% of the fuel input. This bodes well for the efficiency of the system as a whole. The overall efficiency of 35% for the 1980 system is really quite good when compared to most energy systems and represents a significant improvement over the 28% efficiency of the 1960 system. The products of each system were costed using two different techniques : the equality method and the by-product work method (1_,2)- Every case analyzed accounts for maintenance as well as fuel expenses but excludes other operating costs. Capital investment is amortized at an after-tax discount rate of 8.5%. The effects of income taxes, ad valorem taxes, and depreciation (see (3) for the formulation of the annualization factor accounting for capital, taxes and depreciation) are included, while the effects of inflation were neglected. The 1960 system was analyzed without accounting for amortization on the assumption of sunk capital, inasmuch as the system has been almost f u l l y depreciated. In addition to analyses including amortization, costings for the 1976 and 1980 systems were

Gaggioli; Thermodynamics: Second Law Analysis ACS Symposium Series; American Chemical Society: Washington, DC, 1980.


1980

1980

1980

1976

1976

1960

System

6

Equality

By-product

Equality

Cost D i s t r i b u t i o n Method

Equality

By-product

Equality

Sank

By-product

Equality

8.5% 32 y r s By-product

$20.S(10 )

6

8.5% 20 y r s By-product

$20.5(10*)

Sunk

Equality

8.5* 20 y r s By-product

S9.K10 )

Sunk

Capital ization

7.04

4.80

8.37

6.08

8.44

6.14

7.02

5.29

10.0

7.86

6.12

5.22

1.60

2.86

2.07

2.88

2.1

2.40

1.81

3.42

2.68

2.09

1.78

CAWh

$/10*Β$μ44

coat

65 P s i g Staaa

5.27

4.80

6.47

6.08

6.5

6.14

5.25

5.29

7.79

7.86

5.97

5.22

- —

1.81

1.60

2.21

2.07

2.23

2.1

1.80

1.81

2.66

2.68

2.04

1.78

$/klih

175 P s i g Staaa reat $/10*B£4—4

6.79

4.80

8.10

6.08

8.17

6.14

6.39

5.29

9.24

7.86

6.07

5.22

$/10

6

2.30

1.60

2.76

2.07

2.79

2.1

2.18

1.81

3.15

2.68

2.07

1.78

B t u 4 4 4 4

Average s t a a a Cost

-

Back-pr assure

0.92

1.78

1.49

2.37

1.52

2.40

0.97

2.04

1.74

3.02

1.08

2.01

3.12

2.86

4.36

4.13

4.43

4.19

1.22

1.93

1.88

2.61

1.92

2.64

0.97

2.04

1.74

3.02

1.08

2.0J

Average

E l e c t r i c i t y , C flcUh

4-**4** *Condans ing

--

Table I. Unit Available Costs for Cogeneration Systems


Gaggioli; Thermodynamics: Second Law Analysis ACS Symposium Series; American Chemical Society: Washington, DC, 1980. 0

4.overoll" -

2 8

a

STACK 0.9

ELECTRICITY 0.1 MW 2.011/kWh

BOILER (175 pfi) ΊΟΝ -1.8 COMBUSTION -2.2 HEAT TRANSFER T4.0.24

6

FUEL (COAL) 6.3 MW 0.55*/kWh l.62$40 Btu

1.782 t/kWh (O.OIC/lbm)

1.782 t/kWh (O.I77t/lbm)

2.0lf/kWh

1.782 %/ kWh (0.227e/lbm)

Figure 1. Skeleton schematic of 1960 system available-energy flows (megawatts). Also shown are the unit costs of the steam and electricity outputs based on the equality method and sunk capital costs.

- 0.1

STACK 11 .

ELECTRICITY 0.2 MW 2.0l*/kWh

BOILER ( 600 pii) -8.4 COMBUSTION -8.3 HEAT TRANSFER T4.0.37

5psig HEATER

[ PUMP S W»QI

( ρ PUMP W«0.l 74.0.8

0.4

6

FUEL (Ν.GAS) 28.1 MW 0.52c/kWh 1.51 $/l0 Btu



10.

WEPFER

Available-Energy

ELECTRICITY 0.3 MW 3D2t/kWh

FUEL (COAL) 33.2 MW 0.55*/kWh I.62$/I06etu

FEEOWATER

165

Accounting

STACK 1.3

BOILER (600 psi) -10 COMBUSTION -9ft H EAT TRANSFER 4«0.37 13.5

J PUMP \ W«O.I

TURBINE 3.5

V0.78

POWER 3.2

-0.3

3.02 4/ kWh

GENERATOR T4.0.92 175 psiq STEAM 2.9

1.0 6.1 -0.3

0.7 0.6

50 psig FEEOWATER HEATER T4.0.77

PUMP W«O.I 0.8

V

2.68C/kWh " (0.35C/Ibm)

50 psig STEAM

2.68t/kWrt

5.4

(0.28t/lbm)

CONOENSATE 0.5

2.6B*/kWh (O.OOIi/lbm)

overall

= 0.33

Figure 2. Skeleton schematic of 1976 system available-energy flows (megawatts). The unit costs of steam and electricity were computed using the equality method and a capital charge of $9.0(10 ) at an effective after-tax interest rate of 8.5% and an economic life of 20 years. 6


166



FUEL(COAL) 119 MW 0.55*/kWh (1621/10*6 tu)

FEEOWATER

ELECTRICITY IMW 2.64*/kWh STACK 8

BOILE&S(l250psi) - 36 COMBUSTION - 28 HEAT TRANSFER η »0.40 52 TURBINE rj -0.84

175 psig STEAM 2.9

2.1*/kWh (0.281/Ibm)

t

-0.5 Π

PUMP kw0.2 W) 4 - 0 . 8 5

2.7

4.5

ELECTRICITY 3.5 GENERATOR 4j-0.92

1.0 i 18.5

0.2

SO ρ tig STEAM 19.1

-1.3

ELECTRICITY 17.2

2.4*/kWh

2.l*/kWh (0.22*/Ibm) 4.19* /kWh CONDENSING ELECTRICITY 2.4*/kWh BACKPRESSURE ELECTRICITY 2.64*/kWh AVERAGE ELECTRICITY

50 psig FEEOWATER HEATER ηΛ·0.8Ι

2.l*/kWh (0.001 f/Ibm)

Figure 3. Skeleton schematic of 1980 system avaifoble-energy flows (megawatts). The unit costs of steam and electricity were calcutàed with the equality method and for a capital charge of $20.5(10*) at an effective after-tax interest rate of 8.5% and an economic life of 20 years.



10.

WEPFER

Available-Energy

Accounting

167

also done assuming sunk capital since these results are useful for some economic considerations. What c r i t e r i a should be used when deciding which costing method is appropriate? If a company were in the position where it "needed" to produce its own steam (because it could produce it more cheaply, in boilers, than it could purchase it), then the by-product work method would be appropriate for establishing the desirability of investing in a co-generation system. If the resultant average cost of by-product e l e c t r i c i t y is less than it could be purchased for, the investment in co-generation f a c i l i t i e s would be worthwhile. This is one example where the by-product work method would be appropriate, for making internal decisions. It should be mentioned that the conventional technique for costing process steam and shaft work outputs of a co-generating f a c i l i t y is nearly equivalent to the by-product work method (4). In the conventional method the shaft power is charged with the incremental fuel cost associated with producing it as well as the capital charge for the turbine. (This is closely equivalent to charging steam as i f it were produced in a low-pressure boiler.) The cost of process steam is then obtained from a money balance on the turbine. Nevertheless, the commodity of value is available energy—any method which assigns costs on any other basis such as energy or mass is usually invalid. Furthermore, only with available-energy costing can co-generating power plants be analyzed by other methods—equality, extraction, by-product steam— discussed in the preceding paper (2). Once a company has decided to produce steam and shaft work from back-pressure turbines, say because of overall economics, then is it still reasonable to use the by-product work method? The by-product work method makes e l e c t r i c i t y appear to be relatively cheap and steam relatively expensive, compared to the equality method. After fixed expenses for the system are sunk, then the costs associated with delivering available energy in back-pressure steam and in turbine shaft power are the same. (This contention is f o r t i f i e d by the fact that the marginal cost for useful energy in such steam and in shaft output are the same, equal to the averaqe costs, insofar as the efficiencies with which power plant components operate remain practically constant (5). That is, the cost of delivering another unit of available energy in steam equals the average cost of the units already being delivered in the steam output and shaft output- And, likewise for an additional unit of shaft power.) Suppose that a paper m i l l were purchasing all the e l e c t r i c i t y and steam it used, say because the steam and e l e c t r i c generating equipment all belonged to another concern—a u t i l i t y . The u t i l i t y would—or at least should—charge for the steam and elect r i c i t y in proportion to the cost of producing each. Since for the u t i l i t y neither is a by-product of the other, the cost of producing the back-pressure steam and the turbine shaft power is proportional to their available-energy content; this calls for the equality approach.



168


For the case study at hand, the company was engaged in the s a l e o f "excess" e l e c t r i c i t y t o outside customers. Using energybased c o s t i n g t h i s company, even a f t e r the allowed mark-up f o r a p r o f i t , was s e l l i n g e l e c t r i c i t y below c o s t — a t Ι.βΦ/kWh, even lower t h a t the 2.01

Applications of Available-Energy Accounting

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