Prorating methods for coupled production of power, fresh water and energy for district heating

Des&nation. 26(1978)309-317 0 EkevierScientificPublishing Company, Amsterdam- Printediu The Netherlands

PRORATING METHODS FOR COUPLED PRODUCTION OF POWER, FRESH WATER AND ENERGY FOR DISTRICT HEATING B. KUNST Ingenieurwissenschaftliches (West Germany}

Zen&urn. Fachhochschule K6ln. Reiiweg 1. 6000 Koln 21

,J. HAPKE Thyssen Energie GmbH, Posifach 620.4250 (Received October 20,1977;

in

Botirop

(West Germany)

revisedformMay 15,1978)

SUMMARY

The method of allocation of steam generating costs greatly influences the specific costs of heating steam and desalted sea water. This is illustrated by means of a practical example. From the point of view of social economics, the cost allocation method based on the cost of the heating energy generated by a single-purpose heat source yields sound results. The usual criterion for steam cost evaluation, based on business administration viewpoints, is the steam energy content. The advantages of the cost evaluation using the geometric mean of heat and exergy, in comparison with the calorific, the exergetic and the arithmetically averaging methods are shown. INTRODrJCTION Fresh

water,

obtained

by

distillation

from

sea water,

has become

a

basis of economic development for many tropical and sub-tropical countries. The analog in northern latitudes is home heating, which is also a process of high energy requirement. It is standard technology to couple power generation, sea water desalination and, if required, also longdistance heating to a common steam boiler. If a back-pressure turbine is used, only about 60% of the power produced by a condensation turbine of the same throughput is generated but 80% of the live steam heat content will be available for sea water desalination and/or long-distance heating. Nevertheless the rigid relationship between heating energy production and electricity generation is a disadvantage. Therefore an extraction turbine is commonly used, which, in principle, is able to meet performance demands from that of the condensation system to that of the back-pressure system. The repartition of the steam generating costs in such a coupled

B. KUNST AND J. HAPKE

310

system depends very much on local conditions, but cost allocation methods may serve as a guide. The following study therefore is a screening of a number of practicable allocation methods in order to find one which best considers the interests of ah products depending on a common boiler plant. Credit methods, based mostly on the power tariff of the public utility, attribute to the extraction steam the remaining costs of the system (I). Their inherent lack of equity suggests the use of prorating methods. 1. PRORATING

METHODS

Prorating methods divide the steam generating costs into portions in relation to preestablished quantities. The criterion for calculating these quantities may be established by social economics (e.g. market prices for alternative energy or investment) or by business administration viewpoints (e.g. production costs, energy content). If the fixed costs of the steam generation (e.g. capital charges and in general also staff payrolls) are to be allocated, the prorating criterion is usually multiplied by the in-line capacity - i.e. connected load - of the energy consumer, then yielding the prorating quantity. On the other hand variable costs (mainly expenses for fuel) are prorated in relation to the selected criterion of quantities composed by actual energy consumption times. 1.1. PRORATING METHODS BASED ON SOCIAL ECONOMICS CONSIDERATIONS

The prorating methods considering social economic aspects attribute to the steam a market-oriented price, which must be calculated on the basis of a single-purpose energy source. The estimation of the least-cost alternative energy source may be performed with the aid of previously completed projects or cost curves available in literature [see e.g. references (2) and (311. The aim of such calculation is to compare multi-purpose and singlepurpose energy supply as shown diagrammatically in Fig. 1. The various sub-systems are indicated by squares, whose areas are proportional to the annual costs (excluding fuel costs). The fuel supply is indicated by arrows, whose width represents the consumed amount of energy per year. The economic advantage (or disadvantage) of a combined system may be determined from the ratio of steam production cost-sof the multi-purpose boiler plant to the ones of the single-purpose heat source. With this prorating method, benefits accrued by coupling are transferred to all consumers by a uniform discount on the price that would have resulted in the event of heat self-supply. Thus energy consumers obtain variable

PRORATING

METHODS FOR POWER, WATER AND HEATING

multi-purpose holler

p1ont

311

alternatIve

hedt

scurce

50000GJh CO.000 mu/a Fig. 1. Annual costs and energy requirements of the combined and the decomposed systems.

tariffs depending not only on their in-line capacities but also on whether their alternative supplies are a steam boiler, a water boiler or a heat pump. The disadvantage of the alternative price method is, among others, the dependence on changing market prices for investment and manpower. In addition the least-cost alternative energy source may change due 30 technical improvement. 1.2. PRORATING METHODS BASED ON BUSINESS ADMINISTRATION CONSIDERATIONS

If viewpoints of business administration are considered, the unit amount of steam in a coupled system may be e&mated either by the required expenses for its production or by the degree of its usefulness. The required expenses for the production of steam are proportional to the required fuel, which again can be expressed by the calorific steam energy content Ah,. The degree of usefulness of steam in terms of the Clausius-Rankine process is given by the available work or exergy content Ah,. Fig. 2 illustrates the calorific energy content Ah, (shown as a vertically hatched area) of the steam required by, for example, a sea water desalination plant within a coupled system. The associated exergy content A& is also shown (as diagonally hatched area)_ Herefrom two opposite prorating criteria and consequently two prorating methods follow, the well known calorific method and the exergetic one. The calorific method is evident if applied to heat consumers. However the calorific criterion for the power generated by an extraction turbine can be found in two ways. If only the multi-purpose system is considered, the prorating quantity is equal to the thermal energy QL_ which remains after deducting the heating energy Q& - e.g. as extraction steam from the total boiler output Q&:

B. HUNSI’ AND

312

i entropy

5

-

8

-

Fig. 2. Heat and exergy steam content represented in a T-s -rn Q -=

=

J. HAPKE

diagram.

Qh-&&__

Depending-on the energy level and amount of the heating steam, the figures of Qzb,, may vary between the net exergy requirement I?&= and the single-purpose heat requirement Qwwer. In order to maintain the analogy to both social economics and business administration the singlepurpose plant will be considered as the reference system. Then the calorific prorating quantity for the power generation in a combined system is &oweK = (&S.l,

- ~~~*alXM?~~

where I? are the produced or consumed exergies and T&, is the ratio - i.e. thermal efficiency - of the single-purpose process. AkIM, In spite of this modification, the calorific method underestimates the prorating quantity for the generated power. At the same time heating steam cost is overestimated, which is deduced from the fact that calorific energy content does not vanish at exhaust steam level. With the exergetic method [see for instance references (4) and (5)], electric power does not participate in the savings obtained by coupling, because exergy and generated power are nearly proportional to each other. In this case the entire benefit of the combination is allocated to the heating steam, which, in konsequence, is underestimated. The arithmetic mean, f (A& + dh,), between the calorific and exergetic energy contents of the steam has been proposed as a compromise between the two methods (6). The hypothetical energy implicated by this calculation may be understood as an intermediate energy type within the conversion of heat into exergy. This method avoids the bias of the two

PRORATING METHODS FOR POWER, WATER AND HEATING

313

previous ones. It is nevertheless inherent to the properties of the arithmetic mean that the savings made by coupling in principle are distributed between power and heating steam by dividing them into portions of equal absolute values. This is inconsistent with the rules of economics. Instead, it is usual to reckon the participants of a complex production system with constant percentages, e.g. of overhead costs or the like. The same should apply to cost reductions due to a conjunctive production of exergy consuming power and other heat consuming utilities. As an aiternative, the geometric mean. (A& - Ah,)“2, between heat and exergy, may be used. This averaging method implicates an intermediate energy type, which is gained from thermal energy with the same thermal efficiency as exergy and is generated from the intermediate energy. By this method constant rates of energy losses are deducted from the used energies. Consequently, the steam for power generation, exergetically evaluated, is in principle discounted at the same percentage as the heating steam, calorifically evaluated. The geometric mean and the other criteria have been computed on the basis of the expansion line shown in Fig. 8. The results are summarized in Fig. 3, showing that the geometric mean is always smaller than the arithmetic mean, and the more so, the lower the steam pressure. The geometric mean of exhaust steam is zero, just like the exergetic one; nevertheless, that of low grade steam is distinctly greater than the exergetic value.

Fig. 3. Calorific, exergetic and averaged criteriauersussteam pressure.

Fig. 4. Combined system of Wand of Heligoland.

the

2. PERFORMANCE AND COST DATA

The utility system of the Island of Heligoland is particularly appropriate for the demonstration of the influence of the methods discussed above on steam and product costs. It is an isolated system in which

B. KUNST

314

AND

J. HAPKE

different utilities are supplied with centrally generated steam at varying pressure levels as shown in Fig. 2. This is shown in Fig. 4 as a simplified flow sheet without utility grids. More details may be found. in references (71 and (81. The steam supply consists of three heavy-oil-fired radiation-verticaltube boilers with ratings of 10 t/h, 18 t/h and 24 t/h steam at 45 bar and 450°C. The electricity generating installation comprises an extraction turboset with an electric capacity of 3.6 MW and having the extraction steam at 3.4 bar and 200°C; a condensation turbo-set with an output of 1.7 MW, and five standby Diesel emergency power sets with a combined capacity of 1.87 Mw. In the heat distribution station four heat exchangers having a nominal load of 70 GJ/h transfer the heat from low pressure or alternatively high pressure steam to the heating grid. The main component of the fresh water supply system is a multistage flash evaporation sea water desalination plant with 24 stages and a capacity of 800 m3/day of distillate. Th-k has a maximum salt content of 50 ppm, is blended with 200 m3/d of filtered brackish water and hardened by filtration through dolomite. The plant can be supplied either with high pressure or low pressure steam. For the following calculations of cost allocation, it has been assumed that it is supplied mainly with low pressure steam. To allow for a variable demand, there is a 3,200m3 capacity drinking water reservoir. The public swimming pool draws 150 m3/h of preheated sea water at 32OC. For this purpose, the pressure of one of the turbine condensers is raised to about 0.074 bar. Since with total condensation the outlet temperature of the cooling water is of the order of 21°C, preheating to 32°C requires 7 GJ/h. Fig. 5 shows the energy consumptions and in-line capacities within r” 21, 2

20.

<

Fig. 5. Thermal

energy

and exergy

capacities

and consumptions.

the system. The calorific to exergetic energy ratio is plotted vers’sL(s the in-line exergetic capacities of the various production units. The partially

PRORATING

METHODS

FOR POWER,

WATER

AND

-rFEATING

315

hidden background area represents the nominal load of the multi-purpose

boiler plant. The lower (cross-hatched) sections of the blocks give the relative portion of the exergy of the steam produced in each case. The block representing the heating distribution station, has two single blocks of equal areas, one half representing high pressure steam (left) and the other low pressure steam (right). The dashed vertical dividing lines separate the blocks into consumption (oblique hatching) and unused capacity (vertical hatching). The annual costs of the sub-systems and the thermal energy consumptions are shown in Fig. 1. 3. RESULTS

The following results were obtained by means of a FORTRAN program which, in addition to the cost evaluation, also provided data for the heat and exergy contents calculated from steam state and condensate temperature. The equations used are based on the Koch equations of state (given in the VDI Steam Tables of 1956) and complementary correlations. Fig. 6 shows the costs per unit thermal energy consumed (in monetary units per GJ, abbreviated mu/GJ) for a fuel cost of 5 mu/GJ. As

illustrated in section 1, the required heat of the electric power generation is that of the single-purpose plant.

alternative heat cost

calorlfic

exergetic

ardhmetic geometric mean

Fig. 6. Specific heat costs versus cost

proratingmethod(fuel

cost = 5 mu/GJ).

In the upper section of the figure the variable cost portion is plotted versus the five prorating methods considered. The prorating method based on the single-purpose steam cost and the calorific one show heat costs for all subsystems within the diagram error limits. This is due to the fact that all these costs result from prorating the total steam generating costs proportionally to the single-purpose heat requirements. The exergetic

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method obviously yields the greatest differences between the heat costs of power ‘generation, long-distance heating, sea water desalination and swimming-pool heating. Of both averaging methods the arithmetic one does not differ much from the calorific method. This is best illustrated by the low grade heat cost of the swimming pool, which still amounts to 80% of the calorifically calculated value, although it contains less than 10% of the live steam exergy. A much better balanced value results from the geometric mean method. In this case the low grade heat would cost only about 40% of its calorifically calculated value. Although the extremely low temperature level of this heating energy clearly shows the effect of the averaging method, any other heat consumer, including a desalination plant, would experience in principle the same effect, providing no other consumer of still lower grade heat, exists. In the lower section of the figure the fixed cost portion contained in the specific cost of the used heat is shown. The fixed costs prorated to an energy consumer are roughly proportional to the in-line capacity of this sub-system. If they are related to the energy consumption, the fixed cost, portions incre_aseinversely proportionally to the load factor. This is confirmed by the results obtained from the prorating methods considering business administration viewpoints. The method based on a social economic criterion, the cost of alternative energy, shows highest fixed costs of the power generation. This occurs due to the higher specific investments and manpower costs assumed for the single-purpose highpressure boiler (See also Fig. 1). In Fig. 7 the specific production costs of power, water and heating energy have been plotted. They are related to the heat consumed. For electric power produced the outer scale on the left applies, for fresh water the one on the right. Again the costs are subdivided into variable and fixed

costs.

alternatlve heat cost

calorific

exergetic

arithmetic geometric mean

Fig. 7. Specific product costs versus cost prorating method (fuel cost = 5 mu/GJ).

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The need of balanced steam cost allocations is emphasized by comparison with Fig. 6. It can be seen that variable heat costs take a major part in the variable product cost. Also, fixed costs of heat generation have an increasing influence on the fixed costs of water, power and heating energy. 4. CONCLUSIONS The increasing use of programmable computers makes it possible to replace simple but one-sided cost allocation methods by somewhat more sophisticated but balanced ones. If the economic efficiency of a coupled plant has to be compared with that of others or if deficits are to be covered by an external financial source, the prorating based on social economic criteria, as for instance the alternative single-purpose heat cost, are preferable. Less consistent but more easily applicable are the methods

based on business administration criteria expressed in terms of thermodynamics. Nevertheless, the calorific method, either based on singlepurpose or multi-purpose heat consumption, and the exergetic method yield one-sided results. Even the averaging method based on the arithmetic mean offers no satisfactory result. In contrast, the described geometric mean offers maximum consistency due to its agreement with usual cost calculating procedures and thermodynamic rules. REFERENCES 1. 2. 3. 4.

Costing Methods for Nuclear Desalination, IAEA Techn. Rept. No. 69 (1966) K SCHRiiDER, Grosse Dampfkmftwerke, vol. I (1959) Berlin. Th. E. SCHMIDT, Wiihaftlich Planen und Konstruieren von Anlagen mit HiIfe der Progression, Fortschr. Ber. VDI-2 3, no. 21. 2. RANT, Rewertung und praktische Anwendung von Energien, Allg. Wrmetechnik, 8 (1957)

25-32.

5.

W. KijNIG, Aufteilung der Krzeugungskosten auf Strom und Dampf,

6.

H-J. SCHELTZ, Zur Frage der Kosten der elektrischen und Wtieenergie bei deren gleichzeitiger Erzeugung in Kraftwerken, Feuerungstechnik, 29 (1941) 255-258. H. GRUTTNER, AND D. KESTING, Meerwasxrentsalzungsanlage fiir Helgoland, Wasser und Boden. 22 (1970) 282-286. H. STIFF. Hauptbericht der Femwlnneversorgung, Fernw&-me Znternatiorat,

7. 8.

VIK-Mitt.,*

3 (1973) 31-37.

4 (1975)

3642.