Methodological aspects of technico-economic parameters of nuclear desalination plants

Desafinotion- Elsevier Publishing Company, Amsterdam - Printed

METHODOLOGICAL

ASPECTS OF TECHNICO-ECONOMIC

PA’RAMETERS OF NUCLEAR

DESALINATION

Ytf.

AK5

I, KURYAKIN,

in The Netherlands

A. A. LUGfNUV

GovernmentCammittee on the i.Mizatim

PLANTS

V. A. CHERNYAEV

of Nudeor

Energv, Moscow ( U.S.S. RJ

(Received Aptii 14, 1969)

1.

INTRODUCTlON

Computation of technico-economic parameters of nuclear desalination plants and determination of their competitiveness still involve a number of methodotogicai vaguenesses. A thorough study of technical and economic factors is stiif required to determine their true economic significance. The choice of parameters, the comparative analysis and investigation of the eficiency of combined plants for the production of two or more kinds of products are complex and controversial. Thus there are different methodological approaches to the computation of economic parameters (1, 2, 3) which make economic evaluations dificutt and comparison of economic parameters impossible_ The methodology of costing computations for multi-purpose production is acquiring a new meaning in the wake of the growing volume of scientific studies and experimental designs undertaken in connection with the increasing scale of projects for mutt&purpose nuctear desatination plants (2% 4). This methodofogy generally involves both national and particular specific features. Therefore it is difficult to recommend an international method of making technical and economic evaluations. Moreover, a solution found economically suitable in one country may prove to be far from suitable in another country. it is therefore rather ditiicult

to hold ~nter~ationa1discussions on the economics of nuclear energy, in gene&, and of dual-purpose (power and water) nuclear production in particular. Presentation of the methodology of costing computations is nevertheless of some informative value. Knowledge of the methodical approach helps us appreciate the reasons for both the absolute and the relative differences among various economic magnitudes and characteristics, and afso leads to a better understanding of the terms of economic comparisons made among gternative technicaf solutions. The methodology outlined bdcw is ‘based on the economic category of “evaluated expenditure” widely used in the USSR For carrying out alternative economic computations in the different branches of the national economy. Des~li~tion, 7 (1970) 323-342

YU. 1. KORYAKlN

324 11. BASIC D1RECTIVES FOR COSTING

et cl/.

COMPUTATIOIiS

1. Uniformity of costing computation methods must be ensured in the choice of parameters, in ma’xing comparative analyses and in investigating the efficiency of the combined production of electric power and low-potential heat utilized for converting saline water in distillationa! desalination plants using either a conventional or a nuclear source of energy. 2. The approach to computing technical and economic indices of desalination plants is based on the fact that under existing conditions in the USSR electric energy, heat and fresh water are equally important products in the national economy. 3. The purpose

of technical and economic computations is to find the economically most advantageous alternative through the comparison of a number of possible solutions. In comparing a number of possible alternatives, one must consider only mutually reptaceable alternatives which ensure meeting equally the specified production requirements in the class of production under consideration. 4. In the comparison of alternatives, a decisive role is played by the economic (cost) indices. A!! quantitative and qualitative characteristics of every solution must therefore be evaluated in terms of cost. The economic criterion adopted in the comparison of alternatives is that of the total (annual) evaluated expenditure. Among the solutions considered. the optimum one in the rolution with the lowest evaluated expenditure. 5. In the capital investments, there must be included the cost of creating the basic and the operational funds for the alternatives under comparison. Associated capital investments are not taken into account, since the products of contiguous branches are taken at their cost or at their proportional part in the evaluated expenditure. 6. Where among the alternatives under comparison complex undertakings are included that are engaged on the combined provision of several kinds of products (including also products other than power) or affecting the interests of several branches of the national economy, the alternatives must be equalized for a!! kinds of production. 111. COMPARISON EVALUATED

CRITERIA

FOR ECONOMIC

FEASIBILM-Y AND

DISTRIBUTION

OF TOTAL

EXPENDtTURE

I. The criterion for nation plants is a complex sum of current production invested in it defined by a In its genera! following formula:

form,

comparing the economic feasibiiity of nuclear desaliindex. It is the total evaluated expenditure which is the expenditure of the given plant and a part of the capita! normative evaluation coefficient (5).

the total evaluated

expenditure

is determined

Desafinarion,

by the

7 ( 1970) 323-342

TECHNICO-ECONOMIC

PARAMmERS

OF NUCLEAR

tXSALfNAT1ON

PLANTS

325

is the plant construction and running-in period caeffkient of expenditure - ncmnative e&k&on, costs at normal exploitation (after completion Kr - annuaf production of construction and running-in period) A’,: s, - invested capitai and prodcction cost, respectively, during year 1. In the absence of sut5cient economic ins-or~n~tion needed for determining

where T P

in every year of construction and running-in under K, and S,. a simplified formula E = XS + PX.K can 3e used, where CK and XS are total estithe expenditure

mated capital investments and annual production costs respectively, required for setting up the plant. One should note that in this case no account is taken of the time required for construction and running-in. Consequently, the evaluated expenditure at T r 1 becomes understated. When comparing alternative plants, diRering in capitaf investments and production costs, the undertaking in which the production costs are lowest is not necessarily the most ecanomicafly feasible. A necessary condition for such feasibility is that: AZS>PAz:K

(2)

where A I: S is the reduction in production costs A Z Kis the increased capital investment caused

by reduced

production

costs.

In cases where the condition

is met that

A~S=PA~Ic the alternatives under comparison Lastly, if it is found that A’S=PArK

are economically

equivalent.

i+

then the economically preferable alternative (or undertaking) is the one which warrants higher capital investment at raised production costs. The expression for totai evafuated expenditure on nuclear dual-purpose* desalination plants (NDP) is:

* Application of the basic criterion of economic feasibility
YU. 1. KORYAKIN et d.

326

where S,,S,

are the annual production costs of electricity and distillate, respectively capital investment in the power production section and in the q.JL distillation section of the plant, respectively The total evaluated expenditure of a dual-purpose plant on the production of a given amount of electric energy and converted water is made up of the evaluated expenditure on the production of electricity E,. of heat in the heating steam (E,) and of distillate. exclusive of the cost of heat (E,,&: &vDP

=

EP

-I-

Et

+

G(o)

(6)

A nuclear dual-purpose desalination plant is composed of two sections the nuclear power station producing electricity and heat for desalination (NRS) and the desalination installation proper (LPI) producing distillate with the use of the heat of heating steam: E SDP

=

GVTES

f

Esor

(71

where qWTESand A!& are the evaluated expenditure on the power production and the desalination sections of the plant, respectively. The total evaluated expenditure of a single-purpose nuclear desalination plant (producing distillate only) comprises all expenditure on construction and operation of the plant (including expenditure on the provision of the plant’s power requirements, through its own production of electricity or through purchasing it from an outside source at a given price). The apportionment of the totat evaluated expenditure of a duat-purpose plant among its different products - electricity (J?&,~) and distillate (E&,) must be made according to the principle of proportiona allocation of the total economic effect among the different components of the complex:

GDP = ENDP

E KP EKP + EDI

Ed NDP

=

EDI ENDP

ELP + ED,

(9)

where&PI E Df are the minimum evabated expenditure on a nucIear(or conventional) electric power station and on a single-purpose desalination p&t (or a water supply alternative) producing the same amount of electricity and distillate as the dual-purpose plant, respectively. In a similar way the total evaluated expenditure is apportioned in nuclear power stations (NTES) between the production of electricity (E&J and the production of heat supplied for heating purposes (E&J: Desalination, 7 41970) X3-342

PARAMETERS OF NUCLEAR DESALlNATlON PLANTS

TECHNICO-ECONOMIC

327

where EK is the minimum evaluated expenditure on a nuclear (or conventional) boiler installation producing the same amount of heat as the nuclear power plant. In the case of a nuclear reaction being utilized for a triple-purpose installation (electric power, heat supply and converted water) or for a quadruplepurpose installation (nuclear fuel, electricity, heat and distillate). the apportionment of the total expenditure among the various components of the complex can be made in two ways, depending on the principle of distribution of the overall economic effect among these components: a) By a proportional distribution of the economic effect

is the total evaluated

where E,j

debited EL -

to production

expenditure

of the combined

production,

j;

total reduced expenditure on the whole complex;

minimum reduced expenditure on the production of product j in a specialized individual (single-purpose) plant that would be necessary on relinquishing a complex plant; - total minimum reduced expenditure on specialized (single-purpose) pIants replaced by a combined plant-

E.i -

SE’ i-1

b) On transferring the economics from a combined production to that of a single product j, the total evaluated expenditure on that production is determined by the formula: (13) i=l i#j

where 5 is the sum of evaluated expenditure on all speciaiized (single-purpose) i=I plants, exciuding the plant for production j. f+f Determination of specific evaluated expenditure on ~ndividuai kinds of product is made by dividing the respective equations (8-12 and 13) by the annual output of the relevant product. If, in determining the evaluatdd expenditure, allowance is made for the time factor and for the annual output of the product varying with time (e.g. in a Desalinarh,

7 (I 970) 323-342

YU.

328

1. KORYAKIN

Ct a/.

gradual staged increase of power supplied to the plant), the named equations are to be divided by the equivalent (evaluated) annual amount of produce, determined by the formula: -4 = A, f P 2 .4,(t I=1

+ P)T-r

04)

where A, is the annual output of produce under conditions A* - output of produce in year t. T - period of.construction and running-in. iv.

DISTRIBUTION

OF TOTAL

COST OF ELECTRIClTY,

PRODUCTlON

HEAT AND

EXPENDlTURE

of normal production;

AND

DETERMINATION

OF

DISTILLATE

The sum-total of annual production expenditure (annual costs) of u nuclear dual-purpose desatination plant with any type of reactor is determined by the sum of annual expenditure on the production of distillate (S,) and electric power1 (S,,): SNIP -f- S, = Sei Given the annual output amount of electricity produced can be computed as follows:

(1% oi a dual-purpose plant of distillate (M) and the annually (W), the cost of these kinds of product

Distillate

Thus, the problem consists in distributing the total production expenditure among the kinds of product, Le. in determining of a dual-purpose piant (S,,,) the values of S, and S,iThe cost of producing distillate (S,,) can be defined as the sum of production costs of the desalination section proper of the plant (S,) and of producing the heat in the heating steam (S,): s, = Sds +- S,

(17)

On raking into account that hf = (Q,/q) is the quantity of heat expended in the desalination plant of a given where QI construction to obtain a given quantity of distillate gcal/year; specific expenditure of heat OQ producing one ton of distillate in the 9 adopted design of the desalination section of the plant at the adopted parameters for the steam supplied for desalination, g&/t; The cost of. the distillate (6) is, accordingly: Desalination, 7 (1970) 323-342

TECHNICO-ECONOMIC

~~~~re-rms

OF NUCLEAR

OF~ALINATI~N

PLANTS

329

f

section proper OF the ‘plant, without allotiance for the cost of heat in the heating steam (Cz) and oi‘ the component representing the cost of the heat in the heating ste’am (C,,) expended on desalination, and the efliciency of its utilization, Le. the specific expenditure of heat (4). The value of q is determined by the sum of the following components: L..-depreciation allowances on invested capital in equipping the desalination section proper of the plant and the cost of repairs of this section (C,,+,): -_ cost of electricity (at cost) needed for operatin g the desalination section proper which is made: up of the cost component

of the desalination

(CL): -- cost of processing saline water for desalination (C,,.); - expenditure on personnel wages including raises. various payments and social insurance (CJ: other expenditure Cd” =. 5

=

(C,,):

C,+,

+

C,, +

c,,

+

c,

+ C,,.

(19

: The values of these components are computed from norms adopted in designing the desalination section proper of dual-purpose plants. A nuclear dual-purpose desalination plant can be considered as tvvo separate, a nuclear power station (AYES) producing though interconnected objects electricity and heat for desalination from the combustion of nuclear fuel in a reictor, and the desalination section proper (DI) which produces distillate by using the thermal energy received form the NTES. In this case, the total production costs of a NDP (S,,,) are composed of the production cost of the NTES (S,,,,) and the production cost of the desalination section proper (SD,), each of which can be determined by a direct financial estimating cakdation:

S SDP

=

s.4TES

+

sD,

(20)

Thus, in order to determine the production cost of heating steam <.S& and SO its cost, it is necessary to distribute the expenditure of the IVT.S(S_~~~~) between two kinds of product (electricity S,, and heat of the- heating steam S,,) in their .

combined

production.

The distribution problems of production costs in a combined production process and, in particular, of electricity and of heat,- arc complex, insufficiently studied and sometim& highly debatable_ In this connection it appears desirable to. present a review and an analysis of the existing methods of distributing the total costs is rVT& of combined prtiduction of electricity (S,,) and of heat (S,) in pow& plants and to examine their main characteristics. Dedim7rl-on, 7 (167Cb)323-342

W. 1. KORYAKIN

330 v.

REWEW

OF PRODUCTtON

COSTS DISTRIBUTION

et cd.

METHODS

The separation rneiltod In the total tigure of production cczsts one isoiates the cost of one product, the magnitude of which is arbitrarily fixed in accordance with situational considerations. fn energetics this method has been named the Ginter Triangle. The specific production costs of one product of a NOES as defined by this method, depend on the arbitrarilk assumed magnitude of the specific production costs of another product. In its application to a NTES, this method is represented by the equations: s,, = C

(21)

s, = s,,,

- c

(22)

where C is the arbitrarily fixed magnitude of production costs of one product, in the present case - of electricity. A basic shortcoming of this method, apart from its incorrect premise on the unequal vdue of both products is that its application offers no solution to the question of the actual magnitude of expenditure on labor and material and, consequently, the cost of electricity and of heat. Owing to the subjective nature of the distribution of the general expenses, it is possible to overstate the production cost of electricity at a correspondingly understated cost of producing heat, and vice versa. Another shortcoming of this method is also the fact that the final magnitude of production costs of each kind of energy cannot be determined structurally (as elements and items of expenditure). The method is thus far from indicating the actual results of operaticn of a ccmbined plant, and it permits no optimization of its parameters. The coeficients method This method amounts to distributing the total costs of combined production with the aid of coefficients determined on the basis of the value to consumers of the different products, i.e. either in proportion to thecosts of the various products when produced separately, or in proportion to their actual selling prices. In energetics this method has been named the method of Cheapening Coefficients. The method is based on the principle of equal importance of electricity and of heat and proceeds from the premise that the lowering of total costs due to combined production should be credited in equal measure to both products. For nuclear power plants, this method is represented by the following analytical expansions: S ST&S

(

%Z.S

+

se,= SNTES S

(23)

s,,

NES

sN= +

(24)

s”TS

Desalination,

7 (1970) 323-342

TECHNICO-ECONOMIC

st =

SNTES

PARAMETERS OF NUCLEAR

-

SNTS

S NES

+

DESALINATION

PLANTS

331 (25)

&TS

where S,, and &, are the pro&l&ion costs of the replaced amounts of electricity and of heat respectively. The drawbacks of this method are: - absence of interrelation between economic and technical indices; complexity of practical application. since it is necessary to design and compute three different plants, NTES, NES and NTS, while selecting for the latter two the most economic designs; - the arbitrary magnitude of the cheepening coefficient, since the production cost savings made at a NTES depend on the technical perfection, type and power of the single-purpose NES and NTS under comparison with the NTES; - the dynamic character of the cheapening coefficient, which changes with time according to the fluctuations in the heat and electricity supply load.

The method is applied at present to combined heat and electric power stations (TES)under the name of the natural (weight) method. In using this method, the total production costs of a TES is distributed between electricity and heat in proportion to the amounts of initial heat used in their production. The overall costs of combined production are broken down by this method into the costs at the source of energy (in the case of a NTES) incurred on the reactor section (S,,). on the electric power section (S,), on the heat section (S,,) and on other general station costs (S,,), i.e: SNTES =

%*

+

se,

+

se

+

Gw

sgc

The S,, costs are fully debited to the electricity, the S,, costs fully to the heat, whereas the S,, and S,, costs are distributed among the two kinds of energy. In doing so, the electricity is debited with the amount of heat (0,) which represent the difference between the heat energy capacity of the source of energy (QI) and the heat produced for supply (0,). The costs distributed by this method between electricity and heat are defined from the following relationships:

s, = St, f St, $- f

,

s,, +

s,cS

NTES

s,Q’ a

-

(28)

s,,

Desalination, 7 (1970) 323-342

332

YU. I.KORYAKIN et Uf. The physical

differing

in potential

method is based on an assumed equal value of heat units, but equal in the quantity of heat units received from the

YMWCX of energy. In doing so, no allowance is made for the fact that the production of electridty utiiizes heat of high potential, whereas the production of heat utilizes partly used up heat of Iow potential_ Equalizing the heat calories of high and low potential leads to crediting the savings made in the combined production of electricity and heat entirely to the electric power. Thus, the basic drawback of this method is that its application leads to the overstatement of the production costs of heat to a corresponding understatement of the production costs of electricity. which does not correspond to the actual technological process. There may likewise arise a reverse situation, where a considerable part of the costs connected solely with the production of heat in periods of low or zero heat requirements will be charged to the production of electricity.

This method retains without change the relative production costs of efectricity on passing from separate production (NES and NTS) to a combined plant (N;TES) producing the same amounts of electricity and heat. A condition of this method is that on all three plants the same type of reactor must be used. The production costs of electricity and of heat are accordingly represented by the following expressions:

s, =

%T&S

-

%ES

where C, is the amount of relative production costs (self cost) of electricity which is the same for a NTES and a NE.5 with the same type of reactor and at equal

annual

outputs of electricity W,. A shortcoming of this method is that the expense saved from the combined production of electricity and heat is credited to the heat. In this respect, the constancy method represents another extreme opposite to the physical method. The constancy method is even more highly arbitrary than the physical method, since the physical method still shows some lowering in the production costs of heat on passing from a single-purpose plant to a combined plant (a lowering due to the increased reactor power), whereas the constancy of electricity production costs at such a transition is a basic con?ept of the constancy method.

This method distributes the production costs at a NTES between electricity and heat according to the following relationships: DesahaIio?i,

7(1970)323-342

TECHNWB-ECONOMIC

PARAMETERS OF NUCLEAR

DESALINATlON

PLANTS

333

(31)

where tr,, e, are the exergy magnitudes of the working part of the turbine at the initial parameters and at the back pressure parameters, respectivety in kc&/kg.. This method allows for the working capacity of steam in accordance with its potential, and proceeds from the premise that heat used for heating, desalination or industrial purposes must be debited with part of the expanditure at the NT&S proportional COthe working capacity of the steam received from the turbine.

This method is similar to the exergetic method. According to it, the overal production costs are distributed in the following proportions:

where io, it are the enthafpy vatues for the working part of the turbine at the initial and the back pressure parameters, respectively; ir- the enthaipy value of the working part at the exhaust of a condensationa! turbine for the same initial parameters. The thermodynamic method. like the exergetic method, allows for the value of the heat in accordance with its potential. However, both methods entail the drawback explained below. Both exergy and enthalpy are thermodynamic indices of the working capacity of a working part reduced to its unit weight. Eqs (31-34) are therefore, strictly speaking, only correct in the case where at the NTES a turbine is installed with back pressure, without intermediate superheating of the steam, and without regenerating withdrawals, I‘.e, at a constant (idealized) expenditure, by weight, of steam at all stages. Thus, these methods do not allow for the actual process of conversion of heat energy into mechanicai energy, whereas the electricity and heat production costs determined by them are insensitive to changes in the expenditure of steam In the process of its expansion in the turbine. Desalination, 7 (1970) 323-342

W. 1. ICORYAKINet Ui.

334 The

incomplete

production

tFletll0d

If a nuclear reactor of a fixed thermal capacity (and parameters) is used in a dual-purpose plant, the electric capacity of that p!ant (iv,““) will always be less than where the reactor is utihzed in a condenaiional NES (N,N=), which means that it is always possible to compute the magnitude of the decrement in the electric energy produced at the A+TE!% (35) The method of incomplete production proceeds from the premise that production of heat must be debited with part of the general expenditure an NTES, proportional to the decrease in the amount of electricity produced, the production costs of electricity and heat are determined by the following pressions.

the the i.e. ex-

(37) where WC”

and WfEs are the annual output of electricity at the NOES and at the NES, respectively. One can readily see that in the case of a turbine with a constant flow of steam from inlet to exhaust, and without intermediate superheating, the incomplete production method coincides with the thermodynamic method. The incomplete production method is of a more general character than the exergetic or the thermodynamic methods, since its analytical apparatus is applicable not only to an idealized turbine, but also to anjr actual process accompanied by intermediate superheating of steam, separation, regeneration, etc. However, its drawback, as in the case af the fwo previous methods, is that it distributes between the electricity and the heat al1 the expenditure of the NIX’S, including the expenditure of the engine room and of the electricity departments. Such a distribution is unjustified, since the production of heat is relatively simple, whereas the production process of electricity is of considerable complexity. It would be illogical to distribute the expenditure of the turbine and of the electricity departments over both kinds of product, while it is only incurred on the production o.‘eiectricity. This summary distribution of all expenditure of a N7Ei admittedly leads to a marked simplification of the computation work. However, the resulting convenience is incommensurate with the economic bat-m that may result from a sharp rise in the produetio,n cost of heat. Furthermore, this may lead to methodi@ly incorrect conclusions, since the specific production costs of heat in combined production may prove some-what higher than in separate production. Desalination,

7 (1970)

X3-342

TECHNICO-ECONOMIC

PARAMETERS

OF NUCLEAR

DESALINATION

335

PLANTS

The methods described for distributing the total production costs of combined plants producing electricity and helt all have some basically inherent defects. The above review and analysis of their bas!c concepts permit defining the nature of a composite methcd which combines the positive features of each of the considered methods and is at the same time free from the defects brought out by the

analysis.

Like the physical method, this method must take into account the structure of the general production costs of the AWES, i.e. break them down into shares apportioned to the production costs of the reactor section (S,,). the electricity section (SJ, the heat section (S,,) and to general costs (S,J. In doing so, the method must debit the electricity and the heat sections with the full amounts of their respective production costs, while apportioning to their products only the expenditure of the reactor section and the general costs. Furthermore, like the incomplete production method, the composite method must provide for a distribution in proportion to the electricity produced (W,“” VTES ) at the ANTES. in comparison with the NES equipped with the same type reactor. The production costs of electricity and of heat. as defined by the composite method. are expressed by the foilowing relationships: s, = s, + ‘.S

* WES w"ES

+

s

s, + s,, (w,“‘Es/w,“E=) SC ---

c

S .VT&S-

s,c -__---

(38)

(39) It can be seen that the composite method, like the physical method, takes account of the structure of production costs formation at a NTES, and apportions among the two forms of energy only those general costs that cannot be directly debited

to one of them. Like the exergetic and the thermodynamic

methods,

it

puts the value of heat produced by the reaction into dependence on its potential. Finally, like the incomplete production method, the composite method accounts for the actual work done by the steam in the energy cycle (presence of intermediate super-heating, intermediate separation, regeneration, etc). vi.

COMPARI~N

OF THE DIFFERENT

MFTHODS

A comparative computational investigation will now be made of the described methods of distributing the annual costs of a IVIES between electricity Desalirration, 7 (1970) 323-342

336

YU. 1. RORYAKlNCt a/.

and heat. The results ot the computations nave been elaborated in the form of dimensionless parame!ers (8, and #II,). representing the ratio of the production costs of electricity ($1 and heat (S,) to the general expenditure of a ANTES(SST_& i-e_

(441) These coefkients

must obviously

conform to the condition of:

/3, “t-A = 1

(W

Fig. 1 shows the variation of parameters /3, and /?, in relation to the value of the turbine back pressure (I’,) for each of the methods considered.

.6

-

0.03

0.10

50 .O*-

Pt(a

Fig. 1. Comparison of methods of apportioning general production costs of a dual-purpose plant (A’T.&S) with a uranium-mphite canal reactor, between electricity and heat (Q, q 572 MW). I - physical method: 2 - constancy method; 3 - coefficients method; 5 - incomplete production method.

The magnitude of P, varied from the pressure in the condenser (Pk) to the pressure at the intet into the turbine (PO). The study thus embraces the whole theoreticalIy possible range of variations in the quanti~tive interrelations among the different products -, from the operation of a NTES under a regime of a condensational NES up to its operation under a regime of a nuclear thermal station which produces heat only. DesaIinorion,

7 (1970) 323-342

t*)

TECHNICO-ECONOMIC

PARAMETERS OF NUCLEAR

Such an approach under

intermediate

makes

regimes

it possible

of back

DESALlNATION

to follow

pressure,

up every

in which

337

PLANTS

method

the essential

not only differences

between various methods are not brought auf by qurrntitative results, but aiso under exlreme regimes, in which their inherent shortcomings become ctearty apparent. As pointed out above. the exergetic and thermodynamic methods are, strictty speaking, only correct for the special energy cycle. and_ for this reason, two computational alternatives are given: In the first alternative (Fig. 1) a nuctear dual-purpose plant with a Betoyarskitype reactor is considered. having an electric capacity (under a condensational regime) of 200 MW, at an energy cycle with no intermediate superheating and with no heat regeneration in the cycle (idealized process). The initial parameters for the steam are PO = 90 at. and To = 535°C. The pressure in the condenser is Pk = 0.035 at. in the second alternative a NT&S is considered with a reactor of the NovoVoronezh N&S having an electric capacity of 300 MW with an actual energy cycle of saturated steam. which includes intermediate separation of steam and regeneration of heat in the cycle. The initiat parameters of the steam are P, =44 at. and To = 255°C. The pressure in the condenser is Pk = 0.035 at. The results of the second alternative in the comparison are shown in Fig. 2.

Fig. 2. Comparison of different methods of apportioning genenl production costs of a nuclear duaLpurpose plant (NOES) with hydro-water reactor, among the different products

(Qr = 1450 MW). 1 - physical method: 2 - constancy method; 3 -coefficients method; 4 - thermodynamic 5 - incomplete production method: 6 - composite method.

method;

Desalination, 7 (1970) 323-342

YU. 1. KORYAKIN

338

ef d.

Tlte phpied ~ret~l~~ is represented in Fig. I. by Curve I. On changes in the value of P, from Fe to 9, the share of expenditure of the NTES chargeable under this method to the heat f& varies from I to 0.4 and ,then sharply drops to zero. This means that the production costs of electricity throughout the range of variations of P, do not exceed - 0.6 of the total expenditure of the NTE.S. At the same time, in the case of a pureiy condensational operation, 8, = t. i.e. the production costs of electricity are equal to the total costs of the NTE.!& This is so because, even at a slight temperature difference of the required heat from the saturation temperature corresponding to Pk = 0.035 at., the amount of heat produced by the NTES represents a considerable part of the reactor’s heat capacity. This brings out the basic shortcoming of the physical method which lies in the fact that the costs are apportioned in proportion to the gross amount of heat expended on the production of ebzctricity and heat. while failing to allow for the difference in the technotogical production processes of these products. fn other words, no account is taken of the fact that the conversion of heat into electricity is possible only through the process of change of potential of the initiaf heat. The amount of initial heat converted into electricity is expressed by the equation: Q,=G-AJ

(43)

where AJ is the change in heat contents of the initial heat; G- expenditure of steam in the turbine. The amount of initial heat converted into thermal energy is expressed by the equation:

where r, is the heat of the phased transition at the saturation temperature corresponding to the back pressure.. Thus. the change of back pressure is mainly retlected in the amount of electricity produced. The electric capacity of a NTES during the variation of P, from 90 to 0.035 at. changes by 100x, whereas the production of heat varies only by 40%. in other words, the initial heat produced by a reactor can be converted fully into heat, but only in part into electricity - a part determined by the change of potential from Jo to Jk, white the heat of the phased transition at T1 remains unconverted. Since it ignores this difference in the technology of electricity and heat production at a NTES, the physical method unjustifiably relates most savings in the combined production to electriicity, thus overstating the share of general costs of a NTES apportioned to the thermal energy.

7%~ camfuncy method is represented in Fig. 1 by Curve 2. Since the basic concept of this method assumes that’the specific production costs of electricity

TECHNIC~ECONOhlIC

PARAMEXER!! OF NUCLEAR

DESALINATION

339

PLANTS

at a NTES for any fixed value of back pressure f, equals the production costs (self costs) of electricity at a NES of an equivalent electric capacity, this means that all savings in costs, due to the combined production of the two products, are automatically

credited to the heat. At P, = Pt, the share of cost:; at a NTES charged to the electriciiy is the

maximum (J?== I). while the relarive value of these costs is minimal. On raising P# from

Pr, to PO, despite

the share

the increasing cost of electricity at an equivalent NES, of costs at the NTES charged to electricity first goes down slowly and

later. at P, = f,, drops to zero; since in this case the electric capacity of the NTES is equal to zero. From Fig. I it can be seen that theconstancy method and the physical method oppose each other in most parts of the possibte range of variations of P,. and occupy extreme positions in relation to other methods. The cheapening coeficiettrs method is represent

in Fig. 1

by Curve 3. Since

this method proceeds from the condition of uniform distribution products) of the savings on production costs obtained at a NTES in with equivalent single-purpose plants, the parameters /?, and /3, have the range of variations of P, a value greater than zero, and only at

(among all comparison throughout

the extreme

values of P, = fk and P, = PO they become equal to zero. As can be seen from Fig. I. the method of cheepening coefficients occupies an intermediate position between the physical and the constancy methods, since it proceeds from the concept of equivalence of all products and makes it clear that the former overstates the share of costs at the NTES debited to heat, and the latter - to electricity. Powever. while defining the parameters 8, and @, as the rntio of production costs of each product at dual-purpose plants to the,sum of equivalent costs at single-purpose plants, this method fails to account for the fact that on passing from mean values to fk and PO, the technical perfection of single-purpose plants becomes increasingly different. were it only for the reason that their unit thermal capacities differ considerably - a circumstance of special importance to-nuclear power plants. The method of coefficients at low values of back-pressure P, overs’Mc;s the share in the production costs of a NTES debited to heat, and understates the share of costs debited to electricity. whereas, at high values of P,. the situation is reversed. Thus, being more fully justified in comparison with the physical and the

constancy methods. the cheepening coefficients method nevertheless fails to present a correct dist~bution of costs of a NTES for the full range of possible back pressure variations, since it does not take into account :he actual technical aspects

of the production

of electricity

and of heat.

Tfte energetic method is represented

in’ Fig. 1 by Curve

4. This

method

of

Desalination,7 (1970) 323-342

340

YU. I. KORYAKIN

et Of.

apportioning the costs of a NTES proceeds from the working capacity of the initial steam converted into electricity and heat, which depends on its potential and, therefore, a~.rtomatically shows for the difference in the production technology of the two products. The exergetic method is based on technical principles, and in its application it is therefore possible to avoid the mistakes which are unavoidable in utilizing the method of coefficients in ranges where the values of P, are close to Pk and PO_ Indeed. as can be seen from Fig. 1, the results given by Curve 4 at average values of P, are close to the results given by the method of coefficients. where. on transition of P, to PL and PO. it smoothly arrives at the respective values of 0, = 0. & = 1 and 8, = I, j.?, = 0. The drerrrtodptamic md the incomplete production nrethods in the first computational alternative (Fig. I), i.e. in the case of constant expenditure of steam

at all turbine stages. produce the same results. This can easily be demonstrated by writing down their coefficients for apportioning the total production costs:

These methods are represented in Fig. 1 by Curve 5. While they differ from the exergetic method in that they depart from the notion of working capacity, they nevertheless allow for the difference between heat units of different potential, as well as for the technologicai characteristics of producing electric and thermal energy. As can be seen from Fig. I, these methods yield results which are quite close to those obtained by the exergetic method and are therefore a close approximation to it. The results of the second computational alternative are shown in Fig. 2. The physical constancy. cheapening coefficients. incomplete production and the generalized methods are represented in Fig. 2 by broken lines. with leaps at those values of back pressure which coincide with the pressure of regenerative withdrawals. The graphs in Fig. 2 bring out with particular clarity the remoteness of the thermodynamic method from the actual process of electricity production. This method is shown in Fig. 2 by a smooth curve and is thus insensitive to changes in the discharge of steam through the turbine, or to the changes associated with it in the energy produced. Both in the first and in the second alternatives, the basic methods intersect within the interval of back pressure variation from 1 to 3 at. For this interval a Ginter Triangle has been plotted in Fig. 3, on which are shown the ranges of electricity and heat production cost variations, as defined by each of the methods considered. Desalinarion, 7 (1970) 323-342

TECHNICO-ECONOMIC

0.2

PARAMWRS

0.4

DESALINATION

OF NUCLEAR

016

341

PLE NT9

0.8

Fig. 3. lntcrrclation of spheres of variation of production costs debited to electricity and heat under different methods at back-pressure variations from I at. to 3 at. 1 - physical method; 2 -constancy method: 3 - coefficients method: 4 - thermodynamic method: 5 - incomplete production method: 6 - composite method.

Thus,

the review and analysis

given of the existing

methods

of apportioning

the production costs at a combined plant producing electricity and heat, permit bringing out the conventions incorporated in the basic concepts of each. The formulated generalized method combines the positive features of other methods, while

remaining

considered

free to some

the most strictly

extent

correct

from

their

shortcomings.

This

method

is

one.

REFERENCES

Methods for Nuclear Desalination, 1. ~NTERSATIONAL Aro~~c ENERGYAGENCY. Costing Technical Report: Series No. 69, IAEA. Vienna. 1966. 2. INTERNATIONAL ATOMICENERGY AGESCY, Guide to the Costing of Water from Nuclear. Desalination Plants, Technicaf Reports Series NC. SO, IAEA. Vienna. 1967. 3. A. A. LOGISOVASD Yu. I. KORYAKIN. Technical and economic aspects of the use of nu&ar rea~fot-s for desaiination of water and etcctric power generation, in: Nuclear Energy for Water Desalination, Tec!rniccL Reports Se&x No. 51. IAEA, Vienna. 1966. 4. Yu. f. KORYAKIN AND A. A. Lo~rsov, Atomnaya energiya i opresnienie soIenykh voci (Atomic energy and desalination of saline waters). At. Energ., 2Ot3) (1966). Komitet Ministrov SSSR po Nauke i Tekhnike. Mctodika tekhnoekono5. Gosudarstwxrnyi micheskikh raschctov v cncrgetike (Government Committee of USSR MinistenforSciencerutd Technology. Methodology of technical+zonomic computations in energetics). Moscow, 1966. Desalination, 7 (1970) 323442

342 6.

YU. I. KORYAKIN

et a/.

Yu. 1. KCJRYAKIN,A. A: LOGINOV. V. A. CHELNYAEV AND I. 1. SAKHAROV, Metodika rascheta stoimosti vody i elektroenergii dlia yademykh opsesnitelnykh ustanovok (Methodology of computing the cost of water and electricity for nuclear desalination plants), 4. &erg., 19(2) (i%S).

Desalination,

7 (1970) X3-342