Advantage of incorporating geothermal energy into

power-station cycles

A.A.L. White, B.A., D.Phil., M.lnst.P.

Indexing terms: Energy conversion, Power systems

Abstract: The generation of electricity from low-temperature geothermal sources has been hampered by thelow conversion efficiencies of Rankine cycle operating below 150°C. In the paper, the author shows how theelectrical output derived from a geothermal borehole may be substantially improved on that expected fromthese cycles by incorporating the geothermal heat into a conventional steam-cycle power station to providefeedwater heating. This technique can yield thermal conversion efficiencies of 11% which, for a well-headtemperature of 100°C, is 50% greater than the output expected from a Rankine cycle. Coupled with thesmaller capital costs involved, feedwater heating is thus a more attractive technique of converting heat intoelectricity. Although power stations above suitable geothermal resources would, ideally, have the geothermalheat incorporated from the design stage, experiments at Marchwood Power Station have shown that smallexisting sets can be modified to accept geothermal feedwater heating.

1 Introduction

Volcanoes have not erupted in the United Kingdom for thelast 60 million years and the last major earthquake withinthese Isles occurred before historical time. The majorityof the countries of the world share this good fortune, butas a consequence do not possess geothermal manifestationssuch as geysers promising the existence of large hot waterand steam reservoirs close to the surface which could betapped to provide heat and electricity. Nevertheless, theheat contained in the rocks below such 'nongeothermal'countries is enormous and could supply all of the countries'energy needs if it proves possible to extract heat fromimpermeable crystalline rocks.1

With present technology, it is possible to obtain the heatcontained in deep permeable rock strata known as aquifersby extracting the water contained within them,2 but inthe United Kingdom the maximum temperature that can beexpected from aquifers is restricted by geology to 110°C,3

and crystalline rocks will only yield temperatures of 200°Cat most within the next few dacades, owing to the limi-tations of drilling techniques.4

Geothermal energy could then provide the UnitedKingdom and other such countries with large quantities ofrelatively low-temperature heat. In this paper, the thermo-dynamic principles behind the conversion of this heat intoelectricity are discussed, and it is shown that the mostefficient method of conversion is by combination with aconventional steam-cycle generating station.

2 The generation of electricity from low-temperaturegeothermal resources

2.1 Thermodynamic principles

The generation of electricity from low-temperature(< 150°C) geothermal brines has been hampered by the lowconversion efficiencies of the necessary generating plantwhich are imposed by the second law of thermodynamics.

Paper 760 A, first received 12th March and in revised form 21stApril 1980Dr. White is with the Central Electricity Generating Board, March-wood Engineering Laboratories, Marchwood, Southampton, Hants.,England

330

An ideal engine, for example, operating from a hot watersource at 100°C will have, as is shown below, an efficiencyof just over 11% for 30°C rejection temperature. Recently,much attention has been paid to hybrid fossil-fuel geo-thermal energy systems, since it is possible to avoid therestraints of this law by using the geothermal heat toprovide feedwater heating in the steam cycles of conven-tional power stations.

_ J reject heat)

toreservoir

temperature

from production hole

Carnot cycles;source temperature T,<T<T2sink temperature TQ

entropy

Fig. 1 Direct conversion

a Energy conversion systemb Temperature/entropy diagram

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0413-702X/80/050330 + 06 $01-50/0

2.1.1 Direct conversion: Consider a geothermal systemwhere water is produced at a temperature T2 K passedthrough an energy conversion system, where the heat isextracted, and reinjected into the reservoir at Tx K, asshown in Fig. la. For unit fluid mass flow from the produc-tion borehole, the amount of heat given to the energyconversion system is Cp(T2 ~ 7 \ ) and this will be con-verted into electricity with an efficiency 77 which willdepend, amongst other variables, on the temperature atwhich heat is rejected to the environment. The tempera-ture/entropy diagram of such a cycle is given in Fig. \b andmay be seen to consist of a series of Carnot cycles with afixed sink temperature of To and source temperaturesvarying from T2 to 7\ . The heat will be extracted from thegeothermal fluid at temperatures ranging from T2 to Tx K,so the total amount of electricity obtainable by an idealconversion system for unit mass flow will be

W = + f 2

J Cp vc(T)dT0)

where ric{T) is the efficiency of a Carnot engine operatingbetween an infinite source at TK and a sink at To K whichmay be written as r]c(T) = 1 - To/T. Thus

W = Cp 0if Cp does not vary with temperature.

T,r-

temperatureT

pum

entropy s a

temperatureT

turbineexpansion

\. I saturation\-4-curve

Integrating, and dividing by the heat input we derive aconversion efficiency of

Videal = 1 -T2-Tx

(2)

entropy s

This is the largest conversion efficiency possible and wenote that

< 1 r °Videal *** l ~ ~,

the equality occurring as Tx -> T2 as required by the secondlaw.

Conversion systems being designed and built today forsuch geothermal sources are based on the Rankine cycleoperating with an organic working fluid. In order for theirefficiencies to approach those of eqn. 2, it is necessary forthe heat input path of the cycle in the TS diagram to beas close as possible to the cooling curve of the geothermalfluid. Such a path is possible if the cycle is supercriticalas shown in Fig. 2a. This, however, causes excessive lossesin the turbine due to the expansion path crossing thesaturation line. A reduction in pressure produces thefamiliar subcritical Rankine cycle, but as most of the heatis supplied to the cycle fluid at the evaporator temperatureTe, which is less than T2, the efficiency again falls short ofeqn. 2. Studies have been made of the choice of workingfluid for particular geothermal source temperatures and anempirical relationship has been found5 between the idealoperating temperatures of working fluids in terms of theircritical temperatures and specific heat. For temperatures< 180°C, the efficiencies of their optimised cycles werefound to be ~ 0-65 i7ideai and r)Rankine = 0-65 i?ideal againstthe resource temperature T2 is plotted in Fig. 3. We seethat at 100°C, i?Rankine = 7%, which may account for theopinion that the direct generation of electricity from suchcool sources is not economically worthwhile.6

2.7.2 Geothermal feedwater heating: It is possible togenerate greater quantities of electricity from a given low-temperature source by incorporating the geothermal fluidinto a conventional steam power cycle. All the steam-drivenpower stations in the CEGB, and most other utilities, havefeedwater heaters which use steam bled from the turbinesto preheat the boiler feed water (Fig. 4). These areemployed since it is a consequence of the second law ofthermodynamics that the heat of combustion of the fuelwill be converted into work with a greater conversionefficiency, the higher the boiler inlet temperature. The geo-thermal heat may be supplied to the steam cycle byreplacing some of the feedwater heaters and allowing thebled steam to remain in the turbine, thus generating moreelectricity (Fig. 5).

Consider such a 'modified' Rankine cycle in Fig. 4where M{ is the steam flow between the ith and (1 — l)thbled points and the bt& and hts are the bled steam flow ratesand specific enthalpies of the steam at the ith bleed points.The TfS are the feedwater temperatures after the corres-ponding feedwater heaters. The work performed by theturbine is then

W =

Fig. 2 Rankine cycles

a Supercritical Rankine cycleb Subcritical Rankine cycle

where 77,- is the stage efficiency. We now replace the firsttwo feedwater heaters by a heat exchanger whose primary

IEEPROC, Vol. 127, Pt. A, No. 5, JUNE 1980 331

is connected to a geothermal doublet. Let us assume thatthe geothermal water heats the feedwater to a tempera-ture. TG as we show in Fig. 5. The new bleed rates b's andb\ are unaltered, b'2 and b\ are zero, and b'3 depends onthe value of TG. If TG = T2 then b'2=b'3. If they areunequal, then b'3 must be adjusted to ensure that T3 is thesame as T3. We also assume that the enthalpy drops acrossthe stages are not changed by the change in mass flowthrough the turbine. This simplification is reasonable for aturbine built to accommodate the higher steam flows but,as we shall see, it is not strictly true when this is not thecase.

The work performed by the turbine is now

W' = X (3)1 = 4

i i r

10

6h

iFig. 3

60 80 100 120 140geothermal source temperature

Efficiency against resource temperature

160

Reinjection temperature = 35 CHeat rejection temperature = 30° C

condenser

feed water heaters

Fig. 4 Modified Rankine cycle

332

feed water heaters

and so the new cycle's fuel efficiency f is given by

= Soldi* +

where Ae = (W — W)/W is the fractional increase in outputfor given values ofM6,h6.

In Fig. 6, we plot values for Ae for different feedwaterheating temperatures TG using data for two kinds of plantcurrently employed by the CEGB, with ratings of 500 and

M6.

icondenser

heatexchanger

geothemnanfluid

from toreservoir reservoir

Fig. 5 Geothermal feedwater heating

8

60 70 80 90 100 110 120

Fig. 6 Percentage increase in fuel efficiency with geothermalheating temperature TG

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60MWe.* The difference in the two curves arises from thesteam conditions employed by the plant; 500MWe tur-bines have seven feedwater heaters and operate with inletsteam conditions of 160bar at 565°C whereas the smallerunits are supplied with steam at 480" C at 60 bar. Thefraction of heat supplied by the geothermal source to the500 MWe unit is smaller than for the other unit whichleads to the smaller rise in Ae.

The efficiency with which the geothermal energy isconverted into electricity in the form of an increased out-put from the alternator may be written as

Vfwh —eAeP

(TG - T0)mCp

where e is the efficiency of the heat exchanger, m is thecondenser flow rate and P is the normal output of the set.Now, as both curves of Ae against TG are approximatelylinear, Ae may be written in the form

Ae = A(TG-T0)

and we see that Tifwh is independent of TG and in fact hasthe value of 11% for both sizes of turbine if a heatexchanger efficiency of 90% is assumed. This is not a vio-lation of the second law of thermodynamics since, byinspection of Fig. 5, we see that the geothermal heat allowsvarious amounts of bled steam to remain in the turbine andproduce more work. The efficiency with which the heatcontained in this steam is converted into work is deter-mined by its enthalpy at the bleed point and at the con-denser. Varying the geothermal temperature TG just altersthe quantity of steam so saved and not the conversionefficiency.

The advantage of using geothermal heat in combinationwith fossil-fuel power stations over direct conversion cannow be seen, and in Fig. 7 the electrical output obtainablefrom both systems operating from the same source is com-

pared, where that available from direct conversion has beentaken from Fig. 3. Feedwater heating is thus superior todirect conversion at temperatures up to 150°C. Above thistemperature, feedwater heating may still have an economicadvantage since the plant required for organic fluid Rankinecycles is more expensive than the pipework needed forfeedwater heating.

2.2 Modifying existing power stations to acceptgeothermal feedwater heating

Ideally, geothermal feedwater heating would be incor-porated into a suitably sited power station at the designstage. However, very few utilities would contemplate suchan innovation without some previous operational exper-ience obtained from a pilot scheme. The MarchwoodBorehole, sunk by the Department of Energy, may offersuch an opportunity, since it is being drilled adjacent to an8 x 60 MWe power station. It is planned to replace the firsttwo feedwater heaters as the inlet temperature to the thirdis ~ 90°C which is of the same order as that expected fromthe borehole. For a new station the calculations outlinedin the preceding Section are relatively straightforward, asthe last stages of the turbines will be designed to cope withextra steam flow, but the penalty of modifying an existingstation to allow feedwater heating is that it is difficult todetermine, theoretically, the extra output that will be avail-able from the bled steam which is allowed to remain inthe turbine.

The increase in mass flow through the last stages of tur-bines at Marchwood, however, could change the stageefficiencies since the sets would be running in an off-designcondition. This could reduce the benefits expected fromfeedwater heating as is now shown.

2.2.1 Efficiency reductions: Consider the last two stages ofthe turbine in Fig. 5. With the same notation as before theoutput from these stages in the normal condition is

W = r12M2(h2-h1)+ViMl(h1-h0)

In the geothermal mode with the bled steam retained in theturbine,

W = (v + Srih(M2 + b2)(h2-hx)

+ (ri + Sv)x(Ml + b, +b2)(h1-h0)

where orj is the change in stage efficiency caused by theincrease in mass flow and, as in the preceding Section, weassume, for simplicity, that the enthalpy drops areunaffected. For simplicity, we write

and

and the increase in output due to the geothermal sourcebecomes

60 80 100 120 K0 160geothermal source temperature, °C

W'-WG =

-h0)

Fig. 7 Comparison of outputs from feedwater heating and Ran-kine cycle conversion systems from same geothermal source

•Private communications, 1979:Burdett, R.: 'Heat rate data for 500 MWe set'.Coham, C: 'Heat rate data for 60 MW set'.

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Thus, if 6T7 is not zero the predicted output will be reducedby an amount

8rj[M2(h2 -

(4)

333

and if 577 were as large as

- 7 7-ho) b1)(hl-h0)

there would be no gain from feedwater heating. At March-wood, this value of 677/7? is - 7%, and although it is unlikelythat the 10% increase in mass flow through the stageswould cause such a drop in efficiency, it is very difficultto predict accurately the actual efficiency of the last stagesof turbines operating in these conditions. For this reason,an experiment was performed at Marchwood which simu-lated the effect of feedwater heating on a turbine.

2.2.2 Geothermal simulation experiment: A crosslink wasmade between two adjacent sets which allowed the inter-change of the inlets to the third feedwater heaters. Theturbines were run for a period of one hour with the bleedsto feedwater heaters 1 and 2 of set A closed (Fig. 8). Inthis way, set A experienced external feedwater heating andthe fuel efficiency f of the set was determined. The cross-over was then removed, and the sets were run in the normalcondition (Fig. 9). The change in fuel efficiency of set Abetween the two runs enabled a calculation to be made ofthe extra output caused by using geothermal heating tokeep the inlet temperature of the third feedwater heaterat 90°C. The result of the test was an increase in fuelefficiency of 2-8 ± 0-2%. This value should be comparedwith the value of 3-0% as shown in Fig. 6, which was calcu-lated assuming no changes in efficiency. By using eqns. 3

condenser

condenser

Fig. 8 Geothermal simulation experiment with crosslink

334

and 4 with values for the flows and enthalpies, we see thatthe last stages of the turbine suffered a decrease in efficiencyof 0-5 ±0-5%.

The 2-8% increase in output was accompanied by a 16%increase in pressure drop from bleed point 1 to the con-denser and a 6% increase from bleed point 2. Thus, notonly is the assumption that the enthalpies remainedunaltered not strictly valid, but the increased pressure dropcould affect the integrity of the last set of blades on theturbine's rotor. Unfortunately, it is impossible to predictthe blade life from the pressure loadings across it, but sincethe Marchwood sets are not run on base load, it is veryunlikely that any geothermal experiment at Marchwoodwill decrease the life of the station.

3 Conclusion

Unless there is a revolution in drilling techniques, exploit-able geothermal resources in the majority of the worldwill be at temperatures below 200°C for the foreseeablefuture. There are many uses of such low grade heat, but inthis paper we have restricted ourselves to the generation ofelectricity and have shown that for temperatures less than150°C it is best to combine the heat from the geothermalsource with a conventional steam cycle generating station.Whereas such hybrid power stations would be ideallydesigned specifically to incorporate the geothermal heat, anexperiment at Marchwood Power Station has shown thatthe efficiency of an existing turbine is not greatly affectedby modification to accept geothermal feedwater heating.However, large changes in the pressure distribution throughthe turbine caused by such a modification would causeconcern if the turbine were run for a great length of time.

condenser

feedwater heaters

Si 1ontorc S

condenser

Fig. 9 Geothermal simulation experiment without crosslink

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4 Postscript: The Marchwood Borehole

Since the delivery of this paper in February 1979, March-wood has been the site of the United Kingdom's first geo-thermal demonstration project. The existence and positionof aquifers in the sedimentary basins of England are notwell known and the Department of Energy decided to drilla hole in the Hampshire Basin to determine the size of thegeothermal resource in the Southampton area, which wasbelieved to exist as water contained in a sequence ofpermeable rocks known as the Bunter Sandstone. Fig. 10shows the structure of the basin as envisaged in February1979 based on geographical measurements and the resultsof a borehole sunk at Winterborne Kingston in 1976.7'8

Unfortunately, some of the 'Jurassic' rocks are extremelygood reflectors of seismic waves and it proved impossible toextract reliable data from the more deeply buried Permo-Triassic rocks which it is hoped would contain the Bunter.Thus, although the extrapolated depth of the reservoir isshown as ~ 2500—3000 m below Marchwood, the error isquite large and the rocks could be as shallow as the bottomof the Jurassic rocks at 1 -8 km.

The only reliable method of proving the resource was

predictions. The temperature of the reservoir is 70°C butthe yield of the hole has not yet been determined as thiswill require a prolonged pumping test. If the tests aresuccessful it is hoped to connect the borehole to the powerstation within the next year or so.

5 Acknowledgments

The author would like to thank R. Grant and MarchwoodPower Station for their assistance during the turbineexperiment. The work is published by permission of theCentral Electricity Generating Board.

6 References

1 ARMSTEAD,H.C.H.: 'Geothermal energy'(Spon. London, 1979)2 GRINGARTEN, A.C., and SAUTY, J.P.: 'A theoretical study of

heat extraction from aquifers with uniform regional flow',J. Geophys. Res., 1975, 80, pp. 4956-4962

3 OXBURGH, E.R., RICHARDSON, S.W., WRIGHT, S.M.,JONES, M.Q.W., PENNEY, S.R., WATSON, S.A., and BLOOMER,J.R.: 'Heat flow in mainland United Kingdom'. Presented atthe Commission of the European Communities, Second Inter-national Seminar on Geothermal Energy, 1980, pp. 149-152

position ofaquifer atWinterborneKingston

3000-

Fig. 10 Section Winterborne Kingston to Worthing

(By courtesy of J.R. Bloomer)9

thus drilling, and since drilling is so expensive, it wasdecided to drill the hole near a possible heat load in casethe hole proved to be successful. This would enable ademonstration project in which the engineering difficultiesinvolved with geothermal fluids could be investigated. Forthis and other reasons, Marchwood proved to be the bestavailable site and drilling commenced in November 1979.On New Year's Eve, the Bunter sandstone was encounteredat a depth of 1 -7 km, thus towards the shallower end of the

RICHARDSON, S.W., and OXBURGH, E.R.: The heat flowfield in mainland UK', Nature, 1979, 282, pp. 565-567MILORA, S.L., and TESTER, J.W.: 'Geothermal energy as asource of electric power' (MIT Press, Cambridge, Mass., 1976)OXBURGH, E.R.: 'Energy from warm rocks', Nature, 1976,262, pp. 526-528EDMUNDS, W.M., BURGESS, W.G., and ANDREWS, J.N.:'Seminar on geothermal energy'. Presented at the Commissionof the European Communities, 1977, 2, p. 505SMITH, I.: 'Seminar on geothermal energy', ibid., 1977, 1, p. 61BLOOMER, J.: D. Phil. Thesis, Oxford University, 1980

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