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Use of a probabilistic model to design energy transmission and distribution networks for low enthalpy geothermal multiple use schemes
Applied Energy 86 (2009) 284–289
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Applied Energy journal homepage: www.elsevier.com/locate/apenergy
Use of a probabilistic model to design energy transmission and distribution networks for low enthalpy geothermal multiple use schemes John J. Gelegenis * Technological Educational Institution of Athens, Ag. Spyridonos Street, Aegaleo/Athens GR 122 10, Greece
a r t i c l e
i n f o
Article history: Received 23 January 2008 Received in revised form 14 April 2008 Accepted 16 April 2008 Available online 2 June 2008 Keywords: Geothermal energy Multiple use Probabilistic model Probability Location–allocation
a b s t r a c t A probabilistic model is suggested for the design of transmission and distribution network of geothermal energy to potential consumption sites, in cases where the development of various competitive or complementary non-electrical uses is probable, within the broader area of a field. The model can be used to find out (a) the optimum network that may offer the best economic results to the agent who will undertake the development of the field, and (b) the corresponding selling price at which the thermal fluids will be supplied to the end users who are assumed to be other than the above agent. Model input data can be collected in the frame of an appropriate market study, which is roughly specified in this work and commented according to relevant experience from a Greek geothermal field. Finally, applicability of the model is demonstrated through an indicative example. Ó 2008 Elsevier Ltd. All rights reserved.
1. Introduction Since non-electrical uses of low enthalpy geothermal energy have in general difficulties in prospecting as independent and profitable business, establishment of multiple use schemes is more advantageous. In these cases, linear programming can be used to find the optimum distribution of geothermal resources to the various uses, in order to get the maximum total benefit [1]. The decision on the distribution of geothermal energy may not to be restricted to economic criterion only. For instance, for the pilot exploitation of Milos field (Greece), four alternative scenarios were evaluated according to their economy and capability to produce valuable conclusions for the full-scale exploitation [2]. When additional criteria are considered (e.g. jobs created, fuel saved, entrepreneurial risk, environmental impact), the need for a multi-criteria approach arises. The PROMETHEE II method was applied [3] to compare alternative scenarios for the exploitation of the Nea Kessani field (Greece). Later, a multi-criteria group decision-making framework was documented [4], that was also based on PROMETHEE II to be applicable to any renewable energy project. In above works it was assumed that the examined uses will be surely established, and that there is a common economic benefit for all end users. As an alternative, the establishment of the uses could be processed as probable events, while the competing benefits between the end users and the supplier of geothermal energy * Tel.: +30 210 5385816; fax: +30 210 5385306. E-mail address: [email protected] 0306-2619/$ - see front matter Ó 2008 Elsevier Ltd. All rights reserved. doi:10.1016/j.apenergy.2008.04.011
could be also considered. Geothermal energy could be supplied to remote sites, where demand is either more probable or could be provoked via a relevant call for investors. To this aim, an appropriate probabilistic model must be developed to design the extended network for the transmission and distribution of geothermal energy [5], where additionally to an optimization criterion, the network ability to meet feasibility in an uncertain environment should be considered, as usually applied in probabilistic programming [6]. The uncertain environment in geothermal energy utilization has been defined elsewhere [4] in the form of an entrepreneurial risk, that is broken down to distinct characteristics as: new product, new technology, future changes and initial investment. Uncertainty is consequently attributed to the demand, and is actually due to the facts: (a) that geothermal energy is a new product for any broader area where the exploitation of the local geothermal field has not commenced yet (b) that the use of geothermal energy requires technologies that – it is the most usual – people are not familiar with and (c) that the intentions of the potential investors in geothermal applications are unpredictable; these intentions depend on many factors such as the perspectives of each specific geothermal use, the available motives (grants, tax exemptions), the competitive energy sources, the infrastructure of the area, etc., and could be in a way revealed through appropriate market studies. The uncertain environment in geothermal exploitation has impact on the flow rates at which the fluids will be transferred through the network (and hence on the design of the network), and consequently on the expected income, too (and hence on the economy of the geothermal project).
J.J. Gelegenis / Applied Energy 86 (2009) 284–289
285
Nomenclature AE annual energy needs of an application (GJ/year) C NET ðQ 1 ; Q 2 ; . . . ; Q n Þ cost of the network (€) CRF capital recovery factor (1/year) cost of the wells (€) CWELLS D piping diameter (m) f(N) probability density distribution discrete function (value for N probable users) f(Q) continuous density distribution function corresponding to above discrete function f(N), according to the thermal fluids flow rate Q (1/m3 s1) F(Q) cumulative probability function INC(Q) probable income when supplying thermal fluids at Q flow rate (€/year) L length of transmission line (m) LF load factor M maximum number of total potential users for an application at one consumption site ME modification expenses for existing equipment to make use of geothermal energy (€) n number of potential consumption sites
p P(Q) PBT PC PE PE* PE0 PEPRE
PEREJ
PF Q QN QTOT w
probability a potential user to ask for geothermal energy probability of utilization of thermal fluids at Q flow rate pay-back time (year) cost of energy coming from conventional sources (€/GJ) equivalent selling price for geothermal energy (€/GJ) modified selling price for geothermal energy, for partial coverage of the load (€/GJ) reselling price for geothermal energy (€/GJ) maximum price for geothermal energy that makes it still completely preferable than conventional energy supply (€/GJ) minimum price for geothermal energy that is not yet sufficiently low to make a potential user to change from conventional energy supply in favor of geothermy (€/GJ) selling price for thermal fluids (€/m3) thermal fluids flow rate (m3/s) nominal thermal fluids flow rate requirement for a typical unit of an application (m3/s) total production from the wells (m3/s) velocity of the fluids (m/s)
The flow chart of the model is shown in Fig. 1, and the various steps are further explained below.
preference PEPRE) (b) the lower price for which the users would still insist on the use of conventional fuels (price for rejection, PEREJ). For intermediate energy prices, the probability curve may be assumed to get a linear form:
2.1. Assumption of a selling price
p¼
A broad range of the thermal (geothermal or secondary) fluids selling prices PF (€/m3) can be examined. The optimum selling price depends on many factors -fluids temperature (energy content), quality of the fluids, characteristics of demand (intensity, distribution, and approach to the wells) and attitude of potential end users – that should be taken into consideration in the model.
In Fig. 2 it is presented the outcome of a relevant market study [8], that was based on appropriate specifications [9] and conducted in the broader area of the Nea Kessani field. It refers to district heating, and the four sets of data correspond to the nearby villages named Kessani, Koutso, Sellino and Sidini. The mean values are also shown in Fig. 2; a linear probability curve adapted to these data has a standard deviation of 0.018 only, and so Eq. (3) is proved to be a good approximation. For each selling price, a probability distribution function may arise. For an application with an assumed maximum number of potential users M, and for a selling price PE that causes a probability of utilization p – as calculated with Eq. (3) – the following probability distribution discrete function f(N) arises:
2. The probabilistic model
2.2. Conversion to equivalent energy prices A unified selling price for the fluids leads to different prices per energy unit for the various uses [7]. For each application, the geothermal energy equivalent price PE (€/GJ) becomes: PE ¼
3:15 107 Q N LF PF AE
ð1Þ f ðNÞ ¼
where QN is the required nominal thermal fluids flow rate (m3/s), AE are the annual energy requirements (GJ/year) and LF is the load factor. 2.3. Estimation of probability distribution functions For each group of end users, a probability curve can be drawn, expressing – for the various selling prices – the intentions of the users to utilize geothermal energy, as concluded from a market study (e.g. through questionnaires). For an asked total of M persons, a probability curve p(PE) is defined by the points: pi ðPEi Þ ¼ N i =M
PEREJ PE PEREJ ¼ PEPRE
ð2Þ
where PEi are the discrete prices that were considered in the questionnaire and Ni is the number of persons who would utilize geothermal energy if supplied at the price of PEi. Processing all questionnaires allows for the identification of two critical prices: (a) the higher price that is considered still attractive, to make the users change from conventional to geothermal energy (price for
M!pN ð1 pÞMN N!ðM NÞ!
ð3Þ
ð4Þ
To avoid overflow in computations of Eq. (4), the Stirling approxipffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffi mation for n! can be Used: nÀ nn en 2 p n, introducing the following approximation: sffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffi M! M MM ð5Þ N! ðM NÞ! 2 p N ðM NÞ N N ðM NÞMN which has an error of less than 2%, with higher errors being only noted in marginal cases, when N approaches either zero or M. In these marginal cases however, f(N) is almost zero, and so the increased relative error has no practical impact on the accuracy. This is shown in Fig. 3 for various values of N and M up to 100 (for higher values of M accuracy becomes apparently even better). Geothermal energy may be insufficient to completely cover the usually quite high thermal requirements of Industrial applications. The probability of utilization of the distributed thermal fluids to cover a fraction a of the nominal load (and the annual thermal needs, equivalently) can be concluded from Eq. (3), by using an appropriately adapted price PE* (€/GJ), that additionally considers
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1.0
Assume a price for the thermal fluids
0.8
Probability
Characteristics of fluids and requirements of applications
Convert to geothermal energy price for each specific use
Outcome of market study and site visit
Identification of competitive and complementary uses
Kessani Koutso Sellino Sidini Mean Linear
0.6 0.4 0.2 0.0
Estimation of probability distribution function for each application and site
0
40
80
120
Relative energy price (%) Fig. 2. Probability curves for district heating use, as resulted from market investigation in four villages, in the broader area of the Nea Kessani geothermal field. Energy prices are expressed as% percentage of the conventional energy price (data taken from [8]).
Synthesize probability curve and probable income curve for each site Input transmission cost data
10 8
Error (%)
Assume allocation of the fluids to potential consumption sites
Estimate Income Index and Total Probability of utilization
M =10
6
20
4
50
2
100
0 0
0.2
0.4
0.6
0.8
1
N / M ratio Have been examined all possible distribution of fluid to the sites?
Fig. 3. Error by introducing Stirling approximations for n! in Eq. (4) for the estimation of probability distribution function, for various values of maximum number of users M.
NO
YES
proportionally to p(PE0 –PE), with the other operational expenses remaining roughly unchanged. The last expression presents a maximum at PE0 = (PE + PEREJ)/2 which constitutes the optimum reselling price.
Have been examined all possible selling prices? NO
2.4. Synthesis of a composite probability curve for each site
YES
With given: (a) the end uses that can be developed at each site (b) the relative role of these uses (c) an assumed price for the thermal fluids and (d) the consequent probabilities of utilization of fluids at various flow rates (for each use), the following can be estimated:
Conclusion on: - Selling price -Transmission network Fig. 1. The flow chart of the probabilistic model.
ð6Þ
(i) The probabilities various fluid flow rates to be totally utilized on site. (ii) The quantity of fluids, that are respectively expected to be annually supplied to each site, and the corresponding income.
Here, PC is the price of conventional energy (€/GJ) and CRF the capital recovery factor (1/year). In case of reselling geothermal energy (e.g. in District heating) a price must be defined to allow the intermediate agent to be profitable, and geothermal energy to remain attractive. This agent buys geothermal energy at PE and resells it at PE0 , with PE < PE0 < PEREJ. The expected fraction of total users that will probably utilize geothermal energy is approximated by p as calculated with Eq. (3) using the reselling price PE0 . The net reselling income varies
The end uses are distinguished as either competitive or complementary. The case of in series uses is not considered here, because in a cascade utilization scheme the agent cannot guarantee supply of geothermal fluids to the next uses. It is a matter of simple mathematics to extract from the discrete function f(N) of Eq. (4), a continuous distribution function f(Q). Then, the composite probability distribution function fTOTAL(Q) of competitive uses, results as the convolution of their probability distribution functions f1 (Q) and f2 (Q):
the expenses ME (€) for necessary modifications of the existing equipment to accept geothermal energy: PE ¼ PC—a ðPC—PEÞ
ME CRF AE
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fTOTAL ðQ Þ ¼ f1 f2 ðQ Þ ¼
Z
Q
0
f1 ðuÞ f 2 ðQ uÞ du
ð7Þ
The probability for fluids with a flow rate of Q to be utilized in two competitive uses, which have a total maximum capacity of QMAX, will be: Z Q MAX PðQ Þ ¼ 1 FðQ Þ ¼ f1 ðuÞ f2 ðuÞ du ð8Þ Q
where F(Q) is the cumulative probability for fTOTAL (Q). The respective probable income INC(Q) (€/year) is: Z Q MAX INCðQ Þ ¼ 3:15 107 f 1 f2 ðuÞ min½Q ; u < LFðuÞ > 0
PF du
ð9Þ
where is a mean load factor, defined as: RQ ½f1 ðuÞ LF1 þ f2 ðQ uÞ LF 2 du < LFðQ Þ >¼ 0 f1 f2 ðQ Þ
ð10Þ
The above are similarly applicable to more than two competitive uses. When there also exist complementary uses, the probability of utilization P(Q) increases to P0 (Q), with: P 0 ðQ Þ ¼ 1 ½1 PðQ Þ ½1 PC ðQ Þ
INC0 ðQ Þ ¼ INCðQ Þ þ INCC ðQ Þ
ð12Þ
where INCC(Q) is the expected income from the complementary uses (€/year) which is also determined with Eq. (9). 2.5. Evaluation of alternative allocations The evaluation of each network can be based on the probability of utilization of the totally supplied fluids (defined here as the total probability of utilization of the network fluids), the relevant expected income and its cost. The total probable income for a network results as the sum of probable partial incomes from the fluids supplied to the various consumption sites, while the total probability of utilization of the network fluids results as the product of the partial probabilities of utilization of the distributed flow rates at the various sites: n X n INCi ðQ i Þ; Total probability ¼ P Pi ðQ i Þ Probable Income ¼ i¼1
ð13Þ where with i = 1, 2,. . . the various consumption sites are numbered. Optimization is achieved by minimizing the simplified pay-back period PBT of the network and the wells (or equivalently, by maximizing the gross account rate of return). Assuming that annual total expenses constitute a fixed part b of the capital invested, then it is valid: 1 ðProbable IncomeÞ b½ðNetwork CostÞ þ ðWells CostÞ ¼ PBT ðNetwork CostÞ þ ðWells CostÞ ¼ ðIncome IndexÞ b ð14Þ where Income Index is defined as the ratio: ðIncome IndexÞ ¼
ðProbable IncomeÞ ðNetwork CostÞ þ ðWells CostÞ
(
ð11Þ
where PC(Q) is the probability of utilization of the thermal fluids in the complementary uses only, estimated again as per Eq. (8). Lastly, the total probable income INC0 (Q) (€/year) from all potential end uses becomes:
i¼1
Q2, . . .,Qn to the n potential consumption sites, the flow rates that are transferred through the sub-branches of the network can be easily extracted, according to the topography of the broader area and the relative position of the wells. Based on these flow rates, the cost of each branch of the network can be estimated and finally the total cost may arise as a function of the assumed allocation CNET(Q1, Q2, . . .,Qn). Indeed, by assuming a value for the fluids velocity w (e.g. a typical value ranges between 2 and 3 m/s [10]), the diameters of the network branches can be directly estimated from the flow rates of the transferred fluids D = 2{Q/(pw)}1/2. Afterwards, the application of any appropriate cost equation (like the linear relations suggested in [11]), allows the estimation of the cost of each branch from its diameter. Obviously, for all allocations the sum of the flow rates RQi (i = 1,. . .,n) cannot exceed the total production from the wells QTOT. The various allocations are examined provided that their total probability PP(Qi) (i = 1,. . .,n) exceeds a minimum threshold value P0. This last probabilistic constraint restricts significantly the number of the necessary calculations (rejecting the rather improbable allocations), and at the same time leads to the most probable allocations of fluids. Consequently, the optimization criterion of the probabilistic model gets the form:
Maximize
n X
) INCi ðQ i Þ=½C NET ðQ 1 ; Q 2 ; . . . ; Q n Þ þ C WELLS
i¼1
with
n X
Q i 6 Q TOT and
i¼1
n Y
P i ðQ i Þ P P0
ð16Þ
i¼1
Since there are not usually expected to be many potential consumption sites n, the necessary calculations are quite restricted. Hence, no special programming techniques are required to solve the above optimization problem. A simple trial calculating process examining all potential allocations through appropriately nested loops (e.g. for each consumption site i, there are examined flow rates from Qi = 0 up to Qi = QTOT–RQj, where last sum is taken for j = 1 to i) and with a reasonable flow rate increment DQ, is ordinarily expected to be sufficient. Elaborating further on the role of the threshold probability P0, it is noted that the total probability that corresponds to a network does not reflect the economy of the network but how probable it is the assumed flow rates to be consumed at the respective sites. Hence, a low total probability means that it is the most probable, at the end, the quantities of fluids that will be consumed to be smaller than that for which the geothermal network had been specified. Noticeably, the total probability is anyway taken into consideration in the optimization criterion (where the probable income is included) and so it is quite improbable for an allocation with a low total probability to be preferred as the optimum. For this reason the threshold value of P0 cannot be critical for the optimum solution, provided however that a reasonable (e.g. a not very high) value has been introduced in the condition. On the other hand, an allocation with a low total probability is expected to finally lead to flow rates lower than the nominal values, a fact that may have a psychological impact on potential investors who may regard an oversized network as a failed investment. It is consequently suggested to set a meaningful threshold probability, like e.g. the value of 50%, which means that is equally probable for the network to finally supply geothermal fluids at flow rates either higher or lower than their initially specified values.
ð15Þ
The cost of the network CNET, that is required in Eq. (15), can be expressed as a function of the flow rates to be supplied to the various consumption sites. For each allocation of the fluids Q1,
2.6. Comments on the model It is assumed here that the responsible agent for the exploitation of the geothermal field is expected to act according
J.J. Gelegenis / Applied Energy 86 (2009) 284–289
C A G2 A B C
600 1000 1165 1500 1000 1380 2100 2535 1500 2870 G1 G2 A B
B
G1
3. Indicative application of the model Fluids from two geothermal wells G1 and G2 are examined to be optimally distributed to three sites of consumption noted as A, B and C (Fig. 4), to be used for greenhouses, district heating and drying. The data used is concisely presented in Table 1 (flow rates are expressed in m3/h, as a more practical unit). Direct use of geothermal energy is considered. Greenhouse operation is assumed to be competitive to district heating use, while the application of drying is complementary to the two uses. The equivalent energy prices, for the three uses examined, and the respective probability curves are shown in Fig. 5. The results of the optimization process are shown in Fig. 6, where cases with total probability of utilization higher than 50% were only considered. Suggested selling price is PE = 2.05 €/m3 (leads to the higher
Probability of utilization
500 m
ated and the quantity of fuel saved are. Nevertheless, the model is still useful giving the input for the economic criterion, that is ordinarily included in multi-criterion evaluation processes. In this context, instead of using an economic parameter in combination with a risk index [4] (that is arbitrary defined through subjectively selected sub-criteria and relevant weighting factors), the return on investment that is based on the probable income can be alternatively applied, as it can be calculated by the presently suggested model.
G2
Fig. 4. Map with the topography used in the example.
Table 1 Data used in the example Technical data of the uses
25
0.8
20
0.6
15
0.4
10
0.2
5
0.0 0.22 m /h
Load per use
20 kW
3
Greenhouse operation Thermal fluids flow rate per greenhouse unit Load per use
100 kW
Geothermal drying Thermal fluids flow rate per drying plant
10 m3/h
Load factor
30%
2.0 m3/h
0 1
Annual energy needs Load factor
145 GJ
Annual energy needs Load factor
1350 GJ
Annual energy needs
4400 GJ
2
2.5
3
3.5
3
40%
Greenhouses
District Heating
Drying
Fig. 5. Equivalent energy prices, for the assumed uses, and the respective probability curves, for various selling prices of thermal fluids.
40%
Maximum capacity per site
Site A
Site B
Site C
Number of greenhouse units Number of buildings Number of drying plants
10 100 1
10 100 1
10 100 1
Pricing data (prices in €/GJ) Application
Price for preference
Price for rejection
Greenhouses operation District heating Drying
7 10 7
17 20 14
Energy price from conventional fuel
1.5
Fluids price ( /m )
18
Production data
Flow rate (m3/h)
District heating Thermal fluids flow rate per building
Geothermal well G1 Economic data (in €)
1.0
Energy price ( /GJ)
to Private Entities criteria, attempting so to maximize the net return on his investment. This approach is quite in agreement with present trends for liberalization and privatization of the energy sector. But even when a local authority’s owned company is regarded, the model can be still valuable leading to an economically optimum network for any selling price assumed. It is then up to the decision maker to select the suitable selling price (and the respective optimum network) that will not necessarily result to the highest return on investment but may, for instance, lead to the higher consumption of geothermal energy (the volume of the annually supplied geothermal fluids can be also calculated by the model, e.g. by applying Eq. (9) but without using the selling price PF). More generally, the exclusion of social type criteria from the proposed model does not inhibit its applicability for cases where public benefit foundations are assumed. Apparently, for these cases other criteria are equally important, like the number of jobs cre-
120
0.8
100
0.7
80
0.6
60
0.5
40
0.4
20
0.3
0
Income Index
288
0.2 1.5
2
2.5
3
3
40 m3/h
Cost per well Modification expenses for each dryer Transmission piping (with L and DIN in m)
Geothermal well G2
30 m3/h
85,000 20,000 (100 + 640DIN) L
Selling price ( /m ) Flow to A
Flow to B
Total Flow
Income Index
Flow to C
Fig. 6. Optimum distribution of fluids to the consumption sites A, B and C, and the corresponding Income Index, for the various selling prices of thermal fluids.
J.J. Gelegenis / Applied Energy 86 (2009) 284–289
In Figs. 7–9, some intermediate results are indicatively presented, that refer to the demand characteristics of site A, for the optimum selling price (since the same maximum capacities were assumed for all three sites, Figs. 7–9 are also applicable to sites B and C). In Fig. 7 the probabilities to be utilized various fractions of maximum required fluids are presented, for the three uses. In Fig. 8 the probability distribution functions for the two competitive uses are presented, together with the convolution that corresponds to their simultaneous operation. Finally, in Fig. 9, the probabilities various flow rates to be utilized at site A are shown, together with the respective probable income.
1.0
Probability
0.8 0.6 0.4 0.2 0.0 0
20
40
60
80
100
Percentage of maximum capacity (%) District Heating
Greenhouses
289
Dryer
4. Conclusions Fig. 7. Probabilities of utilization of various flow rates of thermal fluids in the potential uses at site A (flow rates in x-axis are expressed as fraction of the maximum capacity required for each use).
Probability distribution
0.6 0.5 0.4 0.3 0.2 0.1 0.0
0
10
20
30
40
50
Thermal fluids flow rate (m3/h) Greenhouses
DistrictHeating Convolution
1.0
250
References
0.8
200
0.6
150
0.4
100
0.2
50
[1] Yuhara K, Sekioka M. Application of linear programming to multipurpose utilization of geothermal resources. In: Proceedings of the second united nations symposium on the development and use of geothermal resources, San Francisco; 1975. p. 2249–53. [2] Caloghirou Y, Gelegenis J, Koumoutsos N. Alternative scenarios for suitable utilization for geothermal energy in Milos. Int J Energy Syst 1988;8(1). [3] Koumoutsos N, Lygerou V, Papagiannakis E, Papaioannou A, Makatsoris J, Caloghirou J, et al. Investigation of the possibilities for the exploitation of low enthalpy geothermal fields – Formation of a program for development, 1990 (Report prepared on behalf of the Greek Ministry of Industry, Energy and Technology, Greek). [4] Haralambopoulos D, Polatidis H. Renewable energy projects: structuring a multi-criteria group decision-making framework. Renewable Energy 2003;28:961–73. [5] Gelegenis J, Karytsas K, Gikas L. Proposal for the specification of stages to the development and exploitation of a geothermal field. Bull Greek Assoc Mech Elect Eng 1991;234 [in Greek]. [6] Sahinidis N. Optimization under uncertainty: state of the art and opportunities. Comput Chem Eng 2004;28:971–83. [7] Lindal B. Industrial and other applications of geothermal energy. In: Armstead HCH, editor. Geothermal Energy. Paris, France: UNESCO; 1973. p. 135–48. [8] ETVA, Techno-economic feasibility study for the development and exploitation of Nea Kessani Geothermal field in Xanthi; 1992 [in Greek]. [9] Karytsas K, Gikas L, Gelegenis J. Technical specifications for the feasibility and techno-economic study for the development and exploitation of Nea Kessani geothermal field, 1990 (Report prepared on behalf of the Greek Bank for Industrial Development ETVA S.A., in Greek). [10] Diamant R, Kut D. District heating and cooling for energy conservation. New York, USA: John Wiley and Sons; 1981. [11] Harrison R, Mortimer N, Smarason O. Geothermal heating. A handbook of engineering economics. UK: Pergamon Press; 1990.
0.0
Income (k /yr)
Probability
Fig. 8. Probability distribution functions of greenhouse operation and district heating and probability function of their combination (competitive uses), that was resulted as the convolution of above two functions.
Utilization of geothermal energy within a broader area around the field may lead to higher demand, more end uses, avoidance of expropriation of land (that is needed for the local exploitation), release of probable oppositions coming from remote potential users. This solution presupposes the installation of a transmission and distribution network, to supply potential consumption sites with geothermal energy. Due to uncertainties about the end uses and the capacity at which they will be finally applied, a probabilistic model can prove to be a valuable tool to design the network, allowing to make decisions on how to distribute the thermal fluids among the various sites and at what price to supply them to the end users. Although design of such a network looks as a typical location– allocation problem, the exploitation of geothermal energy presents many peculiarities (annual variation of demand, simultaneous existence of competitive and complementary uses, use of geothermal energy to cover base loads only, the case of reselling geothermal energy, etc.) that make this problem quite different. The specific probabilistic model to be used to this aim, should be based on (a) a local investigation within the broader area of the field, to find out the potential applications (b) the performance of pre-feasibility studies for these applications and finally (c) a market study to identify the intentions of the potential end users.
0 0
10
20
30
40
50
Thermal fluids flow rate (t/h) Probability
Income
Fig. 9. Probability for the various thermal fluids flow rates to be utilized at site A and the corresponding probable income, for the optimum selling price (2.05 €/m3).
income index, 0.735) and the corresponding optimum network consists of a branch from G2 to B capable to carry 30 m3/h and a second branch from G1 to A capable to carry other 40 m3/h. The last branch is extended from A to C, to carry a decreased rate of 10 m3/h only. Since both flow rates leaving G1 and G2 do not exceed the production capacities of the corresponding wells, inter-connection between the wells is not necessary (although advisable for maintenance purposes).
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Applied Energy journal homepage: www.elsevier.com/locate/apenergy
Use of a probabilistic model to design energy transmission and distribution networks for low enthalpy geothermal multiple use schemes John J. Gelegenis * Technological Educational Institution of Athens, Ag. Spyridonos Street, Aegaleo/Athens GR 122 10, Greece
a r t i c l e
i n f o
Article history: Received 23 January 2008 Received in revised form 14 April 2008 Accepted 16 April 2008 Available online 2 June 2008 Keywords: Geothermal energy Multiple use Probabilistic model Probability Location–allocation
a b s t r a c t A probabilistic model is suggested for the design of transmission and distribution network of geothermal energy to potential consumption sites, in cases where the development of various competitive or complementary non-electrical uses is probable, within the broader area of a field. The model can be used to find out (a) the optimum network that may offer the best economic results to the agent who will undertake the development of the field, and (b) the corresponding selling price at which the thermal fluids will be supplied to the end users who are assumed to be other than the above agent. Model input data can be collected in the frame of an appropriate market study, which is roughly specified in this work and commented according to relevant experience from a Greek geothermal field. Finally, applicability of the model is demonstrated through an indicative example. Ó 2008 Elsevier Ltd. All rights reserved.
1. Introduction Since non-electrical uses of low enthalpy geothermal energy have in general difficulties in prospecting as independent and profitable business, establishment of multiple use schemes is more advantageous. In these cases, linear programming can be used to find the optimum distribution of geothermal resources to the various uses, in order to get the maximum total benefit [1]. The decision on the distribution of geothermal energy may not to be restricted to economic criterion only. For instance, for the pilot exploitation of Milos field (Greece), four alternative scenarios were evaluated according to their economy and capability to produce valuable conclusions for the full-scale exploitation [2]. When additional criteria are considered (e.g. jobs created, fuel saved, entrepreneurial risk, environmental impact), the need for a multi-criteria approach arises. The PROMETHEE II method was applied [3] to compare alternative scenarios for the exploitation of the Nea Kessani field (Greece). Later, a multi-criteria group decision-making framework was documented [4], that was also based on PROMETHEE II to be applicable to any renewable energy project. In above works it was assumed that the examined uses will be surely established, and that there is a common economic benefit for all end users. As an alternative, the establishment of the uses could be processed as probable events, while the competing benefits between the end users and the supplier of geothermal energy * Tel.: +30 210 5385816; fax: +30 210 5385306. E-mail address: [email protected] 0306-2619/$ - see front matter Ó 2008 Elsevier Ltd. All rights reserved. doi:10.1016/j.apenergy.2008.04.011
could be also considered. Geothermal energy could be supplied to remote sites, where demand is either more probable or could be provoked via a relevant call for investors. To this aim, an appropriate probabilistic model must be developed to design the extended network for the transmission and distribution of geothermal energy [5], where additionally to an optimization criterion, the network ability to meet feasibility in an uncertain environment should be considered, as usually applied in probabilistic programming [6]. The uncertain environment in geothermal energy utilization has been defined elsewhere [4] in the form of an entrepreneurial risk, that is broken down to distinct characteristics as: new product, new technology, future changes and initial investment. Uncertainty is consequently attributed to the demand, and is actually due to the facts: (a) that geothermal energy is a new product for any broader area where the exploitation of the local geothermal field has not commenced yet (b) that the use of geothermal energy requires technologies that – it is the most usual – people are not familiar with and (c) that the intentions of the potential investors in geothermal applications are unpredictable; these intentions depend on many factors such as the perspectives of each specific geothermal use, the available motives (grants, tax exemptions), the competitive energy sources, the infrastructure of the area, etc., and could be in a way revealed through appropriate market studies. The uncertain environment in geothermal exploitation has impact on the flow rates at which the fluids will be transferred through the network (and hence on the design of the network), and consequently on the expected income, too (and hence on the economy of the geothermal project).
J.J. Gelegenis / Applied Energy 86 (2009) 284–289
285
Nomenclature AE annual energy needs of an application (GJ/year) C NET ðQ 1 ; Q 2 ; . . . ; Q n Þ cost of the network (€) CRF capital recovery factor (1/year) cost of the wells (€) CWELLS D piping diameter (m) f(N) probability density distribution discrete function (value for N probable users) f(Q) continuous density distribution function corresponding to above discrete function f(N), according to the thermal fluids flow rate Q (1/m3 s1) F(Q) cumulative probability function INC(Q) probable income when supplying thermal fluids at Q flow rate (€/year) L length of transmission line (m) LF load factor M maximum number of total potential users for an application at one consumption site ME modification expenses for existing equipment to make use of geothermal energy (€) n number of potential consumption sites
p P(Q) PBT PC PE PE* PE0 PEPRE
PEREJ
PF Q QN QTOT w
probability a potential user to ask for geothermal energy probability of utilization of thermal fluids at Q flow rate pay-back time (year) cost of energy coming from conventional sources (€/GJ) equivalent selling price for geothermal energy (€/GJ) modified selling price for geothermal energy, for partial coverage of the load (€/GJ) reselling price for geothermal energy (€/GJ) maximum price for geothermal energy that makes it still completely preferable than conventional energy supply (€/GJ) minimum price for geothermal energy that is not yet sufficiently low to make a potential user to change from conventional energy supply in favor of geothermy (€/GJ) selling price for thermal fluids (€/m3) thermal fluids flow rate (m3/s) nominal thermal fluids flow rate requirement for a typical unit of an application (m3/s) total production from the wells (m3/s) velocity of the fluids (m/s)
The flow chart of the model is shown in Fig. 1, and the various steps are further explained below.
preference PEPRE) (b) the lower price for which the users would still insist on the use of conventional fuels (price for rejection, PEREJ). For intermediate energy prices, the probability curve may be assumed to get a linear form:
2.1. Assumption of a selling price
p¼
A broad range of the thermal (geothermal or secondary) fluids selling prices PF (€/m3) can be examined. The optimum selling price depends on many factors -fluids temperature (energy content), quality of the fluids, characteristics of demand (intensity, distribution, and approach to the wells) and attitude of potential end users – that should be taken into consideration in the model.
In Fig. 2 it is presented the outcome of a relevant market study [8], that was based on appropriate specifications [9] and conducted in the broader area of the Nea Kessani field. It refers to district heating, and the four sets of data correspond to the nearby villages named Kessani, Koutso, Sellino and Sidini. The mean values are also shown in Fig. 2; a linear probability curve adapted to these data has a standard deviation of 0.018 only, and so Eq. (3) is proved to be a good approximation. For each selling price, a probability distribution function may arise. For an application with an assumed maximum number of potential users M, and for a selling price PE that causes a probability of utilization p – as calculated with Eq. (3) – the following probability distribution discrete function f(N) arises:
2. The probabilistic model
2.2. Conversion to equivalent energy prices A unified selling price for the fluids leads to different prices per energy unit for the various uses [7]. For each application, the geothermal energy equivalent price PE (€/GJ) becomes: PE ¼
3:15 107 Q N LF PF AE
ð1Þ f ðNÞ ¼
where QN is the required nominal thermal fluids flow rate (m3/s), AE are the annual energy requirements (GJ/year) and LF is the load factor. 2.3. Estimation of probability distribution functions For each group of end users, a probability curve can be drawn, expressing – for the various selling prices – the intentions of the users to utilize geothermal energy, as concluded from a market study (e.g. through questionnaires). For an asked total of M persons, a probability curve p(PE) is defined by the points: pi ðPEi Þ ¼ N i =M
PEREJ PE PEREJ ¼ PEPRE
ð2Þ
where PEi are the discrete prices that were considered in the questionnaire and Ni is the number of persons who would utilize geothermal energy if supplied at the price of PEi. Processing all questionnaires allows for the identification of two critical prices: (a) the higher price that is considered still attractive, to make the users change from conventional to geothermal energy (price for
M!pN ð1 pÞMN N!ðM NÞ!
ð3Þ
ð4Þ
To avoid overflow in computations of Eq. (4), the Stirling approxipffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffi mation for n! can be Used: nÀ nn en 2 p n, introducing the following approximation: sffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffi M! M MM ð5Þ N! ðM NÞ! 2 p N ðM NÞ N N ðM NÞMN which has an error of less than 2%, with higher errors being only noted in marginal cases, when N approaches either zero or M. In these marginal cases however, f(N) is almost zero, and so the increased relative error has no practical impact on the accuracy. This is shown in Fig. 3 for various values of N and M up to 100 (for higher values of M accuracy becomes apparently even better). Geothermal energy may be insufficient to completely cover the usually quite high thermal requirements of Industrial applications. The probability of utilization of the distributed thermal fluids to cover a fraction a of the nominal load (and the annual thermal needs, equivalently) can be concluded from Eq. (3), by using an appropriately adapted price PE* (€/GJ), that additionally considers
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1.0
Assume a price for the thermal fluids
0.8
Probability
Characteristics of fluids and requirements of applications
Convert to geothermal energy price for each specific use
Outcome of market study and site visit
Identification of competitive and complementary uses
Kessani Koutso Sellino Sidini Mean Linear
0.6 0.4 0.2 0.0
Estimation of probability distribution function for each application and site
0
40
80
120
Relative energy price (%) Fig. 2. Probability curves for district heating use, as resulted from market investigation in four villages, in the broader area of the Nea Kessani geothermal field. Energy prices are expressed as% percentage of the conventional energy price (data taken from [8]).
Synthesize probability curve and probable income curve for each site Input transmission cost data
10 8
Error (%)
Assume allocation of the fluids to potential consumption sites
Estimate Income Index and Total Probability of utilization
M =10
6
20
4
50
2
100
0 0
0.2
0.4
0.6
0.8
1
N / M ratio Have been examined all possible distribution of fluid to the sites?
Fig. 3. Error by introducing Stirling approximations for n! in Eq. (4) for the estimation of probability distribution function, for various values of maximum number of users M.
NO
YES
proportionally to p(PE0 –PE), with the other operational expenses remaining roughly unchanged. The last expression presents a maximum at PE0 = (PE + PEREJ)/2 which constitutes the optimum reselling price.
Have been examined all possible selling prices? NO
2.4. Synthesis of a composite probability curve for each site
YES
With given: (a) the end uses that can be developed at each site (b) the relative role of these uses (c) an assumed price for the thermal fluids and (d) the consequent probabilities of utilization of fluids at various flow rates (for each use), the following can be estimated:
Conclusion on: - Selling price -Transmission network Fig. 1. The flow chart of the probabilistic model.
ð6Þ
(i) The probabilities various fluid flow rates to be totally utilized on site. (ii) The quantity of fluids, that are respectively expected to be annually supplied to each site, and the corresponding income.
Here, PC is the price of conventional energy (€/GJ) and CRF the capital recovery factor (1/year). In case of reselling geothermal energy (e.g. in District heating) a price must be defined to allow the intermediate agent to be profitable, and geothermal energy to remain attractive. This agent buys geothermal energy at PE and resells it at PE0 , with PE < PE0 < PEREJ. The expected fraction of total users that will probably utilize geothermal energy is approximated by p as calculated with Eq. (3) using the reselling price PE0 . The net reselling income varies
The end uses are distinguished as either competitive or complementary. The case of in series uses is not considered here, because in a cascade utilization scheme the agent cannot guarantee supply of geothermal fluids to the next uses. It is a matter of simple mathematics to extract from the discrete function f(N) of Eq. (4), a continuous distribution function f(Q). Then, the composite probability distribution function fTOTAL(Q) of competitive uses, results as the convolution of their probability distribution functions f1 (Q) and f2 (Q):
the expenses ME (€) for necessary modifications of the existing equipment to accept geothermal energy: PE ¼ PC—a ðPC—PEÞ
ME CRF AE
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fTOTAL ðQ Þ ¼ f1 f2 ðQ Þ ¼
Z
Q
0
f1 ðuÞ f 2 ðQ uÞ du
ð7Þ
The probability for fluids with a flow rate of Q to be utilized in two competitive uses, which have a total maximum capacity of QMAX, will be: Z Q MAX PðQ Þ ¼ 1 FðQ Þ ¼ f1 ðuÞ f2 ðuÞ du ð8Þ Q
where F(Q) is the cumulative probability for fTOTAL (Q). The respective probable income INC(Q) (€/year) is: Z Q MAX INCðQ Þ ¼ 3:15 107 f 1 f2 ðuÞ min½Q ; u < LFðuÞ > 0
PF du
ð9Þ
where
ð10Þ
The above are similarly applicable to more than two competitive uses. When there also exist complementary uses, the probability of utilization P(Q) increases to P0 (Q), with: P 0 ðQ Þ ¼ 1 ½1 PðQ Þ ½1 PC ðQ Þ
INC0 ðQ Þ ¼ INCðQ Þ þ INCC ðQ Þ
ð12Þ
where INCC(Q) is the expected income from the complementary uses (€/year) which is also determined with Eq. (9). 2.5. Evaluation of alternative allocations The evaluation of each network can be based on the probability of utilization of the totally supplied fluids (defined here as the total probability of utilization of the network fluids), the relevant expected income and its cost. The total probable income for a network results as the sum of probable partial incomes from the fluids supplied to the various consumption sites, while the total probability of utilization of the network fluids results as the product of the partial probabilities of utilization of the distributed flow rates at the various sites: n X n INCi ðQ i Þ; Total probability ¼ P Pi ðQ i Þ Probable Income ¼ i¼1
ð13Þ where with i = 1, 2,. . . the various consumption sites are numbered. Optimization is achieved by minimizing the simplified pay-back period PBT of the network and the wells (or equivalently, by maximizing the gross account rate of return). Assuming that annual total expenses constitute a fixed part b of the capital invested, then it is valid: 1 ðProbable IncomeÞ b½ðNetwork CostÞ þ ðWells CostÞ ¼ PBT ðNetwork CostÞ þ ðWells CostÞ ¼ ðIncome IndexÞ b ð14Þ where Income Index is defined as the ratio: ðIncome IndexÞ ¼
ðProbable IncomeÞ ðNetwork CostÞ þ ðWells CostÞ
(
ð11Þ
where PC(Q) is the probability of utilization of the thermal fluids in the complementary uses only, estimated again as per Eq. (8). Lastly, the total probable income INC0 (Q) (€/year) from all potential end uses becomes:
i¼1
Q2, . . .,Qn to the n potential consumption sites, the flow rates that are transferred through the sub-branches of the network can be easily extracted, according to the topography of the broader area and the relative position of the wells. Based on these flow rates, the cost of each branch of the network can be estimated and finally the total cost may arise as a function of the assumed allocation CNET(Q1, Q2, . . .,Qn). Indeed, by assuming a value for the fluids velocity w (e.g. a typical value ranges between 2 and 3 m/s [10]), the diameters of the network branches can be directly estimated from the flow rates of the transferred fluids D = 2{Q/(pw)}1/2. Afterwards, the application of any appropriate cost equation (like the linear relations suggested in [11]), allows the estimation of the cost of each branch from its diameter. Obviously, for all allocations the sum of the flow rates RQi (i = 1,. . .,n) cannot exceed the total production from the wells QTOT. The various allocations are examined provided that their total probability PP(Qi) (i = 1,. . .,n) exceeds a minimum threshold value P0. This last probabilistic constraint restricts significantly the number of the necessary calculations (rejecting the rather improbable allocations), and at the same time leads to the most probable allocations of fluids. Consequently, the optimization criterion of the probabilistic model gets the form:
Maximize
n X
) INCi ðQ i Þ=½C NET ðQ 1 ; Q 2 ; . . . ; Q n Þ þ C WELLS
i¼1
with
n X
Q i 6 Q TOT and
i¼1
n Y
P i ðQ i Þ P P0
ð16Þ
i¼1
Since there are not usually expected to be many potential consumption sites n, the necessary calculations are quite restricted. Hence, no special programming techniques are required to solve the above optimization problem. A simple trial calculating process examining all potential allocations through appropriately nested loops (e.g. for each consumption site i, there are examined flow rates from Qi = 0 up to Qi = QTOT–RQj, where last sum is taken for j = 1 to i) and with a reasonable flow rate increment DQ, is ordinarily expected to be sufficient. Elaborating further on the role of the threshold probability P0, it is noted that the total probability that corresponds to a network does not reflect the economy of the network but how probable it is the assumed flow rates to be consumed at the respective sites. Hence, a low total probability means that it is the most probable, at the end, the quantities of fluids that will be consumed to be smaller than that for which the geothermal network had been specified. Noticeably, the total probability is anyway taken into consideration in the optimization criterion (where the probable income is included) and so it is quite improbable for an allocation with a low total probability to be preferred as the optimum. For this reason the threshold value of P0 cannot be critical for the optimum solution, provided however that a reasonable (e.g. a not very high) value has been introduced in the condition. On the other hand, an allocation with a low total probability is expected to finally lead to flow rates lower than the nominal values, a fact that may have a psychological impact on potential investors who may regard an oversized network as a failed investment. It is consequently suggested to set a meaningful threshold probability, like e.g. the value of 50%, which means that is equally probable for the network to finally supply geothermal fluids at flow rates either higher or lower than their initially specified values.
ð15Þ
The cost of the network CNET, that is required in Eq. (15), can be expressed as a function of the flow rates to be supplied to the various consumption sites. For each allocation of the fluids Q1,
2.6. Comments on the model It is assumed here that the responsible agent for the exploitation of the geothermal field is expected to act according
J.J. Gelegenis / Applied Energy 86 (2009) 284–289
C A G2 A B C
600 1000 1165 1500 1000 1380 2100 2535 1500 2870 G1 G2 A B
B
G1
3. Indicative application of the model Fluids from two geothermal wells G1 and G2 are examined to be optimally distributed to three sites of consumption noted as A, B and C (Fig. 4), to be used for greenhouses, district heating and drying. The data used is concisely presented in Table 1 (flow rates are expressed in m3/h, as a more practical unit). Direct use of geothermal energy is considered. Greenhouse operation is assumed to be competitive to district heating use, while the application of drying is complementary to the two uses. The equivalent energy prices, for the three uses examined, and the respective probability curves are shown in Fig. 5. The results of the optimization process are shown in Fig. 6, where cases with total probability of utilization higher than 50% were only considered. Suggested selling price is PE = 2.05 €/m3 (leads to the higher
Probability of utilization
500 m
ated and the quantity of fuel saved are. Nevertheless, the model is still useful giving the input for the economic criterion, that is ordinarily included in multi-criterion evaluation processes. In this context, instead of using an economic parameter in combination with a risk index [4] (that is arbitrary defined through subjectively selected sub-criteria and relevant weighting factors), the return on investment that is based on the probable income can be alternatively applied, as it can be calculated by the presently suggested model.
G2
Fig. 4. Map with the topography used in the example.
Table 1 Data used in the example Technical data of the uses
25
0.8
20
0.6
15
0.4
10
0.2
5
0.0 0.22 m /h
Load per use
20 kW
3
Greenhouse operation Thermal fluids flow rate per greenhouse unit Load per use
100 kW
Geothermal drying Thermal fluids flow rate per drying plant
10 m3/h
Load factor
30%
2.0 m3/h
0 1
Annual energy needs Load factor
145 GJ
Annual energy needs Load factor
1350 GJ
Annual energy needs
4400 GJ
2
2.5
3
3.5
3
40%
Greenhouses
District Heating
Drying
Fig. 5. Equivalent energy prices, for the assumed uses, and the respective probability curves, for various selling prices of thermal fluids.
40%
Maximum capacity per site
Site A
Site B
Site C
Number of greenhouse units Number of buildings Number of drying plants
10 100 1
10 100 1
10 100 1
Pricing data (prices in €/GJ) Application
Price for preference
Price for rejection
Greenhouses operation District heating Drying
7 10 7
17 20 14
Energy price from conventional fuel
1.5
Fluids price ( /m )
18
Production data
Flow rate (m3/h)
District heating Thermal fluids flow rate per building
Geothermal well G1 Economic data (in €)
1.0
Energy price ( /GJ)
to Private Entities criteria, attempting so to maximize the net return on his investment. This approach is quite in agreement with present trends for liberalization and privatization of the energy sector. But even when a local authority’s owned company is regarded, the model can be still valuable leading to an economically optimum network for any selling price assumed. It is then up to the decision maker to select the suitable selling price (and the respective optimum network) that will not necessarily result to the highest return on investment but may, for instance, lead to the higher consumption of geothermal energy (the volume of the annually supplied geothermal fluids can be also calculated by the model, e.g. by applying Eq. (9) but without using the selling price PF). More generally, the exclusion of social type criteria from the proposed model does not inhibit its applicability for cases where public benefit foundations are assumed. Apparently, for these cases other criteria are equally important, like the number of jobs cre-
120
0.8
100
0.7
80
0.6
60
0.5
40
0.4
20
0.3
0
Income Index
288
0.2 1.5
2
2.5
3
3
40 m3/h
Cost per well Modification expenses for each dryer Transmission piping (with L and DIN in m)
Geothermal well G2
30 m3/h
85,000 20,000 (100 + 640DIN) L
Selling price ( /m ) Flow to A
Flow to B
Total Flow
Income Index
Flow to C
Fig. 6. Optimum distribution of fluids to the consumption sites A, B and C, and the corresponding Income Index, for the various selling prices of thermal fluids.
J.J. Gelegenis / Applied Energy 86 (2009) 284–289
In Figs. 7–9, some intermediate results are indicatively presented, that refer to the demand characteristics of site A, for the optimum selling price (since the same maximum capacities were assumed for all three sites, Figs. 7–9 are also applicable to sites B and C). In Fig. 7 the probabilities to be utilized various fractions of maximum required fluids are presented, for the three uses. In Fig. 8 the probability distribution functions for the two competitive uses are presented, together with the convolution that corresponds to their simultaneous operation. Finally, in Fig. 9, the probabilities various flow rates to be utilized at site A are shown, together with the respective probable income.
1.0
Probability
0.8 0.6 0.4 0.2 0.0 0
20
40
60
80
100
Percentage of maximum capacity (%) District Heating
Greenhouses
289
Dryer
4. Conclusions Fig. 7. Probabilities of utilization of various flow rates of thermal fluids in the potential uses at site A (flow rates in x-axis are expressed as fraction of the maximum capacity required for each use).
Probability distribution
0.6 0.5 0.4 0.3 0.2 0.1 0.0
0
10
20
30
40
50
Thermal fluids flow rate (m3/h) Greenhouses
DistrictHeating Convolution
1.0
250
References
0.8
200
0.6
150
0.4
100
0.2
50
[1] Yuhara K, Sekioka M. Application of linear programming to multipurpose utilization of geothermal resources. In: Proceedings of the second united nations symposium on the development and use of geothermal resources, San Francisco; 1975. p. 2249–53. [2] Caloghirou Y, Gelegenis J, Koumoutsos N. Alternative scenarios for suitable utilization for geothermal energy in Milos. Int J Energy Syst 1988;8(1). [3] Koumoutsos N, Lygerou V, Papagiannakis E, Papaioannou A, Makatsoris J, Caloghirou J, et al. Investigation of the possibilities for the exploitation of low enthalpy geothermal fields – Formation of a program for development, 1990 (Report prepared on behalf of the Greek Ministry of Industry, Energy and Technology, Greek). [4] Haralambopoulos D, Polatidis H. Renewable energy projects: structuring a multi-criteria group decision-making framework. Renewable Energy 2003;28:961–73. [5] Gelegenis J, Karytsas K, Gikas L. Proposal for the specification of stages to the development and exploitation of a geothermal field. Bull Greek Assoc Mech Elect Eng 1991;234 [in Greek]. [6] Sahinidis N. Optimization under uncertainty: state of the art and opportunities. Comput Chem Eng 2004;28:971–83. [7] Lindal B. Industrial and other applications of geothermal energy. In: Armstead HCH, editor. Geothermal Energy. Paris, France: UNESCO; 1973. p. 135–48. [8] ETVA, Techno-economic feasibility study for the development and exploitation of Nea Kessani Geothermal field in Xanthi; 1992 [in Greek]. [9] Karytsas K, Gikas L, Gelegenis J. Technical specifications for the feasibility and techno-economic study for the development and exploitation of Nea Kessani geothermal field, 1990 (Report prepared on behalf of the Greek Bank for Industrial Development ETVA S.A., in Greek). [10] Diamant R, Kut D. District heating and cooling for energy conservation. New York, USA: John Wiley and Sons; 1981. [11] Harrison R, Mortimer N, Smarason O. Geothermal heating. A handbook of engineering economics. UK: Pergamon Press; 1990.
0.0
Income (k /yr)
Probability
Fig. 8. Probability distribution functions of greenhouse operation and district heating and probability function of their combination (competitive uses), that was resulted as the convolution of above two functions.
Utilization of geothermal energy within a broader area around the field may lead to higher demand, more end uses, avoidance of expropriation of land (that is needed for the local exploitation), release of probable oppositions coming from remote potential users. This solution presupposes the installation of a transmission and distribution network, to supply potential consumption sites with geothermal energy. Due to uncertainties about the end uses and the capacity at which they will be finally applied, a probabilistic model can prove to be a valuable tool to design the network, allowing to make decisions on how to distribute the thermal fluids among the various sites and at what price to supply them to the end users. Although design of such a network looks as a typical location– allocation problem, the exploitation of geothermal energy presents many peculiarities (annual variation of demand, simultaneous existence of competitive and complementary uses, use of geothermal energy to cover base loads only, the case of reselling geothermal energy, etc.) that make this problem quite different. The specific probabilistic model to be used to this aim, should be based on (a) a local investigation within the broader area of the field, to find out the potential applications (b) the performance of pre-feasibility studies for these applications and finally (c) a market study to identify the intentions of the potential end users.
0 0
10
20
30
40
50
Thermal fluids flow rate (t/h) Probability
Income
Fig. 9. Probability for the various thermal fluids flow rates to be utilized at site A and the corresponding probable income, for the optimum selling price (2.05 €/m3).
income index, 0.735) and the corresponding optimum network consists of a branch from G2 to B capable to carry 30 m3/h and a second branch from G1 to A capable to carry other 40 m3/h. The last branch is extended from A to C, to carry a decreased rate of 10 m3/h only. Since both flow rates leaving G1 and G2 do not exceed the production capacities of the corresponding wells, inter-connection between the wells is not necessary (although advisable for maintenance purposes).