Geothermal energy is related to the earth's crust heat, the origin of which is still a ... In this paper, we focus on the use of low-temperature geothermal energy for ...
Energy Vol. 6. pp. 351-3a. Prmted m Great Britain
03~5442/81/040351-iBsM.w/O Copyright @ 1981 Pergamon Press Ltd.
1981 All rights reserved
MODELING THE INTERACTIONS BETWEEN GEOTHERMAL ENERGY USE AND URBAN STRUCTUREt JEAN-MICHELGULDMANN and BRENTD. ROSENTHAL Departmentof City and RegionalPlanning,The Ohio State University, Columbus. OH 43210, U.S.A (Received 11 July 1980)
Abstract-The geophysical, technological and economic characteristics of low-temperature geothermal district heating systems are analyzed and illustrated by a review of actual systems around the world. The various interactions and cost trade-offs which characterize such systems are then integrated within an optimization planning model aimed at minimizing total energy supply costs. The approach emphasizes the spatial dimension of such systems and the interface between their spatial layout and the structure of the urban areas they are designed to serve. I. INTRODUCTION
The energy crisis and the spiraling prices of conventional fuels are increasing the competitiveness of new energy sources as geothermal energy. Although prospection for this source is still only beginning, the presently known reserves are nevertheless tremendous. For instance, the recoverable heat stored under the Hungarian plains and discovered in 1954 represents about 50% of the calorific value of the known petroleum reserves of the world. Unfortunately, in many areas, this energy cannot be recovered economically or because the appropriate technology is not yet available. Nevertheless, this form of energy is bound to become very important in specific locations where the resource is abundant and of easy access. These areas are referred to as geothermal fields. Geothermal energy is related to the earth’s crust heat, the origin of which is still a matter of discussion (see Armsteadi) but seems related to both rocks radioactivity and magma flows and hence to seismic and volcanic activity. This heat is recovered from hot subsurface formations with the help of meteoric water circulating down through fractures, pores and other openings in the rock. The water absorbs the heat and returns to the surface with an elevated temperature. This circulation can be free through natural openings or partially or totally forced through well drilling and pumping. There are considerable variations among geothermal fields in terms of depth and thickness of the aquifer, potential yield, temperature, and chemical composition of the water. Hyperthermal fields contain very hot water and steam usable for electricity generation, as at Lardarello, Italy (since 1913), and at the Geysers, California. At the other extreme, nonthermal fields are characterized by temperature gradients of 10-4o”C per km of depth and have been, for a long time, considered to be non-exploitable. However, recent experiments in France (Melun) have been successful in such fields with the help of heat pumps. In between, areas of geothermal activity having temperature gradients of about 80°C per km of depth are known as semithermal fields and exist in many countries such as Iceland, Hungary, France, the U.S.S.R., New Zealand, Japan, Mexico, and the U.S.A. The developed fields have a current aggregate thermal power of 7000 MW and are used for space heating (400 MW) and cooling (e.g. a hotel in Rotorua, New Zealand), for agriculture and aquaculture (5500 MW), and for industrial processes.+ The major advantages of this direct utilization vs power generation are high conversion efficiency (80-90%), short development times, less expensive well developments and, of course, the higher availability of the low-temperature resources and their usability in several applications where more costly conventional fuels can be saved and the related air pollution avoided. In this paper, we focus on the use of low-temperature geothermal energy for space and
tThis paper has been presented at the European Meetings of the Regional Science Association, Munich, 26-29 August 1980. $For interesting reviews of the international geothermal scene and of the various possible applications of lowtemperature geothermal energy, see, for instance, Lund,2 Nannen et al.,j and Lienau4 351
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JEAN-MICHEL GULDMANN and BRENT D. ROSENTHAL
water heating, within the framework of urban district heating systems. The operation of such systems involves (1) the extraction of the hot water from the underground geothermal reservoir, (2) its transmission through pipelines to the consumption centers, (3) heat conversion at the level of the end-users, with or without such technologies as heat exchangers, heat pumps, water storage, etc., and (4) the disposal of the return cooled waters, generally through reinjection into the same underground geothermal reservoir. The geophysical, technological and economic characteristics and constraints of the different components of the geothermal district system, as well as the numerous interactions which take place among them, are investigated, and a planning optimization model is presented to determine the minimum cost trade-off among the many decision variables of the system, with particular emphasis on the interface between the spatial character of these systems and the spatial structure of the urban areas they are designed to serve. The remainder of the paper is organized as follows. The characteristics of geothermal reservoirs and methods for modeling their thermal and hydraulic behavior are presented in Section 2. The technological and economic characteristics of geothermal exploitation (well drilling, transmission, end-use conversion) are analyzed in Section 3. Case histories of geothermal district systems are reviewed in Section 4, and the planning and optimization methodology is presented in Section 5.
2. GEOTHERMAL
RESERVOIRS
CHARACTERISTICS
AND BEHAVIOR
2.1 General considerations A geothermal reservoir is comprised of four parts: (1) a source of heat, (2) a layer of bedrock, (3) an aquifer (i.e. a permeable area of fractured rock containing large amounts of water), and (4) a source of water to replace fluid losses. Before exploratory drilling takes place, there is generally much uncertainty about the geometric (depth, thickness, porosity), hydrodynamic (natural flow, static pressure, transmissivity and dynamic viscosity of the water), thermal (temperature of the water, thermal conductivity and calorific capacities of the rocks and water), and chemical (salt content, etc.) characteristics of the resource. However, knowledge of these parameters is necessary in order to estimate the available energy and future productivity? and to predict the behavior of the aquifer under different possible exploitation schemes. There are indeed several interactions which take place within the reservoir. Water withdrawal reduces water pressure at the well itself and at neighboring wells, and this may impede extraction and produce surface subsidence. These drawdowns can be alleviated if spent waters are reinjected, but this reinjection may increase water pressure excessively, unfavorably modify the spatial distribution of hydraulic potentials, and lead to mounding (build-up of land). These pressure effects are very similar to those taking place in underground aquifer and oil and gas reservoir exploitations. In addition to this hydrodynamic behavior, the understanding of the reservoir thermal behavior is also very important for the successful planning and management of the geothermal system because spent cooled waters may have to be reinjected into the reservoir to (a) avoid polluting surface waters (if the geothermal water is salty, (b) maintain the production capacity of the reserves, in particular if the natural water inflow is limited,+ (c) maintain adequate pressure to run the system and avoid subsidence, in particular if there is a high density of pumping wells, and (d) increase the quantity of heat extracted from the ground (the calories in the reservoir rocks are recovered by recirculating waters). For instance, it is estimated in the case of the Paris Basin (France) that, if waters were not reinjected, only 1% of the water and 2%0of the heat stored could be recovered. However, these cooled waters may, after some time, reach the productive extraction wells and reduce their potentials. It is therefore necessary to know the rate at which these cooled waters can be reheated and their effect on the hot water in the reservoir to evaluate the life span of the source. Obviously, the magnitudes of both the pressure and thermal interferences will depend upon distances between wells, and therefore the siting of the extraction and injection wells tFor a theoretical thermodynamic analysisof geothermal heatextractionin simplified geological configurations, see, for instance, Bodvarsson.s SThe natural recharge of geothermal reservoirs is highly variable. In the cases of Boise, Idaho (U.S.A.) and Wairakei (New Zealand), the natural water inflow turns out 10 be almost equal to the amount extracted.
Interactions
between geothermal energy use and urban structure
353
may become an important design variable. Mathematical models simulating the above effects have been developed, based on fundamental equations of hydrodynamics and thermodynamics, and calibrated with reservoir parameters. These models, which have much in common with those developed for groundwater and petroleum reservoirs, are described in the next sections. 2.2 Pressure effects In porous media local fluid speed (V) and pressure (P) are related, at any point and time, by Darcy’s law V=-$grad
P,
(I)
where k is the permeability of the porous matrix and p is the dynamic viscosity of the fluid. If the porous matrix is heterogeneous, k varies in space, i.e. k = k(x, y, z), where (x, y, z) are the coordinates of any point in the reservoir. The dynamic viscosity increases when the temperature decreases and therefore p = p[B(x, y, z)], where 0(x, y, z) is the temperature of the water at point (x. y, z). Another fundamental law simply states the conservation of water mass, with div (pV) = 0,
(2)
where p is the volumic mass of water. Combining Eqs. (1) and (2) while neglecting the variations of p with temperature and pressure yields the following condition: (3) If the temperature field 0(x, y, z) is known at time t, then Eq. (3) can be solved under given limit conditions (well flows, aquifer boundaries) to yield the pressure at any point and, subsequently, the filtration speed through Eq. (1). However, the temperature field depends itself upon the progression of the thermal front, which is related to the filtration speed. Thus, the hydraulic and thermal problems are closely interlinked. In general, the variations of /_Lwith 0 are neglected, and this is shown to be a conservative assumption. In the case of a heterogeneous aquifer, Eq. (3) must be solved while accounting for the three dimensions through discretization of the partial derivative components and subsequent computer simulation. For a more comprehensive discussion of the above equations and of their analytic solutions in simplified cases, see Baradat et ~1.~ As mentioned before, numerical techniques have been developed for the management of underground water and oil and gas reservoirs. These simulation models have led to the formulation of linear interference or response models, where a given well pressure is expressed as a linear function of all wells extraction and injection rates.+ If there are N wells, then the basic partial derivative equation is solved by simulation 2 x N times, each solution having only one well operating at a constant extraction or injection unit rate. If then i and i refer to a couple of wells and k to a number of unit time periods, the coefficient afi measures the interference produced by well i on well j during period k after the time the operation has taken place. If, for instance, qik is the extraction level at well i during period k, then the interference effect AHjm on well j during period m is (see Wattenbarger’) (4) It has been shown that the above linearization and superposition of the pressure effects constitute a very good approximation of the true solution, particularly in the case of water See Wattenbarger’and for water reservoirs.
Rosenwald and Green* for discussions of gas reservoirs, and Maddock and Haimes’and
Maddock”’
JEAN-MICHEL GULDMANN and BRENT D. ROSENTHAL
354
reservoirs. In the model presented in Section 5, this linear approach will be retained. The determination of such interference models can also be achieved through multiple-step drawdown tests in real wells. For instance, in the case of new wells development in Reykjavik (Iceland), the drawdown h at a given well was found to be related to the same well pumping rate Q by the following relation: h =BQ+CQ”
(n =2),
(5)
where B is the linear aquifer constant, and C the well loss constant related to turbulence in and around the well. For more details about this direct experimental approach, see Zoega.” Two major types of ground movements can be induced by these pressure changes: subsidence and mounding. Subsidence is of particular concern in urban settings, where potential for building damage is very high. The most likely place of occurrence is in the vicinity of production wells where water would be withdrawn at a high rate. Mounding caused by rapid reinjection of waste waters, is generally likely to occur at about WlOOft above the aquifer water level, although high injection pressures could amplify this effect.
2.3 Thermal effects The propagation of the thermal fronts around the reinjection wells toward the production wells depends upon characteristics of the reservoir (porosity, permeability, thickness) and of the fluid (viscosity, pressure, temperature). Two major types of heat transfer take place: thermal convection in the direction of the flow, and thermal conduction between the porous medium and its contained fluid. These transfers are described mathematically by the equation for mass transport and diffusion while replacing the concentration variable (mass per unit of water volume) by the thermal energy per unit of water volume. Consider a unit volume of the rock-reservoir of porosity 0. This volume receives cold water and loses hot water at the same flowrate, and heat is exchanged between rocks and water. The temperature of the rock and of the water it contains changes under this double phenomenon, and the thermal balance condition is expressed by the following partial derivative equation?: - (PC)” div (N) + div (A* grad 0) = (PC)*$,
(6)
where 8 is the temperature of the rock-water at time t, V the local water convection speed, (PC)” the calorific capacity of water, (PC)* the calorific capacity of the rock saturated with water, and A* the thermal conductivity of the rock saturated with water. Generally, A* is taken independent of the speed V. The transfer of heat from the caprock to the aquifer is also characterized by Eq. (6), but with V = 0. Solving Eq. (6) in the aquifer and the caprock yields the time-space temperature field 0(x, y, z, t) at any point, and in particular at the pumping wells. Of course the solution of Eq. (6) implies the prior knowledge of the speed V, the determination of which was discussed in Section 2.2. Therefore, in practice, it is necessary to solve the hydrodynamic and thermodynamic equations simultaneously. In general, Eq. (6) must be solved through discretization of its components and computer simulation. Various operational models have been developed on this basis, in particular by the French Bureau de Recherches Gtologiques et Minitres (BRGM)” in the case of a dual well system (one production and one reinjection well). The BRGM has developed nomographs indicating the number of years (n) after which a temperature decrease takes place at the production well as a function of (1) the aquifer thickness h, (2) the distance x between the downhole points, (3) the pumping rate Q, and (4) the porosity 0. This relationship is shown to be approximated as follows: n=
tFor more
$$I)).
details about this equation, see Baradat et al.6
(7)
355
Interactions between geothermal energy use and urban structure
Equation (7) and the corresponding nomographs have been established for an injection water temperature of 0”C.t However, when more than two wells are involved, such simplified approaches are no longer appropriate and the complete simulation model must be used. It is however conceivable that, through multiple test runs of the model, some analytical formulation of the temperature impact function could be derived, as suggested in Section 5.3. For additional in-depth discussions about thermal interferences, the reader is referred to Bodvarsson,S” Faust and Mercer,14 Gringarten and Sauty,” and Satman et ~1.‘~ 3. TECHNOLOGICAL AND ECONOMIC CHARACTERISTICS GEOTHERMAL EXPLOITATION
OF
3.1 Drilling and well operation Drilling represents the first step in the process of extracting hot water from the geothermal reservoir. The drilling rigs are generally conventional oil field rotary drilling rigs. However, a new technique, called directional drilling, is also currently being developed and involves siting two wellheads close to each other at the surface but curving the wellbores so that the distance between the bores at the level of the reservoir is much greater. This approach may lower the costs of surface piping and land acquisition and enable the tapping of reservoirs otherwise unattainable because of impenetrable rock or highly developed areas. It may also permit the reinjection of cooled wastewaters without affecting production. For more details about drilling technology, see Maurer.” Drilling costs vary greatly, depending upon rock hardness, depth of the hole, and capacity of the well (diameter). The relation of cost to depth is better known, however, and is roughly the same as that experienced in oil drilling: marginal costs rise steeply up to depths of 2-3 km but then stabilize, increasing between 6.5 and 7% for every additional 1OOm of drilling. It is estimated that a 2000-mwellbore costs 2.75 times more than a 1000-mone. Drilling costs in Klamath Falls, Oregon, up to 3000 ft have been estimated as follows: $1.00 per inch of diameter and foot of depth in “soft” rock, and $2.50 in the case of “hard” rock. The wells may have to be equiped with production or injection pumri, depending upon natural flow conditions and desired yields. The cost of such pumps is about $400 per horsepower. The wells may also be equipped with downhole heat exchangers to avoid piping corrosive waters. This is the case in the shallow geothermal wells of Klamath Falls, Oregon (see Culver and Reistadl*). 3.2 Transmission and distribution Transmission systems serve as the link between the geothermal wells and the points or zones of utilization. They control the flowrates and pressures of the emergent fluids, and separate and remove impurities. The flow of hot water is accomplished by gravity whenever possible. Various technical problems must be solved when designing such systems. First, chemicals and minerals in the geothermal waters can corrode pipes. Although new synthetic materials resistant to corrosion are becoming available, downhole or wellhead heat exchangers may be necessary to avoid such problems (see Delisle et al.19). Second, to counteract pressure losses, circulation pumps may be necessary, at a cost of approx. $100 per horsepower. Finally, heat losses may be significant if the area served is remote from the production field. Insulating the pipe can reduce heat losses to less than 1°C per km, but at a cost. The costs of transmission primarily involve capital outlays for pipelines and pumps. If pumps are necessary, their operating costs must be accounted for. The transmission cost of a unit of heat to the point of delivery is strongly related to the peak load and load factor (the ratio of the average to the peak loads) of the system, because the peak load determines the capacity of the system and the load factor characterizes its level of use. Armstead’ shows, in a specific tThe BRGM studies indicate that distances of 800-1ODOmbetween the two wells will prevent a decrease of the temperature before a minimum of three decades of service in the case of the geothermal system in operation in Melum. It is important to note here that the lower the temperature of the reinjected waters, the better the hot and cold fluids assimilate and thus the lower the temperature decrease impact. Hence the importance of using heat exchangers and heat pumps to remove all the usable heat becomes clear. $Bodvarsson shows, with a simplified theoretical model, that in the case of a continuous mass flow of loo0 kg/set of water during 25 yr, the contamination may reach out to as much as 5 km or more from the point of reinjection.
356
JEAN-MICHEL GULDMANN and BRENT D. ROSENTHAL
case study, that this cost is nearly halved when the load factor increases from 90 to loo%. The transmission distance is another obvious determinant of this cost, as is the level of heat loss. However, the amount of heat loss that can be tolerated will depend upon the characteristics of the resource and end-uses, as well as upon the cost of insulation and other costs. As will be demonstrated by the model presented in Section 5, this amount should be the output of a comprehensive trade-off analysis. On the basis of specific studies, Einarsson” concludes that the economic transportability of geothermal fluids depends primarily on the temperature of the fluids: waters of about 100°Ccan be transported over 10-20 km, while waters of 1%180°C can probably be transported over 50-75 km for space heating purposes, provided a huge concentrated market is available. At the distribution level, i.e. in the areas where the energy consumers are located, the distribution costs are related to street mains and house connections. These costs are highly related to the residential or other land uses densities. This relationship is illustrated in Table 1 for the Boise Geothermal System currently under planning. The data of Table 1 show that the unit cost falls sharply from 2500 to 10,000 users per square mile, but then decreases only gradually to 40,000 users. Therefore, the typical suburban setting is the least economical for geothermal district heating, and the optimal density is in the range of 10,000 to 20,000 users per square mile, including residential users (townhouses or garden apartments) and office complexes and public buildings of high floor density. 3.3 End-use energy conversion and consumption In geothermal district systems, the actual process of heat conversion and consumption takes place at the unit level, i.e. each house, apartment building, etc. The regulating equipment at the individual building level consists of flow regulators, a water meter, a supply valve, and return pipe valves. The water heat is utilized either directly or through heat exchangers and heat pumps.? Direct methods include forced air and convection systems. In areas where the chemical composition of the geothermal waters is highly corrosive, heat exchangers are necessary to prevent the deterioration of the building heat conversion equipment. The heat exchanger has two networks of water circulating through it. In one network the geothermal waters run from and to the transmission system. In the other one hot water runs through the house and returns cooled to the exchanger. The exchanger removes the heat from the geothermal waters and transfers it to those circulating in the house, and the two networks are complete closed cycles unto themselves. The conversion system may also include a heat pump, which is a device made of two parts: an evaporator and a condenser. Spent geothermal waters leaving the exchanger pass through the evaporator, where any remaining heat is removed and used in the pump to further reheat the waters entering the house network. The condenser works in the same way with used waters in the house heating network, lowering further their temperature, which increases the efficiency of the heat transfer in the exchanger. There are various possible heating schemes: (1) a direct conversion system alone or in conjunction with an auxiliary peak heater fired with conventional fuels (or a back-up electrical Table 1. Relationship between geothermal energy cost and housing density. Cost Housing Type
of Heat
$/Therm
Residents Per Square
Mile
t 2,560
Suburban, Detached House
,799
High Density, Single Family
.7a7
4,480
Tcwnhouses/Rowhouses
.432
11,580
Garden Apartments
.382
17,580
High Rise Apartments
.32a
41,580
source:
22 Geothermal Energy Systems Plan for Boise City, City of Boise.
tOf course, as mentioned earlier, heat exchange may already have taken place through downhole or wellhead exchangers or any centralized heat exchange facility.
Interactions between geothermal energy use and urban structure
357
system); (2) a heat exchanger and a peak heater; (3) a heat exchanger and a heat pump with or without a peak heater. For any given technological configuration, the amount of recoverable geothermal energy is, at any time, proportional to the flow of geothermal water and to the difference between the geothermal water input temperature and the temperature of the spent waters returning to the transmission system. For a given time-linked pattern of building energy requirements and input water flowrates and temperatures, the design of the least-cost heating scheme involves the optimal determination of several variables such as the exchanger surface, the heat pump power, the back-up system capacity, the temperature of the spent geothermal waters sent into the transmission system, as well as various intermediate temperatures in the various sections of the networks. An iterative optimization methodology for this least-cost design can be found in Jover et al.** These authors minimize the capital and operating costs of the heat exchanger, heat pump and back-up system subject to (1) the satisfaction of the heat requirements at any point on the temperature load duration curve and (2) heat balances (input = output) at the levels of the exchanger and heat pump. The major features of this methodology will be retained in the modeling approach presented in Section 5.4.4. 4. CASE HISTORIES
OF GEOTHERMAL
DISTRICT SYSTEMS
The historical development, planning process and operational characteristics of three existing low-temperature geothermal systems are reviewed in this section. This review has two purposes: first, to illustrate the various concepts analyzed in the previous sections, and second, most importantly, to underline the integrated character of these systems, and, hence, the need for a comprehensive approach to their planning and management, the subject of the next section. The systems reviewed are those of Reykjavik (Iceland), Klamath Falls, Oregon, and Boise, Idaho (U.S.A.). 4.1 The Reykjavik system Iceland, blessed with a multitude of hot springs and a number of major geothermal steam fields because of its location on the crest of the Mid-Atlantic seismic ridge, has been among the first countries to systematically use geothermal waters for district space heating. A distribution system was completed in the city of Reykjavik in 1930, supplied by 14 boreholes of 400 m depth with an output of 14 I./set of 87°C water. This system, which initially supplied 70 residential homes and some public buildings, has been progressively expanded to include outlying suburbs by tapping resources as far as 18 km from the city, at the Reykir field. Today, the system serves 11,000homes or 88,000 inhabitants (99% of the city’s total) with an aggregate peak heating capacity of 385 MW distributed as follows: (1) the Reykir field: 170 MW (3600 m3/hr at 80°C); (2) the Reykjavik field: 155 MW (1700 m3/hr at 119°C); (3) a peak power plant: 35 MW; and (4) electricity sold by the Electricity Authority peak plant during electrical offpeak hours: 25 MW. Heat production has quadrupled during the last 15 years and should be about 2000GWh in 1980. The system includes holding tanks located on the top of a hill within the city, with a capacity of 8000 m3, as well as an oil-fired peak boiler with a storage capacity of 30 GCal/hr (increasing total storage capacity to 26,000 m3). Deep-well pumps are used to pump water out of the boreholes. The transmission-distribution system includes 46 km of supply mains, 21 km of collecting mains, 146.6km of street mains, and 157.4km of house connections. The total service area has a surface of 12 km*. Because many units served are single-family detached houses, the system’s load density is relatively low (1.9 MW/km when referred to main length). Fully automatic pumping plants are located throughout the city, but are only applied to the return waters since pressure is adequate in the supply mains. The individual houses are generally equiped with central radiator-type heating, with direct connection to the district system. As the climate of Reykjavik is remarkably stable with respect to temperature variations, the load factor of the system is high (46% or 4000 hr of operation per year). However, as the climate is never hot, heating is needed in every single month of the year. Daily peaks are handled by water from the storage tank while seasonal peaks are met with stored waters in conjunction with oil-fired peak heating and a higher production (i.e. differential pumping) from the Reykjavik field. With respect to reservoir behavior, the redevelopment of the Reykir field (19OOmdepth),
358
JEAN-MICHELGULDMANN and BRENTD. ROSENTHAL
located 15-20 km east of the city, was deemed necessary in 1970 to prevent an unacceptable drawdown of the reservoir (this field had been exploited since 1944 at a rate of 360 l./sec, with water temperatures of 86°C). The number and locations of the new wells were chosen after several multiple-step drawdown tests were conducted (see Section 2.2). Unlike the production between 1944 and 1970, which was entirely free-flow, the new wells had to rely on turbine pumps because of the drawdown of the aquifer. Finally, turning to the economics of the system, one can note that the 1974 replacement cost of the Reykjavik system was estimated at $60 million, with the following average construction costs: $27.27/kW for heat production (wells and wellhead pumps), $32.01/kW for transmission (main pipelines from the fields), and $lil.O2/kW for distribution (storage tanks, pumping stations, local pipelines). The operating costs average about 12% of the capital costs. The total annualized costs in 1974 were as follows: O.O6#kWh for heat production, O.OS#/kWhfor transmission, and 0.20#/kWh for distribution, totaling 0.34#/kWh. In 1974, heavy fuel oil and electricity were priced at 0.87 and l.gOQ/kWh,respectively, and this clearly confirms the substantial competitive edge of geothermal energy in the case of Reykjavik. For more detailed economic and technical data about Reykjavik, see Zoega” and Einarsson.” 4.2 The Klamath Falls system Klamath Falls residents have been exploiting their hot water resources since the beginning of this century. Today, more than 500 structures are provided heat by about 400 shallow-depth geothermal wells with downhole heat exchangers. These wells range from 27 to 270m depth (average of 75 m). Buildings either are served by individual wells or share a well or are connected to a distribution network. Total hot water production during the winter often exceeds 2100 gal/min, but this production is falling to 340 gal/min in summer. The heat content of the geothermal field is estimated to lie in the range [12+ 10”-36~ lO’*]calories, with maximum temperatures of 130°C.This would make it the largest known geothermal resource area in the U.S. Until now, the development of the resource has been accomplished on an essentially individual basis. However, a major district heating project, currently in the planning stage, is to supply heat to 54 blocks in an area of Klamath Falls downtown referred to as the commercial district. The heat load of this district has been estimated at 135 MMBtulhr, which will require 6750gallmin of 105°C water. Waters will be supplied through a central heat exchange facility, which was deemed necessary because of economies of scale, risks of pipe corrosion, and high water temperatures (thus, less heat would be lost in the exchanger). The development of the commercial district will take place in three phases. In Phase I, 14 public buildings will be heated with 2 production wells of 1OOOftdepth and 70&8OOgal/min production, with temperatures ranging from 60 to 105°C. Reinjection of the spent waters through one or more wells was deemed necessary to prevent reservoir depletion, pollution of surface waters, and unacceptable drawdowns in the smaller existing individual wells. However, at present the location of these reinjection wells has not yet been determined and current studies of the local hydrology and geology center around minimizing the effects of reinjection on production levels and temperatures. In addition to the commercial district, 24 other districts have been delineated and given supply priorities, with development times ranging from 2 to 20 yr. The potential fields likely to supply these districts were evaluated according to proximity to consumers, elevation (to facilitate gravity transport), availability of public lands, and quality of the geothermal fluids. Several areas were deemed feasible for exploitation, and a typical site will have wells averaging 400 ft in depth and producing about 750 gal/min. A comprehensive cost analysis of the commercial district heating system (Phase I) was done in 1977, with an inflation rate assumption of 7%. The costs of wells and wellhead equipment totaled $169,772; the costs of the distribution piping network amounted to $1,143,235; the costs of the heat exchange facility and the related equipment totaled $197,506; finally, engineering and inflation contingency costs amounted to $226,577. The total capital cost of $1,737,090,when annualized over 20 years and added to estimates of operation and maintenance costs, produced a geothermal energy cost of 19#therm, which should be compared to the following 1977 rates: 35$/therm for natural gas, 61Qltherm for oil, and 73qltherm for electricity. Clearly, the competitive edge of geothermal energy in Klamath Falls does not require further proof. For additional data on geothermal energy use in Klamath Falls, see, for instance, Lund et aLz3 and Lund et aLz4
Interactions between geothermal energy use and urban structure
359
4.3 The Boise system
The city of Boise was the first city in the world to use natural hot water for district space heating. The Boise Warm Springs Water District (BWSWD) started its operations in 1890, when two 400ft wells were drilled to tap the 90°C water and to heat several buildings and mansions lining the city’s major street. By 1930, the system had been expanded to serve 400 residences and commercial establishments at a rate of 1920gal/min. At that time, however, geothermal energy started to be abandoned in favor of cheaper natural gas and electricity, and the number of geothermally heated houses got reduced to 161 (1978). However, with the advent of the energy crisis and increasing prices of conventional fuels, the city of Boise began in the 1970s the renovation and extension of the BWSWD system in anticipation of consumers switching back to geothermal heat. A geothermal development plan has been formulated for the period 1977-85 (City of Boisez5 and City of Boise”) for the Boise metropolitan area (160,000 inhabitants; 114,000inhabitants in the city proper), with an expected total capita1 cost of $15 million. This plan, based on demographic and economic projections, includes six stages. In Stage I, the first new wells will be drilled, the existing wells enlarged, and the transmission and return lines laid, with transmission distances less than 5 km. In Stage II, the water will be supplied to the areas nearest to the resource and with high building density (several downtown buildings). In Stage III, the system will be expanded to serve other downtown buildings, and, in Stage IV, those residential, commercial and institutional buildings closest to the original pipeline route. In Stage V, the second major phase of pipe laying will take place, and the final phase will expand service to densely populated residential areas. With respect to the technical characteristics of this system, one should note that the wells will be equiped with turbine pumps capable of pumping 90°C waters at a rate of lOOOgal/min. Variable pump speeds will be used to adjust production to match the demand characterized by a load factor of 24%. The system’s capacity will be equal to 8OOOgal/min,with an average annual consumption of 134.9 million ft3 of water. The cooled spent waters will be reinjected back into the reservoir, and two reinjection wells are planned. Their locations have not yet been determined, but they will probably be located at sites where the length of the return pipe is minimized and where cascade uses of spent waters can take place. Unlike the system in Klamath Falls which will have a central exchanger, each building in the Boise system will have an individual heat exchanger. Conventional heating systems will be retained, but with modifications in order to be used in conjunction with the geothermal waters which are chemically pure (no corrosion is expected). The total capita1 cost of the system is estimated at $15 million, and the non-capita1 outlays at $370,000. The operating costs include (I) variable costs, expected to be equal to $0.105 per 100 ft3 in 1985 and corresponding to the energy needed to pump the water through the network, and (2) fixed costs of $163,000 (also in 1985), unrelated to the amount of water used. The total capital outlays for the three expected circulation pumping stations will range from $30,000 to $43,000 each, and the pumping costs for the two injection wells will total about $82,000. The Boise plan report (City of Boise”) includes comparisons of the costs to the consumers of delivered heat when supplied by electricity, natural gas and geothermal energy. For small commercial and residential users with an annual demand of 119.4 MMBtu, the annual costs of these sources, in the above order, are: $728, $507, and $275. For commercial buildings of 50,000 ft’, these costs are equal to $24,266, $14,122, and $6763. These results clearly indicate the strong competitiveness of geothermal energy at Boise. For additional data on Boise, see Kunze et ~11.~~ and Post.”
5. A MODELING METHODOLOGY
5.1 The interactions and trade-ofs Numerous interactions occur in an integrated geothermal heating system, as described in detail in the previous sections. At the reservoir level, pressure and thermal effects depend upon extraction flowrates, reinjection flowrates and temperatures, and the locations of the various wells. These locations, as well as the locations of the energy demand centers, determine the spatial extension of the transmission network, the length of which has a definite impact on heat and pressure losses. The magnitude of the heat losses depends also upon reservoir temperatures, while pressure losses are related to reservoir pressures and regional topography.
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JEAN-MICHEL GULDMANN and BRENT D. ROSENTHAL
These losses can be reduced through pipe insulation and circulation pumps. Various geothermal heat conversion schemes are possible at the end-users level, depending upon the flowrates and the input/output temperatures of the geothermal waters, as well as upon the characteristics of alternate energy technologies (conventional fuels, solar energy, etc.). The temperature of the reinjected return waters then has an impact on the thermal balance of the reservoir. Also, the peak load and load factor of the end-users’ requirements, the pattern of which depends upon weather variability, have a significant effect on the capacity and economics of the system, for the system has to be sized to provide the peak load, unless it is complemented by other energy sources such as a centralized fuel-fired peak boiler or back-up systems in each individual house. This peak load effect can also be alleviated by using centralized (case of Reykjavik) or individual storage systems, as well as by the possible use of geothermal energy for cooling during the summer season. Finally, while the locations of the energy markets determine the characteristics of the transmission system, the internal structure of these markets, in terms of land-use mix and density, determines the characteristics of the distribution system (street mains, house connections). There is therefore a large number of decision variables in the design of a geothermal system, and the trade-offs among them are pervasive throughout the system, that is, a decision in one part of the system may have far-reaching implications in totally different components of it. The following are the major questions to be answered: (1) Where to site and how to size the extraction and reinjection wells? (2) What should be the spatial structure, capacity, and insulation of the pipe transmission network? (3) What should be the capacity of and operating mix between geothermal and other possible energy supply systems, including storage? (4) Under the assumption that land uses can be manipulated (case of new towns or redevelopment areas), what are the best locations and densities for these land uses from a geothermal energy perspective? Each decision variable has cost implications, and therefore the various cost trade-offs must be analyzed comprehensively. The approach selected here is to consider the total cost of providing the energy required by the end-users and to determine the system minimizing this cost. The optimal energy supply mix may range from (a) no geothermal use (all end-users with conventional systems), to (b) mixed use of geothermal and conventional systems, to (c) exclusive use of geothermal energy, with time-variable extraction of waters and eventual storage. It is clear that the determination of the optimal system cannot be made intuitively, unless the number of possible decision variables is limited for some exogenous reasons and only a small number of possible alternatives needs to be c0nsidered.t The design of such a system should be the output of an optimization model wherein all the constraints and trade-offs are accounted for. It is the purpose of the following sections to outline the structure of such a model. The next section describes the basic assumptions upon which this model has been developed.
5.2 Basic modeling assumptions (a) At the reservoir level 1. The geothermal reservoir is described by a matrix of wellhead sites, where either extraction or reinjection wells can be drilled. 2. The wellhead sites are all nodes in a potential transmission network. 3. The characteristics of the reservoir are fully known, including the water temperature at each well, the maximum feasible well yield, and all the pressure and thermal interference functions. 4. All the extracted waters must be reinjected into the reservoir. 5. Differential pumping is used in attempting to match energy supply and demand.
tit seems that the cost evaluation of a few alternatives has been the design approach in the case of the actual geothermal systems described in Section 4. A simulation methodology permitting to screen a large number of alternatives has been developed by McDonald and Bloomster,28 whereby the potential costs of geothermal district heating are evaluated for given characteristics of the resource, the demand, and the technology. However, these authors do not attempt any optimal trade-off analysis, and do not account for reservoir interferences.
Interactions between geothermal energy use and urban structure
361
(b) At the transmission level 1. The layout of a potential transmission pipeline network linking the wellhead sites to the energy demand centers is given, and the actual pipeline links are to be selected among these potential links. 2. The temperature drop in each pipe link is related to the initial water temperature, water flow, pipe length and capacity, and thickness of insulation. 3. Pressure losses are not explicitly modeled. However, pipeline capital and operating costs implicitly include average circulation pumping costs. 4. Water losses throughout the system are assumed negligible. 5. The transmission system does not include any centralized storage or peak heater facility. (c) At the end-use market level I. A new town is to be developed near the geothermal reservoir. The urban area is subdivided into well-delineated districts. 2. Total given amounts (stocks) of different land uses (activities) must be allocated among the districts. These land uses are assumed divisible. 3. The climatic pattern of the area is given, and it is assumed possible to subdivide the year into periods with approximately constant temperature. Each such period is characterized by a number of degree-days. 4. Each land use is characterized by land and energy input coefficients. Energy input coefficients are defined for the various weather periods of the year, on the basis of period degree-days and land-use heat loss characteristics (see ASHRAE29). 5. The structure of the geothermal heat conversion system is not explicitly modeled. This system is simply characterized by its capacity, which corresponds to the peak usage of geothermal heat, and is assumed perfectly divisible (an assumption made necessary by the divisibility assumption concerning the land uses). 6. Geothermal heat can be complemented by the energy provided by a back-up system installed at the end-use level. The capacity of this system is to be determined by the model. In order to integrate the above assumptions into the model, it is necessary to formally define the related decision variables and parameters. This is the purpose of the next section. However, reservoir interferences, temperature drop and the various cost functions will be discussed in latter sections. 5.3 Definitions (a) Indices u’ = I + W: i.j = 1+J: r = I + R: I,m = I + ND: k = I -+ K: t = I -+ T:
potential geothermal well site; transhipment nodes in the transmission network; urban district (end-use node); any node (well, transhipment, or district) in the network: land-use (activity) type; intra-annual homogeneous climatic period.
(b) Decision variables Besides the well site selection integer variables, all the variables described below are assumed to be continuous.
x:,:
1 if the well site w is developed as a production well, 0 if not; x;: 1 if the well site w is developed as a reinjection well, 0 if not; [ QKP,: production capacity of well w (during any climatic period); reinjection capacity of well w (during any climatic period): QK;: amount of water extracted from well w during period t; amount of water reinjected into well w during period t; temperature of the water reinjected into well w during period t;
JEAN-MICHELGULDMANN and BRENTD. ROSENTHAL
GEOK,, F kri: FK,,
:
water carrying capacity (during any climatic period) of the directed link (I- m); amount of water carried during period t in the directed link (I- m); insulation thickness of the directed link (I - m); upstream and downstream temperatures of the water in the directed link (I - m) during period t; amount of activity k allocated to district r; amount of geothermal water used by activity k in district r during period t; temperature of the geothermal waters entering district r during period t; temperature of the cooled geothermal waters leaving activity k in district r during period t; geothermal heat conversion capacity installed in district r for activity k (during any climatic period); amount of auxiliary (back-up) energy supplied to activity k in district r during period t; back-up system capacity for activity k in district r (during any climatic period).
(c) Parameters P max. QKw . maximum feasible production capacity of well W; Rmax. QKw . maximum feasible reinjection capacity of well w; T,,,: natural temperature of the geothermal water at well site W; QTi”,““: maximum water carrying capacity of directed pipe link (I - m); max. Y * maximum insulation thickness for any pipe link; Xk: total stock of activity k to be allocated among the districts; ’ Sk: land input COeffiCientfor activity k; A,: amount of land available in district r; energy requirement coefficient for activity k in district r during period ekt : calorific value of the geothermal water; C,: Pg: volumic mass of the geothermal water; E: geothermal heat conversion efficiency.
t;
5.4 The constraints of the model 5.4.1 Wells siting, capacity, and operations. The wells-related constraints pertain to the mode of operation (extraction/reinjection), the maximum capacity and the operating levels of these wells, with
X’, t X”, 5 1, a well site can be used, at most, for either extraction or reinjection;
(8)
QK; s QK: maxX&
maximum extraction capacity;
(9)
QK”ws QK”wmaxX”,, maximum reinjection capacity;
(10)
QL 5 OK;, the extraction level is, during any period, limited by the selected extraction capacity;
(11)
Q”w,5 QKC, the reinjection level is, during any period, limited by the selected reinjection capacity. (12) 5.4.2 Reservoir interferences. The net pressure change at any well wi during period t, AP,,,+, is equal to the difference between the pressure increase due to reinjection and the pressure decrease due to production at the various wells (including Wj)operating during period t. It is assumed that a steady-state pressure pattern is established during each period, depending only upon the extraction and injection rates during the period. The relationship between pressure changes and operating rates is assumed to be linear (see Section 2.2) and the following
Interactions between geothermal energy use and urban structure
363
coefficients are defined: PC,,, pressure decrease at well wi due to a unit extraction rate at well W; PR,,,, pressure increase at well wi due to a unit reinjection rate at well w. The net pressure change AP,, is then defined by (13) If AP,,, >O, there is a net pressure increase, and if AP, < 0 a net pressure decrease. It is assumed that limits to maximum pressure changes are specified, with APc”“‘( < 0), maximum allowable pressure decrease at well w if it is used for extraction; APz.m’x(> O), maximum allowable pressure increase at well w if it is used for reinjection. The pressure constraints are then AP 1,12 AP:imax-- &(I -X:,). AP,.,I 5 APE,max+ M,,(l -X”,).I (M,, = very large number).
(14) (15)
Equation (14) becomes non-binding if no production well is actually installed at site Wj,and the same is true for Eq. (15) in the reinjection case. Of course, it must be recognized that there is some relationship between the maximum pressure changes and the equipment of the well in terms of extraction and injection pumping power, but accounting for such relationships would considerably complicate the mathematical structure of the model. Therefore, the present approach can be viewed as a first approximation which should be further submitted to sensitivity analyses. The temperature at well Wjafter n years of operations, AT& is a complex function of the hydrodynamics of the reservoir, as modified by the various extraction and reinjection flows, and of its thermodynamics, as modified by the reinjected waters temperatures. Baradat et aLh have shown that, even if the flow regime is not constant throughout the year, the resulting thermal front progression is quite close to that obtained with the corresponding total flows spread out uniformly over the year. The following variables are then defined:
amount of water annually reinjected into well w;
QY[: =
2 QL
amount of water annually extracted from well W;
(16)
(17)
Q:,Tt3,
i
T!Z= “‘T 2
Q:t'
average annual temperature of the waters reinjected into well w.
(18)
Given the vectors QYR = (QY:, . . . , QY:, . . . , QY&),
(19)
QYP = (QY:, . . . , QY:, . . . , QY&),
TR=(Tf,.
. . , Tf,. . . , T;,,
(20) (21)
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JEAN-MICHEL GULDMANN and BRENTD. ROSENTHAL
the temperature decrease function can be written, in a generalized form, as --
ATLi = F’,,(QYR, QYP, TR, n), (ATCj~0).
(22)
The form of the function F,,,i has been ascertained only in very simplified conditions [see Section 2.3, Eq. (7)]. In the general case, it is impossible to derive analytical solutions from the system of partial derivative equations describing the system, hence the use of computer simulations. It is however conceivable to use such simulations -- to calculate the values of ATij for a large number of values of the independent variables QYR, QY’, TR, and n, and then to test different functional relationships with regression analysis techniques. As the purpose of the present model is essentially to conceptualize all the interactions of the system, the generalized formulation is retained here. The thermal constraint is expressed in terms of a maximal decrease in temperature at a given horizon year N, ATFmax, with -F,(QYR, QYP, TR, N) zz A,;max t M&l -X:,,,
(MO= very large number).
(23)
The horizon year N will generally be taken as the lifetime of the project. Equation (23) is actually binding only if there is a production well at site wi. Finally, note that the above constraint could be deleted while directly accounting for the impact of the decreased well temperatures on the operation of the system. In this case, a multi-annual dynamic formulation of the model should be used, wherein the temperature of the geothermal water at well w during year n, T:, would be defined by --
T; = T, - F,,,(QYR, QY’, TR, n). 5.4.3 Transmission flows, capacities, and energy balances. As there are no water losses and no actual consumptive uses of water, it is necessary to specify, for each node of the system (well, transhipment, district) and for each period, a flow balance equation. If D(I) and O(f) are the sets of destination nodes and origin nodes linked to node I, these equations are written as fo1lows:
&Q/it-,gi,Qilt = 09 flow balance
at transhipment node i during period t;
,&QI~-,&Qdt= 0, flow balance
at district node r during period t;
&Qw,r - Q:t= 0, flow balance at production well w during period ,&Q,wt- Q"wt = 0, flow balance at reinjection well w during period
t;
t.
(25)
(26)
(27)
(28)
It is assumed that there is a maximum carrying capacity for each pipe link, and the selected capacity acts as a constraint on each period flowrate. In the case of link (I-m), these constraints are written as follows:
QT,, 5 QW,
maximum capacity;
(29)
Q,,, - QT,, I 0, carrying rate limit.
(30)
Finally, it is necessary to specify constraints determining the temperatures of the waters throughout the network. The knowledge of these temperatures is necessary only at the districts and reinjection wells. However, to determine these values, temperatures throughout the network must be calculated. The engineering function expressing the temperature drop TD,,, along link (I- m) during period t can be found in the specialized literature. A general formulation
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between geothermal energy use and urban structure
365
is retained here. with
The upstream and downstream temperatures along link (I- m) are related as follows:
T?m’,, = TYm, - TD/m,.
(32)
It is assumed that the waters arriving at a given node through different links are homogeneously mixed and leave this node at a uniform temperature. If TI;I, is this uniform temperature for node m, the conservation of energy at node m implies the following equations: (33) and TX, = T:,, VI E D(m).
(34)
Equations (33) and (34) must be written for all the transhipment and district nodes. At the extraction wells, it is assumed that no heat loss takes place in the well; thus, T,,, = T:,, VI E D(w).
(35)
In the case of a reinjection well, Eq. (33) is rewritten as follows: (36) 5.4.4 Districts land-use and energy requirements. The land-use allocation process implies that the activity stocks are allocated among the districts subject to land availability. These conditions are expressed as follows: $,
Xkr
=
total stock of activity;
xk,
K 2 Sk& 5 A,
land availability.
(37)
(38)
k=l
For each land use, district, and time period, the sum of the energy flows provided by the geothermal waters and back-up systems must be equal to the required energy; hence, (39) geothermal energy
back-up energy
energy requirement
The capacity constraints for the geothermal heat conversion and back-up systems are written as follows: ~‘?&q,ti( T% - Tf,,) 5 GEOK,,,
(40)
&i 5 F&,
(41)
Finally, it is necessary to write the following flow and energy balance constraints:
,&Q,ti =$ ECY Vol. 6. No. &E
qkm
conservation of flow;
(42)
JEAN-MICHELGULDMANN and BRENTD. ROSENTHAL
366
l uniform temperature mixing = “’ (3, qkn)’ of the spent waters leaving TF, = T,U,VI E D(r), 1 district r.
$, a*%
(43) (44
5.5 The objective function of the model
Three genera1 cost categories can be delineated: (1) well costs, (2) transmission costs, and (3) distribution and end-use costs. Each of these categories includes both capita1 and operating and maintenance costs. Some costs functions are characterized by economies of scale (pipes capacity, etc.) and discontinuities (extraction costs with or without a pump, etc.). Therefore, instead of specifying precise analytical relationships, it was decided to use genera1 functional formulations indicating the determinants of each cost component. The exact formulations will of course be necessary when the model is operationalized. All the costs are expressed on an annualized basis. Well costs include: (1) fixed costs independent of capacity and operating rates (such as exploration, outlays for research, etc.), with CFP, and CFR, for production and extraction wells, respectively; (2) capital capacity costs related to well size and equipment (pumps, etc.), and therefore functions of the wells production and reinjection capacities, with CK&(QKc) and CKf(QK!), respectively; and (3) operating and maintenance costs per period, mainly related to the power used by the extraction and reinjection pumps, and therefore to the operating rates, with COM&(Qg,) and COMR,(Q$), respectively. The total well cost function is then CTW = w$, (CF’J: +
+ CFR,X: + CK:(QK:)
+ CK;(QK;)
2 [COM&(QCt) + comQc,)l).
(45)
Transmission costs include: (1) capita1 costs for each pipe link, depending upon the carrying capacity and insulation level, the soil conditions and other localized factors, and including eventually an average pumping station cost, with, for any link (I - m), CKT,,,,(QT,,,,, ~1,); and (2) operating and maintenance costs per period, related to the pipe link flows, with CO~MQ,,,). The total transmission cost function is then CTT= ,$, tCKT,(QL
yimJ+$, CO~T,m(Q,m,)l.
(46)
[I E 6(m), m E D(l)] Distribution and end-use costs include: (1) capital costs for building distribution pumping stations, street mains, service branches and consumers’ connections; these costs will vary, in each district r, with the district size A, (which is a fixed parameter), the land use occupation ratio L, and the peak load Q:““, with CKD,(QY, L,); (2) distribution operation and maintenance costs per period, mainly related to pumping power, and thus to the flowrates Q,,, with COMDJQ,); (3) capacity costs for the geothermal heat conversion and back-up systems, with (CKG,(GEOK,,) and CKF,(FK,,); and (4) operating and maintenance costs per period for the geothermal and back-up systems; the geothermal costs depend upon the power needed to operate the exchangers and heat pumps, and thus are related to the heat flow &, with COMCk(Hk,); the back-up system costs are simply the costs of the alternate fuel, CFk (with future price increases appropriately accounted for). The total distribution and end-use cost function is then
CTD=
$,[CKDAQY, LA + 2 COMD,(Q~~ +k=l 2 5 [cKGk(Gi?oKk,) t cI(F,(FK,,)] c 2 1 [coMGk(%t)+ cF,&l., k=l r=l
K
R
T
r=l
t=I
+
(47)
Interactions between geothermal energy use and urban structure
367
The function CTD includes new variables (Qf”“, L, Qti, H,,,) which must be defined within the model by adding the following constraints:
(51) The total geothermal system cost function is then CT = CTW + CTT + CTD,
(52)
and the design problem requires minimizing CT subject to the various constraints described in Section 4 and to the constraints (48~(51). 5.6 Discussion and extension of the model The model presented in the previous sections presents a high degree of complexity and includes (1) both integer and continuous variables, (2) nonlinear constraints and objective function, and (3) thermal interference constraints for which the feasibility of using analytical functional formulations is still an open question. In addition, the numbers of variables and constraints are likely to be very large for realistic systems. Thus, it is not feasible to determine the exact solution of the model with currently available algorithms, nor is it clear that this might ever be feasible. However, the formulation of the present model, which explicitly accounts for all the major interactions and trade-offs, is the necessary starting point for operational procedures leading to good solutions, close to the optimum. Such heuristic procedures are likely to decompose the total model into more easily solvable submodels, and to combine both optimization and simulation procedures. For an interesting description of such an approach, see Jacoby and Loucks3’ Complex as it may be, the model may still be extended in many ways. Storage and centralized peak boiler options could be introduced into the model, and the impact of directional drilling investigated. The impact on air quality of the reduced usage of conventional fuels could also be formally accounted for. Finally, the endogenous determination of land-use patterns should not depend only upon energy supply costs considerations, but also on the whole array of the other urban costs and benefits (land development costs, transportation costs, spatial interaction, etc.). Conceivably, then, the present model should be embedded in or interfaced with a general urban land use planning model in order to derive the most efficient land use and energy supply patterns. 6. CONCLUSIONS
The purpose of this paper was to promote an understanding of the interactions between geothermal energy systems and urban structure, in particular those geothermal systems using low-temperature waters for space heating within the framework or urban district heating networks. The geophysical, technological and economic characteristics of the various components (reservoir, wells, transmission and distribution networks, end-use conversion) of these systems have been analyzed and illustrated by a review of geothermal systems either in operation or under planning. The large number of interactions and cost trade-offs was shown to require a comprehensive approach to the design of the most efficient system, leading to the formulation of a mathematical programming model aimed at minimizing the total costs of energy supply. The interface between geothermal energy use and urban structure has been emphasized by letting land-use patterns be determined endogenously to the model. It has been recognized that, for various reasons, the model is not solvable exactly, but must be the starting
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BRENT D. ROSENTHAL
point for designing operational computation procedures leading to good, acceptable solutions. Some extensions have been briefly mentioned, emphasizing, in particular, the need to interface this energy-oriented model with a more general urban land-use planning model. REFERENCES 1. H. C. H. Armstead, Geofhermal Energy. E. R. F. N. Spon, Ltd., London (1978). 2. J. W. Lund, “Direct Utilization-The International Scene”. Working Paper, Geo-Heat Utilization Center, Oregon Institute of Technology, Klamath Falls, Oregon (1976). 3. L. W. Nannen, F. Kreith, and R. E. West, Energy 1, 179(1976). 4. P. J. Lienau, “Agribusiness Geothermal Energy Utilization Potential of Klamath and Snake River Basins, Oregon”. WorkingPaper, Geo-Heat Utilization Center, Oregon Institute of Technology, Klamath Falls, Oregon (1974). 5. G. Bodvarsson, Georhermics 3, 83 (1974). 6. Y. Baradat, A. Lagarde, P. Chaumet and L. Weill, In Ibunker sur I’Emploi de la Geothetmie dans le Chauffcge Domestique et Industriel.Ecole Nationale SupCrieuredes Mines de Paris, Paris, France (1975). 7. A. Wattenbarger, J. Petrol. Tech. 22,994 (1970). 8. G. W. Rosenwald and D. W. Green, Sot. Petrol. Engineers J. 14,44 (1974). 9. T. Maddock, Ill and Y. Y. Haimes, Water Resour. Res. 11.7 (1975). 10. T. Maddock, Ill, Wafer Resour. Res. 12, 818 (1976). 11. J. Zoega, h4uhipurpose Use of Geothermal Energy (Edited by P. J. Lienau and J. W. Lund). Geo-Heat Utilization Center, Oregon Institute of Technology, Klamath Falls, Oregon (1974). 12. Bureau de Recherches GCologiques et Minieres (BRGM), La Gbthermie en France. Bureau de Recherches GCologiques et Miniires, Orleans, France (1975). 13. G. Bodvarsson, Geothermics 1, 63 (1972). 14. C. R. Faust and J. W. Mercer. In Proc. 2nd UnitedNations Conj. on fhe Developmentand Use of Geothermal Energy. United Nations, New York (1975). 15. A. C. Gringarten and J. P. Sauty, In Proc. 2nd United Nations Conf. on the Development and Use of Geothermal Energy. United Nations, New York (1975). 16. A. Satman, W. E. Brigham, and A. B. Zolotukhin, Geotherm. Resour. Council Trans. 3,621 (1979). 17. W. C. Maurer, In Proc. 2nd UnitedNations Conf. on the Developmentand Use of Geothermal Energy.United Nations, New York (1975). 18. G. G. Culver and G. M. Reistad, “Testing and Modeling of Downhole Heat Exchangers/in Shallow Geothermal Wells”. WorkingPaper, Geo-Heat Utilization Center, Oregon Institute of Technology, Klamath Falls, Oregon (1974). 19. G. Delisle, 0. Kappelmeyer and R. Haenel, In Proc. 2nd United Nafions Conf. on the Development and Use of Geothermal Energy. United Nations, New York (1975). 20. S. S. Einarsson, In Proc. 2nd United Nations Conf. on the Development and Use of Geothermal Energy. United Nations, New York (1975). 21. City of Boise, Geothermal Energy Systems Phtn for Boise City. Energy Office, P.O. Box 500, Boise, Idaho (1979). G. Jover, F. Bodaine, and D. Boulenouar, Revue gets. Therm.jr. 168,959 (1975). ;;I J. W. Lund, P. J. Lienau, G. G. Culver and C. V. Highbee, “Klamath Falls Geothermal Heating District”. Working Paper, LLC Geothermal Consultants, Klamath Falls, dregon (1974). 24. J. W. Lund. G. G. Culver. and L. S. Svanevik. In Proc. 2nd United Nafions Cont. on the Develooment and Use of r Geothetmal’Energy.United Nations, New York’(1975). 25. City of Boise, PreliminaryPlan for Boise Geothermal Energy Systems (Low Temperature).Energy Task Force, City of Boise, Boise, Idaho (1977). 26. I. F. Kunze, A. S. Richardson, K. M. Hollenbaugh, C. R. Nichols, and L. L. Mink, In Proc. 2nd UnitedNations Coni. on the Developmentand Use of Geothenal Energy. United Nations, New York (1975). 27. L. Post, Geotherm. Energy Mug. 7,29 (1979). _28. C. L. McDonald and C. H. Bloomster. “The GEOCITY Model: Descriution and Aoalication”. Renort oreoared for ERDA under contract EY-76-C-06-1836,Battelle, Pacific Northwest Laboratories, Richland, Washington il977). 29. ASHRAE, Handbook of Fundamentals. American Society of Heating, Refrigeration, and Air-Conditioning Engineers, New York (1972). 30. H. D. Jacoby and D. P. Loucks, Water Resour. Res. 8, 1401(1972).
