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Energy 34 (2009) 866–872

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Energy

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Geothermal power production from abandoned oil wells

Adelina P. Davis*, Efstathios E. Michaelides 1

Mechanical Engineering, University of Texas at San Antonio, TX 78249, USA

a r t i c l e i n f o

Article history:Received 29 November 2008Received in revised form1 March 2009Accepted 10 March 2009Available online 2 May 2009

Keywords:GeothermalOil wellsEnergyIsobutaneDouble-pipe heat exchanger

* Corresponding author. Tel.: þ1 210 849 7352; faxE-mail addresses: ihm424@my.utsa.edu (A.P.

utsa.edu (E.E. Michaelides).1 Tel.: þ1 210 458 5580; fax: þ1 210 458 6504.

0360-5442/$ – see front matter Published by Elsevierdoi:10.1016/j.energy.2009.03.017

a b s t r a c t

A simulation for the determination of geothermal power production from abandoned oil wells byinjecting and retrieving a secondary fluid was performed. The analysis takes into consideration localgeothermal gradients and typical well depths and pipe diameters. Isobutane is chosen as the secondaryfluid, which is injected in the well at moderate pressures and allowed to heat up and produce vapor. Thecomputational model that was developed takes into account mass, energy, and momentum conservationequations for the well flow, and the simulation helps determine the state of the fluid from injection toretrieval. It is observed that the operation of such systems attains a maximum power that depends on thetemperature of the well bottom and the injection pressure. In general, 2–3 MW of electric power may beproduced from wells that are typical in the South Texas region.

Published by Elsevier Ltd.

1. Introduction

The current economic environment and impending climatechange from the combustion of hydrocarbons makes the use ofalternative energy sources, including geothermal, imperative forthe near future. Geothermal energy has been used since thebeginning of the 20th century for the production of electricity inmore than twenty countries. Geothermal resources that are utilizedtoday are essentially the high temperature resources, where wellsof moderate depth (1000–2000 m) intrude into aquifers andproduce either steam or a mixture of steam and water. Suchresources are utilized with steam turbines (e.g. Geysers) or insingle- and dual-flashing plants (e.g. Wairakei and Imperial Valley).Since most of the high temperature aqueous resources have beenutilized, the next expansion of geothermal power plants willnecessarily be with lower temperature resources where water maycome to the surface as liquid at temperatures in the range of120–150 �C. Binary geothermal systems, which utilize a secondaryfluid such as a refrigerant or a hydrocarbon, are typically used forthe development and exploitation of such resources.

Several recent studies have evaluated the performance ofdifferent organic substances used as working fluids in Rankine and

: þ1 210 458 6504.Davis), stathis.michaelides@

Ltd.

the Clausius–Rankine cycles [1–3]. In all such cases, geothermalwater was used to exchange heat with working fluids in the cycle.Other similar studies were performed based on the exergy andenergy analysis, and new plant designs to improve the performanceof geothermal power plants [4–9]. For low temperature resources,binary-flashing units have been recommended to provide morepower than conventional geothermal units [9]. Michaelides andScott [10] examined Freon, ammonia and isobutane as secondaryfluids for the binary-flashing geothermal power plant. Geothermalheat exchanger with multiple U-shaped pipes is presented forcooling and heating up purposes in Refs. [11,12]. Due to energyconsumption in Croatia, Shneider et al. [13] have analyzed renew-able resources such as geothermal from economic and technolog-ical points of view. Recently Kujawa et al. [14] studied theutilization of geological wells, from which geothermal fluid wasextracted, and they performed calculations on the heat flow andpower produced. Kujawa et al. proposed a double-pipe heatexchanger that would inject water deeply into the geothermalformation, and would extract heat from the well.

A glance at the geothermal potential of the United States and ofthe entire planet {reference map [15]}, proves that there are manyareas where the geothermal gradient is relatively steep, but thereare no aquifers nearby, from which hot water may be drawn. Ifthese geothermal resources are to be utilized, one must inject andretrieve a fluid at a higher temperature in order to extract heat andutilize the energy of the geothermal resource. Several such siteswith excellent geothermal potential exist in the southern part ofTexas, where the geothermal gradient is relatively high. In addition,

To

Twi

Tw

Heattransferfrom therocks

InsulationH

Bottom ofthe well

Heat transferfrom the innerto the outerpipe

a

A.P. Davis, E.E. Michaelides / Energy 34 (2009) 866–872 867

several deep oil wells exist in the same areas that are currentlyabandoned. These are oil wells that were struck dry or are now dry,because the oil reservoir has been depleted. Most of these wells areplugged, and because they are in remote areas, they pose a poten-tial environmental hazard. The production of geothermal powerfrom such wells will not only add more renewable energy to thegrid, but it will also help avert environmental problems associatedwith accidental spillage and neglect of the area around the aban-doned wells.

This study focuses on the total power that may be extracted fromsuch geothermal wells. We are using an existing well and propose torefit it in order to produce a double-pipe heat exchanger. Instead ofusing water as in Ref. [14], we propose to use an organic fluid, such asisobutane, which has thermodynamic properties better suited forthe extraction of heat from geothermal resources. Isobutane boils atlower temperatures than water, and hence, the well would produceisobutane vapor that may be easily used in a small turbine witha condenser. In addition, we performed a simple optimization studyon the effect of fluid injection pressure, and determined that there isalways an optimum value for produced power. This optimumdepends chiefly on the temperature of the well, the injection pres-sure, and the flow rate of the isobutane.

4

2

Δz

R

r

t

b

Fig. 1. (a) Schematic representation of the heat transfer in the well [14]. (b) Thescheme for direction of the flow and the top view of the pipes in the well.

2. Geothermal data and governing equations

Data for the gas and oil wells in Texas are available from theRailRoad Commission of Texas [16]. Based on an extensive review ofsuch data, we have chosen an existing well with a depth of 3 km,bottom-hole temperature of 140 �C, and 0.30 m diameter (1 inch). Adouble-pipe heat exchanger may be easily made by retrofitting thiswell with an internal pipe of smaller diameter and with a smallamount of insulation, as shown in Fig. 1a. The bottom of the wellcould be sealed off by sealants to allow the isobutane to rise on theinternal part of the pipe. Isobutane may be injected at the outer partof the double pipe as a compressed liquid coming from thecondenser at a temperature of 40–45 �C and with pressure in therange of 5–20 bar. It would heat up from the heat extracted from thesurrounding rocks and would reach the bottom of the well, where itstemperature reaches a maximum. There, the flow is reversed; thefluid enters the core of the pipe and ascends to the wellhead.

The conservation equations for this model are continuity,momentum, and energy equations.

2.1. Continuity equation

The continuity equation is as follows:

_m ¼ rVA ¼ const (1)

where r is the density of the fluid, V is the velocity, and A is the areaof the fluid conduit. For the downward part of the flow the area is:

Ad ¼ p�

R2 � ðr þ tÞ2�

(2)

and for the upward flow:

Aup ¼ pr2 (3)

2.2. Momentum equation

The momentum equation is given in terms of two states of thefluid at heights z1 and z2, and is being used for the calculation of thestatic pressure of isobutane as follows:

P1

r1gþ V1

2gþ z1 ¼

P2

r2gþ V2

2gþ z2 þ hl (4)

where P is the static pressure, z is the height, and g is the gravita-tional acceleration. The pressure head loss, hl, is given by a closureequation and the friction factor as follows:

hl ¼12

fV2

1g

Dzdh

(5)

dh is the hydraulic diameter. For the downward flow, the hydraulicdiameter is given in terms of the outer radius, the insulationthickness, and the outer radius is as follows:

dh ¼ 2ffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiR2 � ðr þ tÞ2

q(6)

For the upward flow, fluid is conveyed in a round pipe and thehydraulic diameter is equal to the diameter of the inner pipe:

dh ¼ 2r (7)

The friction factor is calculated by Haaland’s equation [17]:

1ffiffiffif

p ¼ �1:8 log10

"�3=dh

3:7

�1:11

þ6:9Re

#(8)

300

350

400

450

200 250 300 350

Tem

peratu

re, K

Entropy, J/(mol K)

4s 4

3

2

1

Fig. 2. Temperature–entropy diagram of the Rankine cycle.

A.P. Davis, E.E. Michaelides / Energy 34 (2009) 866–872868

where Reynolds number is:

Re ¼ rVdh

m(9)

And the equivalent roughness for the cast iron piping is3¼ 0.26 mm [18].

2.3. Energy equation

The energy equation is essentially the First Law of Thermody-namics for an open system. The rate of external work in the pipelineis always zero, and the heat that enters results in the change of theenthalpy, which includes the kinetic and potential energy. The rateof heat transfer from the rock to the isobutane in the outer pipe is:

_Q ¼ 2pRhðTwðzÞ � T1ÞDz (10)

And the convective heat transfer coefficient is:

h ¼ 0:023kRe0:8Pr0:4

dh(11)

The temperature of the rocks Tw at any height, z, may beapproximated by a linear interpolation of the geothermal gradient,which is obtained from the known temperatures of the surface andthe bottom of the well:

TwðzÞ ¼Tw � To

HZ þ To (12)

The inner pipe has an insulation of thickness, t, as shown inFig. 1b. Therefore, the heat transfer in the inner section 3-4 is:

_Q34 ¼ 2prUðT3 � ToutÞDz ¼ _mðh3 � h4Þ ¼ _mcpðT3 � T4Þ (13)

The overall heat transfer coefficient for the inner pipe is:

U ¼ 1r þ t

r� 1

hiþ r þ t

r þ t2

� tkþ 1

ho

(14)

Of the materials that are available, polystyrene was chosen forthe insulation of the inner pipe, with a thermal conductivity equalto k¼ 0.027 W/mK.

The convective heat transfer coefficients, hi and ho, for the innerand the outer pipes are calculated from Nusselt’s number asfollows:

Nu3 ¼hi2r

k¼ 0:023 Re0:8

3 Pr0:43 (15)

Nu4 ¼ho2ðr þ tÞ

k¼ 0:023 Re0:8

4 Pr0:44 (16)

Thus, one may take into consideration the rate of heat transferfrom the inner pipe to the outer pipe, and hence, derive thefollowing expression for the heat transfer rate to the downwardpart of the system, which is denoted as section 1-2 in Fig. 1b:

_Q12total ¼ _Q þ _Q34 (17)

Equations (1)–(17) constitute a system of governing and closureequations for the double-pipe heat exchanger, which in the presentcase extends to 3 km. In addition to the governing equations, oneneeds to have the properties of the working fluid in the double-pipeheat exchanger, in our case isobutane. We obtained the transportproperties of isobutane, such as viscosity and thermal conductivityfrom Ref. [19], and thermodynamic properties, such as density,

enthalpy, and entropy, from Ref. [20]. Appropriate functions withtemperature and pressure as independent variables were fitted tothese tables in order to obtain expressions that were used in thenumerical subroutines. Throughout the computations we assumethat the dimensions of the well are constant. Also, that thetemperature of the fluid injected to the well is also constant at310 K, and that it is not affected by any other conditions. Thebottom-hole temperature and the injection pressure and flow ratewere parameterized, and their effect on the total power produced isevaluated in the computations.

The double-pipe heat exchanger effectively replaces the pumpand boiler of a simple Rankine cycle. The fluid is compressed andheated in its downward course. Some of the fluid pressure is spentin its upward course, but in general, the working fluid exits thedouble-pipe heat exchanger at a high temperature and supercriticalpressure. The Rankine cycle that results from this operation isshown schematically in Fig. 2.

3. Numerical method and results

The initial conditions of the computer simulation are presentedin Table 1. The thickness of the insulation, t¼ 1 inch (2.54 cm), andthe diameter of the outer pipe, D¼ 12 inches (30.4 cm), are keptconstant for all of the simulations.

Fig. 3 represents the temperature change as a function of depthwith 1-inch polystyrene as the insulator. It may be observed inFig. 3 that the temperature of the extracted isobutane drops by lessthan 3 K in the ascending path. This implies that insulation with 1-inch thickness is sufficient to effectively preserve the enthalpy ofthe fluid. Ascend and descend of the isobutane are indicated by thearrows in Fig. 3.

In the downward direction, the results obtained from thesimulations indicate that the liquid isobutane is further pressurizedby the weight of the column and reaches supercritical pressures atthe bottom of the well. As the direction of the flow is reversed, thefluid moves upwards, and the static pressure is reduced. However,because of the heat addition and the rise of temperature, thedensity of the fluid in the upward direction is lower. Even thoughfrictional pressure losses are always present, the depressurizationof the ascending fluid occurs at lower rates than the pressurizationin the descending part. During ascend, isobutane passes from the

Table 1Initial parameters for the computer simulation.

Depth H, m 3000Temperature of the bottom Tw, K 430Initial pressure of injected isobutane P, bar 10Initial velocity of injected isobutane V, m/s 2Initial temperature of injected isobutane To, K 310Internal radius r, in 4

0

60

120

0 0.5 1

Pressu

re, b

ar

Specific volume, l/mol

Fig. 4. Thermodynamic diagram of pressure versus specific volume for isobutane.

A.P. Davis, E.E. Michaelides / Energy 34 (2009) 866–872 869

state of supercritical vapor to superheated vapor. It was observed inmost simulations that heating up of the fluid in the geothermal wellresulted in the production of superheated vapor without boilingand a two-phase regime. This is illustrated in Fig. 4, which depictsthe thermodynamic P–v diagram for isobutane, as well as the stateof the fluid in the well. Fig. 5 depicts the pressure–enthalpydiagram of the heating process. The arrows in both figures repre-sent ascend and descend of the isobutane. The rise of the staticenthalpy at the upper stages of the well is due to the fact that theenthalpy of isobutane increases significantly when the pressure isreduced. However, since entropy is also increased significantly, thisincrease of the enthalpy is accompanied by an exergy decrease.

The determination of the wellhead conditions enables us tocalculate the specific work and power produced by the well. Thespecific work is the change in the isentropic enthalpy in theturbine:

wt ¼ h1 � h2 (18)

And the ideal power delivered by the turbine may be calculatedfrom the specific work and mass flow rate in the well:

_Wt ¼ _mwt (19a)

In order to obtain more realistic values for the potential of sucha well to produce power, we have assumed in the computationsthat the turbine efficiency is ht¼ 85%, and the pump efficiency ishp¼ 80%.

The ideal pump power is given by the expression:

_Wp ¼ _mwp ¼_mr

DP (19b)

300

370

440

0 1500 3000

Tem

peratu

re, K

Depth, m

Fig. 3. Temperature change with depth when polystyrene is used with k¼ 0.027W/mK.

where r is the density of liquid isobutane as it exits the condenserand DP is the pressure difference in the pump.

Taking the component efficiencies in consideration the network is:

wnet ¼ wtht �wp=hp (20)

And the actual power is evaluated from the expression:

_W ¼ _mwnet (21)

The specific work and power obtained from this well are shownin Figs. 6 and 7 respectively. The three curves in these figures are forthree different bottom-hole temperatures, namely 415 K, 430 K,and 450 K. The injection pressure is the variable in the two figures,and the injection velocity is initially assumed constant at V¼ 2 m/s.This choice specifies the mass flow rate, which is constantthroughout the computations. The velocity of the fluid varies,however, according to the variation of the density. For calculation of

0

60

120

20 40 60

Pressu

re, b

ar

Enthalpy, kJ/mol

Fig. 5. Thermodynamic diagram of pressure versus enthalpy for isobutane.

0

50

100

0 30 60

Net w

ork, kJ/kg

Pressure, bar

T=450 K

T=430 K

T=415 K

Fig. 6. Net work for different temperatures and injection pressures with inner radius3.5 inches.

A.P. Davis, E.E. Michaelides / Energy 34 (2009) 866–872870

the latter, we developed an equation of state of the form v¼ v (P,T)from the data by Goodwin [20] which represents the data within0.6%.

It is observed that there is a flat maximum in all three cases,where the maximum specific work and maximum power may beobtained. The maximum power is obtained in such cases when theinjection pressure is approximately 30 bar. It must be pointed outthat the steep drop at the lower injection pressures in the curve,corresponding to 450 K, is due to a significant reduction of well-head pressure in the fluid. This implies that at injection pressuresbelow 7 bar, there is insufficient pressure to operate the double-pipe heat exchanger.

The outer radius of the well is constant, but the inner radius ofthe well is one of the parameters that may be optimized in sucha study. We used three values of this parameter: r¼ 3.5, r¼ 4.0, andr¼ 4.5 inches, and calculated the specific work and powerproduced as a function of the injection pressure. The injection

0

1500

3000

0 30 60

Net p

ow

er, kW

Pressure, bar

T=450 K

T=430 K

T=415 K

Fig. 7. Net power for different temperatures and injection pressures with inner radius3.5 inches.

velocity at V¼ 2 m/s, and the well with the bottom temperatureT¼ 450 K were chosen for the simulations. The results of thecalculations for specific work and total power produced are shownin Figs. 8 and 9 respectively. It is observed that the specific work ofthe fluid at the wellhead is almost the same in all three cases. This isa consequence of the fact that the fluid exits the well at almost thesame state in the three cases. However, the power produced issignificantly higher in the case where the inner pipe is smaller,because the double-pipe carries a higher mass flow rate of isobu-tane. As in the previous cases, the sharp drop in the curves at verylow injection pressures is due to insufficient pressure to drive thedouble-pipe well/heat exchanger. Sufficient injection pressure isessential for the operation of the double-pipe heat exchanger, theheating of the secondary fluid, and the production of power.

Finally, we conducted a parametric study with the injectionvelocity, which varied between the range of 1 m/s< V< 6 m/s(Fig. 10). The injection pressure is 30 bar, and the well-bottomtemperature is 450 K. At lower velocities, frictional losses aresignificantly lower. The mass flow rate in the well is low, and hence,the produced power would be lower. At very high velocities, fric-tion losses become significant and a great deal of the exergy ofthe fluid is destroyed to friction. It is observed that the net power ofthe well exhibits a sharp maximum at about 3.4 MW when theinjection velocity is approximately 3.5 m/s, and the inner radius is4 inches. The other curves also exhibit sharp maxima at differentvelocities and slightly lower rates of power production. This leadsus to conclude that the exact control of the injection velocity, orequivalently, the injection mass flow rate is very important for thepower production from such wells.

4. Uncertainty analysis

This is a numerical study, where the sources of uncertainty arethe a) modeling of the geothermal well; b) the numerical error; c)the uncertainty in the input data; and d) the condenser tempera-ture. We examine below the overall effects of these uncertaintieson the final results of this project.

a) Modeling: there is no modeling/simulation error because thefull conservation equations have been used as the governingequations of the problem and have been satisfied at every stepof the numerical process. We have used an explicit form of the

0

45

90

0 30 60

Net w

ork, kJ/kg

Pressure, bar

r=3.5 in

r=4.0 in

r=4.5 in

Fig. 8. Net work change with pressure for different inner radii.

0

1400

2800

0 30 60

Net p

ow

er, kW

Pressure, bar

r=3.5 in

r=4.0 in

r=4.5 in

Fig. 9. Net power change with pressure for different inner radii.

Table 2Uncertainty due to the computational step.

Dz, m 2 1 0.5 0.25 0.1

Pinlet¼ 6 bar Pexit, bar 33.022 33.039 33.048 33.052 33.055Pinlet¼ 30 bar Pexit, bar 40.476 40.490 40.498 40.502 40.504

A.P. Davis, E.E. Michaelides / Energy 34 (2009) 866–872 871

continuity, the momentum and the energy equations at everystep of the computations. Thus, for every computational stepwe calculated the velocity, pressure and temperature/enthalpyof the working fluid (isobutane) by the explicit solution of theconservation equations. Thus, the continuity, momentum andenergy equations are satisfied at any step of the computations.

b) Numerical error: this is a one-dimensional, steady-state studyand one does not expect to have the advection–diffusion errorassociated with the time-step of the multidimensionalcomputations [21]. However, it is recognized that the compu-tations are sensitive to the step size used. Since one of the mostimportant output parameters is the wellhead Pressure Pexit, weperformed a sensitivity analysis on the error introduced on thisquantity by the size of the computational step. The results fortwo inlet pressures are shown in Table 2 below.

It is observed that with the choice of the step Dz¼ 1 m in bothcases of inlet pressure, the resulting wellhead pressure is within

0

1700

3400

0 3 6

Net p

ow

er, kW

Velocity, m/s

r=3.5 in

r=4.0 in

r=4.5 in

Fig. 10. Net power change with velocity for three different inner pipe radii.

0.05% of the value obtained for the significant more stringent caseof Dz¼ 0.1 m. This proves that the choice of the computational step,Dz¼ 1 m, introduces minimal error in the computations.

c) Uncertainty in the input data: the uncertainty of the input data,such as the bottom-hole temperature or the inlet pressures isexpected to introduce significant error in the final results ofthis study. An uncertainty analysis on the total power producedwhen the bottom-hole temperature varies between 446 K and454 K is as follows:

Tw¼ 446 K, _W ¼ 1833 kWTw¼ 448 K, _W ¼ 1861 kWTw¼ 450 K, _W ¼ 1887 kWTw¼ 452 K, _W ¼ 1913 kWTw¼ 454 K, _W ¼ 1939 kW

It is apparent that the uncertainty of the input data results insignificant uncertainties on the exergy of the fluid at the wellheadand the total power produced. For this reason the well-bottomtemperature is treated as a parameter, while the inlet pressure,which is controlled by the design of the turbine/condenser system,is the independent variable of the study. Thus, the effects of thissource of uncertainty are included in the parametric study.

d) Condenser temperature: it was assumed throughout the simu-lations that the condenser temperature is constant, a verycommon assumption with this type of computations. However,it is well known that the condenser temperature dependsgreatly on the temperature of the cooling water. Depending onthe method of cooling (wet or dry cooling) the latter willexhibit diurnal and seasonal fluctuations, which may besignificant. This assumption introduces a small uncertainty inthe calculations of the average net work and total power, whichis estimated to be on the order of 3%. However, the diurnal andseasonal fluctuations of the atmospheric air have a very minorinfluence on the soil/well temperature, which assumes thevalue of 14–16 �C at a depth of 5–10 m below the surface.

5. Practical considerations

While this paper pertains to the theory and available powerfrom the novel utilization of geothermal energy using existing,abandoned oil and gas wells, it must be noted that there will beseveral practical considerations one must take into account, espe-cially in the starting phase of the utilization. At first, it is expectedthat the wells would not be completely dry and that they may befilled with saline water. Therefore, at the initial stage the waterwould need to be drained. This can be accomplished either beforeor after the double pipe is constructed using a common pump,which would reach the well bottom. In the case when the internalpipe is built first, this pipe may be used as a conduit for the removalof the water.

Secondly, the proposed double-pipe heat exchanger is verylong; its volume is high and would require a significant amount ofsecondary fluid to fill. With a length of 3000 m the volume of thedouble-pipe heat exchanger is 164.2 m3, comprising 66.9 m3 in the

A.P. Davis, E.E. Michaelides / Energy 34 (2009) 866–872872

outer part and 97.3 m3 in the inner part. In order to maintain themass flow rates contemplated for such a plant, a total of 66,434 kgof the secondary fluid would be required. While this may be a largequantity of fluid, it is not difficult to obtain commercially. If aneconomic study shows that this fluid is expensive for such anundertaking, one may use another cheaper fluid, such as pentane orhexane.

Regarding the construction of the internal pipeline, one shoulduse rolling spacers that would keep separate the inner and theouter parts of the pipe. Friction welding or friction bonding may beused to join the several parts of the internal pipeline and minimizeleakages. In order to eliminate leakages completely the two pipe-lines should be initially treated with sealants. It may also becomenecessary to use polymer bonding compounds mixed with theisobutane at the initial stage of the well operation. Thesecompounds solidify and form a bond at the high pressure gradientareas (e.g. leakage spots) thus, eliminating the leak.

6. Conclusions

The results of the computational study showed that abandonedoil wells have the potential to produce a significant amount ofpower when they are modified to become double-pipe heatexchangers and when a secondary fluid with desired thermody-namic properties, such as isobutane, is injected at the outer rim.The calculations show that the net power produced from sucha well may exceed 3 MW for a bottom-hole temperature of 450 Kand an injection pressure of 30 bar. This amount of power is notintermittent as with other renewable energy sources, and it may beavailable for peak demand as well as basic demand. The powerproduced varies and depends significantly on the down-holetemperature, the injection pressure, the injection velocity, and thegeometric characteristics of the pipe (inner and outer radii andinsulation thickness). For the 450 K bottom-hole temperature with3000 m depth well examined in this study, which is typical of SouthTexas oil wells, it is observed that an injection pressure of 30 bar issufficient and almost optimum for the operation of the system.One-inch (2.54 cm) insulation maintains the fluid temperature toan almost constant in its ascent. When the injection velocity andinner pipe radius are optimized, this system would produceapproximately 3.4 MW of power.

Acknowledgements

The assistance of the office of the Texas Railroad Commissioner,the Hon. Elizabeth Ames-Jones, is acknowledged in obtaining data

for wells in Texas and choosing a typical well for the performance ofthis study.

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