Heat Recover), Systems & CHP Vol. 8, No. 4, pp. 289-297, 1988 08904332/88 $3.00 + .00 Printed in Great Britain. Persamon Press pk

DEVELOPMENTS IN GEOTHERMAL ENERGY IN MEXICO PART SEVENTEEN. THERMAL CONDUCTIVITY

OF DRILL CORES FROM THE LOS AZUFRES GEOTHERMAL FIELD: EXPERIMENTAL RESULTS

AND ACCURATE PREDICTION METHOD

A. GARCiA, E. CONTRERAS, E. IGLEStAS Departamento de Oeotermia, Division Fuentes de Energla, Instituto de Investigaciones Eh~tricas,

Apartado Postal 475, Cuernavaca, Mor., 62000, Mexico

a n d

BERNARDO DOMh~QUEZ A. Comisi6n Federal de Electricidad, Av. Las Camelinas 3527, 10 e Piso Moreha, Michoa ~n, M~xico

(Received 20 November 1987)

Almract--The thermal conductivity of rocks is a basic parameter needed for a number of underlground heat transfer studies. However, data are not readily available and its determination is not straightforward. Available predi~'ve correlations have been developed for sedimentary rocks, while estimative methods are based on fh_~n~cai or mineral analyses. It is thtet convenient to have a method to predict or to estimate the thermal conductivity of igneous rocks from other known, easy to measure rock proper'des.

As a contribution to the solution of this problem, a correlation for predicting the thermal conductivity of igneous rocks has been developed. Data were generated as part of a charactmization project of drill corm from the Los Azufres geotbermal fteld, which included physiml, thermal and mechanieal ~ . For the correlation thermal conductivity, bulk density and total porosity data were determined on sixteen cores. Thermal conductivity varied between 1.05 and 2.34 W m- t K-t , while density varied between 2050 and 2740 kgm -3 and pormity between 1.9 and 24.7°/,. The correlation comists of forming the logarithm of the product between conductivity and denmty and rnnning a polynomial regreaion with total pormity as the independent variable. First and second degree polynomials were tested, with the latter result being more mti~actory.

The correlation obtained is simple mathematically and easy to me. For pormities between 0% and 25% the model predicts thermal conductivity within +22%, with a residual mean square deviation of 0.00462. This is generally satisfactory for ahnmt any ensineering purpnse. A further advantage of this correlation is that density and porm/ty may also be determined from drill c~uttinge, which are more readily available than cores.

A A~ a

B b C~ c, E F k M m n P p $

T v,

N O M E N C L A T U R E

exponent, Anand et aL's correlation, Table 1 (dimensionless) c o e ~ t s of the propmed correlation, equation (5) (dimensionless) comtant (dimemionleu) constant, Anand et aJ.'s correlation, Table 1 (dimensionless) constant (dimemioniess) coefficients of the correlations in Table ! (dimensionless) heat capacity per unit mass [J kg- ' K - n] exponent, Krupi~ka's and Martinez' correlations, Table 1 (dimensionless) formation factor (dimensionless) thermal conductivity [W m- n K- '] mean atomic weight [kgmol °hI exponent, Ammd et ai.'s correlation, Table 1 (dimensionless) exponent, Ammd et a/.'s correlation, Table I (dimensionless) premre [bar] permeability [~m 2] standard deviation [Win -n K -I or kgm -3 or %] temperature [°C or K] volume fraction, mineral i

289

290 A. GARCtA et al.

Subscripts

a air b bulk d dry f fluid L lower limit nl inean s solids sat saturated tot total U upper limit

Greek letters

a thermal diffusivity [m 2 s -j] 6 grain size [ram] 6~0 grain size at which 10% of the grains are coarser [ram] 6~ grain size at which 90% of the grains are coarser [ram] p density [kg m -31 0 porosity [%]

INTRODUCTION

The thermal conductivity of rocks is a basic property which must be known for use in the mathematical models employed in a number of underground heat transfer studies. Among such studies are reservoir modelling and simulation, the'rmal oil recovery, nuclear explosions, thermal energy storage, heat transfer in mines, studies related to the exploitation of geothermal energy, etc. The present study was conducted as part of the research activities for the development and exploitation of geothermal energy in M/.'xico which are being carried out by the Departamento de Geotermia of the Instituto de Investigaciones El~tricas [1].

M~xico possesses large amounts of geothermal energy, some of which is commercially ex- ploitable. At present, M6xico is ranked third in the world among the countries that generate electricity from this source [2], with geothermal energy contributing approximately 5% of the country's electricity requirements, and it is planned to maintain this level of contribution until 1990 [3].

The basic objective in developing a geothermal resource is to recover as much of the heat contained within it as possible. A geothermal reservoir is composed of hot, porous and permeable rocks which act as hosts for the geothermal fluid and thus the rock-fluid pair stores the energy of the system, with the rock containing about 80% of the total energy in the system. Geothermal reservoir engineering is applied to determine the resource's size, heat and mass reserves and extraction capacity. This permits a decision to be taken as to whether the resource is to be developed, the design of exploitation strategies and the assessment of the economics of the resource. However, very little information about the resource is available at this stage. This task thus becomes a dynamic, recursive process throughout the field's useful life. Therefore, it is imperative to obtain data about the thermophysical properties of the reservoir's rocks and fluids. The rock properties which are needed are density, porosity, permeability, specific heat and thermal conductivity and diffusivity. The quality and quantity of the available data will ensure that the discrepancy between estimates and actual figures is as small as possible.

Reservoir rock properties are normally obtained by means of core analysis, but core extraction is difficult and cores are expensive. Thus, the convenience of having correlations to predict properties such as thermal conductivity from a knowledge of other properties which are measurable on drill cuttings cannot be overemphasized. Thermal conductivity of rocks depends on many factors, such as mineral composition, density, porosity, etc. Correlations to predict the variation of conductivity with temperature have been developed [4], while the effect of pressure on conductivity has been studied [5-7].

In this work a brief account of existing methods for B n g the thermal conductivity of rocks is presented. Experimentally determined [8] thermal conductivity, density and porosity results of drill cores from andesite rock from the Los Azufres geothermal field are given. Finally, a correlation to predict thermal conductivity of rocks from density and porosity is developed. The proposed correlation is the first of its kind for igneous rocks.

Developments in geothermal energy in Mexico--Part XVII 291

EXISTING METHODS ~ 0 ~ ~ A S U R I N G AND ESTIMATING THERMAL CONDUCTIVITY

The thermal conductivity of rocks may be obtained by the following procedures.

1. Direct measurement

Thermal conductivity may be measured by steady state or transient methods. These methods have been summarized by Garcia and Contreras [9] and only the experimental method employed to generate the data reported below will be described.

2. From the definition of thermal diffusivity

Thermal diffusivity is defined as a = k/pCp. This method implies that if density, specific heat and thermal diffusivity are known, it is possible to calculate conductivity. Use of this method is limited, since very little data exist about thermal diffusivity and specific heat of most rocks.

3. From the mineral or chemical analysis

The estimation of thermal conductivity of rocks from their mineral constituents implies availability of chemical or mineral analyses and the thermal conductivity of the rock forming minerals. Birch and Clark [6] developed a method for estimation of the thermal conductivity of fresh, igneous rocks from mineral composition and the minerals' thermal conductivity. They found that the series combination of the phases, given by

k ~- ~ ( r l /k l ) -z (1)

is appropriate for this purpose. Woodside and Messmer [10], however, claimed that the geometric mean

k ffi exp{~ [V, In(k,)]} (2)

is most satisfactory, whereas Beck [11] proposed a Maxwell model which was extended to allow for errors in thermal contact resistance. Except for the mean geometric model, equation (2), all the models have a physical basis.

Horai and Baldridge [12] proposed three methods for estimating the thermal conductivity of nonporous, macroscopically isotropic and homogeneous rocks from the mineral and chemical composition. Texture effects are neglected. The first method is based on the arithmetic average of kL and ku, where kL and ku are functions of the minimum and maximum phase conductivities and of the volume fraction and conductivity of each mineral ki. In this case, the mineral composition is obtained by point count on thin sections. The application of this method is not restricted to igneous rocks.

The second method is applicable to igneous rocks of magmatic origin the chemical composition of which is known. In this case, the norm, a hypothetical mineral composition schematically calculated from the chemical composition, usually agrees with the mode or actual mineral composition. This fact permits application of the calculation procedure referred to as the first method.

In the third method, thermal conductivity is estimated from the mean atomic weight M and the rock density. The conductivity of the rock forming minerals is given by

k ffi a + bp, (3)

where a = C o - C~ M, b -- (72, C~ = constant and M is estimated from the chemical analysis. The above methods allow estimation of thermal conductivity of pulverized solids or drill cuttings.

To calculate the rock conductivity as a consolidated medium, a correction for porosity must be made. However, their use requires mineral or chemical analyses, which in turn require techniques or equipment as specialized as those needed to determine the conductivity itself. X-ray techniques are often needed to provide the fine resolution which is not attainable with techniques such as point counts. On the other hand, there exists a database on thermal conductivity and density of the main rock forming minerals [13] and some information is ayailable about temperature effects [6] which might allow their use.

292 A. G~a~clA et al.

Table I. Correlations from the literature for the estimation of the thermal conductivity of rocks

Author Proposed correlation Type of rock Comments

Zierfuu and Vander Vliet [17] log(kF) = ~ C~# ~ i = 0-3 S Dry or saturated rock

Krupiczka [14] ( k / kr ) = ( k, / k r ) "~ granular = Co + ¢ ,0os # ) + ¢,~og@,/kr)l n~mial

Anand, Somerton and Golmna [ 15] k = C o + C , O + C 2 p + C 3 p ' + C 4 F S (dry)

Anand, Somerton and Gomma [15] k/ka= C o + C,(kr/k = - I) A S + C2[(0/(I - ~)(kr/ka)]~(p.Jpd) (saturated)

Reddy [16] log(kp) = ~ C ~ ~ i = 0-2 S

Martin= [71 (k /kr) = (k,/kr) ~ S E = co + c, Ooi ~) + c~pos(k, ltO]

+ Cj0os,;.). + c, pos(6,0/6~0)] S - sedimentary rock.

_+30% of error for 76% of points

± 15% of error for 87% of points

+ 15% of error for 85% of points

:1:29% of error

+ 32% of error

4. Correlations with other properties

The published correlations for estimation of rock thermal conductivity are s ~ in Table 1. Analysis of this table reveals that almost ~ the correlations are for sedimentary rocks, except for that of Krupiczka [14], which was developed for granular materials and is included here for convenience, since Martinez' correlation [7] is an extension of it. Worthy of note is the degree of complexity involved in the correlations of Martinez [7] and Anand et al. [15], contrasting with the simplicity of Reddy's correlation [16]. The exponent E in Krupiczka's correlation [14] is a rather complex function of the solid's and saturant's conductivities and of porosity. It was extended by Martinez [7] by including grain size 6 to account for intergranular contact effects. Zierfuss and van der Vliet's correlation [17] is simple in form and was the basis of the correlation developed by Reddy [16]. The former is complicated by the inclusion of the formation factor F, which is determined from electrical resistivity measurements.

Anand et al. [15] presented multivariate correlations for dry and saturated rock which are complex in form. Variables such as F, k,, p, p, kf, etc. once again appear. It must be noted that the percentage error is slightly smaller in these correlations. This was not the case in the improvement of Kr-apiczka's correlation [14] made by Martinez [7], Finally, there is Reddy's correlation [16], whose degree of prediction is as good as that of any other of the correlations shown in Table 1. This correlation is very simple in form and includes the variables whose effect on thermal conductivity might more easily be reflected in terms of the heat flow path: porosity and density. These variables are easily measurable either in rocks or in drill cuttings. The effect of intergranular contact may be included via permeability and ,this, in turn, may be included via porosity using Kozeney's relation or from permeability-density relations [16], but since porosity and density are easier to determine they are preferred in the correlation. This is the model that inspired the analysis shown below applied to igneous rocks.

EXPERIMENTAL DETERMINATIONS

Thermal conductivity, density and porosity were determined for this study. The conductivity measurements were made using oven dried cylindrical spechnens, 50.8 nun (2 inches) in diameter and 101.6 mm (4 inches) in length. The thermal needle probe transient method, which approximates an infinite line source, was used. It is based on a classic solution of the diffusion equation d ~ by Carslaw and Jaeger [18]. Details about its use may be found el~,where [9, 10]. In the method, the rate of temperature rise along a line heat source within an infinite, homogeneous medium is determined by sample conductivity, which is calculated from the internal heater temperature history and the power input.

The experinumtal procedure is best described with reference to Fig. 1. An electric resistance nickel-chromium heater, 3.2 mm is diameter, is placed along the axis of the sample in a hole 4.8 mm in diameter. A type K thermocouvle is attached to the heater at the mid sample location. This

Developments in geothermal energy in Mexico--Part XVII 293

Thermocoupl.e

insutotion I / / / / , ~ i / / / / I

'N Ill

Heater

Fig. 1. Experimental set up for thermal cond~'tivity measurements.

assembly is "potted" in place with a mixture of ceramic cement and copper powder to minimize contact resistance. Heat losses from the sample end are minimized by using ceramic insulators. The heater length to diameter ratio is about 40, which is well above the minimum L/D ratio needed to approximate the ideal line heat source [18].

Carefully monitored power (voltage and current) is then applied using a Hewlett-Packard d.c. power supply, model 6299A. Voltage and c u ~ n t readings were made using a Fluke Digital Multimeter, model 8050A. The applied power results in a constant heat generation per unit length in the heater. The temperature rise-time variation is recorded simultaneously with the heat input and the conductivity computed from the slope of a best-fit straight line of a plot of temperature rise vs logarithm of time. A Digital Minc 11 data logging computer system is used for data recording and reduction.

To calibrate the experimental procedure and equipment, several test runs were made employing a sample of fused quartz as a standard. Its reported conductivity was reproduced to within + 1%. It is estimated that the determinations performed have an error of about + 0.03 W m- i K- I.

Density and porosity were measured employing well established techniques [20]. Bulk density was determined by measuring mass in an Ohaus electronics balance, model 1500D and total volume was measured by mercury injection in a Ruska universal porometer. Effective porosity was also measured in the porometer. Total porosity was computed from the relation

~, = 1 - ~ o ~ / p , ) , ( 4 )

in which the determination of Pb has been described and p, is the solids density which was determined by measuring grain volume by displacement of an equivalent volume of liquid in a volumetric/]ask.

EXPERIMENTAL RESULTS

Sixteen determinations of thermal conductivity, density and porosity on 15 cores from I I wells from the Los Azufres geothermal field were made. The location of the wells in the field is shown in Fig. 2. It may be seen from this figure that the areal coverage of the sampling spans most of the field, including marginal wells such as AZ 20 and AZ 50. Ambient conditions prevailed in all tests. All the sample cores tested are andesites and basaltic andesites of igneous origin.

The results of the present determinations are shown in Table 2. Effective porosity is also included, since it is routinely determined as part of the basic rock characterization. Also included is a datum

294 A. GARCtA et al.

Table 2, Thermal and physical measured prol~rties of cores from the Los Azufres geothermal field

Density (kg m -3) Porosity (%) Thermal Well, core conductivity and sample Bulk Solids Effective Total (W m- ~ K- ~)

AZ3-NI - I 2340 2760 14.02 15.5 1.68 AZ3-N4.1-1 2560 2940 11.57 13.2 1.84 AZ3-N5-1 2740 2800 1.20 2.2 1.99 AZ4-N3-1 2440 2790 11.07 12.7 1.58 AZ4-N3-2 2430 2790 11.70 12.9 1,53 AZ5-N I - 1 2050 2730 23.42 24.7 1.17 AZ8-N2-1 2600 2790 6.36 6.9 2,34 AZ20-NI- I 2270 2610 10.32 13.0 1.58 AZ20-N3- I 2690 2810 2.39 4.2 1.71 AZ22-N2-1 2450 2800 11.20 12.6 2.17 AZ25-Nl - I 2320 2730 I 1.39 14.8 1.75 AZ26-N2-1 2610 2740 1.60 4,9 2.20 AZ26-N3-1 2430 2700 7.70 10,1 1.55 AZ29-NI- I 2050 2660 14.90 23.1 1.05 AZ47-N4- I 2740 2790 0,68 1.9 1,89 AZS0-N3-1 2490 2680 7.75 7,2 1,52 AZlg -N I-I 2280 18.80 1.97"

*Measured at 80 bar and 25°C [211.

of thermal conductivity of a core sample from well AZ 19 reported earlier by Contreras et aS. [21]. The datum was generated at 80 bar confining pressure and 25°C. It is included here for completeness, but was not used in the correlation arudysis due to unavailability of its total porosity value.

From the table, it is seen that thermal conductivity varies between 1.05 W m- ~ K- ~ for sample AZ 29 NI 1 and 2 . 3 4 W m - ~ K -~ for sample AZ 8 N2 1. The mean conductivity value is

I I I I I I

30

40

14 ? 44 Verde

Presa ~ _ ~ ( / ~ 25 Laguna A.F.

Larga b Campamento , ~ A g u a F r i a - C F E

/ 7 Is_ ~ ! . . ~ 4

oTSS • S t u d i e d w e l l s

o Other wel ls

IOOOm ! I

2O

Fig. 2. L o c a t i o n o f studied wells from the Los Azufres geothermal field.

Developments in geothermal energy in Mexico--Part XVII 295

1.72 W m- ' K- ' , with a standard deviation ot" 0.34 W m z~' K -; for the 16 determinations. Similarly, the range of variation of bulk density is 2050-2740kgm -3, whereas that for solids density is 2610-2940 kg m -3. The corresponding mean density values are 2450 and 2760 kg m -3, respectively. The total porosity range goes from 1.9% to 24.7%, with an average value of 11.2%.

PETROGRAPHIC ANALYSIS

In order to petrographically characterize the core samples, mineral analyses were performed by point count on thin sections. It was not possible, however, to use such information to estimate core thermal conductivity by some of the above methods since the resolving power of this technique

J .

was not sufficient to quantify some of the small sized n~nerals (e.g. clays, glass, accessories, etc.), which were determined only as a group. Since the volumetric contribution of these groups was quite significant, up to 35% in some cases, thermal conductivity could not be assigned to individual minerals, not even by similarity in composition.

CORRELATION ANALYSIS AND PROPOSED CORRELATION

A multivariate correlation analysis, based on Reddy's model [16], was performed between conductivity, density and porosity. The physical reasoning has been put forward in the discussion on published correlations and can also be found in Reddy's paper [16]. For a correlation to have significant practical value, an important criterion for a property to be included in a correlation is its easy availability. From a heat conduction point of view, the heat flow path in a solid is disrupted by pores in the rock matrix and thus porosity should be included in the correlation. This porosity must be the total rock porosity, not the effective porosity, since all void spaces affect heat conduction in the rock.

It has been found [16] that another property which is independent as far as its effect on thermal conductivity is concerned is permeability. This property may be included as a discrete or as a continuous variable in conductivity-porosity correlations. Permeability is a function of size and shape of pore spaces and these, in turn, depend on the geometric properties of mineral grains and their arrangements. Hence, permeability depends on grain packing and cementation: for a given size of spherical, unconsolidated grains, permeability depends only on their packing. Thus permeability should be included in the correlation. However, from the above insights it is apparent that permeability depends on density and, since density is more easily measurable than perme- ability, its inclusion in the correlation is preferred.

The procedure consists of forming the logarithm (base 10) of the product between conductivity and bulk density, product kp, and performing a polynomial regression of this product as a function of total porosity. Total porosity is defined as the fraction of bulk volume that is not occupied by the solid framework of the rock. First and second degree polynomials were tested. It must be mentioned that Reddy's model [16] employs effective porosity, i.e. the percentage of interconnected void space with respect to bulk volume, as the independent variable, since his analysis was performed for sedimentary rocks for which effective and total porosity are practically the same. In the present case, total porosity is used as the independent variable since the analysis is for igneous rocks for which effective and total porosity are substantially different (see Table 2).

The product kp is plotted as a function of total porosity in Fig. 3. It can be seen that the product kp tends to decrease with an increase in porosity in the semi-logarithmic scale of the plot. In the same figure the regression curves obtained from the correlation analysis are shown. The statistical analysis for the linear model gave a correlation coet~cient of 0.829 with a residual mean square deviation of 0.00523, while the corresponding results for the quadratic model are a correlation coefficient of 0.865 and a residual mean square deviation of 0.00462. These results show that the second degree model is better than the first degree model. Furthermore, it may be noted from Fig. 3 that there is little difference between both models for porosities up to about 18%. For larger values there is a separation between the curves, with the quadratic model providing a better fit to the points on the far right. Therefore, this model should be preferred to the linear model.

296 A. GARCiA et al.

icA

8

6

5

4

3

2

,o 3 o

® ®

Ist order modet - x - - x - 2nd order model

I I I I 5 lO 15 20 25

Totot. porosity (%)

Fig, 3. Variation of the kPb product with total porosity and 1st and 2nd order fitted models.

Table 3. Point by point comparison between experimental and predicted thermal ~ldttctivity valuel ulil~ the ter.4~sd order pmp0Rd model

Thermal conductivity OVm-' g-') PerceataSe

Well, core of and lample Exper imenta l Pred ic ted difference AZ3-NI - I 1.68 1.58 -5 .8 AZ3-N4.1-1 1.84 1.59 ' - 13.7 AZ3--N5-1 1.99 1.91 - 4 . 2 AZA-N3-1 1.58 1.70 + 7.4 AZ4-N3--2 1.53 1.69 + 10.6 AZ5-NI - I 1.17 1.08 - 7 . 7 AZS--N2-1 2.34 1.88 - 19.7 AZ20-N i - I 1.58 1.80 + 14.2 AZ20-N3--I 1.71 1.90 + I 1.2 AZ22-N3--I 2.17 1.70 -21 .8 AZ25-Nl-1 1.75 1.65 - 6 . 0 AZ26-N2-1 2.20 1.94 - I 1.8 AZ26-N3-1 1.55 1.86 + 19.7 AZ29-N 1-1 1.05 1.20 + 14.3 AZA7-B4-1 1.89 1.91 + I .I AZS0--N3-1 !.52 !.95 + 28.2

The proposed model is

log,0 (kPb) = A0 + A t 0 t o t + A 2 0 2 t , ( 5 )

where A0 = 3.7228809, Ai = -0.94476092E 3 and A2 ffi -0.581068E 3. Point by point error analysis (see Table 3) shows that the second desree model predicts thermal

conductivity within + 22%, except for one point for which the discrepancy is 28%. This difference is most likely due to the fact that the computed [see equation (4)] total porosity was less than the effective porosity, which is physically incongruent, since in the fimit both porosities must be equal. For the present case, this difference between both porosities falls within experimental error.

CONCLUSIONS

Thermal conductivity, density and porosity of 16 samples obtained from 15 drill cores from 11 wells from the Los Azufres geothermal field were measured. Tests were made at 25°C and zero confining pressure. The mean thermal conductivity value was found to be k = 1.72Wm -~ K -I, with a standard deviation of 0.34Wm-~K-L The corresponding mean and standard deviation values of bulk density and total porosity are 2451 ksm -3 and 211 kgm -3 and 11.2% and 6.4%.

The po~bility of correlating thermal condu~vity with other rock properties was investigated. Correlations with density and porosity were investigated by means of two multivariate correlations, one linear and one quadratic. It was found from s t a ~ comiderations that the second degree model gave a superior correlation coelftcient of 0.864 and residual mean square deviation value of 0.00462 in terms of the kp product. Thermal conductivity predictions fall within +22% maximum deviation in the range of total porosity from 0 to 25%.

Developments in geothermal energy in Mexico--Part XVII 297

Correlation with its mineral composition was alsO Investigated. Point count analysis on thin sections was performed, but the low resolving power of the technique prevented estimation of thermal conductivity with this information.

To the best of the authors' knowledge, the correlation presented here is the first one published for predicting thermal conductivity of igneous rocks. It's simple form contrasts largely with the complexity of other published correlations. A further advantage of this correlation is that density and porosity may also be determined from drill cuttings which are normally extracted during drilling, while cores are not so abundant and thus are expensive.

Acknowledgements--The authors wish to thank Dr David Nieva for his encouragement to publish this work and to Mr Adriln Patifio for drafting the figures. Thanks are also due to the staff of the Gerencia de Proyectos Geotermoei~tricos of Comisibn Federal de Electricidad for their collaboration.

R E F E R E N C E S

I. P. Mulis, D. Nieva and F. A. Holland, Developments in geothermal energy in Mexico--Part One: General considerations, J. Heat Recovery Systems 5, 277-283 (1985).

2. R. DiPippo, Geothermal electric update, the state of the world--1985, in Proceedings of the 1985 International Symposium on Geothermal Energy, International Volume, pp. 3-18. Geothermal Resources Council (1985).

3. H. Alonso, Present and planned utilization of geothermal resources in M~xico, in Proceedings of the 1985 International Symposium on Geothermal Fa~,rgy, International Volume, pp. 135-140. Geothermal Resources Council (1985).

4. W. H. Somerton and G. D. Boozer, Thermal characteristics of porous rocks at elevated temperatures, Trans. Am. Inst. Min. metall. Petrol. Engrs 219, 418--422 (1960).

5. G. Backstrom, Measurement of thermophysical properties of solids under high pressure (invited paper), in Proceedings of the Seventh Symposium on Thermophysieal Properties, pp. 169-180. Standing Committee on Thermophysical Properties, Heat Transfer Division, ASME, Gaithersburg, MD (1977).

6. F. Birch and H. Clark, The thermal conductivity of rocks and its dependence upon temperature and composition, Am. J. Sci. 2,1, 527-558, 613-635 (1940).

7. L. F. Martinez, Thermal conductivity of core samples from the Cerro Prieto geothermal field: experimental results and an improved prediction method, in Proceedings of the First Symposium on the Cerro Prieto Geothermal Field, Baja Califomio, M~xieo, pp. 342-351. Lawrence Berkeley Laboratory, Report LBL 7098 (1978).

8. Instituto de Investigaeiones El6ctrk,~, Apoyo para diagnbsticos de perforacibn de pozos mediante la determinacibn de propied~_d~ fisicas de rocas en medius geot6rmicos Fare I: Correlaciones entre Petrologla y Petrofisica en campos del eje neovolcinico, Informe IIE/I 1/2014/I 03/F, Instituto de Investigaciones El~'tricas, Cuernavaca, Mor., Mexico (in preparation).

9. A. Garcla and E. Contreras, M6todos para la determinacibn de la conductividad t~rmica de rocas: estudio bibliogrifico. Informe IIE/10/I 1/1663/FE G29/I 07/P, Instituto de Investigaciones El6ctricas, Cuernavaca, Mor., Mexico (1985).

10. W. Woodside and J. H. Meumer, Thermal conductivity of porous media: I--unconsolidated sands; II--consofidated rocks, J. appi. Phys. 32, 1688-1699, 1699--1706 (1961).

11. A. E. Beck, An improved method of computing the thermal conductivity of fluid filled sedimentary rocks, Log Analyst, 30 0976).

12. K. Horai and S. Baldridge, Thermal conductivity of nineteen igneous rocks, II: Estimation of the thermal conductivity of rock from the mineral and chemical compositions, Phys. Earth Planet Interiors 5, 157-166 (1972).

13. K. Horai, Thermal conductivity of rock forming minerals, J. geophys. Res. 76, 1278-1308 (1971). 14. R. Krupiczka, Analysis of thermal conductivity in granular materials, Chem. Procen Engng 7, 122-144 (1967). 15. J. Anand, W. H. Somerton and E. Gomaa, Predicting thermal conductivities of formations from other known

properties, J. Soc. Petrol. Engrs 13, 267-273 (1973). 16. M. S. Reddy, Estimating the thermal conductivity of rocks--an analytical approach, in Proceedings of the Seventh

Symposium on Thermophysieal Properties, pp. 404--411. Standing Committee on Thermophysical Properties, Heat Transfer Division of ASME, Gaithersburg, MD (1977).

17. H. Zierfuss and G. van der Vliet, Laboratory measurements of heat conductivity of sedimentary rocks, Bull. Am. Ass. Petrol. Geol. 40, 2475-2488 (1956).

18. H. S. Carslaw and J. C. Jaeger, Conduction of Heat in Solids, 2nd Edn. Oxford University Press, Oxford (1959). 19. J. H. Blackweli, The axial flow error in the thermal conductivity probe, Can. J. Phys. 34, 412-417 (1956). 20. ISRM, Suggested methods for determining water content, porosity, density, absorption and related properties, Society

for Rock Mechanics, Commission on Standardization of Laboratory and Field Tests, Document No. 2. Lisbon, Portugal (1972).

21. E. Contreras, E. Iglesias and R. Oliver, Determinacibn de propiedades fisicas y estudios petrogr~ificos de nticleos de pefforacibn del eampo geot6rmico Los Azufres, Informe IIE/I 1/3753/I 01/F, Instituto de lnvestigaciones El6ctricas, Cuernavaca Mot., Mexico, November (1984).