Simulation of heat transfer at the Kola deep‐hole site: implications

Geophys. J . Int. (1994) 116, 409-420

Simulation of heat transfer at the Kolla deep-hole site: implications for advection, heat refraction and palaeoclimatic effects

Ilmo T. Kukkonen' and Christoph Clauser2 'Department of Geophysics, Geological Survey of Finland, Betonimiehenkuja 4, FIN-02150 Espoo, Finland 'Geowissenschaftliche Gemeinschaftsaufgaben, Niedersachsisches Landesamt fur Bodenforschung (NLfB-GGA), Stilleweg 2, D-30655 Hannover, Germany

Accepted 1993 July 12. Received 1993 June 25; in original form 1993 March 23

S U M M A R Y The drill hole SG-3, 12261 m deep in the Pechenga-Zapolyarny area, Kola Peninsula, Russia, is currently the deepest drill hole in the world. Geothermal measurements in the hole reveal a considerable variation (30-68 mW m-') with depth in the vertical component of heat-flow density (HFD). We simulate heat and fluid flow in the bedrock structure of the Kola deep-hole site. Various potential sources for the observed HFD variation are discussed, with special emphasis on advective heat transfer, palaeoclimatic ground surface-temperature changes and refraction of heat flow due to thermal conductivity contrasts. A 2-D finite-difference (FD) porous-medium model of the Kola structure, constructed from all available data on lithology, hydrogeology , topography, thermal conductivity and heat- production rate in the deep-drilling area, is the basis of all forward-model calculations. A conductive, steady-state simulation indicates that heat production and refraction create a variation of about 15 mW mp2 in the uppermost 15 km, but are insufficient to reproduce the measured HFD-depth curve in the uppermost 2-4 km. However, if topography-driven groundwater flow is considered in the model, the measured HFD variation is easily explained. The most sensitive parameters in fitting the model results to the observed HFD-depth curve are the permeability of the top 4 km ( 10-'4-10-'s m2) and the (constant) HFD applied at the base of the model at 15 km depth (40-50 mWmp2). The palaeoclimatic effect for the Kola structure was calculated with a conductive transient simulation. A simplified ground surface-temperature history (GTH) of the Kola area was simulated by varying the surface temperatures of the model during different intervals of the simulation. Our results indicate that the measured variation in the vertical HFD cannot be explained by the palaeoclimatic effect alone, because its amplitude decreases rapidly from about 16mW m-' near the surface to less than 2 mW m-2 at depths in excess of 1.5 km.

Key words: advection, Fennoscandian Shield, geothermics, heat flow, palaeoclimate, Russia, thermal conductivity.

INTRODUCTION

The 12 km deep drill hole in the Pechenga-Zapolyarny area, Kola Peninsula, Russia, is currently the deepest borehole in the world. Among other unexpected observa- tions, this borehole displays a considerable variation in the vertical component of heat-flow density (HFD) (Kremenet- sky & Ovchinnikov 1986a,b). In the uppermost 1 km, HFD is about 30mWm-2, but reaches 50mWmp2 at 5-6km depth. It reaches its maximum of 67.5 mW m p 2 at 4-5 km.

So far, the reasons and implications of these results have not been studied in detail. Mainly qualitative discussions on convective and palaeoclimatic effects have been presented by Kremenetsky & Ovchinnikov (1986a,b), Moiseyenko (1986), Arhavskaya et al. (1987) and Kukkonen (1993). However, a better insight into the factors responsible for the detected HFD variation in the Kola deep hole would be very instructive for the understanding of heat transfer processes in the crystalline crust in general. The Kola hole is not the only deep hole which displays considerable vertical

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410 I . T, Kukkonen and C. Clauser

variation in heat-flow density. Similar results were reported for the 4 k m deep KTB pilot hole in the Oberpfalz, Germany. These variations can be attributed either to advective heat transfer or to palaeoclimatic surface temperature changes (Burkhardt et ul. 1991; Clauser & Huenges 1992; Jobmann & Schulz 1992). Schellschmidt & Schulz (1991) report a decrease of H F D with depth for a 2 km deep hole, drilled into the crystalline basement of the Rhine Graben. They interpret the variation as due to a convective redistribution of heat by a regional groundwater flow system in the sedimentary graben fi l l .

The aim of this paper is to investigate the advective- conductive heat-transfer regime in the Kola structure using forward (FD) model calculations. We present results for both steady-state and transient conditions, when surface temperatures vary according to a prescribed palaeoclimatic history. With these calculations we demonstrate the parameter ranges (mainly basal H F D and hydraulic permeability) needed to explain by heat advection the H F D variation reported in the Kola deep hole. Further, we estimate the magnitude of the palaeoclimatic effect on the Kola structure.

THE KOLA D E E P - H O L E SITE

The Kola deep hole (Russian code SG-3) is located on the northern rim of the Fennoscandian (Baltic) Shield at 69"24'N, 30"35'E at about 50 km distance from the Barents Sea (Fig. 1). The area has low mountains and fjelds reaching a maximum elevation of about 700m above sea-level (asl). Generally the topography is 150-300 m asl. The drill-hole site itself is at an elevation of 350m. The area was covered by the Weichselian glaciation, which produced the relatively gentle topography. The vegetation cover is thin, and low trees or bushes (fjeld birch) grow on the hills. Alternatively, the ground is just covered by a moss layer a few centimetres thick. Depressions are filled by swamps. In the southern and western part of the area conifers grow at altitudes below approximately 150-200 m asl. Locally, mining various man-made features have modified

activities and the scenery

LEGEND

<3 Lakes. rivers

0 5 10 i 5 20 25

hm

Figure 1. Topographic map of the deep drill-hole area in Kola Peninsula. Simplified from the Tactical Pilotage Chart C-2B at a scale of 1:SOOOOO (United States Air Force, 1971). The vertical cross-sections for the 2-D model calculations are located along profiles AA' and AB. SG-3 denotes the Kola deep hole.

LEGEND

Lower Proterozoic

. - \. a EaJlC Y O l C a n l C S

. - -

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Basic ~olcanlcs + diabases

0 Diabase

Archaean

0 z;;;;Sgi; Heat f low data

5/36 Site numberIHFD in m W t r 2

0 5 10 15 20 25

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Figure 2. Geological map of the deep drill-hole area with HFD data points (Table 1). Simplified from Nalivkina er a/. (1987). Abbreviations in the inset are: A = Archaean, Pr = Proterozoic, C = Caledonides. EEP = East European Platform.

considerably. The annual precipitation is about 400 mm and the mean annual (air) temperature is about 0°C (Geographical Society of Finland 1925, 1988).

The bedrock of the area is of Proterozoic and Archaean age and covered by Quaternary glacial deposits, typically only a few metres thick at the most (Fig. 2). The SG-3 drill hole intersects a sequence of lower Proterozoic and Archaean rocks. The Proterozoic rocks, consisting mainly of metavolcanic, metasedimentary and igneous rocks, form a synclinorium structure. On the eastern rim of this 'bowl' the strata dip at about 40-45" to the SW. O n the western side the strata are more or less horizontal, and the synclinorium ends at a fault structure.

In a larger tectonic framework, the deep-drilling site is not far from the transition of the Shield to the continental shelf of the Barents Sea (Glaznev, Skopenko & Podgornykh 1986). The thickness of the crust and lithosphere in the deep- drilling area are about 40 km and 170 km respectively (Calcagnile 1982; Nalivkina, Rusanov & Suslova 1987). HFD determined in shallow holes (depths of 355-1674 m, Table 1) situated within 40 km from the SG-3 hole ranges from 26 to 39mWm-2, the mean of eight sites being 33 mW mP2. This is in contrast to the H F D determined for the deeper parts of the SG-3 hole, which was about 50 mW rn-' (Table 2).

NUMERICAL SIMULATIONS

The authors do not claim that the present models simulate in detail the real geothermal conditions in the Kola structure. Our models are 2-D, but the structure and topography are actually 3-D. Including three-dimensionality would increase the number of free parameters, and demand more detailed information on lithology and topography, presently not at our disposal. Also, the temperature and HFD data available d o not seem to reflect undisturbed thermal equilibrium conditions. In spite of these reserva- tions we believe that considerable insight into the competing thermal transport mechanisms in crystalline environments

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Aduection, heat refraction and palaeoclimate 41 1

Table 1. Heat-flow density measurements in the Pechenga area. Number WHDB Site Depth H FD

1 su 1 Nikel 1560 26 (1)

2 s u 2 Nikel 1570 31 (1 )

3 s u 3 Nikel 1570 26 (1)

4 s u 4 Sputnik 250-1 1.50 35 (10)

5 SU6 Zapoljarnyi 1002-1674 36 (4)

6 s u 7 Nikel 593-771 36 (4)

7 SU8 Ala-Akkajarvi 355-53 1 39 (3)

8 37 (1)

Mean 33.3 + 5.0

Number WHDB Site Name of the site. Depth HFD Reference

Refers to site number in Fig. 2. The site code used in the World Heat Flow Data Base (Pollack et al. 1989).

Reported maximum depth (m) of borehole. Heat-flow density (mW m--), number of holes in parentheses. 1: Pollack et a/. (1991), 2: Gordienko et a/. (1987).

Reference

1

1

1

1

1

1

2

2

Table 2. Vertical variation of heat-flow density in the Kola deep hole (Kremenetsky & Ovchinnikov 1986b).

Depth r x HFD HFD-c

0- 1200 11.0 2.70 29.70

1200- 1600 12.5 2.95 36.90

1600-2000 12.0 3.10 37.20

2000-2805 12.0 3.35 40.20 39.00

2805-4500 16.5 3 .OO 49.50

4500-4900 18.0 3.75 67.50

4900-5642 21.0 2.55 53.50 50.30

5642-5717 17.5 3.25 56.00

57 17-6400 21.0 2.55 53.55 49.20

6400-6800 23.5 2.50 58.70 51.70

6800-7200 20.0 2.22 44.40

7200-9456 17.0 2.40 45.60

Depth (m) r Mean temperature gradient (mK me ' ) . I Mean thermal conductivity (Wm-' K - ' ) . HFD Heat-flow density (mW m-'). HFD-c Heat-flow density (mW m-') corrected for P-T conditions in the hole.

such as at the Kola peninsula can be gained from these described in Clauser (1988) and Clauser & Villinger (1990) models, particularly with respect to the interaction of and will not be repeated here. We study a 60 km long and steady-state and transient as well as conductive and 15 km deep SW-NE cross-section through the upper crust advective effects. extending from the water divide near the deep-hole site to

Calculations were performed using an F D code solving the Barents Sea coast (Figs 1 and 2). The following the mutually coupled equations of heat and fluid flow in a boundary conditions are applied for all models: porous medium. Physical, mathematical and numerical details of the employed simulation code SHEMAT are (1) no flow of water through lateral and basal boundaries


412 I. T. Kukkonen and C. Clauser

t 0 6004, I-

km 0 4 1 8 12 16 20 24 28 32 36 40 44 48 52 56 60

SG-3

0

2

4

6

E A 8

10

12

14

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-~

Basac VoLc'cs 1 Metasedaments Basac VoLc'cs 2 P r o t Daabase Gneass 1

A r c h Gneiss 2 A r c h Gneiss 3

P r o f i l e SW-NE

Figure 3. Distribution of input parameters for the models calculated with the coarse discretization along profile AA' (two times vertical exaggeration). (a) Distribution of different lithological units in the model (bottom) and of hydraulic heads along the upper boundary of the model (top). (b) Distribution of permeability in the model.

(2) A constant hydraulic head, which is assumed to follow the topography, is prescribed for the upper boundary, permitting groundwater to flow into or out of the model.

(3) No heat flow is permitted across the lateral boundaries.

(4) At the lower boundary a constant basal HFD is applied.

(5) At the upper boundary temperature is held constant.

The 2-D models in this study (Fig. 3) are based on the geological SW-NE cross-section shown in Figs 1.8, 1.13 and 1.80 in Kozlovsky (1987a). The cross-section is perpendicu- lar to the strike of strata a t the drilling site, which supports our 2-D model (Fig. 2). The structures presented in Kozlovsky (1987a) were simplified, mainly in order to be

compatible with the chosen discretization of our model. Although rather detailed structures can be found in Kozlovsky (1987a), even for depths of several kilometres and more than 10 km away from the deep hole, we did not include these in the model. The most detailed knowledge of lithology is available only in the immediate vicinity of the deep hole. However, the uppermost 1 km is relatively well known to a distance of about 10 km from the deep hole from several dozens of shallow mining-exploration holes. We divided the drilled section into seven domains representing the various volcanic, metasedimentary, gneissic and granitic rock sections. Thermal conductivity and heat production of the rock units were taken from Kremenetsky & Ovchin- nikov (1986a,b), Arhavskaya et al. (1987) and Galdin et al. (1986, 1987) (Table 3). Thermal conductivity is assumed to


Advection, heat refraction and palaeoclimate 413

(b)

SG-3 km o 4A 8 12 16 20 24 28 32 36 40 44 48 52 56 60

0

2

4

6 E 2-i

8

10

12

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Figure 3. (Cmtinued.)

depend inversely on temperature, and porosity-weighted specifies elevation variations at 250 feet (76 m) contour fluid-saturated thermal conductivities are updated according intervals (Fig. 1). We assume that the groundwater table to temperature and pressure during calculations as in follows the surface topography, which is typical in an area Clauser & Villinger (1990). with a cool climate and considerable annual precipitation.

Hydraulic heads in the model are constrained from As the deep hole is only a few kilometres from the local topography taken from an aeronautical map of northern water divide, the FD model is cut-off there. Norway, Finland and Russia (US Air Force 1971), which Hydraulic properties of the bedrock in the deep-drill-hole

Table 3. Thermal properties of rocks in the Kola SG-3 cross-section.

Domain Main rock type Age x A

1 Basic volcanics Proterozoic 2.5 0.3

2 Metasediments Proterozoic 3.3 1.4

3 Basic volcanics Proterozoic 3.5 0.3

4 Diabase Proterozoic 2.4 0.7

5 Gneiss

6 Gneiss

7 Gneissigranitoid

Archaean

Archaean

Arihaean

2.4 1.2

2 . 2 1 .o 3.0 1 .o

Domain I A

Number of the domain in the models. Thermal conductivity (Wm- ' K-I) (Kremenetsky & Ovchinnikov 1986a,b; Galdin et al. 1986, 1987). Heat production (pW W3) (Arhavskaya el al. 1987; Kremenetsky et al. 1989).


414 1. T. Kukkonen and C. Clauser

Table 4. Parameters of models calculated with the coarse discretization.

Model name

FRST-50

SECOND-45

THIRD-40

FOURTH-40

FIFTH-40

SIXTH-40

SEVENTH-40

EIGHTH-40

Basal HFD (mW m-?) Permeability (m’)

Basal HFD Permeability

so 0-2 km

1.1Ol4

2-4 km

1.10-’‘

45 5.101h

40

40

40

40

40

At 15 km depth. Below 4 km, permeability decreases one order in magnitude every 2 km from 10-l‘ m2 (4- 6 km depth) to lo-” m2 (14-15 km depth) in all models, except in EIGHTH-40, where a constant value of IO-” is used

section are not available at a scale useful for simulations. Bayuk et al. (1987) report some permeabilities at the sample (cm) scale, but these values are not sufficiently representative (1) to be attributed to the formations shown in Fig. 2 or (2) to be generalized to bedrock volumes at the scale of kilometres (e.g. Clauser 1992a). Considering the aim of this study, and for lack of more specific data, a very generalized, horizontally stratified permeability structure is therefore assumed, with permeability decreasing with depth, which reflects the increase in lithostatic pressure and the associated closing of fractures. This concept is supported by the observation that the most active fresh-water system seems to be confined within the uppermost 1-2km: Borevsky, Vartanyan & Kulikov (1987) report that a zone of ‘exogenous fissuring’ extends to a depth of about 800m (range 500-2000 m) in the Pechenga area, an additional indication of stratification of permeability with depth. Transmissivity in this zone is of the order of 1-2 m’ day-’, which corresponds to a permeability value of about fO-I5m2. On the basis of the limited available information, permeability is therefore assumed to decrease vertically by one order of magnitude every 2 km in the following models. While permeability is varied between models in the upper 4 km, the original distribution remains unchanged below (Table 4).

Porosity of the rock types in the Kola section is small as can be expected for crystalline rocks, usually less than 1 per cent, and even the maximum values reach only 5 per cent (Bayuk et a/. 1987). We use a value of 1 per cent throughout, neglecting a possible further reduction in these laboratory values with overburden pressure.

Two grids with different levels of discretization are used: (1) 0.5 km X 1 .O km and (2) 20 m X 250 m and 250 m X 250 m (Figs 3 and 6). Level 2 includes variable cell size in the vertical dimension in order to describe more accurately the uppermost parts of bedrock in the transient simulations of the palaeoclimatic effect. The model size for the coarse grid is 15 km x 60 km and for the refined grid 10 km x 24 km.

Table 5. Parameters of models calculated with the refined discretization. Model name Type Basal HFD

THREE-45 (S-S) Steady-state 45

Conductive

THREE_45_A,C and C (T) Transient 45

Conductive Basal HFD In mW m-’; at 10 km depth.

COARSE DISCRETIZATION

Steady-state models were calculated on the coarse grid (0.5 km x 1.0 km). Permeability and basal heat flow were vaned until a reasonable fit was obtained with the HFD data (Table 2) by Kremenetsky & Ovchinnikov (1986b). To date, the temperature-depth profile in the Kola deep hole (SG-3) has not been published in numerical form. Therefore, we digitized the T - z curve published by Kremenetsky & Krivtsov (1991). This temperature curve, while providing only a very coarse resolution, is nevertheless probably within a few degrees from the measured values. The available temperature data as a whole, however, are likely to contain a variable amount of transients depending on the depth range, as the SG-3 borehole started in May 1970, reaching a depth of 10 700 m in 1980 (Kozlovsky 1987b), and 12064m by 1986 (Kremenetsky & Ovchinnikov 1986a). As the latest reported depth is 12261 m (Kremenetsky & Krivtsov 1991) technical operations and mud circulation in the borehole have been going on over a period of at least 20 yr, if only quite intermittently. Temperature above 7.2 km was recorded after a shut-in time of 1; yr; below this



Germany between 50 000 and 10 000 yr before present (BP) (Delisle 1991), but a considerably lower value is included for comparison. The G T H is simplified into three periods of different surface temperatures: (1) a glaciated period lasting until 10000yr BP with a surface temperature of 0°C or -6°C; (2) a postglacial warm period from 10000 to 1000yr BP, with surface temperatures 2 K higher than present; and (3) from 1000yr BP to present, with today's surface temperatures. In the postglacial period the surface temperature at each grid point of the upper surface follows an atmospheric adiabatic gradient of 6 mK m- ' according to its actual elevation. Steady-state conditions are assumed for the glaciated period, neglecting the climatic history prior to the last glaciation. The calculated temperature field is then used as initial condition for the second simulation period and, finally, the results of this simulation are again used as initial condition for the third and final simulation period. All calculations were performed for a purely conductive regime. For comparison a steady-state conductive simulation with present-day surface temperature was calculated as well.

Pseudo-logs were extracted from the model results at the approximate location of the SG-3 hole in the cross-section. HFD in the steady-state and transient simulation (surface temperature 0°C during glaciation) differ by about 16 mW m-' at the surface, but converge rapidly with depth. At 1.5 km the palaeoclimatic effect is smaller than 2 mW m P 2 (Fig. 7). The simulation with surface temperature of -6°C during glaciation yields correspondingly higher values for the palaeoclimatic effect. However, even this rather extreme climatic model fails to account sufficiently for the observed variation of H F D with depth (Fig. 7). The present simulations therefore indicate that the variation detected in the vertical HFD profile of the SG-3 borehole cannot be attributed to the palaeoclimatic effect alone, even if the glacier base temperatures are assumed to be as low as -6°C. A certain palaeoclimatic contribution may well be present, but an effect of this size can be easily masked by refraction of heat or even 'washed away' by simultaneous advective heat transfer. This holds even more so if the reported HFD values shown in Fig. 7 are not representative of thermal-equilibrium conditions.

depth temperatures were measured in only short interrup- tions (2-3 weeks) during drilling (Kremenetsky & Ovchinnikov 1986a). Roughly 20 months were required for an equilibration of temperature to within less than 1 K after the 4 k m deep KTB-VB borehole in Germany had been drilled for about 19 months from 1987 to 1989 (Huenges & Zoth 1991). If these results are to be extrapolated to the discontinuous 20 year drilling history of the 12 km deep SG-3 borehole, we are certainly not yet dealing with equilibrium conditions. However, the temperatures published by Kremenetsky & Krivtsov (1991) will be within 5 K of the true virgin rock temperatures for depths above 7.2 km because of the relatively long shut-in time of 1; yr for this part of the profile. No estimate of accuracy can be given for the deeper part. Temperatures there are certain to be systematically too low. The regional mean heat-flow value (33 mW m-', Table 1) determined in shallow holes is very close to the HFD value in the upper 1.2 km of the deep hole (29mWm-*, Table 2). This suggests that this part of the deep hole is rather close to thermal equilibrium.

Table 4 specifies the various values for permeability and basal H F D used in the different models. Fig. 4 shows an example of the simulated temperatures, HFDs and Darcy velocities for one specific model. Generally, the simulations indicate that the variation of H F D and temperature (above 7.2km) with depth observed in the SG-3 hole can be reproduced in our model if permeability in the top 4 k m varies between 1 X and 8 x lo-'' mz and the basal HFD at 15 km is 40 mW m-2 (Fig. 5a and b). H F D is very sensitive to permeability changes, and within one order of magnitude around 1 0 ~ " m 2 there is a transition from a conduction-dominated to an advection-dominated regime. Temperature turns out to be less sensitive to model changes, and for most of the models a reasonable fit ( f 1 0 K) with the measured temperature profile above 7.2 km can be obtained (Fig. 5b). A more accurate fit is not required considering the quality of the measured data.

REFINED DISCRETIZATION

To treat more accurately the effect of palaeoclimate a denser discretization is used. In the previous simulations topography was simulated by assigning corresponding hydraulic heads to the topmost nodal layer. The refined discretization permits the resolution of a variable topography directly in the model structure itself. The topography and the uppermost bedrock are resolved within 20 m in the vertical and 250m in the horizontal, which results in grid dimensions of 20 m X 250 m and 250 m x 250 m (Fig. 6). We calculate a series of transient models in which the thermal boundary condition for the top of the model varies with time in a step-like fashion according to a simplified G T H for the area. Thermal diffusivity K in these models was derived from thermal conductivity A as K = A/(pc), with pc , the volumetric specific thermal capacity equal to 2.3 kJ m-3. For simplicity, we assume that the GTH in the Kola area generally follows that in the central part of the Fennoscan- dian Shield (Kukkonen 1987). During the glaciation we assume the temperature at the base of the ice sheet to be either 0°C or -6°C. Glacier base temperatures around 0°C are supported by model simulations of the accumulation of Scandinavian glaciers and their advance into Northern

DISCUSSION

Model results of advective heat transfer depend essentially on the permeability structure in the bedrock. We assume a horizontally layered structure because of the lack of information on the structural geometry of the real permeability distribution. Increased permeability is known to be related to certain metasedimentary rock types and tectonic dislocation zones intersected by the Kola deep hole (Kremenetsky & Ovchinnikov 1986a,b). It is not possible, however, to include this qualitative information in the model considering both the lack of sufficient information on the hydraulic properties and the dimensions of our F D grid blocks. Therefore, the simulated H F D profiles are unable to reproduce the recorded small-scale variations of H F D around 5 km depth in the SG-3 profile (Fig. 5), which Kremenetsky & Ovchinnikov (1986b) relate to metasediments with increased permeability.

The model results, however, strongly suggest that advective heat transport is the most important mechanism


416 I . T. Kukkonen and C. Clauser

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responsible for the observed HFD variation with depth, heat-production variations are also important factors particularly in the top 2-3 krn. In this depth range a contributing to the measured HFD variation at depths of permeability of the order of lo-'' is required to fit the 5-9 km. Our simulations suggest that palaeoclimatic signals observed HFD data. This value is typical for a crystalline may also exist in the SG-3 data, but their magnitude is bedrock on the scale of our grid, i.e. 0.1-1 km considerably smaller than those due to advective distur- (Clauser 1992a). In addition to advective heat-transfer bances, thermal disequilibrium and structural effects. The effects, heat flow refracted into the inclined strata as well as simplified palaeoclimatic history used in ou r simulations



(a) Kola deep hole cross-section (s imulated and measured HFD i n S G - 3 )

70

60

50 E S 40 E 0- 30 v

20

10

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(b)

' H

'.,V ? I -.- First-50 o- Second-45 I Third-40 -0- Fourth-40 - Y - Fifth-40 -A- Sizth-40

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Kola deeD hole cross-section

450

400

350

300

-250 P -200

150

100

50

F

n

(s imulated and measured tempera tures in C G - 3 )

- 0 - F i r s t 5 0 -.- Third-40 -9- Fourth-40 - v - Fifth-40

0 - Second-45

-A- Szzth-40 +- Seventh-40 * Eighth-40

U 4 U 1 U I d 14

z (km)

Figure 5. Comparison of simulation results (coarse discretization) with data measured in the Kola deep hole (SG-3): (a) HFD (Krernenetsky & Ovchinnikov 1986b) and (b) temperature (digitized from Krernenetsky & Krivtsov 1991).

implies a disturbance decreasing rapidly with depth; already at 1.5 km the conductive transient simulation yields an amplitude smaller than 2 m W m-' (for a glacier base temperature of OOC). Kremenetsky & Ovchinnikov (1986b) estimate the glacial effect (postglacial climatic variations not included) using homogeneous half-space models and glacier base temperatures of -4°C to -6°C. They conclude that the effect due to a glaciation during 21000 to 10000yr BP amounts to only about 2mWm- ' (3-5 per cent of the measured gradient values) at depths of 700-800111. Our simulation with glacier base temperature of -6°C indicates larger variations for the same depths as a result of the postglacial temperature variations. Even in this case, which provides an upper bound for the magnitude of a reasonable palaeoclimatic signal, the recorded H F D variation in the deep hole cannot be explained by the palaeoclimatic effect alone.

Water is assumed to be fresh in our simulations. Groundwaters in the SG-3 hole, however, display dramatic changes in salinity with depth. The uppermost fresh water layer extends to only 800m depth. Below, saline fluids dominate, which contain up to 300 g I - ' dissolved solids

(Kremenetsky & Ovchinnikov 1986a,b; Borevsky et al. 1987). The main components of the fresh (meteoric) groundwater are Ca and HCO, or Ca and SO,, whereas the saline waters are mainly Ca-Na-(Mg)-CI waters. A difference in composition between fresh and saline waters indicates a small or negligible interaction and mixing between these groundwater types. Saline waters are usually considered to be more stagnant than fresh meteoric waters, but whether they are really immobile cannot be stated at the moment (Nurmi, Kukkonen & Lahermo 1988). Recent studies of crustal fluids suggest horizontal movements of fluids over distances of hundreds of kilometres (Rumble 1989; Cathles 1990; Torgersen 1990, 1991; Clauser & Neugebauer 1991). In this study we did not include any regional flow in our models (no-flow lateral boundary conditions) and the chosen permeability restricts the advective heat transfer to forced convection only. Free convection could be easily introduced if the permeability was raised to 10-'sm2 throughout the model, but forced convection alone is sufficient to produce the requested decrease in H F D values in the uppermost 2-4 km.

Published heat-flow values in the drilling area represent sites which are scattered throughout the area, and only one of them (site number 5, 36 mW m-', Fig. 2) is close to our model profile. The site is in a depression and forms a groundwater discharge area in our model. Therefore, the model shows a heat-flow maximum there. Owing to topography discharge and recharge, zones in our models alternate in intervals of a few kilometres. Projecting a particular heat-flow site onto these profiles may be too unreliable. Further, by using a different permeability structure, the advective redistribution of heat is easily changed. For instance, including into the model inclined permeable zones, or, alternatively, a thin, low-permeability uppermost layer, would result in different distributions of the HFD highs and lows. At any rate, it is quite evident that models would need to be better constrained by more temperature, heat-flow density and permeability data, if the results were to be interpreted as truly site specific for the vicinity of the deep hole.

Kremenetsky & Ovchinnikov (1986b) discuss possible advective distrubances using a 1-D infiltration model. They assume that during the postglacial uplift of bedrock and the subsequent release of stress, new fractures open and existing ones increase in aperture, inducing downward migration of groundwater. They estimate that the measured HFD contrast between the uppermost 1.2 km (the zone of fresh-water migration) and deeper parts of the hole can be attributed to this migration of water. Their model, however, is only a 1-D steady-state approximation. Horizontal heat transfer can be of considerable magnitude, as demonstrated by the present simulations.

In general, our simulations demonstrate that a combined inspection of advective, structural and palaeoclimatic effects is necessary for understanding variations in the vertical HFD component. Advective effects may be of considerable magnitude in the continental crust, even in crystalline environments. Using numerical simulations, the size of advective heat transfer can be estimated for a particular case. This, however, is usually limited by the available data on permeability. O n the other hand, if a sufficiently large and representative set of thermal data is available,


418 I . T. Kukkonen and C. Clauser

km SG-3 0 2 4 1 6 8 10 12 14 16 18 20 22 24

0

4

E 24

6

10

4 5 ~ c_ -_ 1 - 2 +""...-3

6 -7 8

Basac Volc ' s I Metsasedaments B a s z c V o l c ' s 2 t Daabase Cneass 1

A r c h Cneass 2 A r c h Cnezss 3 At?-

Pro f i l e SW-NE

Figure 6. Distribution of different lithological domains and variation of surface topography along profile AB for the conductive steady-state and transient models calculated with the refined discretization (variable grid. see text for details).

conductive-advective models can be used for constraining the formation permeability, as has been demonstrated for sedimentary rocks (Willett & Chapman 1989; Clauser 1992b).

Lately, in the context of the greenhouse problem and global climatic changes, the inversion of past surface temperatures from geothermal measurements has been gaining increased attention (Lewis & Wang 1992; Wang 1992; Cermhk, Kukkonen & Safanda 1993). Work on this subject started as early as in the late 1960s [see Wang (1992), for a review]. If the past ground-temperature history (GTH) could be extracted with sufficient accuracy and confidence from the subsurface-temperature field measured in boreholes, the evolution of the world's climate would be much better understood and new and independent data sets for the calibration of atmospheric circulation models could be generated world-wide. The presently available inversion techniques are based on conductive heat transfer in a 1-D layered earth or in a homogeneous half-space (see Wang 1992). Interesting questions are (1) how an advective system would interact with the diffusion of a transient palaeoclimatic signal into the subsurface and (2) how a more complex geology would modify the results obtained for simple geometries. The present model of the Kola structure provides a possibility to test the available inversion techniques using a model optimized to fit the measured profile in SG-3 extending to 9.5 km (Table2). So far, we have run preliminary inversions using the homogeneous half-space model of Mareschal (Beltrami & Mareschal 1991, 1992; Mareschal & Beltrami 1992). These results indicate

certain limitations of half-space inversions of a GTH for a realistic 2-D structure in the presence of both conductive and advective heat transfer. These results will be discussed in a separate paper.

CONCLUSIONS

Our model results indicate that the main factors affecting heat-flow density in the Kola deep-hole section are advective heat transfer and structural effects. In the absence of advection, the variation in the vertical component of HFD would be due to refraction and heat production only, and have an amplitude of about 15 mW m-' over a depth interval of 15 km. In the topmost 4 km the simulated conductive heat flow increases only by 2.5 mW m-'. Including advection into the model increases this amplitude to 20-30 mW m-*, depending on the chosen permeability. The palaeoclimatic effect, which was calculated assuming glacier base temperature O'C, is considerably smaller than advective and structural effects. It decreases rapidly with depth from about 16mWm-* at the surface to less than 2 rnW rn-' at 1.5 km.

ACKNOWLEDGMENTS

This study was initiated in 1991 at the BechynE Castle, Czechoslovakia, dilring a coffee-break discussion at one of Vladirnir CermBk's stimulating international heat-flow meetings. We are grateful to the German Deep Drilling Program (KTB), for providing the practical framework for



Kola deep hole c rosz - sec t ion ( t r an si e n t vs . s t e ad17 - s t a t e s i mu1 at 1 on s )

(a)

,,,, ,;. /" 4

I - Three-45 (transzent. Oj ....-..' Three-/?5 ( transient. -6)

30 --- Three-45 ( s teady-s ta te ) -K& 0 (1986)

1 I

0 0 0.5 1.0 1.5 2.0 2.5 3.c z (km)

Kola deep hole c ros s - sec t ion (b) ( t r a n s i e n t vs. s t eady- s t a t e s i m u l a t i o n s )

70 I I

,- 40 -

8.; 0.5 1lo 1.5 2.0 3.5 3.0 z ( k m )

Figure 7. Comparison of steady-state and transient results for (a) HFD and (b) temperature simulated on the refined grid. The transient results are presented for glacier base temperatures of 0" C and -6°C. HFD (Kremenetsky & Ovchinnikov 1986b) and temperature (Kremenetsky & Krivtsov 1991) measured in the Kola deep hole are included for comparison.

this cooperation, in particular by contributing travel funds for the authors' study visits in Germany and Finland. Professor L. Eskola (Geological Survey of Finland, Espoo), Professor Alan E. Beck (University of Western Ontario, London) and two anonymous reviewers are acknowledged for their helpful comments.

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Simulation of heat transfer at the Kola deep‐hole site: implications