Perturbations to temperature gradients by water flow in crystalline rock formations

Tecronophysics,

PERTURBATIONS CRYSTALLINE

MALCOLM

19

102 (1984) 19-32

Elsevier Science Publishers

B.V., Amsterdam

- Printed

in The Netherlands

TO TEMPERATURE

ROCK FORMATIONS

GRADIENTS

BY WATER

FLOW IN

*

J. DRURY

Diuision of Graoity, Geothermics and Geodynamics,

Earrh Physics Branch, Energy, Mines and Resources

Canada, Ottawa, ON. KIA OY3 (Canada) (Received

August

27, 1982; accepted

October

5, 1982)

ABSTRACT Drury

M.J., 1984. Perturbations

V. term&k,

L. Rybach

of the Lithosphere.

to temperature

gradients

and D.S. Chapman

(Editors),

Tectonophysics,

The flow of water can provide temperature

measurements

a very effective drilled

means for the transfer into crystalline

effects of water flow that in extreme

cases seriously

Such flows appear

in and between

In the

bodies.

measurements significant logged

typical

might be insufficient

error

in measurement

at no more than

horizontal

heat-flux

separation

rock formations.

In:

Heat Flow Studies and the Structure

102: 19-32.

in boreholes

to be widespread

by water flow in crystalline Terrestrial

determination, to indicate of conductive

5 m intervals

disturb

have revealed

the purely conductive

fractures

and

horizontal

( = 3 m)

the thermal

temperature

in what are otherwise

the vertical local&d

of heat. Ciosely-spaced

rock bodies

gradient.

impermeable

spacing

rock

of temperature

water flows. Small flows can, however, produce

heat-flux.

over their entire

It is recommended length,

that boreholes

and that ideally

several

should

a be

holes, with a

similar to the average hole depth, should be logged, in order that the thermal

effects

of water flow can be recognized.

INTRODUCTION

Variations

with

depth

of temperature

because of changes with depth of thermal

gradient conductivity,

measured

in a borehole

because of thermal

arise

refraction

caused by lateral variations of conductivity or because the equilibrium conductive temperature field is disturbed. Such a disturbance can arise from climatic changes, or from water movement, either within the borehole or in fractures or permeable rocks. The effect of climatic changes has been discussed by many authors (e.g. Lane, 1923; Birch, 1948; Beck and Judge, 1969; Cermak, 1971). The thermal effects of water movement in permeable formations have received attention (e.g. Bredehoeft and Papadopulos, 1965; Cartwright, 1970; Sorey, 1971; Mansure and Reiter, 1979; Majorowicz and Jessop, 1981). Less attention, however, has been paid to the possible * Contribution ~40-1951/84/$03.~

from the Earth Physics

Branch

No. 1077.

0 1984 Elsevier Science Publishers

B.V

disturbance

of temperature

formations, are made.

although Although

formations,

gradient

due to water

it is in such environments there is no water

movement

water can flow in fractures

surface

heat flow could

downwards

Shield,

be accounted

in crystalline

zones (e.g. Palmason.

1967).

of heat flow data from 71 boreholes postulated

that their observed

flow contacts

in an

variation

for by the flow of small quantities

from the surface and along volcanic

rock

in the bulk of the impermeable

or brecciated

Lewis and Beck (1977), from an analysis area of 5 km’ of the Canadian

movement

that many heat flow measurements

of

of water

and faults. Drury and

Lewis (1983) analysed heat flow data from three closely-spaced boreholes, which were drilled into a granitic batholjth of the Canadian Shield, and concluded that in one deep hole (830 m) that intersected a gently-dipping fracture zone at approximately 430 m. an increase in heat flow by 14% above the zone could he accounted for by water flow up the fracture zone. Further, both Lewis and Beck (1977) and Drury and Lewis (1983) as well as many other authors, movement

within

boreholes.

Recent detailed

observed

the effects of water

heat flow or temperature

measLirements

in other crystalline bodies have indicated that water movement in what with limited data would be considered to be tight formations is a widespread phenomenon (Lewis et al., 1979; Drury et al., 1984). The types of thermal anomaly associated with the various styles of water flow in or between fractures and/or aquifers has been shown schematicalIy

by Drury

and Jessop (1982).

The World Heat Flow Data Collection-1975 (Jessop et al.. 1976) contained information on 1310 continental sites at which heat flow had been measured in one or more boreholes. Jessop (1983) analysed the data collection statistically and found that the average number of temperature data in the 359 boreholes for which that information

was available

was 16.7. The average

minimum

depth

of use of 1148

boreholes was 384 m, and the average maximum depth of use of 1747 holes was 986 m. The different numbers of holes reflect the various reporting practices. Hence, in the typical

heat

flow

measurement

from a continental

with depth of temperature data was 36 m. The question arises: to what extent are some reported

borehole

the mean

spacing

heat flow values. particti-

larly those from the shield areas of the world. in error because

the thermal

effects of

water flow have not been recognized in their measurement? In this paper an attempt is made to quantify the possible error that could arise in a heat flow determination. from water flow in boreholes and in the formation. Three situations are considered: water flow within the borehole; water forced into a fracture during drilling; and water flow, in a fracture, that existed before drilling and continued after. WATER

MOVEMENT

WITHIN

A BOREHOLE

A borehole is a possible short circuit for water flow from one fracture or fault zone to another at a different pressure. When water does ffow within a borehole its thermal effect can range from being undetectable to making a section of the hole

21

isothermal.

Ramey (1962) performed

fluid moves in a borehole Ramey point

obtained

a detailed

heat is transferred

an equation

analysis

of the phenomenon.

between

for the temperature,

When a

the fluid and the formation.

u, at depth z below (or above) the

of inflow into a well of fluid:

uZ = u0 + zg * [exp( -z/A)

- 11 Ag

(I)

in which u0 is the temperature at the point of entry of the fluid and g is the normal temperature gradient. Parameter A is a measure of the rate of heat transfer, being proportional

to the velocity

of fluid flow in the borehole;

it is also time-dependent,

and it is given by: A = up,C,r*f(

t)/2K

(2)

in which u is the velocity

of the fluid, pr is the density

capacity,

r is the radius

formation

and f( t) is a time function

formation

to the transfer

of the borehole,

that describes

of heat between

of the fluid,

K is the thermal the thermal

C, is its heat

conductivity response

of the

of the rock

the fluid and the formation.

Carslaw and Jaeger (1959) presented solutions for the cases of cylindrical sources losing heat at constant temperature, constant flux, and with a radiative component. Moss hole flux. since

and White (1959) assumed that transient heat conduction between the boreand the formation can be represented by a line source losing heat at constant Taking s as the thermal diffusivity of the formation and t as the elapsed time the beginning of the heat transfer, Ramey (1962) showed graphically how these

various solutions become the same when St/r2 is greater than approximately 1000. In a borehole of radius 45 mm that penetrates rock of diffusivity 1 mm* SK’ the various

solutions

become practically

the same as each other when t is approximately

1 week. Hence for fluid flow times greater than 1 week the disturbance approximated by a line source, for which f(t) becomes: f(t)=

-ln(r/2fi)--lY/2+O(r2/4st)

where P = 0.5772..

may be

(3)

. is Euler’s constant.

Examination of eq. 1 shows that when A is numerically temperature distribution becomes u, = u,, i.e. an isothermal If A is very small compared

to z, the equation

reduces

much greater than z, the condition is established.

to u, = u0 + (z - A)g, i.e. the

flow causes the temperature field to adjust to give a normal gradient but with a constant temperature offset, negative when relatively cool fluid flows downwards or positive when relatively warm water flows up the borehole. The effect of water flow on the observed temperature gradient, g*, is shown in Fig. 1, in which g*, normalized with respect to the undisturbed gradient, g, is plotted against z/A. The normal gradient is re-established at a distance along the borehole from the point of water inflow at which z = lOA, and an essentially isothermal section is established if z ,< O.OlA.The greater the flow rate the greater is the extent of the isothermal interval, since A is proportional to the flow velocity. The extent of

22

the isothermal

section

varies also withf(t).

also increases

with time, for a constant of dimensionless

radius 25 mm that is drilled in rock of thermal only by approximately

In a borehole

is clearly

greater

reference

to Fig. 1 shows that the gradient

30 days and 30

for large values

the conductive

of A. Suppose is disturbed

temperature

that A = 100 m, then

in an interval

of approxi-

1000 m from the point of entry of the water into the borehole.

in determining

can normally

of

1 mm’ s ‘. ,f( t ) increases

of the flow.

for an error being made in determining

gradient mately

time St/r’.

diffusivity

60% from 4.6 to 7.5. over the period between

years after the establishment

measurement

as A

The change with time of A is, however, small. Ramey (1962, fig.

1) shows graphically f( t) as a function

The potential

flow velocity,

be made with an accuracy

the undisturbed

z were less than approximately

gradient

If a gradient

of 576, then a significant

could arise if ~*/g

error

were less than 0.95. or if

2A (i.e. log{ z/A) < 0.3). For the example

of A = 100

m this would mean that the true gradient would not be measured, even allowing for a 5% experimental error, if the interval logged were less than 200 m from the water inflow

point.

Jessop (1982) recommended

that 320 m be the minimum

depth

of a

O-8 -

O-6 -

4+

-4 O-t---

0.2 -

Fig. 1. Plot of observed where z is the distance rate of heat exchange

thermal

gradient,

aiong a borehole between

g*, normalized

to undisturbed

gradient,

g. as a function

from which water enters, and A is a parameter

the flowing water and the walls of the borehole.

of z/A.

that describes

For details.

see text.

the

23

borehole

to be logged for temperature

data to be used in a heat flow determination,

this being the depth at which a 2 K surface temperature

more than lO$, regardless

of when it occurred.

added

another:

temperature

length

in order

that points

inferred. In a 25 mm diameter

data

should

of inflow

borehole

change causes an error of no

To this recommendation

be acquired

and outflow

in a borehole

of water would

drilled into a granitic

pluton

should

be

over its entire be detected

of conductivity

or

3.4 W

m ’ K-’ and diffusivity 1.4 mm2 SC’ in which flow has occurred for 1 year, a value of A of 100 m would occur if the velocity of the water flowing in the hole were approximately 45 mm s-‘. The velocity water available at the point of inflow,

depends on factors such as the volume of and the nature of the driving force that produces the flow. A velocity of 45 mm s-’ is, perhaps, rather high, although there is no reason to suspect that it is not possible. A value for the parameter A of 100 m would be obtained from lower velocities in smaller diameter holes, for example, 12 mm SC’ in a 30 mm diameter

borehole

drilled

in the same hypothetical

granitic

batholith. The spacing of temperature data in a borehole required to detect significant water flow is now considered. At points of water inflow and outflow, large gradient changes

occur over short distances.

the phenomena. be obtained

The minimum

by referring

It is these changes

spacing

required

to Fig. 1, and locating

that indicate

for temperature the point

the presence

measurements

on the z/A

of can

axis at which

the normalized gradient is less than the expected variation in gradient allowing experimental error. This point can also be obtained numerically by differentiation

for of

eq. 1. For example, suppose the accuracy of a gradient measurement is + 5%, then at least two temperature measurements are required in the interval between the inflow zone (g*/g = 0) and the point at which g*/g = 0.95. The latter point occurs when z/A = 0.3. For the example of A = 100 m, the depth interval of temperature data must then be 15 m to ensure that two temperature measurements are made in the interval of rapid gradient change, so that the presence of the flow zone can be detected. A single, apparently anomalous temperature reading, would possibly be interpreted

as the result of a measurement

measurements

error. Ideally,

more than two temperature

should be made in this zone, and it is recommended

that temperature

data be obtained at not more than 5 m intervals. For smaller values of the parameter this spacing is still a reasonable requirement, as although the zone of rapid gradient change decreases in extent, and might not be resolved, the normal gradient becomes re-established closer to the depth of water inflow, so that there is correspondingly less likelihood of there being a significant error introduced in the measurement of interval gradient and ultimately of heat flow. An example

of the thermal

effects of water flow within

a borehole

is shown

in

Fig. 2 (from Drury et al., 1984), which is a temperature log of a borehole drilled into a syenite batholith (Lewis et al., 1979). In the upper 310 m there are several depths at which water enters the hole, indicated on the log by arrows; below that depth a

24

normal

linear gradient

(1982)

estimated

is observed.

that

the velocity

In all cases water flows up the hole. Drury et al. of the

approximately

20 mm s- ‘. It is interesting

determination

from the hole. Suppose

intervals

between

60 m and a point

250 m. The gradient

flow in the section to note the potential

above

130 m is

error in heat flow

it had been logged at approximately

above that of the lowermost

would have been measured

as approximately

inflow

36 m

point,

say

25 mK m

‘, with a correlation coefficient of 0.98. Such values would suggest that a good measurement of gradient had been made. The undisturbed gradient below 310 m, however, is 55 mK m-l. Hence improper cal example, have resulted

temperature logging of the hole, would, in this hypothetiin a heat flow determination that was approximately 55%

lower than the correct value. It is essential that a hole be logged over its entire depth in order that sections within which flow is occurring can be detected. DRILLING

Drury develops

FLUID

STORED

and Jessop during

IN A FRACTURE

(1982) discussed

the drilling

TEMPERATURE 16 1

Fig. 2. Temperature

18 1

a type of transitory

of a borehole,

20 I

log of borehole

22 I

when circulating

anomaly

that or

(“Cl 24 I

in syenite batholith

which water enters the hole from fractures

thermal

fluid enters a fracture

26 1

26 I

showing

and flows upwards

several depths,

to the surface.

indicated

(From

Drury

by arrows,

at

et al., 1984).

25

permeable zone. Heat exchange between the walls of the borehole and the drilling fluid is enhanced at the fracture because of the local increase in fluid-rock contact area. The phenomenon can be modelled as the result of the liberation of heat from a continuous plane source, the basic equation for which is (Carslaw and Jaeger, 1959, p. 262):

-(x-x’)’ 4s(r-t’)

1

dt’

m

(4

Equation 4 represents the distribution of temperature, U, with time, t, and distance, X, from a plane source (at x’) in which heat is liberated at a constant rate p&q per unit time, per unit area, starting at time t = 0. Here, pr is the density of the rock, C, is its heat capacity, and s is its diffusivity. Drury and Jessop (1982) developed equations by extension of eq. 4 that represented the source strength, q, being constant during the period of heat exchange, and increasing linearly during this period. The form of the temperature anomaly is that of a spike, the amplitude of which decreases and the width of which increases with time. In Fig. 3 the variation of temperature with distance from the plane of the heat source is plotted for different times after the end of a period of heat input from a source of uniform strength (solid lines) and from a source of linearly increasing strength during the heating period (dashed lines). Temperatures for each set of curves are normalized to the temperature on the plane x = 0 at the end of the heat input (i.e. at t = 0). Distances from the plane are normalized with respect to the half-width of the curves at f = 0, i.e. the distance from the plane at which the temperature is one-half that on the plane. The parameter y is expressed by y = t/T, where T is the duration of heat input on the plane. The half-width of a curve, x,,, at r = 0, is a function of T and of the thermal diffusivity, s, of the rock. For the uniform source strength x,, = m/2; for the linearly increasing source strength, x,, = m/2. If the fracture is inclined to the horizontal at an angle 8, the apparent half-width in the vertical direction is x,, set 8. The probable maximum effect of the phenomenon in terms of its potential for causing errors in the measurement of conductive gradient can be estimated. The total amount of heat, Q, carried by the fluid into the fracture is: Q = &C&a

(5) where pr and C, are the density and heat capacity of the fluid, q is the source strength per unit area per unit time, T is the duration of the heat input, and a is the area of the fracture. Q is also expressed by: Q = +r,C,f(Ao)T

(6) where tiiz,is the mass rate of entry of fluid into the fracture and f( AU) is a function of the temperature difference between fluid and rock. Equating (5) and (6): 4 = pf( Ao),‘a

(7) where &’is the volumetric rate of entry of fluid. Reasonable estimates of ti, f(Au)

26

0.8 Y

it

=o =1 = 10

C

0.6

Au*

Fig. 3. Temperature accepts Distances drilling

drilling

AU*, above original

fluid. Temperatures

normalized

to half-width

time. Solid lines: uniform

as a function

of distance,

normalized

to temperature

of temperature

distribution

heat source model; dashed

x*. and time, I, from a plane crack that at x * = 0 at the end of drilling

at t = 0. Parameter lines; linearly

y = r/T

increasing

(I = 0).

where T is the

heat source model.

For details. see text.

and a for a borehole-fracture system are necessary. During the drilling of a borehole, fluid is circulated at a rate, typically, of 0.3 . 10P4 m SC’. Suppose that 10% of this fluid enters the fracture system; then i/is = 0.3. 10e5 m3 s I. The parameter f(Au) depends on a number of factors, such as the ease and rate of penetration of the fluid into the fracture, and the temperature difference between the fluid and the walls of the borehole

at the fracture.

In estimating

i/ it is assumed

that the fluid circulates

freely in the fracture. If it is further assumed that heat is exchanged with an efficiency of lOO%, then f(Au) depends primarily on the temperature difference between the fluid at the fracture and that attained by the fluid at the bottom of the hole. In a typical environment of gradient 20-25 mK m-‘, the maximum temperature difference between fluid at the fracture and the bottom of the hole, under equilibrium conditions, would be 20 K for the typical borehole of depth - 1000 m. This is obviously a maximum value for f( Au) as during the drilling the temperature difference will increase with depth of the borehole, and therefore with time. Equation 4 represents the temperature distribution about an infinite plane source; hence the area of the crack must be large compared with the cross-sectional area of

2-l

the borehole.

setting the ratio of crack area/borehole area to be 105, the 200 m2 if the borehole diameter were 50 mm. By area of the crack would be inserting these assumed maximum values of p, f( Au) and a in eq. 7, a value of 4 that represents

Arbitrarily

a probable

strength. The temperature of the heating

maximum

is obtained:

above the original

it is 3 ELK m s-‘,

for a uniform

that results from a uniform

source

source, at the end

period and on the plane of the source, is:

“ln,, = qJT/s?r

(8)

Suppose the heat input period is 30 d in a borehole that is drilled into rock of diffusivity 1.4 mm* s-‘; then u,,, is 2.30 K if q is 3 PK m s-r. The half-width of the thermal intervals

anomaly at this time is 1.35 m, and temperature data obtained would provide one or two values that would be rather obviously

lous. Temperature

logging

for heat flow determinations

after some time has elapsed since the end of drilling disturbance accuracy

from the drilling with

recommends

which

a temperature

that the drilling

times the period tures are measured

to have decayed. gradient

disturbance

of drilling;

is normally

at 5 m anoma-

done, however,

in order for the normal

This elapsed

thermal

time depends

is to be measured.

on the

Bullard

(1947)

should be allowed to decay for at least ten

Jaeger (1961) suggests

that in wells in which tempera-

one year or more after the end of drilling

the measured

gradients

are probably within 1% of the equilibrium gradient. In the present example, suppose that the borehole were logged for temperature data 200 d after the end of drilling, and that the data were obtained at 36 m intervals. At t = 200 d the amplitude of the anomaly at the plane of the fracture is 0.355 K; it is less than 0.001 K, 30 m from the plane. Hence at most only two temperature data would be obtained from the depth range of thermal anomaly, one from above and one from below the fracture. The resulting

increase

the decrease

in apparent

thermal introduce

anomaly

in apparent

might

gradient

gradient not

below,

be detected

above the fracture such

would be balanced

although

in the temperature

a serious error into the final determination

by

the presence

of a

log, it would

not

of heat flow. Logging

is, however,

anomaly obtained obtained

were present; if the spacing were 5 m, 11 temperature data would be from the depth range of the anomaly in this example. More data would be from the zone if the fracture were inclined. FLOW IN A PLANE

as this would show unambiguously

at closer

intervals

WATER

preferable,

that

that a thermal

FRACTURE

If water flows along the dip of a narrow fracture zone, it carries heat, and it is therefore a source or sink for heat that is conducted in the rock formation. Lewis and Beck (1977) showed that the effect of such flow is to increase or decrease the apparent conductive heat flow above the fracture, depending on whether the flow is up or down the dip. By neglecting the effect of the finite dimensions of a

28

fracture-rock body system, they obtained a steady-state in apparent heat flow above and below the fracture: IQ, - Q,l =fCg

solution

for the difference

sin 8

(9)

in which $2, and Q1 are the apparent

heat flow values above and below the fracture,

f is the mass rate of flow of the water, C is the heat capacity

of the water, g is the

undisturbed

(to the horizontal)

thermal

gradient

and 8 is the angle of inclination

of

the fracture. The temperature and gradient distributions about the fracture can be modelled by assuming that the temperature on the fracture remains constant, and that there is another

bounding

plane

of a different

constant

temperature.

such as the ground

surface. The temperature distribution u( x, t) in a body initially at temperature u = 0 that at time t = 0 is bounded by planes separated by a distance I and maintained at temperatures ,:(,,t,++:

u = 0 and II = V respectively

ca

(-1)” c -n ?I=1

is (Carslaw

exp( -‘pi,,‘)

when t X-T-0, in which s is the thermal

diffusivity

and Jaeger, 1959, p. 313):

sin? of the medium.

The distribution

of

-

a =0.003 =o-01 = O-03 = 0.1 = 0.3 = 1.0

Fig. 4. Distribution of temperature. ~1,in a slab bounded by-two planes maintained at different constant temperatures u = 0 at x = 0 and D = V at x = 1. At time f = 0 temperature are uniform in the slab. Curves for different dimensionless separation of the planes.

times. LX= st/12, where s is the thermal diffusivity of the medium and / is the

29

thermal

gradient

distribution

is obtained

of temperature

by differentiation between

u = I/ for time I > 0, plotted

5 shows the distribution

distributions

are shown for different distributions

times, however, The potential single borehole

10. Figure

that are maintained

in the same form as is normally

logs. Figure and gradient

of eq.

two planes

of temperature

that are relevant

the measurement

In both figures

the

The temperature

to eq. 9 arise when LY= 1. At earlier

of the normal

error in determining

the

at u = 0 and

used for temperature

gradient.

times 1y= St/l’.

dimensionless

4 shows

gradient

is subject

to large errors.

the local heat flow by measurements

from a

is greater for this type of flow than for any other, as there’is a strong

possibility that the phenomenon would be undetected. If flow has occurred for a long period of time such that (Y= 1, there would be no indication in a log of a borehole that did not extend to the depth of such a water flow system that the temperature gradient was disturbed. For example, suppose a fracture in which water was flowing existed at a depth of 500 m, and that the temperature

at that depth were

1 K greater than it would be if there were no flow. Assuming that the true, undisturbed conductive gradient were 25 mK m-‘, the gradient measured at depths less than 500 m would be 8% higher, which is greater than the error in accuracy of measurement of a gradient. If cz < 1, the error is less, but it can still be si~ificant:

a

b “d

e

Fig. 5. Distribution

of temperature

Q =0.003 =o*01 =o. 03 =0-l = 1.0

gradients

in slab, parameters

as in Fig. 4.

30

for example,

if the hole in this example

(Y were 0.1, the apparent gradient.

If the rock penetrated

the fracture mately

be 5.5% higher

flow could,

observing boreholes.

than

and

the undisturbed

had a diffusivity

of 1.4 mm* s ‘, the temperature at at a higher than normal level for approxi-

570 years in this case. There is no reason

regional hydrologic Lewis and Beck change in apparent borehole, but they

for example,

to suppose

that such a time scale

have been initiated

by changes

in the

regime by earthquake activity. (1977) did not observe directly the phenomenon of an abrupt heat flow caused by water flow in a fracture that intersected a inferred the presence of the phenomenon at greater depth by

the regional variation of apparent heat flow in a large number of A single borehole data set would have provided no evidence of such

flow. TEMPERATURE

I

6.00

6.50

7.00

7.50

1

I

,

1

I

log of borehole

from water flow: downhole

fluid entering

(%I

5.50

Fig. 6. Temperature resulting

were logged to 400 m at 36 m intervals,

would

would have been maintained

were unrealistic;

deeper

gradient

fractures

250 m. A regional

in granitic

I

batholith-showing

flow from near the surface

three types of thermal to fracture

phenomena

at 250 m; effect of drilling

at 100 m and 250 m; and effect of water flowing down the dip of the fracture

gradient

of 11 mK m-’

has been subtracted

from the log.

at

31

EXAMPLES

Figure 6 is a temperature log of a 500 m borehole drilled into a granitic batholith in the Canadian Shield, obtained 56 d after the end of drilling. A regional gradient of I1 mK m-’

has been subtracted

in order to highlight

the thermal

anomalies

that

occur in the log. Gently dipping fracture zones were encountered at 100 m and 250 m. At both depths there is a “spike” anomaly. In previous logs these anomalies were narrower and of greater amplitude. Hence, the fracture at these depths had received drilling fluid. At 250 m there is an offset in the temperature log that indicates that water is flowing within the borehole of the depth of inflow:

the nature

the hole, and so the inflow change

of the gradient

probably

one temperature

in the interval

There is no lithological reflects

step shows that the flow is down

must be near the surface.

at 250 m, from 9.7 mK m-’

below the fracture. change

and leaving at that depth. There is no indication Further, 200-250

there is a gradient m to 11.0 mK m-’

change at this depth, and so the gradient

the flow of water down the dip of the fracture

log at closely-spaced

intervals

(3 m) in a borehole,

zone. This

has, therefore,

showed all three thermal disturbance phenomena that have been discussed in this paper. Further, the phenomena are quantifiable from analysis of the data: The source strengths, assuming then to be uniform, for the spike anomalies at 100 m and 250 m are 2.3 FK m s-’ and 1.0 FK m s-‘; the flow rate of water within the hole is approximately 2.5 - 10m5 m3 s-‘; and the flow rate down the dip of the fracture zone at 250 m is 0.3 g s-l

m-‘.

DISCUSSION

The depth to which open fractures occur in crystalline rock bodies depends on factors such as local stress patterns in the crust, and sediment loads. In the Canadian Shield fractures that are open to water flow have been observed from boreholes at depths

of greater than 1000 m. Hence, in crystalline

bodies, heat flow measurements

should ideally be made in boreholes of at least 1000 m depth, in order that the possible thermal effects of water flow along fractures could be detected with reasonable confidence. Ideally, a number of such holes, with a horizontal spacing similar

to their

increase the mendations, measured at logged over

average

depth,

should

be logged

wherever

possible.

This

would

probability of detecting a dipping fracture, if it existed. These recomtogether with those presented earlier, that temperatures should be approximately 5 m intervals in a borehole, and that boreholes should be their entire depth provide tight constraints on the measurement of heat

flow. Nevertheless, the thermal effects of water flow may produce serious errors in the measurement of heat flow in what might be assumed to be tight, impermeable rock bodies, and so all possible care must be taken to detect such effects. REFERENCES Beck, A.E. and Judge, A.S., 1969. Analysis of heat flow data. I. Detailed observations in a single borebole. Geophys. J.R. Astron. Sot., 18: 145-158.

32

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