Download The Earth`s Heat

radioactive chains w ith half- li ves on the
order of at least 1 billion yea rs. Elements
w ith shorter half-li ves have long di sappeared, and the new rad ioactivity created
by cosmic bombardment is minimal. More
than half the radiogenic hea t comes from
potassium-40, which occu rs primari ly in the
mantl e, along w ith the radioactive seri es
originated by thorium-232 (see "Signi ficant
Heat-Generating Isotopes," right). Uranium,
the only other significant radioelement, is
found mainly in th e cru st. Although a few
add iti ona l ve r y l ong -li ved isotopes
exist-for example, rubidium-87, lutecium176 and rhenium-187- their concentrations
and heat generati on are insignifica nt.
Since the core is assumed to contain no
heat sou rces, it makes no contribution to
heat flow at th e Earth's surface. The fraction
co ntributed by rad i oac ti v it y i s rising ,
although the absolute rate of heat generation by radioactivity halves about eve ry billion years. Th e current rate of rad iogen ic
hea t flow is about 5 perce nt of its va l ue
when the Earth was formed.
Temperature readings at many points at or
near the Earth 's surface yie ld an average
heat flux of abou t 1.2 X 10' 6 ca l ori es per
square cent im eter (em) per second,
although indi vidual values may vary by up
to one order of magnitude. Hea t flux from
the sun is much larger, but makes no sign ifica nt contribution to the geothermal grad ient- most solar radiation is either refl ected
or rad iated back into space. Furthermore,
diurnal temperature variations penetrate the
surface only about 1 meter [3.3 feet]; annual vari ations penetrate a few tens of meters
on the continents and a few hundred meters
in the oceans. Climati c variations, however,
at the scale of a few thousand years, can
influence measu rements hundreds of meters
below the surface, and variations of 10,000year period ici ty ca n be sensed down to 2
kilometers [1 .2 milesJ.2
How Heat Reaches the Surface
Conduc ti on and convection are th e two
common modes of heat tran sfer in the Earth.
Conduct i on a ri ses from in t e ra ct i ons
between neighboring atom s, w hereas convection transports heat by fluid movement
resulting from the interaction between gravity and thermally induced density cha nges.
First, consider cond ucti on.
In an isotropic medium, conducti ve hea t
flow is q = k VT, w here q is the heat flu x
(calories per square cen timeter per second),
k is th erm al conduc ti vity of th e medium,
Volume 1 Number 1
Significant Heat-Generating Isotopes
Half-life
location
Potassium-40
1.3 billion years
Mantle
Thorium-232
14 billion years
Mantle
Uranium-238
4.5 billion years
Crust
Isotope
Minerals
~Feldspars
""-·
Mtcas
"'
• Quartz
Pyroxenes and
Amphiboles
"
Olivines, Garnet,
Epidote
• Water
• Ice
Rocks
------
/'Rock Salt
- - - - - - - - - - - - - Limestone ""sandstone & Quartz
- - - - - - - - Schist
- - - - - - Gabbro
- - - - - Tuff
0
0.05
0.1
'-.....Granite
0.1 5
0.2
Thermal Conductivity, k cal;cm s. oc
0 Ranges of thermal conductivity for minerals and rocks at standard temperature and pressure. The
range of thermal conductivity of silicates (feldspars, micas, and pyroxenes), for example, is controlled
by silicon-oxygen bonding: the more shared oxygen atoms, the higher the conductivity.
and VT is temperature grad ient. Since co nductivity and temperature gradient can vary
individually with depth, each must be specified for a given location. Near the surface of
the Earth, the gradient is dT/dz (z increasing
w ith depth). Thus, the rate at w hich heat is
co nd ucted ou tward through th e Eart h
depends in a simple way on how temperature and thermal co nductivity vary w ith
depth. However, to pred ict th e variat ion of
temperature w ith depth requ ires knowing
th e ve rtica l d ist ribu ti o n of heat sources
(rad ioact iv it y) and therm al diffusivity-a
mea surement of the r elat ive ability of a
mate ri al to co ndu c t and to retai n heat,
k/pC. in wh ich p is density of the rock- fluid
sys tem and C i s heat capac ity per unit
ma ss.J Because th e verti ca l distribution of
heat sources i s not routinely determined,
most emphasis is given to determini ng thermal diffusivity.
The wide range of thermal diffusivities in
rocks and minerals results from va riation in
compos ition and porosity (above). Water,
w hich responds on ly sluggishl y to th ermal
changes in its envi ronmen t, has a therma l
d iffusivity an order of magnitude less th an
that of typica l rocks and mineral s.
Although there is no consensus on a mixing rule for thermal conductivity, a reason1. Howell BF )r: Introduction to Geophysics. New York:
McGraw-Hill Book Co .• Inc., 1959.
Anderson RN: Marine Geology. New York: John
Wiley & Sons, 1986.
2. Garland GD: lntrodvcliontn GPnphy.< ics-Mantle,
Core, and Crust. Philadelphia: W.IJ. Saunders Co.,
1971.
3. Hearst )Rand Nelson PH : Well Logging for Physical
Properties. New York: McGraw-H ill Book Co., 1985.
Horai K-1: "Thermal Conductivity of Rock-Forming
Minerals," journal of Geophysical Research 76, no. 5
(February 10, 19711: 1278 - 1308.
55
Descending
Convection Currents
Descending
Convection Currents
0 The relation bet ween convection and plate tectonic movement, as proposed by A rthur Holmes in 1929 (vertical scale exaggerated). Rising con vection
currents pull continents apart and create new ocean in a rift zone. M o untain ranges and deep sea trenches form where convection currents descend.
(A fter Press F and Siever R: Earth. San Francisco: WH. Freeman and Co., / 978: 459.)
ably succ ess fu l empiri ca l approach is to
take the volume-weighted geometric mea n
of the conductivities of the constituents:
kmix =D
i<f·
in which kmix is the conductivity of the mixture, and k; and ¢1; are the conductivity and
vo lume fra cti o n, respec tively, of th e i-th
co nstituent. This rule applies to both nonporous and liquid-filled porous rock.4
Conductio n was in itia lly thought to be
responsible for most heat flow in the Earth,
but studies show that convection also transports heat efficiently and often plays a mo re
important role than conduction. In relatively
uncon strained systems, convection occurs
by means o f convection cells, in w hi ch a
rising fl uid carries heat upward and transfers
it to cooler material at the top of the ce ll. As
the fluid ri ses, it cools, becomes more dense
and sinks to the botto m, where it is heated
again . In some environments the fluid may
not find a return path to the bottom. In this
case th e convecti on fluid must be rep lenished from another source, for example,
wa ter entry from the surface through an
aquifer. In either case, the heat flux, q, car-
ri ed by the rising current is Cvt!.T, i n w hich
C is the fluid's heat capac ity (calori es per
cubic centimeter per degree), vi s its vertica l
velocity (centimeters per second), and LiT is
the temperatu re difference between the top
and bottom of the convecti on cell.
The mantle itself is thou ght to be sufficiently fluid to parti c ipate in convec tio n .
For example, a rock flow rate as low as 1
em 10.4 inch! per year across a temperature
d rop of several tens of degrees produces a
heat fl ux of about 10'6 ca lories per square
ce ntimeter per second, th e same order of
magnitude as the total o utward fl ux at the
surface.2 Not o nly does this con vection in
the mantle influence heat fl ow to the crust,
but large-scale convection cell s d rive p late
tectonic movement (above).
Hydrothermal convection takes p lace at
lower temperatures, where w ater can exist
as a separat e pha se . Hi gh -temp erature
hydroth ermal convection is responsible for
loca l heat transfer to th e Earth's surface in
the form o f hot spri ngs and geysers. Lowtemperature co nvecti on is probabl y an
impo rtant mechanism of fl uid (inc lud ing
hydrocarbon) flow in sedimentary basins.
u..
0
~
:::J
~
•
Ql
Q_
E
Ql
f-
105
Ql
0
.r:.
E
0
g
CD
100
95
90 ~--------------------~
1
2
3
tk
+ tlt
M
Measurement of H eat Flow Rate
Direct measu rement of heat flow rates is
difficult to achieve, even in the subsurface
portion of th e Earth immediately avai labl e
to us. Co nseque ntl y, heat fl ow is al most
56
120 . ------------------------ .
O Bottomhole temperature recordings in a Paris
Basin well from fo ur comecutive logging rum
made up to 18 hours since mud circulation
ceased. The measurements are extrapolated on a
Homer-type plot to yield true forma tion temperature. tk is the length of time the mud was circulated; 6 t is the elapsed time between cessation of
circulation and a given logging run . The extrapolated value of 116°F was confirmed by subsequent continuous temperature logging. (After
Dowdle and Cobb, reference 5.)
Oilfield Review
J
alw ays determ ined by independent in situ
m easu rement o f the geo th erm al gradien t
and of the thermal conductivity of rock samp les in the laboratory. Very recently, however, a w ireline method for thermal conductiv- ·
ity determination was successfull y tested in
several we ll s.4
Th e geoth erm al grad ient is most c om monly acquired by w irel ine measurement of
tempera ture in boreho les, alt hough measurements have been made i n ocean sed iments by implan ti ng a spear w ith vertically
spaced temperature sensors (high heat flow
in ocean sediments correlates w ith hyd roca rbon deposits). M ost w ells are logged and
the logging tool invariably records a temperature maxim um, usuall y bottomho le temperature, that depends on the elapsed ti me
since m ud ci rcu latio n ceased. A Horn ertype plot has been found empirically to convert temperatu res recorded on consecutive
logging runs to the true fo rmatio n temperatu re (below left ).5
Bottomhole readings, unfo rtunately, are
not continuou s measurements. At best they
yi eld onl y a grad ient average in a sma ll
area, w hen one bottom hole measurement is
combi ned with another at a different depth
in a nearby w ell .
Co ntinu o u s l o gs o f t emper atur e a re
recorded w ith platin um resistance th ermometers or therm istors, usuall y located at
the bottom of the logging string to min imize
infl uenc e of the sonde body o n the measu r e ment. I f th e dri ll i n g mud h as not
reached ther mal equi librium w ith th e fo rm ati o ns, cor rec ti o ns mu st b e app lied at
each depth . A con ti nuous temperature log
pro vides T(z), from which the local gradient
dT/ dz may be determin ed directly {right;
next page, left, top and bottom ).
Sometimes the gradient at a parti cular
depth in a given w ell does not represent the
regional geo thermal gradient. Local departures can result fro m stratigraphi c conducti v ity c hange s, water flow {convecti ve or
otherw ise), expand ing (coo ling) gas enteri ng
th e ho le, c ement top s not yet i n th ermal
equilibrium, and recent fluid injection.J
Rock thermal conducti vity is determined
preferab ly w ith the so-ca lled d ivided-bar
method.6 A disk cut from a core is held firmly between two materials o f the sa me di a-
Temperature
OF
250
150
Tension
o
150
.c
1,000
lbs
------ ------------
Temperature
OF
a.
<ll
160
0
Casing Collar
Locator
Temperature Gradient
- 0.5
0.5
---------------- ----------------- ----
,_
11-:
l=
i
1- '
I=
; h - t-1..-.::-J
I= ·.
~-
t-H::.
!:
HL~-1-
- I=
~
1-
t--;:_;_
Jd :: ti8-t-=
1--Ef
~-
1- ; ~
r-::t=
1- : c-~
: -~=;
= =
~ ~nf
=
l
1-1-1-1-·
· - - --
1
8 i~
~
CO
-L
_.
~:
l
- L-1-•
·~
~
0
: ~
.
l
.
! ·:
1-
~~
1-
H
:===
't, 1-l
I-!==
I=
1=11="~
1- ; !
f-
1-
8C\J
co
·-
D Use of a temperature log to identify the source of water production in
cased hole, indicated by heating anomalies. Based on production in an offset well, and a sonic log, the operator perforated this well from 8118 to
8133 feet. But the well produced water and the shut-in pressure was considerably higher than expected for a pressure-depleted gas sand. The temperature log shows that very little flow is coming from the perforations, and most
is from an interval belo w, around 8136 feet. The heating anomaly from
8 176 feet upward indicates that water production is coming from at least
that deep and channeling up between the formation and casing. The final
diagnosis: the perforation job ruptured the casing, producing a vertical gash
that permitted water to migrate upward, possibly robbing production from
the perforated zone.
4. Dove RE and W illiams C: " Thermal Conductivity Estimated From Elemental Concen tration Logs," Nuclear
Geophysics 3, 1989 (in press).
5. Dowdle WL and Cobb WM: "Static Formation Temperature from Well Logs-An Empirical Method," journal of Petroleum Technology, 28, no. 35 (November
1975): 98-10 5.
6. Costa in JK and W right PM: "Heat Flow and Precision
Temperature Measurements in Boreholes," Transactions of the SPWLA lOth Annual Logging Symposium, Houston, May 25-28, 1969, paper ).
Vo lume 1 Number 1
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