113
A Thermal Tool for Direct Investigation of the Interior of the Earth By WM.
MANSFIELD A~AMS 1)
S u m m a r y - Direct access to the crust and the upper portion of the mantle m a y be achieved b y letting a high temperature ( > ll00~ reactor core melt the rock in which it is placed and fall through the resulting magma. D a t a gathering and retrieval seem feasible. A schematic design of the proposed instrument is given. There are m a n y problems concerning the composition and conditions of the interior of the earth which will not be solved upon completion of the projected MOnOLE Project. Comparison of the continental crust with the oceanic crust, relative distribution of radioactivity under continents and oceans, and the investigation of the mantle itself require access to greater depths t h a n the present drilling techniques permit. To achieve these aims, it is recommended t h a t a dense, heatgenerating object (such as a nuclear reactor core) be placed in the top of a salt dome. The hot object would melt the salt and fall downward through the molten salt. The sinking object would pass out of the source salt bed into rock a t such a depth, say 35 000 feet, t h a t if a few percent of H~O is present at t h a t depth, t h e n a granitic rock would melt at a b o u t 700 ~C. However, encounter with SiO2 containing no water would require a much higher temperature of a b o u t 1700 ~C. The type of rock t h a t actually exists immediately below the source salt bed is unknown, b u t it is probably not a granitic rock. Thermal considerations indicate t h a t the hole will freeze shut after downward passage of the tool, leaving the tool inside a liquid bubble. If the tool can generate heat long enough to melt its way up, as well as down, it m a y be possible to obtain m a g m a samples. I n s t r u m e n t a t i o n for control and telemetry purposes appears extremely difficult. Initial emphasis is placed on attaining the depth of interest. 1. I n t r o d u c t i o n
T o l e a r n m o r e a b o u t t h e i n t e r i o r of t h e p l a n e t s , e s p e c i a l l y t h e e a r t h , is a b a s i c p r o b l e m of s c i e n c e . T h e r e a r e m a n y r e a s o n s f o r w a n t i n g t o l e a r n m o r e a b o u t t h e i n t e r i o r of t h e e a r t h . S o m e a r e f u n d a m e n t a l ; o t h e r s a r e e c o n o m i c . A m o n g t h e f u n d a m e n t a l reasons are : 1. T o d e t e r m i n e t h e a c c u r a c y of t h e e s t i m a t e s w h i c h h a v e b e e n m a d e c o n c e r n i n g the chemical composition and physical environment inside the earth. Knowing relative a c c u r a c i e s w o u l d p e r m i t e v a l u a t i o n of t h e v a r i o u s m e t h o d s of e s t i m a t i o n a n d i n d i c a t e t h o s e w h i c h m e r i t f u r t h e r use. 2. T o d e t e r m i n e t h e v o l a t i l e c o m p o n e n t s of a m a g m a . T h e n a t u r e a n d a m o u n t of v o l a t i l e c o m p o n e n t s in a m a g m a n o t a b l y a f f e c t i t s c h e m i c a l b e h a v i o r a n d p h y s i c a l p r o p e r t i e s ; h e n c e , s u c h i n f o r m a t i o n w o u l d p e r m i t m o r e m e a n i n g f u l w o r k ill t e c t o n o physics. 1) Hawaii I n s t i t u t e of Geophysics, University of Hawaii, Honolulu, Hawaii 96822 (U. S. A.). 8 P A G E O P H 61 (196511I)
114
W.M.
Adams
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3. To determine the distribution of radioactivity beneath the continents and beneath the oceans. This feature is pertinent to the thermal history of the earth, the estimation of the age of the earth, and the tectonic evolution of the continents. 4. To directly confirm the existence of currents in the mantle, to determine their location and motion, and to relate these aspects with magnetic, thermal, and orogenic phenomena. 5. To study the relationship of earthquakes and faults. Although the vast majority of interpretations for initial P-wave motion by ~BYERLY'Smethod indicate a faultingtype source, actual surface faulting at the time of an earthquake has been observed for only a small fraction of a percent of the earthquakes recorded by the m a n y seismological observatories. Even more disturbing are the earthquakes that are not amenable to interpretation as due to a faulting mechanism. For some of these earthquakes, the S-wave data have confirmed the anomalous character of the course (STAUDER and ADAMS [14]2)). The most obvious economic implication is the possible location of minerals worthy of economic exploitation. Indications of heterogeneity to 90 kilometers depth (BIRCH [31) suggest exploration. The composition which has been induced as occurring below this depth indicates that little of economic value is likely to occur until the metaliferrous core is reached at about 2900 kilometers depth. MEKHTIYEu and KRAVCHINSKIY El2] apparently consider the economic potential to be much greater than does the present writer. 2. Th, e tool
Man has always found the exploration of inner space extremely difficult and costly. This is best evidenced by the fact that the deepest hole at present is less than 5 miles deep. Exploration in outer space has been achieved to more than 5 million miles, greater b y six orders of magnitude. The military consequences have stimulated investment in the exploration of outer space; such implications are also involved in the exploration of inner space but do not seem to have been exploited. Let us speculate on the various methods which could conceivably be used for directly studying inner space. Since the objectives are to measure the ambient physical parameters and to sample the country material, the environment should be perturbed as little as possible. The usual method of drilling is to comminute the country rock and remove the fragments. For deep holes, a fluid material is used to maintain formation pressures. This drilling fluid also transports the fragments up and out of the hole and cools the drilling string. The mechanical energy for the comminution of the rock and circulation of the fluid is usually supplied at the surface. In the case of turbodrilling, jet piercing, or explosive scabbing, the energy is applied directly at the point of drilling. These various modes of gaining direct access to the interior are outlined in figure 1. The column on the left states the four problems, the center column lists the usual solutions, and the column on the right gives the solutions we will consider here. We will imagine a tool in which the energy is supplied directly at the working point in the form of heat for melting the rock. The m a g m a flows upward around the sinking too1 and is left in the hole. Because of the requirements of a large amount of energy in a ~) Number in brackets refer to References, page 122.
Vol. 61, 1968/II)
Direct Investigation of the Interior of the Earth
POSSIBLE
M O D E S OF
115
G A I N I N G D I R E C T ACCESS TO I N T E R I O R
Make a hole
Remove material
Leave material
Location of energy source
On surface
At working point
Movement of excavated materiaI
Comminution and flushing by mud or air
Melting with flow around tool
Type of energy
Mechanical Electrical Chemical
Nuclear
Figure 1 small tool, we will consider that the energy is from a nuclear source; however, this assumption is not meant to exclude other sources of heat. The present discussion will center on achieving a depth of 35000 feet--about 40 percent deeper than the present deepest hole. Other discussions on attaining this depth have concentrated almost exclusively on drilling beneath the sea. (See AMSOC Committee [2] and MEKHTIYEV and KRAVCHINSKIY[12].) This depth is selected here because it is approximately the depth of the base of the mother salt bed for the salt domes along the northern shore of the Gulf of Mexico. A depth of 40 000 feet has been estimated for the source layer of salt by NETTLETON [13]. There is some seismic evidence for this depth (HoLYMAN [7]). Some comments will be made to indicate that greater depths may be attainable if certain rock types are encountered beneath the mother salt or if a sufficiently high temperature tool can be invented. Another advantage of the salt dome is that the chemical composition remains relatively similar for all depths considered. In a salt dome there is almost complete absence of water (GUIDO and WARNER [6]). This is desirable because raising the temperature of water would create high pressures in the liquid bubble surrounding the tool (KENNEDY ~10]). If a nuclear reactor core is considered for the dense, heat generating tool, then the fact that the salt in domes tends to be very impermeable is important. Since we are presently confining our exploration to a salt dome, it should be noted that there are additional geological problems that may be solved. These relate directly to the genesis of salt domes. Some of these are:
11{3
W.M. Adams
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I. I t appears that NaC1 deposited as an evaporite will have about ol:e percent or so of water, however, the water content of rock salt taken from salt domes actually is found to be on the order of 0.03%. (Chemical analyses b y I. FATT, unpublished.) What happens to the water between the time the salt left the mother bed and the time it reached its present position is not known. 2. The same sort of a problem exists for the associated minerals, anhydrite, polyhalite, etc. For physical or chemical properties of NaC1, consult Sodium Chloride, TheProd~lcgio~z a~d Properties ofSatt a~d Bri~e, edited b y DALE W. K A U F ~ A ~ (Reinhold, 1960). Based on the conditions existing in the interior of a salt dome, we now give specifications for a geophysical tool.
3. Specifications for a tool The essential specifications for a tool to explore the interior of a salt dome reIate to density, melting point, and heat generation requirements. The tool should: 1. Be as dense as possible because the downward movement is caused by gravitational attraction. The terminal velocity of a ball falling in an unconfined viscous liquid is directly proportional to the difference of the densities. 2. Be able to withstand the temperatures required at the interior of the tool for maintaining the surface at a sufficiently high temperature. These interior temperatures would fluctuate if the melting point and/or thermal conductivity of the country rock should change. Interception of a dry silica or a shale (such as the sheath on m a n y salt domes) would cause the tool to increase its internal temperature. Furthermore, since the peak interior temperature of the tool is dependent on the thermal conductivity of the material of which it is made, this material should have as high an effective thermal conductivity as possible. 3. Be able to withstand the pressures to be encountered at depth, or in the liquid bubble encompassing the tool. The pressure in the bubble m a y be greater than the ambient pressure due to density differences of liquid and solid, or due to the presence of volatiles. The first step toward solving this problem is to eliminate all voids in the tool. 4. Be able to generate heat sufficient to melt the country rock. For a country rock of salt, this is equivalent to maintaining a surface temperature of 801~ plus. :n particular, this heat generation should be relatively independent of the pressure and temperature. These specifications are minimal. In addition, there are other desirable requirements pertaining to control, data acquisition, and data transmission or retrieval. None of these aspects is considered essential in the initial effort to attain greater depth.
4. Depths greater tha~ 35000 feet Although we have confined our thoughts to melting down through the salt of a salt dome, the design surface temperature of about 800 ~ does not necessarily limit the use of the dense, heat-generating object to the salt dome. Greater depth m a y be attainable with only this temperature. In figure 2, the minimum melting temperature versus depth in the earth is given for granite and for basalt. These minimum melting temperature curves (from YODER and EVOSTER ~15j) depend upon the presence of
Vol. 61, 1965/[1)
Direct Investigation of the Interior of the Earth
S.L!aa
Temperature 800 200
700
117
1700~
7000
7 2
3 5 6 7 8 9
70 17 72 13
140
2
3
4~
5
6
7
8
9
loam
D/Jance
Figure 2 H20. The figure also shows, in dashed lines and to scale, a typical salt dome and the melting temperature of salt. Optimistically, we would expect the tool to travel downward through the salt dome, then penetrate into a watersaturated granitic rock directly beneath the source salt bed, thus working on the minimum melting curve for granitic rocks and permitting further entrance into the earth. It is extremely unlikely, however, that the mother salt bed will be underlain by a granitic rock. Sedimentary rock seems more probable. The success of the dense, heat-generating tool at depths below the salt is very dependent upon the presence of H20. The effect of the presence of H20 is to reduce the melting temperature of the rock by about 300 ~ (GoRANSEN I5]). The elementary design is a rod less than one meter in diameter and of indefinite length: it is encased in insulation on all but the bottom side in order to concentrate the heat flow through the bottom of the tool. This is the smallest diameter reactor that looks feasible at present. Some computer calculations of heat flow from a reactor embedded in rock have been made for reactor cores similar to the one described here. See figure 3. In practice, steel would not be used for the container. 5. Thermal considerations We now consider the heat requirements of the tool. If we assume fission of p % of M kg of U ~35, at a potential energy release of 17 kt per kg, we obtain a heat source strength of Q = 1.7 x 1 0 1 3 p ' M calories.
W. M. Adams
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i
2.5 crn steel
K_ -
BOom
- - - - "
Figure 3 Cross section of reactor model used for computer computations on heat flow A s s u m i n g a heat c a p a c i t y of 0.3 cal/gm a n d a heat of fusion of 200 cal/gm, or abou*: 500 cal/gm t o t a l for a m e l t i n g p o i n t of 1100~ we find t h a t the a m o u n t of rock t h a t could be m e l t e d is R --~ 3.4 • 1010 p 9 M grams. The d e p t h L of a D cm d i a m e t e r hole in a rock of d e n s i t y ~ would be, therefore, Z(cm) =
4.33 • 1010p - M (kg) D 2 (cm~)
U s i n g p = 1~ , M = 100 kg, 9 = 3, a n d D = 100 cm, t h i s g i v e s L ~ 1.44 • 106 cm = 47000 ft. This is almost twice as deep as the deepest hole (25340 ft) a in the world. To achieve greater depth, we would use more fuel. To d e t e r m i n e a m a x i m u m limit for the rate of heat generation required, we need to e s t i m a t e the m a x i m u m velocity of a cylinder falling in a viscous liquid along the axis of a vertical tube. We a p p r o x i m a t e this b y using the solution for a sphere falling in a n u n c o n f i n e d viscous fluid as given b y LA~B I11 U--
where
~ ~ g a # U Letting g
~ = = = = = =
2 9
~'-0 ~
a2 g
'
d e n s i t y of fluid, m e a n d e n s i t y of sphere, g r a v i t y in cm/sec 2, radius of the sphere in cm, a v, where v is viscosity in poise, velocity of fall in cm/sec. 103 cm/secP, a = 50 cm, a n d ~i _ ~ _ 4.5, U --
2.5 • 105 cm/sec. #
The viscosity of n a t u r a l lava versus t e m p e r a t u r e is given in figure 4 for a Mt. Vesuvius lava. A t 1100 ~C, the viscosity is n o t a b l y less t h a n 105 poise, so # should be less t h a n 107. This gives a m i n i m u m value of U = 2.5 • 10 -a cm/sec .
Vol. 61, 1965/II)
Direct Investigation of the Interior of the E a r t h
119
10*~Extrapolatod
705
\
o Dote
',
lOZ I000
?oints
--/nterpototed
,
llO0
,
7200
,
7300 1400 7500og
Temperature Figure 4 Viscosity of Mt. Vesuvius lava versus temperature (per KANI)
For this rate of advance there would have to be about 10a cal/sec supplied. As the reactor design shown provides about 1.2 • 104 cal/sec per linear foot, the tool would have to be at least nine feet long. This optimistically assumes that all the heat generated is supplied to the melting point. The sinking appears to be limited by the rate of heat generation, not by the terminal velocity; however, the terminal velocity would be reduced by including the effect of the sidewall. 6. Data gathering and retrieval Of geophysical interest is the gathering and retrieval of the data desired on the physical environment and chemical composition at depth in the earth's crust. We consider here only the gathering of magma samples and their return to the surface. If a system of sampling bottles be constructed in a ceramic block (figure 5) and each bottle plugged by thin rods of corrodible material and of different lengths, then the corrosion time for eroding the plugs will differ for the various bottles and permit magma to enter at different time intervals. The necks to the bottles are not capped; instead they are purposely narrow (~-~ 1 mm) to minimize diffusion contamination of the sampled magma by magma at other depths. To retrieve the samples, the lower portion of the tool could be made of high density, high-melting-point material and the top portion of material having a low density compared to rock. The heavy bottom part would be fastened to the reactor by a corrosion bolt which eventually corrodes through, dropping the heavy bottom section and suddenly lowering the average density of the tool below the density of the surrounding magma. The tool then floats back up the hole. See figure 5. The rate of retrieval is dependent upon the condition of the magma column which tile tool has passed through. Some indication of its condition at later times may be obtained by considering the problem of cooling of the magma column after passage
W. 5I. Adams
120
(Pageoph,
/ ~lagmasampibbottl g e .
CoffoJ/~le~
Lowdensity tJ/ock
I
t
I fl~at
99, fleralof
Figure 5
of the reactor tool. An approximate answer m a y be obtained from work done b y J. C. JAEGER [8]. Now let us estimate the rate of cooling. To assure that no radioactivity will escape into ground water, it is suggested that the best site for entry into the crust is at a salt dome. As salt melts at only 804 ~C, this would increase the length of hole found in our earlier calculation by about 20~ Using thermal conductivity k = 0.01 cal/cm ~ sec, density o -~ 2.165, and heat capacity c = 0.219 cal/gm ~ (these constants are believed to be appropriate to the salt in a salt dome) the resulting diffusivity a = k/e c = 0.211 cm2/sec. If we assume a salt m a g m a column having an initial radius of 30 cm and a temperature of 1400~ then assuming well mixing, the colunm cools to the melting point in less than one hour according to table 2 of JA~GE.R. It thus appears that the reactor will have to melt its way up as well as down. The temperature field about the sinking tool m a y be estimated b y solving for the heat at any point (x, y, z) due to a constant source of heat falling at a uniform rate d ~ / d t = U along the vertical axis (see figure 6). The reactor is taken as the origin of the x y z coordinate system. This is equivalent to the problem of an infinite medium flowing uniformly p a s t a constant heat source at the origin with a velocity U in the upward direction. This problem has been solved for the case of a point source. The solution, in the usual notation, is / e x p { { Z - U(t-t')}2 + 9 + x2~ U ( x , y, z, 1) =
(z - t')~/~
o c(4 =~c)s/~ o
dt~ "
Vol. 6l, 1965/II)
Direct I n v e s t i g a t i o n of the I n t e r i o r of t h e E a r t h
-
]
112I
r
(0,0, 0)
~.-x
Figure 6
For the steady state conditions, t ~- c~, and the temperature at (x, y, z) is, letting r~ = x~ + y~ + z 2, :7" ==
q 4~Kr
e- d ( ~ z } / 2 ' { .
Introduce the dimensionless quantities, R=---
Ur 2K
Z-=--
Uz 2~
and the equation for the isotherms takes the form T
=- C e (-R+Z)IR .
A plot of e I-R+z)/• for constant values of (T/C) is given in figure 7. Note that all of these estimation procedures have neglected the melting zone.
z=e,J, (§
/ Figure 7 I s o t h e r m s a b o u t a p o i n t source m o v i n g w i t h c o n s t a n t v e l o c i t y in a c o n s t a n t t h e r m a l field
122
W.M. Adams 7. Costs
Drilling 18000 feet of rock in a d e p t h of 12000 feet of water has been estimated to cost at least 68 million dollars. The concept presented here has n o t been engineered a n d costs estimated, hence no comparable figure can be given for the proposed scheme. 8. C o n c l u s i o n s
The concept of a t t a i n i n g access to the m a n t l e b y l e t t i n g a very hot nuclear reactor melt its way down t h r o u g h the crust is sufficiently feasible to merit engineering a n d research efforts for further development. The m a x i m u m effort should be devoted i n i t i a l l y to reaching the Mohorovi~id discontinuity, with less a t t e n t i o n directed to i n s t r u m e n t a t i o n a n d d a t a retrieval. This a p p a r a t u s has been p a t e n t e d b y the a u t h o r i n the U n i t e d States (No. 3115194) a n d assigned to the U n i t e d States of America. The reader is referred to the p a t e n t for a d d i t i o n a l technical features of the apparatus.
REFERENCES
[11 WM. MANSFIELDADA~IS,2f Direct ~Iethod for Investigating the Interior of the Earth, Lawrence Radiation Lab., Livermore, California, UCRL 6306 (1961). eL2] AMSOC Committee, Drilling Through the Earth's Crust--A Study of the Desirability and Feasibility of Drilling a Hole to the 7VIohorovi~i2 Discontinuity, Nat. Aead. Sciences, Nat. Res. Council, Washington, D. C. (1959), Pub. No. 717. E3~ F. BIRCH, Elasticity and Constitution of the Earth's Interior, J. Geophys. Res. 57 (1952), 227. _~4] I-I. S. CARSLAXeVand J. C. JAEGER, Conduction of Heat in. Solids, Oxford University Press, (1948), 223. ~5] R. GORANSEN, Silicate-Water Systems." Phase Equilibrium in the NaA1 SiaOs--H20 and K A1 SiaO~--H20 Systems at High Temperatures and Pressures, Amer. J. Science, 5th Set., Vol. 35 (1938), 71. ~6j R. S. GVlDO and J. E. WARNER, Physical Properties of Salt Samples, Project Cowboy, Lawrence Radiation Lab., Livermore, California, UCRL 6069 (1960), 8. [7] H. WAYNE HOLYMAN, Seismograph Evidence on Depth of Salt Column, 3/Ioss Blatff Dome, Texas, Geophys. 11, 2 (1946), 128. [8] J. c. JAEGER, Numerical Values for the Temperature ira Radial Heat Flow, J. Math. Phys. 34 (1956), esp. p. 318. ~9] KANI, Proc. Imp. Acad., Tokyo 10, 29, 79," taken from: F. BIRCh, J. F. SC;aAIRER,H. CECIL SPICER, Hdb. Phys. Constants, Geolog. Soc. America, Special Paper No. 36 (1934), 243. [10] G. C. KENNEDY, Some Aspects of the Role of Water in Rock Melts, Crust of the Earth, Geolog. Soc. America, Special Paper 62 (1955), 489. ~11] H. LAMB, Hydrodynamics, Dover Pub. (1945), 599, eq. (17). [12] S. M]~;KHTIYEVand Z. KRAVCHINGKIY,Depths of the Earth, Kasnaya Zvezda, Moscow (April 8, 1961), 6. [13] L. L. NETTLETON,Sedimentary Volumes in Gulf Coastal Plain of the United States and ,~Vlexico, Geophysical Aspects, Bull. Geolog. Soc. America 63 (1952), 1221. Et42 W. STAUDEt~and W. M. ADAMS,A Comparison of Some S-Wave Studies of Earthquake 3/lechanisms, Bull. Seismolog. Soe. America 51 (1961), 277. ~15] HAa'TENS. YODER, J~. and H. P. EUGST~R,PhI,ogopite Synthesis and Stability Range, Geochim. Cosmochim. Acta 56 (1954), 157. (Received 12th June 1965)