Distribution Category 

UC-66b 

WWRENCE UVERMORE LABORATORY 

Wversjtyof Cahfmia/livem, califm'+550 

UCRL-62421 

POTENTIAL USES FOR A HIGH-TEMPERATURE 

BOREHOLE GRAVIMETER 

Joseph R Hearst 

Paul W. Kasameyer 

Lawrence B. Owen 

MS date: March 8, 1978 
DISCLAIMER 

This report was prepared as an account of work sponsored by an 

agency of the United States Government. Neither the United States 

Government nor any agency Thereof, nor any of their employees, 

makes any warranty, express or implied, or assumes any legal 

liability or responsibility for the accuracy, completeness, or 

usefulness of any information, apparatus, product, or process 

disclosed, or represents that its use would not infringe privately 

owned rights. Reference herein to any specific commercial product, 

process, or service by trade name, trademark, manufacturer, or 

otherwise does not necessarily constitute or imply its endorsement, 

recommendation, or favoring by the United States Government or any 

agency thereof. The views and opinions of authors expressed herein 

do not necessarily state or reflect those of the United States 

Government or any agency thereof. 
DISCLAIMER 

Portions of this document may be illegible in 

electronic image products. Images are produced 

from the best available original document. 
CONTENTS 

kd Abstract ................................................. . Introduction ............................................... Applications for a High-Temperature Gravimeter ........................... Deposition Around Geothermal Injection Wells 

Density Change and Radius of Deposition 

Vertical Gravity Anomaly from Deposition in Annulus 

Compaction of an Aquifer around a Production Well ....................... 

Density Change from Compaction of an Aquifer ....................... Using a Borehole Gravimeter to Measure Compaction 

Measurement Uncertainty ................................... Finite Size Reservoir ...................................... Gas-Filled Porosity ......................................... Stratigraphy and Structure ..................................... Problems in Designing a Gravimeter for High-Temperature Wells ................... Summary and Conclusions ....................................... 

.......................... Introduction .......................................... ........................... ................... 

Introduction .......................................... 

.................... 

References ................................................ 

1 

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2 

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POTENTIAL USES FOR A HIGH-TEMPERATURE 

W BOREHOLE GRAVIMETER 

ABSTRACT 

It is possible to design a canister to cool a borehole gravimeter for use in geothermal 

and high-temperature (up to 35OOC) gas wells. Repeat surveys with such a gravimeter could 

(1) help estimate the extent of reservoir plugging in geothermal injection well after one year 

of operation and (2) detect compaction of a geothermal aquifer if the change in thickness of 

the aquifer exceeds 1 m. The instrument could be used together with conventional logging 

tools to evaluate radial dependence of density around a well, or to estimate gas-filled porosity around wells drilled with mud. A high-temperature borehole gravimeter could also be 

used to evaluate structure and stratigraphy around geothermal and high-temperature gas 

wells. 

INTRODUCTION 

It has long been recognized that measurements of 

gravity at different depths in a borehole can be used 

to calculate an average value of bulk density of the 

medium over a large volume surrounding the 

hole. 1-3 In recent years, a high-quality borehole 

gravimeter has become commercially available4 so 

that such measurements have become somewhat 

routine.5-7 

From the beginning, it was recognized that stratigraphy and subsurface structure as well as density 

could affect borehole gravity data. With more expe 

rience in the use of the meter, the effects of such 

phenomona as dipping scarps,l0 buried 

reefs,' and structures of regular shape were studied 

in detail.'* A computer program is now available 

for calculating the effects of arbitrarily shaped twodimensional structures on density measurements 

with a borehole gravimeter. lo 

APPLICATIONS FOR A HIGH-TEMPERATURE 

BOREHOLE GRAVIMETER 

We discuss four applications for which a hightemperature gravimeter could provide less expensive or more accurate data than other available 

methods. The first three applications are useful during geothermal energy production, while the last 

two have many uses. 

testing based on variable-permeability models may 

provide some information l3 but such tests should 

be calibrated with measurements of actual porosity 

loss. Cased-hole logging is one possible solution 

(with neutron logsl4 or Thermal Decay-Time 

Logs'3, but standard logs do not penetrate far 

enough into the formation. However, borehole 

gravimetry is sensitive to masses far from the wellDeposition Around Geothermal 

Injection Wells 

bore. By comparing gravity surveys before and after 

long periods of injection, a zone of deposition can 

be mapped. 

Introduction Density Change and Radius of Deposition Dissolved solids in brine may -- ureciuitate and clog 

the pores in the formation around a geothermal injection well; the resulting loss of permeability may 

render the well useless. We are examining methods 

for measuring or estimating this porosity loss. Well 

The quantities in Table 1 were used to estimate 

the volume of the density anomaly from solids 

deposition around a well. The bulk density change 

during deposition is Ap, the rate at which solids are 

b, 

1 
Table 1. Variables used to estimate volume 

of density anomaly. 

Variable Symbol Value 

Porosity logs @ 0.20 

Fluid flow rate q 0.04 m3/s 

Precipitant concentration S 500 ppm (weight) 

Precipitant density ps 2.2 g/cm3 

Fluid density Pf 1 g/cm3 

0.2 m ‘W well radius 

injected in the well is Am/At, and the rate at which 

the volume of rock with filled pores increases is 

AVl At, as defined by: 

Am -- At - Pfsq 9 

and 

Assuming the volume to be a right circular cylindrical annulus about the well with height h and 

outer radius r, then 

V = (AV/At) At = ?rh (r2 - r:) 

and 

r = q(AV/At) At/.rrh t rl 

= 41.45 X lo-’ At/h + r: . (1) 

Vertical Gravity Anomaly from Deposition 

in an AM~W 

A borehole gravimeter measures only the “vertical” gravity field. An infinitely wide slab of density 

p and thickness h produces a gravitational attraction g = Zrkph, where k is the gravitational constant. If the slab is infinitely wide, the magnitude of 

g does not depend on the distance from the slab; 

however, g has different signs on opposite sides of 

the slab. Within the slab, g varies linearly with 

depth, as indicated in Fig. 1. For a density anomaly 

extending a finite distance from the borehole, g is 

more complex. The gravitational attraction falls off 

2h I I‘ I 

-2h 

-1 0 

g/2rkph 

Fig. 1. Vertical gravity component caused by an infmite slab of 

thickness h (solid line) and a finite cylinder of radius 2h and thickness h (dashed line). 

with distance above and below the center of the 

anomaly. 

We have calculated the observed vertical gravity g 

for different cylinders with heights corresponding to 

different aquifer thicknesses and radii at different 

injection times At (Figs. 2-4). Because the curves 

are symmetrical, only the half above the center of 

the layer is shown. 

The gravimeter is normally used by taking the difference in gravity readings at two depths. The difference (Ag) can be measured with a limit of resolution 

of about 0.01 mgal(l0 -’ m/s 3. Measurements of g 

should be made before and after reinjection so that 

variations in rock density with depth are cancelled. 

The density anomaly will be apparent if (l), the vertical gravity anomaly is greater than 0.01 mgal and, 

(2), gravity measurements are taken at intervals 

small enough to observe the changes in vertical 

gravity. The times and observation spacings for 

which the anomaly is detectable can be read from 

Figs. 24. From results shown in Table 2, we conclude that it is possible to detect the gravity anomaly resulting from the deposition of solids around a 

geothermal well. The visibility of the anomaly 

depends strongly on the thickness of the aquifer 

where deposition occurs. The anomalies will be 

2 
. 

u 

!' 

i 

i 

I 

I I 

(r430 rn), E 10- 

I 

5 8- 

8 

6- zi 

% 

r' 4- 

2- P - 

0 

C 

- 

- 

- 

0 .- 

I I 

0 0.2 0.4 0.6 0.8 1.0 1.2 

g - 10-2 mgai 

Fig. 2. Vertical gravity above a 1-m-thick layer of deposited 

solids of density change 0.25 g/cm3. Different deposition times corresponding to different radii of deposition are shown. 

g - 10-2 mgal 

Fig. 3. Vertical gravity above a 1Bm-thick layer of deposited 

solids of density change 0.25 g/cm3. Different deposition times corresponding to different radii of deposition are shown. 

Fig. 4. Vertical gravity above a 100-m-thick layer of deposited solids of density change 0.25 g/cm3. Different deposition times corresponding to different radii of deposition are shown. I 

3 I 

I 
! 

Table 2. Time and observation spacings for detectible __ anomaly. 

Time when anomaly Obsemtion 

Figure No. Layer thickness, m beccnnes deteCtible spscing, m 

2 1 Barely detectile 1 

4 100 1Y 5-20 

3 10 4 wk 2-5 

more difficult to see if the density varies smoothly 

with depth. 

Compaction of an Aquifer around a 

Production Well 

Introduction 

As water and steam are withdrawn from a geothermal reservoir, the reservoir will likely compact 

from pore collapse as the pore pressure drops. Compaction may result in eventual subsidence of the 

ground surface, which can be measured. It is desirable to measure the actual compaction of the reservoir because first, it may take considerable time for 

the deformation to propagate to the surface, and 

second, the relationship between reservoir compaction and the surface deformation is not well understood, partly because little data are available on reservoir compaction. Borehole gravimetry may be a 

way to measure the compaction of an aquifer 

directly. 

Density Change from Compaction of an Aquifer 

Consider an aquifer with original bulk density PO 

and fluid density pf. We determined the increase in 

density if an aquifer of thickness h compacts an 

amount Ah. Assuming that all the volume change is 

a result of porosity loss, and setting A equal to the 

areal extent of the aquifer, then 

h =-- 'rock - 'matrix 'pores 

A A 3 

'pores Ah= A , 

and 

E = "pores 

h 'rock 

The new density is 

new mass - POVrock + "pores pf 

P new volume vrOck t AV~~~~~ 

Therefore, the density change is 

For example, the data in Table 3 show the density 

change needed to produce 1 m of compaction in an 

aquifer (po-pf = 1.5 g/cm 3): 

Using a Borehole Gravimeter to Measure 

Compaction 

If the measurements are in a horizontally infinite 

medium of density p, the difference in two gravity 

measurements separated by depth Az is: 

Ag=2rkpAz . 

If the layer density changes to p' = p + Ap, then a 

second gravity survey would result in an difference: 

Ag'= 2rkp'Az, 

and 

If z is chosen as the initial aquifer thickness h then 

the gravity gradient change A is: 

(5) 6.3 X lo4 mgal . cm of compaction Y 

4 
t measurement is saturated, then 4~ = 0, and 

W PB'pi= 4i(PW-PA), (13) 

and if pw w 1, then PA 0 (for ordinary gas wells) 

* and 

PB- PB' 4L (14) 

the gas-filled porosity. 

At worst, if $A is unknown, we would calculate a 

minimum value for 4i. Also if we measure the 

water content near the hole, (4~) with a properly 

calibrated neutron log, Eq. (11) gives us the true 

water content. 

In the absence of the effects of structure and stratigraphy (for which corrections may be required*? 

gravimetric density is accurate to -0.02 g/cm3. A 

gamma-gamma density log is accurate to -2% 

under good conditions (smooth hole, good corrections for mudcake, etc.), which often will be 

* 

W 

-0.05 g/cm 3. Averaging over the interval used for 

borehole gravimetry at a logging speed of 

-7 m/min is equivalent to taking the mean of 25 

samples, which should make the error of the mean 

-0.01 g/cm 3, neglecting systematic errors. The 

error in the difference will be -0.025 g/cm 3. 

Thus, assuming 10% porosity, we can likely distinguish between 25% and 50% saturation, or in 

general, observe 2.5 vol% water. 

Stratigraphy and Structure 

From Refs. 1-12, we can conclude that with the 

aid of a gravimeter, it is often possible to infer the 

existence of dipping beds or subsurface structures 

that cannot be detected from a single borehole by 

other means. Use of the gravimeter, therefore, can 

often lead the geologist to new interpretations of old 

data or help him recognize that data from seismic 

surveys or boreholes are needed to fully understand 

the geologic situation. 

PROBLEMS IN DESIGNING A GRAVIMETER 

FOR HIGH-TEMPERATURE WELLS 

Most conventional logging tools are limited to ter can extend the temperature limits of existing graoperation in wells below those temperatures at vimeters from 125 to 35OOC. The complete package 

which critical components fail. For a gravimeter, could be designed for use in wells with inner diamthe temperature limit is limited by the necessity to eters of 18 cm or more. A simpler package with a 

maintain a constant temperature in the sensing ele- heat sink that works on heat of fusion might also be 

ment fbr precise results. The newest instruments are satisfactory. 

heated to 126OC. For geothermal and deepgas wells, Another problem in designing a highthe temperature-regulating system of the gravim- temperature gravimeter is that logging cables caneter cannot work because the outside temperature is not withstand temperatures in tfie hotter geotherhigher than that of the gravimeter. Therefore, it is mal wells, nor can they resist the corrosive brine 

necessary to insulate the gravimeter and use a heat found in most geothermal wells. Recent developsink to absorb the heat that enters the insulating ments suggest that a temperature- and corrosioncanister and that is generat the gravimeter. resistant cable can be obtained. A cable made with 

It is possible to cool a g ter for its use in a seven conductors, each surrounded by ceramic inhigh-temperature well. The LLL Geothermal sulation and an Inconel 600 sheath, is 

Energy Program commissioned EG&G to study available. The Bureau of Mines 21 r 

the feasibility of adapting insulation canisters and that some Inconel alloys are sufficiently corrosiontemperature control systems successfully used in the resistant for use as cable armor. Other corrosionLLL Rio Blanco Program l9 to the gravimeter. Un- resistant materials (such as Hastalloy C-276) are 

wanted heat is made to vaporize water, and the re- available that may be suitable for logging cables, 

sultant temperature- and pressure-controlled water but the cost of such a prototype cable made from 

vapor is collected in a calcium oxide chamber.20 this alloy would be an order of magnitude higher 

EG&G concluded that a suitable instrument canis- than cables made from Inconel. 

6 
Table 3. Density change Ap vs thickness h needed 

to produce 1 m compaction. 

h 10m 30m 100m 300m 1h 

Ap 0.17 0.05 0.015 0.005 0.0015 

Measurement Uncertainty 

Measurement uncertainty in A comes from the 

resolution of the gravimeter and uncertainty in 

depth location. The gravity difference can be measured to approximately 0.01 mgal, and the second 

difference A would have an uncertainty of approximately f 0.014 mgal. The uncertainty in the depth 

interval would strongly depend on the measuring 

method. For this example, we used an uncertainty 

of 0.01 Az or 1 m, whichever is less. The uncertainty 

in A is shown in Table 4. The data in this table indicate that compaction of about one meter can be 

observed if it occurs over an infinitely wide aquifer. 

Measurement resolution can probably be improved 

by taking many measurements within the aquifer. 

Finitesize Reservoir 

We can calculate the reduction of the gravity 

effect for a cylinder of finite radius. For measure 

ments separated by the aquifer height (h), the gravity effect is not decreased significantly if the radius 

is 5h. For any distribution of compaction within a 

reservoir, the resulting gravity effect can be easily 

calculated. 

Gas-Filled Porosity 

In many situations, we would like to know the 

amount of gas-filled porosity. A reasonable method 

of doing this, practiced in the gas industry, l7 is to 

compare the density measured by near-hole logs, 

such as gamma-gamma density, to that measured 

with a gravimeter. In some geothermal wells, 

removal of water can reduce the pressure enough to 

cause some of the remaining water to flash to steam. 

For these wells, one can estimate steam-filled 

Table 4. Uncertainty in A and Ah for compaction 

measurements. 

10 m 30m 100m orlamer 

Uncertainty 

in A, mgal 0.015 0.023 0.064 

inah,cm 24 37 45 

Uncertainty 

porosity by comparing pre and post-production 

gravimeter data as follows. When a hole is drilled 

with mud, water is injected into the medium. The 

value of pB, the bulk density measured by the 

gamma-gamma density log (even when corrected 

for the anomalous electron density of water), is not 

representative of the formation because the range is 

only -2Ocm. 

Let the average density over an interval of 10 to 

20 m, measured by a gamma-gamma density log or 

the first gravity run be p~: 

where 4w and $A represent the volume percent of 

water and gas in the invaded zone or the preproduction medium and pa, pw and PA are the 

grain, fluid, and gas densities. We then measure the 

same interval with a borehole gravimeter whose 

range is many tens of meters which should give a 

true value of bulk density, pi: 

where the symbols with primes are the values far 

from the well or at later times. 

If we assume that the medium is homogeneous, 

the total porosity is the same either near or far from 

the hole, or before and after production so that: 

If the medium near the hole or during the initial 

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REFERENCES 

N. J. Smith, “The Case for Gravity Data from Boreholes,” Geophysics 30,605 (1950). 

S. Hammer, “Density Determinations by Underground Gravity Measurements,” Geophysics 30, 637 

(1950). 

T. H. McCulloh, The Promise of Precise Borehole Gmvimetry in Petroleum Exploration and Exploitation, 

U.S. Geological Survey, Circ. 531 (1966). 

T. H. McCulloh, L. J. B. LaCoste, J. E. Schoellhamer, and E. H. Pampeyan, The US. Geological 

Survey-LaCoste and Romberg Precise Borehole Gravimeter System-Instrumentation and Support Equip 

ment, U.S. Geological Survey, Paper 575-D (1967). 

D. H. Healey, Calculated In Situ Bulk Densities from Subsurface Gravity Observations and Density Logs, 

Nevada Test Site and Hot Creek Valley, Nye County, Nevada, US. Geological Survey, Paper 700-B 

(1970). 

L. Beyer, The Vertical Gradient of Gravity in Vertical and Near-Vertical Boreholes, Ph.D. thesis, Stanford University, Stanford, Calif. (1971). 

N. F. Rasmussen, “Borehole Gravity Survey Planning and Operations,” in SOC. Prof. Well Log Analysts’ 14 *Annual Logging Symposium (Lafayette, LA May 6-9, 1973), Paper Q. 

J. R. Hearst, “Estimation of Dip and Lateral Extent of Beds with Borehole Gravimetry,” Geophysics 42, 

900 (1977). 

D. D. Snyder, “Technical Note: Generalized Correction for Dipping Beds for the Borehole Gravity 

Meter,” Log Analyst 18, 41 (1977). 

J. R. Hearst and H. L. McKague, “Structure Elucidation with Borehole Gravimetry,” Geophysics 41, 

491 (1976). 

N. F. Rasmussen, “Borehole Gravimeter Finds Bypassed Oil, Gas,” Oil and Gas Journal 29 (1975). 

D. D. Snyder, “The Borehole Bouger Gravity Anomaly - Application to Interpreting Borehole Gravity 

Surveys,” in SOC. Prof. Well Log Analysts 17 *Annual Logging Symposium (Denver, Colorado, June 

9-12, 1976), Paper AA. 

H. Alfred Sklar, “Evaluation of Injection Well Performance,” in The LLL Geotheml Energy Program 

Status Report Jan 1976-Jan 1977, Lawrence Livermore Laboratory, Rept. UCRL-50046 (1977). 

J. Tittman, H. Sherman, W. A. Nagel, and R. P. Alger, “The Sidewall Epithermal Neutron Porosity 

Log,” Jour. Petr. Tech 42, 1351 (1966). 

A. H. Youmans, E. C. Hopkinson, R. A. Bergan, and H. L. Oshry, “Neutron Lifetime, a New Nuclear 

Log,” J. Pet Tech 16, 319 (1964). 

J. R. Hearst, “On the Range of Investigation of a Borehole Gravimeter,” in SOC. Prof Well Log Analysts 

18*Annual Logging Symposium (Houston, Texas June 5-8, 1977), Paper E. 

A. H. Jageler, “Improved Hydrocarbon Reservoir Evaluation Through Use of Borehole-Gravimeter 

Data,” Jour. Petr. Tech. 16, 709 (1976). 

G. E. Baker, Gravity Instrument Canister Feasibility Study, EG&G Document #GEB7 77-57, 19 . J. Harri, “Rio Blanco Cooling System Operation, Testing and Failure Modes” Lawrence Livermore 

Laboratory Rept. UCRL-51428 (1973) (title U, report SRD) and “The Fielding and Downhole Performance of the Rio Blanco Cooling System,” Lawrence Livermore Laboratory, Rept. UCRL-5 1438 

(1973) (title U, report SRD). 

W. Wells and A. Lundberg, Environmental Control for Nuclear Explosives, Lawrence Livermore Laboratory, Rept. UCRL-72154 (1969). 

J. P. Carter and S. D. Cramer, “Corrosion Resistance of Some Commercially Available Metals and Alloys 

to Geothermal Brines,” in C. S. Tedmon, Ed., Corrosion Problems in Energy Conversion and Generation 

(Electrochemical Society, Princeton, 1974), p. 240. 

CCD 

8 
1 

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SUMMARY AND CONCLUSIONS 1 

Borehole gravimetry is a unique well-logging 

method because it is sensitive to material far from 

the well. By comparing densities measured with 

conventional logging tools and with a gravimeter, 

we can often estimate variations in density away 

from the wellbore. Because gravimetry is effective in 

cased wells, and because repeated measurements 

can detect small changes in density with time, 

gravimetry is an effective way to study changes in 

density caused by production or injection in wells. 

Geothermal energy production requires high flow 

rates of water, so that the potential for plugging or 

compacting the reservoir is great. Furthermore, 

geothermal wells usually have relatively large 

diameters, allowing the use of a relatively large logging tool. For these reasons, borehole gravimetry is 

particularly applicable to the study of geothermal 

production problems. To be useful in geothermal 

wells, gravimeters must be adapted to operate at 

high temperatures in corrosive environments. It 

appears that this adaptation is feasible and would 

be worthwhile. 

I 

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