A borehole gravimety system employs a pair of pressure transducers for lowering into a borehole along with a borehole gravity meter. The pressure transducers are spaced apart vertically within a pressure sonde for producing a pressure differential measurement of the wellbore fluid. A pressure differential measurement and a gravity reading is taken for each of a plurality of vertical locations within the borehole as the borehole gravimetry system is advanced through the borehole.

BACKGROUND OF THE INVENTION 
Borehole gravimetry has now been developed into a reasonably reliable tool 
for oil well logging. Borehole gravimetric techniques provide an 
indication of the bulk density of formation rock surrounding the borehole 
being logged. Gravimetric logging services now commercially available 
include that provided by Exploration Data Consultants (EDCON) of Denver, 
Colo. using a gravity meter of the type developed by LaCoste and Romberg. 
If accurate measurements of porosity of the formation rock are available, 
the residual oil saturation can be calculated to a high degree of 
accuracy. 
SUMMARY OF THE INVENTION 
The present invention is directed toward a method for conducting a 
gravimetry survey of subsurface formations surrounding a borehole. In 
accordance with such method, a borehole is traversed with a logging tool 
employing a borehole gravity meter and a pair of axially spaced pressure 
transducers. The traversing of the borehole is periodically stopped to 
take borehole gravity and wellbore fluid pressure measurements at a 
plurality of measurement stations within the borehole. The pair of 
pressure measurements taken at a first of the measurement stations and 
taken at a second of the measurement stations are used to determine the 
distance along the borehole between the first and second measurement 
stations. 
In a further aspect of the invention, two pressure measurements are taken 
by each pressure transducer at each measurement station. More 
particularly, the traversing of the borehole is stopped at a desired 
measurement station. A first wellbore fluid pressure measurement is taken 
by each of the pressure transducers. Upon completion of these first 
pressure measurements, the borehole gravity measurement is taken by the 
borehole gravity meter. Upon completion of the borehole gravity 
measurement, a second wellbore fluid pressure measurement is taken by each 
of the pressure transducers. Thereafter, the borehole logging tool is 
advanced through the borehole to the next desired measuring station where 
gravity and pressure measurements are again taken. This plurality of four 
pressure measurements taken at successive measurement stations are then 
used to determine the distance along the borehole between such successive 
measurement stations.

DESCRIPTION OF THE PREFERRED EMBODIMENT 
As mentioned above, borehole gravimetry has now been developed into a 
reasonably reliable tool for oil well logging. The general arrangement of 
gravimetric exploration operations is shown in FIG. 1. The LaCoste and 
Romberg type gravity meter 10 is passed down through a well extending from 
the surface of the earth through formations of various types until the 
area of interest is reached. The gravity meter 10 is lowered by means of a 
cable 11 running over a sheave 12, to the depth of interest. Gravimetric 
measurements, yielding signals proportional to the density of the 
surrounding formation, are then made and conducted by way of slip rings 13 
and brushes 14 to an amplifier 15, a filter 16, and a recorder 17 to 
produce a log of gravity measurements as a function of depth. This is a 
log of true gravity over the depth interval of interest, such depth 
interval being measured by the reel 18 rotatably coupled to the cable 11. 
FIG. 2 shows a schematic depiction of the LaCoste and Romberg gravity 
meter; other types of gravity meters are within the scope of the present 
invention. A lever 28 is pivoted more or less against the bias of a spring 
30 in accordance with the vertical component of the earth's gravity in its 
immediate locale. This meter is capable of yielding results proportional 
to the density of the formation within a radius of about 100 feet of the 
borehole itself. A pointer 32 is affixed to the end of the pivoted lever 
28 and indicates a point on a scale 34. The spring 30 is connected to a 
pre-load screw 36 which is moved in order to cause the lever pointer 32 to 
reach a predetermined index point on the scale 34. The amount of 
adjustment of the preload required to index the pointer 32 is proportional 
to local variations in gravity; thus the preload adjustment is effectively 
the data output by the gravity meter 10. The meter is sealed within an 
enclosed container before being passed down the hole. 
The borehole gravity meter, as the name implies, simply measures the 
vertical component of the earth's gravitational acceleration at a desired 
depth in the borehole. Given measurements at two different depths, one 
obtains the gravitational gradient and can proceed to compute the 
formation bulk density .rho..sub.b from the following equation: 
##EQU1## 
where 
F is the free air gradient; 
.DELTA.g is the gravity difference between the two readings; 
.DELTA.Z is the vertical distance between gravity measurement stations; and 
G is the universal gravitational constant. 
Written in units of microgals (one gal-1 cm/sec.sup.2) for .DELTA.g, gm/cc 
for .rho..sub.b, and feet for .DELTA.Z, we have 
EQU .rho..sub.b =3.687-0.039185.DELTA.g/.DELTA.Z. (2) 
The bulk density .rho..sub.b is representative of the horizontal slab of 
material that lies within .DELTA.Z; it is the accurate determination of 
.rho..sub.b by gravimetric techniques which makes a reliable residual oil 
determination feasible. 
As noted above, the gravity meter of FIG. 2 is of conventional design, its 
details forming no part of the present invention. Similarly, the 
operations shown schematically in FIG. 1 are presently commercially 
available from logging contractors and similarly form no part of the 
present invention. Instead, the present invention relates to a depth 
referencing system for more accurately determining the vertical distance, 
.DELTA.Z, between the gravity measurement stations. The accuracy of the 
determination of bulk density is very sensitive to the accuracy with which 
the vertical distance between measurement stations can be measured. Fairly 
accurate measurements of vertical distance can be made from land-based or 
fixed-platform offshore well locations, if the wells from such locations 
are vertical. In the case of non-vertical or deviated wells, sufficiently 
accurate measurements of vertical distance may not be possible. Further, 
in the case of wells drilled from floating drilling vessels, sufficiently 
accurate measurements of vertical distance are generally impossible, due 
to uncontrollable vertical motions of such drilling vessels. Although 
undesirable motions of the borehole gravity sonde due to such vessel 
motions may be prevented by clamping the sonde to the borehole wall, 
accurate measurement of the vertical location of the sonde is still a 
problem. The depth referencing system of the present invention is directed 
toward measuring vertical distance accurately under all such operating 
conditions. 
The depth referencing system is shown in FIG. 3 and employs a pair of 
transducers 20 and 21 housed in a pressure sonde 22 and lowered into the 
borehole by cable 11 along with the borehole gravity meter 10. The 
pressure sonde may be located either above or below the borehole gravity 
meter. When the borehole gravity meter moves a distance Z, the pressure 
sonde would also move the same distance. FIG. 4 illustrates 
diagrammatically the pair of pressure transducers, separated by the 
distance D and located at the vertical positions Z.sub.0 and Z.sub.1 
within the borehole. At these two vertical positions wellbore fluid 
pressure measurements, P.sub.0 and P.sub.1, are made along with the 
borehole gravity measurement and transmitted to the surface. Next the 
borehole gravity meter and the pressure sonde are moved upward through the 
borehole the distance .DELTA.Z and stopped at a point where the pair of 
pressure transducers are located at the vertical positions Z.sub.2 and 
Z.sub.3. Wellbore fluid pressure readings P.sub.2 and P.sub.3 are now 
taken and transmitted to the surface along with the borehole gravity 
measurement for this location in the borehole. The foregoing is repeated 
for as many depth locations as desired within the borehole. 
These wellbore fluid pressure measurements are utilized to accurately 
determine the vertical distance .DELTA.Z between two gravity measurement 
stations. The pressure difference .DELTA.P between two points in a 
fluid-filled borehole separated by a vertical distance .DELTA.Z is given 
by the following: 
EQU .DELTA.P=.rho..sub.f g.DELTA.Z (3) 
where 
.rho..sub.f is the fluid density, and 
g is the gravitational acceleration. 
Thus, the vertical distance .DELTA.Z can be represented as follows: 
##EQU2## 
By the use of a highly sensitive pressure gauge, such as a quartz crystal 
device, sufficiently accurate measurement of .DELTA.P can be made when the 
fluid density is known. By means of two such sensitive pressure gauges an 
accurate determination of the fluid density can be made. In a preferred 
embodiment, a pair of Hewlett Packard HP-2813 pressure gauges are mounted 
in the pressure sonde with vertical separation of about two feet and are 
clamped to the borehole wall by means of a downhole clamp R 1462 supplied 
by Geosystems Div. Geosource, Inc., Fort Worth, Tex., during borehole 
fluid pressure measurements. Various other means have been used in the 
past to clamp borehole tools to the borehole wall such as the bow spring 
clamp of U.S. Pat. No. 4,180,727; the spring biased clamp of U.S. Pat. No. 
3,340,953; and the hydraulic clamping means of U.S. Pat. No. 3,978,939. 
Calculation of vertical distance .DELTA.Z from the four pressure readings 
P.sub.0, P.sub.1, P.sub.2 and P.sub.3 as shown in FIG. 4 will now be 
described. 
For a static fluid column, the pressure as a function of distance Z 
satisfies the differential equation 
##EQU3## 
Over the relatively short distance between the measuring stations in 
borehole gravity logging it can generally be assumed that .rho. varies 
linearly with Z. 
Linearity of .rho. with Z implies that 
EQU .rho.=.rho..sub.0 +m(Z-Z.sub.0) (6) 
where 
##EQU4## 
A more convenient form of Eq. (6) is obtained by writing 
EQU .rho.=.rho..sub.0 +m.sub.1 Z (8) 
with 
##EQU5## 
and Z now represents the distance above Z.sub.0. 
Inserting Eq. (8) into Eq. (5) and integrating yields 
##EQU6## 
where C is a constant of integration. For the lowermost point Z.sub.0, P 
equals P.sub.0 so that 
##EQU7## 
Using Eq. (11), a set of equations can be developed for P.sub.1 and 
P.sub.0. 
##EQU8## 
Likewise, 
##EQU9## 
Thus, the pressure difference between points equals the product of average 
density between the points and the negative of the distance between the 
points. 
From Eq. (8), it can be seen that 
##EQU10## 
or in terms of pressures, 
##EQU11## 
From Eqs. (13) and (16), it follows that 
##EQU12## 
In some cases, the true pressure valves are not the ones recorded by the 
pressure transducers due to errors .theta..sub.i. Instead, at each 
measurement location, a value M.sub.i related to the true value P.sub.i is 
recorded wherein: 
EQU M.sub.i =P.sub.i +.theta..sub.i (18). 
A reasonable assumption is that the errors .theta..sub.i are randomly 
distributed with zero mean, have a common variance and are independent 
from one measurement to the next. To reduce any such error in the pressure 
measurements a plurality of pressure measurements may be made by each 
pressure transducer at a given vertical location in the borehole. In a 
preferred mode of operation, two sets of pressures are measured at each 
such location. The first set is taken from the pair of pressure 
transducers before the borehole gravity measurements are made, and the 
second set is taken from the pair of pressure transducers following the 
borehole gravity measurements and before the pressure sonde and borehole 
gravity meter are advanced through the borehole to the next measurement 
location. Consequently four pressure readings are taken for each borehole 
gravity measurement. Thus, when it is believed that there are significant 
departures of the actual pressure readings M.sub.i from the true values 
P.sub.i and additional accuracy in the determination of .DELTA.Z is 
required over that attainable through the solution of Eq. (17) above, the 
plurality of pressure readings are taken and processed as being from zero 
to three, j being from one to two, and the M.sub.ij rotation being the j 
th pressure reading at vertical position i. These pluralities of pressure 
readings can be used to rewrite Eq. (17) for the vertical distance Z as 
follows: 
##EQU13## 
In a somewhat more detailed approach, Eq. (19) is expanded to yield a 
further estimate for the vertical distance Z as follows: 
##EQU14## 
The derivation of Eq. (20) is contained in the following Appendix with 
.DELTA.Z being identified in such Appendix as Z.sub.3. 
APPENDIX 
Z.sub.3 Calculations 
Determination of Z.sub.3 and its associated variance requires the 
introintroduction of some new notation. To this end, define the state 
vector X.sub.i to be 
##EQU15## 
Let the pressure measurements be written as 
EQU M.sub.ij =I.sub.1 X.sub.i +.theta..sub.ij (A. 2) 
where 
EQU I.sub.1 =(1, 0, 0) (A.3). 
The idea is to use knowledge of the state equation to estimate the state 
X.sub.i given an estimate of the state X.sub.i-1. This estimate X.sub.i is 
then refined by processing the measurement M.sub.i2 to yield a better 
estimate of X.sub.i. Let X.sub.i.sup.- be the estimate based on an 
estimate of X.sub.i-1 and let X.sub.i.sup.+ be the refined estimate 
obtained from X.sub.i.sup.- and M.sub.i2. Further define state estimate 
errors X.sub.i.sup.- and X.sub.i.sup.+ by 
EQU X.sub.i.sup.+ =X.sub.i.sup.+ -X.sub.i (A. 4) 
EQU X.sub.i.sup.- =X.sub.i.sup.- -X.sub.i (A. 5) 
Next, restricting attention to linear estimation, it is desired to 
determine a K.sub.i and H.sub.i such that 
EQU X.sub.i.sup.+ =K.sub.i X.sub.i.sup.- +H.sub.i M.sub.i2 (A. 6). 
With the errors associated with X.sub.i.sup.+ smaller in a mean-square 
sense than X.sub.i.sup.-. This problem is precisely that for which optimal 
linear filtering equations provide the solution. The choice of K.sub.i and 
H.sub.i are derived in any number of texts and are presented here without 
proof below. 
EQU K.sub.i =I-H.sub.i I.sub.1, (A.7) 
where I is the identity matrix, and 
EQU H.sub.i =P.sub.i (-)I.sub.1.sup.T [I.sub.1 P.sub.i (-)I.sub.1.sup.T 
+.lambda..sub.p.sup.2 ].sup.-1 (A. 8) 
where I.sub.1.sup.T denotes transpose if I.sub.1, and P.sub.i (-) is 
defined by 
EQU P.sub.i (-)=E[(X.sub.i.sup.- -X.sub.i)(X.sub.i.sup.- -X.sub.i).sup.T 
]=E[X.sub.i.sup.- X.sub.i.sup.-.sbsb.T ]. (A.9) 
To start the process, we estimate X.sub.1 where 
##EQU16## 
where g.rho..sub.01 is obtained by using the first set of pressure 
measurements at depths Z.sub.0 and Z.sub.1. Thus, 
##EQU17## 
with 
##EQU18## 
Then 
##EQU19## 
From which P.sub.i (-) is calculated to be 
##EQU20## 
Thus, 
##EQU21## 
Using Eqs. (A.6) and (A.7), we have 
EQU X.sub.i.sup.+ =X.sub.i.sup.- +H.sub.i [M.sub.12 -X.sub.i.sup.- ](A.16) 
so that 
##EQU22## 
The state equation for the next part of the calculations is 
EQU P.sub.2 =P.sub.1 -g.rho..sub.12 (Z-D), (A.19) 
so P.sub.2.sup.- is taken to be 
EQU P.sub.2.sup.- =P.sub.1.sup.+ -(Z-D)[1/2(g.rho..sub.01).sup.+ 
+1/2(g.rho..sub.23).sup.- ] (A.20) 
where (g.rho..sub.01).sup.+ is obtained from Eq. (A.18) and 
(g.rho..sub.23).sup.- is estimated to be 
##EQU23## 
and Z is an estimate of Z obtained from the wireline odometer in the case 
of floating rigs, and from the odometer and an estimate of the deviation 
in deviated wells. The estimate Z is assumed to satisfy 
EQU Z=Z+.omega. (A.22) 
EQU E(.omega.)=0 (A.23) 
EQU E(.omega..sup.2)=.sigma..sup.2, (A.24) 
and .sigma..sup.2 is typically on the order of one foot. 
The state estimate X.sub.2.sup.- is given by 
##EQU24## 
where from Eq. (A.20) (g.rho..sub.12).sup.- is seen to be 
##EQU25## 
which follows using Eq. (15). In Eq. (A.26), .epsilon..sub.12 as 
implicitly defined has the properties 
EQU E(.epsilon..sub.12)=0 
and 
##EQU26## 
Using Eqs. (A.26) and (A.22), the error matrix becomes 
##EQU27## 
From Eq. (A.8) it can be seen that only the first column of P.sub.2 (-) is 
needed. Consequently, carrying out the operations required to determine 
the first column entries results in 
##EQU28## 
Thus, 
##EQU29## 
The approximation of Eq. (A.30) follows from the fact that .sigma..sup.2 
(g.rho..sub.12).sup.2 dominates all other denominator terms for 
.lambda..sub.p of 0.01 or smaller. Using this approximation X.sub.2.sup.+ 
becomes 
##EQU30## 
Note that in Eq. (A.31) the value g.rho..sub.12 is required, but this 
quantity is, of course, unknown. Consequently, the value 
(g.rho..sub.12).sup.- must instead be used which results in 
##EQU31## 
so that 
##EQU32## 
Using P.sub.1.sup.+ of Eq. (A.18) and (g.rho..sub.12).sup.- of Eq. (A.26) 
along with Eq. (A.33) results in 
##EQU33## 
which is Eq. (20).