CA2157101C - Logging while drilling method and apparatus for measuring formation characteristics as a function of angular position within a borehole - Google Patents

Abstract

A characteristic of an earth formation surrounding an inclined borehole in which a generally cylindrical logging while drilling tool is received, is determined by the steps of:
determining a bottom contact point of a cross-section of the tool which is orthogonal its longitudinal axis which cross-section contacts the borehole as the tool rotates; separating the cross-section into at least two segments, where one of said segments is called a bottom segment of the borehole which includes the bottom contact point; applying energy into and circumferentially around the borehole from an energy source disposed in the tool, as the tool turns in the borehole; recording measurement signals received at a sensor disposed in the tool from circumferentially spaced locations around the borehole, where the measurement signals are in response to returning energy resulting from the interaction of the applied energy with the formation; associating the measurement signals with a particular segment during the lime such signals are produced in response to energy returning from the formation as the tool turns in the borehole; and deriving an lndlcatlon of a characteristic of the formation as a function of the measurement signals associated with the bottom segment of the borehole.

Description

24.760 APPLICATION FOR PATENT
INVENTORS: JACQUES M. HOLENKA
MICHAEL L. EVANS
PHILIP L. KURKOSKI
WILLIAM R. SLOAN
DAVID L. BEST
TITLE: LOGGING WHILE DRILLING METHOD AND APPARATUS
FOR MEASURING FORMATION CHARACTERISTICS AS
A FUNCTION OF ANGULAR POSITION WITHIN A BOREHOLE
BACKGROUND OF THE INVENTION
1. Field of the Invention This invention relates generally to the field of logging while drilling tools.
In particular it relates to such tools for measurement of formation characteristics such as bulk density, photoelectric effect (PEF), neutron porosity and borehole caliper by means of ultrasonic measurements. Still more particularly, the invention relates to apparatus and methods for making such measurements as a function of angular position about the borehole as the tool is turning in such borehole during drilling.

2. De_cc rjtttion of the Related Art U.S. Patent 5,091,644 of Minette describes a method for analyzing formation data with a logging while drilling tool. Such patent describes dividing the cross section of the borehole into I

~~.~'~i01 two or more sectors. Gamma ray density signals are divided into four quadrants: top, bottom, right and left for operations in deviated boreholes. The gamma ray signals are collected as to their energy level so as to produce energy spectra for each quadrant. The '644 patent indicates that long and short spaced detectors are used to collect gamma ray count rate data to produce compensated density measurements.
Each quadrant measurement is combined with the other, either as a simple average or as a weighted average to produce a density value characteristic of the formation.
If the borehole has minimal washout, all four compensated density measurements are used. If there is extensive washout, the "bottom and the two side measurements" are used to calculate density of the formation. If the borehole suffers extreme washout, only the "bottom"
measurement is used.
The '644 patent describes error minimization whereby the spine and ribs correction is obtained for long and short spaced detector gamma ray spectra and an analysis made from quadrant to quadrant so as to minimize rib error. One or more quadrants are selected so as to minimize the error in arriving at a density value characteristic of the formation.
The '644 patent suggests that the borehole be broken into four quadrants, bottom, right, top and left. It suggests that such measurements can be made from measurements in the tool itself or from information supplied via a communication bus from another tool. It suggests that information from an accelerometer or a magnetometer that is sent to the density tool is sufficient ~~.~'~10i to break such borehole into four quadrants.
The '644 patent also discloses providing an acoustic caliper in alignment with a density source and detector for determination of standoff in front of the detectors at any given time. Such standoff information is used to minimize error of the density characterization of the formation due to standoff. It is also used to determine cross-sectional divisions of the borehole.
The disclosure of the '644 patent fails to identify a method to accurately determine a bottom contact point of a logging while drilling tool operating in a deviated borehole so as to accurately have information as to where the bottom of the borehole is as the sensors of the tool turn in the borehole.

3. Identification of Qbjects of the Invention A primary object of this invention is to provide a logging while drilling method and apparatus by which porosity, density and caliper or other measurements may be made as a function of angular position, or angular distance segment, about a deviated borehole with an accurate determination of the bottom of the borehole.
Another object of the invention is to provide a logging while drilling method and apparatus for determining an indication of lithology of the formation surrounding the borehole as a function of angular position, or angular distance segment, about the borehole.
Another object of the invention is to provide a logging while drilling method and apparatus 1 _21~7~OI
for determining borehole heterogeneity by comparing formation characteristic measurements of one angular distance segment to another.
A preferred embodiment of the method and apparatus of the invention includes a logging while drilling tool operatively designed for connection in a downhole drilling assembly above a drill bit. A direction and inclination sub, a downhole electronics sub, and a communication sub, as well as surface instrumentation, are also provided.
The logging while drilling tool of the preferred embodiment of the invention conducts a plurality of recorded measurements as a function of borehole angular distance segments:
compensated bulk density derived from gamma ray detector count rate energy level spectra;
photoelectric effect (PEF) derived from gamma ray detector count rate energy level spectra;
compensated neutron porosity derived from near and far spaced neutron detector measurements in response to neutrons interacting with the formation; and borehole size and shape using an ultrasonic sensor.
Although such measurements are preferably made in quadrants, in principle, the angular ~1~'~10I
distance segments may be a greater or lesser number than four and need not be of equal angular distance.
The invention is applicable to a slick tool, that is, a generally cylindrical tool without stabilizer blades, as well as to a tool with stabilizer blades, that is, a stabilized tool. For a slick tool operating in a deviated borehole, the density of the formation is determined from gamma ray counts while the tool is in a down or bottom quadrant or angular distance segment. When the borehole is deviated or horizontal, the tool touches the bottom portion of the borehole most of the time. Consequently, the standoff for density measurements is at a minimum, and approximately constant, allowing a good spine and rib correction. A measurement of rotational density derived from a statistical analysis of all density information about the borehole is also made.
The down vector of the tool is preferably derived first by determining an angle ~ between a vector to the earth's north magnetic pole, as referenced to the cross sectional plane of a measuring while drilling (MWD) tool and a gravity down vector as referenced in said plane. The logging while drilling (LWD) tool includes magnetometers placed orthogonally in a cross-sectional plane which produces an identical H vector in the logging while drilling tool as measured in the MWD tool. The angle tp is transmitted to the logging while drilling tool thereby allowing a continuous determination of the gravity down position in the logging while drilling tool.
Alternatively, surveys may be performed periodically by the MWD tool when drilling is 215'7101 temporarily halted to add drill pipe to the drill string. Quadrants, that is, angular distance segments, are measured from the down vector.
The angular position of the sensors with respect to the H vector of the LWD
tool is continuously updated so that such angular position with respect to the various angular distance segments is always known. Measurement data of the sensors thus is always correlated with one of the angular distance segments. Consequently, measurement data from each of the sensors is acquired as a function of the time of their measurement and spatially per their quadrant position in the borehole.
A computer with a computer program is provided for density data to average the count rate per energy window, per quadrant, and for the entire borehole at each record rate. The record rate is typically 20 seconds and is adjustable. An average density for long and short spacing is determined from such data for the entire borehole and for each quadrant. The spine and ribs compensation technique is applied to derive bulk density and correction factor for the entire borehole and for each quadrant.
IS The computer also includes a computer program to determine rotational density around the entire borehole and of each of the quadrants. This technique uses the rotation of the LWD tool to compensate for borehole effect. It is used alternatively to the spine and ribs compensation technique.

_~~~7~~~
A first method of computing rotational density is provided by which the variance of the gamma ray count rate data actually measured is compared with the variance expected of a circular borehole. A rotational correction factor is determined. A second method is provided by forming a histogram of gamma ray counts, and extracting only the counts when the detectors touch the formation.
These methods correct the counting rates for the effect of mud between the detector and the formation.. This effect can either increase or decrease the counting rates in the detectors, depending upon the mud-formation density contrast.
The invention also permits a determination of whether apparent mud density is greater or less than apparent formation density by incorporating infom~ation from an ultrasonic measurement of standoff per quadrant. If the average gamma ray counts in the quadrant with standoff are higher than the average counts in a quadrant with no standoff, then apparent formation density is determined to be higher than the apparent mud density. Therefore, a maximum rotational density is computed using either of the two methods described above.
If the average counts in a quadrant with standoff are lower than the average counts in the quadrant without standoff, then apparent formation density is determined to be lower than apparent mud density. Therefore, a minimum rotational density in computed using either of the two methods described above.

~1~?1Q1 The rotational density technique is applied to derive bulk density and correction factor for the entire borehole and for each quadrant.
The preferred embodiment of the invention also includes a computer program for analysis of gamma ray count data to determine a lithology indicator of the formation photoelectric effect (PEF). The energy window count rates are analyzed to determine average PEF for the entire borehole and for each quadrant, and rotational PEF for the entire borehole and each quadrant is determined in a manner similar to that described above for the determination of rotational density.
Like the density, average porosity for the entire borehole and for each quadrant is determined. A rotational porosity determination is also made for the entire borehole and for each quadrant in a manner similar to that of rotational density and rotational PEF.
An ultrasonic sensor measures standoff between the LWD tool and the borehole wall. A
histogram of such standoffs is analyzed to determine minimum and maximum standoff per quadrant. From such standoffs a horizontal diameter, a vertical diameter and a borehole shape determination is made. The borehole standoff values per quadrant are used also in the determination of rotational density, as described above, and in the compensation of neutron detector data to correct neutron porosity determinations for borehole size.

21~~101 BRIEF DESCRIPTION OF THE DRAWINGS
The objects, advantages and features of the invention will become more apparent by reference to the drawings which are appended hereto and wherein like numerals indicate like elements and wherein an illustrative embodiment of the invention is shown, of which:
Figure 1 is a schematic illustration of a downhole logging while drilling (LWD) tool connected in tandem with other measuring while drilling (MWD) tools above a drill bit at the end of a drill string of an oil and gas well in a section of the well which is substantially horizontal;
Figure 2 is a schematic longitudinal cross section of the LWD tool of the invention illustrating a neutron source and neutron detectors, a gamma ray source and gamma ray detectors and an ultrasonic detector, producing formation neutron data, formation gamma ray data and ultrasonic signal data, respectively;
Figure 3A is a schematic longitudinal cross section of a separate MWD tool having magnetometers and accelerometers placed along orthogonal x and y axes of such tool and a computer For generally continuously or periodically (e.g., at survey times while the drill string is not turning) determining an angle ~ between an H vector and a G vector in a plane of such x and y axes; and further schematically illustrates a downhole electronics module associated with the LWD tool, the illustration showing orthogonal magnetometers placed along x and y axes which are in a plane parallel to the plane of the corresponding axes in the MWD tool;

~15"~101 Figure 3B is a schematic illustration of computer programs in a downhole computer for determining borehole quadrants, sensor position, and for determining bulk density and rotational density, average PEF and rotational PEF, neutron porosity and rotational neutron porosity for the entire borehole and each quadrant, and ultrasonic standoff for each quadrant;
Figure 4A illustrates a cross sectional view taken along line 4-4 of Figure 1 showing a generally cylindrical (not stabilized) tool rotating in an inclined borehole, where the borehole has been divided into four equal length angular distance segments (quadrants) and where the sensor is in a down or bottom position;
Figure 4B illustrates a similar cross sectional view as that of Figure 4A but shows a LWD
tool with stabilizing blades such that there is substantially no difference in standoff from the cylindrical portion of the tool to the borehole wall as the tool rotates, and also further showing an example of heterogeneous formations with the borehole having one formation on one side and another formation on the other side, where the borehole may be inclined or substantially vertical;
Figure SA schematically illustrates magnetometers and accelerometers placed along x, y and z axes of a MWD tool, with a computer accepting data from such instruments to produce an instantaneous angle ~ between a vector H, of Hx and HY and a vector G ~ of Gx and GY;
Figure SB illustrates a cross section of the MWD tool showing the angle ~ as measured from the ~ ~ vector which is constant in direction, but with time has different x and y H

2~~'~101 coordinates while the MWD tool rotates in the borehole;
Figure 6A is an illustration of the magnetometer section and Quadrant/Sensor Position Determination computer program of the electronics module of Figures 3A and 3B, such illustration showing the determination of the angle @ of the vector ~ in terms of the Hx and H
HY signals from the magnetometers in the electronics module, and further showing the determination of the angle of a down vector D as a function of ~(t) and the angle cø transferred from the MWD tool, such illustration further showing the determination of quadrants as a function of the angle of the down vector, and such Hlustration further showing the determination of which quadrant that a sensor is in as it rotates in a borehole;
Figures 6B-6E illustrate angles from the x and y axes of the LWD tool and from the sensors to the H vector as the LWD tool is turning as a function of time in the borehole;
Figure 6F illustrates dividing the borehole into four segments, where a bottom segment or quadrant is defined about the down vector D
Figures 7A and 7B illustrate long and short spaced gamma ray detectors with apparatus for accumulating count rates in soft and hard energy windows;
Figure 8 illustrates a computer program of the LWD computer for determining the number of count rate samples per quadrant in hard windows and in soft windows as well as the total count rate samples for both the long and short spaced gamma ray detectors, acquisition time samples and y .15'7101 count rates;
Figure 9 illustrates a computer program of the LWD computer for determining the long and short spacing densities, the bulk density and ~p correction factor determined by a spine and ribs technique for the entire borehole and for each of the bottom, right, top and left quadrants;
Figures 10A-1 and 10A-2 illustrate a computer program of the LWD computer for determining rotational density output and ~pRO.,. correction factors;
Figure lOB illustrates a LWD tool rotating in an inclined borehole;
Figure lOC illustrates count rates per quadrant where such count rates are fluctuating from quadrant to quadrant;
Figures 10D-1 and 10D-2 illustrate an example of the entire borehole distribution of the number of samples as a function of count rate for the inclined hole of Figure lOB and for an expected distribution of count rates for a circular borehole, and by way of illustration for a particular quadrant Q.,.oP, the method of determining OpRo.,., and pb Ro.,.
for the entire borehole and for each quadrant;
Figures 11A and 11B illustrate a computer program in the LWD computer for determining the average photoelectric effect (PEF) for the entire borehole and for each of the quadrants;
Figures 12A-C illustrate a computer program in the LWD computer for determining rotational photoelectric effect (PEF) outputs for the entire borehole and for each quadrant;

21~'~101 Figures 12D-F illustrate an alternative computer program which may be used in the LWD
computer for determining rotational photoelectric effect (PEF) outputs for the entire borehole and for each quadrant;
Figure 13 illustrates a computer program in the LWD computer which accepts standoff data from the ultrasonic sensor and determines average, maximum and minimum standoff for each quadrant, and determines the horizontal and vertical diameters of the borehole so as to determine the hole shape;
Figures 14A and 14B illustrate a computer program in the LWD computer for determination of average neutron porosity, as corrected of standoff, for the entire borehole and for each quadrant; and Figures 15A-C illustrate a computer program in the LWD computer for determination of rotational neutron porosity for the entire borehole and for each quadrant.
DESCRIPTION OF THE PREFERRED EMBODIMENT
Intt~tiQn Figure 1 illustrates a logging while drilling (LWD) tool 100 connected in tandem with a drilling assembly including drill bit 50. An associated downhole electronics module 300 and MWD tool 200 including magnetometers and accelerometers are also connected in tandem with 21a7101 LWD tool 100. Module 300 may be a separate "sub" or it may be disposed in the body of LWD
tool 100. A communication sub 400 is also provided as illustrated in the drilling assembly.
The LWD tool 100 is shown for illustration purposes as being in an inclined portion of a borehole at the end of a drill string 6 which turns in a borehole 12 which is formed in formation 8 by penetration of bit 50. A drilling rig 5 turns drill string 6. Drilling rig 5 includes a motor 2 which turns a kelly 3 by means of a rotary table 4. The drill string 6 includes sections of drill pipe connected end-to-end to the kelly 3 and turned thereby. The MWD tool 200, electronics module 300 and the LWD tool 100 and communication sub 400 are all connected in tandem with drill string 6. Such subs and tools form a bottom hole drilling assembly between the drill string 6 of drill pipe and the drill bit 50.
As the drill string 6 and the bottom hole assembly turn, the drill bit 50 forms the borehole 12 through earth formations 8. Drilling fluid or "mud" is forced by pump 11 from mud pit 13 via stand pipe 15 and revolving injector head 7 through the hollow center of kelly 3 and drill string 6, and the bottom hole drilling assembly to the bit S0. Such mud acts to lubricate drill bit 50 and to carry borehole cuttings or chips upwardly to the surface via annulus 10. The mud is returned to mud pit 13 where it is separated from borehole cuttings and the like, degassed, and returned for application again to the drill string 6.
The communication sub 400 receives output signals from sensors of the LWD tool 100 and from computers in the downhole electronics module 300 and MWD
tool 200. Such communications sub 400 is designed to transmit coded acoustic signals representative of such output signals to the surface through the mud path in the drill string 6 and downhole drilling assembly. Such acoustic signals are sensed by transducer 21 in standpipe 15, where such acoustic signals are detected in surface instrumentation 14. The communication sub 400, including the surface instrumentation necessary to communicate with it, are arranged as the downhole and surface apparatus disclosed in U.S. Patent 4,479,564 and U.S. Patent 4,637,479.
The communication sub 400 may advantageously include the communication apparatus disclosed in U.S. Patent 5,237,540, assigned to the present assignee.
LWD Tool, MWD Tool and Electronics Module 1. LWD Tool Figure 2 illustrates in a schematic way the LWD tool 100 of this invention. The physical structure of the LWD tool body and associated sensors is substantially like that described in U.S. Patent 4,879,463 to Wraight, et al., and U.S.
Patent 5,017,778 to Wraight. Both of such patents are assigned to the assignee of the invention described herein. Such patents describe a logging while drilling tool as may be used to implement this invention, specifically a compensated density neutron tool used in logging while drilling measurements of formation characteristics. LWD tool 100 hardware as shown in Figure 1 herein is different in at least two respects: (1) an ultrasonic sensor 112 is added to the assembly and (2) stabilizer blades are not illustrated as being provided for LWD
tool 100. The provision of stabilizer blades is, however, an alternative embodiment of the LWD tool 100 as shown in Figure 4B, where a stabilized tool is used with methods of the invention as described below.
The LWD tool 100 includes a source of neutrons 104 disposed axially, and near and far spaced neutron detectors 101, 102. It also includes a source of gamma rays 106 and short and long spaced gamma ray detectors 108, 110. Such LWD
tool 100 also includes an ultrasonic transducer 112 for measuring tool standoff from the borehole wall. Such ultrasonic transducer and system is described in U.S. Patent 5,130,950 in the name of Orban, et al., and is also assigned to the assignee of the invention described herein. This patent provides a detailed description of an ultrasonic sensor 112 of the LWD tool 100 of this invention.
2. MWD Tool A MWD tool 200 is provided in the bottom hole drilling assembly as schematically indicated in Figure 1.
Figure 3A schematically illustrates that MWD tool 200 includes 21~?dal magnetometers 201,202 oriented along x and y axes of the tool. Such x and y axes are in the plane of a radial cross section of the tool. A z axis of the tool is oriented along its longitudinal axis. In a similar way, accelerometers Gx and Cy of accelerometer package 208 (which also includes an accelerometer along the z axis of the tool) are oriented along the x and y axes of the tool. A microcomputer 210 responds to HY and Hx signals and Gx and Gy signals to constantly determine an angle ~ between an H~ vector and the G vector, in the cross sectional plane of MWD tool 200. The H~ vector represents that portion of a vector pointed to earth's magnetic north pole which is projected onto the x - y plane of MWD tool 200.
The ~ vector G
represents the down component in the cross sectional plane of MWD tool 200, of the earth's gravity vector. As illustrated in Figure 3B, a signal representative of such angle ~ is constantly communicated to downhole computer 301 of electronics module 300. Its use in determining a down vector of electronics module 300 and LWD tool 100 is described in the description of a Quadrant/Sensor Position Determination computer program 310 presented below.
3. Electroiics Module The electronics module 300 (which, at the option of a designer, may be part of MWD tool 200 or an independent sub) of Figure 3A includes a magnetometer section 302 and a microcomputer 301. The x and y axes, on which magnetometers of the magnetometer section 302 are oriented, are in a plane which is substantially parallel with the plane of such axes of the MWD

215'~1~D1 tool 200. Accordingly, the H vector generated by the magnetometer section 302 of electronics module 300 is substantially the same vector H determined by computer 210.
Accordingly, the computer program 310 has information to determine the down vector angle with respect to a sensor vector as a function of time. A more detailed description of such determination is presented below.
Electronics module 300 receives data from near and far spaced neutron detectors 101 and 102, short and long spaced gamma ray detectors 108, 110 and ultrasonic transducer 112.
Ultrasonic transducer 112 is angularly aligned with gamma ray detectors 108, 110 and with gamma ray source 106.
As illustrated in Figure 3B, downhole computer 301 includes not only the Quadrant/Sensor Position Determination program 310, but also a data acquisition program 315, a bulk density program 320, a rotational density per entire borehole and per quadrant program 326, an average photoelectric effect (PEF) program 330, a rotational PEF program 335, a neutron porosity program 340, a rotational neutron porosity program 345, and an ultrasonic standoff program 350, and others. Such programs transfer data signals among themselves in certain cases, as described below.

215'101 _Angular Distance Segments and An~lar Position of Set~ors 1. Determination of Down Vector D with respect to x,,v axes Figures SA, SB, and 6A-F illustrate the determination of a down vector in computer 301 (Figure 3B). Figure 4A shows the case of an unstabilized LWD tool 100 which, in an inclined borehole, generally constantly touches the bottom of the borehole. Figure 4B
illustrates the case of a stabilized LWD tool 100'.
Figure SA illustrates the magnetometers H and the accelerometers G oriented along x, y and z axes of the MWD tool 200. As explained above, an angle ~ is constantly computed between the H~ vector (a constantly directed vector, in the x-y plane for the H directed vector to earth's magnetic pole) and a ~ ~ vector (a constantly directed down vector, in the x-y G
plane of a vector G directed to the earth's gravitational center, i.e., the center of the earth).
As Figure SB illustrates, MWD tool 200 is rotating in borehole 12. The x and y axes of the tool 200 are rotating at the angular speed of the drilling string, e.g., 30 to 200 revolutions per minute, so the x and y components of the H~ vector and the G vector are constantly changing with time. Nevertheless, the H~ and the G~ vectors point generally in constant directions, because the borehole direction changes slowly with time during the time that it is being drilled through subterranean rock formations.

_~i~~ioi Figure 6A illustrates the magnetometer section 302 of electronics module 300.
Magnetometers Hx and Hy are oriented along x and y axes of the electronics module 300. Such x and y axes are in a plane which is substantially parallel with the plane of such axes of MWD
tool 200. Accordingly, the Hx and I-Iy, signals transmitted from magnetometer section 302 to computer 301 and computer program 310 are used to form a constantly directed reference with respect to an axis of the module, e.g., the x axis.
As Figures 6A - 6E illustrate, as the MWD tool 200 rotates in borehole 12, an angle 8(t) is constantly formed between the tool x axis and such H~ vector. The angle 8(t) is determined from the Hx and Hr signals from magnetometer section 302 of electronics module 300:
0(t) = cos-' H (t) (Hx(t)Z+HY(t)2) Next, the down vector angle, angle D(t) is determined in QuadrantlSensor Position Determination program 310, as a function of the x and y axes and time, by accepting the angle ~ from the MWD tool 200. The angle of the down vector is determined in program 310 as>
angleD(t) _ ~(t)-~
Four quadrants may be defined by angular ranges about the periphery of the tool:
QeoT(t) = angle D(t) -45° to - 215'101 angle ~ + 45, ) t QLEFf(t) = angle D + 45 to (t) angle ~ + 135, D(t) QTOP(t) = angle D + 135 to (t) angle D + 225, (t) Q~ucFrr(t) = angle D + 225 to (t) angle v - 45 .

( ) t Figures 6B-E illustrate the position of MWD tool 200 and electronics module 300/LWD

tool 100 in borehole 12 at several times, t1, t2, t3, t, as it rotates. The angle 0(t) varies with time, because it is measured from the x axis of the MWD tool 200 (and of the electronics module 3001LWD tool 100) to the H vector. The angle ~ is constant from the H~ vector to the vector.
2. DetermirLa_tion of Angular Distance Se n c Figure 6A further illustrates generation of angular distance segments around the borehole.
The term "quadrant" is used to illustrate the invention where four ninety degree angular distance segments are defined around the 360° circumference of the MWD tool 200 or the LOUD tool 100.
Other angular distance segments may be defined, either lesser or greater in number than four.
The angular distance of such segments need not necessarily be equal.

~mnoi In a preferred embodiment of the invention however, quadrants are defined as illustrated in the computer program representation of the Quadrant/Sensor Position Determination program 310. A bottom quadrant QBOT(t) is defined as extending forty-five degrees on either side of the down vector ~ ) . Left quadrant, Qt F~(t), top quadrant, QTOP(t) and right quadrant, Q&oi,.,.(t) t are defined as in Figure 6A.
3. Deterttitiation of An~lar Position of Seniors As Figures 6B-E further illustrate, the sensors S (e.g., short and long spaced gamma ray detectors 108, 110, ultrasonic transducer 112 and near and far spaced neutron detectors 101, 102) are oriented at a latown angle a from the x axis. Thus, the angle of the sensor is a constant angle a as measured from the x axis of the electronics module or sub 300.
Accordingly, computer program 310 determines which quadrant a sensor is in by comparing its angle from the x axis with the quadrant definition with respect to the x axis. For example, sensors S are in QBO.i. when a is between ~(t)-~~5° and 0(t)-~+45°. Sensors S are in Q.,.oP when a is between O(t)-~-135° and ~(t)-~-225°, and so on.
Figure 6F further illustrates the down vector D and four quadrants, QBO.,., Q,~c,,.l., Q.,.oP, and QLg~. WhICh are fixed in space, but are defined as a function of time with the turning x and y axes of MWD tool 200.

z~~~~m 1. Gamm__a RaYData Acquisition by .n rgy Window Time and bysl ~adran Figure 7A is a pictorial representation of gamma rays returning from the formation which are detected by gamma ray detectors. The detectors 108 and 110 produce outputs representative of the number of counts per energy window of the counts as reflected in the number and magnitude of the gamma rays detected by detectors 108, 110. Such outputs are directed to analog to digital devices {ADC's) and stored in the memory of downhole computer 301.
An illustration of the storage of the rates of such counts, as a function of energy windows, is illustrated in Figure 7B. Certain lower energy windows are designated "soft" windows. Certain higher energy windows are designated "hard" windows as illustrated in Figure 7B.
Figure 8 illustrates that part of a data acquisition computer program 315 of computer 301 which accepts counts from the ADC's in response to detectors 108, 110. It also accepts starting times and end times for the accumulating of the total number of counts in each energy window for (1) the short spaced detector and (2) the long spaced detector as a function of the entire borehole and for each quadrant. The total acquisition time is also collected for the entire borehole, that is all counts, and for the acquisition time for each quadrant.
Such outputs are for hard window counts as well as soft window counts. Computer program 315 also calculates count rates for all samples.
2. Bulk Dencitrr and 0~'.orrection Determination _ Figure 9 illustrates computer program 320 of downhole computer 301 of electronics module 300 which accepts count rate signals of long and short spaced gamma ray detectors for hard window counts by angular distance segment (i.e., quadrant). Accordingly, as shown schematically in Figure 9, a sub program 321, called "SPINE AND RIBS" receives digital data signals representative of the total hard window count rate for the entire borehole from both the long and short spaced detectors and determines long spacing density pL, short spacing density ps, bulk density p"vc and Ap correction. A spine and ribs correction technique is well known in the nuclear well logging art of density logging. Such correction technique is based on a well known correction curve by Wahl, J.S., Tittman, J., Johnstone, C.W., and Alger, R.P., "The Dual Spacing Formation Density I,og", presented at the Thirty-ninth SPE Annual Meeting, 1964. Such curve includes a "spine" which is a substantially linear curve relating the logarithm of long spacing detector count rates to the logarithm of short spacing detector count rates. Such curve is marked by density as a parameter along the curve. "Ribs" cross the spine at different intervals.
Such ribs are experimentally derived curves showing the correction necessary for different mudcake conditions.
The spine and ribs computer program is repeated as at 322, 323, 324 and 325 to determine long spacing density pL, short spacing density ps, bulk density pAVC and 0p correction for each quadrant based on the hard window count rates of the long and short spaced detectors for each quadrant.
Determination of Rotational Density pbROT and ~pROT
Correction for Entire Borehole and for Quadrants Figures 10A-1 and 10A-2 illustrate computer program 326 in downhole computer 301 which determines rotational density, called pbROT and OpROT correction for each quadrant and for the entire borehole. Rotational density or Rotational bulk density is borehole density corrected for borehole irregularity effects on the density measurement. The method is described for an entire borehole in U.S. Patent 5,017,778 to Wraight.
Such patent is also described in a paper by D. Best, P. Wraight and J. Holenka, titled, AN INNOVATIVE APPROACH TO CORRECT
DENSITY MEASUREMENTS WHILE DRILLING FOR HOLE SIZE EFFECT, SPWLA
31St Annual Logging Symposium, June 24-27, 1990.
For the entire borehole, signals representing total hard window count rate samples from the long spaced, or alternatively, the short spaced gamma ray detector, and count rate are transferred from data acquisition computer program 315 (Figure 8). Long and short spacing ~' 215"101 densities, pL and p5, are transferred from computer program 320 (Figure 9). A
sub program 328 determines a theoretical or circular hole standard deviation (or variance), determines a standard deviation of the measured samples of collected data, and determines a delta count rate, ACR, as a function of the variance between the measured standard deviation and the theoretical standard deviation of a circular hole. Next, a rotational bulk density digital signal pb ~.,. is determined.
Digital signals representative of OpROT and pb noT are output.
Figures 10B, 10C, lOD-l and 10D-2 illustrate the method. Figure lOB again shows an unstabilized LWD tool 100 rotating in borehole 12. Figure lOC illustrates long spacing or, alternatively, short spacing hard window count rates of the LWD tool 100 as a function of time.
As indicated in Figure IOC, the time that the detector is in various quadrants (or angular distance segments referenced here as Ql, Qa....) is also shown. For a non-round hole, especially for a non-stabilized tool 100, the count rates fluctuate about a mean value for each revolution of the tool.
In Figure IOC, eight samples per revolution are illustrated. Data collection continues for 10 to seconds.
15 Figures 10D-1 and 10D-2 illustrate the method of computer program 328 for determining Pb ROT and ~PROT for the entire borehole. First, a mean (average) and theoretical standard deviation (a~,~r) for a normal distribution from a circular borehole with a stabilized tool is estimated. Next, a histogram or distribution of the number of samples versus count rate measured 215'101 (CR) is made and a mean and measured standard deviation (o,~~ for all actual counts collected during an actual acquisition time is made. A delta count rate factor ACR is determined:
~~''R = '~ Qzmem azthear where A is a constant which is a function of the data sampling rate.
Next the OpROT factor is determined:
APxor = (~) ~~(CR+OCR)~
CR-ACR
where ds is detector sensitivity.
Finally, the rotational bulk density is determined:
Pb ROT = DPc + EPS + F~pxor where D, E, and F are experimentally determined coefficients;
p~ _ long spacing density obtained as illustrated in Figure 9; and p5 = short spacing density obtained as illustrated in Figure 9.
As indicated in Figures IOC, 10D-1 and 10D-2 also, such pb Roi. factor and ACR
factor is also determined in the same way for each quadrant, but of course, rather than using all of the samples of Figure IOC, only those samples collected in the Q.,.oP quadrant, for example, are used ~1~'~101 in the determination. As indicated in Figures 10A-1 and 10A-2, the ~pRO.,.
factor and p6 Ro.,. value are determined, according to the invention, for the entire borehole and for each quadrant.
Determination for Averag~~nd RotatiorLl Photoelectric Effect IPEFI Ou(puts for Entire Borehole and ac a Function of fyadran s 1. Determination of PEF.v~
Figures 11A and 11B illustrate computer program 330 which determines photoelectric effect parameters as, alternatively, a function of short spaced detector soft window count rate and short spaced detector hard window count rate or long spaced detector soft window count rate and long spaced detector hard window count rate. Using the short spaced or long spaced detector count rate for the entire borehole and the p,,v~ as an input from computer program 320, the factor PEFA~ = UAW
pavc is determined, where the macroscopic cross-section, _ K _ SOFT COUNT RATE C
-B
HARD COUNT RATE

The terms K, B and C are experimentally determined constants.
In a similar manner, as shown in Figures 11A and 11B, the U,,vGBOT~
Unvc~uctrr~ UAVG~roP.
and U"vc LEFT are determined from short spaced or long spaced detector soft and hard window count rates while the sensor is in the bottom, right, top and left quadrants, respectively.
2. I?etermination of RotatiorLl PEF
Figures 12A-C illustrate computer program 335 in downhole computer 301. The total soft and hard window count rate distributions from the long spaced or, alternatively, the short spaced gamma ray detector, and the corresponding count rates are accumulated.
In a manner similar to that described above with regard to the calculation of rotational density, a ACRso~. factor is determined from the soft count rate distribution, 2 _ 2 ~CR~~. = A a ",em a theor where A is a constant which is a function of the data sampling rate.
Similarly, a OCR is determined from the hard count rate distribution. Next, macroscopic cross-section, URor, and PEFROr factors are determined:
_ K _ SOFT COUNT RATE - OCRSp~. C
-B
HARD COUNT RATE - ACRx~

21~7~01 where K, B and C are experimentally determined constants, and PEF~T = UR°T
pb ROT
where pe Ror is determined in computer program 328 as illustrated in Figures 10A-1, 10A-2, 10D-1 and 10D-2.
Rotational Photo Electric Factor is borehole Photoelectric factor corrected for borehole irregularity effects on the PEF measurement.
In a similar manner, the PEFROT factor for each quadrant is also determined, as illustrated in Figures 12A-C.
The PEF is an indicator of the type of rock of the formation. Accordingly, PEFAVG is an indicator of the type of rock, on the average, of the entire borehole. The PEFAVO per quadrant is an indicator of the type of rock per each quadrant and hence heterogeneity of the formation.
PEFRO,. signals, as determined by program 335 (Figures 12A-C) provide further information as to the kind of rocks of the formation.
An alternative methodology for determining rotational PEF is illustrated in Figures 12D-F.
The total soft count rate and total hard count rate from the long spaced or, alternatively, the short spaced gamma ray detector are accumulated for a plurality of acquisition time samples. Next, for each such acquisition time sample, a macroscopic cross section factor U~ is determined as a function of acquisition time t:
Ut = - C
SOFT COUNT RATE _ B
HARD COUNT RATE
where K, B and C are experimentally determined constants.
Next, the standard deviation is determined from the distribution of Ut factors. Finally, a rotational value of photoelectric effect, PEFROT, is determined from the distribution of Ut's. Such rotational value is determined in a manner similar to that i.Llustrated in Figures 10A-1, 10A-2, 10D-1 and 10D-2 for the determination of phROT from a distribution of count rate samples as a function of count rate.
The methodology then proceeds as previously described to a determination of the overall PEFROT and PEFuoT for each quadrant .
Ultrasonic Standoff Determination As illustrated in Figure 13, computer program 350 of downhole computer 301 determines borehole shape from standoff determinations based on ultrasonic signals. As mentioned above, U.S. Patent 5,130,950 describes the determination of standoff. Such standoff, i.e. the distance between the ultrasonic sensor and the borehole wall, is determined as a function of quandrant and collected for each quadrant.
A distribution of standoff values are collected per quadrant for a predetermined acquisition time. From such distribution, for each quadrant, an average, maximum and minimum value of standoff is determined. From such values, a "vertical" diameter of the borehole, using the average standoff of the bottom quadrant plus the tool diameter plus the average standoff of the top quadrant is determined. The "horizontal" diameter is determined in a similar manner.
As described above, rotational density is determined around the entire borehole and for each of the quadrants to compensate for borehole effects as an alternative technique to the spine and ribs technique. The invention further provides a determination of whether apparent mud density in the borehole, that is the measured density including ghotoelectric effect, is greater than or less than apparent formation density by incorporating information from the ultrasonic measurement of standoff per quadrant as described above with respect to Figure 13. If the average gamma ray counts in a quadrant with standoff (e.g., top quadrant) are higher than the average gamma ray counts in a quadrant with no standoff (e.g., bottom quadrant), then apparent formation density is determined to be higher than apparent mud density.
Therefore, a maximum rotational density is determined.
If the average gamma ray counts in a quadrant with standoff (e.g. top quadrant) are lower than the average gamma ray counts in a quadrant with no standoff (e.g. bottom quadrant), then ~15'~101 apparent formation density is determined to be lower than apparent mud density. Therefore, a minimum rotational density is determined.
Figures 14A and 14B illustrate a computer program 340 of downhole computer 301 which accepts near and far detector neutron count rates from LWD tool 100. It also accepts horizontal and vertical hole diameter digital signals from computer program 350 (Figure 13 discussed above.) Neutron count rate is affected by hole diameter. Correction curves for hole size for neutron count rates are published in the technical literature. Accordingly, measured near and far neutron count rates are corrected, in this aspect of the invention, by using correction curves or tables for hole size as determined by the ultrasonic sensor and associated computer program 350 as described above. Average porosity determination from program 340 using all borehole counts and compensated for offset of the tool from the borehole as a function of quadrants is made in a conventional manner.
In a similar way a porosity digital signal is determined for each of the individual quadrants from far and near neutron detector count rates per quadrant and from such hole shape data.
As illustrated in Figures 14A and 14B, a method and a programmed digital computer is disclosed for determining neutron porosity of an earth formation surrounding an inclined borehole 21~'~141 in which a logging while drilling tool is operating. See Figures 1 and 2. The tool 100 includes a source of neutrons 104 and near spaced and far spaced detectors 101,102 of neutrons which result from interaction of neutrons from the source of neutrons 104 with the formation. An ultrasonic sensor or transceiver 112 is also provided with tool 100. The method includes first determining a bottom contact point of the tool 100 which contacts the inclined borehole while the tool 100 is rotating in the borehole. See Figure 4A. Next, a bottom angular distance segment, called SEGMENTBO.,.,.oM of the borehole is defined which includes the bottom contact point. See Figures 4A and 6A for the preferred way of determining a bottom quadrant QBO,.(t).
Next, as illustrated by Figures 14A and 14B, for a predetermined length of time, a far neutron count of the far spaced neutron detector 102 and a near count rate of the near spaced neutron detector 101 is recorded for the bottom angular distance segment.
With the ultrasonic sensor 112, the average BOTTOM STANDOFF is made from ultrasonic measurements while the tool is in the bottom angular distance segment QBOT(t). Next, an average neutron porosity is determined as a function of the near neutron count rate and the far neutron count rate measured in the bottom segment and corrected by the BOTTOM
STANDOFF
determined above.
The procedure described above is repeated respectively for the angular distance segments called Q~,e,~.,., Q,r.op and Q,~.. The total borehole average neutron porosity is also determined as 21~'~ 101 a function of near and far neutron count rates detected in QBO,., Q~,cFrr>
Q~ror and QLE~. Each of such count rates is corrected by standoff measurements of the respective segments: average BOTTOM STANDOFF, average RIGHT STANDOFF, average TOP STANDOFF and average LEFT STANDOFF.
As illustrated in Figure ISA, a method and computer program is provided for determining rotational neutron porosity. First a histogram of near and far neutron count rates for the entire borehole is produced. Next, a signal (e.g., produced by program 345)representative of the standard deviation of the histogram of near count rates and a signal representative of the standard deviation of the far count rates is determined. For the entire borehole, a signal is determined IO which is proportional to the difference in the variance of all near count rates from the near spaced detector and a signal proportional to the expected variance of the count rates for a circular borehole is determined. From such signals, a porosity rotation correction factor is representative of a porosity measurement correction needed to correct a porosity measurement of the borehole for borehole irregularity about the entire borehole.
Rotational porosity, PROT, is determined as a function of ~PROT, and near and far spaced neutron detector signals which are representative of porosity. Such signals are called PN and PF
respectively. The rotational porosity PRO.,. may be determined as PST = M PN t IV ~ PF + Q ' OP~r ~157I01 in a manner similar to the way rotational bulk density is determined as described above. The constants M, N, and Q are experimentally determined coefficients.
Figures 15A-C illustrate computer program 345 of downhole computer 301 which accepts total near and far neutron count rates. Histograms, that is distributions, are produced from all such count rates during the acquisition time. The standard deviation of each distribution is determined. Such standard deviations are used to determine rotational neutron porosity for the entire borehole and for each quadrant in a manner similar to that described in Figures 10D-1 and 10D-2 for the determination of rotational bulk density. Rotational neutron porosity is neutron porosity of an earth formation surrounding a borehole corrected for standoff measured as a function of angular distance around the borehole.
Figure 4B illustrates a borehole which is surrounded not by a homogeneous formation, but by two different rock formations. The methods of this invention are ideally suited for accessing the degree of formation heterogeneity which exists about the borehole.
Using density measurements, or porosity measurements as disclosed herein, such signals as associated in each particular one of the plurality of angular distance segments defined by the apparatus of Figure 1 and Figures 3A and 3B, and according to computer program 310, a signal characteristic of the formations surrounding the borehole, such as density, PEF or porosity, is derived for each of the angular distance segments. Formation heterogeneity is assessed by comparing one signal characteristic of the formation from one angular distance segment to another. Such comparison may take the form of a simple differencing of such characteristic from one segment to another, or it may take the form of determining a statistical parameter such as standard deviation or variance of a characteristic, such as porosity or density, and comparing (e.g.
by differencing) such statistical parameter of one segment with another.
In_forrmtion Storm All of the output digital signals may be stored in mass memory devices (not illustrated) of computer 301 for review and possible further analysis and interpretation when the bottom hole drilling assembly is returned to the surface. Certain data, limited in amount due to band width limitations, may be transmitted to surface instrumentation via the drill string mud path from communications sub 400.
Various modifications and alterations in the described methods and apparatus which do not depart from the spirit of the invention will be apparent to those skilled in the art of the foregoing description. For this reason, such changes are desired to be included in the appended claims. The _~1~7101.
appended claims recite the only limitation to the present invention. The descriptive manner which is employed for setting forth the embodiments should be interpreted as illustrative but not limitative.

Claims (29)

1. A method for determining a characteristic of an earth formation surrounding an inclined borehole in which a generally cylindrical logging while drilling tool is received, including the steps of:
defining a cross-section of said tool which is orthogonal to a longitudinal axis of said tool, determining a bottom contact point of said cross-section of said tool which contacts said inclined borehole as said tool rotates in said borehole, separating said cross-section into at least two segments, where one of said segments is called a bottom segment of said borehole which includes said bottom contact point of said cross-section of said tool with said inclined borehole, applying energy into and circumferentially around said borehole from an energy source disposed in said tool, as said tool is turning in said borehole, recording measurement signals received at a sensor disposed in said tool from circumferentially spaced locations around said borehole, where said measurement signals are in response to returning energy which results from the interaction of the applied energy with said formation, associating said measurement signals with a particular segment during the time such signals are produced in response to energy returning from said formation as said tool is turning in said borehole, and deriving an indication of a characteristic of said formation as a function of said measurement signals associated with said bottom segment of said borehole.

2. The method of claim 1 wherein an indication of a characteristic of said formation is derived for each of said segments

3. The method of claim 1 wherein said energy applied into and circumferentially around said borehole is in the form of gamma rays radiated from a source of radiation, and said returning energy is in the form of gamma rays which result from interaction with said formation.

4. The method of claim 1 wherein said energy applied into and circumferentially around said borehole is in the form of neutrons radiated from a source of radiation, and said returning energy is in the form of radiation which results from interaction of said neutrons with said formation.

5. The method of claim 1 wherein said energy applied into and circumferentially around said borehole is in the form of ultrasonic pulses, and said returning energy is in the form of ultrasonic pulses which reflect from said borehole.

6.~The method of claim 1 wherein said cross-section is divided into bottom, right, top, and left segments.

7.~The method of claim 6 wherein said energy applied into said borehole is in the form of gamma rays, and said returning energy is in the form of gamma rays which result from interaction with said formation, the method further comprising the substeps of, recording the identity of a segment that said sensor is in while said tool is turning in said borehole, and recording the number of gamma ray counts of said sensor per segment for a certain recording time.

8. ~The method of claim 7 wherein said sensor includes short and long spaced gamma ray detectors spaced from an energy source which emits gamma rays into the formation, and further comprising the substeps of recording the number of gamma ray counts of said short spaced gamma ray detector per segment for a certain recording time, and recording the number of gamma ray counts of said long spaced gamma ray detector per segment for said certain recording time.

9. ~The method of claim 1 wherein the step of determining a bottom contact point of said cross-section of said tool which contacts said inclined borehole comprises the steps of, in a sub having x, y, z axes corresponding to respective axes of said logging while drilling tool, determining a .PHI. signal representative of an angle called .PHI. between an H x, H y vector, from magnetometers oriented along respective x and y axes of said sub and a G x, G y vector from accelerometers oriented along respective x and y axes of said sub, in an electronics portion of said logging while drilling tool, determining an signal representative of an H x, H y vector, with magnetometers oriented along respective x and y axes of said tool, transferring said .PHI. signal from said sub to said electronics portion of said logging while drilling tool, as said logging while drilling tool rotates in said borehole, determining a signal representative of an angle .PHI.(t) between an axis of said cross section of said tool and said signal measured with said magnetometers of said tool, and determining a signal representative of the angle of a down vector by subtracting said .PHI. signal from said .PHI.(t) signal.

10. The method of claim 9 wherein the step of defining a bottom segment includes the step of adding and subtracting fixed angles about said angle of said down vector to produce a bottom interval Q BOT(t) about said down vector

11. The method of claim 10 further comprising the steps of defining additional segments about the periphery of said tool.

12. The method of claim 10 wherein said bottom segment, Q BOT(t) is defined as a ninety degree quadrant bisected by said vector.

13. The method of claim 12 wherein four quadrants are defined by angular ranges about the periphery of said tool:
Q BOT(t) = ~angle - 45 ° to angle + 45°, Q LEFT(t) = ~angle + 45 ° to ~
angle + 135°

Q.TOP(t) = ~angle + 135° to angle + 225°, Q RIGHT(t)= ~angle + 225 ° to angle - 45°

14. The method of claim 13 wherein said sensor is oriented at a predetermined angle, called .alpha., with respect to an axis which is orthogonal to a longitudinal axis of said tool, and further comprising the step of determining the time interval that said sensor is in each quadrant by comparing said angle a with the angular range of each quadrant.

15. ~In a logging while drilling tool and system, having a source of gamma ray radiation and long and short spaced gamma ray detectors, a method for assessing density of an earth formation surrounding an enlarged borehole, including the steps of dividing a cross section of said borehole into plural borehole angular distance segments, detecting signals representing hard window count rates of gamma rays from said formation during successive time increments from said long spaced gamma ray detector and from said short spaced gamma ray detector while said tool is rotating and associating each of said count rate signals with one of said plural borehole angular distance segments, for a down segment of said borehole angular segments, determining a signal proportional to the difference in the variance of all said count rates from one of said gamma ray detectors for such down segment and an expected variance of such count rates for a circular borehole for such down segment, for said down segment, determining a density rotation correction factor, called .DELTA..RHO. ROT, representative of a density measurement correction needed to correct a density measurement of said down segment for borehole irregularity along said down segment, determining from said long and short spaced gamma ray detectors hard window count rates and associated with said one of said plural borehole angular distance segments, signals representative of density, called .RHO. segment,L, .RHO. segment,S, respectively, and determining a signal proportional to density of said angular distance segment, called .RHO.bROTsegment, as a function of said .RHO.segment,L, .RHO.segment,S, and .DELTA..RHO. ROT signals.

16. ~The method of claim 15 further comprising the steps of for each of said plural borehole angular distance segments, determining a .DELTA..RHO. ROT signal and a .RHO.bROTsegment signal.

17. ~The method of claim 15 wherein said down segment is determined as a function of time while said tool is rotating in said borehole according to the steps of in a sub having x, y, z axes corresponding to respective axes of said logging while drilling tool, determining an vector of H x, H y signals from magnetometers oriented along x and y axes orthogonal to a z axis along the longitudinal axis of said borehole, determining a vector of G x, G y signals from accelerometers oriented along respective x and y axes of said sub, and determining an angle .PHI. between said vector and said vector, and in an electronics section of said logging while drilling tool, determining an vector of H x, H y signals from magnetometers oriented along respective x and y axes of said tool, transferring said .PHI. signal from said sub to said logging while drilling tool, as said logging while drilling tool rotates in said borehole, determining a signal representative of an angle .THETA.(t) between an axis of said cross section of said tool and said vector measured with said magnetometers of said tool, and determining a signal representative of a down vector which constantly points to a contact point of said sub to the bottom of the borehole by subtracting said .PHI. signal from said .THETA. (t) signal, and adding and subtracting fixed angles about said down vector to produce a bottom interval about said down vector .

18. ~A method for determining photoelectric effect, called PEF, of earth formations surrounding a borehole in which a logging while drilling tool is received, said tool including a source of radiation, a short spaced gamma ray detector and a long spaced gamma ray detector, the method including the steps of identifying a down segment of said borehole, identifying particular angular segments of said borehole associated with said down segment through which said short spaced detector and said long spaced detector pass while said tool is rotating in said borehole, recording for a predetermined time period a count rate of gamma rays in said short spaced detector and in said long spaced detector as a function of said particular angular segments, where said gamma rays result from interaction of gamma rays from said source with said formations, and where said count rate of gamma rays of said short spaced detector and of said long spaced detector are recorded as to their respective energy levels called windows, thereby producing a spectrum of count rates with certain higher energy level windows being designated as hard windows and with certain lower energy level windows being designated as soft windows, determining average density, called .RHO.AVG, of the entire formation, and 46a determining a macroscopic cross section, called U AVG, of the entire formation as a function of total soft window count rate of one of said detectors and total hard window count rate of said one of said detectors, and determining an average PEF of said formation as a ratio of said macroscopic cross section to said average density, that is,

19. The method of claim 18 wherein said average density P AVG of said entire formation is determined from the steps of determining a total hard window count rate from said short spaced detector, determining a total hard window count rate from said long spaced detector, and applying said short spaced detector hard window count rate and said long spaced detector hard window count rate to a spine and ribs representation of the response of a two-detector density device to formation density and drilling mud and mudcake.

20. The method of claim 18 further comprising the steps of determining average density of a particular angular segment, called p AVG
segment, determining a macroscopic cross section of said particular angular segment, called U AVG segment, as a function of soft window count rate of said one of said detectors for said particular angular segment and hard window count rate of said one of said detectors for said particular angular segment, and determining an average PEF of said particular angular segment as a ratio of said U AVG segment to said p AVG segment, that is

21. A method for determining formation heterogeneity surrounding a borehole in which a logging while drilling tool is received including the steps of defining a cross-section of said tool which is orthogonal to a longitudinal axis of said tool;
separating said cross-section into a plurality of angular distance segments;
determining a bottom contact point of said cross-section which contacts said borehole as said tool rotates in said borehole;
applying energy into said formation surrounding said borehole from an energy source disposed in said tool as said tool turns in said borehole during drilling;
recording measurement signals received at a sensor disposed in said tool where said signals are in response to returning energy which results from the interaction of applied energy with said formation;
associating said measurement signals with energy returning from said formation while said sensor is in each particular one of said plurality of angular distance segments;
deriving at least one signal characteristic of said formation surrounding said borehole as a function of said measurement signals for each of said angular distance segments associated with said bottom contact point, and identifying formation heterogeneity as a function of said angular distance segments by comparing said at least one signal characteristic of said formation from one segment to another.

22. The method of claim 21 wherein said energy applied into said formation is in the form of gamma rays produced from 48a a source of radiation;
said sensor of said tool is at least one gamma ray sensitive detector;
said signals are gamma ray counts of said at least one detector; and said at least one signal characteristic of said formation as a function of said measurement signals for each of said angular distance segments is characteristic of bulk density.

23. The method of claim 21 wherein said energy applied into said formation is in the form of gamma rays produced from a source of radiation;
said sensor of said tool is at least one gamma ray sensitive detector;
said signals are gamma ray counts of said at least one gamma ray sensitive detector;
said at least one signal characteristic of said formation as a function of said measurement signals for each of said angular distance segments is characteristic of photoelectric effect.

24. The method of claim 21 wherein said energy applied into said formation is in the form of neutrons produced from a source of radiation;
said sensor of said tool is at least one neutron sensitive detector which responds to neutrons generated as a result of neutron-formation interaction; and said at least one signal characteristic of said formation as a function of said measurement signals for each of said angular distance segments is characteristic of porosity.

25. The method of claim 21 further comprising the step of determining a component of earth's gravity force vector in said cross-section of said tool according to the substeps of:
in a sub having x, y, z axes corresponding to respective axes of said logging while drilling tool, determining an vector of H x, Hy signals from magnetometers oriented along x and y axes orthogonal to a z axis along the longitudinal axis of said borehole, determining an vector of G x, G y signals from accelerometers oriented along respective x and y axes of said sub, and determining an angle .PHI. between said vector and said vector; and in said logging while drilling tool determining an vector of H x, H y signals from magnetometers oriented along respective x and y axes of said tool, transferring said .PHI. signal from said sub to said logging while drilling tool, as said logging while drilling tool rotates in said borehole, determining a signal representative of an angle .theta.(t) between an axis of said cross section of said tool and said vector measured with said magnetometers of said tool, and determining a signal representative of a down vector which constantly points to said bottom contact point of the borehole by subtracting said .PHI. signal from said .theta.(t) signal.

26. The method of claim 25 wherein the step of separating said cross-section into a plurality of angular distance segments includes the step of adding and subtracting fixed angles about said down vector to produce a bottom interval about said down vector

27. The method of claim 21 further comprising the step of approximately centering said logging while drilling tool in said borehole while said tool turns in said borehole during drilling.

28. Apparatus for determining a characteristic of an earth formation surrounding an inclined borehole comprising:
a generally cylindrical logging while drilling tool having a radial cross-section which is orthogonal to its longitudinal axis, means for determining a bottom contact point of said cross-section of said tool which contacts said inclined borehole as said tool rotates in said borehole, computer program means for separating said cross-section into at least two segments, where one of said segments is called a bottom segment of said borehole which includes said bottom contact point of said cross-section of said tool with said inclined borehole, energy source means for applying energy into and circumferentially around said borehole from an energy source disposed in said tool, as said tool is turning inside said borehole, sensor means disposed in said tool for producing signals in response to energy stimuli, means for recording measurement signals received at said sensor means, from circumferentially spaced locations around said borehole, where said measurement signals are in response to returning energy which results from the interaction of the applied energy with said formation, computer program means for associating said measurement signals with a particular segment of said borehole during the time such signals are produced in response to energy returning from said formation as said tool is turning in said borehole, and computer program means for deriving an indication of a characteristic of said formation as a function of said measurement signals associated with said bottom segment of said borehole.

29. Apparatus for determining formation heterogeneity surrounding a borehole comprising a logging while drilling tool having a cross-section which is orthogonal to a longitudinal axis of said tool, said tool including an energy source and a sensor for generating signals from energy stimuli returning to said tool from said formation surrounding said borehole;
means for separating said cross-section into a plurality of angular distance segments;
means for determining a bottom contact point of said cross-section which contacts said borehole as said tool turns in said borehole;
means for applying energy into said formation surrounding said borehole from said energy source disposed in said tool as said tool turns in said borehole during drilling;

means for recording measurement signals received at said sensor disposed in said tool where said signals are in response to returning energy which results from the interaction of applied energy with said formation;
means for associating said measurement signals with energy returning from said formation while said sensor is in each particular one of said plurality of angular distance segments;
computer program means for deriving at least one signal characteristic of said formation surrounding said borehole as a function of said measurement signals for each of said angular distance segments associated with said bottom contact point, and computer program means for identifying formation heterogeneity as a function of said angular distance segments by comparing said at least one signal characteristic of said formation from one segment to another.