STATISTICAL PRECISION OF NEUTRON-INDUCED GAMMA RAY ... · STATISTICAL PRECISION OF NEUTRON-INDUCED...

SPWLA TWENTY-SEVENTH ANNUAL LOGGING SYMPOSIUM, JUNE 9-13,1986

STATISTICAL PRECISION OF NEUTRON-INDUCEDGAMMA RAY SPECTROSCOPY MEASUREMENTS

B. A. RoscoeSchiumberger Weii Services

J. A. GrauSchh.imberger-DollResearch

P. D. WraightSchlumberger Well Services

ABSTRACT

With the increased use of neutron-induced gamma ray spectroscopy in the borehole environment, itis becoming more important for the user to understand the statistics of the measurement. The statisticsof both inelastic and capture induced radiation are affected by parameters such as borehole size andsalinity, formation sigma, neutron burst timing, and casing. By understanding how these parametersaf feet the statistical uncertainty, logging conditions can sometimes be optimized to produce better results.For example, the statistical uncertainty of the inelastic carbon-to-oxygen ratio is affected by the salinityin the borehole because of the increased capture background that is associated with the chlorine. Eventbough the saltwater does not affect the value of the carbon-to-oxygen ratio, it does affect the precisionto which it is determined. For the capture measurement, various parameters affect the partitioning ofthe signal coming from the borehole versus the formation; thus, the statistical uncertainty of themeasurements is affected by the magnitude of the borehole correction required. This paper shows howthe statistics in the borehole spectroscopic measurement are propagated and how these statistics affectthe interpretation models.

INTRODUCTION

The statistical precision of borehole measurements made for the oil industry is always a concern, Forelectric or sonic tools, the statistics are sufficiently good that there is rarely a concern for the repeatabili-ty of the logs even at relatively fast logging speeds. For nuclear logs, however, the statistics of the in-dividual measurements are usually noticeable even at low logging speeds. These statistics result fromthe physics of the measurement and are usually controlled by limiting the logging speed and by optimiz-ing the tool design for maximum count rates and minimum borehole signal. Because the statistical varia-tions of nuclear measurements are large relative to those of other logs, a thorough understanding is usefulin order to properly run and interpret a nuclear log. This paper will concentrate on the statistical analysisof spectral data acquired from the GST* gamma spectrometry tool. Background information on theusage and interpretation of the GST measurements may be found in the literature 1-’2and, hence, willnot be covered here.

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A gamma ray spectrum is a display of gamma ray energy versus intensity. As can be seen in Fig. 1,the spectrum can be due to several different elements superimposed on each other. Normal processing

,-*Mark of Schlumberger

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SPWLA TWENTY-SEVENTH ANNUAL LOGGING SYMPOSIUM, JUNE 9-13, 1986

of this type of spectrum results in the contribution of each element to the total gamma ray spectrum.For example, potassium, uranium, and thorium elemental yields are obtained from the spectrum of theNGS* natural gamma ray spectrometry tool, while hydrogen, silicon, calcium, chlorine, iron, sulfur,oxygen, and carbon are obtained from the GST spectrum. There is another type of gamma ray spectrumcalled a backscatter spectrum. This spectrum is not a superposition of spectra from different gammarays, but a spectrum of scattered gamma rays from a monoenergetic source. This type of spectrum isused in the Litho-Density* tool and will not be described in the statistical analysis given here. The statisticalanalysis presented here will deal specifically with the measurements obtained with the GST tool but couldalso be applied to those obtained with the NGS tool.

For the GST measurement, the measured spectrum is analyzed within a wide energy interval usinga weighted least-squares technique to produce elemental yields. The elemental yields are then used asinput to an interpretation program so that various petrophysically interesting parameters may be deriv-ed; e.g., oil saturation, water salinity, lit hology, and porosity. This paper describes the statistical errorsassociated with obtaining the elemental yields from the acquired spectrum. How these errors fold intothe interpretation model for determining oil saturation is also discussed.

THE WEIGHTED LEAST-SQUARES MODEL

The weighted least-squares model used for the GST data assumes that the measured spectrum canbe represented as a linear sum of single-element standard spectra. This assumption is valid as long as:1) all the elements producing gamma rays are included in the weighted least-squares fit and 2) pulsepile-up or other effects do not change the shape of the measured spectra. This linear model of measuredspectra can be expressed as:

ui=Esu Yj, . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . ...(1).i

where Ui is the number of counts in channel i of the unknown (measured) spectrum, Yjis the numberof counts from standardj in the measured spectrum, and SOis the relative number of counts in channeli of standard j, normalized such that

Xsjj= l . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . ...(2)i

In matrix form, Eq. I can be written as:

U=SY ...............................................................................(3)

where U is a matrix of the measured spectrum, S is a matrix of standards, and Y is a matrix of elementalyields. Since the spectral shape of the standards are known and the equation is overdetermined, the elemen-tal yields Y can be solved for by weighted least squares. The solution has the exact form given below: 13-15

Y= (Sws)-l swu, . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . ...(4)

-,,,

“---

-2-


,-,.

where W is a diagonal weighting matrix. The formulation of the weight matrix will be described later.

Since, for the GST tool the neutron output is varied with logging conditions to maintain a high con-stant gamma ray count rate, the elemental yields of Eq. 4 are divided by the total number of acquiredcounts to give relative yields; i.e., that fraction of the measured spectrum that is from each element.

YY

norm =—, . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . (5)u tot

where

u =X U;. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . ...(6)lot i

STATISTICAL ANALYSIS

For nuclear counting measurements, where one counts the number of events ZV,the standard devia-tion of the raw measurement is simply the square root of the number of counts observed in any periodof time. 16

u= fi . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . ...(7)

The variance of this measurement is the square of the standard deviation and is written as U2.Whenperforming weighted least-squares fitting, the fit is weighted by the variance of the data being fit. Forsolving Eq. 4, the weight matrix is a diagonal matrix W where the diagonal terms have the form

Wig= + ............................................................................(8)‘i

where u? is the variance of the data in channel i.13-15

If the spectrum being fit is the measured spectrum (i.e., no background subtraction), then W can beeasily calculated from Eqs. 7 and 8. If a background subtraction is performed on the measured spec-trum, then the spectrum being fit is

Ui=Fi_~Bi, . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . ...(9)

where Fi and Bi are the number of counts in channel i of the foreground and background spectra and/3 is the background subtraction factor. Both the foreground and background spectra have variance,and the variance must be propagated through the subtraction to give the variance of the net spectrumbeing fit, U. It can be shown that the variance in channel i of the background-subtracted spectrum is13

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u~=Fi+~2Bi . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . ..(10)

-3-


If one defines

~Bi

a=Fi. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . (11)

then

~~=Fi(l +~a) . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . ..(12)

For the weighted least-squares solution ofEq.4, with the normalizationof Eq.5, itcan beshown thatthe error intheelementzd yields Yno,m can be calculated from14

CT*Ev= —, ..................................................... . . . . . . . . . . . . . . . . . . . ..(13)

u tot

where E is defined by

E =(StWS)-l >. . . . . . . . . . . . . . . . . . . . . . . . . .. . . . . . . . . . . . . . . . . . . . . . - . . . . . . . . . . . . . . . . . . . . . (14).,..

and

CA+ . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .(15)i

Matrix E iscalled the error matrix of the weighted least-squares fit and is actually a variance-covariancematrix. Thediagonal terms ofEcontain the relative variances ofthe parameters being fit while the off-diagonal terms contain the covariances between these parameters. When the total variance&is multipliedbytherelative varianc&covariance matrix E, thetotal variance-covariance matrix Vofthe fit can befound. Itshould be noted that Utotisin thedenominator of Eq. 13totransform thevarianceof Ytothe variance of Ynorn.

To better look at the sources of error in the measurement, it is useful to rewrite Eq. 8 to show explicit-ly the count rate information it contains. If the variance of channel i is divided by the total numberof counts Ufof,then

u totWii = —~2 ‘ “”””””””””””””””””””’””””””” ““” ”””””””””””””””””””””””””” ‘“”””””””””””””

.(16)i(n)

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where u? represents a normalized variance independent of count rate. Definingl(n)

E’ =EUtot . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . ...........................(17)

and combining Eqs. 6, 9, 11, 12, 13, 15, and 17,

“ = E’ (BSVF)

F, . . . . . - . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .(18)

tot

where the background subtraction variance factor BSVFis

l+cY/3BSVF =

(l-a)2' """"" """" ""'" """" """"" """" """"" """"" """"" "o<" """"" """" """"" fl""" """"(19)

and the number of counts in the foreground spectrum Fto[ is

Ftot =ZFi . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .........(20)i

SOURCESOFERROR

As can beseen from Eq.18, theerrorin the final normalized elementalyieldsYno,M for aGSTmeasure-ment is a function of three factors: 1) the shape of the elemental standards E’, 2) the amount ofbackgroundsubtracted fromtheforeground BSVF, and3)the total numberofcounts intheaccumulatedspectrum. If one wishes to improve the statistics of a measurement, more counts will increase FIOl anddecrease V. This can be achieved either by increasing the count rate by increasing the source strengthor by reducing the logging speed. Increasing the source strength assumes that the detector and electronicscan handle the higher count rates. Since most nuclear tools are run at their maximum count rates, thisis not always possible. Therefore, running at lower logging speeds is the usual alternative.

It is not generally possible to reduce the value of E‘ since the shape of the elemental standards isfixed by the physits. However, it can be optimized by having the best possible detector resolution.

The amount of background subtracted varies with several parameters and can be improved to somedegree. Basically, the less background there is in the measurement, the better the statistics will be. Theamount of background may be minimized by tool shielding and tool timing considerations. The amountof background will also vary depending on the tool environment. For example, in the GST carbon-to-oxygen ratio (COR) measurement, the ratio of inelastic to capture gamma rays will be lower in a highlysaline area relative to a freshwater area. Since there are more capture gamma rays in the saline case,more background must be subtracted from the foreground measurement. Therefore, the error on thedetermination of COR in a saline area will be larger than that in a freshwater environment.

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ERRORS IN COR

Once the errors of the normalized elemental yields are found, errors on elemental ratios can becalculated. The COR is calculated from the elemental yields of inelastic carbon (IC) and oxygen (IO).

IcCOR = —

10 ““”””””””””’”””””””””””””””””””””””““”””””””””””””””””””””””””””””””””..(21)

The error in the COR is calculated from the variances of carbon and oxygen and the covariance betweencarbon and oxygen. The equation to calculate this has the following form:

(~2 <

;Or=cOR&+—02

)

–2~Ic 10

!.........’.....................................Ic 10

(22)

where O&r, o:, and u: are the variances of COR, IC, and IO, respectively. u: ~ is the covariance be-tween carbon and oxygen and is obtained from the variance-covariance matri; V of Eq. 18. For pur-poses of discussion, it is helpful to make a simplifying assumption to Eq. 22. The assumption is thatthe second and third terms of Eq. 22 are small compared to the first term. These terms are not negligi-ble, but are small for many situations. With this assumption, Eq. 22 will reduce to

.0:

~2=_

IO “ ““” ””””””””””””””””””””””””””””’””” ““” ””””””””””””””””””””””””””””””””. . (23)

Cor

Eq. 23 adds insight to the GST COR measurement since the statistics on COR are dominated by theerror on carbon and by the amount of inelastic oxygen present. Since the oxygen content measured ina cased hole is less than that measured in an open hole, the error on COR will always be larger in acased hole than in an open hole. This can also be said for an oil-filled borehole since the water, whichcontains oxygen, is replaced by oil, which does not contain oxygen. It should also be noted that foroil-filled boreholes, the second and third terms of Eq. 22 become larger and the actual increase in theerror of COR is larger than one would predict from Eq. 23.

Since u: is controlled by the parameters of Eq. 18, the error on COR is also directly influenced by them.As described earlier, the salinity of the borehole environment will affect the variance on carbon by af-fecting the value of BSVF. Other parameters that affect BSVF will also affect the error on COR. Forexample, if the neutron burst is not properly positioned, the capture background in the inelastic spec-trum will increase and cause BSVF to increase. On the other hand, the presence of the fluid displacersleeve on the tool will reduce the capture background since it is loaded with boron. The boron competeseffectively with other elements in the borehole to absorb thermal neutrons. Since boron’s gamma rayis below the energy where the spectral fitting is performed, the boron effectively reduces the capturebackground in the measurement. This will cause BSVF to decrease.

The effect of detector resolution on u: is nonnegligible due to the increase of E‘. For the weighted least- ---%squares fitting process, the detector resolution is parameterized by the resolution degradation factor (RDF).

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,—

The RDF is a relative measure of detector resolution and represents the amount of gaussian broadeningthat must be applied to the standard spectra to degrade them to the same resolution as the measuredspectrum. As can be seen in Fig. 2, at an RDF of three, the error on carbon would be 10qo higher thanat an RDF of zero. This loss in precision is purely statistical and is recoverable by increasing the totalnumber of counts; i.e., by logging longer.

EXPERIMENTAL VERIFICATION OF STATISTICAL ERROR ANALYSIS

Having derived the theoretical statistical analysis for the gamma ray spectral measurement, it mustbe experimentally verified. The experimental verification serves two purposes: 1) insures the derivationwas done properly and 2) insures that the tool is working as it should. If the obtained statistical precisiondoes not match the theoretical precision, then there is a serious problem in the operation of the tool.

To verify the agreement between the actual and theoretical precision, many repeat measurements havebeen made to compare the theoretical precision with the actual obtained precision of the tool. Fig. 3shows an example of the repeatability of the GST COR measurement taken in a 15-P.u. limestone for-mation. The tool was run in a 6-in. open hole with a 4.25-in. fluid displacer sleeve and the data wereacquired by taking 799 18-second spectral accumulations. A theoretical precision of 0.0307 was calculatedfor an 18-second measurement. Fig. 3 is a histogram showing the distribution of COR values actuallyobtained in the 799 18-second measurements. The symmetric and gaussian shape of the distribution in-dicates the stability of the measurement. The width of this distribution is 0.0302 and is the standarddeviation of an 18-second measurement. The agreement between the theoretical value of 0.0307 and ob-tained value of 0.0302 indicates the statistical, electronic, and nuclear robustness of the GST measurement.

CONCEPT OF STANDARD DEVIATION

At this time, it is advantageous to discuss the concept of error in a truly statistical manner since thisis usually a point of confusion. A simple example is useful. Suppose you measure the length of a 24-in. -long steel rod to the nearest one-thousandth of an inch. If you did this 20 times, you would not getthe same length each time; you would get a distribution of measured lengths. The standard deviationof these 20 measurements would be a measure of how well you could measure the length, and the averagevalue would be your best approximation of the true length. For example, assume you measure the lengthto be 24.002 f 0.003, where the 0.003 is the standard deviation of all your measurements. This doesnot mean that all 20 measurements were within 0.003 of your average value; some measurements mayhave been 0.005 away from the average value. One standard deviation means that 68070of yourmeasurements were within 0.003, or that there is a 68V0 probability that any one of the measurementsis within 0.003 of the true value. This is called the 1-u error and is illustrated in Fig. 4. If you wantto be more confident that the true length is within your error bars, you could report a 2-u error of 0.006on the measured value. This means that there is a 95070probability that the true length of the rod iswithin 0.006 of your measured value. For normal physical measurements, such as length, 3-u errors areusually reported. The 3-u error is the 99070confidence level. For this example, the 3-a error would meanthat there is a 99V0 probability that the true length is within 0.009 of the measured value.

Unfortunately, 3-u errors are used by the average person on the street while l-u errors are usuallyreported in any measurement where truly statistical processes are concerned. Hence, errors on CORmeasurements are reported at the 1-u level and therefore mean that the true value of COR has a 68qo

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-.chance of being within the error bars. If one desires more confidence in the reported value of COR,he must look at the 2-u or 3-u level of confidence. This is an important consideration in properly evaluatinglog data.

OPTIMUM COR LOGGING

As is obvious from the earlier discussion, the error on COR is not a constant for all conditions. Theerror will vary depending on how much chlorine is present downhole, the neutron burst position, casedor open hole, logging speed, and several other parameters. Because of this, it is important to have agood logging strategy before going to the wellsite to insure one comes back with the required informa-tion. The suggested logging procedure involves three steps: 1) establish the desired confidence level ofthe data: l-u, 2-u, or 3-u; 2) establish the error in COR required to obtain this confidence level; and3) log until that error in COR is reached (if it is obtainable in a reasonable period of time).

The best way to explain this logging strategy is by example. Assume the well to be logged is a sand-stone lithology of about 25qo porosity. The borehole is 8.5 in. with a 5.5-in. 14-lb/ft casing. The oilsaturation needs to be measured to * 10 S.U. The chart of Fig. 5 roughly represents the conditions ofthis example. The required COR precision for A 10 S.U. is about 0.013. This is the 1-u error, or the68% confidence level. If a 95V0 confidence level (2-u) is required, then the required l-u precision wouldbe halved and 0.007 would be required. Fig. 6 shows the ‘approximate’ time required to achieve a specificprecision for cased boreholes. As can be seen, a precision of 0.013 can be obtained in about 3 minutes,whereas the 2-u precision of 0.007 would require about 12 minutes; i.e., to double the precision of theCOR measurement requires quadrupling the logging time.

It is very important to note that the times given in Fig. 6 are approximate, since the error on CORvaries with many parameters as was described in the previous sections. If it is found, during the actualjob, that extra time is required to obtain the required COR precision, then the extra time should be taken.This is possible since a measure of the l-u COR error is constantly updated while COR stationmeasurements are being made. One simply continues the measurement until the required precision isobtained. An example of this can be seen in Fig. 7.

If one repeats the above example with oil in the borehole, another important observation can be made.From Fig. 8, the required COR precision for A 10 S.U. is about 0.021, which is much higher than therequired precision with water in the borehole. However, from Fig. 6, the approximate time to reachthis COR precision is still about 3 minutes. Therefore, nothing has been gained statistically by havingan oil-filled borehole.

There is one more source of error that needs to be taken into account before coming up with the oilsaturation. That is the error resulting from the propagation of borehole corrections into the interpreta-tion model. It is obvious that the amount of borehole correction on COR is much larger for an oil-filledborehole than for a water-filled borehole. This can be seen in Fig. 9 in the fact that the correction re-quired to COR for the oil-filled borehole is larger than the dynamic range of the measurement in thewater-filled borehole. This is described in more detail in the literature.9 Since a larger correction is re-quired for the oil-filled borehole, the final error left in the value of oil saturation will be larger. Thisis why it is preferable to log in a water-filled borehole rather than in an oil-filled one. The worst situa-tion is a mixture of oil and water in the borehole.saturation is dominated by how well the borehole

In this case, the error on the determination of oiloil-water mixture is known.

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Because of the reasons described in this paper, there is a difference in the final statistics of the oil-saturation determination depending on the borehole condition. The best condition is a freshwater borehole.Saltwater in the borehole is the second choice because of its effect on the carbon yield statistical error.Oil in the borehole is the third choice since the corrections required to the COR are large. A mixtureof oil and water in the borehole will have the highest uncertainty since the oil-saturation uncertaintywill be dominated by the uncertainty in the mixture of oil to water.

CONTINUOUS COR LOGGING

In some situations, it is practical to log COR in the continuous mode with adequate statistical preci-sion. To determine if this is possible, one must first determine the required precision. Second, one mustdetermine what COR precision can be obtained in 5 minutes. This should be determined downhole byperforming a 20-minute station (the precision obtainable in 5 minutes is two times the precision obtainedin 20 minutes). However, the chart of Fig. 6 could be used beforehand to get a rough estimate. Theratio of tool precision in 5 minutes to the precision required may then be calculated. From this ratioand Fig. 10, the necessary logging speed can be obtained (if one assumes how much depth averagingto use). Since more depth averaging implies that less vertical resolution will be obtained, the amountof depth averaging must be considered carefully. For example, suppose the required COR precision is0.015 and the precision in 5 minutes is 0.012. From Fig. 10, the necessary logging speed is about 45ft/hr with the data averaged over 2.5 ft. Having determined this, the number of continuous passes that ccneed to be averaged over the zone of interest is the practical logging speed divided by the necessary log-ging speed. For this example, assume that the practical logging speed is 200 ft/hr. The number of passesrequired will be 200/45, or about five passes.

SUMMARY AND CONCLUSIONS

This paper has described the basic factors affecting the statistical precision of the GST tool. Withan understanding of these factors and by the use of a proper logging strategy, quality data and inter-pretation to determine oil saturation may be obtained. Even though the details of GST capture loggingstatistics were not covered here, the general statistical analysis described also holds for capture yieldsand ratios.

Finally, this paper has given a general derivation of the statistical precision that can be obtained froma spectroscopic measurement. It must be pointed out that the derivation given here is based strictly ontheoretical grounds. To insure that the theoretical derivation is correct, many repeat measurements havebeen performed,with the GST service to prove that the statistical precision obtained matches the theory.This is an important test in the proving of any downhole measurement. If the actual tool performancedoes not match the predicted theoretical performance, then there is a serious problem in the tool itself.Problems of this nature do not surface unless tests of this sort are performed. The GST performancedoes match the theoretical performance described in this paper and, hence, can be considered a wellunderstood and statistically robust measurement.

f-

-9-


F“’’’’’’’’’ r”’’’’’’’’’’’’’’’’’’”

L10nl

234567Energy (MeV)

Figure l—Example of a multielemental gamma ray spectrumcontaining only iron and silicon. The standard spectra ofsilicon and iron are also shown.

I

0.15 0.20 0.25 0.30 0.35

Value Of COR

Figure 3—Distribution profile of COR values obtained from799 18-second spectral accumulations made in a 15-p.u.limestone formation. The tool was run in a 6-in. open holewith a 4.25-in. fluid displacer sleeve.

I I I ! I

1 2 3 4 5 6

Resolution Degradation F!actor

Figure 2—Relative precision of carbon versus resolutiondegradation factor. The precision is relative to the precisionof carbon at a resolution degradation factor of zero.

23.994 23.987 24 24.003 24.006

Measured Rod Length (in.)

..

3-o99% Confidence

k------ 2-095%Confidence

k

b- 1-U ~: 68% Confidence ;

Figure4—Gaussian probability distribution for measuringa 24-in. rod with a 0.003 standard deviation.

,-..

-1o-


\ 1 1 I 1 J

0045;!---::--:

,-.

/-.

0.040

Gg 0.035.*oE 0.030alx~ 0.025

0.010

0.005

[am””-’’:’-;”/”12-b Borehck S54 -ill. U1-lb/ft csalns . . :.-.....- . . .

. 6-lIL Borehola 5-iII. lS-lb/ft CaaiDI

:::

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

,.. it 1 1 1 1 1

10 20 30 40

Porosity (%)

Figure 5—Required COR precision to obtain 10 S.U.repeatability on the value of Sw for water-filledcasedholesof various sizes.

WcF I --r”’ ‘-.D “ W.**4

9M–So.i,@

Sm!xcn )#.i 39**. 7000.8

Scgfi ~-8. ●-* C. S99G .03s0 -.8s80 . 6s88.a

ICs. __ ___ cmS.**o@ -s. 000 -.mc* ,.igimii----,o,,o,

@u?-19.00 1*.D9D -e.000 3.0004

av~-Q!3w nDcG

I.mba 2.000 3.9*JJ

I I I I I I

,,

.,,..a:>o~!,:~.!~ad,n,p.~ho~:,,,

. . . ... . . . .

----- ;-. :... . . . . . . . . . . . . . . . . .. . . . . . . . .. . -.---- z....

t’””-’”:”-””””:””””--:”””;-~--’-~

Figure 6—Approximate time required to obtain a specificCOR precision for various borehole configurations.

0.050

0.045

z 0.040%

“~ 0.035t

; 0.030

0a 0.025~

.3 0.020

g 0.015

0.010

0.005

:,....!%?f!wp!?kiyf?yf?.... . .. ... ...... ....... ......-In. I+-lb/ncamillg_. a-in. Bomsiola: s-in. Is-lb/n earinr

::: ::

..

:,,

./: . . . . . . . . . . . . . . . . . . . . . . .:.....,.....:.....:,..

,::r 1 i 1 1 1

10 20 30 40

Porosity (Z.)

Figure 7—Log time station output film. The curve SCOA Figure 8—Required COR precision to obtain 10 S.U.shows the standard deviation of the final COR value in real repeatability on the value of Sw for oil-filled cased holes oftime. The curve NBPR shows the neutron burst position, various sizes.and the curves ADCG and ADCZ show the gain and offsetregulation stability.

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Gov

0.5

0.4

0.3

0.2

0.1

0.0

I I I I,’

-EiizEzl d,.’

,.’,..

.,.,

.,,.~.

-.. .

..-

1 1 I I I I10 20 30 40

Porosity (%)

Figure 9—COR fan curves for an 8-in. borehole, with 5.5-in.casing, in a sandstone formation with water and oil in theborehole. Note that the offset in COR caused by oil in theborehole is about as large as the dynamic range of the CORmeasurement.

-s 120

&

~ 100G‘Gilam 60

3

0.6 0.8 1.0 1.2 1.4 1.6 1.8

Tool Precision In 5 MinutesRequired Precision

Figure 10—Necessary logging speed for continuous inelasticlogging at different vertical resolutions.

.

REFERENCES

1. Hertzog, R.C.: “Laboratory and Field Evaluation of an Inelastic-Neutron-Scattering and Capture Gamma Ray SpectroscopyTool,” Sot. Pet. .Errg. J. (1980) 327-333.

2. Westaway, P., Hertzog, R., and Plasek, R.E.: “The Gamma Spectrometer Tool Inelastic and Capture Ganrma-Ray Spec-troscopy for Reservoir Analysis, ” Paper SPE 9461 presented at the 1980 SPE Annual Technical Conference and Exhibition,Dallas.

3. Hertzog, R. and Plasek, R.: “Neutron-Excited Gamma Ray Spectrometry for Well Logging,” Trans. on Nuclear Science,

IEEE, NS-26 (1979).

4. Schweitzer, J .S., Manente, R.A., and Hertzog, R.C.: “Gamma-Ray Spectroscopy Tool Environmental Effects,” J. Pet.

Tech., 36 (1984) 1527-1534.

5. Flaum, C. and Pirie, G.: “Determination Of Lithology From Induced Gamma-Ray Spectroscopy,” Trans., SPWLA 22ndAnnual Logging Symposium, Paper H, 1 (1981).

6. Gilchrist, W.A. Jr., Quirein, J. A., Boutemy, Y.L., and Tabanou, J. R.: “Application Of Gamma-Ray Spectroscopy To For-mation Evaluation, ” Trans., SPWLA 23rd Annual Logging Symposium (1982).

7. Grau, J. A., Antkiw, S., Hertzog, R.C., Manente, R. M., and Schweitzer, J. S.: “In Situ Neutron Capture Spectroscopy OfGeological Formations, ” Proc., 1985 AIP Conference, 125, 799.

8. Grau, J.A. and Schweitzer, J .S.: “Elemental Analysis Of Oil Wells Using NaI(Tl) and 14-MeV Neutrons,” Tmns., AmericanNuclear Society, 43260 (1982)

9. Roscoe, B.A. and Grau, J. A.: “Response of the Carbon/Oxygen Measurement For An Inelastic Gamma Ray SpectroscopyTool,” paper SPE 14460 presented at 1985 SPE Technical Conference and Exhibition, Las Vegas.

10. Grau, J. A., Roscoe, B.A., and Tabanou, J. R.: “A Borehole Correction Model For Capture Gamma-Ray Spectroscopy Log- -,

ging Tools,” paper SPE 14462 presented at 1985 SPE Technical Conference and Exhibition, Las Vegas.

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11. Hull, R.L. and Johnson, D.E.: “The Muldoon Field: An Evaluation Of Behind-Casing Pay Zones,” paper SPE 14464presentedat 1985 SPE Technical Conference and Exhibition, Las Vegas.

12. McGuire, J. A., Rogers, L. T., and Watson, J .T.: “Improved Lithology and Hydrocarbon Saturation Determination Usingthe Gamma Spectrometry Log, ” paper SPE 14465presented at 1985 SPE Technical Conference and Exhibition, Las Vegas.

13. Bevington, P. R.: Data Reduction and Error Analysis for the Physical Sciences, McGraw-Hill, New York (1969).

14. Clifford A. A.: A4uhivariate Error Analysis, Applied Science Publishers, London (1973).

15. Montgomery, D.C. and Peck, E. A.: Introduction to Linear Regression Analysis, John Wiley & Sons, New York (1982).

16. Knoll, G. F.: Radiation Detection and Measurement, John Wiley & Sons, New York (1979).

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