615 IEEE TRANSACTIONS ON NUCLEAR SCIENCE, VOL. 42, NO. 4, AUGUST 1995

Abstract

ACCURACY OF SPECTRAL GAMMA-LOG INTERPRETATION MODELS

D.A. Kozhevnikov*, N.Ye. Lazutkina**, and B.Yu. Melchuk** * State Oil&Gas Academy, Lenin avenue 65, 117917 Moscow, Russia VNIIGeosystem, Varshavskoe shosse 8, 113 105 Moscow, Russia **

Considered are benefits of new interpi&ition models of tlic natural spectial gamma-lay log based on the application of the analytical algorithms of radial "geometrical factors". A combined technique of computer simulation and analytical interpretation niodcls is used to study the influence of geological and downhole conditions and statistical errors on the accuracy of interpretations of spectral gainnia logs. A coniparisoii bctwceii analytical algorithms and those based on the reduction to standard downhole conditions is presented. The analytical structure of tlie new interpretation algorithms provides upper estimates of the interpretation accuracy and concurrent coniputation of radionuclide abundances.

I. INTRODUCTION

Analysis of the accuracy of potassium, uranium, and tlioriuni abundances is of crucial importance for tlie natural spectral gaiiinia log (SGL) in tlie petroleum sections characterized by Clarke's abundances of natural radioactive elenicnts (NRE). One should take into coiisideration tlie intensity and character of various technological effects influencing abundance estimates derived from spectial gamma logs. lliese estimates are of special importance for subsequent quantitative geological and petrophysical interpretation of SOL data involved in the coniplex interpretation of logging results.

This paper presents the SGL interpretation model and results of its verification. The analytical interpretation algorithiii allows one to calculate upper estimates of tlie interpretation accuracy, detection thresholds and abundances of NREs in intermediate zones of the "borehole-formation" system concurrently with those in formation as itself.

Basic enviroriniental effects and sourccs of errors produced in a conventional correction-based intciprctation tcchniquc arc analyzed. The benefits of tlie aiialytical algorithm allowing the direct "correction-free" interpretation and its accuracy characteristics are considered. The assessment of potential errois is based on tlie original software system combining the solution of direct and inverse problems of tlie spectral gamma log.

11. INTERPRETATION ALGORITHMS AND MODELS

Conventionally the accounthig of geological- technical downhole conditions in the "boreliole- formation" system is made with tlie aid of various experimental correction cliaits which do not cover a whole diversity of environmental effects [.1].

The proposed interpretation model provides a quantitative description of a static anomaly amplitude of the spectrometer response J i in tlie it11 spectral channel for a thick-saturated formation at given nieasurement conditions and NRE abundances: specified separately for all intermediate zones and formation as itself (formation is tlie Ntli zone) 121:

k j where Cjj is the tool's response in the itli channel

related to a uiiit mass abundance of the jtli radionuclide if no intermediate zones are present (dry open hole); G h j is a relative contribution of the kth zone into tlie resultant count rate relating to tlie jtli radiator in tlie ith channel (an integral radial geonietrical factor of thc ktli zone); qkj is thc . abundancc of the jth radiator in tlie ktli zone; k is the zone index (k=l, ..., N).

Actually the interpretation algoritlini is an analytical conversion of tlie interpretation inode:. Latter can be oresented as follows:

i Ii = Ji - 4 ;

N-1 (3)

k=I j

where Cjj is tlie concentration sensitivity defined as the increment in tlie count late in tlie itli differential channel per a unit mass coiitent of the jtli radiator at tlie absence of intermediate zones; Fi is the it11 background response conipoaent; Ji is total radiation of all zones registered by the itli channelof tlie tool; Ti is tlie formation radiation to tlie ith channel. Mas:. abundaiices of NRE are computed by calculatitig background response components and solving system

The mathematical apparatus of geometrical factors allows a- detailed accounting of, geological and

(3).

0018-9499/95$4.00 0 1995 IEEE

open and cased lioles of various constiuctions, with various drilling mud compositions and densities. Those cliarts for the spectral correstion factors allow one to convert a lionstandard spectrum covering tlie range of 0.1-2.8 MeV iiito an equivalent standard spectrum (relating to nieasureniei!t conditions assumed as standard ones) for a given radiator type. Thorium (with its fission products) was used as the radiator.

We have computed a iadhl sensitivity as the function of energy for an open water-fdled hole (Fig.2). Based on this depeiidence and model (l), we computed energy depeiidence of correction factors for cased lioles of various constiuctions. Holes were filled witli tlie C ~ C I ~ solution of tlie 1.2 g/c1113 annulus - filled with the cement of tlie 2.2 g/cm density3

sizes, 111111

density. Tlie coniparison of our results exyeriniental ones [4] is presented in Fig.3.

K, % I U, ppni I TIi, yyni I I

Soectral Correction Facrors

50 X 150

50 X 250

0.0 0.6 10 I6 2.0 2.6 3.0

Energy (MeV)

0.065M.009 0.254M.050 1.30M.39

0.033M.005 0.390M.066 0.53M. 1 1

Fig.3. Coniparison of correction factors for different cased holes coniputed by formula (1) line) vcisus those presented in [4) (thin lines).

with

three (solid

Wlieii applying a niul tichannel iiiodification of SGL one has new iiietliodical capabilities: accounting of variations of background abundances over the borehole and of corrosion wear of casing strings, determination of forniation photoelectric absorption index, and so on.

111. THRESHOLDS OF NATURAL RADIONUCLIDE DETECTION IN THE

"BOREHOLE-FORMATION'' SYSTEM

As applied to the gamma-lay spectrometry, tlie detection threshold is such mass abundance of tlie jtli radiator (at given abundances of other iadiatow) which guarantees a reliable idcntificatioti of an

absolute anomaly at tlie triple mean-square deviation background level. The proposed interpretation nioilz' allows to take into considemtion measuremen\ geometry parameters and abundances of radiators in intermediate zones for an arbitraty type of spectral gaiiiiiia logging tool.

thresholds grow with iiiass thickness of interniediate zones (Fig.4,a) and with abundance of radiatols in those zones (Fig.4,b). I n a practically valuable case of active intermediate zones, tlie detection thresholds of large-volume detectois may be both higher or lower tlian those of small-volun1e detectois depending on the yropoitions of radiatots i n tlie intermediate zones. The table presents detectioll thresholds for two sizes of ciystnl detectois relating to basic conditions.

Tlie NRE detection

Borehole Diameter, cm

t J Minimal I Detectable 'Vdue8, ppm I I 1

0 1 8

Uraniun Content Ir Mud Fluid, ppm

Fig.4. N RE dclectioii tliicslioltls VCISIIS I I I ; ISS

abund:iiice (b) (at fixed potnssiuiii and tlwriuiit Iiiickircss 'I' or flusliiiig lluitl (il) iiiid umiiiiiii

clbu 1id:r IICCS).

Table I Crystal I Detection tliresliolds: I

617

borehole measurement conditions owing to the

- radial sensitivities Ai- [2]. This characteristic is where d ~ , is tlie geometrical factor of the jtli defined as a logarilhmic decrement of the radiator of formation fro the ith differential channel; intermediate zone geonietrical factor with respect to T is the total mass thcikness of the intermediate zone. its mass thickness:

introduction of new tool's metrological characteristics Ai' = 6(ln GNij)/GT, (4)

Fg.1. Algorithm of the SGL inverse problem solution.

111. VERIFICATION OF INTERPRETATION Since the drilling mud always comprises particles of

bored rocks and proportions of NRE in the SPECTROMETRY. intermediate zones (drilling mud, mud cake, colniatage zone, etc.) always vary, the inteipretation algorithm must take into account those variations.

MODEL OF THE MULTICHANNEL

Interpretation model (I) is valid at an arbitmy number of spectral channels. Yet, at a large number of

Particularly, these formulas define the Channels, metrological characteristics C;; and Aij turn interpretatioti- parameter of the integral gamma-ray out to be functions of gamma-ray enc channel - the total mass abundance of radionuclides, expressed in the units of equilibrium uianium abundance (uianium equivalent units eU [3]):

eU = C e U j . q j , (4) i

where eUj is the uranium equivalent of the jtli radionuclide; qj is the mass content of the ith radiator. Thus, the value of eU has an exact petrophysical sense.

The algorithm defines background response components in spectial channels and also the thresholds of the sensitivity to tlie NRE abundances with due regard of actual mass thicknesses of

Ti'. ACCURACY OF SPECTRAL GAMMA-RAY LOGGING METHOD

Tofal error of SGL L

The accuracy of SGL deterinination has been assessed as tlie upper estiniates of its error. The SGL resultant error includes two basic error types (Fig.5). There exist noriremovable systeniatic errors which can be estimated a priori, Le., before logging operations (errois owed to calibration discrepancies and prograni- algorithmic ones). Other erron are random by their nature, they occur immediately in the couise of logging measurement.

I I

Fig.5. Mechanism of error propagation in the SGL.

The systematic error components of SGL were coniputed by direct comparison of experimental data (obtained in certified formation models) and high- precision Monte-Cai-lo modeling results (mathematical simulations) versus theoretical results based on

0 5 1 0 1 5 2 0 2 5 k 1

"geometrical factois" technique. Systematic errors are formed as an accumulating sum of the following uniformly distributed components: errors of certification of formation models reproducing NRE refererice values; calibration errois owed to discrepancies in concentration and radial sensitivities, and program-algoritliiilic ones.

Random error components were estimated with thc aid of sensitivity coefficients which are defined as tlie ratio of the variation of the jtli mdionuclide mass abundance to the variation of an arbitraiy factor xlii (geological, environniental, etc):

(5) v w l , 1 var(xn,)

s n y =

The sensitivity coefficient SIlij is the measure of the influence of the nitli factor variation on the accuracy of the jtli radionuclide abundance. It was found that tlie influence of sonic factois, studied i lk ;I wide range of values, has a nonlinear behavior. The influence of measurement statistics error was calculated as the ratio of the variation in tlie jtli radionuclide abundance to tlie count rate variation i n the it11 spectrometer channel simulated by tlie Monte- Carlo method.

V. ANALYSIS OF BASIC DEPENDENCIES

From the analysis of the analytical intei-pretation model it follows that depending on proportions of the same radiators in intermediate zones and mass thicknesses of those zones, latter can play the role of shielding screens or can be additional radiatois. This results in principally different effects of environniental conditions on the spectrometer response at vaiyinL proportions of radiator abundances in formation and intermediate zones. It should be noted that the latter factor cannot in principle be accounted for within tlic framework of n coiivcntional "reduction to stnndara conditions" teclinique.

0 1 2 3 4 5 6

1.4

1.2

1 .

- lo/' 0.0 I I

0 0.2 0.4 0.0 0.0 1

T(mud cake), g/cm2 E Ttmud f luid) . g/cm2

Fig.6. Dependence of paranieter P(.) on the mass thicknesses of drilling mud and mud cake, and tool's eccentricity for different proportions of radionuclide abundances in formation and flushing fluid. Legend - the ratio of radionuclide abundance in formation to that in flushing fluid.

619

2 23%

ti 30%

Uranium tJ 6% 0%

Potassium

"SPECTR" logging tool; formation 1 ni in thickncss; logging speed of about 100 ni/liour; radiatoa abuiidaiices are rcspectively qK = O S % , q u =50 ppni, 41 , = 0.5 ppni; niud cake tliickness of about 20 nini; tool is held against the borehole wall; borcliolc diameter is equal to 200 nini. Discrepancies of drilling mud aiid mud cake mass densities were taken as much as 3% and 5%, respectively. Upper estimates of tlie total errois of potassium and uranium abundances were found to be 12% (relative) and 3.9% (reliitive), respectively.

Fig. 7. Partial contribution of basic factow iiito the total error of uraniuni and polassiu~ii abunduiccs calibration (1). measurement statistics (2), borehole diameter (3), drilling niud density (4), niud cake tliickttcss (3, logging 'tool eccentricity (6).

Tlic iatio P, = x,/qj depends on niass thicknesses of intermediate zones, position of a tool (and a casing string) ia the hole, and tlie proportions of NRE abundances in foriiiation aiid intermediate zones.

The effects caused by cliai-acteristics of drilling mud, niud cake tliickness, and tool's position (eccentricity) in tlie liole are illustiated in Fig.6 (ii,b,c). The density of cenient casing ring material weakly affects the Pa value. The effects of intermediate zones grow substanthy at the eccentric position of a cirsitig slritig. Maxiniuni valucs of Pj relate to potassium (i= 1) and niininiuni values - to thorium (j=3). This is owed to substantially different penetrating capabilities of appropriate gamma-lays produced by those radionuclides (including those produced by thorium fission products).

VI. RESULTANT ACCURACY OF NRE DETERMINATIONS

The resultant accuracy of the jtli abundance Aqj is tlie supelposition of svsteniatic components: - Ai = l . l . [ cSz +1/3.&..] 2 112 I"'

ni ni

wlierc zlll and xm arc the systematic variations (erroon) of the nitli fiictor, respectively; Sjli! is the sensitivity of tlie jtli abundance to the varwtion of the iiith factor.

Total accuracy of ;ibuiidaiiccs {qj) dcpclids 011 a great number of factois varying over the boreliole section. Based on tlie interpretation model, one can describe sensitivity coefficients Sjlil as inultidiiiieiisioiial univeisal ("autoniodel") functions of dimcnsioi\lcss pclt'ilnicteis wliose nuiiiber is substantially lesser than that of influencing factors: s,m = J Y & k k { ~ , h , k ) , s q ) , x , k = A , 4 ( 7 )

where Tk is tlie mass thickness of the ktli intermediate zone. Fig.7 presents contributions of partial components iiito the total error of potassium aiid thorium abundances in a yniticular case:

radionuclide mndoiii and

(6)

and random

VIJ. CONCLUSIONS

Matlieniatical modeling of a conventional correction tecliriology rcqu ires a considclublc I I u tiibcr of downliole situations to be riiodellcd. The diveisity of problenis involved can be effectively solved with the aid of tlie proposed interpretation model, allowing an interactive modeling of various environniental conditions. Pri tic iple d isad van toges of a co rrec t io I 1 - based teclinology put substantinl li~iiitiitioii~ to its iipplicetiotl donxiin. The proposed "corrcctioii-frcc" interpretation algorithni does not have sucll disadvantages since it is the direct analytical co~iversiori of intcrprctation niodel(1). Cotiipiired to empirical algoritlinis, it provides a substmitially iinproved accurircy of deterniin;ition of rxliotiuclidc abundanccs by virtue of:

- reduced effects of conventional tool's calibration and standardization ~ r r o i s owing to tlic usc of individual metrological cliaracteristics of a -tool;

- substantially lesser erron of data processing algorithms.

An itiiprovcd accllriicy of Iiidioti~~clide a b ~ n d a t i c ~ in its turti provides better accurilcy of reservoir properties, iniproved determination of the foriiiation coniponents, and better solution of other geological problenis involved in tlie interpretation of SGL dat;i conibiiied with other logs.

VITI. REFERENCES

[I] Interpretation of the Spectral Gamma Ray. Gearliait Industries, Inc., 1986.

[3] V.M. Dobrynin, B.Yu. Vendelstein, and D.A.Kozhevnikov, Petrophysics, Nedra, Moscow, 1991 (in Russian).

[2] D.A. Kozhevnikov, "Algorithmic Accounting of Boreliole Envi ronine nt a 1 Conditions in "Gam inn - Spec t mine t iy of Rock Formations", Alomnaya Energiya (Atomic Energy), V.61, Iss.2, 1986, pp. 52-53 (in Russian).

[4] C. J. Koizuin i, T o m put c r Deterin i nnt ion of Ca I ibra t ion and Environmental Con-eclions for a Natural Spectial Gainina Ray Logging System", SPE Formation Evaluation, September 1988, pp.637-644.