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Gamma Ray-Density Logging

By Downloaded from http://onepetro.org/SPEPBOGR/proceedings-pdf/59PBOR/All-59PBOR/SPE-1253-G/2087146/spe-1253-g.pdf by guest on 27 September 2021 Albin J. Zak and Joe Ed Smith, Junior Members AIME Core Laboratories Inc., Dallas, Tex.

ABSTRACT In the practical logging tool, a beam of gamma rays is emitted into the formation. A This paper presents a review of current small fraction of these photons find their way methods of interpreting and applying gamma ray­ back to the detector. Normally, the detector density logs in evaluating fundamental reservoir used is a Geiger-Muller counter or scintillation data. The basic theories and physical principles counter. Studies of other detecting devices, underlying the techniques of density logging with such as cloud chambers and ionization chambers, gamma rays are discussed along with some of the have shown them to be unsuitable for this purpose. problems associated with the instrumentation of The most common gamma ~ay source for this tool is such a tool. An effort has been made to evaluate radioactive cobalt (CobO ). The source is Shielded the instrument calibration techniques, and discus­ from the detector with lead such that the majority sion and figures are presented which describe the of the gamma rays counted by the detector are effect of borehole conditions, pressure, tempera­ those back-scattered from the formation. ture, etc. The relationship of natural density, grain density, and interstitial fluid density to Initial calibration of the instrument is made porosity is presented. Field data illustrate how in special testholes in which the density of the density logs can be correlated with porosity and calibrating material is carefully controlled. grain density data. With the aid of adequate core These experiments are made in various hole sizes analysis data, a reasonably accurate estimate of in each of several different mud densities. From formation porosity can be obtained from density this, an adequate prediction has been established log interpretation. The paper also offers a dis­ as to the effect of borehole diameter and borehole cussion of the limitations of the density log as a fluid density on the log response. To date, there porosity tool. The current applications of the are no valid correction factors proposed for the density log to geologic work are cited, and the effects due to poor borehole geometry. The rules prospective uses and future developments are and limitations of logging speed, time-constant, briefly explored. bed thickness, etc., that apply to conventional radioactivity logs also apply to density logging. SUMMARY The effects of temperature and pressure are those effects that are imposed on the response of the The principle of gamma ray absorption as a gamma ray counter, and the effects on the densi­ function of density was adapted to the logging of ties of the interstitial fluids. petroleum formations through the utilization of a phenomenon known as "back-scattering". This tech­ The basic interpretation of the density log nique uses a tool which contains both a gamma ray is fairly simple; the possible applications are source and detector. The detector measures the numerous. The most prominent denSity log applica­ intensity of the gamma rays emitted from the tions are: (1) lithological eorrelations, (2) source that have been back-scattered to the de­ i determination of density grad:"ents for gravity tector by the formation. After proper instrument , meter surveys, (3) determination of borehole fluid calibration, the log response can be used to denSity for gradient surveys, (4) location of compute the natural density of the formation. casing shoe and cement top, (5) location of casing Since there is a definite relationship between leaks, (6) aid in the interpretation and evalua­ natural density and porosity, it is possible to tion of other logs, and (7) method of estimating predict formation porosity from density logs. It formation porosity. Application 7 is probably is necessary to correlate carefully density log the most important and most widely used. data with core analysis data before the direct correlation of density log response with porosity Maximum use of the density log nas not been can be made. fully realized. Although there are some severe limitations in its use, there are many cases where References and illust!13,tion~~t,~~?f p_~_~~_.___ -,- ______---' 2 GAMMA RAY-DENSITY LOGGING 1253-G

the density log is an effective tool, and serves recall that atoms with nuclei of the same Z but as a valuable aid in f'ormation evaluation. different A are forms of the same element and are called isotopes. INTRODUCTION Beta rays (~) are believed to be physically Gamma ray-density logging has progressed far equivalent to electrons if the beta radiation since its original experimental stage. Numerous has a negative charge. If the beta rays have a major oil companies and several service companies positive charge, they are equivalent to positive­ have made significant contributions to its ad­ charged electrons and are called positrons. When vancement. Although the tool was originally con­ talking about positrons, the term negatron is ceived as an al~iliary exploration device, con­ usually used instead of electron; negatrons and tinued research and development has created new electrons are exactly the same. Beta radiations, Downloaded from http://onepetro.org/SPEPBOGR/proceedings-pdf/59PBOR/All-59PBOR/SPE-1253-G/2087146/spe-1253-g.pdf by guest on 27 September 2021 and improved equipment and techniques. This positrons, and negatrons all have the same rela­ paper is an analysis of the theories, modern tive charge, either plus or minus one, and they techniques and interpretation procedures applic­ all have the same relative mass of one. (As able to formation evaluation. shown in Table 1, a proton (p+) has a relative charge of plus one, and a relative mass of ap­ Often, the reservoir geologist, petroleum proximately 1,836; a neutron (n) has a relative engineer, and log analyst are not familiar with charge of zero, and a relative mass of approxi­ the basic theory and physical principles that mately 1,840.) Unless otherwise stated, the underlie a particular logging tool. This results charge of beta radiation is always assumed to be in the interpreter being unable, or limited in negative and equivalent to an electron. Hence, his ability, to evaluate logs. An attempt is when a nucleus decays by beta emission, Z will made herein to "bridge the gap" between theory increase by one unit and A will remain constant. and application. It should be pointed out that the exact value of mass will decrease very slightly; this is a The purpose of this paper is to inform the necessary conclusion in order to explain the re­ user of the basis of gamma ray-density logging; lease of energy. to describe the equipment used; present the ac­ cepted principles of interpretation; illustrate Alpha particles (0<) are equivalent to the uses and applications; and cite the known accelerated helium atoms that have been stripped advantages and limitations. of their electrons. Thus, the alpha particle will have a nuclear charge of plus two and an THEORY AND PHYSICAL PRINCIPLES atomic mass of four. Therefore, if a nucleus decays by alpha emiSSion, Z will decrease by two Basic Nuclear Concepts and A will decrease by four. Note that in either beta or alpha decay, isotopes of the mother ele­ In order to fully understand the nuclear ment are not formed; the residual that is formed processes that occur when a gamma ray-density log is always a different element. However, the is run, it will be necessary to briefly review series disintegration of an element tr~ough both some basic radiochemical theory and physical con­ alpha and beta decay will often produce isotopes cepts. The discussion here will not begin with I of the original element. the most elementary principles; for introductory material on the subject of atomic PhYSicS the In atomic physics, it is conventional to reader may refer to the works of Bttter,l3 express energy in terms of elec~ron-volts. An Fermi,25 Friedlander and Kennedy,2b Lapp and electron-volt is equal to 1.6 x 10-12 ergs; it is Andrews,31 and Semat.36 From the beginning, the further defined as the kinetic energy required by inquirer must realize that gamma ray-density an electron to move through a potential difference logging is different from conventional gamma ray­ of one volt. Since the electron-volt is a rather neutron logging. The gamma ray-density log is small unit, thousands of elect:ron-volts (Kev) , often referred to as the gamma-gamma log, which I and millions of electron-volts (Mev) have been means that the source emits gamma rays and the adopted as standard units. Occasionally, units detector counts gamma rays. This paper will of electron-volts (ev), and billions of electron­ present only that material which is related and volts (Bev) are used. Alpha particles will nor­ necessary to the understanding of gamma ray­ mally exhibit energies in the range of several density logging. Mev; beta particles have no normal energy range -­ some are as low as one ev, whereas some are as The definitions of nuclear terms presented high as ten Mev. Gamma rays have energies in the by Faul,24 will be sufficient for this paper; the order of one Mev for naturally occurring decay. atomic number Z, or nuclear charge as it is some­ It is interesting to note that cosmic rays have times called, is the integral number of protons energies in the order of several Bev, and are in the nucleus of an atom. The mass number A, capable of penetrating ten to fifteen feet of or atomic mass, is the total number of nucleons lead. in the nucleus of an atom; a nucleon can be either a proton or neutron. The reader will Nuclear reactions can be expressed in a 1253-G ALBIN J. ZAK AND JOE ED SMITH 3

manner similar to chemical reactions. The state­ nuclear disintegration was fully accepted by the ment must involve at least four terms: target, scientific world, its mathematical development is (projectile, product) residual. The projectile very simple: It is observed that the1loss in and product particles are commonly abbreviated. radioactive nuclei (-dN) that occurs during an A classic example would be that of a lithium7 interval (Jt) is directly proportional to the atom* being bombarded with an energetic proton. total number of nuclei (N) that is present after Since the proton has a positive charge, it will the time (dt ). Thus, experience an electrostatic repulsion as it ap­ proaches the nucleus of the lithium atom; but if . . . . (1) the proton is accelerated to a sufficiently high energy level, it will penetrate inside the nuclear radius where the strong, short-range attractive where ~ is a proportionality constant. By Downloaded from http://onepetro.org/SPEPBOGR/proceedings-pdf/59PBOR/All-59PBOR/SPE-1253-G/2087146/spe-1253-g.pdf by guest on 27 September 2021 forces are at work. At this point, the proton separation of variables, will disappear into the nucleus of the Li7 atom, forming an excited nucleus. This nucleus will dN \\\ .... (2) then split into the product particle (0<) and the jN =-1j dt: residual nucleus (He~). Fau124 estimates that the time necessary for this process is in the Integrating Eq. 2 leads to: order of 10-12 seconds. This reaction is written: Li 7 + p+_o<-tHe'for more commonly, L', 7(p +,0<) He'+. If the projectile and product particles are the same, the process is known as scattering. The scattered particle (product) will always have Using algebra, Eg. 3 will simplify to: N = ce-~t less energy than the projectile particle because where C = some constant of integration. The some of the energy will be transferred to the constant C can be evaluated by setting t = 0, residual nucleus as kinetic recoil energy. This such that N = C; therefore, C must be equal to scattering process should be carefully noted No, where No is the number of radioactive nuclei it is the cardinal principle upon which the present at t = O. Hence, the classic exponential gamma ray-density log is based. The process will law of nuclear disintegration is normally written: be discussed in detail after introductory mater­ ial on gamma radiation has been presented. N . . . . (4) One other definition must be stated before going into the discussion of the nuclear disin­ where'\. is a constant universally called the tegration processes. It is possible to express disintegration constant. The time required for No the probability of a projectile particle inter­ to decrease to Noh is called the half-life (T) acting with a target nucleus in terms of nuclear or decay period. By Eq., cross sections. The cross section is said to be large when the probability of a reaction is very I/,'\ ... I _~T . . . . (5) higb, and conversely, the cross section is said T\NoJ = l'-loe to be low when the probability of a reaction is remote. Nuclear cross sections vary over a wide Using algebra, Eg. 5 clears to: range; they are dependent on the type of particles energy of particles, type of target, and type of \T = LOSe Z. .... (6) process. The common unit of nuclear cross section is the barn (10-24 cm2 ). This concept of cross Eg. 6 then becomes: sections will be used later to help explain gamma ray attenuation. . (6a)

It took many years to define the nuclear where T is the half-life of the substance. Since disintegration processes in terms of mathematical N and No are very difficult numbers to measure, expressions. The first significant conclusion the exponential law is often expressed in terms was that the amount of radioactivity of a pure of: substance decreases with time according to some parabolic or hyperbolic function. It was later observed that radioactive decay is statistical in nature, that it could not be predicted when any where R is the disintegration rate or nuclear given atom would disintegrate, and that some sta­ activity of the material. (Halliday28 presents tistical hypothesis would have to be developed to adequate explanation of this paramet~r.) It explain the process.28,31 Although it was a long will suffice here to say that R- dN or something time before the contemporary, exponential law of -(ff proportional to it. The decay period (1l) is * Superscripts above names of elements are Atomic normally found by plotting Log R vs t. From Eq. 7 Masses and not reference numbers in the it can be seen that ~ is the slope of the straight Bibliography. line through these data, thereby allowing the 4 GAMMA RAY-DENSITY LOGGING 1253-G calculation ofT with Eq. 6a. This technique is ~~ important with respect to the calibration of the IDO density log. Before an instrument is put into \Cxt,() service, it is necessary first to calibrate the If the period (T) is known, then,\(x), '\.(y) and instrument response with the radioactive source, \(x+y) can be calculated. Halliday28 has given usually Cobalt (A = 60). Then as the tool is put adequate treatments to this matter. He states into actual use, it is necessary to know the that the type of detector is unimportant; it can strength of the radioactive source at all times be counting alpha particles, positrons, or both - in order to utilize the calibration curves. Since a plot of Log R vs t will always give the same the strength of the C060 is constantly decreasing period rO.693 J. The period ~ is that by radioactive decay, it is necessary to apply h(x+y) J \(y) the exponential law to predict the source strength period which would occur if the alpha decay did at any time. not occur simultaneously with the positron decay. Downloaded from http://onepetro.org/SPEPBOGR/proceedings-pdf/59PBOR/All-59PBOR/SPE-1253-G/2087146/spe-1253-g.pdf by guest on 27 September 2021

An enlightening subject in the study of The reader is referred to the literature for nuclear radiation is the radioactivity decay detailed discussions of the exact nature of alpha series. There are numerous series; only the and beta emission. No attempt will be made to heavy end elements of the nuclear chart have been present such information in this paper since ~ thoroughly explored in this respect. Most of the and (3 have very little direct bearing on gamma other radioactive elements are too short-lived to ray-density logging. Gamma emission is the im­ be followed in a decay series. There are four portant process here and will be treated in recognized heavy disintegration series~ Thorium, such a manner as to give sufficient explanation Neptunium, Uranium-Radium, and Actinium. The of the behavior of the gamma ray-density log. heavy end elements are best known because of their rather long-lived radioactive members. The Gamma rays are highly penetrating radiations Thorium series is illustrated on Fig. 1. Reac­ that originate in radioactive materials; they are tions that move from left to right occur through unaffected by electric or magnetic fields. Gamma alpha emission, whereas reactions that move up or radiation is actually a part of the classic down occur through some type of beta decay. Note electromagnetic spectrum -- their wavelength is that isotopes are formed only through the com­ in the order of 0.1 Angstrom Uni.t or less, an ex­ bined efforts of both alpha and beta radiation. tremely high frequency. Cosmic rays have some­ An excellent example of this would be Uranium- what shorter wavelengths and X-rays have slightly 240 decaying to Uranium-236 in three steps~ longer wavelengths. The differences between "2.40 7...'l-C> gamma rays and cosmic rays are not fully under­ (a) U --. Np + stood at this time. The only known difference f- is that cosmic rays have a higher frequency and 2 shorter wavelength which consequently explains (b) N;4\) ~ 9u '?\ r­ their higher energy level and greater penetrat­ ing power. The only difference between X-rays (c) PUL'f() ~ U U\, ~ 0<... and gamma rays is that X-rays originate within Before discussing gamma emission, it can be the radioactive atom, outside the nucleus; where­ pointed out here that nuclei do not change in A as gamma rays always originate from within the or Z due to gamma radiation; however, there is a nucleus. Gamma rays and X-rays are otherwise loss of nuclear energy. identical. Although seldom the case, it is pos­ sible to have gamma rays existing at energy An interesting aspect of the nuclear dis­ levels less than the normal X-rays energy level. integration process is that a great many nuclei The nomenclature of gamma rays and X-rays is decay by two or more types of radiation. An ex­ purely a matter of their atomic origin. These ample from Fig. 1 will illustrate this phenome­ definitions are greatly simplified, but are ade­ non: Ac224 will decay by alpha emission to Fr220 quate for the purpose of this paper. Semat's in X per cent of the disintegrations and by discussion of gamma rays and X-rays offers an positron decay to Ra22)~ in Y per cent of the academic treatment of the subject matter. Since disintegrations. X and Yare experimentally there is no difference in the type of inter­ determined; X + y: 100 per cent. By differen- actions that gamma rays and X-rays (of the same tiation of Eq. 7, rt.(l£) = - (~~t R-' ,and energy level) have with matter, this paper will use the generic term "photon" to mean either or both. \ tv) :: - (~:)y R- \ . Also, '\6t- ... '<) = \l)() ~ \l\') Interaction of Photons with Matter

. • . . (8) According to Fan022, there are four kinds of interaction between photons and atomic par­ where ~(x), ,\(y) 'and Y\h+y ) are the diSintegration ticles: (1) basic interaction with atomic constants for 0<. decay, f3 decay, and the combined electrons, (2) basic interaction with particles decay. From the given data: within the nucleus, (3) interaction with electric 1253-G ALBIN J. ZAK AND JOE ED SMITH 5 field surrounding charged particles, and (4) in- I 1.022 Mev before pair-production can occur since teraction with meson field surrounding the nu- I this amount of energy is needed to supply the rest cleus. It is further observed that each of these I energy. For large values of E., Ee- is four kinds of interaction may produce three dif- I ferent effects: photon absorption, elastic i essentially equal to E_ e+· For the values of scattering of photon, and inelastic scattering of ! photon. Referring to the basic definition of I, Eyemmitted by Co "0 , Er -Z>'Y\c2.may be shared scattering, the process is called elastic if the projectile acts upon the target as a whole, in any proportions between E e 1- and E e -. Ac­ whereas the process is termed inelastic if the cording to Halliday, the positron usually receives projectile acts upon and produces some effect on more energy since it is accelerated by the nucleus a constituent part of the target. There are whereas the negatron is restrained by the nucleus. twelve possible interaction processes between The positron will eventually combine with an Downloaded from http://onepetro.org/SPEPBOGR/proceedings-pdf/59PBOR/All-59PBOR/SPE-1253-G/2087146/spe-1253-g.pdf by guest on 27 September 2021 photons and matter. Some of these have never atomic electron, probably a free electron, and been observed and exist only as physical hypothe­ form two quanta of annihilation energy; i.e., the ses. It is believed that only four of these positron-electron combination disappears and two twelve processes have any influence on the gamma photons appear, each with the rest-mass of an ray-density log: photoelectric absorption, pair­ electron. The negatron is absorbed in a manner production, Compton scattering, and Rayleigh described for beta particles by Faul. The pair­ scattering. In all of these processes, the inci­ production effect predominates for energies dent photon is either absorbed or scattered away greater than 2 Mev and large values of A. by the atom or some part thereof. The Compton effect for a single interaction In the photoelectric process, a photon ex­ is quite simple and is mathematically well defined periences a collision with an atomic electron and A photon of moderate energy (0.5 Mev to 2.0 Mev) immediately disappears. The electron which ab­ collides with a presumably free electron. The sorbs the photon is ejected from its orbit and incident photon is briefly absorbed, probably less retains its own energy plus the photon energy than 10-12 second, and is ejected into a trajec­ minus the binding energy of the electron. This tory that is usually slightly different from the process does not occur for free electrons, and it incident path. Since the projectile and product is reasoned that the effect is more prevalent for are identical, the process is called scattering, the tightly bound electrons in the K-shell. Nu­ clear physicists normally treat the photoelectric commonly written, e-(') r ) e -. This scattering effect as an interaction with the entire atom and process is normally considered to be inelastic not with the ejected electron. Although this since a photon acts upon a constituent electron of treatment is not exactly correct, it simplified an atom. However, some physicists like to think the theoretical analysis of the process. Because of the target electron not only as free but also of the higher energy level of the photon, the as being isolated. In this respect, the process ejected electron generally flies off in the di­ is elastic. The scattered photon always has less rection of the incident photon. The process is energy than the incident photon. It can be seen most likely to occur for gamma ray energies less that after a sufficient number of collisions, the than 0.5 Mev and for material with large values photon is susceptible to photoelectric absorption. of Z. The recoil electron flies off in the general direction of the scattered photon. In the pair-production process, an energetic photon is absorbed in or around the nucleus of an When a photon is scattered in such a manner atom, and an electron-positron pair is ejected that it loses only a small fraction of its inci­ from the proximity of the nucleus. If it is dent energy, the recoil energy imparted to the assumed that there is total conservation of electron is very small. This is especially true energy in the process, when the incident gamma ray energy is initially low. When this situation exists, the recoil elec­ tron is sometimes absorbed by an atom or even a whole molecule. This is a noticeable variation from the Compton process and is known as Rayleigh 2 where Er = energy of incident photon, mc = rest scattering. Fano points out that, insofar as the observer can tell, the scattering action of dif­ energy of each member of the pair, E e+ = energy ferent atomic electrons seems to combine coherent­ ly. Since the effects of the process are limited of the ejected positron and Ee,- ==- energy of the to low photon energies (<.0.3 Mev) and dense ej~cted negatron. DuMond and Cohen20 state that mc = 0.511 Mev*. Thus, Ey must be greater than materials, it will not be discussed in detail and will not be considered as a measurable factor in 2 the gamma-gamma log. There are data in the liter­ * mc is defined as the electron energy equivalent ature to support this assumption.22,29,37 where m = electron rest-mass, and c2 = mass - energy equivalence; refer to DuMond and Cohen for The three prominent processes that have an details. influence on the gamma-gamma log are illustrated 6 GAMMA RAY-DENSITY LOGGING 1253-G 0:-;~g~~ -;: :h~- p:otoelec::~c effect, the photons (-dP) that is absorbed or scattered away photon expells an atomic electron from the K­ in an additional absorber thickness (dx) is pro­ shell. In the pair-production process, the portional to P and to (dx). Therefore, I gamma quantum vanishes, and an electron-positron pair is produced. The photon is scattered by an - dP: k Pdx .. (n) electron in the Compton process; the photon loses some of its energy, and the electron is recoiled or from the atomic radius. Also, note that there is I

In Fig. 3, Po is the number of photons that ...... •(14) enter the absorber and P is the number of photons that pass through the absorber without having an At this point, the theory will be greatly simpli­ interaction. Af is the area of the absorber fied by stating that: face, and x is the absorber thickness, such that the product of x and Af is the bulk volume of the • . • . . . . . (15) absorber. Each dot within the absorber medium indicates a photoelectric, pair-production or where~ is the combined mass absorption coeffi­ Compton process. In the first two processes, the cient, or attenuation coefficient, of the three photon is absorbed; in the latter process, the predominant interaction effects. It is immedi­ photon is not absorbed but disappears as far as ately noted tha~ is a function of both incident the detector is concerned. The reader should be photon energy and atomic mass of the absorber advised that Fig. 3 is a simplified schematic material. The equation of gamma ray attentuation diagram of the experimental model, and that the is now writter": !!good geometry!! previously mentioned is necessary D '" 1- -:-pel( in actually making these experiments. It is fur­ P 0 e . . . (16) ther necessary that the incident photons be mono­ energetic and collimated into narrow beams. P and P~ are normally expressed in units of Mev; / in cm /gmj e in gm/cm 3, and x in cm. Numerous The value of P will depend on the values of narrow-beam attenuation experiments have verified Po and x. If an additional absorber thickness Eq. 16, and have measured values of~ .10,18,21, (dx) is added, P will decrease by (-dP). If stil 29,37 another absorber thickness (dx) is added, (P-dP) will decrease by (-dP). Thus, there is a definitE Separate theories have been worked out for mathematical pattern observed: each of the three absorption processes. Remember tha~ is the attenuation constant for the P C( Pc.lX .(lOa combined effects of photoelectric absorption, pair-production, Compton scattering, and such that: -~~ C{ ~ d)(. . (lOb) .I - c\~' (?- ~\» dx' .(lOc) ex: / where/.. ,"p6 vVc.- are the partial attenuation co­ It is hence reasoned, that if P photons pass efficien£s due to photoelectric effect, pair­ through an absorber thickness x, the number of production, and Compton scattering~ respectively. * See Physics Review, Vol. 74, (1948), page Baker3 has pointed out that the density of the 1841. absorber material will increase when A increases l253-G ALBIN J. ZAK AND JOE ED SMITH 7 even though the number of atoms per uni t vOl~eTw~e-: (\ and-A' a~: the quantum wavelengths of the remains unchanged. When density increases in I photon radiation before and after collision, ~ this manner,~ must also increase; but the in- is Planck's Constant, m the electron rest-mass, crease in~is not directly proportional to the c the velocity of light, and~the photon scatter- mass number. In the Compton effect~c is di- ing angle as indicated on Fig. 4. It should be rectly proportioned to A; however, in the photo- noted that the wavelength change is not a functio electric and pair-production processes~~ and of the wavelength. By using Eq. 21 and: ~ are proportional to some power function of \ C the value of A. Halliday develops the defini- 1\= ~ ...... (22)

tions of the three values o~ in the following II manner:

I . . . (23) Downloaded from http://onepetro.org/SPEPBOGR/proceedings-pdf/59PBOR/All-59PBOR/SPE-1253-G/2087146/spe-1253-g.pdf by guest on 27 September 2021 · (100) I where v is the frequency of the photon radiation, /h =: n" (s) · (18b) and E~is the energy of the photon, the fractional energy loss in any individual Compton collison can /c =0 n,JS) · (18c) be computed from:

where S is the equivalent disk area of each tar­ I I Ex: get nucleus; l\a., Ylb , and >lc.. are the number of ~ y::::' I E(" (r ) .... (24) atoms, nuclei, and electrons per unit volume of + meZ: 1- vcs-G- the absorber. This equation proves that the energy degradation of scattered photons is quite large for energetic Note that: hQ.'::: r}b .:: NA ~ · (19) photons and large scattering angles. Fig. 5 is a V\/ graph showing the results of calculations made and nc.. =c Z-NA ~ .(20) with Eq. 24 for gamma ray energies up to 10 Mev vV and scattering angles from 50 to 1200 . Naturally, where NA is the number of molecules in a mole of if -= 0) = Y Klien and the absorber substance, ~ is the mass density, -e- E / E and W the atomic weight. This definition of at­ Nishima used a quantum mechanics approach to cal­ tenuation coefficient is essentially the same as culate the nuclear cross section per electron for that previously presented. the Compton process.33 Their basic assumption is: the gamma ray energy is so great that all elec­ In gamma ray-density logging, the radio­ trons can be considered free. The Klien-Nishima active source emits photons with energies in the formula has been well proven by numerous experi­ order of 1.0 to 1.5 Mev. Most of the atoms that ments in this field. constitute reservoir rocks and interstitial fluids have nuclei of low A values; hydrogen, 'I'he theory of Compton scattering is of pri­ carbon, oxygen, silicon, calcium, magnesium, mary importance in the density log, and will be sodium, chlorine, sulfur, etc. Hence, the most used throughout the remaining discussion. By ju­ predominent process active during a gamma-gamma dicious choice of gamma ray source and carefully log-run is Compton scattering. Since the varia­ engineered source-detector arrangement, the tion in~is directly proportional to variations response of the gamma ray-density logging tool can in A, P is very nearly an exponential function of be made to depend primarily on the density of the ~. (Refer to Eq. 16). The reader should note formation rock and interstitial fluids. that P is an indication of the average density along the traversed path, not the density at the INSTRUMENTATION OF LOGGING DEVICES point from which the photons are scattered. If it were not for the small amount of photoelectric Gamma Ray Detection absorption and pair-production, a plot of Loge P vs f would be a straight line, with (~x) as the Radiation detectors that have been used to slope of the line. date in the gamma ray-density log are of three general types: (1) ionization chambers; (2) The first attempt to describe the Compton Geiger-Muller tubes; and (3) scintillation count­ effect was done with the classic diagram shown ers. Each type has its own particular advantages on Fig. 4*. By using the relativistic laws for and disadvantages. The following discussion will conservation of momentum and total energy, an present a very brief statement as to the princi­ equation has been derived that predicts the ples of operation of each, will highlight the change in quantum wavelength of the photon per operational characteristics of each, and show how Compton collision:18,2l,2b they are adapted to the problem of gamma-gamma logging. A'_A=~(I-Cos~) ..... (2l) The theory and operation of ionization cham­ *See A. H. Compton, Bulletin of National Research bers is adequately covered in the literature cited. Council, Vol. ~, No. 20 (1922). 24,48,54,64 Basically, this instrument consists 8 GAMMA RAY-DENSITY LOGGING 1253-G 1------~--~-----"-='------'1 of a chamber containing an inert gas. Two I thin wire replaces the small tube or cylinder used electrodes, usually in the form of concentric in the ionization chamber as an anode. Again, the cylinders, are placed within the sealed chamber. counter chamber is filled with an inert gas but at As photons penetrate the wall of the chamber, the much less pressure (in the order of one atmosphere gas molecules will ionize into charged atoms. or less). There is also an electrical field set- If an electric field is set up in the vessel, the! up across the electrodes of the Geiger counter, ions will move toward the electrodes and cause an but the field strength is much greater than that electric current to flow that is proportional to of the ionization chamber. As in the ionization the degree of ionization produced by the radia- chamber, the photons that enter the chamber will tion entering the chamber. The negative ions ionize gas molecules, but since the electric field move toward the positive electrode, and con- is very strong, the ions are greatly accelerated

versely, positive ions toward the negative elec- as they move toward the electrodes. These highly Downloaded from http://onepetro.org/SPEPBOGR/proceedings-pdf/59PBOR/All-59PBOR/SPE-1253-G/2087146/spe-1253-g.pdf by guest on 27 September 2021 trode. A single radiation entering the gas is energized ions will ionize more gas molecules as capable of creating a large number of ions and they speed through the tube toward the electrode, producing an electrical impulse; a succession and thereby cause a phenomenon called "ionic of incoming radiations will produce a succes - avalanche". This avalanche of ions will produce sion of these electrical impulses. The recorded an electric charge within the tube that is com­ electrical signal can be derived by: (1) count- pletely independent of the energy of the photon ing the impulses in a given time period; (2) re- that caused it. The pulse height of a Geiger cording the average current flowing through the counter signal is always the same regardless of circuit. Should the detector time-constant be the type or energy of the radiation that caused so small that the ions collect at the electrodes it. The Geiger counter merely counts the number in less time than the interval between individual of these pulses in a given time, or it can measure radiations, then the instrument is classified as the average current flowing in the external a pulse chamber or differential ionization cham- circuit. ber. In this type of chamber, each ionization event will produce a pulse that is proportional With respect to gamma ray-density logging, to the magnitude of the event. the Geiger counter is a desirable detector for several reasons: (1) a fairly weak photon is On the other hand, if the ionization chaw­ nearly as capable of producing a pulse as a strong ber has a very long time constant, the succession photon; (2) the magnitude of the output signal is of impulses will overlap and the current produced of no significance -- only the number of pulses will be averaged over the time interval. This per time interval are counted; (3) efficiency and type of detector is termed an integrating ioniza­ sensitivity are unaffected by elevated tempera­ tion chamber. It requires an expensive, high­ tures; (4) zero reference is well-defined; and (5) gain, direct current amplifier; its sensitivity it can be used in a small diameter logging tool is sufficient only when the gas is under high quite readily. The Geiger-Muller tube is undesir­ pressure. As the chamber wall is thickened to able for gamma-gamma logging because short coun­ contain the higher pressures, the counting ef­ ters will not give a sufficiently reliable signal ficiency is drastically reduced. The ionization at practical logging speeds and it has a very poor chamber is not very suitable for gamma ray-den­ measuring efficiency -- less than one per cent of sity logging for several reasons: (a) the meas­ the photons that enter the tube cause the ionic uring efficiency of integrating chambers is avalanche. generally very poor; (b) short, small diameter chambers will not give a sufficiently reliable The scintillation counter is an old instru­ signal at practical logging speeds; (c) an exact ment; nearly fifty years ago, physicists used zero reference is almost impossible to determine; sphalerite crystals to observe the behavior of and (d) the small, direct-current, output signal alpha particles. Of course, modern scintillation requires an intricate and expensive system of counters are far removed from their ancestral amplifiers, filters, rectifiers, etc. before the models. DiGiovanni, Graveson and Yoli,49 signal can be recorded. Hurley,53 Russell and Scherlatskay,67 Toelke,69 Youmans,71 and Lapp and Andrews31 present abundant The Geiger-Muller tube was developed by Hans material on the theory, operation and applications Geiger and Walther Muller in 1928. Since its of modern scintillation counters. inception, excellent reviews of theory, technique, and applications of modern Geiger-Muller tubes In Geiger-Muller tubes and ionization cham­ (commonly referred to as Geiger counters) have bers, an electric charge is freed when a radiation been published by Brown,43 Curtiss,47 Peirson,62 particle creates an ion-pair by acting on the iner Russell,66 and Slack.68 Lapp and Andrews31 also gas molecules. But in scintillation counters, the present excellent introductory material in their radiation sets the electrons within a crystal in nuclear physics textbook. motion (there is no electric field involved). These excited electrons "bounce-around" within the A Geiger counter is similar in many respects crystal lattice and cause minute flashes of light to the ionization chamber. The electrode ar­ to be emitted. These tiny light flashes are trans rangement is the same except for the anode; a mitted through a lense to a photo-multiplier tube. 1253-G ALBIN J. ZAK AND JOE ED SMITH 9

The photo-multiplier has a series of thin,~ight- 'I Large volumes of literature have been writte sensitive plates mounted in a vacuum. The plates, I that explain how these three basic gamma ray de­ or stages, of the photo-multiplier tube are nega- i tectors are adapted to practical well logging tively charged. As a flash of light strikes the ' tools. (Refs. 38, 39, 48, 50, 52, 56, 66, and first stage, electrons are liberated from the 68.) There is an even larger volume of informa- metal plate. These electrons are expelled at high tion that deals with the calibration, interpreta- velocities because of the negative charge of the tion, and application of these gamma ray logging plate. The parabolic shape of the plate and high tools. (Refs. 40, 42, 44, 45, 51, 57, 58, 59, kinetic energy of the electrons cause the elec- 60, 61, 63, 65, and 70.) The remaining portion trons to strike the plate of the second stage; but of this discussion will review the specific prob- they are immediately repelled and, in so doing, lems of adapting gamma ray detectors to gamma- cause more electrons to be expelled from the gamma logging, the calibration of these instru- second stage. This routine is repeated for each ments, and the interpretation of the curves re- Downloaded from http://onepetro.org/SPEPBOGR/proceedings-pdf/59PBOR/All-59PBOR/SPE-1253-G/2087146/spe-1253-g.pdf by guest on 27 September 2021 stage in the tube. The electrons are finally corded by these tools. collected at the anode near the end of the tube. This process tremendously multiplies the number Basic Instrument Design of electrons received at the anode as compared i with those released from the first stage where the At this time, there are two different gamma light flash originally fell. The authors are ray-density logging instruments available to the familiar with a counter that has ten stages and industry: Type I, which uses a radial source and is capable of multiplying the effect of one scin­ a Geiger-Muller detector, and Type II, which uses tillation one-half million times. a collimated source and scintillation counter. The Type I tool is available through the Lane­ There are some very definite advantages of Wells Co., Houston, Tex.; Type II is available scintillation counters over Geiger-Muller counters through the McCullough Tool Co., Los Angeles, when applied to gamma ray detection: (1) The Calif. If the reader needs more details on a counting efficiency is much higher than that of specific tool, he should write directly to the Geiger counters. Sodium iodide crystals currently service company. It is not the purpose of this in use have better than 90 per cent efficiency. paper to give all the details of any particular (2) The height of the output signal is proportion­ tool. They will be compared only as to type and al to the energy of the detected photon. (3) as to the response that they give. Sondes can be constructed that lend themselves to logging in much thinner beds than tools utilizing Fig. 6 is a schematic drawing of the Type I G-M counters. (4) In some logging tools, the tool. In the case of a formation logging instru­ zero reference is better defined than in G-M ment, it would be impossible to place a gamma ray counters. (5) Scintillation counters are rela­ source such that the formation would be in a tively much less affected by cosmic ray-background direct path between the source and detector. How­ radiation. (6) Resolving time is much less than ever, this difficulty can be thwarted due to the that of the Geiger-Muller tube. fact that most matter has the property of scatter­ ing gamma rays. With respect to the design of a On the other hand, there are some distinct practical gamma-gamma logging tool, a strong, disadvantages: (1) Not only is the behavior of gamma ray source can be placed below the detector the crystal affected by temperature variations, and shielded from the intervening parts of the but the crystal is damaged beyond restoration at instrument such that leakage radiation up the too~ temperatures above 1400 F. Hence, logging tools or up the borehole fluid, can be kept at a mini­ with scintillation counters must be insulated and mum. Photons from the source will penetrate the refrigerated for efficient and accurate operation formation, scatter throughout the formation, and in deep boreholes. (2) Large sodium iodide crys­ be ultimately absorbed within the formation, ex­ tals are the most desirable; but the time neces­ cept for a small percentage of this scattered sary to grow such crystals is excessively long. radiation which will find its way back to the de­ Consequently, scintillation crystals are expen­ tector. Insofar as the detector is concerned, the sive. (3) The pulses generated in the photo-mul­ scattered gamma rays that reach the detector tiplier circuitry are very small compared to those appear to come from that portion of the formation generated in the Geiger-Muller counter, thereby where the scattering occurs. ThiS, in effect, requiring an intricate and expensive amplifier develops a gamma ray source within the formation. component. (4) Photo-multiplier tubes create ex­ By applying the information gained from the de­ traneous "noise signals" that are observed in the velopment of Eq. 16, it is seen that the Geiger output signals. A discrimination circuit must be counter will respond to the changes in natural employed to eliminate pulses ariSing from this formation denSity that occur between the spurious source. (5) The scintillation crystal and photo­ gamma ray source and the detector tube. As the multiplier tube must be housed in total darkness. logging tool is moved up the hole, the Geiger­ (6) Even with the most expensive models, it is im­ Muller counter responds as if a gamma ray source pOSSible, at the present time, to manufacture were moving with the logging instrument but back photo-multiplier tubes that operate at the same in the formation at an indeterminate, fixed dis­ noise level and same sensitivity. This compli­ tance from the counter. Fig. 6 is designed to cates the calibration roblem. 10 GAMMA RAY_::Q~~__ L_OG_G_IN_G __ ~~~~~~~~~~~~~--=12=.,5,,-,,3'---=,G I illustrate most of these concepts. The source i large vertical angle of emission but also a large material in the Type I tool is radioactive cobalt;! polar angle. There has been no previous attempt

the photons emitted from C060 are polyenergetic, II to define the resulting scattering region with but the 1.1 Mev and 1.3 Mev gamma rays are pre- i dimensions. (2) The detector does not discrimi­ dominant. Lead is used to shield the source from I nate against the photons that it receives; it the detector, and it appears that the efficiency I treats them all the same. A photon of 0.5 Mev of this shielding is quite sufficient. However, energy will produce the same result as a photon of some of the gamma rays will escape the source I 1.5 Mev. As to the depth of the effective scat­ chamber and enter the mud column. The probabilit~ tering region, for the 20 in. source-detector that some of these photons will find their way I spacing and C060 source, it is highly probable back to the detector through the mud is higher that gamma rays penetrating more than six in. of than leakage across the shielding. Naturally, thel formation will experience scattering at such large Downloaded from http://onepetro.org/SPEPBOGR/proceedings-pdf/59PBOR/All-59PBOR/SPE-1253-G/2087146/spe-1253-g.pdf by guest on 27 September 2021 magnitude of the error imposed on the density log i values of -e- that the scattered radiation will suc- due to this leakage is related to the mud density,' cumb to photoelectric absorption before it reaches hole diameter, and source-detector spacing. The the Geiger counter. This prediction is based on authors have found that the error is significant calculations made with Eq. 24 for the 1.1 and 1.3 for mud densities less than 14 lb/gal; the error Mev photons. The Klein-Nishina formula will pre­ for muds heavier than 14 lb/gal is detectable but dict a slightly deeper scattering region. diminishes rapidly with increasing density. The error due to this leakage increases as borehole The Type II instrument operates with a some­ diameter increases. Since the source-detector what different physical arrangement of source and spacing is always the same for any given instru­ detector, and the response of the tool is conse­ ment, this factor in the leakage error is a con­ quently different from that of the Type I tool. stant value. Inasmuch as this inherent leakage Fig. 7 is a schematic drawing of such a logging affects the response of the density log, the re­ tool. This tool also has a bow-spring to hold the corded amplitude on the density log curve there­ instrument in close contact with the formation fore requires a correction for both borehole wall, and a shoulder to wipe the mud cake from diameter and density of the borehole fluid be­ the borehole wall. The gamma ray source in this fore an accurate interpretation of the gamma­ tool is collimated into a narrow beam; both the gamma log in terms of formation density can be vertical angle and polar angle are small. This made. geometry also applies to the detector opening. The detector and source are shielded in a manner Some of the other features of this tool are: similar to that of the Type I sonde. As can be strong bow-spring that holds the instrument seen from Fig. 7, the scattered photons that are against the side of the borehole wall; shoulder accepted by the scintillation counter are those that wipes the mud cake from the borehole wall -­ that are scattered back in "one-shot" from the the reproducibility of the density log indicates scattering region. However, some extraneous that this is highly effective except for sands of photons will find their way into the detector extremely high permeability; and natural gamma ray opening, but in order to do so they must undergo activity of the formation is eliminated from the I multiple scattering, and thereby will have lost detector by shielding the counter completely with I more energy than those received from the "one­

lead. Two small "windows", consisting of a much 'I' shot" scattering region. Since the scintillometer lighter material than lead, permit the moderate, has a pulse height discriminator in its circuitry, scattered gamma rays to enter the G-M counter, but it is possible to "pick-out" particular photons absorb the soft, natural gamma rays. and record only that effect which is due to the Compton process that occurs in the small, well­ As a compromise between detector efficiency defined scattering region. By using the physical and the critical relationship of source-detector arrangement depicted on Fig. 8, it is possible to spacing to formation boundary definition, it has calculate the average scattering angle (t8, aver­ been found that the most desirable spacing from age depth of scattering (hs ), average length of the midpoint of the detector to the source seems photon path (-y.+;t,'), and energy of the scattered to be about 18 to 20 in. for an optimum detector photon (EY)' The only data needed for this cal­ length of ten in. When time-constant and logging culation is energy of incident photon (E (") , speed are considered, the reader will see the ad­ source-detector spacing (b), and collimation angle vantage of these suggested dimensions. (I). Of course, this calculation assumes mono­ energetic gamma radiation from the source. Since Some excellent reviews have been prepared such a borehole source is impossible, it is neces­ on the Type I gamma ray-density logging tool. The sary to choose the most predominant energy level reader will find of particular interest the works of the source photons, calculate Ey', and discri­ of Anderson,l Campbell and Wilson,5 Newton, minate the pulse height which represents E; . Skinner, and Silverman,7 and Faul and Tittle.6 There are several articles that have been There are two features of this Type I tool published in recent months which describe gamma that should be noted: (1) The source emits gamma ray-density logging tools utilizing collimated rays in a radial pattern -- not only is there a sources and scintillometers. Of particular 12 -G ALBIN J. ZAK AND JOE ED c:=SM~IT""H,=--______-=l=-,l I interest is the works of Baker,3,11 Caldwell, 4, 16 I those of Type I. Baker3 indicates that there are Sippel and Hodges,9 and Caldwell and Sippel.17 I no borehole diameter effects for smooth holes I and little or no effects due to the presence of The scintillation counter and its associated! borehole fluid. The reason for this is that the electronic components are very intricate and delil scintillation detector and pulse height discrim­ cate. The behavior of the crystal is extremely i inator accepts and records the gamma ray energy sensitive to temperature changes above 800 F, and I band that corresponds to Compton processes that the necessity of insulating and refrigerating i occur in the predetermined scattering region. the counter cannot be over emphasized. It is i I Fig. 8 shows how the various dimensions of the felt that a large majority of the early sondes I physical arrangement of source and detector can were insufficiently protected against the temper- be controlled such that Eg. 24 will allow the atures encountered in wellbores. Photo-multi- I prediction of the scattered photon energy to be Downloaded from http://onepetro.org/SPEPBOGR/proceedings-pdf/59PBOR/All-59PBOR/SPE-1253-G/2087146/spe-1253-g.pdf by guest on 27 September 2021 plier tubes are difficult to calibrate with re­ accepted and recorded. Although this tool great­ spect to a common reference due to the dissimi- i ly reduces the number of back scattered photons larity of tubes even of the same make and model. I that are accepted by the detector, its statis­ Pulse height discrimination is a relatively new I tical accuracy is comparable to the Geiger technique as applied in gamma-gamma logging, al- I counter tool; this is because the scintillometer though it is a standard procedure in X-ray I has a measuring efficiency about 100 times great­ analysis. I er than Geiger-Muller tubes. Caldwell and Sippel17 present some interesting conclusions on To the present time, the Type I sonde has calibration and response of the Type II tool. been more widely used in the Mid-Continent and I Baker is optimistic enough to anticipate that a Gulf Coast areas. Consequently, calibration I universal calibration curve will be established curves and interpretation aids on this tool are in the near future for the Type II instrument. readily available. The Type I tool has a Until better electronic components for the de­ limited-detail caliper that ,is run simultaneously tector system are available, it is necessary to with the gamma-gamma curve, thus eliminating the have an individual calibration curve for each chance of miscorrelation of "wash-outs" on the field tool. density log. Fig. 10 is an example of the density log Calibration of Instrument calibration curves for the Type I sonde. Note that the curves are for borehole diameters of The attenuation of gamma rays using good 6, 10, 16, and 26 in.; the IRF is 300.00; and geometry and monoenergetic, narrow, collimated, the borehole fluid density is 11.0 lb/gal. The gamma ray beams is predicted by Eq. 16. The calibration curves are available through the Compton process is well-defined with Eqs. 21 and logging company for values of IRF from 100 to 24, but only for a monoenergetic photon experi­ 350, and for the following borehole fluid den­ encing a single scattering in one plane. The sities: air, 8.34, 11.0, 14.0, 16.0, and 18.0 complete process of gaJJllDa ray scattering and ab­ lb/gal. sorption is so complex that it is mathematically prohibitive to attempt computing the response of Since the amplitude of any density log curve this instrument in a borehole. Consequently, the is proportional to the response factor of the preliminary calibrations were made in special instrument with which the log is made, it is al­ test holes of several diameters. Rocks and spe­ ways necessary to calculate the instrument re­ cial concrete mixtures of known density were used sponse factor (IRF) for each log-run before any as the scattering media. When the density log­ interpretation can be made: From the log heading, ging tools were used in the field with boreholes obtain values of source strength (6) and instru­ that had been cored, values of density derived ment factor (F). By the method illustrated on from core analysis were correlated with density Fig. 9, determine the instrument sensitivity (bS). measured with the gamma-gamma log. This combina­ Find the instrument response factor by: tion of data has been used to construct the basic calibration charts necessary for density log •. (25) interpretation. In the case of the Type I tool, these charts (See Fig. 10) give density log de­ The value of IRF is usually between 250 and 300. flections as a function of natural rock density If the log deflections of any number of logs are (e~) for any instrument response factor (IRF) at adjusted to a COJJllDon IRF, the curves can be com­ various values of borehole diameter (D) and pared directly with only small corrections for borehole fluid density (~~). Campbell and borehole diameters and borehole fluid necessary. Wilson5 have presented an excellent review of the Before interpreting for values of natural forma­ calibration of this tool, source strength and tion density, the log deflections must be cor­ sensitivity adjustments, and mud weight and hole rected by use of charts similar to Fig. 10. More size corrections. often than not, an interpolation between curves and between charts will be necessary. There are The calibration curve for the Type II several methods of making such interpretations. density log instrument is much less complex than The authors have worked out an accurate but 12 GAMMA RAY -DENBITY LOGc--=-:cG-=ING'-'-'-______l_25'--'3'------,G com:~~-ca-ted-tr~-p-l-e-l-·n-t-~r-p-o-l-a-t-ion-p-r-o-c-e-d-ur-~.--F-o-r- I localities as a correlation log. When a forma­ methods of statistical correlations, curve fit- I tion is known to be homogenous and non-porous, or ting and curve interpolation, see Ref. 75, 76, i only slightly porous, the density log makes an 77,78,85,88,89. The entire interpretation isl, excellent log from which to construct cross sec­ programed on an electronic digital computer I tions and follow the general lithology of an (IBM 650) thus minimizing the manual efforts. area.

A brief note on statistical error, sensitiv­ Estimation of Porosity from Formation Density ity, time-constant, and logging speed is in order A very comprehensive analysis of these parameters The density log measures the average or is presented in literature published by Lane­ composite density of the formation near the bore­

Wells Co.56 Any geologist or engineer confronted hole walls. Therefore, the fluids filling the Downloaded from http://onepetro.org/SPEPBOGR/proceedings-pdf/59PBOR/All-59PBOR/SPE-1253-G/2087146/spe-1253-g.pdf by guest on 27 September 2021 with the analysis of radioactivity logs should pore spaces are averaged into the value of forma­ have a thorough understanding of these factors. tion density that is determined from the density Assuming that the reader is familiar with this log. This value of formation density shall be subject matter, this paper will recognize a few referred to as "natural denSity" (~n)' The defi­ of the important points that apply specifically nition of "natural density" should be differenti­ to gamma ray-density logging: ated from "bulk density". The bulk density (~" ) is the composite density of the formation grains (A) Make certain that the log quality is and the void pore spaces, whereas natural denSity sufficient. Experience is the best formula here, accounts for the presence of fluids in the pore but the "quality index number" makes a good rule spaces. The relationship between porOSity, grain of thumb for the inexperienced. This number is density, fluid density, and natural denSity is the ratio of the distance between maximum and minimum deflections of the logged section to the ~::: eC] -€n. X 100 ..•. (26) distance between maximum and minimum peaks on the statistical recording. This index number should ~~ - e-f be greater than five for safe interpretation. where e~ is the density of the individual sand Experience in local areas may indicate that a grains, and ef is the weighted average density of much higher quality index should be expected for the fluids filling the pore spaces. reliable interpretation. Presented below is an account of a procedure (B) The density logging instruments auto­ used by the authors in estimating porosity for a matically correct for lag. It is important that large, multi-zoned reservoir. In this applica­ the logging reference point on the sonde is under tion of the density log, several modifications stood in this respect. were necessary. There were 39 wells having den­ sity logs, 16 of which also had core analyses in (c) Normally, density logs are run at speed some of the sands. Of the available density log~ from 20 ft/min to 50 ft/min. Logging speed is an 34, or 87 per cent, were run in oil base mud, important parameter with regard to density log with the average mud density being 10.0 lb/gal. interpretation, and logging speed and time-con­ Also, 29 wells, or more than 74 per cent of the stant should be selected such that good log wells with density logs, had 9-1/2 in. boreholes quality is assured. through the productive interval. Therefore, it was decided that density log calibrations would (D) Repeat runs should be made over the first be made based on the response of an instru­ sections of interest along zero and statistical ment run in a 9-1/2 in. hole with 10.0 lb/gal oil checks. Instrument sensitivity should be deter­ base mud. It was also decided that all deflec­ mined both before and after the log is run. tion readings would be adjusted, for convenience, to an instrument response factor (IRF) of 300. INTERPRETATION AND APPLICATIONS It was first necessary to interpolate be­ Geologic Applications tween the calibration charts to get a curve for 10.0 lb/gal mud. Using Eq. 26, and er = 1.00 It is anticipated that the density log will gm/cc and e~ = 2.65 gm/cc as suggested by Campbell have great utility to the geophysicist, petrole­ and Wilson, initial calculations from this chart um geologist and engineer. DenSity measurements were consistently higher than those reported by will expedite the solution of a great number of the core analyses. This is to be expected because geophysical problems that are common in explora­ denSity log deflections are related to total poro­ tion work. Values of natural density are im­ sity whereas core analyses measures effective portant in the interpretation of gravity meter porOSity. Using core analyses data, grain densi­ surveys. Newton, Skinner, and Silverman7 were ties were calculated from the information on the among the first to use a density logging tool for original data sheets. Several hundred of these this purpose. Geologists were later able to make grain densities were calculated from the core use of the concept. It has been used in several data, and the average value for (e~) derived from 1253-G - ALBIN J. UK ANDI JOE ED SMITH______- -=1""'3 these calculations was 2.647 gm/cc, confirming I logging company were used to determine the mag­ the assumed value. nitude of these corrections. They were prepared I in the form of a cross plot of borehole diameter The influence of the type of fluid lost to - drilling fluid density - density log deflection the formation on wells logged in oil base mud was correction factor. The curves were then stored considered to be significant. It was assumed in the computer and calculations of porOSity were that any infiltration that took place around the made in rapid order. walls of the borehole would tend to increase the oil saturation in the invaded zone. Since the No interpretations were made in some sands density log investigates to about four to six in. because of poor borehole geometry, close prox­ behind the wellbore, it is the saturation distri­ imity to the water table, insufficient bed thick­

bution within the flushed zone that is of inter­ ness, etc. Generally, the interpretations made Downloaded from http://onepetro.org/SPEPBOGR/proceedings-pdf/59PBOR/All-59PBOR/SPE-1253-G/2087146/spe-1253-g.pdf by guest on 27 September 2021 est. Standard evaluation of the oil base core I were in close agreement with core analysis data fluid saturations provided a means for determin- I as is shown on the two examples of core analysis ing So/Sw distribution within the flushed zone. porosity vs corrected density log-derived poro­ (See Ref. 82, 83, 84, 96, 97, 102, 112, 114, 119.~ sity given on Fig. 11. Such consistent agree­ Electronic digital computers were used to sort ment promotes the acceptance of the density log and compute this information from the core analy­ as an effective tool for estimating porosity. sis data, and an average value of So/Sw = 70/30 was derived. It was then assumed that the 30 per After working with density logs from many cent water was formation water and 70 per cent other fields; there are several conclusions the of the total pore volume contained a mixture of authors have reached in respect to porosity the original reservoir oil and a common diesel estimation: fuel (drilling fluid filtrate). By using the values of density for the water, reservoir oil, (1) The type and denSity of drilling fluid and diesel fuel at reservoir conditions of tem­ filtrate will have a very definite effect on the perature and pressure, a composite or average interstitial fluid density (e~) within the in­ formation fluid density (ff) within the invaded vaded zone. Of course, hydrostatic head of mud zone was computed as 0.795 gm/cc. column, formation type, formation permeability, drilling rate, etc. will also have an effect on By interpolating on the calibration charts ef· One approach is suggested which uses simple for a 10.0 Ib/gal mud, the foregoing equation was flood-pot test to determine the average residual solved using e~ = 0.795 gm/cc and a borehole oil or average irreducible water saturations. diameter of 9-1/2 in. The results were plotted The interpreter then assumes that complete flush­ on a semi-log graph of density log derived ing to residual oil occurs within the four or six porosity vs density log deflection in inches. At in. of formation examined by the density log. this point, it is usually necessary to make em­ Hence, if water base mud is used, he reasons that pirical corrections to effective porosity. the interstitial fluid denSity is determined by connate water saturation+ residual oil satura­ In a similar manner, the computations were tion + invaded filtrate saturation. Values of repeated for density logs run in 9-1/2 in. holes pressure and temperature are easily estimated. drilled with a 10.0 Ib/gal water base mud. These The majority of the material in Reference Group two curves were the basis of the interpretation V will be helpful in determining an accurate of the density logs, and the following set of value of ~f' Core analYsis data is of paramount conditions was stipulated with respect to their importance in this respect.82,84,101,102~113 use: Preliminary reports on displacement logging are encouraging in this respect.lll,120 A study of (1) Bore hole diameter = 9-1/2 in. - 1/2 in. the hydraulics of the invasion process is of (2) Drilling fluid density = 10.0 Ib/gal - interest.97,98,112,119 0.4 Ib/gal (3) Density log deflections corrected to (2) It is recognized that grain density has IRF = 300 an appreciable effect on porosity interpretation (4) Average grain density = 2.647 gm/cc and specific measurements should be made wheneve; (5) Ef = 0.795 (oil base mud) or 0.926 possible. When cores are taken, it is inexpen­ (water base mud) sive and convenient to obtain grain denSity data. (6) Bed thickness ~4 ft The laboratory measurement and calculation from (7) Logging speed? 20 but.::... 50 n/min core analYSis of grain denSity is quite simple. (8) Time constant consistent with bed thick­ 93,94,99,105,110 ness and logging speed (9) Consistent borehole geometry *The authors' experience in density log interpre­ It was evident that suitable corrections were tation include Northeast Texas, Upper Texas Gulf necessary when the drilling fluid density and Coast, Mississippi-Alabama Gulf Coast, Southwest borehole diameter did not fit conditions (1) and Texas, Permian Basin, South Central Oklahoma, and (2). The calibration charts prepared by the Paradox Basin. 14 GAMMA RAY-DENS:rrY LOGGING 1253-G ~--~~

(3) Borehole geometry is important. detection and counting of gamma rays. Through experience the log analyst must learn to I recognize the effects of poor borehole geometry. Group IV: Correlation of phenomenological laws with mathematical expressions; elementary (4) Porosity values developed from core and advanced theory of statistical correlations; analysis data should be used in the development and methods of curve fitting and curve interpo­ of field calibration curves. The analysis should lation. include porosity, permeability, fluid saturations, grain density, and rock descriptions. Adequate Group V: Petrophysics of petroleum core data must be available to construct the reservoir materials; evaluation of interstitial field calibration curves and to check the valid­ fluid properties and interstitial fluid hydrau­ ity of this correlation as the field develops. lics with respect to the quantities measured by Downloaded from http://onepetro.org/SPEPBOGR/proceedings-pdf/59PBOR/All-59PBOR/SPE-1253-G/2087146/spe-1253-g.pdf by guest on 27 September 2021 the density log. An interesting evaluation of the density log as a porosity tool is presented by Northcote.8 GROUP I It is unfortunate that similar such investiga­ tions have not been published on other area of 1. Anderson, R. H.: "Applications of the activity. The work of Andersonl highlights ef­ Densilog", (Paper originally presented at the fects of variations in grain density and inter­ Oklahoma Geological Society Annual Meeting, stitial fluid density on density log-derived Oklahoma City, Spring, 1958). porosity. 2. "New Logging Technique Measures Density and Porosity", World Oil (Dec., 1954) m, 7. other Applications of Density Logging 3· Baker, P.E.: "Density Logging with Gamma Rays", Trans •.• AIME (1957) 210, 289-294. Gamma ray-density logging instruments are 4. Caldwell, Richard L.: "Using Nuclear Methods finding other useful applications. Caldwell and in Oil Well Logging", Nucleonics (Dec., 1958) Sippel17 give an account of a borehole fluid 16, 12, 58-65. density tool and a cement-top locator. The for­ 5· Campbell, John L. P., and Wilson, John C.: mer device has application in locating casing "Density Logging in the Gulf Coast Area", leaks or making gradient surveys. Sippel and Jour. Pet. Tech., (July, 1958) 10, 7, 21-25. Hodges9 have presented a tool that is used to 6. Faul, Henry, and Tittle, C. W.: "Logging of log LPG storage wells for the location of fluid Drill Holes by the Neutron-Gamma Method and interfaces. McLendon59 cites a density logging Gamma Ray Scattering", Geophysics, (1951) 16, device used to locate gas sands. Campbell and 261-276. Wilson5 suggest that the tool may be useful in 7· Newton, G. R., Skinner, J. E., and Silver­ sulfur prospecting. The future applications of man, Daniel: "Subsurface Formation Density the density log are prospectively unlimited; the Logging", Geophysics, (1954) 12, 3, 636 - tool can be run in any borehole in any type of abstract. (Paper originally presented at fluid. Its usefulness will be limited only by 24th Annual Meeting of Society of Exploration the wellbore conditions which prevent the precise Geophysicists, St. Louis, Mo., April 12-15, measurements of density. 1954 ) • 8. Northcote, K. E.: "A Preliminary Investiga­ REFERENCES tion of the Density Log As A Porosity Log", Canadian Oil and Gas Industries, (April, 1958 General information concerning the interpre­ 97-106. tation and application of density logs is listed 9· Sippel, R. F., and Hodges, D.: "Simplified under Group I; more specific information on the Gamma Ray Technique Used in LPG Storage Well theory, physical principles, instrumentation, Logging", Pet. Engr. (1958) 3Q, 4, B-u8. and logging techniques are listed in Groups II and III. Research workers and log analysts will GROUP II find literature of interest in all five groups. 10. Aronson, R., and Goldstein, H.: "Status of The five reference groups are defined as Calculations of Gamma Ray Penetration", NDA follows: Report No. 15C-l, (1952), Nuclear Develop­ ment Associates, White Plains, N. Y. Group I: Direct reference to interpreta- 11. Baker, P. E.: ''Neutron Capture Gamma Ray tion and application of density logs; brief dis­ Spectra of Earth Formations", Jour. Pet. Tech. cussions of physical principles. (March, 1957) 2, 3· 12. Belcher, D. J., Herner, R. C., Cuykendall, Group II: Theoretical aspects of the den- T. R., and Sack, H. S.: "Use of Radioactive sity log; academic treatment of the physical laws Material to Measure Soil Moisture and Den­ governing the behavior of gamma rays. sity", AS'lM Tech. Paper No. 134 (1953) American SOCiety of Testing Engineers, Group III: Detailed survey of instrumen- Philadelphia, Pa., 10-22. tation and logging techniques involving the 13. Bitter, Francis M.: Nuclear Physics (1950) 1253-G Addison-Wesley and Co., cambri~::::~. ZAK ANDI3:~E :lm~::. T.: "Graphs of the Compton fuer~: 14. Blatt, S. M., and Weisskopf, V. F.: Theo-, Angle Relationships and the Klein-Nishina retical Nuclear Physics, (1952) John Wiley Formula from 10 Kev to 500 Mev", National and Sons, New York, N. Y. I Bureau of Standards Circular No. 542 (1953) 15· Caldwell, Richard L.: "Gamma Radiation from U. S. Dept. of Commerce, Washington, D. C. Inelastic Scattering of 14-Mev Neutrons in 34. Occhialini, G. P. S., and Powell, C. F.: the Common Earth Elements", Bull., Am. Phy- I "Nuclear Disintegration Produced by Slow sics Society, Series II (Feb. 24, 1956)}, I Charged Particles of Small Mass", Nature No.2, 90. (1947) 122, 186-190. 16. Caldwell, Richard L.: "Nuclear Physics in 35. Pocock, B. W.: "An Analysis of Certain Petroleum Exploration Research", World Pet. Mathematical Assumptions Underlying the De-

(1956) ~, No.4, 59. sign and Operation of Gamma Ray Surface Downloaded from http://onepetro.org/SPEPBOGR/proceedings-pdf/59PBOR/All-59PBOR/SPE-1253-G/2087146/spe-1253-g.pdf by guest on 27 September 2021 17· Caldwell, Richard L., and Sippel, Robert F.: DenSity Gages", Michigan State Highway De- I~ew Developments in Radioactive Well Log- partment Report No. 261 (July 17, 1956). ging Research", Bull., AAPG (Jan., 1958) 42, 36. Semat, Henry: Introduction to Atomic Phys- No.1, 159-171. ics, (1946) Rinehart and Co., New York, N. Y. 18. Compton, A. H., and Allison, S. K.: X-Rays 37. White, G. R.: "X-Ray Attenuation Coeffici- in Theory and Experiment, (1935) D. Van Nos- ents from 10 Kev to 100 Mev", National Bureau trand and Co., New York, N. Y. of Standards Report No. 1003 (1952) U. S. 19· Dienes, C. J.: "Radiations Effects in Dept. of Commerce, Washington, D. C. Solids", Annual Review of Nuclear Science (1953) g, 187-220. GROUP III 20. DuMond, J. W. M., and Cohen, E. R.: "Least­ Squares Adjustment of the Atomic Constants", 38. Armstrong, F. E.: "A Small Diameter Transis­ Reviews in Modern Physics (1953) £2, 691-708. tor Operated Probe for Gamma Ray Logging", 2l. Evans, R. D., and Evans, O. R.: "Studies of (Presented at Symposium on Applications of Self-Absorption in Gamma Ray Sources", Re­ Radioactivity in Petroleum Exploration and view of Modern Physics (1948) 20, 305-326. Production, No~ 6-8, 1957, Houston, Tex.). 22. Fano, Ugo: "Gamma Ray Attenuation", 39· Atkins, E. R.: "Fundamental Theory and In­ Nucleonics (1953) 11, No.8, 8-12 and No.9, strumentation of Radioactivity Logging", 56-61. -- AIME Tech. Paper No. 586-G. (Paper presented 23· Fano, Ugo: "Principles of Radiological at Formation Evaluation Symposium, Houston, Physics", National Bureau of Standards Report Tex., Oct. 27-28, 1955.). No. 1002 (1951) U. S. Department of Commerce, 40. Blanchard, A., and Dewan, J. T.: "The Cali­ Washington, D. C. bration of Gamma Ray Logs", Pet. Engr. (Aug., 24. Faul, Henry, et al: Nuclear Geology, (1954) 1953) B76-B80. John Wiley and Sons, New York, N. Y. 4l. Bousquet, A. G.: "Counting Rate Meters vs 25· Fermi, Enrico: Nuclear Physics, (1950) Scalers", Nucleonics (1949) ~, No.2, 67-76. University of Chicago Press, Chicago, Ill. 42. Brannon, H. R., and Osaba, J. S.: "Spectral 26. Friedlander, G., and Kennedy, J. W.: Intro­ Gamma Ray Logging", Jour. Pet. Tech. (Feb. duction to Radiochemistry, (1949) John Wiley 1956) 30. and Sons, New York, N. Y. Brown, S. C.: "Theory and Operation of 27· Glasstone, S. H.: Sourcebook on Atomic Geiger-Muller Counters", Nucleonics (1948) Energy, (1950) D. Van Nostrand and Co., New g, No.6, 10-22; (1949) }, No.2, 50-64 and York, N. Y. No.4, 46-6l. 28. Halliday, David: Introduction to Nuclear 44. Bush, Robert E., and Mardock, E. S.: "The PhYSics, 2nd Edition, (1955) John Wiley and Quantitative Application of Radioactivity Sons. Logs", Trans. AIME (1951) 192, 191-198. 29· Hirshfelder, J. 0., Magee, J. L., and Hull, Bush, Robert E., and Mardock, E. S.: "Some M. H.: "The Penetration of Gamma Radiation Preliminary Investigations of Quantitative Through Thick Layers", Physics Review (1948) Interpretations of Radioactivity Logs", 1.3., 852-862. Trans. AIME (1950) 189, 19-34. 30. Lane, D. A., Torchinsky, B. B., and Spinks, 46. Cooke-Yarborough, E. H., and Pulsford, E. W.: J. W. T.: "Determining Soil Moisture and "A Counting-Rate Meter of High Accuracy", Density by Nuclear Radiations", AS'lM Tech. Proc., Institute of Electrical Engineers, Paper No. 134 (1953) 23-34. London, fugland (1951) 2§, Part II, 191-195. 3l. Lapp, R. E., and Andrews, H. L.: Nuclear Curt is s, L. F.: "The Geiger -Muller Counter", Radiation Physics, (1954) Prentice-Hall, USNBS Circ. No. 490 (1950) U. S. National New York, N. Y. Bureau of Standards, Washington, D. C., 1-25. 32. Lind, D. A., Brown, J. R., and DuMond, J. W. 48. Curtiss, L. F.: "Measurements of Radioac­ M.: "A Precision Determination of the Energy tivity", USNBS Circ. No. 476 (1949) u. S. of the 1.1 and 1.3 Mev Gamma Radiations from National Bureau of Standards, Washington, c060 by Direct Crystal Diffraction", Physics D. C., 1-84. Review (1949) 12, 591. DiGiovanni, H. J., Graveson, R. T., and Yoli, A. H.: "Scintillation Unit for Drill Hole 16 ------GAMMA RAY-DENSITY--r-- LOGGING 1253-G Logging", Nucleonics (1953) ll, No.4, 34-39.1 69· Toelke, L. W.: !!Scintillation Spectrometer 1:. Fearon, R. E.: "Gamma Ray Well Logging", I Well Logging", AIME Tech. Paper No. 495-G Nucleonics (1949) ~, No.4, 67-75. I (Presented in Denver, Colo., May, 1955.). I 51. Fearon, R. E., and Mardock, E. S.: "The I 70. Vomocil, J. A.: "In Situ Measurement of Soil Quantitative Interpretation of Radioactivity I Bulk Density", Agricultural Engr. (1954) l2., Logs", Oil and Gas Jour. (March 24, 1952) I No·9· 188-194. I 71. Youmans, Arthur, and Monaghan, Ralph: "Sta­ 52. Guelke, R. J., Heydenrych, C. R., and Ander- bility Requirements for Scintillation Coun­ son, F.: !Measurement of Radioactivity and I ters Used in Radioactivity Logging", Trans.

Temperature in Narrcw Boreholes and the II AIME (1957) 210, 231. Development 'Jf Instruments for this Purpose!!,

Jour. of Scientific Instruments and Physics GROUP IV Downloaded from http://onepetro.org/SPEPBOGR/proceedings-pdf/59PBOR/All-59PBOR/SPE-1253-G/2087146/spe-1253-g.pdf by guest on 27 September 2021 in Industry (1949) 26, 150-153. 53· Hur ley, P. M.: !!Direct Radiometr ic Measure­ 72. Aitken, A. C.: Statistical Mathematics, 7th ment by Gamma-Ray Scintillation Spectro­ Edition, (1952) Oliver and Boyd Publishing meter!!, Bull. GSA (1956) fil, 395, 405. Co., London, England. 54. Korff, S. A.: Electron and Nuclear Counters, 73. Churchill, Ruel V.: Modern Operational (1946) D. Van Nostrand Co., New York, N. Y. Mathematics in Engineering, First Edition, 55· Lane-Wells Co.: !!Basic Principles of Radio­ (1944) McGraw-Hill Book Co., New York, N. Y. activity!!, Radioactivity Well Logging, Lane­ 74. Cowden, Dudley J.: Applied General Statis­ Wells Publication No. LR-91-C (1956). tics, (1940) Prentice-Hall, Inc., New York, 56. Lane-Wells Co.: "Instrumentation and Log- N. Y. ging Procedures!!, Radioactivity Well Logging, 75. Crout, P. D.: "Integral Equations and Physi­ Lane-Wells Publication No. LR-92-C (1956). cal Problems", Jour. of Math. and Physics 57· Lane-Wells Co.: !!Other Radioactivity Curves (1940) 12., 34. and Their Uses!!, Radioactivity Well Logging, 76. Deming, W. E.: "Some Notes on Least Lane-Wells Publication No. LR-95-C (1956). Squares", Bull. U. S. Dept. of Agriculture 58. Loevinger, R., and Berman, M.: "Efficiency (1938) 136-141. Criteria in Radioactivity Counting", Nucle­ 77· Ezekiel, Mordecai: !!A First Approximation onics (1951) 2, No.1, 26-39. to the Sampling Reliability of Multiple Cor­ 59· McLendon, Dan H.: !!Radioactivity Logs for relation Curves Obtained from Successive Gas Location!!, World Oil (Feb., 1959) 148, Graphic Approximations", Math. Statistics No.2, 79-84. Annual (Sept., 1930) 1. 60. Mercier, V. J., and Redford, W. H.: "New 78. Ezekiel, Mordecai: "A Method of Handling Calibration and Conversion Techniques for Curvilinear Correlation For Any Number of Radioactivity Logs!!, Jour. Pet. Tech. (Sept., Variables", Bull. Am. Statistics Assn. 1957) IX, No·9, 11-15. (Dec. 1924) XIX, 431-453. 61. Muench, N. L., and Osaba, J. S.: "Identifi­ 79· Ezekiel, Mordecai: Methods of Correlation cation of Earth Materials by Induced Gamma Analysis, (1941) John Wiley and Sons, Inc., Ray Spectrol Analysis", Tr~ AIME (1947) New York, N. Y. 210, 89. 80. Fisher, R. A.: !!Statistical Methods for Re­ 62. Peirson, D. H.: !!The Background Counting search Workers", Seventh Edition (1938) Rate in a Geiger-Muller Counter", Proc. Oliver and Boyd Publishing Co., London, International Physics Society, London, Eng­ England. land (1951) B-64, 427-428. 81. Hoel, Paul G.: Introduction to Mathematical Pirson, Sylvain J.: "Radioactivity Well Statistics, (1954) John Wiley and Sons, Inc., Logging", Oil Reservoir En ineerin , Second New York, N. Y. Edition (1958 McGraw-Hill Book Co., New 82. Kelton, Frank C., et al: "A Statistical Cor­ York, N. Y., 212-232. relation of Total Water As Measured by Core 64. Rossi, B. B., and Staub, H. H.: Ionization Analyses With Actual Connate Water", (Unpub­ Chambers and Counters, (1949) McGraw-Hill lished data in confidential files of Core Book Co., New York, N. Y. Laboratories, Inc., Dallas, Tex.). Russell, William L.: !!The Total Gamma Ray Law, Jan: "A Statistical Approach to the Activity of Sedimentary Rocks as Indicated by Interstitial Heterogeneity of Sand Reser­ Geiger Counter Determinations", Geophysics voirs", Trans. AIME (1944) ill. (1944) 2, 180-216. 84. Law, Jan, and Cerini, William F.: "A Sta­ 66. Russell, William L.: !!Well Logging by Radio­ tistical Approach to Core-AnalYSis Interpre­ activity!!, Bull. AAPG (Sept., 1941) £2., No. tation", Drill. and Prod. Prac., API (1946) 9, 1775-1788. 373-385· Russell, William L., and Scherlatskoy, S. A.: 85. Rachford, H. H., and Schultz, W. P.: "Some "The Use of Sensitive Gamma Ray Detectors in Useful Tables for Approximating Smooth Curves Prospecting", Economic Geol. (1951) 46, 427- by Fifth and Lower Degree Polynominals", 446. Trans. AIME (1955) 204, 289-290. 68. Slack, H. A.: !~ield Measurement of the 86. Snedecor, George W.: Statistical Methods, Radioact i vi ty of Rocks", Trans. AGU (1952) (1956) Iowa State College Press, Ames, Iowa. 897-901. 1253-G ALBIN J. ZAK AND JOE ED SMITH 17

Sokolinkoff, Ivan S., and Sokolinkoff, (1936) 20, 1389-1412. Elizabeth S.: Higher Mathematics for En­ 105· Imbt, William C., and Ellison, Sam P.: I gineers and Physicists, (1941) McGraw-Hill "Porosity in Limestone and Dolomite Petro­ Book Co., New York, N. Y. leum Reservoirs", Drill. and Prod. Prac., 88. Tolley, H. R., and Ezekiel, M.: "A Method API (1946) 364-372. of Handling Multiple Correlation Problems", 106. Jones, Park J.: Petroleum Production - Me­ Bull. Am. Statistics Assn. (Dec., 1923) chanics of Production of Oil, Condensate, XVIII, 994-1003. and Natural Gas, Vol. I, (1946) Reinhold Worthing, A. G., and Geffuer, J.: Treatment Publishing Corp., New York, N. Y., 30-50. of Experimental Data, (1943) John Wiley and 107· Katz, Donald L.: "Prediction of the Shrink­ Sons, Inc., New York, N. Y. age of Crude Oils", Dr ill. and Prod. Prac., API (1942) 137. GROUP V 108. Kay, W. B.: "Density of Hydrocarbon Gases Downloaded from http://onepetro.org/SPEPBOGR/proceedings-pdf/59PBOR/All-59PBOR/SPE-1253-G/2087146/spe-1253-g.pdf by guest on 27 September 2021 and Vapors", Ind. Engr. Chern. (1936) 28, 90. Archie, G. E.: "Classification of Carbonate 1014. Reservoir Rocks and Petrophysical Considera- 109· LeRoy, L. W., et al: Subsurface Geologic tions", Bull. AAPG (Feb., 1952) .3Q, No.2, Methods, Second Edition, (1951) A. B. 278-298. Hirschfield Press, Denver, COlo., 329-341. 91. Archie, G. E.: "Introduction to Petrophys­ 110. Nafe, J. E., and Drake, C. L.: ''Variation ics of Reservoir Rocks", Bull. AAPG (May, with Depth in Shallow and Deep Water Marine 1950) ~, No.5· Sediments of Porosity, Density, and Velocity 92. Arps, J. J.: "The Effect of Temperature on of Compressional and Shear Waves", Geophys­ the Density and Electrical Resistivity of ics (July, 1957) 22, No.3. Sodium Chloride Solutions", Jour. Pet. Tech. Ill. Pritchett, W. C.: "Displacement Logging - (Oct., 1953) 2, No. 10. A New Concept in Resistivity Logging", Pet. 93· Athy, L. F.: "Density, Porosity and Compac- ~. (Feb., 1959) XXXI, No.2, B56-B70. tion of Sedimentary Rocks", Bull. AAPG (1930) 112. Prokop, C. L.: "Radial Filtration of Drill­ 14, 1-24. ing Mud", Jour. Pet. Tech. (Jan., 1952) ~ 94. Brooks, C. S.: "An Evaluation of the Proce- No. 1. dures Used in the Determination of the Grain 113. Pyle, H. C., and Jones, P. H.: "Qu8,ntita­ Densities of Petroleum Reservoir Minerals", tive Determination of Connate Water Content Trans. AJME (1957) 210, 235 -243. of Oil Sands", Drill. and Prod. Prac., API 95· Campbell, W. M., and Martin, J. L.: "Dis­ (1936) 171-180. placement Logging", Trans. AJME (1955) 204, 114. Schilthuis, Ralph J.: "Connate Water in Oil 233-239· and Gas Sands", Trans. AJME (1938) 127, 199- 96. Clark, A. P.: "A Method for Determining Re- I 214. sidual Connate and Drilling Water Saturations 115. Standing, M. B.: "A Pressure-Volume-Temper­ for Cable -Tool Cores", Drill. and Prod. Prac., ature Correlation For Mixtures of California API (1947) 175-185. Oils and Gases", Drill. and Prod. Prac., API 97· deWitte, L.: "Resistivity and Saturation (1947) 275-287. Distribution in Infiltrated Zones of Porous 116. Standing, M. B.: "Oil Field Hydrocarbon Formations", Oil and Gas Jour. (July 27, Systems", (1952) Reinhold Publishing Corp., 1950) ~, No. 12, 246. I New York, N. Y. 98. Doll, H. G.: "The Invasion Process in High 117· Standing, M. B., and Katz, Donald L.: "Den­ Permeability Sands", Pet. Engr. (Jan., 1955). sity of Natural Gases", Trans. AIME (1942) 99· Griffiths, J. C.: "Grain Size Distribution 146, 140. and Reservoir Rocks Characteristics", Bull. 118. Standing, M. E., and Katz, Donald L.: "Den­ AAPG (Feb., 1952) 3Q, No.2. sity of Crude Oils Saturated with Natural 100. Hanson, G. H., Kuist, B. B., and Brown, G. Gas", Trans. AJME (1942) 146, 159. G.: "Liquid Densities of Volatile Hydro- 119· Stuart, R. W.: "Use of Oil-Base Mud at Elk carbon Mixtures", Ind. Engr. Chern. (1944) Hills Naval Petroleum Reserve", Drill. and 3Q, 1161. Prod. Prac. (1946) American Petroleum Insti­ 101. Horner, William L.: "Contamination of Cores tute, 69-75. by Drilling Fluid Can Be Estimated by Dis- 120. Winn, R. H.: "A Report on Displacement solving Simple Chemicals in Mud", Oil Weekly Logging", Jour. Pet. Tech. (Feb., 1958) K, 2. (1935) ]§, No·3, 29· 102. Horner, William L., and Lewis, James A.: "Differentiation of Water in Oil Field Cores", Prod. Monthly (Aug., 1943) 1, No.8, 45. 103. Horner, William L., and LeWis, James A.: "Interstitial Water Saturation in the Pore Space of Reservoirs", Oil Weekly (1936) 86, No.6, 36. 104. Howard, W. V., and David, M. W.: "Develop­ ment of Porosity in Limestones", Bull. AAPG 56

PAIR -PRODUCTION~ 54

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\~Y---e-.----- / -----= ~y' Particle COMPTON SCATTERING~ 'C---_----.__ ~ __ photon e-' MASS NUMBER, A e­ electron e+ positron DIAGRAM SHOWING THREE POSSIBLE FIGURE I n neutron INTERACTIONS .OF GAMMA RADIATION DISINTEGRATION CHART FOR p+ proton WITH THE SILICON+4 ATOM THE THORIUM DECAY SERIES FIGURE 2 (AFTER HALLIDAY)

THE COMPTON EFFECT ® e­ Erel £(1l~ hll'

GAMMA RAY DETECTOR I ~"l@

p ",r In! ~J-- CD y------.(x\:)~i- ..

GAMMA RAY e-' COLLIMATOR @ FIGURE 3 SCHEMATIC OF MODEL USED TO DETERMINE GAMMA RAY Figure: 4 A Compton collision in which a photon of energy EtYl CD collides ATTENUATION COEFFICIENTS with an electron of energy E(e-l ® at ®. The scattered photon moves off at angle e with energy Efyf @, and the electron is deflected at angle 'IV with energy E(e-)' ®. 10

> 9 / ::i<'" V / >- 8 t9 ~ 0::: W 7 / V z !/ ],/,0" w / /' z 6 0 VV I-

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INITIAL PHOTON ENERGY, Mev

FIGURE 5 FIG URE 6 GRAPH SHOWING ENERGY SCHEMATIC OF TYPE I SONDE LOSS OF SCATTERED PHOTONS FOR (RADIAL SOURCE AND GEIGER - MULLER COUNTER) VARIOUS SCATTERING ANGLES

DETECTOR REGION

1

REGIO N b b and I are known· , b '"'b" 2ToST h"Z TonI -e- " 21

I

,- .! h-----I SL SOURCE REGION FIGURE 7 SCHEMATIC OF TYPE n SONDE (COLLIMATED SOURCE AND FIGURE 8 SCINTILLATION COUNTER) GEOMETRY OF TYPE IT SONDE 10.00

FIGURE 10 L EXAMPLE OF DENSITY LOG 9.00 CALIBRATION CURVE FOR TYPE I SONDE 8.00

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WITH 215 STo. SOURC£ :z STANDARD ,NCALIBRATOR,400" 6.00 0 SEM1SIVITY,TIWE CALIBRATOR (~ I- AS '4.00" COMSUNT' 5 SEC <..> w -' 5.00 u... '\ w - 0 I\V - '"0 4 00 -' >- l- V) of-- 300 :z w 0

2.00

FIGURE 9 Instrument Response Factor = 300.00 Density of Bore Hole Fluid = II Olbs/gcl METHOD OF DETERMINING 1.00 DENSITY LOG SENSITIVITY FOR TYPE I SONDE 0 1.8 2.0 2.2 24 2.6 2.8 3.0 3.2

~ NATURAL DENSITY, cc

POROSITY, %

--P f!!~T.!.I,Q'L I)!T.!_ CORE DATA

o 2 ... ~ e ,0 ,2 14 '6 'EI 20 0 2

TABLE I

CHARACTERISTICS OF FUNDAMENTAL PARTICLES

Relative Relahve Year of Particle Synlbol Charge Mass Discovery Electron (Negatron) I 1896 Positron e+ + I 1932 Proton + I 1836

Neutron 1840 1932 Photon y o PI 1901

Alpha Particle + 2 7352

Beta Particle (J: (J-

FIGURE II COMPARISON OF CORE ANALYSIS PO RO SIT Y WITH POROSITY DERIVED FROM DENSITY LOGS