Gamma ray well logging for radial tracer distances

Abstract

 Gamma ray well logging to obtain relative distance indications of tracers from the well bore comprises separating a measured gamma ray spectrum into component parts attributable to individual tracers, using standard spectra, and then obtaining the relative distance indicators from those parts of the spectrum. For cased borehole, using standard spectra as a guide, the proportions of the borehole component and the formation component can be determined and a composite spectrum obtained for each individual tracer by adding the borehole and formation components together. A Compton ratio R_c of gamma ray counts in an energy region of the spectrum which is sensitive to Compton scattering to gamma ray counts in an energy region of the spectrum which is not sensitive to Compton scattering is then obtained. By a linear transformation which parameterizes the Compton ratio R_c with the inverse square of the annulus diameter of a distributed region of tracer surrounding the well bore, a relative distance indication of the distribution of each tracer with respect to the well bore is obtainable for each tracer.

Description

[0001] This invention relates generally to gamma ray well logging and, more particularly, to a method of gamma ray well logging for use in determining the radial distance of a radioisotope tracer from a gamma ray spectroscopy tool in a well bore.

[0002] Radioactive isotopes are widely used in the petroleum industry in a variety of field operations. The most common applications include their use as radioactive tracer elements in techniques for monitoring the effectiveness of downhole operations, such as well completion operations wherein a well is cased and cemented before being placed in production so that the geologic zones of interest can be isolated and so that a seal can be maintained between adjacent geologic formations and the surface. In this respect, techniques utilizing radioactive tracers have been devised for determining cement thickness, in addition to the extent of cement covering throughout the well bore. Radioactive tracers are also used in techniques for monitoring the effectiveness of flow stimulating operations, such as hydraulic fracturing of geologic formations for stimulating the flow of oil or gas from hydrocarbon-bearing formations. By such techniques it has become possible to improve estimates of vertical fracture height or to determine the mean depth of penetration of one or more radioactive tracers injected by a hydraulic fracturing process into a fractured formation disposed about the well bore as an indication of the extent of radial fractures.

[0003] In the construction of artificial structures such as gravel packs, it is helpful to tag the sand in the pack itself as well as in the pre-packed sand placed in the artificial formations outside the perforated casing.

[0004] In the various techniques noted above, it is customary procedure to add one or more radioactive tracers to the materials or slurries which are pumped downhole. A gamma ray energy-detecting tool for detecting the gamma rays emitted by each radioactive tracer is then run in the well for obtaining a well log of spectroscopy measurements which shows the locations of the tracers, presumably where the accompanying materials or slurries which have been placed in the well are also located.

[0005] Many times the desired well completion or stimulation procedures can require that several different materials be placed in a single operation. In the past, it has usually been necessary to limit the complexity of such operations because only one tracer could be monitored by means of gross gammas ray counting tools which are sensitive only to the overall presence of gamma rays and not to the individual gamma ray energy signatures characteristic of different tracers. However, gamma ray spectroscopy tools have since been devised which make it possible to efficiently and accurately monitor multiple radioactive tracers, and thus multiple materials, in downhole operations. In particular, these tools measure the energies of gamma rays emitted by radioactive tracers located in a well and the geologic formations in the immediate vicinity. Gamma ray spectroscopy logs utilizing this technique have been found useful in a variety of situations and an increasing number of applications.

[0006] We have now devised a way of utilizing gamma ray well logging to obtain a relative distance indication of the placement of a radioisotope tracer with respect to the well bore.

[0007] According to the present invention, there is provided a method of gamma ray well logging of one or more radioactive tracer isotopes in an unknown cased or uncased well borehole to obtain a relative distance indication of each radioisotope trace with respect to the well bore, said method comprising: obtaining standard gamma ray energy spectra for one or more individual tracer elements disposed in at least two different geometrical regions spaced apart from a gamma ray detector in a known well bore environment; moving a well logging instrument through the unknown well bore and detecting gamma radiation emitted from one or more selected radioactive tracer isotopes at different depth levels in the well borehole; separating said detected gamma radiation into a measured unknown gamma ray energy spectrum at each of a plurality of depth levels in the unknown borehole; separating said measured unknown gamma ray energy spectrum into component parts attributable to each such selected radioactive tracer isotope disposed in each of said geometrical regions by comparing said measured unknown gamma ray energy spectrum with said one or more standard gamma ray energy spectra of said selected tracer elements taken with said tracer elements disposed in said geometrical regions; and obtaining a relative distance indicator with respect to said well borehole for each tracer from the component parts of the unknown spectrum attributable to each tracer disposed in each said geometrical region.

[0008] The invention also provides a method of gamma ray well logging of one or more radioactive tracer isotopes in an unknown cased well borehole to obtain a relative distance indication of each radioisotope trace with respect to the well bore, said method comprising: moving a well logging instrument through the unknown well bore and detecting gamma radiation emitted from one or more selected radioactive tracer isotopes at different depth levels in the well borehole and the formation adjacent said borehole; separating said detected gamma radiation into a measured unknown gamma ray energy spectrum at each of a plurality of depth levels in the unknown borehole; at such depth levels in the unknown borehole, separating said measured unknown gamma ray energy spectrum into component parts attributable to each such selected radioactive tracer isotope disposed in specific geometrical regions relative to the borehole by comparing said measured unknown gamma ray energy spectrum with said one or more standard gamma ray energy spectra of said selected tracer elements; forming a composite spectrum for each said radioactive tracer isotope by summing respective portions of the spectra of the tracer attributable to such said geometrical regions; forming a Compton ratio R_c of gamma ray counts in a first energy region of said composite gamma ray spectrum which is sensitive to Compton scattering of gamma rays to gamma ray counts in a second energy region of the composite gamma ray spectrum which is not sensitive to Compton scattering of gamma rays to a degree sufficient to markedly affect said ratio R_c; and obtaining a relative distance indication for each said tracer with respect to said well borehole from a predetermined functional relationship of the Compton ratio R_c and the diameter of the annulus of the region of distribution of the tracer about said well bore wherein said diameter represents the outer limit of tracer distribution as measured from said well bore.

[0009] The standard spectra can, for example, be obtained from artificial geologic formations simulating a standard cased hole environment, by placing a radioactive tracer in the various annuli of the calibration formations and detecting the gamma radiation therefrom using a detector positioned in the simulated well casing. Standard energy spectra of the tracer can thus be obtained representing the presence of the tracer in specific geometrical regions, such as tracer only in the formation, tracer only in the cement annulus about the casing, and tracer only in the borehole.

[0010] These (or other) standard energy spectra, or signature spectra of the tracer, are then used in the method of the invention in, for example, a weighted-least-squares algorithm into which is input an arbitrary measured spectrum obtained from logging a well borehole in a field operation. A solution is then obtained for the individual tracer concentrations. In particular, using borehole and formation signature spectra obtained from the calibration formations, it is possible to obtain, for example, the borehole and formation concentrations for each radioisotope tracer present in the field well and its immediate environment. This means that each tracer used in the field well can be represented by a linear combination of the borehole and formation components. Then, from these components, a composite spectrum for each individual radioisotope tracer may be constructed by summing the component spectral from each geometrical region. This composite spectrum contains peak structure due to unscattered gamma rays reaching the detector, and also due to scattered, lower energy gamma rays. The relative intensity of the lower energy scattered gamma rays to the higher energy less scattered (or unscattered) gamma rays is indicative of the amount of scattering material between the tracer and the detector, and therefore to the radial.

[0011] From each composite, a Compton ratio R_c, of gamma ray counts in a first energy region of the composite spectrum which is sensitive to Compton scattering to gamma ray counts in a second energy region of the composite spectrum which is not sensitive to Compton scattering, can be obtained and transformed into a quantity proportional to the radial distribution of the associated tracer.

[0012] In order that the invention may be more fully understood, reference is made to the accompanying drawings, wherein:

Figure 1 is a view in perspective and part cut­ away, of a first tank structure containing one embodiment of artificial geologic formation which can be used in calibrating the tracer response of gamma ray spectroscopy tools;

Figure 2 is a view in perspective and part cut­away, of a second tank structure containing a second embodiment of artificial geologic formation which can be used in calibrating the tracer response of gamma ray spectroscopy tools;

Figure 3 is a schematic drawing of one form of well logging system which can be employed in practising the present invention;

Figure 4 is a graphical representation of formation and borehole spectra for ¹⁹²Ir obtained in gamma ray spectroscopy measurements of ¹⁹²Ir tracer distributed in the casing fluid and artificial geologic structure contained in the tank of Figure 2;

Figure 5 is a graphical representation of formation and borehole spectra for ⁴⁶Sc tracer obtained in gamma ray spectroscopy measurements of ⁴⁶Sc tracer distributed in the casing fluid and formation annuli of the artificial geologic structure in the tank of Figure 1;

Figure 6 is a graphical comparison of the cement annulus spectrum shown in Figure 5 with a composite annulus spectrum obtained by summing 61% of the formation spectrum and 39% of the borehole spectrum of the spectra shown in Figure 5; and

Figure 7 is a graphical illustration of tracer concentration and radial distance curves obtained by the method of the invention, from a sample well log where a fracturing operation was performed using ⁴⁶Sc for tagging the fracturing fluid and ¹⁹²Ir for tagging the proppant material.

[0013] A series of calibration experiments was performed to establish the response of three gamma ray spectroscopy tools to six common tracer isotopes with the principal purpose of determining tool sensitivities to different isotopes so that a weighted-least-squares algorithm could be implemented to process multi-tracer logs. Two artificial geologic formations were constructed to simulate a typical cased hole environment. These artificial test formations are illustrated in Figures 1 and 2. Each formation was constructed utilizing a cylindrical steel tank 10, 30 inches (76cm) in diameter and 36 inches (91cm) deep, mounted on four 30 inch (76cm) high steel legs 11. A 5½ inch (14cm) diameter, 17 lb/ft. (25.3 kg/m), 60 inch (1.52m) long casing 13 was welded to the center of each tank 10 in coaxial relation thereto. A stainless steel cylinder 15 was also welded to each tank 10 in concentric spaced relation to the casing 13 to provide a 1½ inch (3.8cm) thick annulus adjacent to the casing 13 in order that a cement sheath 16 could be simulated. The tank 10 in the test formation illustrated in Figure 1 was further subdivided into inner, middle and outer annuli by means of additional stainless steel cylinders 16 and 17. The diameters of the cylinders 16 and 17 were such as to provide the inner annulus with a radial thickness of 2 inches (5.1cm), the middle annulus with a radial thickness of 3 inches (7.6cm), and an outer annulus with a radial thickness of 5-¾ inches (14.6cm).

[0014] On each tank the casing and each annulus were separately plumbed so that each individual region could be isolated and filled or emptied as required. The formation and cement "matrix" materials were simulated using loose-­packed sandstone gravel such that each test formation has a porosity of about 40%.

[0015] Each tracer used was in water-soluble form and added to fresh water in a supply barrel in sufficient concentrations to give count rates in the range of 500-1000 gamma ray API units. This corresponded to radioactivity levels of only a few tens of microcuries. The tracer-tagged water was transferred between the formation and the supply barrel through plastic tubing using a peristaltic pump driven by a reversible electric motor. The experimental procedure was to make background measurements with fresh water in the pore space and then to measure the tracer spectra in each annulus by successively filling each annulus from the outermost to the innermost, as well as filling the casing for the final measurement. The tracer spectra for each individual region were obtained by subtracting the spectra from adjoining regions as appropriate.

[0016] Six of the most commonly used radioactive tracers, having half lives ranging from 2.7 to 250 days, were selected for the tracer calibration experiments with characteristics as shown in TABLE 1 below.

TABLE 1.

ISOTOPES IN TRACER CALIBRATION EXPERIMENTS
TRACER	ISOTOPE	HALF-LIFE	GAMMA-RAY ENERGY* (keV)	INTENSITY+
Gold-198	198Au	2.70 days	412	0.96
			676	0.01
Iodine-131	131I	8.04 days	284	0.06
			364	0.81
			637	0.07
			723	0.02
Antimony-124	124Sb	60.2 days	606*	1.05
			720*	0.15
			1353*	0.05
			1691	0.49
			2091	0.06
Iridium-192	192Ir	74.0 days	311*	1.42
			468	0.48
			603*	0.18
Scandium-46	46Sc	83.8 days	889	1.00
			1121	1.00
Silver-110m	110mAg	250 days	666*	1.32
			773*	0.34
			885	0.73
			937	0.34
			1384	0.24
			1502*	0.18

+Intensity values give fraction of nuclear decays which result in gamma ray emission.

*Energies of weak gamma ray transitions omitted. An asterisk indicates a weighted composite of multiple gamma rays which cannot be resolved by Nal(Tl) detectors.

[0017] Three gamma ray spectroscopy tools were used to collect the tracer spectra. Two were large diameter (3-5/8 inch - 9.2cm) tools with 2 inch (5.1cm) diameter Na(T1) detectors. One of the large tools had a tool case of low atomic number (Low-Z) material so that photoelectric gamma rays could be observed and the other was provided with a titanium housing designed for high temperature, high pressure applications. The third tool had a small diameter (1 11/16 inches - 4.29cm) and a steel tool housing.

[0018] A typical gamma ray logging system which may be used for practising the invention is illustrated schematically in Fig. 3. The system, which can be used in field applications, comprises a logging tool 30 suspended in a well borehole 31 from a logging cable 32 supported by a reel 34 on a logging truck or the like. The borehole 31 passes through earth formations 33 and may be lined with a steel casing 35 set in place by an annulus of cement. The tool 30 can however, be used in an uncased borehole as well. The casing contains a well bore fluid 36. In conventional manner, rotation of the reel 34 provides an indication of tool depth as the cable 32 is moved in or out of the borehole. The tool 30 is provided with a steel housing 37 having a section 37a which surrounds the radiation detector 38. The section 37a is constructed from a material having a low atomic number (Z) and low density to facilitate observation and measurement of photoelectric absorption of low energy gamma rays. Such a tool case is described in our U.S. patent specification no. 4,405,354. For high temperature, high pressure applications, section 37a could be made of titanium. Incident gamma rays, whether from natural radiation or from tracers, are detected in a large NaI(T1) scintillation detector crystal 38, the scintillations of which are coupled to a photomultiplier 40 to produce electrical pulses of magnitudes proportional to the energies of the impinging gamma rays.

[0019] The system gain can be maintained with ± 0.5% by a coincidence stabilization technique for which purpose the apparatus includes in close proximity to detector 38, a smaller crystal 42 containing an embedded ²⁴¹Am source. Such a technique is described in U.S. patent specification no. 4,585,939. Other gain stabilization techniques, such as are common in the art, could alternatively be used if desired.

[0020] After amplification by photomultiplier 40, coincidence and anti-coincidence data pulses are digitized by an analog-to-digital converter 44, accumulated in a data accumulator 46, and sorted by a microprocessor controller 48 which synchronizes transmission of data from the tool 30 to equipment at the surface. The coincidence (stabilizer) events are converted into a 256 channel spectrum which spans the energy range from 0-350 keV so as to enable the automatic downhole gain stabilizer feedback circuit to maintain system gain to approximately ± 0.5%. The anti-­coincidence (external gamma radiation) events are converted into two spectra, one of which spans the low energy range from 0-350 keV and the other of which spans the high energy range from 0-3000 keV. The three spectra are accumulated in accumulator 46 and then transmitted along the cable conductors, approximately each 0.25 ft. (7.6cm) while logging, to the logging system located at the surface. At the earth surface, the data are demodulated by a demodulator 50 prior to recording in a magnetic tape recorder 52 and display in a spectral display device 54. The external gamma ray spectra are also transferred to the computer 56 in which the high energy spectrum is separated into energy windows or regions dependent on the particular tracers used. High energy windows are selected to encompass specific gamma ray energy peaks between 150 keV and 0-3000 keV characteristic of the particular tracer being used, whereas low energy windows are selected to include primarily downscattered radiation, generally between 150 and 350 keV. For the low energy spectrum, windows are selected for providing photoelectric sensitivity ratios under the constraint of minimizing statistical uncertainty.

[0021] The primary purpose of the tracer calibration measurements was to determine the sensitivities of the three spectroscopy tools to different tracer isotopes so that a weighted-least-squares (WLS) algorithm could be implemented for processing gamma ray spectroscopy logs. The WLS method has been described previously in a paper by Smith, H.D. Jr., Robins, C.A., Arnold, D.M., Gadeken, L.L. and Deaton, J.G., "A Multi-Function Compensated Spectral Natural Gamma Ray Logging System", SPE Paper No. 12050, Fifty-Eighth Annual Technical Conference, San Francisco, California, October 5-­8, 1983. The WLS method thus described was applied to the estimation of the potassium, uranium, and thorium concentrations from natural gamma ray spectra. For that application, the elements of the sensitivity matrix were defined to be the individual window count rates per unit concentration for each natural constituent. Since for tracer applications, the parameters of interest are generally the relative amounts of each tracer present, the elements of the tracer sensitivity matrix were defined to be the individual window count rates per unit gamma ray API for each isotope. The sensitivity matrices for each tracer isotope were constructed by summing together the spectral count rates in each of the standard 13 energy windows and dividing by the observed API value for the appropriate calibration spectra. Also in this respect, reference is made to our European patent specification no. 198615A and to our U.S. patent specification no. 4825071. These specifications disclose techniques of weighted-least squares fitting of standard gamma ray spectra for tracer elements utilized in well bore logging to measured gamma ray spectra taken in arbitrary boreholes.

[0022] The original assumption for such data was that it was generally sufficient to consider only two regions containing tracers. These two WLS solution components were (1) the borehole region inside the casing and (2) the formation region outside the cement annulus. It was assumed that the cement annulus was impervious to the tracer. If conditions were such that the tracers were in the cement annulus, then this contribution would be approximated by combining appropriate fractions of the borehole and formation components. The spectral signatures for ⁴⁶Sc from these three regions are shown in Figure 4 for the Low-Z tool. The differences due to increased Compton downscattering effects as more and more material is interposed between the source region and the detector are clearly evident. For the illustration of Fig. 4 the spectra were normalized so that each 1121 keV (channel 99) peak had the same amplitude.

[0023] Figure 5 compares the cement annulus spectrum from Figure 4 with a composite spectrum obtained by summing 61% of the formation tracer spectrum and 39% of the borehole tracer spectrum from Figure 4. The Values of 61% and 39% were found by analyzing the cement annulus tracer spectrum using the WLS algorithm and assuming that the input data were made up of a formation component and a borehole component. Figure 5 illustrates a fact that has been observed in the spectroscopy log field data and verified using various combinations of calibration spectra from different annuli in the test formations. It is generally possible to determine a linear combination of formation and borehole standard spectra which matches any observed tracer spectrum, no matter where the isotope is located. The quality of the fit is good enough in most cases that the composite spectrum cannot be distinguished from the true spectrum for typical logging statistics.

[0024] A corollary of this observation is that a negative com­ponent is perfectly legitimate, at least mathematically. For example, if a spectrum was measured for which a tracer was present only in the outer annulus of test formation # l shown in Figure 1, the WLS solution assuming only formation and borehole components would result in a positive formation value and a negative borehole value. The reason for this can be seen easily. The tracer spectrum from the outer annulus has a greater Compton downscattered component than that for the whole formation annulus. Therefore, the borehole value determined from the WLS algorithm must be negative since it represents a less Compton scattered portion of the signal. A fraction of the borehole must be subtracted from the for­mation signature to obtain the composite spectrum which most closely matches the spectrum from the outer annulus. This mathematically sound, yet physically unreasonable, concept of negative concentrations has led to a reformulation of the gamma ray spectroscopy log presentation in terms of a rela­tive distance indicator for each tracer. Although mathemati­cally consistent with the division into formation and borehole components, it has the desirable feature of elimi­nating negative concentration values from the output log as well as providing information on the radial distributions of the tracers which is independent of the actual tracer con­centrations.

[0025] For a particular downhole operation, where information is desired as to the distribution of radioisotope tracers in the vicinity of the zone of interest in a well bore, the unknown gamma ray spectrum is measured by moving a well logging instrument, such as shown in Figure 3, through the well borehole. The resulting gamma ray spectrum as measured in the depth region of interest in the well bore in the field is fitted to the standard energy signature spectra for the individual tracers by a weighted-least-square technique as referred to above. Accordingly, using borehole and for­mation signature spectra obtained from the calibration for­mations, it is possible to obtain the borehole and formation concentrations for each radioisotope tracer present in the field well and its immediate environment. This means that each tracer can be represented by a linear combination of the computed borehole and formation components (. Then, from these com­ponents, a composite spectrum for each individual radioiso­tope tracer may be constructed and from each composite spectrum a Compton ratio, R_c, of gamma ray counts in a first energy region of the composite spectrum which is sensitive to Compton scattering to gamma ray counts in a second energy region of the composite spectrum which is not sensitive to Compton scattering is obtained. As will thereafter be shown, the Compton ratio can then be transformed into a quantity proportional to the radial distribution of the associated tracer.

[0026] In a previous publication by Gadeken, L.L.; Smith, H.D. Jr.; and Seifert, D.J.: "Calibration and Analysis of Borehole and Formation Sensitivities for Gamma Ray Spectroscopy Measurements with Multiple Radioactive Tracers", The Log Analyst (May-June, 1988) 159-177, a Compton ratio, R_c, was defined to be a high energy count rate (350 keV-3000 keV) divided by a low energy count rate (150 keV-350 keV). This makes it convenient to quantify the effects of Compton downscattering on the observed gamma ray spectra. An addi­tional result illustrated in Figure 6 is that the Compton ratio obtained from the formation-plus-borehole composite spectrum is nearly the same (usually within measurement sta­tistics) as the Compton ratio found from the actual spectrum. This observation makes it possible to determine an R_c value for each tracer, even when more than one tracer is present, since borehole and formation components are obtained for each isotope using the WLS algorithm.

[0027] It was also shown in the Log Analyst publication noted above that the Compton ratio is directly related to the inverse square of the annulus diameter. By data analysis, it has been found that the Compton ratio data can be linearized by parameterizing it with the inverse square of the annulus diameter, D, as follows:
R_c = A +

where A and B are constants which are dependent on the tracer type and the casing diameter. This relation was used in this invention as the basis for the development of a relative distance indicator. Detailed data analysis has shown that this indicator is best used only qualitatively, which is mainly a result of the uncertainty in the diameter estimate induced by the statistics of the Compton ratio measurement. The effects of borehole size, casing size and tool position also contribute to the problem. Nevertheless, such analysis has established that this rela­tive distance measurement can be qualitatively used to indi­cate the average depth of tracer penetration. Further development may permit quantitative results to be obtained.

[0028] One of the unique features of the gamma ray spectroscopy logging system described herein is that measurements in the low energy photoelectric region can be made when using the Low-Z toolcase. As with Compton scattering effects, it is convenient to parameterize the photoelectric information using the ratio of a higher energy count rate window (80-150 keV) to a lower energy count rate window (20-80 keV). The measurement principle is that gamma rays from tracers inside the well casing undergo much less low energy photoelectric absorption than those from outside the casing. It was shown that the photoelectric ratio, R_p, usually makes it possible to distinguish the location of tracers inside versus outside the casing. Operationally, however, the R_p log value must also be used qualitatively due to a number of factors including counting statistics, borehole and casing diameter effects and increased sensitivity to tool response variations as well as whether or not the natural gamma ray background was removed.

[0029] It is to be noted therefore, that the Compton relative distance indicator is related to the average placement distance for individual tracers and that the photoelectric ratio is primarily an indicator of the relative tracer count rate inside versus outside the casing. These relative distance indicators which are derived from gamma ray spectroscopy logs of radiation from tracer tagged materials placed downhole are quite helpful in the interpretation of the effectiveness of the particular downhole operations.

Log Example

[0030] The gamma ray spectroscopy log presented in Fig. 7 is a typical field example which shows the utility of the WLS pro­cessing algorithm for tracer concentrations coupled with both Compton and photoelectric relative distance indicators. It is to be noted, however that since the depth of investigation of any gamma ray tool is about one foot from the borehole wall, the tracer concentrations and average distances shown on the log reflect information from a limited radial region surrounding the borehole. Nonetheless in many situations the near well bore environment reflects approximately the state of affairs in the formations far removed from the well bore.

[0031] There are four steps recommended to obtain a complete set of gamma ray spectra: (1) a "before" log is run to deter­mine the natural gamma ray background, (2) the materials tagged with radioactive tracers are placed downhole, (3) an "after" log is run to measure the gamma ray spectra from the tracers and from the natural background, and (4) the "before" data is subtracted from the "after" data and a resulting log is generated which shows the tracer concentrations and the relative distance of the tracers as a function of depth. It should be recognized that it is possible to skip Step 1 and estimate the natural background contribution together with the tracer response, or to ignore the natural background if the tracer concentrations used are high enough such that the natural gamma ray background is not a significant contribution to the total observed spectra. However, not subtracting the natural background does degrade the quality of the tracer estimates since in general one should solve the three natural gamma concentrations (K,U,Th), as well as each of the tracer concentrations in the WLS algorithm. This leads to greater uncertainty in the calculated tracer results. An approximate composite natural gamma ray sensitivity treated in the WLS algorithm just like another tracer sensitivity can give an adequate result for the value of the natural gamma ray background in many cases.

[0032] It appears that three isotopes are a practical limit for obtaining relative distance indicators using a large (3-5/8 inch - 9.2cm) spectroscopy tool. The small (1-11/16 inch - 4.29cm) spectroscopy tool is limited to two isotopes due to its smaller gamma ray detector and the corresponding reduced sensi­tivity to the different tracer signatures.

[0033] The log example shown in Fig. 7 is from a well (completed with a 7 inch (17.8cm) diameter cemented casing in a 10 inch (25.4cm) diameter borehole) in California where a single stage foam fracturing operation was performed. The fluid pumped downhole was tagged with ⁴⁶Sc while the proppant was tagged with ¹⁹²Ir. The perforated interval extended from X258 ft to X358 ft (X78.6m to 109.1m). The spectra data were obtained with a large tool with a Low-Z housing around the detector, permitting the photoelectric, as well as the Compton distance indicators to be measured. Figure 7 shows the resulting log. The base log natural gamma ray curve and the Fit-Error curve are shown in Track 1. The total tracer concentrations (individual contri­butions shaded) are displayed in Track 2 together with the Rp (photoelectric ratio) curve. The Compton relative distance curves for ⁴⁶Sc and ¹⁹²Ir tracers are given in Track 3. The relative distance curves were obtained by using the borehole and formation components to construct a composite spectrum for each isotope. The Compton ratio values were obtained and converted to relative distance values as described above.

[0034] The concentration curves indicate that the fracturing fluid and the proppant are both present throughout the logged interval. The predominance of ⁴⁶Sc in the upper and lower sections leads to the suspicion that this signal is due to residual fluid in the borehole. This is supported by the consistently low value of the R_p curve which shows the pre­sence of tracer material in the borehole above X230 and below X358. The R_p curve gives a qualitative outside casing indi­cation in the zone between X230 and X300 since its values are greatest in this interval. The Compton relative distance curves show that the most effectively fractured and propped interval in the well occurred between X220 and X264. The ⁴⁶Sc relative distance curve shows the fractured zone extends downwards to X356 while the ¹⁹²IR relative distance curve shows somewhat less effective propping of the formation in this interval. The "peaky" fine structure of the relative distance curves may be statistical artifacts and should not be interpreted unless verified by repeat passes over the zone of interest. However, the similar trends for both the Compton and photoelectric relative distance curves over extended intervals in the well stand out clearly. It is apparent that these curves can be used to assist in interpreting gamma ray spectroscopy logs.

[0035] Information from the operating company states that the quality of the cement job across the logged interval was rather poor and that higher than desired pumping rates were used in an attempt to avoid a premature screen-out. This could have resulted in significant amounts of sand being deposited in or around the borehole and not out into the for­mation as desired. The overall results of this log indicate that the fractured interval extended beyond the perforations and that the proppant was not placed as effectively as desired, which was confirmed by subsequent production rates which were lower than anticipated.

[0036] It is therefore to be noted that calibration experiments and analysis results with the use of both large and small gamma ray spectroscopy tools for six different isotopes have been described from which it is possible to determine both formation and borehole gamma ray spectral sensitivities for each tracer in a multi-tracer operation so that a weighted-­least-squares algorithm can be implemented. The use of bore­hole as well as formation components in the solution results not only in more accurate total concentration measurements for each tracer, but also in the qualitative determination of the radial location of the tracers. This is possible by use of the two-component solution for each isotope to find a Compton ratio for each. A relative distance estimate can then be extracted from the composite Compton ratio for each material tagged with a distinct radioactive isotope.

Claims

1. A method of gamma ray well logging of one or more radioactive tracer isotopes in an unknown cased or uncased well borehole to obtain a relative distance indication of each radioisotope trace with respect to the well bore, said method comprising: obtaining standard gamma ray energy spectra for one or more individual tracer elements disposed in at least two different geometrical regions spaced apart from a gamma ray detector in a known well bore environment; moving a well logging instrument through the unknown well bore and detecting gamma radiation emitted from one or more selected radioactive tracer isotopes at different depth levels in the well borehole; separating said detected gamma radiation into a measured unknown gamma ray energy spectrum at each of a plurality of depth levels in the unknown borehole; separating said measured unknown gamma ray energy spectrum into component parts attributable to each such selected radioactive tracer isotope disposed in each of said geometrical regions by comparing said measured unknown gamma ray energy spectrum with said one or more standard gamma ray energy spectra of said selected tracer elements taken with said tracer elements disposed in said geometrical regions; and obtaining a relative distance indicator with respect to said well borehole for each tracer from the component parts of the unknown spectrum attributable to each tracer disposed in each said geometrical region.

2. A method according to claim 1, wherein the step of comparing said measured unknown gamma ray energy spectrum and said standard gamma spectra is performed by fitting said measured unknown spectrum to said standard spectra using a weighted-least-squares fitting technique of all selected tracer isotope standard spectra components to the measured unknown spectrum.

3. A method according to claim 1 or 2, wherein said relative distance indication for each said tracer with respect to the well borehole is obtained by solving for the quantity D in the linear relationship R_c = A +

where A and B are constants which are dependent on the particular tracer and the casing diameter, and D is the outer diameter of an annulus cylindrical region of distribution of the tracer with respect to the well borehole.

4. A method according to claim 1,2 or 3, which further includes modifying the measured unknown gamma ray spectrum by removing therefrom the background gamma radiation due to naturally occurring gamma rays in the formations adjacent the well borehole which are emitted from uranium, thorium, and potassium isotopes and their daughter products, to obtain a modified measured gamma ray spectrum representing solely the energy spectrum of gamma radiation attributable to radioactive tracer elements.

5. A method according to any of claims 1 to 3, which further comprises the step of including one or more standard spectra for natural gamma radiation as background standard spectra in the step of separating the measured unknown spectrum into component parts, wherein the natural gamma ray background is assumed to be a part of the measured unknown spectrum.

6. A method of gamma ray well logging of one or more radioactive tracer isotopes in an unknown cased well borehole to obtain a relative distance indication of each radioisotope trace with respect to the well bore, said method comprising: moving a well logging instrument through the unknown well bore and detecting gamma radiation emitted from one or more selected radioactive tracer isotopes at different depth levels in the well borehole and the formation adjacent said borehole; separating said detected gamma radiation into a measured unknown gamma ray energy spectrum at each of a plurality of depth levels in the unknown borehole; at such depth levels in the unknown borehole, separating said measured unknown gamma ray energy spectrum into component parts attributable to each such selected radioactive tracer isotope disposed in specific geometrical regions relative to the borehole by comparing said measured unknown gamma ray energy spectrum with said one or more standard gamma ray energy spectra of said selected tracer elements; forming a composite spectrum for each said radioactive tracer isotope by summing respective portions of the spectra of the tracer attributable to such said geometrical regions; forming a Compton ratio R_c of gamma ray counts in a first energy region of said composite gamma ray spectrum which is sensitive to Compton scattering of gamma rays to gamma ray counts in a second energy region of the composite gamma ray spectrum which is not sensitive to Compton scattering of gamma rays to a degree sufficient to markedly affect said ratio R_c; and obtaining a relative distance indication for each said tracer with respect to said well borehole from a predetermined functional relationship of the Compton ratio R_c and the diameter of the annulus of the region of distribution of the tracer about said well bore wherein said diameter represents the outer limit of tracer distribution as measured from said well bore.

7. A method according to claim 6, which further includes modifying the measured unknown gamma ray spectrum by removing therefrom the background gamma radiation due to naturally occurring gamma rays in the formations adjacent the well borehole which are emitted from uranium, thorium, and potassium isotopes and their daughter products, to obtain a modified measured gamma ray spectrum representing solely the energy spectrum of gamma radiation attributable to radioactive tracer elements.

8. A method according to claim 6 or 7, wherein the step of comparing said modified measured unknown gamma ray energy spectrum and said standard gamma ray spectra is performed by fitting said measured unknown spectrum to said standard spectra using a weighted-least-squares fitting technique of all selected tracer isotope standard spectra components to the measured unknown spectrum.

9. A method according to claim 6,7 or 8, wherein said relative distance indication for each said tracer with respect to the well borehole is obtained by solving for the quantity D in the linear relationship R_c = A +

where A and B are constants which are dependent on the particular tracer and the casing diameter, and D is the outer diameter of an annular cylindrical region of distribution of the tracer with respect to the well borehole.

Drawing