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(1)Abstract
Slim-hole gamma ray tools using sodium iodine (NaI) scintillation crystal detectors (1 in. x 4 in.) are best suited for high radioactivity environments such as those encountered in radioactive minerals exploration. Recent sediments at the Lawrence Livermore National Laboratory (LLNL) Livermore Site, Livermore, California, have very low natural gamma radiation levels, with minimal sand/clay gamma ray contrasts. In this setting, the 1- x 4-in. detectors generate inadequate counting statistics to provide reliable sand/clay discrimination or stratigraphic correlation. This inadequacy is characterized by highly unstable detectors and poor agreement in log repeat sections.
At the LLNL Livermore Site, slim-hole natural gamma ray log detector stability and log repeat section agreement has been significantly improved by using gamma ray logging tools with 1- x 8-in. NaI scintillation crystal detectors. The improvements obtained by doubling the scintillation crystal volume greatly exceeded those obtained by reducing the logging speed by a factor of two and/or lengthening the counting time windows. This approach should be of value to other low radioactivity logging environments.
Figure 1 (large) is a physiographic rendering of the Livermore Valley, showing the location of the LLNL Livermore Site. The Site is located just east of the town of Livermore, California, approximately 40 miles east of San Francisco. The Livermore Valley is a 16-mi-long topographic and structural basin that trends east-west transecting the regional structural fabric of northwest-trending ridges and valleys of the Central Coast Range Province of California. It separates the Mount Diablo antiform to the north from the Diablo Range to the south. The 2,000-ft-high Altamont Hills, east of Livermore, separate the Livermore Valley from the San Joaquin Valley to the east. The East Bay Hills separate the Livermore Valley from the San Francisco Basin to the west.
Figure 2 shows the structural setting of the Livermore Valley (Raber and Carpenter, 1983; Thorpe et al., 1990). The valley occupies an en echelon tear created by differential right-lateral movement between the Greenville Fault Zone to the east and the Calaveras-Sunol Fault Zone to the west. The Las Positas Fault Zone accommodates the en echelon rotation along the valley's southern border. Sediments eroded from the surrounding topographic highs have filled this tear, forming the Livermore Valley. As much as 10,000-22,000 ft of Eocene, Miocene, and Plio-Pleistocene sediments may fill this structural trough. Figure 3 shows a generalized stratigraphic column for the Livermore Valley (Carpenter et al., 1984). Environmental restoration work at the LLNL Livermore Site involves the shallowest sediments: Quaternary alluvium and terrace deposits and the Plio-Pleistocene Livermore Formation. The Lower Livermore Formation (Tpl) is dominated by silt and clay. The Upper Livermore Formation (QTl) is dominated by coarse-grained sand and gravel. Both Tpl and QTl underlie the LLNL Livermore Site and outcrop south and east of the site near the valley margin.
The shallow Quaternary alluvial and terrace deposits consist of complex, inter-fingered channel deposits of sand and gravel encased in lower permeability silt and clay. The channel deposits show evidence of repeated erosion and redeposition common to alluvial fan deposits. An additional complication, shown by Figure 4, is caused by the Livermore Site being located at the confluence of two contemporaneous fans: the Arroyo Las Positas and Arroyo Seco (Thorpe et al., 1990). The resulting complex stratigraphy of clay, silt, sand, and gravel is difficult to map and, as shown by Figure 5, individual sand and gravel lenses were initially considered very difficult to correlate (Blake et al., 1995).
Recently, Hydrostratigraphic Unit (HSU) analysis, a variation of subsurface geology, has been successfully applied to the near surface sediments at the Livermore Site to map subsurface channels of high-permeability fluid flow (Blake et al., 1995). This approach uses wireline measurements (gamma ray, SP, and resistivity), hydraulic testing data, aqueous geochemistry, and core descriptions to correlate interconnected high permeability zones of sand and gravel. The use of wireline measurements and hydraulic testing data focuses on overall depositional environment, enhancing correlation, while core descriptions focus on individual depositional environments at the flow stage level. A critical component of HSU analysis mapping is reliable wireline measurements for correlation over large distances.
Figure 6 is a cross section based on HSU analysis. The use of HSU to map subsurface high permeability fluid flow channels has enhanced the Livermore Site remediation efforts by greatly reducing the number of exploratory boreholes required to plan remediation, and better defining subsurface contaminant flow (Figure 7; Blake et al., 1995). Figure 8 shows subsurface fluid flow channels mapped at the Livermore Site using HSU Analysis.
Repeatability of gamma ray logging tools and stability of the detectors have been significant problems at the Livermore site for at least two slim-hole wireline vendors. Near-surface sediments at this site present two gamma ray logging problems:
At the Livermore Site, typical gamma ray log values range between 40 and 110 American Petroleum Institute (API) units, and sand/clay contrasts are 20-30 API units. The combined effect allows little tolerance for error in gamma ray log measurements.
Gamma ray logs are run as part of Livermore Site environmental site characterization and optimization to:
All of these applications require low noise gamma ray log values.
A fourth use of gamma ray logs at many Department of Energy (DOE) sites is to characterize the extent of subsurface radionuclide contamination. This use is more tolerant of uncertain gamma ray count rates because of the high count rates encountered. At LLNL, this particular use is not as critical as at other DOE sites because no significant radionuclide releases have occurred.
Borehole geophysical (wireline) logs are repeatable measurements of physical properties of the materials surrounding the borehole. Failure to repeat these measurements indicates changes in the physical condition of the borehole environment between repeat measurements, serious problems with the instrumentation making these measurements, and/or the way in which the instruments are being used. All well logs should have a short repeat section re-logged to document the repeatability of the log measurements.
Some tools, such as the induction tool, are limited only by the tool sensitivity and should repeat very closely. Radioactive measurements, such as the gamma ray, are statistical in nature and have lower repeat standards. Figure 9 shows a typical gamma ray log repeat section from a major logging vendor to the petroleum industry. As shown, the 1.5- x 7.875-in. NaI scintillation crystal detector provides excellent repeatability, even though the log was run at 30 ft/min (1,800 ft/hr). Expected repeatability for these tools is commonly 2-3 API units. The main log and repeat section data shown in Figure 9 are essentially indistinguishable.
Figure 10 shows
a gamma ray repeat section from Livermore Site well MW-5, exhibiting
discrepancies of as much as 25 API units between the primary and
repeat section logs. Large discrepancies between the main log and
repeat sections occur at the intervals 26-28 ft, 29-34 ft, 38-46 ft,
56-58 ft, 60-68 ft, and 72-81 ft. More importantly, what appears to
be a sand at
72-81 ft on the main log appears to be a clay on the repeat section,
and what appears to be a clay at 60-68 ft on the main log appears to
be a sand on the repeat section. This type of repeat uncertainty is
unacceptable.
The gamma ray log data shown in Figure 10 was acquired with a 1- x 4-in. NaI scintillation crystal detector gamma ray tool run at a logging speed of 20 ft/min, with a 3-sec time constant. These smaller detector tools (the Figure 10 tool crystal is approximately 0.226 the volume of the Figure 9 tool crystal) were designed for high resolution radionuclide ore exploration where count rates are much higher than at the Livermore Site. To compensate for the smaller crystal size, these slim-hole gamma ray tools are generally run at slower logging speeds and with longer time constants than those used for petroleum logging.
Livermore Site sediments have low overall radioactivity and low gamma ray contrast between clay and sand. Under these circumstances, gamma ray log repeatability becomes extremely important if used to distinguish between sand and clay or to correlate HSU between wells.
The nature of gamma ray emission is statistical and must be averaged over time (Hearst and Nelson, 1985). The length of time required to obtain a stable count rate depends upon the radioactivity of the target and the efficiency of the detector. The more efficient gamma ray detectors require less time to obtain stable count rates than the less efficient detectors. Conversely, count rates obtained by less efficient detectors will be less stable than count rates obtained by more efficient detectors over the same time period.
Different types of gamma ray detectors have different efficiencies. For example, NaI scintillation crystal detectors are more efficient than Geiger-Müller tube detectors of comparable size (Hearst and Nelson, 1985). Large gamma ray detectors sample gamma radiation passing through larger volumes than can be sampled by smaller detectors of the same type; consequently, the large detectors are more efficient.
Detector stability also depends on the radioactivity of the target. Highly radioactive targets yield stable count rates faster than weakly radioactive targets. Low efficiency gamma ray detectors may yield satisfactory results with highly radioactive targets, and may even be preferred because the high efficiency gamma ray detectors can become saturated at very high count rates.
The repeatability problems shown in Figure 10 can be related to detector instability, as documented by detector stability checks. These statistical stability checks are obtained by suspending the gamma ray tool below the ground level and recording the variation in the count rate over some time window (usually 2-3 minutes) at a constant depth. Figure 11 is a 2.5-min, gamma ray, statistical stability check record for Livermore Site piezometer SIP-ETS-205, showing excursions of ±12-15 API units. The instability shown in Figure 11 is not acceptable for Livermore Site needs.
Initial Livermore Site gamma ray logs, using 1-in. x 4-in. NaI scintillation crystal gamma ray detectors, were run using a 20 ft/min (1,200 ft/hr) logging speed and a 3-sec detector time constant. Slower logging speeds allow longer detector residence times at any one depth. Longer time constants provide average count rates for longer time intervals. Logging at slower speeds and using longer time constants should improve log repeatability without changing the detector efficiency. However, attempts to do this at the Livermore Site have met with mixed results.
Figure 12 shows a gamma ray repeat section from Livermore Site borehole B-913 that was run at a 10-ft/min logging speed and a detector time constant of 4 sec. The overall agreement between the primary and repeat section logs is very good, with good tracking and discrepancies of 10 API units or less. Figure 13 shows a gamma ray repeat section from borehole B-1006 that was run with logging conditions similar to those of Figure 12. In this case, the overall agreement between the primary and repeat section logs is very poor, with discrepancies up to 23 API units. Therefore, using slower logging speeds and longer time constants alone are not the solution to the repeatability problems with the gamma ray log.
Gamma ray emissions occur during radioactive decay of unstable radioisotopes. Macroscopic observations of radioactive decay involve counting the number of decay emissions from millions of unstable isotopes over finite lengths of time. Because of the large number of events (radioactive decay emissions) and the small probability for a given unstable nucleus to decay, radioactive count rates can be modeled by either Poisson or Gaussian probability distributions. For either of these probability distributions, the distribution standard deviation, s, of an estimate, , is equal to the square root of the estimate (Knoll, 1989).
For gamma ray measurements, if is the total event count recorded for a time window, t, the standard deviation of is then given by:
(1)More important than the total count standard deviation is the fractional or relative total count standard deviation, srel, given by:
(2)For example:
A total count of 900 events would have a standard deviation of ± 30 events and a relative standard deviation of 0.0333.
A total count of 100 events would have a standard deviation of ± 10 events and a relative standard deviation of 0.1.
Equations 1 and 2 refer only to the directly measured counts, not to count rates. Count rate error is estimated, using the rules of propagation of error (Taylor, 1990):
then:
(3)where:
Using the above examples:
A total count of 900 events, obtained during a counting window of 5 sec, would have a standard deviation of ± 30 events, a count rate of 180 counts per second (cps), and a count rate standard deviation of ±6 cps. The relative total count and count rate standard deviations would both be 0.0333.
A total count of 100 events, obtained during a counting window of 5 sec, would have a standard deviation of ±10 events, a count rate of 20 cps, and a count rate standard deviation of ± 2 cps. The relative total count and count rate standard deviations would both be 0.1.
Equations 1-3 have special significance for gamma ray logging, because they allow estimation of the uncertainty of any gamma ray log value.
Gamma ray count rates frequently vary significantly between detectors, even those of the same design. For this reason, gamma ray detectors are calibrated in normalized count rate units. Gamma ray logs run in low radioactivity environments are often calibrated in API units. Gamma ray API calibration units are based on gamma ray logging tool response to the API Calibration Pits (three blocks of concrete buried below the surface; two containing only Ottawa Sand above and below one containing Ottawa Sand spiked with 13 ppm uranium, 24 ppm thorium, and 4% potassium salts) maintained by the University of Houston (Anonymous, 1974).
The API unit is a normalized count rate. The two test pit environments described above are defined to span 200 API units of gamma ray tool response. A tool API calibration gain, GAPI, is defined as:
(4)where:
Both rh and rl are subject to the statistical uncertainty described by Equations 1-3 standard deviations of sh and sl, respectively. Count rate difference standard deviation is estimated, using the rules of propagation of error (Taylor, 1990):
(5)Tool gain standard deviation is estimated, using the rules of propagation of error (Taylor, 1990):
(6)where:
For the example:
A high count rate, rh, of 180 cps, and a high count rate standard deviation, sh, of ± 6 cps. A low count rate, rl, of 20 cps, and a high count rate standard deviation, sl, of ± 2 cps.
The count rate difference, Dr,
is 160 cps, with a difference standard deviation, sD,
of
± 6.325 cps.
The tool API calibration gain, GAPI, is 1.25 API/cps, with a tool gain standard deviation, sG, of ± 0.0494 API/cps.
The gamma ray tool response, gAPI, in API units is given by:
where rt is the raw tool count rate and
subject to statistical uncertainty with standard deviation
of st. The tool
calibration offset or bias reference is assumed to be 0 API units at
0 cps. The resulting API unit standard deviation, sAPI,
is estimated, using the rules of propagation of error (Taylor,
1990):
(8)Using the above tool calibration gain and tool gain standard
deviation, the API-calibrated gamma ray value for a count rate,
rt, of 80 cps, with a count rate standard
deviation, sr,
of
± 4 cps, would be approximately 75 API units with a standard
deviation, sAPI, of
± 6.374 API units.
The standard deviation is a rather coarse error estimator. Only approximately 68% of a normal distribution is contained within ±1 standard deviation of its mean value; two standard deviations about the mean contain approximately 95% of normally distributed data; and three standard deviations contain approximately 99.7%. For the above example of a 75-API-unit gamma ray value with a standard deviation of ± 6.4 API units, a reliable error estimate would be ± 13-19 API. This error spread is within the range of the main log/repeat section discrepancies and stability check deviations observed at the Livermore Site. Any action that increases the number of radioactive emissions counted will reduce the standard deviations of the measured quantities, rh, rl, and rt, and improve the relative standard deviation of the API calibrated gamma ray log values.
A logging sonde will detect gamma ray emissions only from those source nuclei in relatively close proximity to the detector. This means the logging tool response is sensitive to radioactive nuclei within a finite (roughly) cylindrical volume of borehole centered on the logging tool axis. For a moving sonde, this finite cylindrical volume is continuously moving along with the tool. Slow logging speeds keep the logging tool sampling at a given depth longer than fast logging speeds. Some high precision spectral gamma ray logging systems use station logging, where the detector is kept at a given depth until the total counts build up to values that will generate low error statistics. This approach is generally only practical for very short intervals and not for production logging. Site specific limits will determine how slow gamma ray logs can be run and remain cost effective. At the Livermore Site, this limit was about 10 ft/min.
One method of increasing the total counts (to improve counting
statistics) is to increase the counting time window, or time
constant. Using the above example with a count rate of 20 cps, a time
window of 5 sec will yield 100 counts, with a standard deviation of
± 10 counts and a relative standard deviation of 0.1. A time
window of 20 sec will yield 400 counts with a standard deviation of
± 20 and a relative standard deviation of 0.05. In both cases,
the count rate will be
20 cps and the relative count rate standard deviation will be the
same as the relative total count standard deviation. As a result of
quadrupling the length of the counting time window, the resulting
total count and count rate standard deviations will be reduced by a
factor of 2.
There are limits to extending the counting window, or detector time constant, for gamma ray logging if the logs are to be collected at a practical, constant logging speed. If the time constant is too long, the logging tool will average count rates over a large volume, blurring bed boundaries and contrasts between individual stratigraphic units with different radioactivity. The maximum practical time constant will be a function of logging speed and desired resolution of bed boundaries.
The gamma ray log examples shown in Figures 10-13 were obtained using standard slim-hole 1-in. x 4-in. NaI scintillation crystal gamma ray detectors. An alternative to using slower logging speeds and/or longer detector time constants is to use gamma ray tools with larger volume NaI scintillation crystals.
The number of gamma rays analyzed by a specific type of detector is approximately proportional to the volume of the detector (Conaway, 1994; Hearst and Nelson, 1985). Using the above statistical models, quadrupling the volume of a specific type of gamma ray detector would reduce the resulting count rate relative standard deviation by one-half.
Figure 14 shows a gamma ray repeat section from Livermore Site borehole B-1010, using a 1-in x 8-in NaI scintillation crystal detector run at 10 ft/min logging speed, with a detector time constant of 5 sec. Figure 15 illustrates the increased detector stability for this larger crystal detector. Comparison of Figures 10-15 illustrates that the larger (1-in x 8-in NaI) crystal volume detector yields more stable count rates and better repeat section agreement than had been obtained by either slowing the logging speeds and/or increasing the time constants (within practical limits) for the smaller detectors. This increased detector stability and improved repeat section agreement has continued with subsequent 1-in x 8-in NaI scintillation crystal detector gamma ray logs obtained at the Livermore Site.
Using larger volume NaI scintillation crystal detector gamma ray tools at the Livermore Site resulted in increased detector stability, better repeatability, and more reliable wireline measurements for identifying subsurface lithology and correlating between boreholes. This improvement in data quality has greatly enhanced the HSU analysis mapping at the Livermore Site, significantly reducing the number of exploratory boreholes required to better define subsurface fluid flow and plan remediation at the site. Use of larger NaI scintillation crystal gamma ray detectors for other natural, low radioactivity environments should provide similar results
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