An experimental study concerning the depth difference between apparent and true interface depths determined by short spaced neutron logging tools is reported. For 16 cm or zero spaced thermal and epithermal neutron logging tools , errors in the depth location of interfaces between dry sand and 10% and 20% water unconsolidated sands inside an empty 5 cm diameter steel pipe passing through the sands range from zero to 5 cm. In case of the zero spaced logs, the causes included differences in slowing down and diffusion lengths in the two adjacent media. The vertical resolution is a minimum of 12 cm for the zero spaced epithermal log.
INTRODUCTION
Accurate determinations of depth to formation and formation fluid interfaces are often important. Assuming perfect measurements to a fixed measure point on the logging tool, the question remains as to the depth difference between this fixed measure point on the tool and an apparent interface indicated by the log. The depth of the apparent interface is often formation dependent. Normally a fixed measure point is assumed for a logging tool, e.g., half way between a neutron source and a neutron detector in a neutron-neutron logging system.
Smith (1990) showed that the vertical response function of a long-spaced thermal neutron log depends on the effective migration length of the thermal neutrons in the formation. Since the effective migration length changes with formation porosity, and the apparent depth to an interface changes with the vertical response function, the apparent depth of an interface changes with porosity. Therefore the true "measure point" of a tool changes with porosity and is not fixed on a tool.
Also Hall (1995) reported experimental work showing the effects of non-reciprocity in neutron gage measurements for air-water interfaces, and also showed that the "measure point" varies on the tool for such interfaces , dependent on which is leading, source or detector, into an air-water interface.
The objective of the work reported herein was to determine experimentally the distance between the generally assumed fixed "measure point" of a short space neutron tool and the position of the apparent interface in an empty steel cased borehole. Two types of neutron tools were investigated, both used a fast neutron source, but one detector was almost pure epithermal and the other was a combination of thermal and epithermal. Work is reported for water contents of 0%, 10%, and 20% in unconsolidated sand formations with a source to detector spacing of 16 cm. in an empty 5 cm. i.d. steel casing. A zero source to detector spacing was also used.
One can consider that there are two effects related to interface location from neutron logs, both involving diffusion. One effect is due to slowing down and diffusion (e.g. effects seen on a zero spaced neutron log) and a second effect due to non-reciprocity (e.g. when the apparent interface depth changes due to interchange of source and detector). For zero space epithermal and thermal neutron logs, the apparent interface, defined to be the depth at which the response changes by 50% in going from one formation to a different second formation, is different than the true interface location due to the different slowing down and diffusion characteristics of two adjacent media. For example, using a zero spaced thermal neutron log through an air water interface in an empty lucite cased hole, the apparent interface is shifted toward the water (Hall, 1995) approximately 5 cm.
A second effect is the non-reciprocity effect, that is, in finitely spaced neutron tools, when the source and detector are interchanged and there is a boundary located between the source and detector, the response is not the same. This assumes the source is a fast neutron source and the detector is a slow neutron detector. Henry (1975) specifically pointed out that in theory the detector output would not be the same upon interchange of the source and detector unless the detected neutrons were the same energy as the source neutrons. Calculations by Mathis (1994) showed this same effect.
A 252Cf neutron source of approximately 105 n/s was used at a source to detector spacing of 16 cm from a 1.25 cm diam x 2.5 cm long GS-20 Li glass scintillator coupled through a quartz light pipe to a Hammatsu R3991 photomultiplier tube. The scintillator is approximately 100% efficient for detecting thermal neutrons. Measurements were made (1) with the scintillator covered with a 0.5 mm thick cadmium cover (considered to be an epithermal log after spectrum stripping to correct for gamma background) and (2) with a bare scintillator (considered to be a thermal neutron log after background correction).
A zero spaced log was taken using the same detector but with a 252Cf source of approximately 103 n/s, both bare and cadmium wrapped, except the bare data was not taken in the dry to 10% water sand.
The experimental arrangement consisted of a 2 meter long horizontal box, open on top, 0.3 x 0.3 m in cross section, with a 5 cm i.d., 6 cm o.d., 2.2 m long empty steel pipe running lengthwise through the center of the box. The box was filled with sand, separated into two equal length compartments by a 2 mm thick aluminum sheet with a hole for the pipe. The entire box was filled with dry sand initially, then 10% water by weight was added to half the box, and then 20% water by weight was added. The porosity of this unconsolidated sand was measured to be 31%.
For the 16 cm spacings, station measurements for 200 seconds were taken in 5 cm increments (maximum increment) over a range of approximately 200 cm, with the range covering the interface. For zero spacings, 500 second station measurements were taken. The pulse height spectrum output from the detector consisted of one main neutron peak due to slow neutrons superimposed on a decreasing gamma radiation background. With the detector bare at 16 cm, the gamma background was less than 5% of the total count, so that the background was neglected and the slow neutron response taken as the integral number of counts under the neutron peak. In the case of the 16 cm spaced epithermal log, the spectrum consisted of a logarithmically decreasing background and an exponentially modified Gaussian. Fits using Peakfit with residuals less than 0.01 were obtained. The area under the modified Gaussian was taken to be the epithermal neutron counts with the detector cadmium wrapped. In the zero spaced epithermal case, the background was assumed to be linear under the neutron peak, with the background being interpolated between regions of interest above and below the neutron peak.
Experimental results are shown in figures 1-4. Statistical errors are less than the symbol sizes. The dry sand-wet sand interface is located at a depth of 137.5 cm, with the wet sand always being deeper than the dry sand. The source is below the detector for the solid squares and above the detector for the crosses. The solid triangles represent the difference between the log using the source above the detector and below the detector. All depths were measured relative to a fixed measure point on the tool half way between the source and detector. Figures 3 and 4 show the results for the bare detector. It is obvious in all cases that the apparent depth to the interface is dependent on whether the source is above or below the detector. This illustrates the non-reciprocal nature of this measurements. The difference in the two logs shows the quantitative amount of this non-reciprocity. Note on figure 3 that there is some indication of a thermal peak on the right side of the interface near 170 cm.
More quantitative results can be made from the expanded (around the interface) plots of figures 1-4, an example of which is shown in figure 5. The apparent interface is taken to be that depth at which the response changes 50% in going from one formation into another. A vertical line at 137.5 cm represents the true depth of the interface.
The apparent depth shifts, i.e., the apparent depth relative to the actual depth, are summarized in table 1. It is seen from table 1 that in general these shifts are dependent on porosity and range from positive to negative 5 cm. The shifts shown in table 1 for the 16 cm spaced logs are due both to non-reciprocity and other diffusion effects. The apparent depth shifts due only to neutron non-reciprocity are shown in table 2. The non-reciprocity errors are somewhat greater ( 6-7 cm) for the thermal log than for the epithermal log ( 5 cm).
Due to these non-reciprocity errors, zero spaced epithermal and thermal tools were run under the same conditions. The results are shown in figures 6 and 7. Typical statistical errors are shown on figure 6. On these figures the interface is at a depth of 122 cm. Data taken from expanded plots are included in tables 1 and 3.
Assuming a definition of vertical resolution to be the depth interval over which the log changes from 10% to 90% of the total change in going over a step change in formations, table 3 shows the vertical resolution for the various configurations. It is seen that for the 16 cm spaced logs, the vertical resolution is greater than the source-detector spacing. This would be due to neutron streaming up the empty borehole. Of the cases shown, the vertical resolution is best for the zero spaced epithermal log.
The effect of non-reciprocity using a finitely spaced thermal or epithermal log under these conditions is obvious from table 2. To eliminate such an error a zero spaced log, in which there is no effect in reversing source and detector, was run. One might suspect that the "depth of investigation" of a zero spaced log would be quite small. However, calculations by Brooks quoted by Zwager (1994) show that over the range of source-to-detector spacings 7.5 to 15.7 cm in an empty 21.5 cm diameter borehole in 20% and 40% porosity formations using a bare Li glass neutron detector, the "depth of investigation" increases slightly from the longer to the shorter spacings, being 6.7 cm at the shorter spacing.
At zero spacing, a peak in the neutron distribution as a function of depth below the interface is evident in both the epithermal and thermal logs (see figures 6 and 7). These peaks are probably due to neutron reflection in the dry sand, with the location of the peak being below the interface a depth dependent on the migration length of epithermal and thermal neutrons respectively. The peak in epithermal neutrons is approximately 10 cm below the peak and approximately 20 cm for the thermal neutrons. In his calculations of neutron logging tools across interfaces with no boreholes, Mathis (1994) showed that there was a peak in the thermal flux versus depth near certain interfaces for 30 and 60 cm source-to-detector spacings. If either thermal or epithermal neutron gages are being used for quantitative water determinations, this peak could make an error in such determinations in some cases. There is also an indication of such a peak in the 16 cm spaced data (figures 1 and 3).
Since the amount of hydrogen present and the density are the governing factors for an epithermal log, it should be possible to derive a correction for the apparent shift of an interface using a zero spaced epithermal neutron log given a sufficient amount of experimental data. Additional data to those reported here would be needed.
As is well known, diffusion of thermal neutrons depends on the capture cross section of elements present in the formation. Since such cross sections affect the migration lengths in various formations, variable thermal neutron cross sections would be another variable in depth determinations of interfaces if thermal neutron logs were used. It would be expected that a determination of depths to interfaces using an epithermal log will be less variable than when using a thermal neutron log when considering changes in the thermal neutron cross sections of the formations.
The conclusions which can be reached from the above concerning measurements made in empty 5 cm diameter steel casings passing through 31% porosity dry, 10% water, and 20% water loose sands using a 252Cf neutron source and a Li glass neutron detector (cadmium wrapped for an epithermal log) follow.
(1) For interfaces between dry and 10% and 20% water content sands, the apparent depths to dry sand-wet sand interfaces using a 16 cm spaced tool neutron log depends on whether the source or detector crosses the interface first, i.e. there is a neutron non-reciprocity effect. Errors due to this effect in interface depth determinations using a 16 cm spaced tool are 6-7 cm using a thermal neutron log and 5 cm for an epithermal log.
(2) Errors in determining the depth to an interface for 16 cm spaced and zero spaced epithermal and thermal neutron logs depend on the amount of hydrogen in the wet formation. Errors are on the order of +5 cm for dry-10% water and dry-20% water interfaces for both logs. This error can be attributed to differences in the slowing down and diffusion lengths in the two media.
(3) The vertical resolution, 10% to 90% points, is best for a zero spaced epithermal neutron log, being 12 cm for an interface between a dry sand and a 20% water wet sand. The vertical resolution is greater than the 16 cm source to detector spacing. This is thought to be due to neutron streaming in the empty borehole.
(4) A zero spaced epithermal neutron log eliminates the error due to non-reciprocity in determining the depth to interfaces, and has the best vertical resolution of the configurations tested.
(5) There is a peak in the thermal and epithermal neutron distributions in a wet formation next to a dry formation, probably due to back scattering of neutrons from the dry formation. Such peaks could cause errors in hydrogen content determinations using neutron gages.
Acknowledgments: This research was sponsored in part by the D. Hall Corporation. The detector was furnished by Baker Hughes Inteq.
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