Computer analysis of digital well logs

TABLE

Well-logging service companies have used truckmounted computers for field-data acquisition and analysis for several years (Moseley, 1976; Kinkade and others, 1978; Best and others, 1978). These commercial computer-based systems are generally designed for speed, simplicity of operation, efficiency and reliability of data acquisition, and they have turned out to be highly successful for routine well logging. However, they are not flexible enough for research studies where ease of program modification is more important than standardization of results. The U.S. Geological Survey's research well-logging system uses a Hewlett Packard 9845B minicomputer1 with BASIC programming language, 318K bytes of core memory, and cathode ray tube (CRT) graphics with a capability for hard-copy output of graphics and printed data. Programs and data are stored on cartridge magnetic tapes or flexible disks, and are read into the computer under keyboard or program control.

The general design of the analytical programs is described in the first section of this report. The second section contains detailed descriptions of individual programs with examples of results given for each one.

All programs begin with a section that reads the digital field tapes or disks into the computer for rough editing. Invalid numbers and overlapping depth intervals are removed if they exist. A block of calibration information, normally stored at the end of the recorded data, is read, checked for validity, and stored for later use. Acquisition of field data is occasionally terminated prematurely because of a power failure or recording problem, and if this happens, calibration information is not available. This condition is detected by the program, and the user is prompted to enter the necessary calibration values from the keyboard.

Next, the program calls for keyboard entry of depth corrections, if needed, and for keyboard entry of the upper depth of valid data, which gives the user an opportunity to delete invalid data that occur in the vicinity of the borehole fluid level for some logs, particularly electric logs and sonic logs. The new arrays of depths and log readings are computed at evenly spaced depth intervals by interpolation of recorded values at a spacing that is determined by the user. Evenly spaced depth intervals are needed to facilitate subsequent data manipulation of well-log data (such as filtering, applying hole-diameter corrections, drift corrections).

Basic corrections and calibration algorithms are then applied to the interpolated raw data. Depth corrections are applied for the vertical offsets of the various detectors located at different positions on the probes, dead-time corrections are applied to nuclear counting measurements, and linear or nonlinear calibration functions are applied to convert digitizer output units (millivolts) to log measurement units (ohm meters, microseconds per foot). After the basic corrections and calibration algorithms have been applied, the logs are plotted on the CRT and edited, if necessary, while displayed on the CRT. The editing routine provides for keyboard manipulation of a cursor that is also displayed on the CRT and that can be positioned at any point on the log trace. Special-function keys on the computer keyboard are used to move the cursor up and down along the log trace, to delete erroneous data points, or to move them to the left or right of their original position. After editing, the log can be filtered if necessary to remove noise, and then stored on magnetic tape, or output

as a paper copy of the CRT plot, or plotted on an X-Y plotter. In the next stage of operation, unit conversions are applied to convert the log measurement values to the desired final output values (for example, neutron counts per second to neutron porosity in percent). The measurement units and converted units for all logs discussed in this paper are given in table 1. After the unit conversions are applied, the logs may be replotted on the CRT, edited and (or) filtered again if necessary, and stored on magnetic tape or output as a paper copy of the CRT plot, or replotted on a high-resolution X-Y plotter. A generalized flow chart of the computer programs is given in figure 1.

1. Natural gamma-ray and neutron-neutron log

program Gamma-ray (total count) and neutron-neutron (porosity) log analyses are combined in one program because digital field logs are obtained with a probe that simultaneously measures both parameters. The gamma-ray measurement is made with an Nal(Tl) detector mounted near the top of the probe and the neutron measurement is made with an He-3 tube that detects neutrons scattered back to the detector from an Am(Be) source attached to the bottom of the probe, 40 cm (centimeters) below the detector. After field data are read into the computer from magnetic tape, the program compares the calibration check count rates with count rates known to be valid from previous calibration runs to assure that the probe sensitivity was within statistically acceptable limits when the field measurements were made. Then the logs are scanned and invalid or redundant data points are deleted. Depth corrections are made for the different vertical positions of the two detectors on the probe, and for any changes that might be needed in the zero-depth reference point (such as casing collar versus ground level). New arrays at evenly spaced depth intervals are generated and dead-time corrections are applied using values of dead time determined by the two-source method (Scott, 1980). Dead-time corrections are made rapidly by use of matrix arithmetic operations available in the BASIC programming language. Only three program steps are needed to correct an array of observed count-rate values X, for dead time, T:

MAT X = 1.

MATX = X-(T), and 2.

MAT X = 3. When step 3 is executed, the corrected count rates are stored in array X. These matrix statements are equivalent to the much slower FOR-NEXT loop evaluation of the standard form of the dead-time correction formula: X(n=X(n/(l-X(D*T) Corrections for down-hole dividers that reduce the observed count rate by dividing by 2, 4, or 8, are also made at this time. After these corrections are made the user can plot, edit, apply a smoothing filter to reduce statistical noise, and then re-record the log data on an output tape in units of counts per second.

In the next section of the program, the user can convert the gamma-ray log values from units of counts per second to API (American Petroleum Institute) units or to eU308 grade (percent), and the neutron-neutron log values from counts per second to API units or neutron porosity index (percent). Transformation of the gamma-ray and neutron-neutron logs to API units is accomplished with conversion factors established by empirical calibration of the logging probes in the API test pits at the University of Houston (American Petroleum Institute, 1974). API units are converted to porosity index (percent) by use of empirical calibration data obtained from the Birdwell-SSC test pits in Tulsa (Seismograph Service Corporation, 1973). Figure 2 gives an example of calibration data used to convert neutron API units to porosity. Because the conversion to porosity index depends on hole diameter, the program requires that the user either (1) specify a constant value of hole diameter, or (2) read a caliper log into the computer from an output tape. The program makes the conversion to porosity index by interpolating values between curves relating API units to porosity index for various values of hole diameter (see fig. 2). Transformation of the gamma-ray log units from counts per second to percent eU308 is accomplished by an iterative numerical modeling procedure known as GAMLOG (Scott, 1962, 1963) for which coefficients have been derived for digitizing intervals of 0.2, 0.5, and 1.0 ft, for mud-filled and air-filled boreholes. The calibration factors relating count rate to percent eU308 (for an infinitely thick slab of uranium ore) and for making corrections for mud-filled holes of varying diameter were obtained from the U.S. Department of Energy-Bendix calibration pits in Grand Junction, Colo. (Mathews and others, 1978).

The GAMLOG procedure sometimes produces negative U308 grade values as the result of statistical fluctuation in count rate, particularly when small (0.2 ft) digitizing intervals are used. An iterative routine is appended to the GAMLOG section of the program to test for the presence of negative grade values, and if any are found, to redistribute them along adjacent points of the log to avoid this physically impossible condition.

After the gamma-ray and neutron-neutron logs are transformed to API, eU308, or porosity units, the user can plot, edit, and filter the logs, and (or) record them on output tape.

The filtering routine that is used in this program is a Hamming smoothing filter described by Blackman and Tukey (1958) that conserves area under the curve. The number of points comprising the filter is selected by the user; values of 5-11 have been found to be most effective in practical application.

Examples of unit conversion of analyzed gamma-ray and neutron-neutron logs are given in figure 3.

2. Dual-detector density and caliper log program This program analyzes gamma-gamma log den-

sity measurements and caliper log-hole diameter measurements made with a combination probe. The probe utilizes two collimated gamma-ray detectors spaced at 17 and 37 cm from a gamma-ray source (125 mCi Cs-137), and a single caliper arm that presses the detectors against the hole wall and measures hole diameter. The program starts by reading the digitized caliper and gamma-ray well-logging data from magnetic tape, and reading in calibration information that is recorded at the end of the logging data. Calibration information consists of count-rate values obtained when the probe is placed in density calibration test blocks, one aluminum and the other Plexiglas, having effective densities of 2.62 and 1.28 g/cm3 (grams per cubic centimeter), respectively. The program compares the calibration count rates with values obtained with the same probe previously, shortly after calibration runs were made in test pits at the Denver Federal Center, Colo. (Snodgrass, 1976). If the observed count rates agree with the previously obtained values within reasonable limits of statistical error, the calibration coefficients obtained during the previous calibration runs in the test pits are used to convert log count rates to apparent density values. If not, the user is offered the opportunity of using new calibration coefficients that are computed from the count rates obtained in the aluminum and Plexiglas blocks.

After the calibration coefficients are determined, the program searches for and removes any invalid data or redundant depth values. Depth corrections are then made for the offset positions of the various detectors on the probe and for error in the zero-depth reference point, if any. The caliper log values, digitized by a 5V2 digit DVM and recorded in millivolts, are converted to inches by fitting a polynomial curve to calibration readings stored at the end of the field-data tape. The order of the polynomial can be selected by the user. The caliper arm on the logging probe is pivoted at the top and swings out under spring pressure to make contact with the hole wall. When the arm is fully extended, the depth of the caliper measurement is shallower than when the arm is compressed against the probe, because of the geometry of the pivoting motion of the caliper arm. A depth correction is made by the program for this error by use of the following formula:

where Zc is corrected depth,

New arrays of caliper and gamma-ray detector count-rate values are generated at evenly spaced depth intervals, and then corrections are applied for dead-time errors and downhole scaling of count rate (division by 8 in the probe). At this point the user can plot, edit, and filter the corrected near- and far-detector count rate and caliper logs, and (or) record them on output tape.

The next section of the program converts the near- and far-detector gamma-gamma logs from units of count rate to apparent-density (g/cm3), and applies hole-diameter corrections to the converted values. The user can again plot, edit, filter, and re-record the converted apparent-density data. The final section of the program applies a density compensation algorithm using the nearand far-detector apparent density values as input. The compensation algorithm and its development are described by Scott (1977, 1978b). After the compensated density values are computed, the user can plot, edit, filter, and record the final logs on output tape. This final set of corrected and compensated logs includes compensated density (g/cm3), amount of compensation (g/cm3), and Zc = Za -(L-/L2 -(C-D)2)

Za is apparent depth, L is length of caliper arm, C is caliper measurement (hole diameter), and D is probe diameter. caliper (inches or centimeters). Figure 4 presents examples of dual-detector density logs in the three stages of analysis.

3. Magnetic susceptibility and conductivity log

programs This program analyzes the magnetic susceptibility and conductivity logs obtained with a probe that makes both measurements by use of a single induction coil connected in a Maxwell bridge (Scott and others, 1981). The program reads the twochannel logging data stored on magnetic tape in the form of digitized voltage outputs of phase discriminators that separate the magnetic susceptibility response from the conductivity response of the probe. Invalid raw data values and overlapping depth values are removed, and depth corrections are made for zero reference-depth offset, if any. Next, a calibration factor is computed as a function of the logging sensitivity scale and a calibration check value obtained by switching a capacitor of known value into a loop surrounding the coil in the probe. The magnetic susceptibility log, initially recorded in millivolts, is converted to relative micro cgs (centimeter-gram-second) units by multiplication by the computed calibration factor. Minimum and maximum values of the converted magnetic susceptibility log and the conductivity log are determined, and appropriate plotting multiplication by the computed calibration factor. Minimum and maximum values of the converted magnetic susceptibility log and the conductivity log are determined, and appropriate plotting scales and ranges are computed. Next, the program prompts the user to enter measurementdrift correction tie points at depths of his choice. Measurement drift is caused by temperature variation of the sensing coil. If laboratory measurements of magnetic susceptibility are available from drill core or cuttings, these values may be used to establish drift-correction tie points. If not, the user must estimate values based on his knowledge of the lithology, or by arbitrarily assigning zero values of magnetic susceptibility to the lowest points along the log trace. If the drift of the log is linear with depth, which is usually true, only two tie points are needed one near the top and the other near the bottom of the log. If the drift is not linear, more tie points are needed. The drift correction is made by forcing the log trace to pass through the specified values of magnetic susceptibility at the tie points. Values in between the tie points are interpolated linearly if only two tie

- J- -

4= " I " 4-

points are used, and by use of a spline curve fitted to the tie points if more than two points are available. Values above and below the top and bottom tie points are drift-corrected by linear extrapolation of data at the two tie points closest to the top and bottom of the log. After the drift correction is made, the user is prompted to plot, then to edit and (or) filter the magnetic susceptibility log, and to record it on output tape if desired.

The next section of the program corrects the magnetic susceptibility log for hole diameter, a correction that is established empirically by use of test pits such as those available at the Denver Federal Center, Colo. (Snodgrass, 1976). An example of empirical hole-diameter correction data is given in figure 5. Values of hole diameter are input to the computer by reading a caliper log output tape, or if a caliper log is not available, by entering a constant value of hole diameter from the keyboard.

After the hole-diameter corrections are completed, the user can reapply the drift correction, and then plot, edit, filter and (or) record the analyzed data on output tape. This completes the analysis of the magnetic susceptibility log. The conductivity log is plotted in relative form, and is not analyzed quantitively in the present program because of lack of reliable calibration information.

Figure 6 gives examples of magnetic susceptibility and conductivity logs before and after corrections for drift and hole-diameter variations have been applied.

4. Resistivity and single-point resistance log pro-

gram This program analyzes resistivity logs made with either the normal or the Wenner configuration (Dobrin, 1952) using electrode spacings of 8, 16, 32, and (or) 64 in. (20.3, 40.6, 81.3, and (or) 162.6 cm), and a single-point resis tance log made with the same probe. The program reads the four-channel resistivity log data and the single-point resistance log data from magnetic tape where it is stored in the form of digitized voltage output of a four-channel solid-state resistivity module

(Scott and Farstad, 1977) that has been modified to provide single-point resistance log output on a fifth channel. The single-point resistance log is computed by dividing digitized samples of the voltage and current transmitted to the current elec-

CONDUCTIVITY relative micro cgs units 0 20 40

micro SI units 0 500

trode on the logging probe. After resistivity and resistance logs are read into the computer, invalid data and overlapping depth values are removed and depth corrections are made. Scale factors are computed from the transmitter and receiver range- switch settings that are recorded on the field tape, and the four digitized voltage outputs from the resistivity module are converted to apparent resistivity values for the four electrode spacings. Appropriate scales and ranges are computed for plotting, and the user is prompted to plot, edit, and filter the logs and then record the processed logs on output tape if desired.

The next section of the program applies corrections for the presence of fluid in the borehole. The user is required to enter values of borehole fluid resistivity, probe diameter, and hole diameter from the keyboard. These parameters and the electrode spacing are used to compute the correction. If the hole diameter varies significantly, as is usually true, a caliper log may be read into the computer from an output tape to provide a value of hole diameter for every resistivity reading in the hole. The correction algorithm is based on resistivity departure curves published as a correction chart entitled, "Normal device, no invasion" by the Schlumberger Well Surveying Corporation (1949). The curves can only be expected to remove first-order effects, because they are based on the simplifying assumptions that the layer thickness is infinite and that there is no invasion of drilling fluid into the formation. The numerical algorithm was developed and described by Scott (1978a). After the correction algorithm has been applied, the user can again plot, edit and (or) filter the logs, then record them on output tape.

Figure 7 gives examples of analyzed resistivity and single-point resistance logs before and after applying corrections to the resistivity logs for borehole fluid resistivity and hole diameter.

5. Sonic velocity and amplitude log program This program analyzes continuous velocity logs

made with a two-receiver probe and a module that computes the reciprocal velocity (delta-0 of the sonic pulse traveling between the two receivers and measures the relative amplitude of the first arrival compressional-wave energy picked up by one or the other of the two receivers. The program reads the digitized delta-i and relative amplitude values from magnetic tape, edits invalid and redundant values, and then offers the user an opportunity to plot, edit, and filter the raw data. A special filtering routine is available in this program for removing invalid delta-t values that are caused by errors in the electronic detection of first-arrival energy at the two receivers. This type of error, known as cycle skipping, is common in boreholes where fractured rock or severe rugosity causes poor signal-to-noise response of one or both of the receivers. The filtering technique works as follows. First, starting at the top of the log and working downward, a moving average is obtained over a specified number of points in a manner similar to the application of a boxcar filter, but with one important difference the center point is not included in the average. Then a test is made to see if the value of the center point deviates more than a specified amount from the value of the average. If the value of the center point is beyond the specified limit, it is considered to be in error because of cycle skipping, and is replaced by the average value of the nearest two valid adjacent points. This simple scheme is about 90 percent effective in identifying and removing invalid data points caused by cycle skipping. In most applications, effective cycle-skip removal has been accomplished by using filter half-widths of 5-10 points and delta-t deviation test limits of 10- 20 microseconds/ft. After cycle-skipping errors have been removed, the log may be replotted, and any remaining cycle-skip points that are identified visually by the user can be deleted manually by the editing routine that is programmed for use with the CRT plot of the log.

The next part of the program converts the delta-£ values to velocity in units of either feet per second or kilometers per second, selectable by the user. After the conversion is complete, the user can replot, re-edit or refilter the logs with a Hamming smoothing filter, then record the final data on output tape. Figure 8 gives an example of a noisy delta-t log before and after cycle-skip filtering, and then after conversion to velocity units.

6. Temperature log program This program analyzes digitized absolute tem-

perature logs and computes differential temperature logs from them. The program reads the absolute temperature log from magnetic tape, edits and removes invalid and redundant data, and then computes a differential temperature log using a depth-lag interval specified by the user, after which the logs may be plotted, then optionally edited and (or) smoothed by a Hamming filter as

n:

5000 H I

90-- SONIC DELTA-T micro sec/ft

H I H

SONIC DELTA-T micro sec/ft 0 50 100 H \ h

SONIC VELOCITY SONIC VELOCITY feet/sec 15000 AMPLITUDE relative 50 100

I I I I-

desired. The user may record both the absolute and differential temperature logs on output tape after any stage of editing and smoothing. Figure 9 gives an example of an absolute temperature log and the corresponding computed differential temperature log.

tu 1100

1600 TEMPERATURE degrees C 35 50

7. Induced polarization, resistivity, and self-po-

tential log program This program applies corrections and plots logs made with a digital IP (induced polarization) measurement system. In addition to the IP log, resistivity and self-potential values are recorded on

DIFFERENTIAL TEMP degrees C -1 I

magnetic tape as subsidiary logs because these measurements are needed by the logging module to compute IP values electronically. The program reads the field logs from magnetic tape, culls out invalid and redundant data, and then applies scale factors computed from module range-switch set-

IP (16" Normal) RESISTIVITY (16" N) »V/V 0 30 60 0 200 400 H I I 30--

tings and electrode spacings. The program prompts the user to select options for plotting, editing, and filtering the data, then recording the reduced data on output tape if desired. An example of a plot of IP, resistivity, and self-potential logs is given in figure 10.

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