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A Model-Based Method to Supply Missing Log Information*
By
Michael A. Frenkel1
Search and Discovery Article #40106 (2003)
*Adapted 
from
“extended abstract” for
presentation at the AAPG Annual Meeting,
Salt Lake City, Utah, May 11-14,
2003.
1 Baker Hughes, Houston, Texas
Joint interpretation of well logging data requires that all logs involved in the interpretation process be mutually consistent. We have developed a model-based method that achieves raw data quality and consistency improvement by means of log data depth matching, recalibration of abnormal logs, and reconstruction of missing logs.
To perform model-based log depth matching, we select a log to serve as a depth reference. Using this log, we generate a reference earth model and calculate all the synthetic logs that must be depth-matched. Depth matching is accomplished by shifting each log to the appropriate depth level of the synthetic log in order to match the main features of both curves. In many practical cases, a single depth shift is not enough. A more general approach is based on the application of our method to a sequence of depth windows.
To perform the model-based log calibrations, we apply the following two-step procedure. At the first step, we execute the raw data inversion by using the undisturbed (normal) measurements. At the second step, to reconstruct abnormal or missing logs, we calculate all the synthetic logs by using the inversion results. These reconstructed synthetic logs can then be used in the petrophysical interpretation process.
Practical
applications of the method to the raw data are presented. In the first example,
we perform depth matching and recalibration for a suite of old electrical logs
(data from Western Siberia). In the second example, we perform a correction of
abnormal absolute voltage measurements made with the array lateral log tool
(data from Western Australia).
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The evaluation process for oil and gas reservoirs includes the accurate
estimation of underground formation resistivities. The use of In practice, however, especially when we are dealing with the suite of old electrical logs, the latter are often not properly calibrated and depth matched (due to multiple runs of the logging instruments in the same well). Some important logs (e.g., mud resistivity) may not be available for an interpretation process. Some logs could exhibit measurement offsets. Such a problem could appear, for example, on normal galvanic logs, when the absolute voltages in low-resistive formations exhibit an offset (level shift) due to the physical nature of this type of measurement (Frenkel and Walker, 2001). Special correcting procedures must be applied to prepare the raw data for joint, inversion-based interpretation. Once the logs pass through these procedures, they can be used to accurately determine formation resistivity, and then to perform more reliable petrophysical analysis of the reservoir properties.
A Model-based Log Data Correction and Restoration Method In this section, we describe a model-based method to supply missing and to correct abnormal logs. The method consists of a set of preprocessing procedures, designed to perform log depth matching, recalibration, offset elimination, and recalculation of missing logs. Generally, each preprocessing procedure involves three steps. First, we generate a reference earth model using the accurate log readings or executing the raw data inversion on a set of measurements assumed to be valid. Then, we calculate the synthetic logs based on the generated earth model. Finally, we perform depth matching, missing log reconstruction, and abnormal log correction. The reconstructed and corrected logs can be used in the further petrophysical interpretation. It should be noted that, for the preprocessing procedures we describe below to be feasible, we must make certain assumptions regarding data quality and availability.
Let us assume that the mud resistivity log (Rm) and the
caliper log are known; we select one log (preferably one more explicit
to the depth features; e.g., focused-type resistivity log LL3) as the
depth reference. To perform depth matching in a simple and fast manner,
we first calculate all the synthetic logs by doing forward modeling
based on a simple, non-invaded earth model. The earth model parameters
are defined directly Depth matching is accomplished by shifting each log to the appropriate level of the synthetic log to match the main features of the two curves. This could be achieved with log cross-correlation. In practice, such a depth matching procedure should be executed sequentially, using a set of overlapping and sliding windows along the borehole (Frenkel et al., 1997).
Let us assume that the Rm and the caliper logs are known and that they are depth-matched. To define the earth model structure, we apply radial, one-dimensional (1-D), or point-by-point inversion to a set of logs, including the poorly calibrated ones. We apply this inversion over a short interval within a relatively thick and uninvaded formation (Frenkel et al., 1997). The log scaling (calibration) factors determined by the above inversion procedure can then be used to recalibrate the logs. This procedure provides the most reliable and stable results when only two logs with similar resolution are used in the correcting process.
This procedure is similar to the previous one. The difference is that we apply inversion to logs that do not exhibit measurement offset. To determine an offset value, it is sufficient to run the inversion algorithm over a short interval. Then, one calculates all the synthetic logs using the generated formation model. The log offset is calculated as the difference between the raw and the synthetic logs.
Missing log reconstruction procedure This procedure is quite similar to the offset correction approach. As an example, we show here how to restore the mud resistivity log (Rm). Let us assume that the caliper log is known. We select resistivity logs that are depth-matched and properly calibrated. Applying the 1-D inversion to a shallow-reading log in a relatively thick uninvaded interval, we recover the true Rm value. Finally, using the temperature log, we can reconstruct the entire Rm log.
In this section, we present two case studies for vertical exploration
wells
Case Study 1 - B Russian BKZ Data
A suite of BKZ logs (L045, L105, L225, L425, and L850) (Wiltgen and
Truman, 1993; Harrison, 1995; Frenkel et al., 1997) Analysis of the raw data indicated that the logs were not properly depth-matched, and that estimation of mud resistivity was required. Application of the preprocessing procedures described in this paper allowed us to perform depth matching of the BKZ logs and estimate accurately the mud resistivity value, Rm = 0.7 W∙m, for the interval of interest.
The 2-D inversion was next used to determine a picture of the formation
resistivity around the borehole over a selected 100-meter interval. The
SP log was used for both detecting layer boundary positions and
estimating intervals of high shale content. These layers were assumed to
be impermeable while constructing an initial resistivity model. Initial
resistivity values were determined
Case Study 2 B -
This section covers the
At a well site, the resistivity image of the formation around the
wellbore, derived The SFR resistivity curves indicated an anomalous response over the water-bearing section of the Lower Barrow Formation below 480 m. The shallow SFR curves overlay each other, between 0.6 and 0.7 W∙m, while the 20”, 30”, and 40” SFR curves overlay each other at about 1.0 W∙m, with the 50” SFR reading around 1.2 W∙m (Figure 2, track 7). There does not seem to be any explanation for this response, as invasion should have produced a more gradual increase in resistivity. It was suspected, however, that a voltage discrepancy caused by offset measurements was the reason for these unexpected SFR results. The 2-D inversion performed with the first differences only is immune to offsets in the absolute voltages. The inversion results, Lxo, Rxo, and Rt curves (depth of invasion, resistivity of invaded zone, and resistivity of uncontaminated zone, respectively), are displayed in Figure 2 (tracks 3-4). Evident in the hydrocarbon zone is the minor amount of separation between the Rxo and Rt curves. This indicates a low degree of invasion, probably due to a strong mud cake.
It was then possible to simulate all the theoretical curves, including
the first differences and voltages, using the final earth model derived
by inversion. The excellent match of the
To investigate this problem, let us consider a 3-layer synthetic
formation model presented in Figure 3. It will allow us to illustrate
the effect of the reference electrode V4 offset on the SFR curves. This
model was generated using a simplified formation model
Track 1 shows V4 accurately calculated for this model and V4S shifted by
a constant 25% of its value calculated far away In the model case, the accurate SFR curves calculated using the accurate voltage V4, provide a correct radial resistivity profile (Figure 3, track 3). In the field case, the SFR curves recalculated using the synthetic V4 log, more closely support the results of the rigorous 2-D inversion (Figure 2, track 8).
A model-based method that allows for fast logging data consistency
improvement by means of log data depth matching, recalibrating abnormal
logs, and supplying missing log information has been developed and
tested. The field tests were performed with the old electrical logs
Frenkel, M.A., et al., 1996, Rapid well-site inversion of
full-spectrum Frenkel, M.A., Mezzatesta, A.G., and Strack, K.-M., 1997, Enhanced interpretation of Russian and old electrical resistivity logs using modeling and inversion methods: Paper SPE 38688, presented at the SPE ATCE, San Antonio.
Frenkel, M.A., and Walker, M.J., 2001, Impact of Hakvoort, R.G., et al., 1998, Field measurements and inversion results of the high-definition lateral log: Paper C in 39th SPWLA ALS. Harrison, B., ed., 1995, Russian-style formation evaluation: LPS, London. Hilchie, D.W., 1979, Old electrical log interpretation: Golden, Colorado. SPWLA, Houston Chapter, 1979, The art of ancient log analysis. Wiltgen, N.A., and Truman, R.B., 1993, Russian lateral (BKZ) analysis: Paper SPE 26433, presented at the SPE ATCE, Houston.
Thanks to Baker Atlas for granting permission to publish this work, to
Woodside |
Figure 1. Interpretation results of the BKZ resistivity logs for well
WS-1.
Figure 2. Raw logs and inversion results for the interval, 470-500 m,
Well E-1 
Figure 3. Effect of the reference voltage V4 offset on the SFR curves.
Model parameters: Rm=0.06 