Digital Log Calculation of the Compensated Density Log

Abstract

Summary Calibration and recording of the compensated density log with a digital logging system are discussed. The mathematical definition of the spine and ribs and the technique of computing compensated bulk density and amount of correction from tool count rates are explained. Calibration Standards The primary calibration standard for the compensated density log is freshwater-filled limestone blocks. The secondary calibration standards are blocks of aluminum and magnesium alloys of known composition. Since the compensated density log responds to the electron density index, Pe, a relationship exists that converts the electron density index to apparent bulk density, Pa. Pa = 1.0704, ...................(1) where Pa= apparent bulk density as read by the tool, and Pe= electron density index. By quantitative analysis of the two secondary blocks, the electron density index was computed and converted to apparent bulk density by Eq. 1. The values of apparent bulk density (more commonly known as bulk density) for the two blocks are 2.59 g/cm3 for aluminum and 1.71 g/cm3 for magnesium. Spine Calibration Calibration of the compensated density log with the Direct Digital Logging unit is performed by placing the tool in aluminum and magnesium blocks, accumulating the counts for 3 minutes in each block, and averaging the count rates. The count rates for the aluminum block (short-spaced and long-spaced counts/sec) define for each tool the response at a bulk density of 2.59 g/cm3, and the count rates in the magnesium block (short-spaced and long-spaced counts/sec) define a bulk density of 1.71 g/cm3. Fig. 1 shows the relationship of the magnesium block, the aluminum block, and the linear spine through the two calibration points. First, the four count rates are converted to logarithms where Las is the log of the short-spaced aluminum counts/sec, Lal is the log of the long-spaced aluminum counts/sec, Lms is the log of the short-spaced magnesium counts/sec, and Lml is the log of the long-spaced magnesium counts/sec. The slope of the spine is Lml - Lal m spine = .....................(2) Lms - Las The y intercept of the spine is b spine = Lal - m spine (Las)................(3) Since the values of bulk density and calibration count rates are known for both the magnesium and aluminum blocks, the ratio of difference in density to distance on the spine is F spine = ..........(4) F spine, m spine and b spine are stored on the digital program tape for a matched tool and source. These program tape for a matched tool and source. These calibration values are read from the program tape and are placed in memory when the log is to be run. placed in memory when the log is to be run. JPT p. 167