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  INDUCTION LOG CONCEPTS
The induction log was invented by Henry Doll of Schlumberger and described in 1947. It was developed from electromagnetic research undertaken during World War II on mine detectors. The first commercial success for the tool began in 1956. Many evolutionary developments have occurred over the last 50 years, providing better vertical resolution and deeper depth of investigation.

Conventional induction logs measure conductivity perpendicular to the axis of the tool. In a vertical well, this is the horizontal direction. Vertical conductivity may be quite different. Recent developments have introduced a log that can measure vertically as well as horizontally. It is in the commercialization phase of development, and promises to be very useful in thin bedded and dipping reservoir rocks.

The tool works in air, oil,  or mid filled open holes but salt muds give poor results. It does not work in cased holes.

Induction logs are designed to measure the conductivity of rock formations by using the electromagnetic principles outlined by Faraday, Ampere, Gauss, Coulomb and unified in a single theory by James Maxwell in 1864. The process involves the interaction of magnetic and electric fields:

1. alternating current applied to transmitter coils
2. creates alternating magnetic field in rocks
3. which generates alternating current in rocks (current loops, eddy currents)
4. current loops generate out of phase magnetic field in rocks
5. which generates in-phase voltage in receiver coils
6. calculate resistivity Rt = RES = K * V / I

The basic equations for a single transmitter – receiver coil pair, in EXTREMELY simplified form, are shown below.

1: Bt = uo * dI/dt    magnetic field due to current “I” in transmitter coil
2 : I = C * dBt/dt    current in formation induced by magnetic field “Bt”
3: Br = uo * dI/dt   magnetic field due to current “I” circulating in  the rock
4:  V = N * A * (dBr/dt)    voltage induced in receiver coil by magnetic field Br

Where;
  Bt = the magnetic field strength in the formation created by an induction log transmitter
  uo = the magnetic permittivity
  dI/dt = rate of change of the current jn the transmitter coil
  I = current circulating in the rock
  C = conductivity of rock
  dBt/dt = rate of change of transmitted magnetic field
  Br = out-of-phase magnetic field strength in the formation created by the currents in the rock
  dI/dt = rate of change of the current in the rock
  V = voltage induced in an induction log receiver coil
  N = number of turns on the coil
  A = area of the coil
  dBr/dt = rate of change of the magnetic field created by the currents circulating in the rock

The magnetic fields, and currents in the rock and receiver-transmitter system are vectors (amplitude and direction). The in-phase component measured at the receiver coil is called the Real (or R) component. The signal that is 90 degrees out of phase is called the Imaginary (or X) component. Older tools could measure only the R component. Newer tools measure both R and X components. The X component is used to enhance bed resolution by use of proprietary algorithms.

If you can handle advanced calculus and know what the “curl” operator does, refer to “Basic Theory of Induction Logging” by J. H. Moran and K. S. Kunz, SEG Oct 1959 for the real story on induction log theory.

The illustration at right shows a simple two coil induction log and a single "ground loop" of current circulating in the rock around the tool. An infinite number of ground loops exist, but only those near the tool will generate a magnetic field strong enough to produce a voltage in the receiver coil.

A real induction logging tool consists of several transmitter-receiver coil pairs within a logging tool housing. A 20,000 Hz regulated alternating current is produced in the transmitter coils, which induces eddy currents by electromagnetic induction into the rocks surrounding the coil system. The eddy currents generate a magnetic field, which in turn induces voltages in the receiver coils. By keeping the transmitter current constant, the magnitude of the eddy currents are proportional to the conductivity of the formation and 90 degrees out of phase with the transmitter current. Voltages at the receiver coil induced by these eddy currents are also proportional to the formation conductivity and approximately in phase with the transmitter current. The electronic circuitry of the receiver is designed to detect the in-phase component of the receiver coil voltage and this serves as a measure of the conductivity of the formation.

The eddy currents induced in a conductive formation experience phase shift and attenuation. The loss due to attenuation is known as skin effect (or propagation loss) and is corrected by proprietary service company algorithms.

RADIAL and VERTICAL GEOMETRIC FACTORS
The voltage at the receiver from a unit loop of radius, r, and altitude, z, with respect to the center of the coil system is given by: Vr = K * G * COND, where K is a function of the area of the transmitter and receiver coils, distance between the coils, current in the transmitter, and frequency of the transmitter current. G is the geometric factor, which depends on the geometric position of the unit loop as related to the transmitter and receiver coils.

The radial geometric factor G considers the formation as the combination of a large number of cylinders coaxial with the borehole. The integrated radial geometric factor, Gr, is the sum of all the G values for the total volume within a cylinder of radius, r. This represents a thick homogeneous formation invaded by mud filtrate where conductivity changes radially, and includes a small portion of the borehole.

The signal measured by an Induction log positioned opposite a thick formation usually reflects the conductivity of that formation; however, in thin formations, the signal is affected by the conductivities of the adjacent formations. In a similar manner, the integrated vertical geometric factor, Gv, becomes the sum of the G values for all of the volume above (or below) a horizontal plane at a distance, z, from the center of the coil span. The integrated vertical geometric factor increases with the vertical distance, z, and must equal unity for all space.

Development of the geometric factor for a focused induction log can be accomplished by adding algebraically all combinations of transmitter-receiver coil geometric factors times each coil pair's contribution to the total instrument response. This is done by computer modeling at the time the tool is designed.

To illustrate the geometric factor concept, assume borehole size = 8 in, invasion diameter = 40 in, Cm = 1000 mmho/m, Ci = 50 mmho/m, Cu = 100 mmho/m. For a particular induction log, assume:
      Gm = G8 = –0.001
      Gi =  G40 – G8 = 0.025 – (–0.001) = 0.026
       Gu = 1 - G40 = 1 – 0.025 = 0.975.

Where Cm, i, u = conductivity of the mud, invaded zone, and undisturbed zone
and Gm, i, u = radial geometric factor for the mud, invaded zone, and undisturbed zone respectively.

      1: CONDa = Gm * Cm + Gi * Ci + Gu * Cu
                      = 1000 * (–0.001) + 50 * 0.026 + 100 * 0.975 = 97.8 mmho/m

The borehole and invasion create a 2.2 mmho/m error (100 – 97.8) in the measured value of the un-invaded zone conductivity.

Illustration showing radial geometric factor for a 6 coil induction log

Bed thickness correction charts are provided by service companies for their particular tools, based on the vertical geometric factor concept. The following example illustrates the geometric factor for thin bed response for a typical logging tool:

Given: Bed Thickness = 4 ft, CONDb = 100 mmho/m, CONDs = 1000 mmho/m, Gb = 0.728,
Gs = 1 – 0.728 = 0.272, where CONDb = conductivity of the bed of interest, and CONDs = conductivity of the surrounding beds.

CONDa = 100 * 0.728 + 1000 * 0.272 = 345 mmho/m

The apparent conductivity is 3.45 times the actual conductivity of the zone (100 mmho/m), a 345% error, illustrating the large error inherent in typical induction log readings in thin beds. A resistive formation needs to be at least 24 feet thick for the vertical geometric factor to approach 1.0.

BED BOUNDARIES ON INDUCTION LOGS
Bed boundaries on induction logs should be picked on the conductivity curve halfway between the high and low conductivity values, as shown below.

Depth of bed Boundary is chosen at mid-point of conductivity – not the resistivity

Unfortunately, most modern induction logs display resistivity on a logarithmic scale, not conductivity on a linear scale. As a result, the mid-point rule is impossible to apply directly. You could do two quick resistivity to conductivity conversions (COND = 1000 / RESD), find the mid-point, and convert it back to resistivity (RESD = 1000 / COND). This might be a bit onerous, so another rule is to pick the resistivity inflection points, then move the top boundary of resistive resistive beds up 2 to 4 feet, and move the bottom down by the same amount. Conductive beds get the same shift, but in the opposite direction - make the bed thinner. 

This helps to compensate for the curve shape distortion caused by transforming conductivity to resistivity. Newer induction logs have better focusing and this stretch may not be needed - compare to core or microlog or formation microscanner to see if a bed boundary shift is needed. This shift is NOT required on array induction logs. The illustration below shows the problem for a typical middle induction log.

Bed boundaries on induction log

INDUCTION LOG CURVE NAMES
Notes: * = optional curve.  Abbreviations varied between service companies - common abbreviations are shown as well as the generic abbreviation as used elsewhere in this Handbook.

 Induction-Electrical Survey (IES)

 Dual Induction - LL8 or SFL (DIL or ISF)

Phasor Induction Log (DIT-E)

Array Induction Log (AIT)

EXAMPLES OF INDUCTION LOGS
Sample log presentations are shown below. The shallow resistivity curve has evolved over time, from the 16” normal in the 1960’s, laterolog-8 (LL8) in the 1970’s, spherically focused log (SFL) in the 1980’s, to a shallow (10”) induction curve on the current array induction log.

 Induction log showing logarithmic scale (left) and linear scale (upper left) with conductivity curve as well as resistivity curves. Many varieties of Induction logs are run today, some with interpretive images of resistivity profiles or saturation. Combination log presentations with porosity curves, such as sonic (right) or density are found in some locations. The SP and/or gamma ray curve is in track one. Logarithmic scales compress the resistivity range into a smaller space, reducing the need for backup scales. 

Typical layout of a dual induction log or equivalent, with GR and SP in Track 1, and shallow, medium, and deep resistivity on logarithmic scale in the wide track. Note bad deep induction log and low resistivity spikes caused by fractures. There is a 6 meter transition zone into the water zone at the bottom of the log.

The newest array induction logs use multi-coils combined with higher transmitter currents, plus very intensive inverse modeling to obtain conductivity focused to 1, 2, or 4 feet.

Commercial software is available to perform similar inverse modeling on older logs, but the results will not be equal to  a modern array induction because the software has much less data to work from. It is still worth doing, but don't expect miracles..

The standard presentation of an array induction log has 5 resistivity curves, with progressive depths of investigation of 10, 20, 30, 60, and 90 inches. Some tools are focused to reach 120 inches. A calculated value for Rxo and Rt are often found in the digital data file. These are derived from the inverse modeling of the inferred invasion profile using proprietary algorithms. The invasion profile can be displayed as an image log.
 

Copyright © E. R. (Ross) Crain, P.Eng.  email
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