**WELLOG **** ****
****INDUCTION LOG**

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**THE INDUCTION LOG:**

Conventional
electric logging requires a conductive path for current to flow. When oil based
muds are used for drilling a well, there may be little or no conductive fluid in
the borehole. The induction log overcomes the need for conductive fluid. It
will operate in oil based mud, water, or air drilled holes.

**THE INDUCTION METHOD:**

The induction
method utilizes an electromagnetic transmitter coil to generate an alternating
magnetic field. The alternating magnetic field induces current flow in the
surrounding earth and the induced currents generate a secondary alternating
magnetic field. A second coil called a receiver coil is located in close
proximity to the transmitter and on the same axis. The secondary magnetic field
(earth loop) is changed in amplitude and phase by the surrounding electrical
properties of the earth. View induction tool
schematic.

**PROPAGATION AND SKIN DEPTH:**

Inductive
methods are best described as transformer coils linked by their mutual
inductances. Electromagnetic energy coupling the loops undergoes attenuation
and phase shift as it propagates. Skin Depth is a measure of the distance to
which an electromagnetic wave will penetrate. Skin depth is a function of
frequency and resistivity. The more conductive the medium the larger the
currents and the shorter the distance over which the electromagnetic wave can
penetrate.

Skin Depth =
d
= (2/mwC)^{1}^{/2}

Where:

Permeability
= m =
Newtons per ampere squared (SI) dimensionless (cgs)

Angular
frequency
=
w
= 2 * p * F

Conductivity
=
C
= Siemens per meter (Note: S
replaces the older mho)

Example:

Permeability = 1 (air),
Frequency = 20,000 Hz, and resistivity = 100 ohm-meters ( C
= 1/100 = .01 mho-meters)

Skin depth = 50 meters

**INDUCTION NUMBER:**

We can
represent the electrical properties of an elementary loop by discrete circuit
elements i.e. resistance R in ohms and inductance L in Henries.
In this case the earth loop is considered to be a coil that creates the
secondary magnetic field.

For a single
turn loop:

Induction Number
= θ
= wL/R

**NORMALIZED SIGNAL:**

The normalized
signal is the product of two terms. The first term is called the radial geometric factor. It
incorporates only the distances between the coils and the loop. The second term
is called the induction factor. It depends only upon the properties of the
elemental loop as given by the induction number. The induction factor is
complex-valued. The received voltage consists of components which are in phase
and out of phase with the transmitting coil. At large values of induction
number, the in-phase component dominates. At small induction numbers, the out
of phase component becomes more dominant. Induction tools sense the out of
phase (Quadrature) signal using a phase sensitive detector.

Radial
geometric factor example:

The medium
induction tool derives ____ percent of its signal from within 80 inch diameter?

View high
resolution radial geometric factors chart.

FOCUSED
INDUCTION TOOL:

At small
induction numbers, the transmitter signal can be orders of magnitude greater
than the desired signal. It is common practice to null out the primary field by
coil arrange. It is also common practice to use supplementary coils to cancel
the contribution of the field above and below the main coils and reduce the
near-borehole field allowing more penetration into the formation.

View a focused induction
tool schematic.

Full solution
for homogeneous medium:

In conformity
with the geometric factor development, apparent conductivity can be defined as
V_{2}/K.

Where:

V_{2}
= Receiver voltage

K =
correction factor

Apparent
conductivity (Ca) will be less than the true earth homogeneous conductivity C
because of the contribution of inductance/skin effect. If the geometric theory
were strictly valid, Ca would equal C. In general, correction will be required.
When the value of inductance/skin effect = .1, then the correction is about 7
percent. At induction/skin effect of 1, the correction is 60 percent. This
correction is called the propagation factor or skin effect correction. The
effect on current flow in the formation increases with distance to the
transmitter rather than being greatest near the well-bore.

Evaluation of
Formation Parameters:

Both
induction and galvanic sondes can be designed to obtain different depths of investigation
into the formation. When apparent resistivity (conductivity) is measured by a
combination of methods, the data can be used to infer the resistivity profile
as a function of radius. If three independent resistivity measurements are
available, the Rxo, di, and Rt can be determined. Refer to a tornado chart.

View a
high resolution tornado chart.

Correction
for Borehole effect:

Induction
tools measure the conductivity of the borehole fluid. Corrections must be
applied for hole size and Mud resistivity (Rm).

Example:
Borehole diameter = 14 inches, Mud resistivity = .47 ohm-meters, what is the
borehole contribution to the total signal?

Using the chart – enter the
bottom left at borehole size of 14 inches move up to the 1-1/2 “ standoff. Draw
a line from that point on the chart through the Rm line at .47 (scale A) and
read borehole signal in millivolts = 13 also on scale A.

Bed thickness
Correction:

Induction log
response in thin beds is affected by resistivity of surrounding formations. In
the case of low resistivity surrounding formations, The
effect is reduction of the apparent resistivity in the thin bed.

Example:
what is the correct resistivity (Ra’) of a 3 ft thick
bed reading 4 ohm-meters (Ra) and surrounded by 1 ohm-meter formation (Rs)?

Using the
Induction Log Bed Thickness correction chart for
1 ohm-meter surrounding formation;

Solution:
Enter with Ra’ = 4 ohm-meters move to the right to 3 feet and down to 20
ohm-meters.

When the
surrounding formation resistivity is 5 ohm-meters – less correction is
necessary.

Given a 3
foot thick zone having resistivity of 4 ohm-meters and surrounding resistivity
of 5 ohm-meters,

Using the Induction
Log Bed Thickness correction chart for
5 ohm-meter surrounding formation;

Resistivity
(Ra’) = 4 ohm-meters.

Bed boundary
determination:

Bed
boundaries occur at the inflection point of the induction resistivity
curve. The inflection of the curve is the point at which a tangent line
moving along the curve reverses direction.

Revised
11-24-2018 © 2007-2018 WELLOG All Rights Reserved