Geology Reference
In-Depth Information
Over the past two decades, a “skunkworks” type project was initiated to
build highly validated models that withstood strong scientific challenges, and
importantly, models that would be released in their entirety to the general public.
The goal was simply stated: explain limitations with existing models, formulate
and solve new models that remedy these deficiencies, address modern
exploration needs, and disclose all details and results to provide a much-needed
basis for further scientific development. The body of work that resulted for
induction and propagation tools appears in the present author' s recent topic
Electromagnetic Well Logging: Models for MWD/LWD Interpretation and Tool
Design
(John Wiley, 2014), while additional work on laterolog and micro-
resistivity pad tools will be presented in the forthcoming topic
Resistivity-Fluid
Interactions: Propagation, Laterolog and Micro-Tool Analysis
(John Wiley,
2015). Because of space limitations, we can only provide a “bird' s eye” view of
our approach and offer samples of unique results. However, the reader will, in
retrospect, find that the new approaches serve important needs defined by
modern logging applications in deviated and horizontal wells.
8.1 Induction and Propagation Resistivity
Imagine a long metal rod suspended in space, say by rings at each end,
held in place by free-hanging rope. A hammer suddenly strikes one end. The
rod reacts, multiple waves travel back and forth, and the reverberation can be
sensed as vibratory sound in the surrounding air. This is wave motion. Waves
propagate. Propagating waves that superpose will form standing waves. Waves
are governed by wave equations. Now reconsider the same rod, except that a
blow torch is used to heat the same end, suddenly if one must. The “heat wave”
that results does not propagate, as the local weather anchor might suggest. Heat
transmission is relatively slow. Heat diffuses. Heat satisfies heat equations.
In
Electromagnetic Well Logging
(Chin, 2014) we describe electrodynamic
problems not only in terms of (electric and magnetic)
E
and
B
fields, but their
equivalent vector and scalar
A
and V potential formulations. We need not delve
into specifics here, except note how Maxwell' s equations, which govern all
electromagnetic phenomena, take the general form
2
A
-
2
A
/ t
2
-
A
/ t -
(
-
h
)
V= -
J
s
(8.1)
2
V -
2
V/ t
2
= -
V/ t -
/
(8.2)
h
which are solved subject to further boundary conditions. Note that
B
and
E
are
computed from
B
=
A
and
E
= -
A
/ t - V. The complete current is taken
as a source
J
s
plus a conduction current
E
, where is a diagonal conductivity
tensor [
h
,
h
,
v
] and “h” and “v” are horizontal and vertical directions
relative to an inclined bed. Also, and are (for simplicity) isotropic inductive
capacities; when
h
and
v
are equal, we recover the standard isotropic model.
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