Open Journal of Geology, 2013, 3, 81-86
doi:10.4236/ojg.2013.32B017 Published Online April 2013 (http://www.scirp.org/journal/ojg)
Effective Electromagnetic Log Data Interpretation
in Realistic Reservoir Models
M. Epov, C. Suhorukova, V. Glinskikh, M. Nikitenko, O. Nechaev, I. Surodina
Institute of Petroleum Geology and Geophysics SB RAS, Novosibirsk, Russian Federation
Received 2013
ABSTRACT
This paper analyzes some specific features of the numerical interpretation of high-frequency electromagnetic logging
data in vertical, deviated and horizontal boreholes entering oil- and water-saturated formations. The interpretation is
based on numerical modeling for signals.
Keywords: High-frequency Electromagnetic Logging; VEMKZ; 2D & 3D Modeling; Numerical Interpretation
1. Introduction
High-frequency electromagnetic soundings (VEMKZ)
are designed for estimation of electrical resistivity dis-
tribution around borehole [1]. The system involves five
or nine three-coil arrays. Phase shift (and amplitude ratio
in some tools [2]) between two neighboring coils are
measured. Frequencies of an exciting field are chosen in
the range from 875 kHz for a 2 m long probe to 14 MHz
for a 0.5 m long probe. A sounding curve is a combina-
tion of all probes signals at one measurement point. The
curve demonstrates resistivity distribution from borehole
to the uninvaded formation.
The VEMKZ method enables us to solve several prob-
lems of practical importance in inclined and horizontal
boreholes: estimation of formation and invaded zone
resistivities; location of a reservoir top and base as well
as gas-oil and water-oil contacts position with respect to
a borehole; estimation of resistivities’ radial distribution
from the borehole to formation in boreholes filled with
high-conductive drilling mud.
In order to analyze the high-frequency electromagnetic
soundings with realistic problem formulations algorithms
were developed and calculation programs created, which
implement the numerical analytic [3-5] and fi-
nite-difference approaches [6,7], and finite-element
method [8].
2. Electromagnetic Properties of Geological
Media
As has been observed for the decades of electrical log
data numerical interpretation, every so often estimates of
electrical resistivity (ρ) from electromagnetic sounding
data and estimates from direct current sounding (lateral
logging sounding - LLS or Russian BKZ) disagree with
each other.
The signals measured by various techniques were
compared at intervals of thick homogeneous argillaceous
deposits in marker beds, primarily, in terms of accuracy
level assessment of the measuring. Signals from VEMKZ
probes running at frequencies ranging from 0.875 to 14
MHz, in such formations tend to be consistent with
model containing low resistance invasion zone, whereas
BKZ signals are attributed to models either with missing
invasion zone, or with narrow high-resistivity zone.
The said apparent contradiction is eliminated by an
extension of geoelectric model parameters, like introduc-
tion of dielectric permittivity (ε) allowing to exclude in-
vasion zone from VEMKZ data interpretation in the in-
tervals with impermeable rocks. Figure 3 shows the re-
sult of fitting resistivity model and model including (ρ,
 )
parameters according to VEMKZ and BKZ data for
clayey formation drilled with nonsaline clay mud.
In the course of inversion a certain effective  value
was determined in which all processes of polarization in
the heterogeneous medium are reflected. Consequently,
with such an approach employed,
 estimate is often
higher, than values for each individual component com-
posing rocks. Different researchers suggest different es-
timates for relative permittivity as high as several hun-
dreds and thousands of relative units, based on the results
of samples investigation (sandstone, loams, clay, [9]),
and of LWD data interpretation (frequencies 0.4 and 2
MHz, pyritized shales, [10]), with
 frequency dispersion
also being observed therewith.
According to VEMKZ logs, frequency dispersion of
dielectric permittivity in some clayey formations is de-
termined when the signal measured at each operating

M. EPOV ET AL.
82
frequency corresponds to its own  value. Estimates of
dielectric permittivity vs. frequency, obtained in several
clayey formations, are consistent with the values ob-
tained on shale samples [9].
Resistivity model is determined by BKZ data. Then
such  values are matched for the obtained ρ values, that
calculated VEMKZ signals would fit with the measured
ones. An example of such fitting in a clayey formation is
shown in Figure 1. BKZ and VEMKZ measurements
were simultaneous, and the well is drilled with nonsaline
clay mud. BKZ signals are shown on the top in the se-
lected resistivity model, in the middle are VEMKZ
signals measured (the solid line) and calculated in resis-
tivity model (the dotted line), at the bottom are VEMKZ
signals measured and calculated in model with fitted ef-
fective value . The fitted values are ρ = 3.4 ohm·m, and
 = 133 (rel.units).
The VEMKZ signals and medium dielectric permittiv-
ity relationships have been experimentally validated by
the measurements performed in fresh waters of Lake
Teletskoye [11]. As a result of numerical inversion of the
signals recorded in the water and air-water boundary
profiling, the values of electrical resistivity and relative
dielectric permittivity of water (170 - 190 ohm·m and 62
- 67 rel. units) were obtained. The resistivity value was
supported by independent measurements, and  estimate
corresponds to expected value for water with similar sa-
linity.
Figure 1. BKZ and VEMKZ responses measured in clayey
formation.
3. Realistic Problem Formulation and
Interpretation of Model
3.1. Borehole Rugosity Influence
Borehole rugosity is brought about when drilling both
vertical [12], and inclined wells, in particular, using de-
flectors [13]. They can be represented by spiral cuttings,
periodic thickening (when drilling with deflectors), as
well as individual fractures, or their system. Hole rugosi-
ties, when filled with drilling mud with high electrical
conductivity, cause quasiperiodic or chaotic big ampli-
tude fluctuations (from a fraction of degree to several
tens) to come up on the VEMKZ logs. The fact that
changing signals account for intense rugosity of a bore-
hole wall is supported by the correlation of caliper and
VEMKZ logs.
According to the modeling results, signal fluctuations
similar in form and amplitude are localized opposite
shallow (some mm deep) cavities and thin fractures. The
fluctuations period along the hole tend to associate with
rugosity zones, and their amplitude increases with the
cavity depths and operating frequency of probe, while the
fluctuations pattern depends on the form of cavity and
smoothness of their edges. The deviation from the level
of signal in undisturbed rocks, appear to be identical on
the amplitude, no matter whether it increases or de-
creases. This allows to exclude the influence of cavities
and fractures on the signal, by its averaging.
Identical fluctuations of signals are modeled in con-
stant diameter boreholes, however, the borehole shape
can be both sinusoidal and spiral [14]. The fluctuations
period is equal to the spiral period in case of spiral bore-
hole shape, while in a sinusoidal borehole it is twice as
less than the sinusoid period.
Relying on log data it is possible to evaluate rugosity
parameters (Figure 2) as follows: on the basis of the fit-
ting signals it was defined that cavity depth equals 0.007
m, fracture depth is 1.5 m, fracture width is 0.029 m,
fracture resistivity 0.2 ohm·m.
3.2. Eccentricity Effect
High electrical conductivity of drilling mud cause tool
eccentricity to influence VEMKZ logs in the borehole
[14]. As calculations have it, the bigger the borehole ra-
dius is, and the more contrasting are the electrical con-
ductivities and the probe operating frequency, the higher
is the influence. Therefore, in order to increase reliability
of numerical interpretation of the data measured in wells
with high electrical conductivity of drilling mud, proper
correction must be made for eccentricity effect.
The algorithm, allowing to correct eccentricity effect,
uses signal database calculated in the “borehole – forma-
tion” model, given the nonconducting body of the [8].
The algorithm allows to build transformation of the

M. EPOV ET AL. 83
measured signal into apparent resistivity including the
borehole and probe eccentricity effects, and also to cal-
culate signals for the position on the borehole axes.
Figure 3 represents the result of algorithm applied to
practical VEMKZ log data. Probe designation includes
probe length in decimeters. The borehole radius is 0.062
m, resistivity of drilling mud is 0.03 ohm·m. When ec-
centricity effect is taken into account in the clayey por-
tion of formation, apparent resistivities for different
probes become almost identical, and any noticeable di-
vergence remains only in sandstones intervals.
Figure 2. Measured (the solid line) and modeled (the dot-
ted line) VEMKZ responses. Hole radius = 0.108 m, mud
resistivity = 0.1 ohm·m.
Figure 3. Measured responses and corrected responses.
With eccentricity effect taken into account, the sound-
ing curve behavior changes, normally, in such a manner
that when inversion is applied both thickness and resis-
tivity of low-ohmic near-well zone tend to decrease. The
said regularity is typical for VEMKZ logs in small-di-
ameter boreholes with low resistive drilling mud.
3.3. Vertical Boreholes
Intermediate range of frequencies is used in VEMKZ,
where signal is affected not only by diffusive, but also
wave processes in the media. Phase shift and amplitude
ratio measured in electromagnetic logging, when jointly
applied, allow to reconstruct a full range of electrophysi-
cal parameters. The paper addresses the solutions of for-
ward linear and inverse two-dimensional problems on
the basis of linearized representation of relative ampli-
tude and phase characteristics of electromagnetic field
(the theory of pseudogeometrical factors) [3]. With this
problem formulation, it is possible to approximate al-
lowance for offset currents as diffusion input from wave
processes, caused by  spatial distribution.
The linearized representations of electromagnetic sig-
nals measured in conducting media, given the offset cur-
rents, allow to effectively employ linear inversion in the
solution of inverse problem. The solution of inverse
problem includes the inversion of matrix composed of
sensitivities calculated for phase shift and amplitude ratio
to model parameters. Stage-by-stage approach is used for
inversion. The first stage was reduced to one-dimen-
sional inversion, which included identification of elec-
trophysical parameters of both near-well zone and the
formation, whereas during stage two they were specified
(ρ, ) in the course of two-dimensional inversion.
Figure 4 presents the results of two-dimensional in-
version of practical VEMKZ logs in the carbonate reser-
voir interval penetrated by a well with the oil-based flu-
ids. The previously identified thin beds testify to the ex-
tent of the detailed investigation. Their thicknesses vary
from 0.3 to 1.1 m, which appears to be significantly less
than the probing system length.
Vertical distributions of ρ and  in the invasion zone
and within formation, based on the results of one-di-
mensional (1) and two-dimensional (2) inversions are
shown. The reliability of the results obtained can be
validated in comparative analysis of the practical and
calculated for the recovered model of synthetic curves
for phase shifts, provided therewith. Average values of
relative divergences on the considered interval account
for 3% - 4% for short probes and do not exceed 2% for
long ones.
3.4. Inclined and Horizontal Wells
Let’s consider typical model for the upper part of oil- and

M. EPOV ET AL.
84
water-saturated reservoir, overlain by clayey deposits
(Figure 5). The calculation has been made for horizontal
beds. Clay resistivity is 4 ohm·m, resistivity of reservoir
is 15 ohm·m. The borehole track (at the top of Figure 5)
Figure 4. The results of the inversion of practical VEMKZ
logs within carbonate reservoir. The recovered 1D and 2D
distributions are ρ (left) and  (middle). Practical (solid
lines) and synthetic (dotted lines) curves for phase shifts
(right).
Figure 5. Model of a well with horizontal completion,
penetrating the reservoir; and apparent resistivity logs.
is typical in the context of West Siberia geological envi-
ronment. Apparent resistivity was calculated with the use
of phase shift (


a



, at the middle) and amplitude
ratio (


21a
A
/A  , at the bottom).
It is known that when VEMKZ tool penetrates the bed
boundary there will appear electrical charges propor-
tional to the formation resistivity contrast ratio at this
boundary. The said charges affect the responses. The
influence is particularly strong for the phase shift (∆φ):
the phase shift diagrams show maximum peaks, which
correspond to the points of boundary crossing. The more
inclined is the well the higher are the spikes. Responses
from the second layer appear at the intervals where dis-
tance from the boundary to the receivers is less than an
offset from the transmitter to the nearest receiver (0.8 of
probe length) the influence from, for example, another
medium becomes evident, with apparent resistivity in the
reservoir decreasing to 13 ohm·m and increasing in the
clayey bed up to 6 - 7 ohm·m. All the apparent resistivity
values reach true reservoir resistivity only in the lowest
part of the well (80 - 200 m), where these points are re-
moved further than the sonde length from boundary. In a
higher conductive clayey cap rock the charge response is
a bit lower and apparent resistivity reaches resistivity of
the clayey formation at shorter distances from the
boundary, about half of sonde length. True resistivity of
the clayey formation was shown by sondes with length
0.5 - 1.1 m. The interval where the well extends almost
along the boundary (360 - 600 m) is characterized, firstly,
by difference in


a



readings from sondes with
various spacing, which would mean that there is an con-
ductive invaded zone when traditional interpretation
techniques are applied; and, secondly, diagrams for the
main and additional groups of probes differ. The latter
could be useful in distinguishing the effects, conditioned
by nearing the horizontal boundary, or by lateral inho-
mogeneity of reservoir properties.
Amplitude ratio is less influenced by the charge than
the phase shift. The


21a
A
/A  logs do not show big
peaks, as the boundary crossing boundaries. The logs for
two deepest sondes don’t reach the value of the reservoir
resistivity. Sondes with lengths from 0.5 to 0.8 m reach
the value of clay resistivity. The fact that shoulder effect
is more significant for 21
A
/A than it appears for ∆φ
because the medium interval governing the amplitude
ratio is bigger than the one governing the phase shift.
For water-saturated reservoirs in West Siberia resistiv-
ity values are the same as for clays. Therefore, the fol-
lowing reservoir model is divided into oil-water-satu-
rated and water-saturated parts with resistivity of 15
ohm·m and 4 ohm·m, respectively (Figrue 6). The influence
of the more conductive lower part takes place in the points
located at a distance less than sonde length for


a



and less than one and a half length for

21a
A
/A  . In

M. EPOV ET AL. 85
the interval, where the well is closer than half-length to
the boundary, apparent resistivity at the

a


  curves
increases and reaches maximal value at the lowest point
of the well (0.3 m from boundary).
If we add a thin resistive layer to the model (usually it
is carbonated sandstone with resistivity 30-100 ohm·m) it
would significantly change a

near the boundary. Let’s
place the layer with thickness 0.2 m and resistivity 50
ohm·m at the boundary. In the model at Figure 5 maxi-
mum values

a


  near the boundary increase highly;
under the boundary clay produces almost imperceptible
lowering effect, whereas


a



in the subhorizontal
interval are significantly enhanced. At the


21a
A
/A
a

diagram maximum peaks appear in points where the well
crosses the boundary. In the model shown at the Figure 6
the influence of the lower medium on the phase shift
proves even smaller. At the bottom part of the well a
high resistive interlayer caused an increase in

for
both parameters and changed the shape of


21a
A
/A 
curve related to the short sonde.
In general, the increase in resistivity of high-resistance
interlayer leads to the enhanced resistivity contrast and
its greater growth whith the tool crossing boundaries, and
to lesser dependence on the medium at the other side of
the interlayer. We should note that the interlayer with
these parameters is not reflected in the signals of induc-
tion logging in vertical wells.
The calculations attest to the fact that the VEMKZ
signals in deviated and horizontal wells depend neither
on enclosing rocks nor contrasting interlayers in the beds
thicker than double probe length. In the middle part of
the layer of this kind its true resistivity will be shown by

a


  diagrams for all the probes and


21a
A
/A 
diagrams, but not including long-spaced probes. How-
ever, characteristic behavior of signals near the bounda-
ries and singlevalued dependence on the contrast of elec-
trical properties allows to estimate formation parameters,
using program for modeling responses of the deviated
tool, in case the well track is known.
Calculations of a signal in realistic model (including
borehole) shows that the main curve features are not
changed; it’s only the extreme points that are subject to
changes caused by charges at the boundaries, which is
evidenced by the sharp spikes accounting for short
probes getting smoothed out. The signals of long probes
(Epov, Martakov et al, 1999) are practically independent
from conductive solution in the borehole. In practice, the
commonly used diameter of a hole is 0.124 m, which
dehotes its lesser impact.
4. High Performance GPU-based Computing
Parallel algorithms are developed for higher productivity
in solving forward and inverse problems of electromag-
netic logging in calculations on GPU [15]. Development
of algorithms performed with the use of Nvidia CUDA
technology. Data on efficiency of the developed parallel
algorithms of modeling and inversion on GPU are ana-
lysed. The most significant information is execution time
of functions on the graphic device, device/host copying
times, and time to copying ratio, and calculations on the
device.
Efficiency estimates of calculations on the Nvidia Ge-
Force, Tesla graphic cards (Figure 7) were obtained. Ap-
parently, when using GPU for parallel computations, it is
possible to significantly increase productivity in com-
parison with identical sequential calculations on the cen-
tral processor (Intel Core 2 Quad 2.4 GHz). With the use
of parallel algorithms and high-performance calculations
on multiprocessing devices the creation of new automated
interpretation systems has been reduced to practice.
Figure 6. The model of well with horizontal completion
near oil-water contact and apparent resistivity logs.
Figure 7. Efficiency increang with GPU computing. si

M. EPOV ET AL.
86
n created for the solution of forward
[1] “VIKIZ Methoas Boreholes,” Ed.
g-
ova, M. N. Nikitenko and Ju. N.
ikitenko and K. V. Suhorukova, “On
ard 2D Problems
uency Induc-
5.
Algorithms have bee
Conclusions
of E
and inverse problems in numerical interpretation of elec-
tromagnetic logs in realistic models of terrigenous reser-
voirs penetrated by vertical, inclined or horizontal wells.
There also have been developed algorithms for numerical
correction of borehole rugosities and probe eccentricity
effects. Effective algorithms for fast two-dimensional
modeling and inversion were developed. Joint two-di-
mensional inversion for relative amplitude and phase
characteristics measured in electromagnetic logging al-
lows to estimate electrical conductivity and dielectric
permittivity. Algorithms for modeling in inclined and
horizontal wells allow to investigate signal features when
approaching and crossing boundaries. High-performance
calculations on GPU allow to carry out numerical inter-
pretation of data in real time.
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