SPWLA 54th Annual Logging Symposium, June 22-26, 2013
A NEW MULTI-FREQUENCY TRIAXIAL ARRAY INDUCTION TOOL
FOR ENHANCING EVALUATION OF ANISOTROPIC FORMATIONS
AND ITS FIELD TESTING
Junsheng Hou, Luis Sanmartin, Dagang Wu, David Torres, and Turker Celepcikay, Halliburton
Copyright 2013, held jointly by the Society of Petrophysicists and Well Log Analysts (SPWLA) and the
submitting authors. This paper was prepared for presentation at the SPWLA 54th Annual Logging Symposium
held in New Orleans, Louisiana, June 22-26, 2013.
ABSTRACT
Since its introduction to the oil industry in 2000, multicomponent induction (MCI) or triaxial induction logging has
been one of the most remarkable developments of both wireline and logging while drilling (LWD) induction
operations. Over the years, successful applications have proven its usefulness for characterizing varied types of
anisotropic reservoirs, which are frequently overlooked or mistaken by conventional induction tools and their
associated processing and interpretation approaches. It is commonly known that, around the world, significant
amounts of hydrocarbon reservoirs are located in formations such as laminated sand-shale sequences and
fractured/faulted formations that exhibit complicated resistivity/conductivity anisotropy. To help improve the
evaluation of anisotropic formations in conventional/unconventional borehole-formation environments, the oil and
gas industry has been relying much more on the use of MCI logging. To the authors’ knowledge, currently, very few
MCI-type tools have been developed and commercialized. And the previous tools only provide multi-frequency but
single-array measurements or multi-array measurements with no detailed information regarding the use of multiple
frequencies. To meet the increasing requests in anisotropic formation evaluations, a new MCI-type tool with both
multi-array and multi-frequency measurements and the associated data processing algorithms has been developed.
This paper first introduces the newly developed MCI tool, with its primary feature being the use of both multiple
arrays and frequencies to measure full-tensor data in vertical or deviated wells drilled with oil-based mud (OBM) or
in air-filled wells. This new tool has a transmitter triad (collocated triaxial and orthogonal coils) and six sets of
receiver coils. The two receivers closest to the transmitter triad are conventional induction coils, while the remaining
four sets of coils are built as receiver triads. The tool operates at multiple different frequencies in the range of 12 to
84 kHz by sequentially energizing each of the coils (X, Y, and Z directions) in the transmitter triad and measuring
the signals in each of the receiver coils. Hence, each of the four receiver triads measures nine signals per frequency
at every logging depth. Secondly, the newly developed, fast data processing algorithm and its software system are
presented, which is able to accurately recover formation horizontal resistivity (Rh), vertical resistivity (Rv), dip, and
strike/azimuth from the multi-array, multi-frequency full-tensor measurements. This data processing can provide
improved evaluation in difficult anisotropic formation environments. In addition to the unconventional resistivity
anisotropy, dip, and strike, the tool also provides bed boundaries and conventional array-induction logs resulting
from the use of identical spacing as conventional tools. Furthermore, this new processing system contains accurate
calibration and temperature correction, data quality evaluation, bed-boundary estimation, horn-effect reduction
based on adaptive low-pass filtering, radially one-dimensional (R1D) multistep inversion, borehole correction, and
fast vertically one-dimensional (V1D) inversion combined with a zero-D (OD) inversion in homogeneous
formations. These features are explained and are validated with synthetic data and with field logs obtained at the
service provider’s test wells and in worldwide client wells.
Several prototypes of the newly developed MCI tool were built. To date, the new MCI tool has completed its field
testing in two test wells and a number of client wells around the world. Since December 2012, it has logged in at least
two commercial-job wells. All field-tested and commercial applications show that this new tool can deliver wellmatched multi-array formation Rh, Rv, dip, strike/azimuth, bed boundaries, three sets of conventional induction logs
(ACRt-type logs), and invasion information from the MCI processing with multiple subarrays operated at multiple
frequencies in real time. This capability greatly enhances anisotropic formation evaluation in both conventional and
unconventional resources.
1 SPWLA 54th Annual Logging Symposium, June 22-26, 2013
INTRODUCTION
Conventional induction logging has been one of the most used well loggings for almost over half of a century
because of its critical role in identifying reservoirs and computing water/oil saturation (Strickland et al., 1987;
Barber et al., 1991; Beste et al., 2000; among others). However, the conventional coaxial induction can only provide
formation Rh information in vertical wells because of limitations of the tool physics. Because of the sensitivity of
MCI measurements to both formation resistivity anisotropy and direction, the MCI logging is capable of providing
the additional information of formation Rv, dip, and strike/azimuth for the formation evaluation of conventional and
unconventional reservoirs. And MCI logging has been one of the most remarkable and practical developments of
wireline and LWD resistivity loggings in recent years. For many years, the oil and gas industry has been requesting
this logging service to help in solving for complex formation evaluations, such as thinly laminated shale-sand
reservoirs frequently overlooked by conventional induction.
To the authors’ knowledge, only a few MCI-type tools for both wireline and LWD logging operations have been
developed and commercialized to date. The first wireline MCI-type tool was introduced to the petroleum industry in
2000, and then its updated version was released in 2004 (Kriegshauser et al., 2000; Rabinovich et al., 2005). This
tool only contains a single spacing of the x-, y-, and z-direction coils but can be operated at ten different frequencies
between 20 and 220 kHz. After removal of the borehole and near-borehole effects in measured signals based on the
so-called multi-frequency focusing (MFF), the processing software is finally capable of delivering formation Rh,
Rv, dip, and azimuth for one subarray at every logging point. As such, its single-array inverted logs will not allow
describing the invaded formation properties if this occurs. In addition, it also needs to be combined with a
conventional induction tool for obtaining conventional induction logs with multiple radial depths of investigation.
Rosthal et al. (2003) and Barber et al. (2004) present a multi-array triaxial induction tool, which is also used for the
wireline operation. This tool consists of a triaxial transmitter, six fully triaxial receiver subarrays, and three
conventional axial receiver subarrays. Its spacings include those of the conventional array induction tool, resulting to
the identical conventional logs to be produced from the conventional induction measurements. The wellsite software
corrects for the borehole effect in the measured data and provides the similar formation parameters of resistivity
anisotropy, dip, and azimuth for multiple subarrays plus conventional array induction logs (Wang et al., 2006; Wu et
al., 2010). However, it only operates two frequencies of 13 and 26 kHz, and therefore it will be challenging to
deliver accurate inverted logs in high-resistivity formation environments. A good review of the latest wireline MCI
tools and their applications can be found in Zhang et al. (2007) and Rabinovich et al. (2007). In addition, Bittar et al.
(2011) present a new LWD triaxial induction tool with multiple subarrays containing both titled transmitter and
receiver sensors that operate multiple frequencies. This tool can provide formation resistivity anisotropy and dip in
vertical and deviated wells by data inversion.
With significantly increasing amounts of oil and gas reserves located in formations that exhibit complicated
electrical anisotropy, the petroleum industry is relying much more on the use of MCI logging for identifying and
quantifying different types of anisotropic reservoirs. To meet these applications to enhance anisotropic formation
evaluations, a new MCI-type tool and the associated data-processing algorithms (and software system) have been
developed. This new MCI tool includes multiple triaxial subarrays with sharing of a common triaxial transmitter. It
operates multiple frequencies in the range of 12 to 84 kHz. As such, it can acquire multi-array (R-signal and Xsignal) full-tensor measurements at multiple frequencies. Compared to previous tools, this new tool not only has the
capability of acquiring both multi-array and multi-frequency measurements, but also has a wider frequency
operation range to target high-resistivity formation evaluation for multiple triaxial subarrays. At the same time, the
developed real-time data processing algorithms and the software system are used to perform the borehole correction
in measured data and recover the formation Rh, Rv, dip, and azimuth/strike for multiple arrays at multiple
frequencies in addition to formation bed positions as well as conventional array induction logs.
In the following sections, the tool configuration and its response functions are described. Then, the data process
algorithms and the workflow are discussed. Finally, the model-data validation is performed and the field testing
results are presented. All model and field examples demonstrate the capability of this new tool to deliver accurate
formation Rh, Rv, dip, and strike/azimuth as well as conventional induction logs. The addition of formation
anisotropy and direction can help reduce evaluation uncertainty and so provide accurate reserve estimates in
complicated anisotropic reservoirs.
2 SPWLA 554th Annual Logging Sympo
osium, June 2
22-26, 2013
TOOL
L CONFIGUR
RATION AND
D GEOMETR
RICAL FACTO
ORS
The newly developeed MCI tool em
mploys a triad of transmitterr coils (T) and six sets of recceiver coils ( R (1) through
T transmitter triad is locatedd at the top of all receiver cooils. The schem
matic layout
R ( 6) ) spaced along the tool axis. The
is pressented in Fig. 1. The transmiitter triad has three
t
collocatedd and orthogonnal coils ( Tx , Ty , and Tz ) inn the X, Y,
and Z directions. The
T two sets of receiver coils
c
( R (5) andd R (6) ) closest to the transm
mitter triad arre the two
conven
ntional coaxial induction sub
barrays, while the remainingg four sets of the receiver ccoils are built aas receiver
triads ( R (1) through R ( 4) ). Each recceiver triad is a proprietary aarrangement off six coils: threee orthogonal (X, Y, and
m
m
b
nd Rz ) and annother three coiils for a buckinng receiver triaad ( Rx , Rby ,
Z) coils for a triad of main receivers ( Rx , Rym , an
b
odel for a threee-triad subarrayy is representedd diagrammatically in the rigght panel of
and Rz ). The equivaalent dipole mo
Fig. 1. Both the maain and buckin
ng coils are co
ollocated, and the bucking ccoils are wound to minimizee the direct
coupliing signals and
d other spuriou
us coupling beetween transmiitters and receiivers. Each off the coils in thhe triads is
paralleel to the corressponding ones of the other triiads. The tool operates at muultiple frequenccies (e.g., 12, 336, 60, and
84 kH
Hz). These freq
quencies ensure the tool has the adequate signal level inn the full rangee of the targett formation
resistiv
vities/conductiivities. In addiition, this new tool uses the identical spaciings to the connventional induuction tool
(Xiao et al., 2006), and it also hass all its subarrrays on one sidde, which resuults in a minim
mized tool lenggth without
sacrifiicing the multip
ple targeted rad
dial depths of investigation
i
(ee.g., 10, 20, 300, 60, and 90 innches).
Fig. 1 Diagram of thee new MCI too
ol configuration and the equivaalent dipole moodel for a three--triad subarray. Here, ( xt ,
yt , z t ) represents thee tool/measurem
ment coordinate system, Lm is tthe spacing betw
ween transmitteer and main receeiver triads,
and Lb is the spacing between
b
transmitter and buckin
ng receiver triadds. See the text for explanationns of other param
meters.
The to
ool operates by
y sequentially energizing eacch of the coilss of three orthogonal directioons (X, Y, andd Z) in the
transm
mitter triad and
d measuring th
he signals in each of the recceiver coils. Hence, each onee of the multipple triaxial
subarrrays produces nine induction
n voltage sign
nals per frequeency at every logging depthh. Then, meassured ninecompo
onent voltages are collectiveely written as a 3  3 tensorr (or matrix) ffor multiple trriaxial arrays ooperated at
multip
ple frequencies:

V ( i , j ) ( z t )  V IJ( i , j )

( 3 3 )
, I , J  x / X , y / Y , z / Z , i  1, 2, ..., and N , j  1, 2 , ..., and M .................................. (1)
(i, j )
(i, j )
( z t ) reppresents the measured
where V
m
nine--component vooltage tensor aalong logging depth z t , couupling VIJ
t J-direction receiver and eexcited by thee I-direction traansmitter for a given i-th
denotees the voltage measured by the
subarrray operated at the j-th frequeency, N is the total
t
number off the triaxial arrrays (N = 4 foor the new MCII tool), and
3 SPWLA 54th Annual Logging Symposium, June 22-26, 2013
M is the total number of the operating frequencies (M = 4 for the new MCI tool).
After the amplified and digitized process through electronic circuits and firmware, and then calibration and
temperature correction (see Appendices A and B for more details), the induction voltages measured on all receivers
are converted/calibrated into apparent conductivities with a linear transformation. Also, the apparent conductivities
are symbolically expressed as a 3  3 tensor for multiple triaxial arrays operated at multiple frequencies:
 a(i , j )
(i , j )
(i , j )
(i , j ) 
  xx
 xy
 xz


   (yxi , j )  (yyi , j )  (yzi , j )    IJ(i , j )
 (i , j )

(i , j )
  zx
 zy
 zz(i , j ) 



(33)
, .............................................................................................. (2a)
or, another notation often used for the apparent conductivity tensor is
 a(i , j )
 XX (i, j)

  YX (i, j)

 ZX (i, j)

XY (i, j)
YY (i, j)
ZY
(i, j)
XZ (i, j) 
YZ (i, j)   IJ (i, j)

ZZ (i, j) 



( 33)
, ...................................................................................... (2b)
where  a(i , j ) is referred to as the MCI (R- or X-signal) apparent conductivity tensor in the tool/measurement
(i, j)
coordinate system ( xt , yt , z t ) and IJ (or IJ
Consequently, for example, when I , J = x/X,
 (yyi, j) (or YY (i, j) ), and when I , J = z/Z,
(i, j )
) are the measured-conductivity couplings of  a(i , j ) .
 IJ(i, j ) is the direct coupling xx(i, j) (or XX (i, j) ), when I ,
 IJ(i, j ) is  zz(i , j ) (or
(i, j)
J = y/Y, IJ is
ZZ (i, j) ), which are the traditional multi-array induction
measurements. Hence, the total should be the 2M×9 signals (M×9 R-signal and M×9 X-signal data) per triaxial
subarray for every log point. However, for two axial subarrays, even though they are capable of acquiring signals of
(i, j)
(i, j)
(i, j)
(i, j )
 zx
,  zy
, and  zz , the tool only acquires  zz couplings, so tensor  a(i , j ) reduces to a scalar, and therefore
(i, j)
only 2M signals (M R-signal and M X-signal data) are present per co-axial subarray. Additionally, IJ =
(i, j)
VIJ(i, j )  K IJ(i, j) , where K IJ(i, j) are the calibration factors (or gain) of the coupling IJ
determined by the calibration
experiments or tool constants determined by the analytical equations. For the accurate calibration of the new MCI
tool, an extension of the calibration method of conventional array induction tools is proposed and implemented (for
details, please refer to Appendix A).
As stated in the previous discussion, the primary features of this newly developed MCI tool are the use of both
multiple arrays and frequencies to measure full-tensor data in vertical or deviated wells filled with air or OBM.
Moreover, extensive numerical simulations already showed multi-array and multi-frequency tensor measurements
contain the sensitivity to formation anisotropy, dip, and direction.
In addition to the induction measurements mentioned, the new MCI tool also acquires the sonde temperatures for its
temperature-effect correction. This tool is usually run with a directional package so that true formation dip and
strike/azimuth can be found, and it also is run with a multi-arm caliper to find the borehole size and relative position
of the tool in the hole.
In the previous sections, the tool configuration was presented, which shows the capability of measuring conductivity
tensors at multiple subarrays operated at multiple frequencies. Next, the tool’s two important geometrical factors are
discussed — vertical geometrical factor (VGF) and integrated radial geometrical factor (IRGF). These factors
describe the tool’s vertical resolution and estimate the depth of investigation (DOI), respectively. The VGFs of MCI
measurements can be obtained using the following equations for multiple arrays at multiple frequencies:
4 SPWLA 54th Annual Logging Symposium, June 22-26, 2013

(i , j )
VGFIJ(i , j ) ( z,  )    g IJ
( z,  ,  ,  )  dd , I , J  x / X , y / Y , z / Z , i  1, 2, ..., and N , j  1, 2 , ..., and M ..... (3a)
0 
where g IJ( i , j ) ( z ,  ,  ,  ) is the two-dimensional (2D) Born response function for a three-coil array in cylindrical
coordinates at (  ,  , z ) . It can be determined by simply summing the 2D Born response functions for two 2-coil
arrays; the 2D Born response function for a two-coil array can be found in Barber et al. (2004). Theoretically, the
result should show a VGF tensor with nine VGFs for the given (i, j) but only VGF xx( i , j ) ( z ,  ) , VGF yy( i , j ) ( z ,  ) , and
(i , j )
VGF zz( i , j ) ( z ,  ) are non-zero and VGF xx( i , j ) ( z ,  ) = VGF yy ( z ,  ) . Fig. 2 presents the VGFs for a ZZ coupling (top)
of six arrays (A1 through A6) and a XX (or YY) coupling (middle) of four triaxial arrays (A1 through A4) at 12
kHz; the background conductivity shown is 1 mS/m. Following Gianzero and Gao (2004), the so-called combo
VGFs can be defined by the expression
(i , j )
VGF zzxxyy
( z ,  )  a ( i , j )  VGF zz( i , j ) ( z ,  )  b ( i , j )  VGF xx( i , j ) ( z ,  )  c ( i , j )  VGF yy( i , j ) ( z ,  ) ......................................... (3b)
(i , j )
where VGF zzxxyy
( z ,  ) are referred to as the combo VGFs from the combination of VGF xx( i , j ) ( z ,  ) , VGF yy( i , j ) ( z ,  ) ,
and VGF zz( i , j ) ( z ,  ) , which are shown in the bottom panel of Fig. 2. The undetermined parameters a (i, j ) , b (i , j ) , and
c (i , j ) can be chosen so as to have the optimized vertical characteristics of the combo VGFs. For instance, in Fig. 2,
a (i, j ) = 1.5, b (i , j ) = c (i , j ) = -0.5. By comparison, it can be seen that the long-tail effects in the profiles of VGF xx( i , j ) (or
(i , j )
VGF yy( i , j ) ) are sharply reduced in the profiles of VGF zzxxyy
( z ,  ) . Hence, this combination can lead to the enhanced
resolution of the combined logs, which offers a reduction of undesirable effects, such as the shoulder-bed effect.
The IRGF can be used to evaluate the cumulative contribution of the enclosed measurement volume to the overall
measurement and to estimate the DOI for an induction array, which is normally defined to be the depth at which the
IRGF equals 0.5. The IRGF is defined as
  
(i , j )
IRGFIJ(i , j ) (  ,  )     g IJ
( z,  ,  ' ,  )  dzd ' d ............................................................................................ (4)
0   
In the same way as above, we can verify that only IRGF xx( i , j ) (  ,  ) , IRGF yy( i , j ) (  ,  ) , and IRGF zz( i , j ) (  ,  ) are nonzero and IRGF xx( i , j ) (  ,  ) = IRGF yy( i , j ) (  ,  ) . Fig. 3 shows the IRGFs of a ZZ coupling (top) for six arrays (A1
through A6) and a XX or YY coupling (middle) for four triaxial arrays (A1 through A4) at 12 kHz; the background
(i , j )
conductivity shown is 1 mS/m. The combo IRGFs IRGF zzxxyy
(  ,  ) are presented in the bottom of Fig. 3. From
IRGF
(i, j )
( ,
zz
) of Fig. 3, the DOIs are found for all six ZZ arrays (A1, A2, A3, A4, A5, and A6): 113, 69, 40, 23,
14, and 9 inches. From IRGF xx( i , j ) (  ,  ) (or IRGF yy( i , j ) (  ,  ) ) of Fig. 3, the DOIs are found for all XX/YY arrays
(A1, A2, A3, and A4): >150, 119, 68, and 40 inches. Note that, because of the large negative contribution near the
hole, the DOIs for all four XX/YY arrays are deceptively deeper than the traditional ZZ arrays. From the
(i , j )
IRGF zzxxyy
(  ,  ) in Fig. 3, the DOIs are found for all four combo arrays (A1, A2, A3, and A4): 73, 45, 26, and 15
inches. The DOIs of the combo arrays are less than those of the ZZ arrays, but this could be a small disadvantage
compared to the greatly enhanced vertical resolution and much reduced shoulder-bed and borehole effects provided
by the combined logs. Keep in mind that all DOIs are functions of both frequency and background conductivity. For
example, if the operating frequency is higher and the background conductivity is fixed, then the tool’s DOI will
become shallower. Hence, an indirect way to correctly estimate the DOI for the XX/YY arrays is available.
5 SPWLA 54th Annual Logging Symposium, June 22-26, 2013
Fig. 2 VGFs for six ZZ-coupling arrays (A1 through A6) in the top, four XX or YY couplings (middle), and their combo
(bottom) arrays (A1 through A4) at 12 kHz; the background conductivity is 1 mS/m. The undesirable complicated
responses near the origin are clearly observed in the VGF profiles of the four XX- or YY-coupling arrays.
Fig. 3 IRGFs for six ZZ-coupling arrays (A1 through A6) in the top, four XX or YY couplings (middle), and their combo
(bottom) arrays (A1 through A4) at 12 kHz; the background conductivity is 1 mS/m.
DATA PROCESSING AND WORKFLOW
It is commonly known that the primary objective of MCI logging is fast and accurate delivery of formation
anisotropy, dip, and azimuth/strike from multi-array tensor measurements. Because of the complication of measured
data, as mentioned in the literature, they cannot be interpreted using “eyeball” inspection. Therefore, the associated
data processing algorithm and related software system must be developed to obtain the above mentioned formation
properties requested for evaluation of complex formations. The workflow for the newly developed data processing
algorithms and software is shown in Fig. 4. It generally consists of two parts—a down-hole part and an up-hole part.
The MCI down-hole tool acquires the voltage signals from all triaxial subarrays and the data from all of the
conventional short-spacing axial arrays at the multiple operating frequencies. These acquired data are digitized and
sent back to the up-hole part as its inputs. The advanced-processing software in the surface system removes noise,
stacks, and samples in depth for depth alignment, compensates for temperature effects on the sonde and electronics,
and converts the measured voltages that miss the unit into apparent conductivity signals using the so-called
calibration. Then, the data are processed to produce formation anisotropy, relative dip, azimuth, borehole-effect
corrected (BHC) logs as well as the bed boundaries, the conventional array induction logs, and invasion parameters.
All of these answer products can be available in real-time, and they are also processed for speed correction. Next,
6 SPWLA 54th Annual Logging Symposium, June 22-26, 2013
some important parts in the whole processing system are introduced.
ZZ-Coupling Processing. The MCI ZZ-coupling data measured on the z-directional receivers when the z-directional
transmitter is fired, in conjunction with the data from the short arrays, are processed using the conventional array
induction processing algorithms to obtain the same logs as the conventional array tools. The ZZ-coupling data
processing includes skin-effect correction, borehole correction, 2D software focusing, and ZZ-R1D inversion to
produce three sets of conventional resistivity logs in addition to invasion parameters (depth of invasion and flushedzone [Rxo] and virgin-zone resistivity [Rt]). For the detailed algorithms and application results, see Xiao et al.
(2006).
Adaptive Low-Pass Filtering. For the purpose of adaptive low-pass filtering, the Kaiser window is used as the lowpass filter function because it is a nearly optimal window function. The Kaiser window is defined by the following
equation:
K
w

I0 


( , m ) 
1 (
2m
 1) 2
M
I 0 ( )



 ,0  m  M ; K
w
(  , m )  0 for other cases ....................................... (5)
where I0 is the zero-order modified Bessel function of the first kind, parameter α is an arbitrary real number that
determines the shape of the low-pass window, and the integer M is the length of the window. The larger the value of
|α|, the narrower the window becomes. Conversely, for larger |α|, the width of the main lobe increases in its Fourier
transform, while the side lobes decrease in amplitude. Thus, this parameter controls the tradeoff between main-lobe
width and side-lobe area. For a large α, its shape tends toward a Gaussian window. For a given M, the Kaiser
window is totally defined by the parameter α. Hence, for the purpose of reducing high-frequency noise, α is
determined based on the data noise level (or uncertainty); for the purpose of reducing the horn effect in some
couplings of the MCI tensor, α is determined based on both the data uncertainty and the distance between the current
logging point and the bed boundaries.
Bed-Boundary Estimation. Numerical simulations show that the coefficients of variation (CV) of different
combined MCI signals, such as 3ZZ-(XX+YY)/2, 2ZZ-XX, or 2ZZ-YY, have good sensitivity to bed boundaries, so
they can be used to estimate the position of boundaries. First, the CVs of the selected combined MCI signals are
computed within a predetermined depth window (here, the window length should be great or equal to the vertical
resolution of the MCI tool). The CV is defined as a function of log depth, and the depth of the window center is
assigned to the computed CVs. Then, a maxima larger than a predetermined threshold value is searched for, and
tentative boundaries are placed at these depths. If the thickness of two boundaries is less than the vertical resolution
of the tool, then an average of the two boundaries is used as the new boundary and the two original ones are
removed.
R1D Inversion and BHC. The R1D inversion is based on a R1D model implemented by splitting the inversion
problem of one high-dimension unknown vector into several lower-dimension ones, based on their sensitivity to
different components of measured conductivity tensors for different subarrays operated at different frequencies. This
reduction in dimensionality makes the non-linear inversion considerably faster, more reliable, and robust. Another
critical element for this accurate and fast inversion is the use of the prebuilt lookup table/library as the forward
engine to replace the time-consuming three-dimensional (3D) simulation in the inversion. To remove the MCI
borehole effects, the conductivity tensor of one of the triads, usually the shorter arrays (e.g., A3 or A4), must be first
used to estimate the formation-, borehole-, and tool-position parameters (Rh, Rv or Rvh, borehole size, tool
eccentricity and its azimuth, dip, and azimuth/strike) by using the R1D inversion. This inversion assumes no
invasion and no shoulder-bed effects. It uses a prebuilt library (or BHC library) that includes the response of the tool
to the various formation-borehole parameters. After these parameters are obtained, the algorithm calculates and
removes the borehole effects for all triads and for all frequencies. More details on the algorithms of the R1D
inversion and MCI BHC are described in Hou et al. (2012).
V1D Inversion. The V1D inversion is also a model-based inversion processing method. It assumes the formation is
7 S
SPWLA 54th Annual
A
Loggin
ng Symposium
m, June 22-26,, 2013
oof a vertically transverse-iso
otropic (TI) an
nisotropic layeered structure. The newly ddeveloped V1D
D inversion is a
rrigorous and faast approach fo
or determining the horizontal and vertical reesistivities, bedd-boundary poositions, dip, annd
aazimuth/strike angles from BH
HC MCI log data.
d
In its firstt step, the azim
muth/strike anggle is determineed by rotating to
aan equivalent formation
f
mod
del with a zerro azimuth/striike angle. Theen, a variance//CV-based meethod is used to
eestimate the initial position of
o the bed boun
ndaries to be used
u
in the invversion. Next, an OD inversion algorithm is
ssolved in an infinitely homog
geneous mediu
um to obtain a good initial guuess model to bbe used as inittial inputs in thhe
V
V1D layered in
nversion algorrithm. Finally, the V1D layeered inversionn problem is trransformed intto a constraineed
nnonlinear miniimization prob
blem that can be solved ussing the regullarized Levenb
nberg-Marquarddt minimizatioon
m
method (Van den
d Bos, 2007)). To speed up the V1D layeered inversion, the Jacobian/ssensitivity mattrix is computeed
uusing forward differences on
nly once at thee beginning off the inversionn process. Durring subsequennt iterations, thhe
JJacobian matrix
x is updated by
y the Broyden’’s method. Forr real logging iinversion proceessing, a large number of bedds
m
must be inverted, which will result in a laarge V1D layeered inversion problem withh many unknowns. Too manny
uunknowns in an
a inversion model
m
will inccrease computaation complexxity and deteriiorate inversioon accuracy annd
eefficiency. To avoid this, a so-called layeer-sliding inveersion method is introducedd: the original large inversioon
pproblem is equ
uivalently and efficiently so
olved by subseequently inverrting a set of small V1D laayered inversioon
pproblems and combining
c
theiir results simu
ultaneously. Mo
oreover, the paarallel-program
mming implem
mentations of thhe
tiime-consuming operations further
f
lead to
o the reduced computation ttime in the enntire inversion.. Its applicatioon
rresults of synth
hetic data can be
b found in Hou
u et al. (2012).
F
Fig. 4 New MC
CI data processin
ng workflow in
ncluding down-hole and up-hoole parts (modiffied from Hou eet al., 2012). Thhe
ddown-hole part is for the dataa acquisition, an
nd the up-hole part is for deliivering the ansswer products thhrough data prrepprocessing and advanced
a
proceessing.
B
Before its appllication to field
d data, the dev
veloped data processing
p
worrkflow associat
ated with softw
ware system waas
tested on a nu
umber of MCI synthetic datta sets, which were generateed by using a fast and accuurate 3D finitteddifference (FD)) forward apprroach developeed by Hou et al. (2011). Fig. 5 shows one bborehole-formaation model thhat
w
was used to tesst the processin
ng workflow an
nd its software system describbed above. Thhis testing model consisted off a
550-degree deviiated borehole filled with OBM surroundeed by a nine-llayer TI formaation. This moodel assumes nno
innvasion of borrehole mud fluiid into the form
mation. The borrehole diameteer was 8 inchess, and the mud resistivity (Rm
m)
w
was 1000 ohm--m (or OBM). The MCI tool logs through th
he hole at the eeccentricity of 10% and an ecccentricity anggle
oof 30 degrees. As this was a fully 3D mod
del, the synthettic logs only ccould be generaated using a fuully 3D forwarrd
ccode. The synthetic logs werre assumed to be
b acquired with
w the new M
MCI tool (multiiple operating frequencies annd
ffour triaxial an
nd two axial arrrays). All otheer remaining model
m
parameteers are shown in Fig. 5. Thee simulated MC
CI
loog data were contaminated
c
with
w a 5% pseu
udo-random errror. All contam
minated syntheetic log data weere the inputs oof
thhe data processing system fo
or the adaptive low-pass filterring, horn reduuction, verticall-resolution enhhancement, beddbboundary detecction, R1D inveersion, BHC, and
a other proceessing.
F
Fig. 6 presentss the recovered
d model param
meters of Rh, Rv, dip, and strike logs forr four triaxial subarrays from
innversion of th
he contaminated MCI data att 12 kHz. For the purpose oof comparison with the recovvered formatioon
8 8
SPWLA 554th Annual Logging Sympo
osium, June 2
22-26, 2013
param
meters, the correesponding truee model param
meters are also sshown in Fig. 6. The true annd recovered R
Rh, Rv, dip,
and strrike logs are presented in Traacks 1 through
h 4 (from left too right). The trrue model paraameters are shoown by the
dashed
d-dot lines in magenta,
m
whilee the inverted ones
o
for four trriaxial subarrayys (A1, A2, A33, and A4) aree plotted by
the solid lines in diffferent colors (b
blue, green, read, and cyan). After comparrisons with the true ones, it w
was noticed
he true and inv
verted strike, Rh,
R and Rv as well as the truue and recoverred dip, exceppt the isotropicc formation
that th
section
ns, agree very
y well. After the comparisson among thhe inverted reesults for diffferent frequencies, good
consisstency was alsso found. The good agreem
ment between the inverted aand true form
mation parametters clearly
demon
nstrates that th
his R1D inverssion algorithm
m performed veery well, evenn for the contaaminated data with a 5%
random
m noise level. This confirmss the validity and
a robustnesss of the R1D iinversion approoach. On the oother hand,
one sh
hould be awaree that accurate recovered
r
dip results
r
of the R
R1D inversion are only possibble in formatioon intervals
with reesistivity aniso
otropy as there is no sensitivitty of the MCI m
measurements to dip in isotroopic formationns.
Fig. 5 Schematic diaagram of a fully
y 3D model used for the data--processing validation. This 3D
D model consissts of a 50hole filled with OBM
O
and surro
ounded by a horrizontal nine-layyer formation w
without invasion.. Each layer
degreee deviated boreh
is charracterized by Rh
h, anisotropic rattio (Rvh = Rv/R
Rh), and top andd bottom layer-bboundary locatioons. Layers 1, 3, 5, 7, and 9
are TI and have the saame Rh and Rvh
h of 2 ohm-m an
nd 5; the remainning layers are isotropic and havve the same Rh of 20 ohmol logs through an 8-inch boreehole and is deccentralized insidde the hole witth eccentricity oof 10% and
m. Thee new MCI too
eccentrricity angle of 30 degrees. Heree, ( x f , y f , z f ) designates the fformation beddding-plane coorddinate system.
Fig. 6 Recovered Rh, Rv, dip, and sttrike for four triiaxial subarrayss (A1, A2, A3, aand A4) from pprocessing of coontaminated
MCI data
d with a 5% error at 12 kHzz are presented.. They are show
wn with solid liines in Tracks 1, 2, 3, and 4 (ffrom left to
right), respectively. For
F comparison purposes,
p
the tru
ue model param
meters are show
wn as magenta daashed lines for every track.
t Rh and Rv logs
l
are plotted in a log scale, and the dip andd strike logs are plotted in a linnear scale. Noticce that good
Also, the
consisttency exists amo
ong the four-array results, but th
he recovered Rhh and strike are more accurate.
9 SPWLA 54th Annual Logging Symposium, June 22-26, 2013
After the R1D inversion discussed previously, the BHC is performed to the synthetic MCI logs at multiple
frequencies. Fig. 7 shows the BHC-corrected MCI nine-component logs of six subarrays at a frequency of 12 kHz
for the model shown in Fig. 5. The true formation horizontal and vertical conductivities (Ch and Cv) are only
included in this figure for reference. For the validation purpose of the corrected logs, the MCI logs are also
computed without the borehole effect in the same layered formation without a hole, as shown in Fig. 5 with an EM
semi-analytical solution in V1D layered TI formations (Zhong et al., 2006). The computed results are shown as the
dashed lines in Fig. 7. By comparison, it can be observed that all corrected components have a good match with the
corresponding simulated V1D results, with exception of the logging intervals around the boundaries. These
discrepancies could be primarily caused by the BHC model, which does not account for shoulder-bed effects.
Finally, the BHC data are used as inputs for the ensuing further processing, such as for the V1D inversion and ZZ
array processing without BHC for producing ACRt-type logs described previously.
Fig. 7 BHC-corrected MCI nine-component logs of six arrays (A1 through A6) at a frequency of 12 kHz for the synthetic
logs of the 3D model shown in Fig. 5. The BHC-corrected logs are shown as solid lines in different colors (blue, red,
magenta, black, cyan, and yellow). The synthetic logs produced by a V1D code are plotted in the dashed lines. Notice that
good agreement exists between the corrected and V1D logs. Here, Ch and Cv denote the true formation horizontal and
vertical conductivity shown as the green and red dot-dashed lines for every panel. Only the ZZ couplings are plotted in a log
scale.
FIELD-TESTING EXAMPLE
The new MCI tool was designed and several prototypes of the new tool were built. To date, the new MCI tool has
completed its field testing in two test wells and a number of client wells. Since December 2012, it has logged in at least
two commercial-job wells. All application examples demonstrate that the targeted tool capability to provide accurate
formation anisotropy (Rh and Rv) and direction information for enhancing complicated formation evaluations has been
achieved. This evaluation involved different borehole-formation environments, such as low- and high-resistivity
formations, large and small holes, and low- and high-dip formations. Because of the limitation of acquired data release
from the operators, only one example is presented to illustrate the tool’s field testing applications. The application
results in one test well from Texas can be found in Hou et al. (2012).
The MCI data for this example was acquired in a well from South America drilled using OBM and an 8.5-inch bit. This
well’s deviation angle was between 40 to 50 degrees, and its azimuth angle was between 150 and 170 degrees. Aside
from the MCI induction data for multiple arrays and multiple frequencies, the borehole imaging data, the directional
data, the six-arm caliper data, neutron, and density data were also acquired and were available for this same well. The
borehole imaging data were interpreted to determine the formation dip and azimuth angles. The directional data were
used to determine the final true/structural dip, azimuth angles of the MCI, and imaging relative angles. Fig. 8 shows the
measurements of three direct couplings (ZZ, XX, and YY) and the combo (XX+YY)/2 of XX and YY of three
subarrays of A2, A3, and A4 for a 500-ft interval of this well and their comparisons between the main (M) and
repeat (R) runs. As expected, for longer spacing arrays in the OBM well, the ZZ-coupling data from both
10 SPWLA 54th Annual Logging Symposium, June 22-26, 2013
acquisitions perfectly overlay, but the virtual differences of the two horizontal direct couplings of XX and YY can
be observed for three arrays between the two runs because of their sensitivities to the tool position and direction in
the hole, especially for short array A4. Because of the function of the combo (XX+YY)/2 of XX and YY to reduce
the tool-position effect, perfect agreement is observed for the combo (XX+YY)/2 data for the two runs, as shown in
the rightmost track of Fig. 8. All shown good data repeatability indicates the good data quality of the MCI
measurements. In summary, both ZZ and the combo signals can be used to evaluate the data quality by the
comparisons between the M and R runs. Following the evaluation of raw data quality, the real-time data processing
software previously discussed is run to produce the conventional array induction logs (or ACRt-type logs) for the
main run over the same interval as Fig. 8 and to recover formation Rh, Rv, dip, strike/azimuth logs, and bed
boundaries from the measured MCI data for four triaxial subarrays (A1, A2, A3, and A4) at multiple frequencies (e.g.,
12 and 36 kHz).
Fig. 9 shows the three sets of conventional array induction logs and Rxo, Rt, and depth of invasion logs from the ZZ
R1D inversion. These logs show very little resistivity changes over the whole interval, and the resistivity values are
between 1and 5 ohm-m in most parts. All resistivity logs stack together, which shows there almost is no invasion in the
profile. Fig. 10 shows the recovered four-array formation Rh, Rv, dip, and strike/azimuth logs from the 12-kHz MCI
measurement plus the two conventional logs (R10 and R90) for the purpose of comparison with the inverted Rh logs.
The Rh, Rv, dip, and strike/azimuth logs are plotted in Tracks 1, 2, 3, and 4 (from left to right) in Fig. 10. It can be first
noticed that the four-array inverted results are fairly consistent with each other. The inverted Rh logs correlate fairly
well with the ZZ measurements, and the conventional array induction logs, such as R10 and R90. As expected, the Rh
logs are less than or equal to the conventional logs, especially in high-dip sections (e.g., the zone between 050 and
250 ft) or low-dip ones, respectively. However, the inverted Rv logs clearly indicate there is formation resistivity
anisotropy for the whole interval, and these Rv logs show relatively obvious resistivity change. Moreover, good
correlation can be observed between the inverted Rv and XX/YY logs shown in Fig. 8. So both Rh and Rv can
provide more accurate Rsand (sand resistivity) and saturation. Multi-array inverted logs can further reduce their
uncertainty. The recovered dip logs present relative dips that vary from approximately 30 to 60 degrees and
recovered azimuths that vary between 100 to 180 degrees. Again, good correlation can be observed for the recovered
dips and azimuths from MCI and direction data as well as those of borehole imaging data processing. In addition, for
the validation of the recovered Rh, Rv, dip, and azimuth, the inverted results from multi-frequency measured data
and different runs (M and R) were compared, and good consistency was found among them.
Fig. 8 Comparison of three direct couplings (ZZ, XX, and YY) and the combo (XX+YY)/2 of XX and YY between the M
and R runs for a 500-ft interval between 000 to 500 ft in a well from South America. Tracks 1, 2, and 3 (from left to
right) present the comparisons of the three direct couplings (ZZ, XX, and YY) for three triaxial subarrays of A2, A3, and
A4 at 12 kHz. The rightmost track shows the comparisons of the combo (XX+YY)/2 of XX and YY over the same
interval. Also, A2M, A3M, and A4M denote the M run measurements for 3 arrays of A2, A3, and A4, and A2R, A3R, and
A4R denote the R run measurements for the same three arrays.
11 SPWLA 54th Annual Logging Symposium, June 22-26, 2013
Fig. 9 Conventional array induction logs and ZZ-R1D inversion logs are presented for the M run over the same interval as
Fig. 8. Here, RO, RT, and RF shown in the three leftmost tracks are the 1-, 2-, and 4-ft array induction logs with the DOIs
of 90, 60, 30, 20, and 10 inches. Rxo and Rt logs from the ZZ R1D inversion are shown in Track 2. The rightmost track
shows the results of the inverted depth of invasion.
Fig. 10 Four sets of recovered formation Rh, Rv, dip, and strike/azimuth logs for four triaxial subarrays (A1, A2, A3, and A4)
are presented for the M run over the same interval as Fig. 8. They are plotted in Tracks 1, 2, 3, and 4 (from left to right) and
represented by the solid lines. In every track, the recovered results for four arrays are given by the blue, green, read, and
cyan colors. Here, in the leftmost track, R10 and R90, shown by the magenta and yellow dashed lines, are the two 2-ft
conventional array induction logs (or ACRt-type logs) with the DOIs of 10 and 90 inches, respectively. Notice that the fourarray inverted parameters show good consistency with each other.
CONCLUSIONS
The new MCI tool targeting OBM-well operations has been successfully developed and field-tested. This new tool is
a multi-array triaxial induction tool. It operates multiple frequencies in the range of 12 to 84 kHz. The associated
fast and accurate data processing algorithms and their software system also have been developed and implemented.
The accurate and fast data processing system can recover answer products of formation Rh and Rv, dip, and
strike/azimuth, along with the bed-boundary position, the three sets of conventional array induction logs (ACRt-type
logs), and the invasion parameters.
To date, the new MCI tool has completed field testing in two test wells and a number of client wells. And it has
logged in at least two commercial wells since December 2012. The field-testing and commercial application results,
12 SPWLA 54th Annual Logging Symposium, June 22-26, 2013
and the related model data tests, demonstrate the capability of this new tool to deliver accurate multi-array formation
Rh and Rv, dip, and strike/azimuth, as well as the bed-boundary position and the conventional array induction
resistivity logs, which can provide enhanced reserve estimates in complicated anisotropic reservoirs, such as lowresistivity or fractured/faulted formations.
NOMENCLATURE
MCI
LWD
OBM
BHC
Rh
Rv
Rvh
Dip
Strike
Ch
Cv
R1D
OD
1D
V1D
3D
Multicomponent induction
Logging while drilling
Oil-based mud
Borehole-effect correction
Horizontal resistivity
Vertical resistivity
Anisotropic ratio (Rv/Rh)
Formation relative dip
Formation strike/azimuth
Horizontal conductivity
Vertical conductivity
Radially one-dimensional
Zero-dimensional
One-dimensional
Vertically one-dimensional
Three-dimensional
ACKNOWLEDEGEMENTS
The authors thank the oil companies for consent to release their field data. The authors also thank Halliburton for
permission to publish this paper. Special thanks go to EM-physics colleagues Drs. Burkay Donderici, Turker
Celepcikay, Baris Guner, and Yumei Tang for their contributions related to the issues of tool calibration, MCI
library, as well as V1D inversion, and also John Purba and James Wang of Halliburton for providing valuable
support concerning field data processing and real-time software development.
REFERENCES
Barber, T., Anderson, B., Abubakar, A., Broussard, T., Chen, K., Davydycheva, S., Druskin, V., Habashy, T.,
Homan, D., Minerbo, G., Rosthal, R., Schlein, R., and Wang, H., 2004, Determining formation resistivity anisotropy
in the presence of invasion: Paper SPE 90526 presented at the SPE 80th Annual Technical Conference and
Exhibition, Houston, Texas, USA, 26–29 September.
Barber, T. and Rosthal, R., 1991, Using a multiarray induction tool to achieve high-resolution logs with minimum
environmental effects: Paper SPE 22725 presented at the SPE 66th Annual Technical Conference and Exhibition,
Dallas, Texas, USA, 6–9 October.
Beste, R., Hagiwara, T., King, G., Strickland, R., and Merchant, G., 2000, A new high resolution array induction
tool: Paper presented at the SPWLA 41st Annual Logging Symposium, Dallas, Texas, USA, 4–7 June.
Bittar, M., Althoff, G., Beste, R., Li, S., and Wu, H., 2011, Field testing of a new LWD triaxial sensor for anisotropy
and dip measurement in vertical and deviated wells: Paper presented at the SPWLA 52nd Annual Logging
Symposium, Colorado Springs, Colorado, USA, 14–18 May.
Gianzero, S. and Gao, L., 2004, Method of combing vertical and horizontal magnetic dipole induction logs for
reduced shoulder and borehole effects: US Patent No. 6,819,112 B2.
Hou, J., Bittar, M., Wu, D., Sanmartin, L., and Guner, B., 2011, New scattered potential finite-difference method
13 SPWLA 54th Annual Logging Symposium, June 22-26, 2013
with anisotropic background to simulate multicomponent induction logs: Paper presented at PIERS 2011, Suzhou,
China, 12–16 September.
Hou, J., Sanmartin, L., Wu, D., Celepcikay, T., and Torres, D., 2012, Real-time borehole correction for a new
multicomponent array induction logging tool in OBM wells: Paper presented at the SPWLA 53rd Annual Logging
Symposium, Cartagena, Colombia, June 16–20.
Kriegshauser, B., Fanini, O., Forgang, S., Itskovich, G., Rabinovich, M., Tabarovsky, L., Yu, L., Epov, M., and
Horst, J.v.d., 2000, A new multicomponent induction logging tool to resolve anisotropic formations: Paper presented
at the SPWLA 41st Annual Logging Symposium, Dallas, Texas, USA, 4–7 June.
Rabinovich, M., Tabarovsky, L., Corley, B., and Horst, J., 2005, Processing multicomponent induction data for
formation dip and azimuth in anisotropic formations: Paper presented at the SPWLA 46th Annual Logging
Symposium, New Orleans, Louisiana, USA, 26–29 June.
Rabinovich, M., Gonfalini, M., Rocque, T., Corley, B., Georgi, D., Tabarovsky, L., and Epov, M., 2007,
Multicomponent induction logging: 10 years after: Paper presented at the SPWLA 48th Annual Logging Symposium,
Austin, Texas, USA, 3–6 June.
Rosthal, R., Barber, T., Bonner, S., Chen, K.C., Davydycheva, S., and Hazen, G., 2003, Field test results of an
experimental fully triaxial induction tool: Paper presented at the SPWLA 44th Annual Logging Symposium,
Galveston,. Texas, USA, 22–25 June.
Strickland, R., Sinclair, P., Harber, J., and DeBrecht, J., 1987, Introduction to the high resolution induction tool:
Paper presented at the SPWLA 28th Annual Logging Symposium, London, England, 29 June–2 July.
Van den Bos, A., 2007, Parameter estimation for scientists and engineers: Wiley-Interscience.
Wang, H., Barber, T., Morriss, C., Rosthal, R., Hayden, R., and Markley, M., 2006, Determining anisotropic
formation resistivity at any relative dip using a multiarray triaxial induction tool: Paper SPE 103113 presented at the
SPE 82nd Annual Technical Conference and Exhibition, San Antonio, Texas, USA, 24–27 September.
Wu, P., Wang, G.L., and Barber, T., 2010, Efficient hierarchical processing and interpretation of triaxial induction
data in formations with changing dip: Paper SPE 135442 presented at the SPE 86th Annual Technical Conference
and Exhibition, Florence, Italy, 19–22 September.
Xiao, J., Buchanan, J., Bittar, M., Davis, E., Sanmartin, L., Hu, G., Zannoni, S., Morys, M., and Liu, W., 2006, A
new asymmetrical array induction logging tool: Paper SPE 101930 presented at the SPE 82nd Annual Technical
Conference and Exhibition, San Antonio, Texas, USA, 24–27 September.
Zhang, Z., Akinsanmi, O., Ha, K., Bourgeois, T., Jock, S., Blumhagen, C., and Stromberg, S., 2007, Triaxial
induction logging – an operator’s perspective: Paper presented at the SPWLA 48th Annual Logging Symposium,
Austin, Texas, USA, 3–6 June.
Zhong, L., Shen, L., Li, S., Liu, R., Bittar, M., and Hu, G., 2006, Simulation of tri-axial induction logging tools in
layered anisotropic dipping formations: Paper presented at the SEG International Exhibition and 76th Annual
Meeting, New Orleans, Louisiana, USA, 1–6 October.
ABOUT THE AUTHORS
Junsheng Hou received his BS and MS degrees in applied geophysics from Wuhan College of Geosciences, China, in
1984 and China University of Geosciences at Beijing (CUGB) in 1988, respectively. He obtained his PhD degree in
geophysical/geological exploration from Northeastern University, China, in 1993. Dr. Hou began his career as a field
geophysicist with Chinese Henan Geophysical Exploration in 1984. Junsheng joined Halliburton in 2005 and currently
is working as a scientific advisor in Halliburton’s Houston technology center. Dr. Hou has published extensively on the
14 SPWLA 54th Annual Logging Symposium, June 22-26, 2013
topics of resistivity logging, formation evaluation, and surface geophysics. His current research focuses primarily on
3D numerical simulation, data processing, inversion, log interpretation, and tool development of multicomponent
induction logging. Email: Junsheng.Hou@Halliburton.com
Luis Sanmartin is a senior technical professional leader in the sensor physics group at Halliburton in Houston. He
received his PhD degree in physics from the University of Illinois at Urbana-Champaign in 1998 and joined
Halliburton after graduation. His primary interest is in design and development of electromagnetic instruments. Dr.
Sanmartin is a member of SPWLA, IEEE, and SPE. Email: Luis.Sanmartin@Halliburton.com
Dagang Wu is a principal scientist at Halliburton in Houston. He received his PhD degree in electrical engineering
from the University of Houston in 2006. His current interest is in development and processing of
electromagnetic/resistivity logging tools. Dr. Wu is a member of SPWLA. Email: Dagang.Wu@Halliburton.com
David Torres is the project manager for the multicomponent induction tool and is responsible for overseeing the
development, testing, and marketing of the tool. For more than 20 years, Torres has worked in various management
and R&D positions in the oil industry. He began his career in 1980 with Gearhart Industries in Brazil. He moved to
Texas and held several positions within the organization. He holds several patents and has authored various papers
in signal and image processing. Torres holds an EE degree and a MSEE degree from the University of Madison,
Wisconsin. Email: David.Torres@Halliburton.com
F. Turker Celepcikay holds a BS degree in electrical and electronics engineering from Bilkent University, Ankara,
Turkey (2005) and a PhD degree in electrical engineering from the University of Houston, USA (2010). Celepcikay
has worked as a senior scientist in the formation evaluation group in Halliburton Energy Services in Houston. His
current interest is in development and improvement of electromagnetic/resistivity logging tools. APPENDIX A: CALIBRATION OF NEW MCI TOOL
The calibration method of the new MCI tool is similar to the calibration routine of conventional array induction
tools, such as ACRt tool. The important difference is that the new MCI tool has three transmitter orientations and
three receiver orientations that give rise to nine-coupling signals for each triaxial subarray at each frequency. In the
MCI calibration, the seven components of XX, XZ, YY, YZ, ZX, ZY, and ZZ are first calibrated. Then, from the
measurements of the seven experimental values, the gains for the remaining two components (XY and YX) can be
derived.
After the gains have been found, the offsets can be evaluated by lifting the tool from the surface to a height of 20 ft,
in a so- called “air-hang” experiment. The offsets are evaluated as:
 offset  S air _ hang  G ...........................................................................................................................................(A-1)
where  offset is the offset, G is the gain, and S air _ hang is the signal received at the “air-hang” step.
Finally, with gains and offsets evaluated, the apparent conductivities for every component at every frequency are
obtained from the following equation:
 a  S  G   offset ...............................................................................................................................................(A-2)
or
 a  ( S  S air _ hang )  G .......................................................................................................................................(A-3)
15 SPWLA 54th Annual Logging Symposium, June 22-26, 2013
where  a is the calibrated apparent conductivity, S is the received signal, and
 offset is the additive constant, also
called the sonde error. On a rigorous calibration formulation, the calibration accuracy depends on the compensation
for the temperature effect, the earth ground effect, and the suppression of the random noise. For details of how to
incorporate these corrections into a rigorous calibration scheme, see Xiao et al. (2006).
APPENDIX B: TEMPERATURE CORRECTION OF NEW MCI TOOL
A typical logging tool consists of a sonde section and an electronics section. Temperature causes performance drift
for the electronic section and produces response changes for the sonde. The sonde response change with temperature
is referred to as the temperature effect. The temperature effect is a function of the temperature and temperature
distribution inside the sonde. The temperature effect comes from thermal expansion of the sonde and the physical
property variation of the sonde materials with temperature. Modern electronics can self-compensate the performance
drift by periodic performance of self-calibration. In this appendix, methods are described for effectively monitoring
the temperature inside the sonde and for compensating for the sonde response change.
The temperature effect of induction tools primarily comes from three sources: (1) the conductivity of the feed pipe
that shields the wires, which varies as temperature changes; (2) thermal expansion, which changes the distances
between coils, the radii of the coils, and the radius of the feed pipe; and (3) the resistance of the coils, which varies
as temperature changes.
The coil radius expansion is controlled by the temperature at the coils. The temperature effect from the feed pipe
depends on the temperature of the feed pipe. The axial expansion is even more difficult to evaluate. This
heterogeneous temperature distribution complicates the temperature correction with two questions: (1) how to
effectively measure the temperature and temperature distribution of the tool body, and (2) how to accurately correct
for the temperature effect of multiple sources. These questions were answered by developing a thermodynamic
analysis of the heat flow within the tool for the conventional array induction tools. The same analysis is applicable
to the new MCI tool. The analysis shows that two temperature sensors are sufficient to achieve accurate correction.
The two sensors are placed spaced apart along the pipe. The temperature effect of the sonde is evaluated in an oven,
and the drift is fit to a cubic polynomial approximation in three variables: temperature of Sensor A, time derivative
of temperature in Sensor A, and temperature difference between Sensors A and B. The precise expression of the
cubic polynomial is:
 T  a0  a1 (TA )  a 2 (TA ) 2  a3 (TA ) 3    b1 (TAB )  b3 (TAB ) 3   ............................ (B-1)
T
T
 c1 ( A )  c3 ( A ) 3   ,
t
t
where the coefficients a 0 , a1 , a 2 , a 3 , b1, b3 , and c1, c3 are obtained by optimal fitting to the heat run test of each of
the measurements of the MCI tool. For more details on the temperature correction, see Xiao et al. (2006).
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