1.—Technical Field
Embodiments disclosed herein generally relate to the measurement of electrical characteristics of formations surrounding a borehole, and using the measured electrical characteristics to estimate additional, non-measured, formation parameters. In particular, the disclosed embodiments are related to estimating formation parameters using only the imaginary, or reactive, components of the measured data.
2.—Description of Related Art
Induction logging is important in the search for and recovery of subterranean petroleum deposits. In particular, induction logging is used to determine the resistivity, conductivity, and other parameters of earth formations surrounding a borehole. Induction logging involves using a transmitter to produce a field that is directed into the earth formations. The field induces eddy currents to flow in the formations and the response from the formation is measured by a receiver. Specific properties of the received signal can then be analyzed to determine specific formation properties which is logged at the surface as a function of the depth of the tool in the borehole.
In typical induction logging tools, the formation response to the resultant field can be difficult to measure because most of the signal at the receiver arrives directly from the transmitter to the receiver. This field that is received at the receiver directly from the transmitter is known as the direct signal. To allow for improved measurement of the formation response, the receiver is now typically made of two functional parts, a main portion of a receiver and a bucking portion of a receiver. In typical induction logging tools, the transmitter and receiver are one or more coils, and the bucking coil is wound in the opposite direction to the main receiver coil to cancel the direct signal.
The voltage generated by the direct signal has a phase offset of about 90 degrees with respect to the phase of the current in the transmitter, and contributes to the imaginary or reactive portion of the voltage measured in the receiver. Even though most processing algorithms are based substantially on the real part of the voltage and ignore the imaginary portion, it is still necessary to cancel the direct signal because it can be several orders of magnitude larger than the signal received from the formation and, thus, even small phase measurement errors of the direct signal can produce a significant deviation in the measurement of the real part of the measured voltage. In addition, any movement of the coils caused by change in temperature or mechanical vibration can produce additional direct imaginary or reactive parts of signals that are comparable in magnitude to the imaginary parts of signals that are normally generated by the formation. This makes it difficult to accurately measure the imaginary signals and, thus, the imaginary part of the signal is generally disregarded and not used.
However, even using the real part of the signal does not provide optimal results at all times. For example, when performing induction logging at or near boundaries between geological beds, known as bed boundaries, formations often have different resistivities on either side of the bed boundary such that the measure voltages exhibit what is known as horns. As defined in, for example, U.S. Pat. No. 5,241,273 to Luling, horns are defined as “a sharp local maximum with a peak resistivity at least twice the resistivity on either side of the local maximum.” These horns grow as the dip angle of the formation increases, and may provide unsuitable results and errors near bed boundaries.
Consequently, there is a need to provide an induction logging tool that is capable of producing more accurate results of formation characteristics at or near bed boundaries.
Consistent with some embodiments, there is provided a system for determining formation parameters. The system includes an induction logging tool that includes a plurality of transmitter coils, the plurality of transmitter coils transmitting an induction signal into the formation. The induction logging tool further includes a plurality of receiver coils, each of the receiver coils being spaced apart from the transmitter coils by a predetermined distance and receiving a response signal from the formation. The system also includes circuitry coupled to the induction logging tool, the circuitry determining voltages induced in the plurality of receiver coils by the response signal, wherein the circuitry is further configured to separate real portions of the determined voltages from imaginary portions of the determined voltages and determine formation parameters using imaginary portions of the measured voltages, wherein the real portions of the determined voltages are in phase with a current on at least one of the transmitter coils and the imaginary portions of the determined voltages are ninety degrees out of phase with the current on the at least one transmitter coil.
A method of determining selected parameters of a formation is also provided. The method includes transmitting, by a plurality of transmitters of an induction logging tool, an induction signal into the formation and receiving, by a plurality of receivers of the induction logging tool, a response signal from the formation. The method further includes measuring voltages induced in the plurality of receivers by the response signal and separating, by circuitry, imaginary components of the measured voltages from real components of the measured voltages, wherein the real components of the determined voltages are in phase with a current on at least one of the transmitters and the imaginary components of the determined voltages are ninety degrees out of phase with the current on the at least one transmitter. The method also includes determining, by the circuitry, selected parameters of the formation using the imaginary components of the measured voltages.
These and other embodiments will be described in further detail below, with reference to the following drawings.
Wherever possible, the same reference numbers are used throughout the drawings to refer to the same or like elements.
Typically, a formation model is used to interpret the logged voltage measurements to determine the formation parameters using circuitry 114. A typical model is a uniaxial anisotropy model that assumes that formation 104 is isotropic in the horizontal direction (parallel to the bedding plane) and anisotropic in the vertical direction (perpendicular to the bedding plane). By preparing a coordinate system specific to formation 104 such that the z-axis is perpendicular to layers 106-110, and the x- and y-axes are parallel to layers 106-110 allows for a conductivity tensor to be defined
where σh is a horizontal conductivity of formation 104 and σv is a vertical conductivity of formation 104.
However, the axes of the formation coordinate system typically do not correspond to the axes of the tool coordinate system. Indeed, as shown in
Of course, any vector v″ in the coordinate system of formation 104 can be expressed in the coordinate system of induction logging tool 102 by another rotational transform:
v=Rv″
where the rotation transform matrix R is
Following the definition of the rotational transform, the measurements of the induction tool can be explained.
Consistent with some embodiments, receiver coils Rx, Ry, Rz may be used to measure voltage indicative of formation parameters. The overall voltage detected by coil arrangement 300
The diagonal components of the measured voltages in Equation (1) (Vxx, Vyy, and Vzz) will be heavily influenced by the direct signal, which will make it difficult to use the imaginary or reactive portion of the measured voltages in determining formation parameters. On the other hand, the off-diagonal terms (Vyx, Vxy, Vyz, Vzx, Vxz and Vzy) will be relatively free from the direct signals, and the measurements of those components in vacuum is, with or without bucking coils, approximately zero. Thus, the imaginary or reactive portions of the measured off-diagonal voltages may be used in determining formation parameters that are relatively free from errors attributed to a strong measured direct signal Moreover, the imaginary or reactive portions of the measured voltages may be used to determine formation parameters in much the same way that the real portions of the measured voltages are used. Consistent with some embodiments, the real and imaginary (or reactive) portions of the measured voltages are defined with respect to the current of a transmitter, and more particularly with respect to the active transmitter. Consequently, according to such embodiments, the real portion of the measured voltage is the portion that is in phase with the current of the active transmitter and the imaginary portion of the measured voltage is the portion that is 90 degrees out of phase with the current of the active transmitter. For example, in measuring the voltage Vzy, the real portion of the measured voltage is the portion that is in phase with the active transmitter (Tz), and the imaginary portion of the measured voltage is the portion that 90 degrees out of phase with the active transmitter (Tz). Although the voltage tensor shown in equation (1) is obtained using an arrangement of three transmitters and three receivers, fewer transmitters and receivers may be used in embodiments when logging tool 102 is rotating. Moreover, consistent with other embodiments, when the transmitter coils are operating at different frequencies, one or more of the transmitter coils may be operating simultaneously and the receiver coils may differentiate the received voltages attributed to each transmitter coil by using frequency-based filtering.
The magnetic field responses in a tool coordinate system for multi-coordinate induction logging tool, such as tool 102 having coil arrangement 300 in transverse-isotropic formations with zero strike may be expressed as a matrix H having the form:
The voltage
Based on a standard Euler rotation, a relationship between the voltage
where R is the rotation matrix with respect to strike angle β:
From the above equations, we can determine that the components of the voltage in
Finally, based on equation (2), we can obtain the following solutions for strike angle β:
These equations may be rewritten to use only the imaginary portions of the measured voltages as follows:
As discussed in, for example, U.S. Pat. No. 6,393,364 to Gao et al., and assigned to the same assignee as the present disclosure, equations for calculating an approximate estimation for the dip angle α, can be derived from the magnetic field responses in a tool coordinate system for a multi-component induction logging tool in a homogenous dipping anisotropic formation as
where kh is the horizontal wave number determined by kh=√{square root over (iωμσh)}, σh is the horizontal conductivity, σv is the vertical conductivity, and ω is the frequency, λ is the anisotropy coefficient determined by
A is the anisotropy factor determined by
and LM is the transmitter-receiver spacing for a bucking receiver and a main receiver.
Assuming a transmitter-receiver spacing that is approaching zero, based on the equations above, the following equation may be derived for the real part of the magnetic field components:
where δ is the skin depth for horizontal conductivity and resistivity given as
The dip angle α can then be determined as
Finally, because the real component of the magnetic field is identical to the imaginary or reactive component of the voltage other than a constant value, the dip angle α can be determined based on the imaginary component of the measured voltage using the following equation:
The formation resistivities Rh and Rv and formation conductivities σh and σv may be further estimated based on calculated dip angle α and strike angle β, calculated using the equations above, as discussed in the article by Moran and Gianzero, entitled “Effects of formation anisotropy on resistivity-logging measurements,” Geophysics, vol. 41, no. 7 (July 1979), pp. 1266-1286 using the following equations:
σxx=σh+(σv−σh)sin2 α cos2 β (15)
σyy=σh+(σv−σh)sin2 α sin2 β (16)
σzz=σv−(σv+σh)sin2 α (17)
σxy=σyx=(σv−σh)sin2 α sin β cos β (18)
σxz=σzx=(σv−σh)sin α cos α cos β (19)
σyz=σzy=(σv−σh)sin α cos α sin β (20)
The apparent resistivities Rij of formation 104 are proportional to the measured voltages, as discussed in U.S. Pat. No. 6,765,386, assigned to the same assignee as the present disclosure, and can be used to determine the apparent conductivities, which are the inverse of the apparent resistivities:
Knowing the apparent conductivities, the determined dip angle α, and the determined strike angle β, the horizontal conductivity σh and the vertical conductivity σv may be estimated using equations (15)-(20). The estimated horizontal conductivity σh and vertical conductivity σv may be further corrected using skin effect correction and borehole effect correction to provide corrected values for the horizontal conductivity σh and the vertical conductivity σv. Similarly, because the resistivity is the inverse of the conductivity, such that
the horizontal resistivity Rh and vertical resistivity Rv may further be determined from the estimated or corrected horizontal conductivity σh and vertical conductivity σy. Although the equations presented herein are valid for triads arranged in an orthogonal arrangement, such as shown in
As demonstrated herein, determining formation parameters using the imaginary portions of the measured voltage provide improved results over formation parameters determined using the real portions of the measured voltages, particularly in the presence of dipping bed boundaries and in anisotropic formations.
Consequently, embodiments described herein provide a method for determining formation parameters using the imaginary or reactive portions of a measured voltages which provide improved accuracy over the real portions particularly in the presence of bed boundaries and layered anisotropic formations including a borehole. Embodiments described herein are exemplary only. One skilled in the art may recognize various alternative embodiments from those specifically disclosed. Those alternative embodiments are also intended to be within the scope of this disclosure. As such, the embodiments are limited only by the following claims.
Filing Document | Filing Date | Country | Kind | 371c Date |
---|---|---|---|---|
PCT/US2011/034994 | 5/3/2011 | WO | 00 | 10/29/2013 |
Publishing Document | Publishing Date | Country | Kind |
---|---|---|---|
WO2012/150934 | 11/8/2012 | WO | A |
Number | Name | Date | Kind |
---|---|---|---|
3706025 | Regat | Dec 1972 | A |
4359687 | Vinegar | Nov 1982 | A |
4857852 | Kleinberg | Aug 1989 | A |
5600246 | Forgang et al. | Feb 1997 | A |
5757191 | Gianzero | May 1998 | A |
5966013 | Hagiwara | Oct 1999 | A |
6393364 | Gao | May 2002 | B1 |
6556016 | Gao et al. | Apr 2003 | B2 |
6591194 | Yu et al. | Jul 2003 | B1 |
6727706 | Gao et al. | Apr 2004 | B2 |
6969994 | Minerbo et al. | Nov 2005 | B2 |
7386430 | Barber et al. | Jun 2008 | B2 |
7536261 | Omeragic et al. | May 2009 | B2 |
7557580 | Bittar | Jul 2009 | B2 |
7737697 | Yu et al. | Jun 2010 | B2 |
20040108853 | Rosthal | Jun 2004 | A1 |
20050083061 | Tabanou | Apr 2005 | A1 |
20050083063 | Omeragic et al. | Apr 2005 | A1 |
20050122116 | Liming et al. | Jun 2005 | A1 |
20100082255 | Davydycheva et al. | Apr 2010 | A1 |
Entry |
---|
Extended Search Report, European Application No. 11864656, dated Sep. 21, 2015, 7 pages. |
Office Action dated Mar. 27, 2015, in related Canadian Application No. 2,833,777. |
International Preliminary Report on Patentability and the Written Opinion dated Nov. 14, 2013, in related International Application No. PCT/US2011/034994. |
Examination Report dated May 9, 2014, in related Australian Application No. 20140512. |
International Search Report and the Written Opinion dated Jul. 25, 2011, in related International Application No. PCT/US2011/034994, 9 pages. |
Moran, J.H., et al, “Effects of formation anisotropy on resistivity-logging measurements,” Geophysics, vol. 44, No. 7 (Jul. 1979); pp. 1266-1286 (21 Figs., 4 Tables). |
Number | Date | Country | |
---|---|---|---|
20140067272 A1 | Mar 2014 | US |