Virtual steering of induction tool attenuation and phase difference measurements

An apparatus and method that provide steerable measurements of attenuation and phase difference are disclosed. In a preferred embodiment, a logging tool is provided with two triads of orthogonal receivers and a triad of orthogonal transmitters. A controller in the logging tool fires selected transmitters singly and in pairs, and determines measurements of ratios between signals received by the receiver triads. The measurement of sixteen ratios is sufficient to allow determination of attenuation and phase difference that would be measured by virtually steered receivers according to equations provided herein.

BACKGROUND

1. Field of the Invention

The present invention generally relates to the measurement of properties of earth formations. More particularly, the present invention relates to a method for virtual steering of induction tool measurements to determine formation properties such as dip angle and formation resistivity.

2. Description of the Related Art

The basic principles and techniques for electromagnetic logging for earth formations are well known. Induction logging to determine the resistivity (or its inverse, conductivity) of earth formations adjacent a borehole, for example, has long been a standard and important technique in the search for and recovery of subterranean petroleum deposits. In brief, the measurements are made by inducing electrical eddy currents to flow in the formations in response to an AC transmitter signal, and measuring the appropriate characteristics of a receiver signal generated by the formation eddy currents. The formation properties identified by these signals are then recorded in a log at the surface as a function of the depth of the tool in the borehole.

Subterranean formations of interest for oil well drilling typically exist in the form of a series relatively thin beds each having different lithological characteristics, and hence, different resistivities. Induction logging is generally intended to identify the resistivity of the various beds. However, it may also be used to measure formation “dip”.

Wellbores are generally not perpendicular to formation beds. The angle between the axis of the well bore and the orientation of the formation beds (as represented by the normal vector) has two components. These components are the dip angle and the strike angle. The dip angle is the angle between the wellbore axis and the normal vector for the formation bed. The strike angle is the direction in which the wellbores axis “leans away from” the normal vector. These will be defined more rigorously in the detailed description.

The determination of the dip angle along the length of the well plays an important role in the evaluation of potential hydrocarbon reservoirs and in the identification of geological structures in the vicinity of the well. Such structural and stratigraphic information is crucial for the exploration, production, and development of a reservoir. Further, the dip angle determination may be used to compensate for boundary effects on the resistivity measurements. See Gianzero, U.S. Pat. No. 5,757,191, filed Dec. 9, 1994, hereby incorporated by reference.

An induction dipmeter was first suggested by Moran and Gianzero in “Effects of Formation Anisotropy on Resistivity Logging Measurements” Geophysics, Vol. 44, No. 7, p. 1266 (1979), which is hereby incorporated by reference. A pulsed electromagnetic dipmeter with spatially separated coils was proposed by Gianzero and Su in U.S. Pat. No. 5,115,198, filed September 1989. This patent is also incorporated by reference.

The above dipmeters employ multi-axial transmitter and receiver “triads”. Transmitter-receiver coupling measurements may be made along each axis and between axes as well. Because the principle of linear superposition applies to electromagnetic fields, rotational transforms can be used to manipulate the coupling measurements. The measurements of “virtual” transmitters and receivers having arbitrary orientations can be synthesized in this manner.

However, the most reliable induction tools are not configured to measure transmitter-receiver couplings. Rather, they are configured to make inherently compensated measurements of signal attenuation and phase difference between a pair of receiver coils. Unfortunately linear superposition does not apply for signal attenuation and phase differences, so the measurements of these tools cannot be manipulated using existing techniques.

SUMMARY OF THE INVENTION

Accordingly, there is disclosed herein an apparatus and method that provide steerable measurements of attenuation and phase difference. In a preferred embodiment, a logging tool is provided with two triads of orthogonal receivers and a triad of orthogonal transmitters. A controller in the logging tool fires selected transmitters singly and in pairs, and determines measurements of ratios between signals received by the receiver triads. The measurement of sixteen ratios is sufficient to allow determination of attenuation and phase difference that would be measured by virtually steered receivers according to equations provided herein.

DETAILED DESCRIPTION OF PREFERRED EMBODIMENTS

Turning now to the figures,FIG. 1shows a well during drilling operations. A drilling platform2is equipped with a derrick4that supports a hoist6. Drilling of oil and gas wells is carried out by a string of drill pipes connected together by “tool” joints7so as to form a drill string8. The hoist6suspends a kelly10that lowers the drill string8through rotary table12. Connected to the lower end of the drill string8is a drill bit14. The bit14is rotated and drilling accomplished by rotating the drill string8, by use of a downhole motor near the drill bit, or by both methods.

Drilling fluid, termed mud, is pumped by mud recirculation equipment16through supply pipe18, through drilling kelly10, and down through the drill string8at high pressures and volumes to emerge through nozzles or jets in the drill bit14. The mud then travels back up the hole via the annulus formed between the exterior of the drill string8and the borehole wall20, through a blowout preventer (not specifically shown), and into a mud pit24on the surface. On the surface, the drilling mud is cleaned and then recirculated by recirculation equipment16. The drilling mud is used to cool the drill bit14, to carry cuttings from the base of the bore to the surface, and to balance the hydrostatic pressure in the rock formations.

For Logging While Drilling (LWD) operations, downhole sensors26are located in the drill string8near the drill bit14. The sensors26preferably include an induction tool having multi-axial transmitters and receivers. In a preferred embodiment, downhole sensors26are coupled to a telemetry transmitter28that transmits telemetry signals by modulating the mud flow in drill string8. A telemetry receiver30is coupled to the kelly10to receive transmitted telemetry signals. Other telemetry transmission techniques are well known and may be used. The receiver30communicates the telemetry to a surface installation (not specifically shown) that processes and stores the measurements. The surface installation typically includes a computer system of some kind, e.g. a desktop computer.

The drill bit14is shown penetrating a formation having a series of layered beds32dipping at an angle. A first (x,y,z) coordinate system associated with the sensors26is shown, and a second coordinate system (x″,y″,z″) associated with the beds32is shown. The bed coordinate system has the z″ axis perpendicular to the bedding plane, has the y″ axis in a horizontal plane, and has the x″ axis pointing “downhill”. As shown inFIG. 2, the two coordinate systems are related by two rotations. Beginning with the sensor coordinate system (x,y,z), a first rotation of angle β is made about the z-axis. The resulting coordinate system is denoted (x′,y′,z′). Angle β is the strike angle, which indicates the direction of the formation dip. A second rotation of angle α is then made about the y′ axis. This aligns the coordinate system with the beds32. Angle α is the dip angle, which is the slope angle of the beds.

Any vector in one of the coordinate systems can be expressed in terms of the other coordinate system by using rotational transform matrices. Thus, if v is a vector expressed in the (x,y,z) coordinate system, it can be expressed mathematically in the (x″,y″,z″) coordinate system as:
v″=RαRβv=Rv   (1)
where

As with all downhole well components, induction tools are exposed to a harsh environment that includes a wide temperature and pressure range. To avoid a correspondingly wide variation in tool performance, various compensation techniques are employed. One useful compensation technique for induction tools is to provide the tool with a symmetric configuration.FIG. 3shows one such tool.

Induction tool102includes two sets of transmitter coils104,112and two sets of receiver coils108,110. As discussed further below, each set may preferably comprise a “triad” of orthogonally oriented coils. Each transmitter coil is preferably excited in turn (time division multiplexing), although frequency division multiplexing may be optionally employed. Receiver coil measurements may be made substantially simultaneously if desired.

In operation, transmitters104and112alternately transmit interrogating electromagnetic signals that propagate through the wellbore and surrounding formation. Receiver coils108,110detect the interrogating electromagnetic signals and provide a measure of the amplitude attenuation and phase shift between coils108and110. From the amplitude attenuation and phase shift, the resistivity of the formation can be estimated using conventional techniques.

Oscillator114generates a sinusoidal signal. Amplifier116amplifies the sinusoidal signal and switch118routes the amplified signal through one of the impedance matching circuits120,122to the selected transmitter coil. Signals from the receiver coils108,110pass through corresponding impedance matching circuits124and126and are amplified by corresponding amplifiers128and130. Attenuation detector134measures the amplitude of the signals from the amplifiers128,130, and determines attenuation by finding the ratio of the signal amplitudes. Phase difference detector132measures the phase difference between the signals from amplifiers128,130. The digital signal processor144reads the attenuation and phase difference measurements from the detectors132,134. The digital signal processor controls the setting of switch118to measure the attenuation and/or phase shift of signals propagating from any selected transmitter coil. One implementation of attenuation detector134and phase difference detector132is described in U.S. Pat. No. 5,389,881 (Bittar, et. al.) which is hereby incorporated herein by reference. The digital signal processor144preferably provides the attenuation and phase difference measurements to the telemetry transmitter28for communication to the surface.

A derivation is now made to demonstrate how two symmetric halves of a resistivity tool can be used to provide compensation. The voltage induced in a receiver coil R by a signal in a transmitter coil T can be written:
V=ξTξRAei(φ+øT+øR),   (3)
where ξTand ξRare intrinsic efficiencies of the transmitter T and receiver R, respectively, and øTand øRare intrinsic phase shifts induced by the transmitter T and receiver R, respectively. In subsequent equations, subscripts1and2will be used to differentiate between the upper and lower transmitter and receiver coils. The ideal amplitude A and ideal phase φ will be provided with subscripts “+” and “−” to indicate whether they correspond to the transmitter receiver spacing of L2or L1(L1and L2are shown inFIG. 3).

The ratio between voltages induced in the two receiver coils from the upper transmitter is:

VR2⁢T1VR1⁢T1=ξR2ξR1⁢η1⁢ⅇⅈ⁡(δφ1+ϕR2-ϕR1),(4)
where η1=A+/A−is the ideal attenuation, and δφU=φ+−φ−is the ideal phase shift in the signal from the upper transmitter. Similarly, the ratio between voltages induced by the lower transmitter is:

The intrinsic receiver efficiency and phase can be eliminated by combining equations (4) and (5) to get:

VR2⁢T1VR1⁢T1⁢VR1⁢T2VR2⁢T2=η1⁢η2⁢ⅇⅈ⁡(δφ1+δφ2)/2.(6)
Equation (6) therefore represents a way of compensating for variations in intrinsic efficiency and phase and to obtain correct attenuation and phase shift measurements. Accordingly, attenuation and phase shift measurements may be preferred over direct amplitude and phase measurements, because the intrinsic circuit biases can be eliminated.

In the next portion of the discussion, a simplified model of the tool is used to determine a method for steering measured attenuation and phase differences. The resulting method can also be applied to attenuation and phase differences measured by a compensated tool as previously described.

FIG. 4shows a conceptual sketch of a coil arrangement for a downhole induction tool. A triad of transmitter coils Tx, Tyand Tz, each oriented along a respective axis, is provided. Two triads of similarly oriented receiver coils (R1x, R1y, R1z) and (R2x, R2y, R2z) are also provided, separated from the transmitter triad by L1and L2, respectively. Each of the coils in the triads is parallel to the corresponding coils of the other triads, and the triads are spaced apart in the z-axis direction. The receiver coil voltages VRjcan be expressed in terms of the transmitter coil voltages VTas follows:
VRj=CjVT,   (7)
where Cjis the coupling matrix between the transmitter triad and receiver triad Rj, j=1,2. In terms of each of the coils in the triad, the voltages are:

From the elements of the coupling matrix, the response of an arbitrarily oriented receiver coil to an arbitrarily oriented transmitter coil can be synthesized. The coupling between a transmitter coil oriented at an azimuthal (“strike”) angle of φ and an elevational (“dip”) angle of θ, and a receiver coil oriented at the same azimuthal and elevational angles, is:

Equations (8) and (9) apply to direct amplitude and phase measurements. To apply these equations to attenuation and phase difference measurements, we make the following definitions:

VR2⁢x/VR1⁢x=ζ,⁢VR2⁢y/VR1⁢y=ɛ,a⁢⁢n⁢⁢dVR2⁢z/VR1⁢z=γ.⁢(10)
When the transmitters are separately and individually fired, the following ratios can be measured:

Equations (7) and (9) can be combined to determine the attenuation and phase difference between two receivers oriented at arbitrary azimuthal and elevational angles that is caused by a transmitter oriented at the same azimuthal and elevational angles. The ratio is:

C2⁡(φ,θ)C1⁡(φ,θ)=sin⁢⁢θcosφ(C2⁢x⁢⁢x⁢sin⁢⁢θcosφ+C2⁢x⁢⁢y⁢sin⁢⁢θsinφ+C2⁢x⁢⁢z⁢cos⁢⁢θ)+sin⁢⁢θsinφ(C2⁢y⁢⁢x⁢sin⁢⁢θcosφ+C2⁢y⁢⁢y⁢sin⁢⁢θsinφ+C2⁢y⁢⁢z⁢cos⁢⁢θ)+cos⁢⁢θ(C2⁢z⁢⁢x⁢sin⁢⁢θcosφ+C2⁢z⁢⁢y⁢sin⁢⁢θsinφ+C2⁢z⁢⁢z⁢cos⁢⁢θ)sin⁢⁢θcosφ(C1⁢x⁢⁢x⁢sin⁢⁢θcosφ+C1⁢x⁢⁢y⁢sin⁢⁢θsinφ+C1⁢x⁢⁢z⁢cos⁢⁢θ)+sin⁢⁢θsinφ(C1⁢y⁢⁢x⁢sin⁢⁢θcosφ+C1⁢y⁢⁢y⁢sin⁢⁢θsinφ+C1⁢y⁢⁢z⁢cos⁢⁢θ)+cos⁢⁢θ(C1⁢z⁢⁢x⁢sin⁢⁢θcosφ+C1⁢z⁢⁢y⁢sin⁢⁢θsinφ+C1⁢z⁢⁢z⁢cos⁢⁢θ)(12)
One way of rewriting this ratio is:

Accordingly, if the following ratios can be determined, the steered ratio of equation (13) can be evaluated. The ratios are:

These ratios can be determined from measurements made when two transmitters are simultaneously fired. In the following derivation, the notation of equation (10) is preserved, but a subscript is added. The measurements made when transmitters Txand Tzare energized simultaneously are denoted ζ1, ε1, and γ1. The measurements made when transmitters Tyand Tzare energized simultaneously are denoted ζ2, ε2, and γ2. The following relationships can be manipulated to reach the results shown:

With regard to the third ratio set, the four ratios are related as follows:

C2⁢xzC2⁢zz=[C2⁢xzC1⁢xz]⁡[C1⁢zzC2⁢zz]⁢C1⁢xzC1⁢zz.(26)C2⁢yzC2⁢zz=[C2⁢yzC1⁢yz]⁡[C1⁢zzC2⁢zz]⁢C1⁢yzC1⁢zz.(27)
where, as before, the bracketed terms are known from measurement (11). So, the determination of two of these ratios allows the calculation of the remaining two.

These ratios may be measured directly from the ratio between voltages induced in the Rjxand Rjzcoils, j=1, 2, and the ratio between voltages induced in the Rjyand Rjzcoils, j=1, 2, in the same receiver triad. Alternatively, these ratios may be rewritten in terms of attenuation between triads:

C1⁢xzC1⁢zz=[C1⁢xzC2⁢xz]⁢C2⁢xzC1⁢zz.(28)C1⁢yzC1⁢zz=[C1⁢yzC2⁢yz]⁢C2⁢yzC1⁢zz.(29)
Again, the bracketed terms are known from measurements in (11). The ratio between voltages induced in the Rjxand Rkzcoils, j≠k, and the ratio between voltages induced in the RJyand Rkzcoils, j≠k, may be directly measured. This latter method offers the possibility of better compensation in the final system.

FIG. 5shows a flow diagram of a method for determining a steerable coupling ratio. To evaluate equation (13), the following seventeen ratios are measured:

{C2⁢xxC1⁢xx,C2⁢xyC1⁢xy,C2⁢xzC1⁢xz,C2⁢yxC1⁢yx,C2⁢yyC1⁢yy,C2⁢yzC1⁢yz,C2⁢zxC1⁢zx,C2⁢zyC1⁢zy,C2⁢zzC1⁢zz},{ζ1,ɛ1,γ1,ζ2,ɛ2,γ2},{CjxzCkzz,CjyzCkzz}
where j=1 and kε {1,2}, as in equations (28), (29). Many of these may be measured in parallel. For example, in a compensated tool such as that shown inFIG. 3, C2xz/C1xz, C2yz/C1yz, C2zz/C1zz, Cjxz/Ckzz, and Cjyz/Ckzz, can be measured together when each of the Tztransmitters are fired. Similarly, C2xy/C1xy, C2yy/C1yy, and C2zy/C1zy, can be measured together when each of the Tytransmitters are fired. C2xx/C1xxand C2yz/C1yxcan be measured together when each of the Txtransmitters are fired. ζ1, ε1, and γ1can be measured together when transmitters Txand Tzare energized simultaneously, and ζ2, ε2, and γ2can be measured together when transmitters Tyand Tzare energized simultaneously. Hence, no more than five iterations of the loop inFIG. 5are necessary for each measurement interval.

The loop ofFIG. 5includes blocks302-314. The ratios to be measured in each iteration of the loop are identified in block302. In block304, the appropriate transmitters from the first triad are energized, and in block306the selected ratios are measured. In block308the appropriate transmitters from the second triad are energized, and in block310the selected ratios are again measured. The ratio measurements are combined in block312to determine compensated ratios. In block314, a test is made to determine if all the desired ratios have been measured. If not, the loop repeats. Otherwise, each of the compensated ratios is transmitted to the surface. This process is repeated for each measurement interval.

At the surface, the compensated ratios may be used in equations (14)-(27) to determine the values necessary for equation (13). Equation (13) may then be evaluated for any desired orientation, thereby providing a virtually steered attenuation and phase difference measurement.

For clarity, it has been assumed that the three coils in each triad represent actual coils oriented in mutually perpendicular directions, with the z-axis corresponding to the long axis of the tool. However, it is noted that this coil arrangement can be “synthesized” by performing a suitable transformation on differently oriented triads. Such transformations are described in depth in U.S. patent application Ser. No. 6,181,138 entitled “Directional Resistivity Measurements for Azimuthal Proximity Detection of Bed Boundaries”, filed Feb. 22, 1999 by T. Hagiwara and H. Song, which is hereby incorporated herein by reference.

The disclosed method can be utilized to determine regional dip and strike information in wells where conditions are not favorable for the operation of traditional resistivity wireline dipmeters or resistivity imaging tools. Such conditions include, but are not limited to, wells drilled with oil based mud and wells with highly rugose wellbores. It is noted that the disclosed method can be used for both wireline operations and Logging While Drilling (LWD) operations. In LWD operations, the method, in addition to determining regional dip and strike, can be further used to facilitate geosteering in highly deviated and/or horizontal wells.

The new method may provide the following advantages: (1) As an induction apparatus, the current invention can be applied in situations where the condition are not favorable for the focused-current pad dipmeters, e.g., in wells drilled with oil based mud or when the wellbore has high rugosity. (2) The disclosed apparatus may provide a deeper depth of investigation than the microinduction pad dipmeter, and hence may be less vulnerable to adverse borehole conditions. (3) The disclosed apparatus may provide more accurate results because of inherent compensation.