The present invention is described in more detail below by way of examples and with reference to the attached drawing figures, wherein:
The present invention will now be described in relation to particular embodiments, which are intended in all respects to be illustrative rather than restrictive. Alternative embodiments will become apparent to those skilled in the art to which the present invention pertains without departing from its scope.
It will be understood that certain features and sub-combinations are of utility and may be employed without reference to other features and sub-combinations specifically set forth. This is contemplated and within the scope of the claims.
Embodiments of the invention relate to analysis of electromagnetic (EM) induction signals and to a system and method for determining distance and/or direction to an anomaly in a formation from a location within a wellbore. The analysis is sensitive to electromagnetic anomalies, in particular electromagnetic induction anomalies.
Both frequency domain excitation and time domain excitation have been used to excite electromagnetic fields for use in anomaly detection. In frequency domain excitation, a device transmits a continuous wave of a fixed or mixed frequency and measures responses at the same band of frequencies. In time domain excitation, a device transmits a square wave signal, triangular wave signal, pulsed signal or pseudo-random binary sequence as a source and measures the broadband earth response. Sudden changes in transmitter current cause transient signals to appear at a receiver caused by induction currents in the formation. The signals that appear at the receiver are called transient responses because the receiver signals start at a first value after a sudden change in transmitter current, and then they decay (or increase) with time to a new constant level at a second value. The technique disclosed herein implements the time domain excitation technique.
As set forth below, embodiments of the invention propose a general method to determine a direction from a measurement sub to a resistive or conductive anomaly using transient EM responses. As will be explained in detail, the direction to the anomaly is specified by a dip angle and an azimuth angle. Embodiments of the invention propose to define an apparent dip (θapp(t)) and an apparent azimuth (φapp(t)) by combinations of multi-axial, e.g. bi-axial or tri-axial, transient measurements. The true direction, in terms of dip and azimuth angles ({θ, φ}), may be determined from the analysis of the apparent direction ({θapp(t), φapp(t)}). For instance, the apparent direction ({θapp(t), φapp(t)}) approaches the true direction ({θ, φ}) as a time (t) increases, if the anomaly has a high thickness as seen from the tool.
Time-dependent values for apparent conductivity may be obtained from coaxial and coplanar electromagnetic induction measurements, and can respectively be denoted as σcoaxial(t) and σcoplanar(t). Both read the conductivity in the total present formation around the tool. The θapp(t) and φapp(t) both initially read zero when an apparent conductivity σcoaxial(t) and σcoplanar(t) from coaxial and coplanar measurements both read the conductivity of the formation surrounding the tool nearby. The apparent conductivity will be further explained below and can also be used to determine the location of an anomaly in a wellbore.
Whenever in the present specification the term “conductivity” is employed, it is intended to cover also its inverse equivalent “resistivity”, and vice versa. The same holds for the terms “apparent conductivity” and “apparent resistivity”.
In
In
Referring again to both
Each transmitter 16 and/or receiver 18 may comprise a coil, wound around a support structure such as a mandrel. The support structure may comprise a non-conductive section to suppress generation of eddy currents. The non-conductive section may comprise one or more slots, optionally filled with a non-conductive material, or it may be formed out of a non-conductive material such as a composite plastic. Alternatively, the support structure is coated with a layer of a high-magnetic permeable material to form a magnetic shield between the antenna and the support structure.
Each transmitter 16 and each receiver 18 may be bi-axial or even tri-axial, and thereby contain components for sending and receiving signals along each of three axes. Accordingly, each transmitter module may contain at least one single or multi-axis antenna and may be a 3-orthogonal component transmitter. Each receiver may include at least one single or multi-axis electromagnetic receiving component and may be a 3-orthogonal component receiver.
A tool/borehole coordinate system is defined as having x, y, and z axes. The z-axis defines the direction from the transmitter T to the receiver R. It will be assumed hereinafter that the axial direction of the wellbore 4 coincides with the z-axis, whereby the x- and y-axes correspond to two orthogonal directions in a plane normal to the direction from the transmitter T to the receiver R and to the wellbore 4.
The data acquisition unit 14 may include a controller for controlling the operation of the tool 2. The data acquisition unit 14 preferably collects data from each transmitter 16 and receiver 18 and provides the data to the surface computing unit 10. The data acquisition unit 14 may comprise an amplifier and/or a digital to analogue converter, as described in co-pending U.S. application Ser. No. 11/689,980 filed on 22 Mar. 2007, incorporated herein by reference, to amplify the responses and/or convert to a digital representation of the responses before transmitting to the surface computing unit 10 via cable 12 and/or an optional telemetry unit 13.
The surface computing unit 10 may include computer components including a processing unit 30, an operator interface 32, and a tool interface 34. The surface computing unit 10 may also include a memory 40 including relevant coordinate system transformation data and assumptions 42, an optional direction calculation module 44, an optional apparent direction calculation module 46, and an optional distance calculation module 48. The optional direction and apparent direction calculation modules are described in more detail in already incorporated US patent application publication 2005/0092487 and need not be further described here, other than specifying that these optional modules may take into account formation anisotropy.
The surface computing unit 10 may include computer components including a processing unit 30, an operator interface 32, and a tool interface 34. The surface computing unit 10 may also include a memory 40 including relevant coordinate system transformation data and assumptions 42, a direction calculation module 44, an apparent direction calculation module 46, and a distance calculation module 48. The surface computing unit 10 may further include a bus 50 that couples various system components including the system memory 40 to the processing unit 30. The computing system environment 10 is only one example of a suitable computing environment and is not intended to suggest any limitation as to the scope of use or functionality of the invention. Furthermore, although the computing system 10 is described as a computing unit located on a surface, it may optionally be located below the surface, incorporated in the tool, positioned at a remote location, or positioned at any other convenient location.
The memory 40 preferably stores one or more of modules 48, 44 and 46, which may be described as program modules containing computer-executable instructions, executable by the surface computing unit 10. Each module may comprise or make use of a computer readable medium that stores computer readable instructions for analyzing one or more detected time-dependent transient electromagnetic response signals that have been detected by a tool suspended inside a wellbore traversing a subterranean formation after inducing one or more electromagnetic fields in the formation. The instructions may implement any part of the disclosure that follows herein below.
For example, the program module 44 may contain computer executable instructions to calculate a direction to an anomaly within a wellbore. The program module 48 may contain computer executable instructions to calculate a distance to an anomaly or a thickness of the anomaly. The stored data 42 may include data pertaining to the tool coordinate system and the anomaly coordinate system and other data for use by the program modules 44, 46, and 48. Preferably, the computer readable instructions take into account electromagnetic anisotropy of at least one formation layer in the subterranean formation. For further details on the computing system 10, including storage media and input/output devices, reference is made to US patent application publication 2005/0092487, incorporated herein by reference. Accordingly, additional details concerning the internal construction of the computer 10 need not be disclosed in connection with the present invention.
Procedure C may comprise determining a distance and/or a direction to the anomaly may be determined. Procedure C may comprise creating an image of formation features based on the transient electromagnetic responses. Electromagnetic anisotropy of at least one of the formation layers may be taken into account.
In order to practice embodiments of the method,
Similarly,
The method is additionally based on the relationship between the transient responses in two coordinate systems. The magnetic field transient responses at the receivers [Rx, Ry, Rz,] which are oriented in the [x, y, z] axis direction of the tool coordinates, respectively, are noted as
wherein the right-hand side of the equation represents all combinations of receiver axis and transmitter axis, whereby Vij=RiTj denotes voltage response sensed by receiver Ri (i=x, y, z) from signal transmitted by transmitter Tj (j=x, y, z). Each transmitter may comprise a magnetic dipole source, [Mx, My, Mz], in any direction.
When the resistivity anomaly is distant from the tool, the formation near the tool is seen as a homogeneous formation. For simplicity, the method may assume that the formation is isotropic. Only three non-zero transient responses exist in a homogeneous isotropic formation. These include the coaxial response and two coplanar responses. Coaxial response Vzz(t) is the response when both the transmitter and the receiver are oriented in the common tool axis direction. Coplanar responses, Vxx(t) and Vyy(t), are the responses when both the transmitter T and the receiver R are aligned parallel to each other but their orientation is perpendicular to the tool axis. All of the cross-component responses are identically zero in a homogeneous isotropic formation. Cross-component responses are either from a longitudinally oriented receiver with a transverse transmitter, or vise versa. Another cross-component response is also zero between a mutually orthogonal transverse receiver and transverse transmitter.
The effect of the resistivity anomaly is seen in the transient responses as time increases. In addition to the coaxial and the coplanar responses, the cross-component responses Vij(t) (i≠j; i, j=x, y, z) become non-zero.
The magnetic field transient responses may also be examined in the anomaly coordinate system. The magnetic field transient responses at the receivers [Ra, Rb, Rc,] that are oriented in the [a, b, c] axis direction of the anomaly coordinates, respectively, may be noted as
wherein the right-hand side of the equation represents all combinations of receiver orientation and transmitter orientation, whereby Vij=RiTj denotes voltage response sensed by receiver Ri (in orientation i=a, b, c) from signal transmitted by transmitter Tj (in orientation j=a, b, c). Each transmitter may comprise a magnetic dipole source, [Ma, Mb, Mc], along the orientation a, b, or c.
When the anomaly is large and distant compared to the transmitter-receiver spacing, the effect of spacing can be ignored and the transient responses can be approximated with those of the receivers near the transmitter. Then, the method assumes that axial symmetry exists with respect to the c-axis that is the direction from the transmitter to the center of the anomaly. In such an axially symmetric configuration, the cross-component responses in the anomaly coordinates are identically zero in time-domain measurements.
The assumptions set forth above contribute to determination of target direction, which is defined as the direction of the anomaly from the origin. The tool is in the origin. When axial symmetry in the anomaly coordinates is assumed, the transient response measurements in the tool coordinates are constrained and the two directional angles may be determined by combinations of tri-axial responses.
V
xx=(Vaa cos2ν+Vcc sin2ν)cos2φ+Vaa sin2φ
V
yy=(Vaa cos2ν+Vcc sin2ν)sin2φ+Vaa cos2φ
V
zz
=V
aa sin2ν+Vcc cos2ν (9)
V
xy
=V
yx=−(Vaa−Vcc)sin2ν cos φ sin φ
V
zx
=V
xz=−(Vaa−Vcc)cos ν sin ν cos φ
V
yz
=V
zy=−(Vaa−Vcc)cos ν sin ν sin φ (10)
The following relations can be noted:
V
xx
+V
yy
+V
zz=2Vzz+Vcc
V
xx
−V
yy=(Vcc−Vaa)sin2ν(cos2φ−sin2φ)
V
yy
−V
zz=−(Vcc−Vaa)(cos2ν−sin2ν sin2φ)
V
zz
−V
xx=(Vcc−Vaa)(cos2ν−sin2ν cos2φ) (11)
Several distinct cases can be noted. In the first of these cases, when none of the cross-components is zero, Vxy≠0 nor Vyz≠0 nor Vzx≠0, then the azimuth angle φ is not zero nor π/2 (90°), and can be determined by,
the dip (deviation) angle ν is determined by,
Also, with regard to the second case, If ν=0, then Vxx=Vyy and Vzx=0. If φ=±π/2 (90°) and ν=±π/2 (90°), then Vzz=Vxx and Vzx=0. These instances are further discussed below with relation to the fifth case.
In the third case, when Vxy=0 and Vxz=0, then φ=±π/2 (90°) or ν=0 or φ=0 and ν=±π/2 (90°).
If φ=π/2, then the dip angle ν is determined by,
If φ=−π/2, then the dip angle ν is determined by,
Also with regard to the third case, If ν=0, then Vxx=Vyy and Vyz=0. If φ=0 and ν=±π/2 (90°), Vyy=Vzz and Vyz=0. These situations are further discussed below with relation to the fifth case.
In the fourth case, Vxz=0 and Vyz=0, then ν=0 or π(180°) or ±π/2 (90°).
If ν=±π/2, then the azimuth angle φ is determined by,
Also with regard to the fourth case, if ν=0 or π(180°), then Vxx=Vyy and Vyz=0. This situation is also shown below with relation to the fifth case.
In the fifth case, all cross components vanish, Vxz=Vyz=Vxy=0, then ν=0, or ν=±π/2 (90°) and φ=0 or ±π/2 (90°).
If Vxx=Vyy then ν=0 or π(180°).
If Vyy=Vzz then ν=±π/2 (90°) and φ=0.
If Vzz=Vxx then ν=±π/2 (90°) and φ=±π/2 (90°).
In the above analysis, all the transient responses Vij(t) (i, j=x, y, z) are specified by the x-, y-, and z-axis directions of the tool coordinates. However, the tool rotates inside the borehole and the azimuth orientation of the transmitter and the receiver no longer coincides with the x- or y-axis direction as shown in
The azimuth angle φ is measured from the tri-axial responses if the tool rotation angle ψis known. To the contrary, the dip (deviation) angle ν is determined by
without knowing the tool orientation ψ.
The dip and the azimuth angle described above indicate the direction of a resistivity anomaly determined by a combination of tri-axial transient responses at a time (t) when the angles have deviated from a zero value. When t is small or close to zero, the effect of such anomaly is not apparent in the transient responses as all the cross-component responses are vanishing. To identify the anomaly and estimate not only its direction but also the distance, it is useful to define the apparent azimuth angle φapp(t) by,
and the effective dip angle νapp(t) by
for the time interval when φapp(t)≠0 nor π/2 (90°). For simplicity, the case examined below is one in which none of the cross-component measurements is identically zero: Vxy(t)≠0, Vyz(t)≠0, and Vzx(t)≠0.
When t is small and the transient responses do not see the effect of a resistivity anomaly at distance, the effective angles are identically zero, φapp(t)=νapp(t)=0. As t increases, when the transient responses see the effect of the anomaly, φapp(t) and νapp(t) begin to show the true azimuth and the true dip angles. The distance to the anomaly may be indicated at the time when φapp(t) and νapp(t) start deviating from the initial zero values. As shown below in a modeling example, the presence of an anomaly is detected much earlier in time in the effective angles than in the apparent conductivity (σapp(t)). Even if the resistivity of the anomaly may not be known until σapp(t) is affected by the anomaly, its presence and the direction can be measured by the apparent angles. With limitation in time measurement, the distant anomaly may not be seen in the change of σapp(t) but is visible in φapp(t) and νapp(t).
Before discussing anisotropy in more detail, isotropic formations will first be illustrated with resistivity R(=R//=R⊥) (or its inverse σ=σ//=σ⊥).
The effect of the resistivity anomaly A (as depicted in
is shown in
The apparent conductivity (σapp(t)) from both the coaxial (Vzz(t) of
Note that the true direction from the tool to the salt face (i.c. 30°) is reflected in the apparent dip θapp(t) plot of
The distance to the salt face can be also determined by the transition time at which θapp(t) takes an asymptotic value. Even if the salt face distance (D) is 100 m, it can be identified and its direction can be measured by the apparent dip θapp(t).
In summary, the method considers the coordinate transformation of transient EM responses between tool-fixed coordinates and anomaly-fixed coordinates. When the anomaly is large and far away compared to the transmitter-receiver spacing, one may ignore the effect of spacing and approximate the transient EM responses with those of the receivers near the transmitter. Then, one may assume axial symmetry exists with respect to the c-axis that defines the direction from the transmitter to the anomaly. In such an axially symmetric configuration, the cross-component responses in the anomaly-fixed coordinates are identically zero. With this assumption, a general method is provided for determining the direction to the resistivity anomaly using tri-axial transient EM responses.
The method defines the apparent dip θapp(t) and the apparent azimuth φapp(t) by combinations of tri-axial transient measurements. The apparent direction {θapp(t), φapp(t)} reads the true direction {θ, φ} at later time. The θapp(t) and φapp(t) both read zero when t is small and the effect of the anomaly is not sensed in the transient responses or the apparent conductivity. The conductivities (σcoaxial(t) and σcoplanar(t)) from the coaxial and coplanar measurements both indicate the conductivity of the near formation around the tool.
Deviation of the apparent direction ({θapp(t), φapp(t)}) from zero identifies the anomaly. The distance to the anomaly is measured by the time when the apparent direction ({θapp(t), φapp(t)}) starts to deviate from zero or by the time when the apparent direction ({θapp(t), φapp(t)}) starts approaches the true direction ({θ, φ}). The distance can be also measured from the change in the apparent conductivity. However, the anomaly is identified and measured much earlier in time in the apparent direction than in the apparent conductivity.
As set forth above, apparent conductivity can be used as an alternative technique to apparent angles in order to determine the location of an anomaly in a wellbore. The time-dependent apparent conductivity can be defined at each point of a time series at each logging depth. The apparent conductivity at a logging depth z is defined as the conductivity of a homogeneous formation that would generate the same tool response measured at the selected position.
In transient EM logging, transient data are collected at a logging depth or tool location z as a time series of induced voltages in a receiver loop. Accordingly, time dependent apparent conductivity (σ(z; t)) may be defined at each point of the time series at each logging depth, for a proper range of time intervals depending on the formation conductivity and the tool specifications.
The induced voltage of a coaxial tool with transmitter-receiver spacing L in the homogeneous formation of conductivity (σ) is given by,
and C is a constant.
The time-changing apparent conductivity depends on the voltage response in a coaxial tool (VzZ(t)) at each time of measurement as:
and VzZ(t) on the right hand side is the measured voltage response of the coaxial tool. From a single type of measurement (coaxial, single spacing), the greater the spacing L, the larger the measurement time (t) should be to apply the apparent conductivity concept. The σapp(t) should be constant and equal to the formation conductivity in a homogeneous formation: σapp(t)=σ. The deviation from a constant (σ) at time (t) suggests a conductivity anomaly in the region specified by time (t).
The induced voltage of the coplanar tool with transmitter-receiver spacing L in the homogeneous formation of conductivity (σ) is given by,
and C is a constant. At small values of t, the coplanar voltage changes polarity depending on the spacing L and the formation conductivity.
Similarly to the coaxial tool response, the time-changing apparent conductivity is defined from the coplanar tool response VxX(t) at each time of measurement as,
and VxX(t) on the right hand side is the measured voltage response of the coplanar tool. The longer the spacing, the larger the value t should be to apply the apparent conductivity concept from a single type of measurement (coplanar, single spacing). The σapp(t) should be constant and equal to the formation conductivity in a homogeneous formation: σapp(t)=σ.
When there are two coaxial receivers, the ratio between the pair of voltage measurements is given by,
where L1 and L2 are transmitter-receiver spacing of two coaxial tools.
Conversely, the time-changing apparent conductivity is defined for a pair of coaxial tools by,
at each time of measurement. The σapp(t) should be constant and equal to the formation conductivity in a homogeneous formation: σapp(t)=σ.
The apparent conductivity is similarly defined for a pair of coplanar tools or for a pair of coaxial and coplanar tools. The σapp(t) should be constant and equal to the formation conductivity in a homogeneous formation: σapp(t)=σ. The deviation from a constant (σ) at time (t) suggests a conductivity anomaly in the region specified by time (t).
As will be illustrated below, apparent conductivity (σapp(t)), whether coaxial or coplanar, may reveal three parameters in relation to a two-layer formation, including:
(1) the conductivity of a local first layer in which the tool is located;
(2) the conductivity of one or more adjacent layers or beds; and
(3) the distance of the tool to the layer boundaries.
To illustrate usefulness of the concept of apparent conductivity, the transient response of a tool in a two-layer earth model, as in
In the present example, a horizontal well is depicted such that the distance from the tool to the layer boundary corresponds to the distance of the horizontal borehole to the layer boundary. Under a more general circumstance, the relative direction of a borehole and tool to the bed interface is not known.
The calculated transient voltage response V(t) for the L=1 m transmitter-receiver offset coaxial tool at various distances D between the tool 80 and the layer boundary 55 is shown in
The apparent conductivity plots reveal a “constant” conductivity at small t, and at large t but having a different value, and a transition time tc that marks the transition between the two “constant” conductivity values and depends on the distance D.
As will be further explained below, in a two-layer resistivity profile, the apparent conductivity as t approaches zero can identify the layer conductivity σ1 around the tool, while the apparent conductivity as t approaches infinity can be used to determine the conductivity σ2 of the adjacent layer at a distance. The distance to the bed boundary 55 from the tool 80 can also be measured from the transition time tc observed in the apparent conductivity plots.
At small values of t, the tool reads the apparent conductivity σ1 of the first layer 5 around the tool 80. Conductivity at small values of t is thought to correspond to the conductivity of the local layer 5 where the tool is located in. At small values of t, the signal reaches the receiver directly from the transmitter without interfering with the bed boundary. Namely, the signal is affected only by the conductivity σ1 around the tool.
At large values of t, the tool reads 0.4 S/m for a two-layer model where either σ1=1 S/m (R1=1 Ωm) and σ2=0.1 S/m (R2=10 Ωm), or σ1=0.1 S/m (R1=10 Ωm) and σ2=1 S/m (R2=1 Ωm). The value of 0.4 is believed to correspond to some average between the conductivities of the two layers, because at large values of t, nearly half of the signals come from the formation below the tool and the remaining signals come from above, if the time for the signal to travel the distance between the tool and the bed boundary is small.
This is further investigated in
Numerically, the late time conductivity may be approximated by the square root average of two-layer conductivities as:
Thus, the conductivity at large values of t (as t approaches infinity) can be used to estimate the conductivity (σ2) of the adjacent layer when the local conductivity (σ1) near the tool is known, for instance from the conductivity as t approaches zero as illustrated in
The distance D from the tool to the bed is reflected in the transition time tc. The transition time at which the apparent conductivity (σapp(t)) starts deviating from the local conductivity (σ1) towards the conductivity at large values of t depends on D and L, as shown in
For convenience, the transition time (tc) can be defined as the time at which the σapp(tc) takes a cutoff conductivity (σc). In this case, the cutoff conductivity is represented by the arithmetic average between the conductivity as t approaches zero and the conductivity as t approaches infinity. The transition time (tc) is dictated by the ray path RP:
that is the shortest distance for the electromagnetic signal traveling from the transmitter to the bed boundary, to the receiver, independently of the resistivity of the two layers. Conversely, the distance (D) to the anomaly can be estimated from the transition time (tc), as shown in
By analyzing apparent conductivity or its inherent inverse equivalent (apparent resistivity), the present invention can identify the location of a resistivity anomaly (e.g., a conductive anomaly and a resistive anomaly). Further, resistivity or conductivity can be determined from the coaxial and/or coplanar transient responses. As explained above, the direction to the anomaly can be determined if the cross-component data are also available. To further illustrate the usefulness of these concepts, the foregoing analysis may also be used to detect an anomaly at a distance ahead of the drill bit.
The calculated transient voltage response of the L=1 m (transmitter-receiver offset) coaxial tool at different distances (D=1, 5, 10, 25, and 50 m) as a function of t is shown in
The same voltage data of
The σapp(t) plot exhibits at least three parameters very distinctly in the figure: the early time conductivity; the later time conductivity; and the transition time that moves as the distance (D) changes. In
Hence, the transient electromagnetic response method can be used as a look-ahead resistivity logging method.
Numerically, the late time apparent conductivity may be approximated by the arithmetic average of two-layer conductivities as:
This is reasonable considering that, with the coaxial tool, the axial transmitter induces the eddy current parallel to the bed boundary. At later time, the axial receiver receives horizontal current nearly equally from both layers. As a result, the late time conductivity must see conductivity of both formations with nearly equal weight.
Thus, the late time apparent conductivity (σapp(t→∞)) at t=1 second can be used to estimate the conductivity of the adjacent layer (σ2) when the local conductivity near the tool (σ1) is known, for instance, from the early time apparent conductivity (σapp(t→0)=σ1).
The transition time (tc) at which the apparent conductivity starts deviating from the local conductivity (σ1) toward the late time conductivity clearly depends on D, the distance of the tool to the bed boundary, as shown in
For convenience, the transition time (tc) is defined by the time at which the σapp(tc) takes the cutoff conductivity (σc), that is, in this example, the arithmetic average between the early time and the late time conductivities: σc={σapp(t→0)+σapp(t→∞)}/2. The transition time (tc) is dictated by the ray-path RP, D minus L/2 that is, half the distance for the EM signal to travel from the transmitter to the bed boundary to the receiver, independently on the resistivity of the two layers. Conversely, the distance (D) can be estimated from the transition time (tc), as shown in
While the coaxial transient data were examined above, the coplanar transient data are equally useful as a look-ahead resistivity logging method.
Corresponding to
Like it was the case in the co-axial geometry, it is also true for the coplanar responses that the early time apparent conductivity (σapp(t→0)) is the conductivity of the local layer (σ1) where the tool is located. Conversely, the layer conductivity can be measured easily by the apparent conductivity at earlier times.
The late time apparent conductivity (σapp(t→∞)) is some average of conductivities of both layers. The conclusions derived for the coaxial responses apply equally well to the coplanar responses. However, the value of the late time conductivity for the coplanar responses is not the same as for the coaxial responses. For coaxial responses, the late time conductivity is close to the arithmetic average of two-layer conductivities in two-layer models.
as is shown by line 78 in
To summarize, the late time conductivity (σapp(t→∞)) can be used to estimate the conductivity of the adjacent layer (σ2) when the local conductivity near the tool (σ1) is known, for instance, from the early time conductivity (σapp(t→0)=σ1). This is illustrated in
The transition time tc at which the apparent conductivity starts deviating from the local conductivity (σ1) toward the late time conductivity clearly depends on the distance (D) of the tool 80 (e.g. the transmitter T) to the bed boundary 55, as shown in
The transition time (tc) may be defined by the time at which the σapp(tc) takes the cutoff conductivity (σc) that is, in this example, the arithmetic average between the early time and the late time conductivities: σc={σapp(t→0)+σapp(t→∞)}/2. The transition time (tc) is dictated by the ray-path, D minus L/2 that is, half the distance for the EM signal to travel from the transmitter to the bed boundary to the receiver, independently of the resistivity of the two layers.
Conversely, the distance (D) can be estimated from the transition time (tc), as shown in
The next model shows a conductive near layer, a very resistive layer, and a further conductive layer. The geological configuration is depicted in
In either case, the tool “sees” the anomaly 83 as a first layer at a first distance D1 away and having a thickness Δ, and it “sees” the formation on the other side of the anomaly 83 as a second layer 84 at a second distance D2=D1+Δ away and having infinite thickness.
The first climb of Rapp(t) is the response to the salt and takes place at 10−4 s with an L=1 m tool when the salt is at D1=10 m away. If the salt is fully resolved (by infinitely thick salt beyond D1=10 m), the apparent resistivity should read 3 Ωm asymptotically. The subsequent decline of Rapp(t) is the response to a conductive formation behind the salt (resistive bed). Rapp(late t) is a function of conductive bed resistivity and salt thickness. If the time measurement is limited to 10−2 s, the decline of Rapp(t) may not be detected for the salt thicker than 500 m.
With respect to the resistive bed resolution, the coaxial responds to a thin (1-2 m thick) bed. The time at which Rapp(t) peaks or begins declining depends on the distance to the conductive bed behind the salt. As noted previously, when plotted in terms of apparent conductivity σapp(t), the transition time may be used to determine the distance to the boundary beds.
Another three-layer formation was also modeled, as shown in
The decrease in Rapp(t), which can be seen in
Still another three-layer model is set forth in
The response to the intermediate resistive layer is seen at 10−4 s, where Rapp(t) increases. If the first layer 83 is fully resolved by an infinitely thick bed, the apparent resistivity approaches a 2.6 Ωm asymptote. As noted in
Though complex, the apparent resistivity or apparent conductivity in the above examples delineates the presence of multiple layers. The observed changes of apparent conductivity (or apparent resistivity) allow determination of the distances D1 and D2.
As stated above, an electromagnetic anomaly may display anisotropic electromagnetic properties. An example is shown in
Various mechanisms may give rise to a macroscopic electromagnetic induction effect. For instance, oriented fractions may generate an anisotropic response. Electromagnetic anisotropy may also arise intrinsically in certain types of formations, such as shales, of may arise as a result of sequences of relatively thin layers.
In the way as depicted in
In the following it will be explained how electromagnetic anisotropy of at least one of the formation layers may be taken into account when analyzing time-dependent transient response signals. This may comprise determining one or more anisotropy parameters that characterize the anisotropic electromagnetic properties. Amongst anisotropy parameters are anisotropy ratio α2, anisotropic factor β, conductivity along a principal anisotropy axis σ⊥ (or resistivity along the principal anisotropy axis R⊥), conductivity in a plane perpendicular to the principal anisotropy axis σ// (or resistivity in a plane perpendicular to the principal anisotropy axis R//); tool axis angle relative to the principal anisotropy axis.
Using the concepts of apparent conductivity or apparent resistivity and/or apparent dip or azimuth, the distance and/or direction to an anomaly may be determined from the time-dependent transient response signals even when the anomaly, and/or a distant formation layer, comprise(s) an electromagnetic anisotropy or when the transmitter and/or receiver antennae are embedded in an anisotropic formation layer.
Using the principles set forth above, the analysis taking into account anisotropy may be extended to multiple bedded formations, including those where only a distant formation layer or target anomaly gives anisotropic electromagnetic induction responses (such as for instance in
In the forthcoming explanation, for reasons of simplicity, it will be assumed that the anisotropy has a vertically aligned principal axis, such that the angle between the tool axis z and the principal anisotropy axis corresponds to the dip angle or deviation angle θ. The term horizontal resistivity RH may be employed, which generally corresponds to the resistivity in the anisotropy plane perpendicular to the principal anisotropy direction. The term vertical resistivity RV generally refers to resistivity in the principal anisotropy direction or normal direction.
Considered is an anisotropic formation, in which a vertical resistivity RV (or its inverse vertical conductivity σV) is different from the horizontal resistivity RH (or horizontal conductivity σH). Assumed is that the formation is azimuth-symmetric, in the horizontal direction. The tool axis z is deviated from the vertical direction by the dip (deviation) angle θ in the zx-plane. The transmitter antenna is placed at origin. The receiver antenna is placed at (x=L·sin θ, y=0, z=L·cos θ). There may be four independent combinations of transmitter and receiver orientations that render non-zero responses.
In addition to a coaxial response, VZz, there are two coplanar responses, VXx and VYy, and one cross-component response VXz=VZx. One coplanar response, VXx, is from a transverse transmitter antenna and receiver antenna that are oriented within the zx-plane. Another coplanar response, VYy, is from a transverse transmitter and receiver both of which are oriented in the y-axis direction. The cross-component response is from a transverse receiver antenna with the longitudinally oriented transmitter antenna, or vise versa. The transverse receiver antenna is directed within the zx-plane. Any cross-component involving either a transmitter or a receiver oriented in the y-axis direction, i.e. VYx and Vxy and VYz and VZy are all vanishing.
The above has been set forth in tool-coordinates. It is further remarked that any antenna that is sensitive to a transverse component of an electromagnetic induction field suffices as a transverse antenna.
Applicants have derived the transient response in time domain, expressed in terms of horizontal conductivity σH and anisotropic factor β, are given by:
and C is a constant. The anisotropic factor β is defined as:
The following remarks may be made based on these equations:
1. The coaxial response depends only on the horizontal resistivity RH(=1/σH) and the anisotropic factor β that is determined by the anisotropy ratio α2=σV/σH=RH/RV, and the dip angle θ. Conversely, neither the anisotropy nor the dip angle can be determined from coaxial measurements alone.
5. Because u2→0 as t→large, the dip angle is determined by:
whereby O(u2) denotes a remainder on the order of u2.
Similar to the investigation set forth above with regard to layer models, the late time limits may be derived. As t→∞, u2→0, and therefore these limits converge. Taking into account anisotropy, the late time limits of equations (41) to (44) are:
The dip (deviation) angle is determined by:
The anisotropy ratio α2 may be determined from:
When the dip angle θ is known or estimated, the anisotropy ratio may alternatively be determined from:
It is further remarked that the sum of the co-axial response with the Xx coplanar response is independent from the approach angle.
Similar to the investigation set forth above with regard to layer models, apparent conductivity is also a useful derived formation quantity in case of an anisotropic formation layer.
The apparent conductivity is defined for both coaxial (σZz(t)) and coplanar (σXx(t), σYy(t)) responses. The apparent conductivity is the time-varying conductivity that would give the measured coaxial or coplanar response at time t if the formation would be homogeneous and isotropic.
As before, the time-changing apparent conductivities depend on the voltage response in a coaxial tool (VzZ(t)) or in a coplanar tool (VXx(t) at each time of measurement as:
Then, at large t, the apparent conductivity approaches the value determined by the anisotropic conductivity and the dip angle as follows:
The anisotropy ratio α2 may be estimated from the ratio of equations (61) and (60), and the estimated θ as:
Of these Figures,
In each of
The resulting straight line demonstrates the linear relationship. When taking into account the anisotropy, the correct value of the horizontal formation resistivity (or conductivity) can thus be extracted from the asymptotic coaxial apparent conductivity values.
Even for highly anistropic formations, the apparent conductivity is almost indistinguishable from apparent conductivity of a homogeneous isotropic formation with a lower conductivity. Interpretation mistakes may thus easily be made if anisotropy is not taken into account when analyzing.
As follows from the above, anisotropy can be taken into account, for instance by combining co-axial responses with coplanar responses. The precise embodiment depends on which of the parameters are known or estimated. The sum of the co-axial response with the Xx coplanar response is independent from the approach angle. If C and σH are known or estimated then the anisotropy ratio α2 follows from the late time value of sum VZz+VXx. If, on the other hand, the approach angle θ is known, C and σH don't need to be known because the anisotropy ratio α2 may be derived from Eq. (53). If none of the other parameters is known, Eq. (52) may be employed requiring combining co-axial response with two independent co-planar responses.
In
While each sub-layer in the laminate of thin layers may have isotropic properties such as isotropic conductivity, the combined effect of the sub-layers may be that the formation layer that consists of the sub-layers exhibits an anisotropic electromagnetic induction. If each sub-layer 112, 114 in the formation layer 110 acts as an individual resistor, the macroscopic resistivity (inverse of conductivity) of the formation layer in a planar direction may be a resultant of all the layer-resistors in parallel while the macroscopic resistivity in a normal direction (i.e. perpendicular to the layers) may be a resultant of all the layer resistors in series.
In equation form:
for the resistivity in the vertical, or principal direction, and
for the conductivity in the horizontal, or in-plane, direction perpendicular to the principal direction. Of course, σV can be found using σV=1/RV, and RH can be found using RH=1/σH. Hence the in-plane resistivity is typically lower than the resistivity in the principal direction. These equations also hold for more general cases whereby the sub-layers are not of equal thickness and/or the sublayers are not of equal conductivity.
The apparent resistivity represented by lines 115 and 116 reflect the near-layer resistivity of 1 Ωm at short times after the switching off of the transmitter. After a time span of approximately 2E-5 sec, the apparent resistivity starts to increase due to the higher resistivity of 10 Ωm in the first adjacent sub-layers 112. So far, the apparent resistivity reflects what was set forth above for formations comprising two or three isotropic formation layers.
However, for later times the sub-layers are no longer individually resolved in the responses, in which case apparent resistivity is believed to reflect contributions from the sub-layer where the tool 80 is located, the adjacent layers and next adjacent layers, and so on. Effectively, the transient responses will show the macroscopic anisotropic behavior. In the example of
The dotted lines 117 and 118 in
The combined, “macroscopic,” anisotropic effect of a sub-layered anomaly, such as is shown in
Using the principles set forth above, the analysis taking into account anisotropy may be extended to multiple bedded formations, including those where only a distant formation layer displays macroscopic electromagnetic induction responses (such as for instance in
As stated before in this specification, electromagnetic anisotropy may arise intrinsically in certain types of formations, such as shales. A shale may cap a reservoir of mineral hydrocarbon fluids. It would thus be beneficial to precisely locate a shale during drilling of a well, and drill between for instance 10 m and 100 m below the shale to enable optimal production of the hydrocarbon fluids from the reservoir. This can be done either by traversing the shale or steering below the shale in a deviated well such as a horizontal section.
In other cases, the hydrocarbon containing reservoir may have materialized in the form of a stack of thin sands, which itself may exhibit anisotropic electromagnetic properties. It would be beneficial to identify the presence of such sands and steer the drilling bit into these sands.
In each of these cases, geosteering may be accomplished by performing the transient electromagnetic analysis while drilling and taking into account formation anisotropy. This may be implemented using the system as schematically depicted in
More generally, geosteering decisions may be taken based on locating any type of electromagnetic anomaly using transient electromagnetic responses. Such geosteering applications allow to more accurately locate hydrocarbon fluid containing reservoirs and to more accurately drill into such reservoirs allowing to produce hydrocarbon fluids from the reservoirs with a minimum of water.
In order to produce the mineral hydrocarbon fluid from an earth formation, a well bore may be drilled with a method comprising the steps of:
suspending a drill string in the earth formation, the drill string comprising at least a drill bit and measurement sub comprising a transmitter antenna and a receiver antenna;
drilling a well bore in the earth formation;
inducing an electromagnetic field in the earth formation employing the transmitter antenna;
detecting a transient electromagnetic response from the electromagnetic field, employing the receiver antenna;
deriving a geosteering cue from the electromagnetic response.
Drilling of the well bore may then be continued in accordance with the geosteering cue until a reservoir containing the hydrocarbon fluid is reached.
Once the well bore extends into the reservoir containing the mineral hydrocarbon fluid, the well bore may be completed in any conventional way and the mineral hydrocarbon fluid may be produced via the well bore.
Geosteering may be based on locating an electromagnetic anomaly in the earth formation by analysing the transient response in accordance with the present specification, and taking a drilling decision based on the location relative to the measurement sub. The location of the anomaly may be expressed in terms of distance and/or direction from the measurement sub to the anomaly.
To facilitate executing the drilling decision, the drill string may comprise a steerable drilling system 19, as shown in
Accordingly, the geosteering cue may comprise information reflecting distance between the target ahead of the bit and the bit, and/or direction from the bit to target. Distance and direction from the bit to the target may be calculated from the distance and direction from the tool to the bit, provided that the bit has a known location relative to the electromagnetic measurement tool.
Transient electromagnetic induction data may be correlated with the presence of a mineral hydrocarbon fluid containing reservoir, either directly by establishing conductivity values for the reservoir or indirectly by establishing quantitative information on formation layers that typically surround a mineral hydrocarbon fluid containing reservoir.
In preferred embodiments, the transient electromagnetic induction data, processed in accordance with the above, is used to decide where to drill the well bore and/or what is its preferred path or trajectory. For instance, one may want to stay clear from faults. Instead of that, or in addition to that, it may be desirable to deviate from true vertical drilling and/or to steer into the reservoir at the correct depth.
The distance from the measurement sub to an anomaly in the formation may be determined from the time in which one of apparent conductivity and apparent resistivity begins to deviate from the corresponding one of conductivity and resistivity of formation in which the measurement sub is located and/or determining time in which one of apparent dip and apparent azimuth and cross-component response starts to deviate from zero. The distance may also be determined from when one of apparent dip and apparent azimuth reaches an asymptotic value.
The electromagnetic anomaly may be located using at least one of time-dependent apparent conductivity, time dependent apparent resistivity, time-dependent dip angle, and time-dependent azimuth angle from the time dependence of the transient response, in accordance with the disclosure elsewhere hereinabove.
Any of the above mentioned time-dependencies can provide a useful geosteering cue.
Apparent conductivity and apparent dip may also be used to create an “image” or representation of the formation features. This is accomplished by collecting transient apparent conductivity data at different positions within the borehole.
The apparent conductivity should be constant and equal to the formation conductivity in a homogeneous formation. The deviation from a constant conductivity value at time (t) suggests the presence of a conductivity anomaly in the region specified by time (t). The collected data may be used to create an image of the formation relative to the tool.
When the apparent resistivity plots (Rapp(z; t)) or apparent conductivity plots ((σapp(z; t)) at different tool positions are arranged together to form a plot in both z- and t-coordinates, the whole plot may be used as an image log to view the formation geometry, even if the layer resistivity may not be immediately accurately determined.
An example of such an image representation of the transient data as shown in
Another example is shown in
In still another example, the apparent dip θapp(t) may be used to generate an image log. In
Summarising, the subterranean formation traversed by a wellbore may be imaged using a tool comprising a transmitter for transmitting electromagnetic signals through the formation and a receiver for detecting response signals in a procedure comprising steps wherein
the tool is brought to a first position inside the wellbore;
the transmitter is energized to propagate an electromagnetic signal into the formation;
a response signal that has propagated through the formation is detected;
a derived quantity is calculated for the formation based on the detected response signal for the formation;
the derived quantity for the formation is plotted against time.
Then the tool is moved to at least one other position within the wellbore, whereafter the steps set out above are repeated. Optionally, this can be done again. Then an image of the formation within the subterranean formation is created based on the plots of the derived quantity.
Optionally tool is then again moved to at least one more other position within the wellbore and the whole procedure can be repeated again.
Creating the image of the formation features may include identifying one or more inflection points on each plotted derived quantity and fitting a curve to the one or more inflection points.
Thus an image of the formation may be created using apparent conductivity/resistivity and apparent dip angle without the additional processing required for inversion and extraction of information. This information is capable of providing geosteering queues as well as the ability to profile subterranean formations.
The present application claims benefit under 35 USC § 119(e) of U.S. Provisional application No. 60/797,556 filed 4 May 2006.
Number | Date | Country | |
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60797556 | May 2006 | US |