FIELD OF THE INVENTION

The invention is related to the field of induction logging of subsurface earth formations. Specifically, it relates to the use of induction logging for obtaining structural information of the subsurface away from a borehole.

BACKGROUND OF THE INVENTION

Induction resistivity well logging devices are known in the art for measuring the electrical resistivity of earth formations penetrated by wellbores. Electrical resistivity measurements are used for, among other things, to infer the fluid content of pore spaces of the earth formations.

Induction electrical resistivity instruments known in the art, such as one described in Hunka, J. “A New Resistivity Measurement System for Deep Formation Imaging and High Resolution Formation Evaluation”, paper no. 20559, Society of Petroleum Engineers, Richardson, Tex., 1990, typically measure voltages induced in receiver coils positioned at spaced apart locations along the instrument. The voltages are induced by magnetic fields generated by eddy currents flowing in the earth formations around the instrument, in response to alternating currents of various frequencies being passed through a transmitter coil. The voltages induced in a particular one of the receiver coils are dependent on the electrical conductivity (which is inversely related to resistivity) of the media, including the earth formations, surrounding the instrument, and are dependent on the spacing of the particular receiver coil with respect to the transmitter coil. Generally, the greater the spacing between the transmitter coil and the particular receiver coil, the greater is the radial depth from the wellbore into the earth formation from which the measurement at that receiver coil corresponds. The vertical resolution of the measurements made by the closer-spaced receiver coils, however, is proportionately finer than is the vertical resolution of the measurements made by the more distant receiver coils.

When the wellbore is drilled, fluids from the drilling process may be forced into the pore spaces of some of the earth formations, changing their fluid content and therefore their resistivity. The process of fluid being forced into the pore spaces is generally referred to as “invasion”. Wellbore can be drilled with fluids having differing electrical resistivities, and the wellbore itself can have widely varying diameters over its length. The effects of variable wellbore diameter and differing wellbore fluid resistivity can indeterminately affect the total voltage being induced in each one of the receiver coils, because eddy currents also can flow within the conductive wellbore fluid and within that portion of the earth formations surrounding the wellbore subject to the invasion (the so-called “invaded zone”).

U.S. Pat. No. 5,703,773 (referred hereafter as the “'773 patent”) having the same assignee as the present application and the contents of which are fully incorporated herein by reference, discloses a method of inversion processing signals from an induction well logging instrument. The instrument includes a transmitter and a plurality of receivers at axially spaced apart locations. The method includes skin effect correcting the responses of the receivers by extrapolating the receiver responses to zero frequency. A model is generated of the media surrounding said instrument. Conductivities of elements in the model are adjusted so that a measure of misfit between the skin-effect corrected receiver responses and simulated receiver responses based on the model is minimized. The geometry of the model is adjusted so that the measure of misfit between the skin-effect corrected receiver responses and the simulated receiver responses based on the model is further minimized.

The method of the '773 patent and other prior art processing methods for well logs are developed for vertical or near vertical wells. If the well deviation exceeds 30

0

-45

0

, traditional methods may fail. To interpret the data, 3-D modeling and inversion must be carried out. However, 3-D modeling and inversion is rarely practical due to the computational time requirements and the unavailability of powerful computers. As would be known to those versed in the art, some information about the subsurface is obtained using measurement-while-drilling (“MWD”) methods in horizontal or near horizontal boreholes. In an MWD environment, there is relatively little invasion of the formation by the drilling mud and the relatively short transmitter to receiver spacings may be able to provide sufficient information about the formation resistivity to be useful in applications such as geosteering.

It is desirable to have an invention that is able to give information further away from the borehole in a near horizontal well.

FIG. 1

is an end-on view of a borehole

10

within a reservoir rock

20

. Surrounding the well is an invaded zone

12

. Also shown in

FIG. 1

are interfaces

22

and

26

marking a resistivity contrast between the zone

20

and zones

24

and

28

. Typically, the interfaces

22

and

26

could be bed boundaries marking the separation between a reservoir formation

20

and non-reservoir formations

24

and

28

. However, the boundary

26

could also be a fluid contact within a formation marking the separation between a water wet region

28

and a hydrocarbon wet region

20

while formation

22

is the caprock. Another possible configuration is that

20

is a water wet reservoir rock while

24

is the hydrocarbon saturated region with

28

being the seal beneath the reservoir.

As part of the reservoir evaluation process, it would be desirable to map the boundaries such as

22

and

26

accurately. Such information is useful in the estimation of reserves and in development of completion procedures for developing the reservoir. The present invention satisfies this need for situations such as in FIG.

1

and also in other situations where information relating to formation properties away from the borehole is needed.

SUMMARY OF THE INVENTION

The present invention is a method for making induction log measurements in an inclined borehole and determining properties of subsurface formations formation away from the borehole. Measurements are made using an induction logging instrument having a plurality of transmitter-receiver (T-R) distances. After correction of the data for skin effects and optionally correcting for eddy currents within the borehole, the shallow measurements (those from short T-R spacing or from high frequency data) are inverted to give a model of the near borehole (invaded zone resistivity and diameter) and the resistivity of the formation outside the invaded zone. Using this model, a prediction is made of the data measured by the mid-level and deep sensors (long T-R spacings). A discrepancy between these predicted values and the actual measurements made by the midlevel and deep sensors is indicative of additional layer boundaries in the proximity of the wellbore. The midlevel and deep sensor data are corrected for invasion effects and inverted using the model derived from the shallow data to give an estimate of the distance to these additional layer boundaries and of the resistivity beyond these additional boundaries. In this manner, resistivity measurements in a near horizontal borehole may be used to map subsurface layers away from the borehole. In one embodiment of the invention, the quadrature component of the signal induced in the receiver coils is used. This quadrature component is independent of T_R spacing and has a larger depth of penetration than the commonly used in-phase component of the receiver signal.

BRIEF DESCRIPTION OF THE DRAWINGS

FIG. 1

s a transverse cross section of a logging tool within a near horizontal borehole showing subsurface formations in proximity to the borehole.

FIG. 2

is a schematic illustration of a logging tool within a near horizontal borehole showing the transmitter and receiver configuration.

FIG. 3

is a flow chart of the major steps of the method of the present invention for obtaining information about subsurface formations in the vicinity of a borehole.

FIG. 4

is an illustration of the geometry of an inclined borehole within the subsurface with uncomformable beds.

DESCRIPTION OF THE PREFERRED EMBODIMENT

The present invention is a method for determination of boundaries and material properties of regions having different electrical resisitivities away from a near horizontal borehole. The invention is best understood by reference to

FIGS. 1-4

and the related discussion hereunder.

FIG. 2

shows an induction well logging instrument

100

disposed in a generally horizontal wellbore

110

penetrating earth formations. The instrument

100

is typically lowered into the wellbore

100

at one end of an armored electrical cable

102

by suitable apparatus at the surface of the earth (not shown). An instrument which will generate appropriate induction signals for performing the process of the present invention is described, for example, in U.S. Pat. No. 5,452,761 issued to Beard et al. and having the same assignee as the present application. The instrument described in the Beard et al '761 patent is not an exclusive representation of well logging instruments which can generate signals for performing the process of the present invention and therefore is not meant as a limitation on the present invention.

The instrument

100

can include a telemetry/signal processing unit

104

(SPU). The SPU

104

can include a source of alternating current (not shown separately) to be conducted through a transmitter coil

106

disposed on the instrument

100

Receiver coils

108

A-

108

F can be disposed at axially spaced apart locations along the instrument

100

The SPU

104

include receiver circuits (not shown separately) connected to the receiver coils

108

A-

108

F for detecting voltages induced in each of the receiver coils

108

A-

108

F The SPU

104

can also impart signals to the cable

102

corresponding to the magnitude of the voltages induced in each of the receiver coils

108

A-

108

F. It is to be understood that the number of receiver coils and the arrangement of the coils shown in the instrument in

FIG. 1

is not meant to be a limitation on the present invention. It is to be further understood that the receiver coils shown in

FIG. 1

can either be single coils or a type of coil known in the art as “mutually balanced” wherein a second coil(not shown) is series connected in inverse polarity to the primary coil (not shown) so as to reduce the effect of direct induction from the transmitter coil

106

.

As is understood by those skilled in the art, the alternating current passing through the transmitter coil

106

induces eddy currents in the earth formations

120

,

124

and

128

. The eddy currents correspond in magnitude to the electrical conductivity of the earth formations

120

,

124

and

128

and to the relative position of the particular earth formation with respect to the transmitter coil

106

. The eddy currents in turn induce voltages in the receiver coils

108

A-

108

F, the magnitude of which depends on both the eddy current magnitude and the relative position of the earth formation with respect to the individual receiver coil

108

A-

108

F.

A more closely spaced receiver coil such as

108

A would have more of its voltage induced by eddy currents flowing from entirely within a closer formation such as

120

than would be the case for a longer spaced receiver coil such as

108

F. Conversely, the eddy currents which induce the voltages in receiver coil

108

A would more likely correspond to the conductivity within a zone such as shown at

112

, which is affected by fluid “invasion” into its pore spaces from the liquid phase of a fluid used to drill the wellbore (commonly known as “drilling mud”, the liquid phase known as “mud filtrate”).

The drilling mud itself can be electrically conductive. Eddy currents can flow in such conductive drilling mud, and therefore the voltages induced in each of the receiver coils

108

A-

108

F can also partially depend on the conductivity of the mud and the diameter of the wellbore. As is understood by those skilled in the art, the wellbore diameter is subject to variation as a result of “caving” or “washout”.

The signals corresponding to the voltages in each receiver coil

108

A-

108

F can be transmitted along the cable

102

to surface electronics (not shown). The surface electronics can include processors (not shown) for analyzing the signals from the instrument

100

according to the present invention.

As is understood by those skilled in the art, the correspondence between the magnitude of the voltages induced in each receiver coil

108

A-

108

F and the conductivity of the media surrounding the instrument

100

is affected by a phenomenon referred to as the “skin effect”. In the present embodiment of the invention, the voltage signals induced in each receiver coil

108

A-

108

F can be adjusted to compensate for the skin effect to more precisely correspond to the conductivity of the media surrounding the instrument

100

. The present invention uses the method described in the '773 patent to compensate for the skin effect and produce a calculated response for the zero frequency limit of the apparent conductivity at each of the receiver coils

108

A-

108

F.

After the skin effect correction is performed, it is desirable to further adjust the signals from each one of the receiver coils

108

A-

108

F for the effect of the eddy current signal which originates in the wellbore

110

. Methods for correcting the receiver coils signals are known in the art, one of which is described, for example in G. P. Grove and G. N. Minerbo, “An Adaptive Borehole Correction Scheme for Array Induction Tools”, SPWLA 32nd Annual Logging Symposium, pp 1-25, 1991). It is to be understood that the step of correcting the receiver coil signals for the effects of the conductivity of the wellbore

110

is optional in performing the process of the present invention. Correction for wellbore

110

conductivity can improve the accuracy of the final result. Under some conditions, however, particularly when the drilling mud comprises a substantially non-conductive liquid phase, the diameter of the wellbore D is relatively small (typically in a range of 5 to 8 inches where the diameter of the instrument

100

is about 3 ⅝ inches), and the instrument

100

is substantially centralized in the wellbore

110

, the overall effect of the wellbore

110

on the receiver coil signals can be negligible, and the step of correction can be omitted without seriously affecting the accuracy of the result of the inversion process.

The '773 invention describes a method in which data from an instrument such as the one described above are used to determine a conductivity model for the formation surrounding a vertical borehole. As would be known to those versed in the art, in a vertical borehole that intersects a number of substantially horizontal layers, the conductivity model of the earth formations is a lot more complicated than in the present situation. For a vertical borehole, each layer has a different conductivity associated with it and the response of each receiver coil depends upon the relative position of the receiver coil to the individual layer boundaries.

The use of the method of the '773 invention here is best understood with reference to FIG.

3

. The process starts at

200

with the data from all the receivers

108

A-

108

F. The skin effect correction is applied

202

and optionally, a correction for fluid in the borehole is applied

204

. With the configuration of the tool in a near horizontal borehole as shown in

FIGS. 1 and 2

, those versed in the art would recognize that the near receivers, e.g.,

108

A-

108

B are responsive almost entirely to the invaded zone

12

,

112

, while the intermediate receivers

108

D-

108

D are also affected by the material immediately outside the invaded zone

20

,

120

, referred to hereafter as the uninvaded zone. Finally, the far sensors

108

E-

108

F are also affected by data from the shoulder zones described below. Using the method of the '773 patent, these data from the near and intermediate receivers are inverted to give parameters of the invaded zone and the uninvaded zone. These include the conductivity of the invaded zone and the uninvaded zone and the thickness of the invaded zone. Those versed in the art would recognize that what is important is the depth of penetration into the formation of the induced electromagnetic signal. In the embodiment of the '773 patent, the near receivers are “shallow” sensors, the intermediate receivers are “midlevel” sensors and the far receivers are the “deep” sensors. Other embodiments exist in which shallow data is obtained by high frequency signals while the deep data is obtained by low frequency electromagnetic induction signals. Such variations are intended to be within the scope of the present application. Accordingly, the near receivers such as

108

A-

108

B will hereafter be referred to as the shallow sensors,

108

C-

108

D as sensors and the far receivers such as

108

E-

108

F will be referred to as the deep sensors.

Using the conductivity derived for the near zone, a predicted values for corrected measurements in the midlevel and deep sensors are obtained

208

assuming that there are no boundaries such as

122

and

126

, i.e., that the formation is radially substantially homogenous with respect to the borehole axis. These predicted values at the midlevel and deep sensors are compared to the actual measurements

210

. At

212

, a comparison between the predicted and actual corrected measurements is made. If this difference is less than a set threshold value, then the process stops

214

: the midlevel and deep data are consistent with the model derived from the shallow data and there are no boundaries such as

122

and

126

present. If the difference between the predicted and actual corrected measurements exceeds the threshold

212

then the midlevel and deep data are not consistent with the shallow data. At this point, the data are corrected for invasion

215

and the inversion method of the '773 patent is used to derive an enhanced model

216

including therein a distance to a boundary such as

122

,

126

and a conductivity on the far side

124

,

128

(i.e., away from the borehole) of the boundary.

Those versed in the art would recognize that with azimuthally symmetrical tools such as used in the '773 patent, the inversion would not provide any information regarding the direction of the additional boundary. The additional boundary in the enhanced model is called a shoulder boundary and the layer on the side of the shoulder boundary away from the borehole is called a shoulder layer.

Using the enhanced model, corrected data for the midlevel and deep sensors is predicted and compared with the actual corrected midlevel and deep sensor data

218

. If this difference

220

is less than a set threshold value, then the process stops

214

: the deep data are consistent with the enhanced model having a single shoulder layer. If the difference between the predicted and actual corrected data exceeds the threshold then the deep data are not consistent with the shallow data and a model having a single shoulder layer. At this point, the method of the '773 patent is used to derive an refined model

224

including therein a distance to a second shoulder and a conductivity for the second shoulder layer.

In a preferred embodiment of the invention, the two shoulder layers are on opposite sides of the borehole and are parallel to each other, i.e., the inversion and modeling is one dimensional. As noted above, the enhanced model and the refined model by themselves cannot define the direction in which the one or two shoulders lie. However, based upon the relative values of the resistivity of the uninvaded zone and the one or two shoulder layers, an inference can be drawn as to the nature and position of the shoulder layers.

As an example only, and without limitation, if the uninvaded zone has a low conductivity, consistent with a hydrocarbon rich reservoir rock and the first shoulder layer has a very high conductivity, it suggests that the first shoulder layer is a water layer. This water layer would be positioned below the borehole. The second shoulder layer would then be a caprock above the borehole. Conversely, if the uninvaded zone has a high conductivity, indicative of a water saturated reservoir, then a shoulder zone with low conductivity could be indicative of a hydrocarbon/water boundary positioned above the borehole. Those versed in the art would recognize various combinations of the resistivities of the invaded zone, the first and second shoulder zones, as being diagnostic of various combinations of water saturated rock, gas saturated rock, oil saturated rock and impermeable caprock.

FIG. 4

illustrates a situation in which a near horizontal wellbore

410

intersects a plurality of steeply dipping formations

412

,

414

,

416

,

418

. Inversion of induction log data acquired in such a wellbore makes it possible to determine the subsurface structure in terms of layer thicknesses. Data from the shallow sensors are inverted in a 2-D inversion to give properties of the formation in the immediate vicinity of the borehole and, in particular, layer thicknesses l

1

, l

2

. . . of the layers as traversed by the borehole. These layer resistivities are then used as an initial estimate for a 1-D inversion of the data from the deep sensors to give the shoulder boundaries

420

,

422

and the shoulder beds

424

,

426

. The methodology discussed above may be used to obtain a resistivity model of the subsurface.

Another aspect of the invention uses multifrequency and/or quadrature data as input to the inversion process. U.S. Pat. 5,884,227 having the same inventors and assignee as the present application and the contents of which are fully incorporated herein by reference, shows that when data are acquired at m angular frequencies &ohgr;

1

, &ohgr;

2

, &ohgr;

3

, . . . &ohgr;

m

, the in-phase components of voltages in the receiver coils

108

A-

108

F in

FIG. 2

generally correspond to the imaginary component of the magnetic field. This imaginary component of the magnetic field may be represented by a Taylor series of the form

픍

⁡

(

H

z

)

=

∑

k

=

1

k

=

∞

⁢

Θ

k

/

2

⁢

ω

k

/

2

(

1

)

A general representation of the apparent conductivity from the imaginary component of the magnetic field is given by a Taylor series expansion of the form

σ

a

=

∑

k

=

0

k

=

∞

⁢

s

k

/

2

⁢

ω

k

/

2

;

s

2

⁢

j

-

1

=

0

;

j

=

1

,

2

,

…

⁢

,

∞

(

2

)

where s

k/2

are coefficients depending on the conductivity distribution and the tool's geometric configuration. They do not depend upon the frequency.

Considering the series for each of the measured frequencies, this gives

[

σ

a

⁡

(

ω

1

)

σ

a

⁡

(

ω

2

)

⋮

σ

a

⁡

(

ω

m

-

1

)

σ

a

⁡

(

ω

m

)

]

=

[

1

ω

1

1

/

2

ω

1

3

/

2

…

ω

1

n

/

2

1

ω

2

1

/

2

ω

2

3

/

2

…

ω

2

n

/

2

⋮

⋮

⋮

…

⋮

1

ω

m

-

1

1

/

2

ω

m

-

1

3

/

2

…

ω

m

-

1

n

/

2

1

ω

m

1

/

2

ω

m

3

/

2

…

ω

m

n

/

2

]

⁢

[

s

0

s

1

/

2

s

3

/

2

⋮

s

n

/

2

]

(

3

)

where m represents the number of component frequencies, and n can be selected from a Taylor series expansion for an apparent conductivity integral.

The ultimate objective of the expansion series in Eq. (3) is to solve for the coefficient at the zero-frequency limit- s& Solving a system according to Eq. (3) will calculate a receiver coil response approximately equal to that described in H. G. Doll, “Introduction to Induction Logging and Application to Logging Wells Drilled with Oil Base Mud”, AIME Transactions Vol. 1, No. 6, pp 148-162 (1949), for the zero frequency limit of the apparent conductivity at each one of the receiver coils (

108

A-

108

F in FIG.

1

).

The leading terms of the expansion given by Eq. (1) are of the form

h(f

1

)=f

1

h

1

+f

1

3/2

h

2

+f

1

2

h

3

+ . . .  (4)

where f

1

is the frequency. The components f

1

h

1

is substantially dependent on the conductivity in the wellbore region, i.e., this term depends mainly on the conductivity of the wellbore fluid. PCT Patent Publication WO 98/0073 shows that by making the magnetic field measurement at a second frequency f

2

, a second field measurement h

2

is obtained

h(f

2

)=f

2

h

1

+f

2

3/2

h

2

+f

2

2

h

3

+ . . .  (5)

A linear combination of the measurements at the two frequencies

h(f

1

,f

2

)=h(f

1

)−(f

1

/f

2

)h(f

2

)  (6)

makes it possible to eliminate terms that are linear and frequency. As would be known to those versed in the art, the term that is linear in frequency is primarily responsive to the borehole. Having done this, it is possible to invert the multiple frequency data to obtain the bed boundaries for the configurations of

FIGS. 1

,

4

or

5

.

Specifically, for the configuration of

FIG. 1

, a two-dimensional (2-D) inversion of the shallow data is carried out to give the formation resistivity for the region

20

of

FIG. 1

as at

206

in FIG.

3

. The rest of the analysis proceeds as discussed above with reference to FIG.

3

.

For the subsurface configuration of

FIG. 4

, single-frequency shallow data may be used to derive the borehole and formation resistivities as discussed above with respect to FIG.

1

. Alternatively, multiple frequency data may be used for a one-dimensional inversion of the deep data to obtain the positions of the boundaries

420

,

422

and the resistivities of the layers

424

,

426

. In a preferred embodiment of the invention, the multiple frequency data are acquired at two frequencies.

One embodiment of the present invention includes measurements of the quadrature component of the induced signals in the receiver coils (the quadrature component is 90° out of phase with the phase of the transmitter signal). The quadrature component of eq. (2) gives the following equation:

ω

⁡

[

σ

a

⁡

(

ω

1

)

σ

a

⁡

(

ω

2

)

⋮

σ

a

⁡

(

ω

m

-

1

)

σ

a

⁡

(

ω

m

)

]

=

[

1

ω

1

3

/

2

ω

1

2

…

ω

1

n

/

2

1

ω

2

3

/

2

ω

2

2

…

ω

2

n

/

2

⋮

⋮

⋮

…

⋮

1

ω

m

-

1

3

/

2

ω

m

-

1

2

…

ω

m

-

1

n

/

2

1

ω

m

3

/

2

ω

m

2

…

ω

m

n

/

2

]

⁢

[

s

-

1

s

3

/

2

s

2

⋮

s

n

/

2

]

(

7

)

In eq. (7), the &sgr;

a

's are the apparent conductivities measured at the corresponding frequencies. Solving the system of eq. (7) with respect to s

3/3

gives the zero-frequency limit for quadrature measurements. It is known in literature that this component is independent of the tool spacing and it also has a large depth of investigation. These two properties are important for induction logging in near horizontal boreholes and inversion of the data makes it possible to identify bed boundaries a distance from the borehole.

Those versed in the art would recognize that if the number of frequencies m at which quadrature measurements are made is greater than n, the number of terms in the series expansion given by eq. (2), then eq. (7) is an overdetermined system of equations. Inversion of the values of s

3/2

makes it possible to obtain the subsurface model corresponding to any of

FIGS. 1

,

4

and

5

. In a preferred embodiment of the invention, the in-phase components of the shallow data are used to obtain the resistivity of the formation near the borehole and the quadrature component data at a low frequency limit are used to obtain the distances and resistivities of the shoulder beds.

Those skilled in the art will devise other embodiments of this invention which do not depart from the spirit of the invention as disclosed herein. Accordingly, the invention should be limited in scope only by the attached claims.