CA2346193A1 - Method for evaluating formation resistivity at a selected depth of investigation - Google Patents

Abstract

Accordingly, there is disclosed herein a method for radially profiling a property of a formation around a borehole that is suitable for combining measurements from multiple tools. In one embodiment, the method includes: (i) using a first downhole tool to obtain property measurements associated with multiple investigation depths; and (ii) determining from the property measurements estimated property values in predetermined radial zones.
The predetermined radial zones preferably include one zone that is the region of investigation by a second tool. This allows the estimated property value to be used in conjunction with any measurements by the second tool, or alternatively, provides a reference for calibrating the second tool. The estimated property values for the various predetermined radial zones are preferably those that minimize a distance metric value (e.g. the Euclidean distance) between the actual property measurements and the measurements expected to result from a formation profile having the estimated property values. The first downhole tool could illustratively be a resistivity tool, and the second downhole tool could illustratively be a nuclear magnetic resonance tool.

Description

METHOD OF EVALUATING FORMATION RESISTIVITY
AT A SELECTED DEPTH OF INVESTIGATION
FIELD OF THE INVENTION
The present invention relates generally to the interpretation of downhole property measurements. More particularly, the present invention relates to an improved method for interpreting the measurements made by tools having multiple depths of investigation.
BACKGROUND OF THE INVENTION
The gathering of downhole information has been done by the oil well industry for many years. Modern petroleum drilling and production operations demand a great quantity of information relating to the parameters and conditions downhole. Such information typically includes the location and orientation of the well bore and drilling assembly, earth formation properties, and drilling environment parameters downhole. The collection of information relating to formation properties and conditions downhole is commonly referred to as "logging", and can be performed by several methods.
In conventional wireline logging, a probe or "sonde" having various sensors is lowered into the borehole after some or all of the well has been drilled. The sonde is typically constructed as a hermetically sealed steel cylinder for housing the sensors, and is typically suspended from the end of a long cable or "wireline". The wireline mechanically suspends the sonde and also provides electrical conductors between the sensors (and associated instrumentation within the sonde) and electrical equipment located at the surface of the well. Normally, the cable transports power and control signals to the sonde, and transports information signals .from the sonde to the surface. In accordance with conventional techniques, various parameters of the earth's formations adjacent the borehole are measured and correlated with the position of the sonde in the borehole as the sonde is pulled uphole.
An alternative to wireline logging entails the collection of data during the drilling process itself. Designs for measuring conditions downhole along with the movement and location of the drilling assembly, contemporaneously with the drilling of the well, have come to be known as "measurement-while drilling" techniques, or "MWD". Similar techniques, concentrating more on the measurement of formation parameters, have commonly been referred to as "logging while drilling" techniques, or "LWD". While distinctions between MWD and LWD may exist, the terms MWD and LWD often are used interchangeably. For the purposes of this disclosure, the term LWD will be used with the understanding that this term encompasses both the collection of formation parameters and the collection of information relating to the movement and position of the drilling assembly.
The sensors used in a wireline sonde or a bottom hole assembly may include a source device for transmitting energy into the formation, and one or more receivers for detecting the energy reflected from the formation. Various sensors have been used to determine particular characteristics of the formation, including nuclear sensors, acoustic sensors, and electrical sensors.
For an underground formation to contain petroleum, and for the formation to permit the petroleum to flow through it, the rock comprising the formation must have certain well known physical characteristics. For example, one characteristic is that the rock in the formation have space to store petroleum. If the rock in a formation has openings, voids, and spaces in which oil and gas may be stored, it is characterized as "porous". Thus, by determining if the rock is porous, one skilled

-2-in the art can determine whether or not the formation has the requisite physical properties to store and yield petroleum. Various well known sensors may be used to measure formation porosity.
One type of logging tool used to measure porosity is a nuclear magnetic resonance tool.
These tools generally function by pulsing the formation with a strong magnetic field and measuring the electromagnetic signatures of hydrogen nuclei falling into and out of alignment with the magnetic field. The electromagnetic signatures are used to determine relaxation time distributions for the hydrogen nuclei, which can be used to infer several secondary attributes such as porosity.
For accurate interpretation of the measurements, it is helpful to have other sensors measuring other properties of the formation.
To identify the fluids held by porous rock formations, other sensors are used.
One property that may be used to distinguish between liquid petroleum and brine in a formation is the formation resistivity. Porous formations having a low resistivity are likely to contain brine, whereas formations that contain petroleum are likely to have a high resistivity. In a type of formation called "shaley-sand," for example, the shale bed can have a resistivity of about 1 ohm-meter. A bed of oil-saturated sandstone, on the other hand, is likely to have a higher resistivity of about 10 ohm-meters or more. The sudden change in resistivity at the boundary between beds of shale and sandstone can be used to locate these boundaries. Various tools well known to those of skill in the art may be used to acquire the resistivity measurements. Examples of suitable tools include galvanic tools, induction tools, and resistivity tools.
A typical formation does not have a uniform (or "homogeneous") resistivity throughout, so it is usually desirable to measure the resistivity in various regions around the borehole to fully characterize the formation. Tools commonly measure the resistivity along a concentric volume around the borehole, at an average radius which is called the "depth of investigation" or "radius of

-3-investigation." To thoroughly characterize the formation, measurements are taken with a variety of depths of investigation and at a variety of vertical positions within the borehole. The depth of investigation generally is determined by the distance between the transmitter and receiver, with a longer spacing resulting in a deeper depth of investigation and a shorter spacing providing a shallower depth of investigation. Other factors also influence the depth of investigation, such as the signal frequency and whether phase resistivity or attenuation resistivity is used.
The tools of interest to the present application make several measurements that have corresponding different depths of investigation. The need for multiple depths of investigation is in part motivated by a phenomenon known as "formation invasion". As the formations near the borehole are exposed to fluids contained in the borehole (such as drilling mud), the borehole fluids diffuse a short distance into the formation, significantly altering the formation resistivity in the immediate proximity of the borehole. To determine the true resistivity of the undisturbed formation, it is necessary to account for the effects of invasion. Existing methods for doing this treat the invaded region as a cylinder of uniformly altered resistivity but variable diameter.
While effective for determining undisturbed formation resistivity, this approach provides only a crude support for identifying the present resistivity of a formation at a particular radius.
Consequently it is inadequate for use in conjunction with Nuclear Magnetic Resonance logging tools that benefit from accurate estimates of the resistivity in their specific volumes of investigation.
2o SLJwIMARY OF THE INVENTION
Accordingly, there is disclosed herein a method for radially profiling a property of a formation around a borehole that is suitable for combining measurements from multiple tools. In one embodiment, the method includes: (i) using a first downhole tool to obtain property

-4-measurements associated with multiple investigation depths; and (ii) determining from the property measurements estimated property values in predetermined radial zones.
The predetermined radial zones preferably include one zone that is the region of investigation by a second tool. This allows the estimated property value to be used in conjunction with any S measurements by the second tool, or alternatively, provides a reference for calibrating the second tool. The estimated property values for the various predetermined radial zones are preferably those that minimize a distance metric value (e.g. the Euclidean distance) between the actual property measurements and the measurements expected to result from a formation profile having the estimated property values. The first downhole tool could illustratively be a resistivity tool, and the second downhole tool could illustratively be a nuclear magnetic resonance tool.
BRIEF DESCRIPTION OF THE DRAWINGS
A better understanding of the present invention can be obtained when the following detailed description of preferred embodiments is considered in conjunction with the following drawings, in which:
Figure 1 shows a computer system that will support execution of a resistivity profile determination method;
Figure 2 shows a first resistivity profile model;
Figure 3 shows a second, preferred resistivity profile model;
Figure 4 shows an environmental view of a well in which a resistivity tool according to the present invention may be used; and Figure 5 shows a LWD resistivity tool having multiple volumes of investigation.

-5-DETAILED DESCRIPTION OF THE PREFERRED EMBODIMENTS
Given a set of property measurements at multiple depths of investigation, it is desired to interpret the measurements so as to determine the formation property in a given region. Recall that the measurements for the deeper depths of investigation correspond to regions that include the regions having the shallower depths of investigation, and that all measurements are influenced by the properties of the borehole fluid. Accordingly, to estimate the actual formation property values in selected regions, it is necessary to perform compensation on the measurements provided by the tool.
The interpretation methods are systematic algorithms that may be carried out by a processor of microcontroller of any kind, including that found in a general purpose computer system such as that shown in Fig. 1. The system of Fig. 1 includes a computer "tower" 102, a display device 106, and a user input device 108. The computer tower 102 houses a power supply, a processor, short and long term data storage, and input/output cannectors for peripheral devices.
Typically, the computer tower 102 also includes one or more types of readers for portable data storage media. A user initiates via user input device 108 retrieval and execution of the compensation method. The processor in computer tower 102 retrieves the compensation method from the internal or portable data storage media, converts it to executable form if necessary, and executes it. The interpretation method is normally embedded in a larger software module that specifies where the resistivity data is found, and specifies where the compensation results are to be stored. Most such software modules will also provide feedback to the user via display device 106. It is noted that the compensation method can also be performed in hardware or firmware as an application-specific integrated circuit (ASIC).

-6-For any set of resistivity measurements a finite number of investigation depths, there are an infinite number of resistivity profiles that could produce those measurement values.
Consequently, the best interpretation approach is to use a model of the resistivity profile. The number of "degrees of freedom" (i.e. independent parameters) in the model is less than or equal to the number of measurements. An example of a resistivity profile model is shown in Fig. 2.
In the model of Fig. 2, it is assumed that the radius of the borehole (rb,,) and the resistivity of the borehole fluid (R",) are known. Indeed, these can be directly measured by other instruments. The model has three parameters: the near-borehole resistivity (RXO), the invasion depth (D;), and the undisturbed formation resistivity (R,). These parameters can be determined by processing measurements from a tool that has three or more depths of investigation. The parameter values are preferably those that minimize the measurement error E:

E= ~ LRk °g - Rk °ae~ (R~ ~ Rx° ~ Dr ~~ ~ (Eqn 1 ) k=1 where Rk°g, i=1,2,...N, are the log measurements at different investigation depths, and Rk odel (~, ~°, D~ ) are the expected log measurements for the model profile. If the expected log measurements are in the form of analytic expressions, this minimization can be done by evaluating the derivative of Eqnl and setting it equal to zero. If not, or even if they are, this minimization can be done using standard numerical computation techniques, such as those taught in William H. Press, Saul A. Teukolsky, William T. Vetterling, and Brian P.
Flannery, Numerical Recipes in C: The Art of Scientific Computing., 2°d edition published January 1993 by Cambridge University Press; ISBN: 0521431085. If repeated evaluation of the Rk odel (~, ~°, Dt ) function is unduly burdensome, a look-up table for each Rk °de' (IZ~, Rx°, D; ) as a function of the parameters may be created and iteratively accessed by a processor that identifies the parameters corresponding to the minimum error.
In an alternative embodiment, a look-up table for the parameter set as a function of the log measurements Rk°g can be created. In this table, the solutions for a range or probable log measurements are precalculated and stored. The solution parameter set can then be easily retrieved (by interpolation if necessary) without iterative processing.
Because the delineation between resistivity regions is mobile, this model is not suitable for determining the resistivity of the formation at a specific radius, unless that radius happens to be very close to the borehole or very far away from the borehole. The ability to estimate the resistivity at a specific radius is desirable for combining the measurements of the resistivity tool with other downhole measurements, such as, e.g., those obtained using a nuclear magnetic resonance tool.
Accordingly, a preferred resistivity profile model is that shown in Fig. 3, where the resistivity zones are predetermined. In other words, a number of zones is selected and the limits of the zones defined before resistivity values are calculated. One of the zones is preferably selected to correspond to the region of interest for other instrument measurements (e.g. rl-r2), while another zone is preferably selected to correspond to the invaded region (e.g. rbh-rl), and yet another zone is selected to correspond to the undisturbed formation region (e.g. >r4). In the model of Fig. 3, the values for Rm, rb,,, rl, r2, and r3 are fixed, and the resistivity values Rl, R2, R3, and R4 are determined from the log measurements. The procedure is similar to that previously described. Namely, the measurement error E:

E-~~Rk~g -~°aBr~R~~~~R3~R4~ ~ (Eqn2) k=1 - g -is minimized using analytic or numerical computation techniques. Since four parameters are being determined, resistivity measurements for at least four investigation depths are needed.
It is noted that while the example uses four parameters, the preferred resistivity profile model is not so limited. The actual number of parameters will vary as needed up to the number of resistivity measurements available.
This profile model can be used for calculating the resistivity in preselected zones from measurements made by any multi-depth-of investigation resistivity tool.
Advantageously, the resistivity from one of the zones can then be used for comparison, calibration, or adjustment of the measurements made by other tools specific to that zone. This approach may also be applicable to other formation property measurements, such as porosity and density.
The following description is now provided to describe an illustrative environment where this technique may be used. Fig. 4 shows a well during drilling operations. A
drilling platform 2 is equipped with a derrick 4 that supports a hoist 6. Drilling of oil and gas wells is carried out by a string of drill pipes connected together by "tool" joints 7 so as to form a drill string 8. The hoist 6 suspends a kelly 10 that is used to lower the drill string 8 through rotary table 12. Connected to the lower end of the drill string 8 is a drill bit 14. The bit 14 is rotated and drilling accomplished by rotating the drill string 8, by use of a downhole motor near the drill bit, or by both methods.
Drilling fluid, termed mud, is pumped by mud recirculation equipment 16 through supply pipe 18, through drilling kelly 10, and down through the drill string 8 at high pressures and volumes to emerge through nozzles or jets in the drill bit 14. The mud then travels back up the hole via the annulus formed between the exterior of the drill string 8 and the borehole wall 20, through a blowout preventer (not specifically shown), and into a mud pit 24 on the surface. On the surface, the drilling mud is cleaned and then recirculated by recirculation equipment 16. The drilling mud is used to cool the drill bit 14, to carry cuttings from the base of the bore to the surface, and to balance the hydrostatic pressure in the rock formations.
In a preferred embodiment, downhole sensors 26 are coupled to a telemetry transmitter 28 that transmits telemetry signals by modulating the mud flow in drill string 8. A telemetry receiver 30 is coupled to the kelly 10 to receive transmitted telemetry signals. Other telemetry transmission techniques are well known and may be used.
One of the sensors 26 is a resistivity tool having multiple depths of investigation. An example of one such resistivity tool is shown in Fig. 5. Resistivity tool 40 has a series of transmitters 42 and a pair of receivers 44. When one of the transmitters 42 is excited by an oscillatory signal, it generates an electromagnetic wave that propagates into the formation. The receiver pair 44 detects the electromagnetic wave as modified by the formation. The attenuation and phase difference between the receivers may be used to identify the average resistivity in a volume around the borehole 20 having an average depth of investigation 46 determined by the transmitter/receiver-pair spacing.
1 S Since resistivity tool 40 has six transmitter/receiver-pair spacings, the resistivity for at least six depths of investigation may be measured. It is important to note that because the larger volumes of investigation include the smaller volumes of investigation, the resistivity measurements for the deeper depths of investigation are influenced by the resistivities nearer the borehole. Conceptually, the shallower depth resistivity measurements are used to compensate the deeper depth resistivity measurements, so that a more accurate estimate of the undisturbed formation resistivity may be obtained.
It is noted that the use of the term resistivity tool is intended to include both induction tools, galvanic tools, and any other tools that produce resistivity or conductivity measurements at multiple depths of investigation. The selected resistivity profile model may have two, but preferably has three or more, fixed zones for which the resistivity is calculated.
Numerous variations and modifications will become apparent to those skilled in the art once the above disclosure is fully appreciated. For example, the present invention is not limited to resistivity, but may alternatively be applied to the interpretation of other downhole property measurements. It is intended that the following claims be interpreted to embrace all such variations and modifications.

Claims (18)

I claim:

1. A method for radially profiling a property of a formation around a borehole, wherein the method comprises:
obtaining a plurality of property measurements associated with a corresponding plurality of investigation depths; and determining from the plurality of property measurements a plurality of estimated property values in a corresponding plurality of predetermined radial zones.

2. The method of claim 1, further comprising:
comparing the estimated property value from a given one of said plurality of predetermined radial zones to a property value determined from measurements distinct from said plurality of property measurements.

3. The method of claim 1, wherein the plurality of estimated property values minimize a distance metric between the plurality of property measurements and a corresponding plurality of expected property measurements that result from the estimated property values.

4. The method of claim 3, wherein the distance metric is the Euclidean distance.

5. The method of claim 3, wherein the plurality of predetermined radial zones includes three or more predetermined radial zones.

6. The method of claim 5, wherein said determining includes:
applying a set of estimated property values to a look-up table to obtain a set of expected property measurements;
comparing the set of expected property measurements to the plurality of property measurements to obtain a distance metric value;
updating the set of estimated property values according to a change in the distance metric value;
repeating said applying, comparing, and updating until the distance metric value reaches a minimum value.

7. The method of claim 5, wherein said determining includes:
applying the set of property measurements to a look-up table to obtain the estimated property values.

8. The method of claim 1, wherein said property measurements are resistivity or conductivity measurements, and wherein said obtaining includes passing an induction tool through a borehole.

9. The method of claim 1, wherein said property measurements are resistivity or conductivity measurements, and wherein said obtaining includes passing a galvanic tool through a borehole.

10. A method of using multiple tools in a borehole, wherein the method comprises:
using a first tool to obtain at a given position in the borehole property measurements in multiple regions of investigation around the borehole;

using a second tool to obtain a related property measurement in a specific radial zone around the borehole; and determining from the property measurements in multiple regions an estimated property value for each of a plurality of predetermined radial zones around the borehole, wherein one of the plurality of radial zones is said specific radial zone.

11. The method of claim 10, further comprising:
combining the estimated property value for the specific radial zone with the related property value to calibrate the second tool.

12. The method of claim 10, wherein the first tool is a resistivity tool.

13. The method of claim 12, wherein the second tool is a nuclear magnetic resonance tool.

14. The method of claim 10, wherein the plurality of predetermined radial zones includes at least three predetermined radial zones around the borehole.

15. The method of claim 14, wherein the estimated property values minimize a distance metric between expected property measurements based on the estimated property values, and the obtained property measurements.

16. The method of claim 15, wherein the distance metric is the Euclidean distance.

17. The method of claim 15, wherein said determining includes:
applying a set of estimated property values to a look-up table to obtain a set of expected property measurements;
combining the set of expected property measurements with the obtained property measurements to obtain a distance metric value;
updating the set of estimated property values according to a change in the distance metric value;
repeating said applying, combining, and updating until the distance metric value reaches a minimum value.

18. The method of claim 15, wherein said determining includes:
applying the obtained property measurements to a look-up table to determine the estimated property values.