NO315099B1 - Borehole measurement system using electromagnetic wave propagation - Google Patents

Description

Field of the invention

The invention concerns the determination of geophysical parameters for soil formations penetrated by a borehole. More particularly, the invention is directed to the determination of geophysical properties based on measurements of electromagnetic properties of soil formations in the vicinity of a borehole, either during the drilling of the borehole or after the drilling of the borehole.

Background technology

A measure of geophysical parameters for soil formations penetrated by a borehole, as a function of depth in the borehole, is commonly referred to in the oil and gas industry as a "well log". The first well log was measured or "run" in 1927 and consisted of a measure of the spontaneous potential (SP) properties of a soil formation penetrated by the borehole. The log was run after the borehole was drilled using a downhole instrument operating on an electrical wireline. The wireline served as a means of transporting the downhole instrument or "logging tool " along the borehole, and also as an electrical path for transmitting data from sensors in the downhole instrument to the earth's surface. In the intervening decades, wireline well logging techniques have evolved in sophistication and complexity, using electromagnetic, acoustic, nuclear and mechanical techniques to determine geophysical parameters of interest Probably the most important geophysical parameters for producers of hydrocarbons are the formation's hydrocarbon (or water) saturation, the formation's porosity, and the formation's permeability. These parameters, in turn, are used to determine (a) whether hydrocarbon is present in the formation, (b) how much hydrocarbon is present, and (c) the ease with which the hydrocarbon can be extracted or "produced" from the formation.

Over the past two decades, well logs of increasing complexity and sophistication have been measured while drilling the borehole. The benefits of measurement-undcr-drilling or MWD (MWD = mcasurement while drilling) logs are well known in the art. Electromagnetic, nuclear and acoustic techniques have been used in MWD systems that approach the accuracy and precision of their wire counterparts.

Electromagnetic induction techniques have been used for a number of years in wireline and MWD logging operations to determine the resistivity and other electromagnetic parameters of soil formations penetrated by a borehole. One or more transmitters in a borehole induction logging instrument induce an alternating voltage within the borehole and the earth formation near the instrument. The amplitudes and phases of the signals produced by these alternating electromagnetic fields are measured by one or more receivers in the borehole instrument. Resistivity and other electromagnetic properties are calculated from the basic amplitude and phase measurements. Using the basic assumptions that hydrocarbon-saturated formations are more resistive than a formation that is Hydrocarbon-saturated formations are more resistive than a saltwater-saturated formation, the presence and amount of hydrocarbon is determined "in place".

The accuracy and precision of hydrocarbon measurements calculated from formation resistivity measurements is governed by the accuracy and precision of the underlying resistivity measurements. Errors in resistivity measurements, whether wireline or MWD measurements, occur in prior art systems from a variety of sources. These sources of error must be discussed briefly under the following categories:

1. Instrument calibration

In previously known systems, borehole machines or logging tools, both wireline and MWD type, are typically calibrated at the fire scene (or in the laboratory), using an "air-hang" calibration operation during which the logging tool's transmitter and receiver antennas are used to send and receive electromagnetic signals that propagate through the atmosphere around the tool. These air tension calibration operations provide no data whatsoever on the operation of the tool once it is driven downhole and operated in the borehole environment. Calibration values obtained during the air span may not apply to the downhole environment, or the logging tool may go out of calibration as soon as it is driven downhole.

Prior art downhole instruments typically include a significant number of analog, electrical and electronic components in both the transmitting and receiving circuits, and these tend to introduce an error component when exposed to changes in temperature. This type of failure component is typically identified as a "thermal drift" failure component. In prior art devices, this thermal drift error component introduces significant inaccuracies in measurements, which can reduce the overall accuracy of the logging instrument

Many prior art MWD logging tools are claimed to be capable of providing some indication of the size and shape of the borehole, during operations commonly referred to as "caUbermålin<g>s," ("calipering" operations). Such caliber measurement operations depend of the ability to detect slight changes in the amplitude attenuation or phase shift in the logging measurements that can be attributed to changes in borehole size. A wide variety of factors are taken into account during borehole measurement operations, including the diameter of the logging tool, the resistivity of the drilling fluid or "drilling mud", the diameter of penetration of the drilling mud into the formation , the resistivity of the formation and drilling mud in the invaded zone, and the resistivity of the formation for non-invaded parts of the formation. Calibration error and thermal drift error components, along with other inaccuracies associated with the utilization of such a large number of variables, typically make the changes in wellbore resistivity appear smaller, rendering previously known wellbore calibration needle operation techniques essentially meaningless.

Another problem typically encountered during logging operations is unwanted mutual magnetic field coupling that can occur between two or more receiving antennas. Considered broadly, the mutual magnetic coupling between receivers can be considered as a loss of information attributable to the magnetic interaction between the receivers, and which can be considered as an error component. More specifically, mutual coupling occurs when a propagating electromagnetic field produces a current in a particular receiver, and the current generated in a particular receiver itself generates a propagating electromagnetic field which combines with the primary or "interrogating" electromagnetic field to affect the amount of current generated in one or more adjacent receiving antennas.

In brief, some of the most important technical problems associated with downhole instruments, and particularly MWD logging tools, include the following: (1) the inability to achieve a meaningful and accurate calibration, (2) the difficulty of achieving the calibration, (3) the inability to determine when a tool is out of calibration during logging operations, (4) the significant impact on the accuracy of thermal drift error components, (5) the inability to obtain accurate borehole caliber data when utilizing a logging tool, mainly due to the combined effect of error components associated with the variables used to derive borehole caliber data, °g (6) the effects of unwanted mutual magnetic field coupling between receiving antennas in a logging facility.

2. Serial processing of measured data

As previously mentioned, amplitude and phase measurements are used to calculate the resistivity and other electromagnetic properties of the formation and the borehole in the vicinity of the borehole logging instrument. It is quite common practice to use two or more transmitter-receiver pairs with different distances along the axis of the borehole. It is also quite common practice to operate one or more transmitters on different frequencies. Both practices are aimed at obtaining electromagnetic measurements of various radial survey depths in the formation, near the borehole and borehole areas. These measurements are then combined to obtain resistivity measurements that have been corrected for adverse environmental conditions, such as formations invaded by drilling fluid, formations with limited vertical thickness, the diameter of the borehole, the resistivity and other electromagnetic properties of the drilling fluid urn, and the like. The environmental corrections are carried out continuously or "serially" in the known technique. Series ambient correction tends to propagate or propagate errors associated with each correction, thereby maximizing the error associated with the ambient corrected resistivity measurement.

It is known in the art that measurements carried out with different transmitter-receiver distances and at different frequencies exhibit different vertical resolutions. The known technique has found the counterpart to the vertical resolutions by using different convolution and deconvolution techniques prior to combining a large number of measurements. This is again referred to as serial data processing in the prior art. US Patent 4,609,873 (Percy T. Cox et al.) discloses the use of a wireline logging system comprising at least three transmitter coils and at least two receiver coils to determine the resistivity and dielectric constant of an underground formation close to a drilling fluid invaded zone. The transmitters are operated on a single frequency of 30 MHz. Amplitude and phase measurements are performed, and serial processing of the data is used. At relatively low transmitter frequencies, serial processing only introduces negligible errors. At higher transmitter frequencies in the range of 2 MHz or higher, vertical resolution is affected not only by the physical arrangement of the transmitter-receiver combinations, but also to a significant extent by the electromagnetic properties of the borehole surroundings and formation. The functional dependence of vertical resolution and transmitter frequency is addressed in the publications "2-MHz Propagation Resistivity Modeling in Invaded Thin Beds", by W. Hal Meyer, The Log Analyst, July-August 1993, p. 33 and "Inversion of 2 MHz Propagation Resistivity Logs" by W.H. Meyer, SPWLA 33rd Annual Logging Symposium, Paper H, 14-17 June 1992. Expressed in another way, previously known serial processing of data can introduce significant error at transmitter frequencies in the range of 2 MHz and higher. In order to obtain accurate and precise parametric determinations at these frequencies, it is necessary to calculate the parameters of interest and at the same time to perform the necessary corrections, including corrections for the effects of different vertical resolutions.

US patent 5 187 661 shows a logging device and a method for determining resistivity and/or dielectric constant in a formation near a borehole, and further for determining the depth of invasion in the formation, using several transmitters and receivers for electromagnetic energy, and an oscillator where the choice of output frequency is controlled digitally. The logging device also includes a device for transporting a measuring probe along the borehole.

3. Borehole parameter determinations.

The known technique's correction of resistivity measurements for the adverse effects of ambient conditions, and particularly for borehole conditions, has been briefly described in the previous section. In order to perform valid corrections for wellbore readings, it is usually necessary to know the wellbore or near-borehole conditions, which include the borehole diameter, the electromagnetic properties of the drilling fluid, the degree of penetration or invasion of the drilling fluid, and the like.

Borehole and near-borehole parameters also provide other extremely useful information. As an example, the borefJuidum penetration profile is an indication of formation permeability. As a further example, the physical properties of the borehole, such as wrinkling and ellipticity, can be related to the mechanical properties of the rock mass and to the efficiency of the drilling operation. Knowledge of the properties of the rock mass is extremely useful when specifying later completion activities, such as possible fracturing and also perforation programs. As yet another example, knowledge of wellbore conditions can often be used to increase the efficiency of the wellbore drilling operation, such as modification of drilling parameters to increase bit penetration rates. The prior art has traditionally considered borehole parameters as sources of error or "noise" in desired formation measurements. Efforts to quantify borehole parameters have generally been pursued only to the extent necessary to obtain reasonable corrections to the formation parameters that have been considered the "signal".

4. Quantification of errors

Errors in resistivity or other electromagnetic properties of the formation, near-borehole and borehole parameters can arise from many sources. As previously discussed, instrument calibration is a major source of error in previously known devices. Algorithms or "models" used to transform raw amplitude attenuation and/or phase shift patterns into the desired information and borehole parameters of interest may also introduce errors at certain borehole and formation conditions. Errors of both types can only be properly compensated for if the error is first clearly identified and quantified. Previously known systems have not been aimed at identifying and quantifying errors, particularly in real time. Failure analysis, if performed at all, is usually performed by the analyst long after the well has been logged.

5. Additional sources of error

In addition to the above sources of error, fundamental problems exist when converting measurements of resistivity to measurements of hydrocarbon saturation. As previously mentioned, formation resistivity has historically been the primary parameter of interest in MWD and wireline logging, as it is used to delineate hydrocarbons from salt water. Resistivity measurements cannot be used to delineate hydrocarbons from relatively fresh bodies of water due to the lack of contrast in the resistivities of the two fluids. Hydrocarbon and water, whether salt water or fresh water, exhibit different dielectric constants. A simultaneous measurement of formation dielectric constant and formation resistivity has been used in wireline logging to distinguish between hydrocarbon and water-saturated (freshwater or saltwater-saturated) formations. However, this technique has not been used in MWD logs.

Summary of the invention

The invention is directed to the measurement or "logging" of electromagnetic properties of an earth formation penetrated by a borehole. Electromagnetic wave propagation techniques are used to determine parameters of interest to the formation and the borehole in the vicinity of a downhole instrument. The downhole instrument contains one or more transmitter-receiver pairs operating at one or more frequencies. The borehole instrument is preferably transported along the borehole using a drill string. The invention is therefore primarily aimed at MWD operations, but is also applicable to cable logging. Measurements of amplitude attenuation and phase shift are preferably transferred to the surface for processing and transformation into parameters of interest using a model of the logging instrument's response and a suitable calculation device. Alternatively, the transformation of the amplitude and phase measurements can be carried out with a processing device that is contained in the borehole instruments, and the parameters of interest are transferred to the surface, or stored in the borehole instrument for later retrieval at the surface.

An object of the invention is to provide a logging system which provides accurate and precise measurements of amplitude attenuation and phase shift of electromagnetic radiation which is induced in the formation by means of the borehole instrument's transmitter elements. This in turn results in more accurate and precise formation and borehole parameters of interest which are calculated from the basic amplitude and phase measurements using the instrument response model. More specifically, the downhole instrument uses a digital circuit that minimizes errors arising from the thermal operation of the system's electronics. In addition, calibration of the system before, during and after logging is improved, so that equipment-related errors are further reduced. The system also corrects for mutual coupling of receiver antennas in the borehole instrument, thus further reducing systematic error in the basic amplitude and phase measurements, and the parameters of interest calculated from these. These special features in combination are not offered in previously known systems.

Another object of the invention is the reduction of errors in the particular parameters of interest resulting from ambient corrections. Simultaneous or "parallel", rather than serial, data processing methods are used to transform the basic amplitude attenuation and phase shift measurements into formation and borehole parameters of interest. Parallel data processing reduces the propagation of errors associated with the correction of data for individual environmental parameters. Serial processing is used to a large extent in previously known MWD and cable logging systems.

Yet another purpose of the invention is the determination of borehole as well as formation parameters of interest. Such borehole parameters can be used as indicators of the overall efficiency of the drilling programme. In addition, measured borehole parameters, such as borehole wrinkling, caliber and ellipticity, can be used to estimate or calculate mechanical properties of the penetrated formation, which in turn can be used as construction parameters in future well completion programmes. Accurate determinations of borehole parameters result in more accurate and precise correction of formation parameters for ambient borehole conditions. Previous MWD and wireline systems have directed little effort into the specific determination and use of borehole parameters.

Yet another object of the invention is the provision of a device for identifying and quantifying total errors which are linked to parameters of interest. Such determinations can be used both to assign a quality factor to the logged parameters and to serve as an indicator of equipment or instrument response model problems at certain formation and borehole conditions. Such comprehensive fault indication systems are not available in previously known systems.

A further object of the invention is to simultaneously measure the resistivity, the dielectric constant and the porosity of the formation in the vicinity of the borehole. A formation dielectric constant measurement is necessary to delineate hydrocarbon-bearing zones from freshwater-bearing zones or low-salinity water-bearing zones. Simultaneous measurements of resistivity, dielectric constant and porosity are not known to have been carried out with an MWD logging system.

In order to achieve the above stated purposes, a logging device has been provided which includes the features stated in the introduction to claim 1, and which according to the invention is characterized in that it includes a device for determining the radial position in the borehole in which the at least one parameter that can be attributed to the induced primary electromagnetic field is measured.

In order to achieve the stated purposes, a logging method has also been provided which includes the features stated in the introduction to claim 6, and which is characterized by the fact that it includes the step of determining the radial position in the borehole in which at least one parameter can attributed to the induced, primary electromagnetic field, is measured.

Brief description of the drawings

In order that the manner in which the above-mentioned distinctive features, advantages and purposes of the invention are achieved can be understood in more detail, a more detailed description of the invention, which is briefly summarized above, shall be given with reference to the embodiments thereof shown on the attached drawings.

Fig. 1 shows the invention in an embodiment that uses measurement during drilling,

fig. 2 shows a more detailed view of a transmitter, a receiver and a control circuit subassembly of the downhole instrument portion of the system,

fig. 3 shows a block diagram of the sending and receiving systems in the logging-while-drilling device according to the invention,

fig. 4 shows an electrical connection diagram of the receiving circuits in the block diagram of % 3,

fig. 5 shows a block diagram of the numerically controlled oscillators in the block diagram of fig. 3,

fig. 6 shows a block diagram of the digital signal processor in the block diagram of fig. 3,

fig. 7A, 7B and 7C show high-level flow diagram representations of tool operation in accordance with the preferred embodiment of the invention;

fig. 8 shows a high-level flow diagram illustration of a digital calibration operation in accordance with the invention;

fig. 9 shows a graphical representation of amplitude, frequency and phase shift data derived using a digital cabling operation,

fig. 10A, 10B and 10C graphically depict a number of different comparison operations that can be performed using data derived from a digital calibration operation,

fig. 11 shows a simplified block diagram of circuit and data processing components that can be used to measure the unwanted mutual coupling between special antennas,

fig. 12 shows an equivalent electrical circuit for the circuit of fig. 11,

fig. 13 shows a block diagram of the technique for eliminating mutual coupling,

fig. 14 shows a detailed electrical connection diagram of the block diagram of fig. 13,

fig. 15A, 15B, 15C, 16A, 16B and 16C show types of measurements obtained with the circuit of FIG. 14,

fig. 17 shows a flow chart illustration of the technique for elimination of destructive effects of mutual coupling and antenna drift,

fig. 18 illustrates measured amplitude and phase resistivities over a relatively thin formation which is limited by formations with essentially infinite vertical extent,

fig. 19 shows a graphical representation of an algorithm for serial correction of apparent resistivity for the effects of invasion of the drilling fluid,

fig. 20A and 20B show graphical representations of algorithms for serially correcting phase and amplitude resistivity measurements, respectively, for the effects of finite or finite layer thickness,

fig. 21 graphically illustrates the interdependence of apparent phase and amplitude resistivity, true formation resistivity, and instrument-borehole eccentricity for a borehole fluid with a resistivity of 20 ohm-meters,

fig. 22 graphically illustrates the interdependence of apparent phase and amplitude resistivity, true formation resistivity, and instrument-borehole eccentricity for a borehole fluid with a resistivity of 0.2 ohm-meter,

fig. 23 shows logs of apparent resistivity determined at four transmitter frequencies and recorded as a function of depth in a wellbore,

fig. 24 shows logs of apparent dielectric constant determined at four transmitter frequencies and recorded as a function of depth in a wellbore,

fig. 25 illustrates the variation of measured relative dielectric constant and conductivity as a function of transmitter frequency,

fig. 26 shows a graphical presentation of calculated variations in dielectric constant as a function of transmitter frequency, and a comparison of theoretical values with measured values at four different transmitter frequencies,

fig. 27A and 27B illustrate the variation of the real part of effective dielectric constant and the real part of effective formation conductivity as a function of water resistivity, at different formation porosities, and

fig. 28 is a graphical representation showing how amplitude attenuation and phase shift measurements can be used to determine borehole diameter.

Detailed description of the preferred embodiment

The invention used in a MWD environment is illustrated in a very general way in fig. 1. Elements shown in fig. 1, will be described in more detail in later sections of this description. The drill bit 31 is attached to a borehole instrument 36 which in the MWD embodiment is preferably a metallic weight tube which in turn is mounted on the borehole drill string 37. This assembly is shown suspended in a borehole 34 which penetrates the soil formation 32. A device for rotation of the drill string 37 is denoted by the number 40. The drill string 37 and the borehole instrument 36 are axially hollow, so that drilling fluid or "mud" can be pumped down through these and out through ports in the drill bit 31, and returned to the surface via the drill string-borehole annulus which is denoted as 34a. The sludge circulation system, including surface sludge pumps, is not shown. It is well known in the art that the mud provides a means of returning drill bit cuttings to the surface, cools and lubricates the drill bit 31, and provides hydrostatic pressure to capture internal pressures in formations penetrated by the drill bit 31. Four transmitter antenna coils with one or more windings are denoted by the numbers 207, 209, 205 and 203. The axes of the coils coincide with the axis of the borehole instrument 36. The coils are electrically isolated from and slightly recessed in the outer diameter of the collar, and thus constitute integral elements of the collar assembly. Two receiver antenna coils are designated by the numbers 213 and 211. The geometries of these coils are exactly the same as the geometries of the transmitter coils, and these coils also form integral elements of the borehole instrument 36. The transmitter coils are preferably arranged symmetrically on either side of the center point of the receiver coils 213 and 211. Power sources and control circuits for the transmitters and receivers are schematically indicated as a subassembly 201 in the downhole instrument 36 for purposes of description. In the embodiment of the invention as an MWD device, the control circuits are preferably located inside pressure- and fluid-tight spaces within the wall of the borehole instrument 36 which is preferably a weight tube. Data recorded by the receivers can either be transmitted in real time to the surface using a drilling fluid pulsing device (not shown), or can alternatively be recorded with a recording device (not shown) down the borehole, for later retrieval. For the real-time data transmission embodiment, signals are transmitted from the receivers to the surface by means of a track device generically designated 46, transmitted to a processing unit (CPU) 42 for processing, and correlated with depths from a reed depth indicator 43, and output to a recording unit 44 which displays the calculated parameters of interest as a function of depth at which the input measurements were taken. are measured by the receiver elements, to formation and borehole parameters of interest. The model is preferably derived from theoretical calculations of the response of the transmitter-receiver pairs, and also derived from measured responses of the transmitter-receiver pairs at known test formation and test borehole conditions. The model can alternatively be stored in a storage (not shown) in the CPU unit 42. An alternative embodiment of the invention comprises a processor unit (not shown), with a response model stored therein, which is mounted in the neck tube 36 to perform data processing down in the borehole. Storage capacity is usually limited in MWD wellbore arrangements. For the most efficient utilization of storage capacity, it is often desirable to process measured data down the borehole and store processed results instead of the more voluminous, measured data.

Various elements, special features and methods according to the invention shall be described in more detail in the following paragraphs. It must be borne in mind that although the preferred embodiment of the invention is MWD logging, the invention can alternatively be realized for wireline logging or any logging operation that involves transporting a measuring instrument along a borehole.

1. The borehole instrument

The borehole logging instrument 36, preferably a weight tube, comprising the transmitter-receiver coil arrangement, is shown in more detail in FIG. 2. The two receiver coils are denoted by the numbers 213 and 211. The transmitter coils 207 and 209 are separated in the longitudinal direction by respective distances 23 and 21 from the center point 25 between the receiver coils 213 and 211. The transmitter coils 205 and 203 are likewise separated in the longitudinal direction by respective distances 23 and 21 from the center point 25. Power sources and control circuits for the transmitters and receivers are again shown schematically as a subsection 201 of the borehole instrument 36.1 the preferred embodiment is the circuit arrangement, which will be described in more detail in the next section, contained in pressure and fluid-tight spaces within the borehole instrument 36 wall. The pattern with symmetrical distance between the transmitters and the receivers about a point 25 in the middle between the receivers 213 and 211 is preferred, but is not a necessary condition for the embodiment according to the invention.

1.1 Sending and receiving systems

Fig. 3 shows a block diagram of the logging instrument or logging "tool" 36 shown as an example, with the subassembly 201, which is shown in fig. 2 and constructed in accordance with the invention. The logging tool subassembly 201 comprises upper transmitters 203, 205, lower transmitters 207, 209 and intermediate series resonant receiver antennas 211, 213. A central processor 215 is preferably a microprocessor device which is used to coordinate the operation of the components in the logging tool 36 and the subassembly 201, in order to record and process the data obtained from measurements carried out by the intermediate series resonance receiver antennas 211, 213, and to interface with a sludge pulse telemetry data transmission system (not shown) preferably carried in the adjacent neck tube portion. A processor 217 is arranged and adapted for controlling a numerically controlled oscillator 223. A processor 219 is arranged and adapted for controlling a numerically controlled oscillator 225. The central processor 215 communicates with the processors 217, 219 via respective data buses 241 and 243. The numerically controlled oscillators 223, 225 are adapted to receive a binary command signal as an input signal, and to produce an analog output signal having particular frequency, phase and amplitude characteristics. The frequency, phase and amplitude characteristics are determined at least in part by the command signals supplied from the processor 217,219 to the input of the numerically controlled oscillators 223,225, and the data contained in various registers of the numerically controlled oscillators 223,225. The numerically controlled oscillators 223, 225 provide the analogue signal to transmitter circuits 227 and 229. The components that make up the transmission circuits 227,229 shall be described in more detail in connection with a technique according to the invention for quantifying the unwanted, mutual magnetic field coupling between special antennas.

The receiving antennas 211, 213 communicate via an analog receiving circuit 231 with the first and second data input channels of a digital signal processor 221. The digital signal processor 221 receives data on the first and second inputs after they have been converted from analog form to digital form by analog/digital- converters 220, 222, and records the data items in a circular storage buffer. The central processor 215 extracts data from the buffers in a prescribed and predetermined manner to sample the current generated in the receiving antennas 211, 213 in response to the propagation of the electromagnetic signal through the adjacent formation. As is conventional, the resistivity of the formation surrounding the logging tool 36 and the subassembly 201 can be determined either (1) by determining the amplitude attenuation of an electromagnetic wave propagating through the formation adjacent to the receiving antenna 211 and the receiving antenna 213, or (2) by determining the phase shift between the electromagnetic signal propagating through the formation adjacent to the receiver antenna 211 and the receiver antenna 213, or from both. These measurements include a relative measurement of the amplitude attenuation and a relative measurement of the phase shift.

The present invention also allows other techniques for quantifying the electromagnetic field that propagates through the formation surrounding the logging tool 36. Since precise control can be achieved with the invention over the frequency, phase and amplitude of the electromagnetic wave generated by the transmitter antennas 203, 205, 207 and 209, the invention allows measurement of the absolute amplitude attenuation of an electromagnetic signal between any particular transmitting antenna 203, 205, 207 and 209 and any receiving antenna 211, 213. Furthermore, the logging tool 36 according to the invention allows absolute measurement of the phase shift of an electromagnetic signal between any particular transmitting antenna 203, 205, 207, 209 and any particular receiving antenna 211, 213. Prior art devices do not allow such optional techniques for determining amplitude attenuation and phase shift, as prior art devices are unable to readily and accurately determine the frequency, phase and amplitude of a signal generated at any particular transmitting antenna.

The operation of the numerically controlled clock oscillators 223,225 is controlled by the output signal from a reference clock or reference clock unit 237 which is preferably at 12 MHz. The operation of the receiving circuit 231 is controlled by the output signal from a numerically controlled oscillator 233 which is also clocked by the output signal from the reference clock unit 237, which is 12 MHz. Thus, a clock pulse is provided to the numerically controlled oscillators 223, 225 with a frequency that is identical to that provided to the numerically controlled oscillator 233 which establishes the operating frequency for the receiving circuit 231. The digital signal processor 221 is clocked by the output signal from a dividing circuit 239, and thus samples the output signal from the receiving circuit 231 with a particular frequency which is much smaller than that used to energize the transmitting antennas 203,205,207 and 209.

The numerically controlled oscillator 233 produces a phase-locked sine wave signal with a center frequency of 1.995 MHz which is used as a local oscillator signal by a receiving circuit (not shown) which is located in the wall of the logging tool 36.

Reference is now made to fig. 4. The overall function of the circuit shown in block diagram and connection diagram form in fig. 4, is to respond to the local oscillator signal and one of the two receiver coil output signals to produce a receiver phase output signal relative to the transmitter and a receiver amplitude output signal. A conventional preamplifier circuit generally shown at 271 is responsive to the receiver capture signal and its output is applied to a mixer circuit arrangement generally shown at 273. The mixer circuit arrangement 273 includes an integrated circuit 275 conveniently implemented by an integrated circuit manufactured and sold by Motorola and other companies under the designation MC 1596.

Because the frequency of the pickup signal and the local oscillator signals are phase-locked to a common frequency reference and differ by 6 kHz, the intermediate frequency (EF) produced by the mixer circuit arrangement 273 is 6 kHz. A bandpass tuning circuit arrangement generally shown at 277 passes through the 6 kHz intermediate frequency signal to an amplifier circuit arrangement generally shown at 279. An active bandpass filter circuit arrangement generally shown at 281 provides additional bandpass filtering and provides a signal to an analog/digital converter which supplies a digital input signal to a particular input channel of the digital signal processor 221 (in Fig. 3).

Fig. 5 shows a block diagram of the numerically controlled oscillators 223, 225, 233 in fig.

3. As the numerically controlled oscillators are identical, only the numerical oscillator 223 shall be mentioned and described. In the preferred embodiment of the invention, the numerically controlled oscillator 223 comprises a CMOS, DDS modulator manufactured by Analog Devices, Norwood, Massachusetts, USA, and identified as Model No. AD7008. The numerically controlled oscillator 223 comprises a 32-bit phase accumulator 301, a sine and cosine look-up table 303 and a 10-bit digital to analog converter 305. A clock input 307 is provided to receive a clock signal from a device external to it numerically controlled oscillator 223. The particular numerically controlled oscillator of the invention is adapted to accept clock rates as high as 20 to 50 MHz, but is adaptable to much lower clock rates. The device is claimed to have a frequency accuracy that can be controlled to one part in four billion. The numerically controlled oscillator 223 comprises a 32-bit serial register 309 which receives serial data on a serial data input pin 311, which data is clocked into the register in accordance with a clock signal supplied to a serial clock input 313. There is also arranged a 32-bit parallel register 313 which receives parallel binary data from an MPU interface 315. A data bus 317 comprises sixteen digital input pins identified as DO to D15. The chip select pin 321 is used when writing to the parallel register 313. The write pin 319 is also used when writing to the parallel register 309. The transfer control address bus 323 is used to determine the source and destination registers used during a transfer. A source register can be either the parallel assembly register 313 or the series assembly register 309. The destination register can be any of the following registers, namely the command register 325, the FREQ.O register 327, the FREQ.1 register 329, the phase register 331 or the IQMOD. register 333. The command register is only assigned via the parallel assembly register 313. The contents of the command register determine the operating state of the numerically controlled oscillator 223. In the preferred arrangement used in the present invention, the command register is a 4-bit register. Table 1 provides an overview of the possible operating states of the numerically controlled oscillator 223 which is used in the present invention. During logging operations, the logging device according to the invention is programmed to provide commands from the processors 215, 217, 219 (in Fig. 3) with 8-bit commands, and the "CR0" bit is thus 0. Normal operation is desired, and the "CRl^ bit is thus 0. In the present invention, amplitude modulation is bypassed, and the "CR2" bit is thus 0. In the present invention, the synchronizer logic is activated, and the "CR3" bit is thus 0. The FREQ.O register 327 defines the output frequency from the numerically controlled oscillator 223, when the F select pin is 1, as a fraction of the frequency of the clock signal applied to the clock pin 307. The FREQ.1 register 329 defines the output frequency of the numerically controlled oscillator 223, when the F select pin is equal to 1, as a frequency of the clock signal which is supplied to the clock pin 307. The content of the phase register 331 is added to the output signal from the phase accumulator 301. The IQMOD. register 333 is not used in the present invention.

The operations that can be performed with the registers by applying command signals to the transfer control address bus 323 are tabulated in Tables 2 and 3. Three basic operations can be performed. The contents of the parallel assembly register 313 can be transferred to the command register 325; the contents of the parallel assembly register may be transferred to a selected destination register, in accordance with the destinations identified in Table 3, and the contents of the serial assembly register 309 may be transferred to a selected destination register.

The load register pin 335 is used in connection with the transfer control address bus 323 to control the loading of internal registers from either the parallel or serial assembly registers 309, 313. The test pin 337 is used only for factory testing. The reset pin 339 is used to reset the registers. The reset pin is used specifically to clear the command register 325 and all modulation registers to 0. The current output pins 341, 343 are used to supply an alternating current to a selected final device. In the particular embodiment according to the invention, only one of these outputs is used for a special transmitter antenna, as one current is the complement of the other current. The compensation pin 342 is used to compensate for the internal reference amplifier. The voltage reference pin 343 can be used to override an internal voltage reference, if desired. The full-scale adjustment pin 345 determines the magnitude of the full-scale current on the output pins 341, 343. The ground pin 347 provides a ground reference, while the positive power supply pin provides power for the analog components of the numerically controlled oscillator 323. The frequency select pin 351 controls the frequency registers FREQ. The O register 327 and the FREQUENCY register 329, by determining which register is used in the phase accumulator 301, with the help of the controlling multiplexer 353. The contents of the phase register 331 are added to the output of the phase accumulator 301 in an adder 355. The IQMOD. registers 333 is arranged to allow either quadrature amplitude modulation or amplitude modulation, and the sine and cosine output signals from the lookup table 303 are thus added together in an adder 357, and are unaffected by the IQMOD. registers 333. The output signal from the adder 357 is provided to a digital/ analog converter 305 which produces an analog signal with a frequency in response is to either the contents of the FREQ.O register 327 or the FREQ.1 register 329, a phase determined by the output of the adder 355 supplied as an input to the lookup table 303, and an amplitude determined by the full-scale control 359 which is set by the full-scale adjustment pin 345 and the reference voltage pin 343. The numerically controlled oscillator of FIG. 5 can therefore provide an analogue output signal with a precise frequency characteristic, phase characteristic and amplitude characteristic. As the device is extremely accurate, it is possible to provide a drive current for the transmitter antennas 203, 205, 207, 209 in fig. 3 which is precisely controlled. In the preferred embodiment of the invention, one of the transmitter antennas 203, 205 is operated at 400 kHz, while the other of the transmitter antennas 203, 205 is operated at 2 MHz. The same applies to the antennas 207, 209, as one is operated at 400 kHz and the other is operated at 2 MHz. However, the processors 215, 217, 219 can be programmed to provide any particular frequencies for the transmitter antennas. This will be used to good advantage, as will be described below in connection with a calibration routine.

During operation, a command signal is applied to the F select pin 351 to determine which frequency will be used for energizing a particular transmitter antenna. The FREQ.O register 327 and the FREQ.1 register 329 may be preloaded with two particular frequencies (such as 400 kHz and 2 MHz). The binary signal applied to the F select pin 351 determines the operation of the multiplexer 353 which supplies the contents of either the FREQ.O register 327 or the FREQ.1 register 329 to the input of the phase accumulator 301. The phase accumulator 301 accumulates a phase step for each clock cycle or beat period. The value of the phase step determines how many clock periods are necessary for the phase accumulator to count 2 5 radians, i.e. one period of the output frequency. The output frequency is determined by the phase step multiplied by the frequency of the signal applied to the clock input pin 307, divided by 2<32>. In practice, the phase accumulator 301 is emptied and then loaded with the output signal from the multiplexer 353. A predefined time interval is then allowed to pass, during which the signal applied to the clock input pin 307 advances the output signal from the phase accumulator 301 through an incrementally increasing phase for that particular frequency. In other words, the phase accumulator steps forward from 0° phase to 180° for a particular frequency. At any time, the output signal from the phase accumulator 301 can be changed with a phase shift supplied by the phase register 331. The phase register 331 can be loaded in response to commands from the processors 215, 217, 219. The phase value is supplied as an input signal to the look-up table 303 which transforms the output signal from the phase accumulator 301 (and a any desired offset) into a digital bit stream that is representative of an analog signal. This digital bit stream is supplied as an input signal to the 10-bit digital/analog converter 305 which also receives amplitude information from the full-scale control 359. The digital/analog converter 305 supplies an analog output signal with a particular frequency characteristic, phase characteristic and amplitude characteristic. For example, an output signal of 2 MHz, with a phase of 15° and a particular peak amplitude current can be provided as the input signal to a particular transmitting antenna.

Fig. 6 shows a block diagram of the digital signal processor 221 of Fig. 3. In the preferred embodiment of the invention, the digital signal processor 221 comprises a DSP microcomputer manufactured by Analog Devices, Norwood, Massachusetts, USA, which is identified as Model No. ADSP-2101. This is a single-chip microcomputer used for high-speed numerical processing applications. Its base construction 379 is a fully compatible superset of the ADSP-2100 instruction set. The basic construction includes three independent calculation units, namely a shifter 371, a multiplier/accumulator (MAC) 373, and an arithmetic and logic unit (ALU) 375. A program sequencer 369 supports a variety of operations, including conditional jumps, subroutine calls, and returns in during a single cycle. A data address generator 367 comprises two address generators. The digital signal processor 221 comprises a serial port 381 which contains two input channels, namely an input channel 383 and an input channel 385. A clock register 387 provides clock signals for the data processing operation, and receives as an input signal a clock signal from the dividing circuit 239 (in Fig. 3). An external address bus 389 and an external data bus 391 allow digital communication between the digital signal processor 221 and the central processor 215 of FIG. 3. A store 393 contains a program store 395 and a data store 397. As is typical with digital signal processors, the data store 397 defines at least two circular buffers which are associated with the serial ports 383, 385 and which are designed to receive asynchronous digital data and store these indefinitely or in a predetermined time interval. The digital signal processor 221 receives digital input signals on channel inputs 383, 385 from an analog/digital converter, as shown in the circuit of FIG. 4. The receiving circuit in fig. 4 receives a current representative of the response of a special receiving antenna 211, 213 to electromagnetic radiation propagating through the borehole. This electrical signal is processed via the circuit components in fig. 4 and is provided as an input signal to the digital signal processor 221. In the preferred embodiment of the invention, the receiving antenna 211 is identified with a special input channel in the digital processor 221, while the receiving antenna 213 is identified with the second input channel in the digital signal processor 221. The central processor 215 (in fig. 3) utilizes the external address bus 389 and the external data bus 391 to address a particular input channel and read digital data into the central processor 215 for processing. In the preferred embodiment of the invention, the digital signal processor 221 can sample data from the receiving antenna ncnc 211,213 at a very high sampling rate which can be read periodically by the central processor 215 which processes the data to determine the amplitude attenuation and phase shift of the electromagnetic signal propagating through the borehole. One particular routine for calculating amplitude attenuation and phase shift is set forth in more detail below, in connection with a discussion of the error cancellation feature of the invention. As a rough overview, the central processor 215 can extract a selected amount of data from each channel in the digital signal processor 221, and from this data calculate the amplitude attenuation and phase shift of the electromagnetic wave as it propagates through the borehole and past the receiving antenna 211 and the receiving antenna 213.1 the preferred embodiment of the invention sends an upper transmitter an interrogating electromagnetic signal with a particular frequency which propagates downwards past the receiving antennas 211, 213. A particular one of the lower transmitting antennas 207, 209 then emits an interrogating electromagnetic signal upwards . Measurements from the receiving circuit 231 are stored in the input channels of the digital signal processor 221 and read by the central processor 215 in a way that allows calculation of amplitude attenuation and phase shift.

Another important feature of the invention arises from the fact that a precise energizing current can be utilized to energize a particular one of the transmitter antennas 203, 205, 207, 209. This will establish the frequency characteristic, the phase characteristic and the amplitude characteristic of the electromagnetic interrogation signal. A single receiving antenna can therefore be used to measure the electromagnetic interrogation signal when it passes through the borehole. The amplitude and phase of this interrogation signal can be recorded in a store, and compared with values in the store for the energizing current. This allows a single receiving antenna to be used to provide an accurate measurement of the amplitude attenuation between this particular receiving antenna and the particular transmitting antenna, and the phase shift of the spread signal between the transmitting antenna and the receiving antenna. The amplitude attenuation and phase shift of the electromagnetic interrogation signal as it passes through the formation is of course an indication of the resistivity of the borehole and the surrounding formation. Figures 7A, 7B and 7C show high-level flow diagram representations of logging operations performed in accordance with the preferred embodiment of the invention. Fig. 7A depicts logical steps performed by central processor 215. Fig. 7B depicts operations controlled by processors 217, 219. Fig. 7C depicts operations controlled by digital signal processor 221 and central processor 215. Transmit operations begin in a block 401. The processor 215 performs a calibration operation on the receiving antennas 211, 213, as will be described in more detail elsewhere in the description. After the calibration operations have been carried out, the central processor 215 instructs the processor 217 to energize the transmitter antenna 203 with a 400 kHz current. Then, in accordance with a block 407, the central processor 215 instructs the processor 219 to energize the transmitter antenna 209 with a 400 kHz current. Next, the central processor 215 instructs the processor 217 to energize the transmitting antenna 205 with a 2 MHz kHz current, in accordance with a block 409. Then, in accordance with a block 411, the central processor 215 instructs the processor 219 to energize the transmitting antenna 207 with a 2 MHz current. The process stops at a block 413. In actual practice, the send operations will be performed continuously over predetermined intervals. Fig. 7B depicts the control operations performed by the processors 217, 219 to cause the numerically controlled oscillators 223, 225 to energize particular transmitters. The process begins in a block 415. It continues in a block 417 where the processor 217 or 219 clears the registers in the numerically controlled oscillators (NSO) 223 or 225 by providing the appropriate instruction. Then, in accordance with a block 419, the processor 217 or 219 loads a predetermined value into the FREQ.O register and the FREQ.1 register. These values determine the frequency of the energy separation current that is supplied to a particular transmitting antenna. Then, in accordance with a block 421, the processor 217 or 219 loads a predetermined phase value into the phase register of the numerically controlled oscillator 223 or 225. The processor 217 or 219 then provides a binary command to the F select input pin of the numerically controlled oscillator 223 or 225 to select a particular operating frequency. Then, in accordance with a block 425, a particular time interval is allowed to pass. This time interval determines how many periods of energy separation current are supplied to a particular transmitting antenna. The process ends in a software block 427. Each time the processor 217 or 219 is instructed by the central processor 215 to energize a particular transmitter antenna, the steps of FIG. 7B. Fig. 7C presents the receiving operations in flowchart form. The process begins in a block 429. The process continues in a block 431 where the current in the receiving antennas 211,

213 are sampled by the receiving circuit 231. Then, in accordance with a block 431, these samples are loaded to the appropriate input channels 283, 285 of the digital signal processor (DSP) 221.1 in accordance with a block 435, the central processor 215 retrieves selected samples from the storage buffers that are linked to the digital signal processor's input channels. In accordance with a block 437, the sampler may optionally be modified to compensate for error components due to "miscalibration" of the antenna, which will be further described elsewhere in the specification. Then, in accordance with a software block 439, the digital samples may be digitally filtered with either a digital low-pass filter, a digital high-pass filter, or a digital band-pass filter. Alternatively, one can average the samples over pre-defined intervals to provide stability to the samples and eliminate the influence of spurious or erroneous samples. Then, in accordance with a block 441, the amplitude attenuation and phase shift are calculated, as described elsewhere in the specification. The process finally ends in a block 443.

1.2 Antenna calibration operations

The invention provides several new calibration features for the receiving antennas. Utilization of microprocessors and numerically controlled oscillators (see Fig. 3) in the invention allows very precise calibration measurements to be made of the sending and receiving of the interrogation signal, either outside the borehole or preferably in the borehole, during logging operations. This is achieved by having a calibration program permanently stored in a store in the processors 217,219, or in the central processor 215, which causes a numerically controlled oscillator to run or sweep through a particular frequency range. This is achieved by continuously providing a command signal from the processors 217, 219 to the numerically controlled oscillators 223, 225, which establishes a frequency for the energizing current supplied to a particular transmitter antenna. In addition, a command from the processors 217, 219 is supplied to the numerically controlled oscillators 223, 225 to determine the phase characteristic of the signal. In practice, the frequency sweep should cover a fairly wide range of frequencies. Normal receive operations are performed while a particular transmitter is swept through a range of frequencies. The data is recorded and provides a combined measure of the response of the transmitting antenna and the receiving antenna.

In the preferred embodiment of the invention, each transmitting antenna coil is swept through a predetermined frequency range, while the receiving antennas are sampled. The result is eight data sets, one for each possible transmitter/receiver combination, which quantify the operating condition of the particular transmitting antenna and the particular receiving antenna. Malfunctions in a particular receiving antenna or transmitting antenna can be determined using comparisons between the eight data sets. Suppose, for example, with reference to FIG. 3, that the transmitter antenna 203 is damaged or out of calibration. The data set that establishes the operating state of the transmitting antenna 203 and the receiving antenna 211 can be compared with the data set that establishes the operating states of the transmitting antenna 203 and the receiving antenna 213, to determine that the transmitting antenna 203, and not a particular receiving antenna, is damaged or out of calibration. The identification of a damaged or uncalibrated antenna is an important diagnostic tool. It can be used during logging operations to exclude one or more of the transmitting or receiving antennas from the normal duty cycle, as soon as it is detected to be damaged, in order to maintain high quality logging information. Alternatively, the calibration data can be used in post-logging operations to modify, interpret or manipulate the logging data to correct for measurement intervals during which a particular transmitter antenna was damaged or fell out of calibration. Fig. 8 provides an eye-level flow chart representation of calibration operations, which is of course set forth in conjunction with the flow charts of Figs. 7A, 7B and 7C. The process begins in a block 445. The process continues in a block 447 where the calibration operation is initiated or initiated by the central processor 215. Then, in accordance with a block 449, a particular transmitting antenna is selected, and in accordance with a block 451, a particular receiving antenna is selected. The calibration operations will be carried out using this special transmitting antenna and this special receiving antenna. The resulting data will provide information about the operating condition of both of these antennas. In accordance with a block 453, an energization sequence is set. This is accomplished by providing an appropriate command to the numerically controlled oscillator 223. Then, in accordance with a block 455, the transmitting antenna is energized. In accordance with a block 457, the receiving antenna is sampled and the data is stored in a store. In a block 459, one or more of the processors determines whether all frequencies have been swept. If this is not the case, the process continues in block 453 where the energization frequency is set again, with a higher frequency than the previous frequency that was used. If, however, it is determined in block 459 that all frequencies have been used, the process ends in a block 461.1 the preferred embodiment is reviewed a particular frequency range in increments of fractions of 1 Hertz. For practical purposes, the calibration operation can be considered to be a sweep through all frequencies within a predetermined frequency range. The data stored in the storage can be analyzed in a manner to be described below, in order to assess the operating condition of the transmitting antenna and the receiving antenna. Fig. 9 provides an illustration of an example of the type of data that can be acquired during a calibration operation. During logging operations, the data will of course not be recorded or presented in graphic form. Instead, a data array or data table will be defined that contains information about the amplitude and phase characteristic of the receiving antenna's response at a particular frequency. The graphic representation in fig. 9 is provided for explanatory purposes. In the drawing in fig. 9, the amplitude of the response of the transmitting and receiving antenna is plotted by a curve 463. In FIG. 9, the phase of the response of the transmitting and receiving antenna is represented by a curve 465. In order to determine when a malfunction occurs, it is necessary that a normal operating condition be established in advance. This must be done with respect to a range of acceptable operating conditions. The graphic representation in fig. 9 illustrates normal operation over a range from 300 kHz to 3.3 MHz. In the drawing in fig. 9, peaks 467, 469, 471, 473 define two resonant frequencies for the transmitting and receiving antennas, with resonance occurring at 400 kHz and 2 MHz, as the particular antennas used to generate this calibration curve were in resonance at both 400 kHz and 2 MHz. Based on the information contained in the measurements carried out when the tool is working normally, parameters can be established to alert about malfunctions. Figures 10A, 10B and 10C graphically depict three techniques for antenna malfunction detection. The first technique for detecting antenna malfunctions is shown in fig. 10A where a peak 475 represents either an amplitude or phase peak for normal operation. In contrast, a peak 477, which is generated as a result of calibration operations during logging, indicates to the operator that a shift in the resonant frequency has occurred. A range of acceptable resonant frequencies can be established. If the measurement falls outside an acceptable range, a determination can be made that either the transmitting antenna or the receiving antenna is malfunctioning. Fig. 10B illustrates another technique for detecting malfunctioning antennas. A peak of 479 represents normal operation, while a peak of 481 represents a measurement made during logging. The antenna's Q value for the real measurement is significantly different from the antenna's Q value for the normal operating condition. A change in the antenna's Q value can thus be used to indicate a malfunction.

1.3 Correction for changes in antenna impedance and mutual antenna coupling

When an interrogation or interrogation signal is received at the receiving antenna, the electrical parameters that quantify the signal, phase and amplitude, are functions of not only the desired signal from the transmitter, but also functions of the antenna impedance. The antenna impedance can change during tool operation as a function of temperature and pressure. As the functional form of this change may not be known in advance, the present invention provides a method for measuring the effects of these functional changes on the desired signal.

Fig. 11 gives an electrical, schematic representation of an equivalent circuit which shows the relationship between antenna impedance and antenna transfer function. This can be used to explain the parameters that affect the impedance of a receiver in a logging tool. In this electrical circuit diagram, the impedance of a receiving circuit is identified as R,. The voltage Emn across the receiver circuit's input represents the receiving antenna's response to the measurement of the propagating electromagnetic field. represents the receiving antenna's impedance as seen from the receiving electronics. The impedance includes Ram which is the receiving antenna's resistive component, Ca which is the receiving antenna's capacitive component, and La which is the receiving antenna's inductive component. This equivalent circuit is mutually magnetically coupled to the steel weight pipe logging tool subassembly R^, the surrounding formation Rfamationj and the transmitter. The subassembly is essentially a resistive component which via the inductive component Lj is mutually coupled to the receiving antenna denoted by the mutual coupling M^. The formation is essentially a resistive component which is magnetically coupled to the receiving antenna through an induction coil Lf via the mutual inductance Maf. The voltage induced in the receiving antenna from the transmitter is the desired signal, and the effect of the formation, subassembly and antenna impedance on the measurement of this voltage are variables that the invention takes into account. The transmitter is essentially a voltage source which is connected to the receiving antenna via an induction coil Lt. The circuit of fig. 11 can be reduced to the circuit shown in fig. 12, with the impedances of the antenna, subassembly, formation, and transmitter represented as Z^em», Zsub, ZfomiIlstion, and Z[, respectively. Et is the equivalent voltage source in the receiver circuit resulting from the transmitter. A current I is induced to flow through this equivalent circuit by means of the voltage source Ef. As shown in fig. 12, a voltage Ehm is developed across the receiving circuit as a result of this current. The combined effect on the antenna of the impedance of the antenna, the neck tube subassembly, the formation and the transmitter is shown in this diagram as Z^. The impedance of the receiving antenna, together with the impedance introduced due to normal operation and unwanted crosstalk, constitutes the impedance Z^, as given below:

The antenna's transmission impedance is expressed as:

This transfer impedance indicates that the total current in the equivalent circuit of fig. 12 is a function of the transmitter antenna's voltage Et, and all the impedances in the circuit in fig. 12.

The current can also be expressed as a function of Ej^, and Rr, as a consequence

The antenna's transmission function can be determined from these relationships in accordance with equation (4):

(4) Transfer function = E/Eim

Combining equation (1) with equation (4) gives:

Note that the transfer function is a simple function of the receiver impedance Rf and the measured antenna input impedance Z^.

In the present invention, the particular technique used to measure Ziim is a conventional "network analysis method". In accordance with this technique, a reflection coefficient p is obtained by measuring the ratio between an incident wave and the reflected wave. A directional coupler or bridge is typically used to detect the reflected signal, and a network analyzer is used to supply and measure the signals. With the present invention, the numerically controlled oscillator can function as a network analyzer, as its output signal properties (frequency, phase and amplitude) can be precisely controlled, and then further the real output signal is measured over a predetermined frequency interval. Directional couplers are devices used to separate or sample the traveling electromagnetic wave traveling in one direction on a transmission line, while remaining virtually unaffected by the traveling electromagnetic wave traveling in the opposite direction. They are thus typically used when analyzing power transmission lines and the like. They are often used in combination with power splitters that receive an input signal and provide two equal output signals. In the present invention, both directional couplers and power splitters are used to derive the measurements used in the elimination of the unwanted effects of mutual coupling between receiving antennas.

The reflection coefficient is derived from the voltage of the signal reflected from the antenna, and the voltage of the signal entering the antenna, in accordance with the following equation: (6) p = reflection coefficient = (voltage of signal reflected from the antenna)/(voltage of signal which goes into the antenna)

Furthermore, the antenna's impedance can be derived from the reflection coefficient and the directional coupler's impedance Zo in accordance with equation (7) as follows:

Equations (5) and (7) can be combined to determine the transfer function FVEm expressed in terms of Rr (the impedance of the receiver circuit, which is known), Zo (the impedance of the directional coupler, which is also known), and p (the reflection coefficient, which can be calculated from a measurement of the incident signal and a measurement of the reflected signal) as stated in equation (8):

From this transfer function, the voltage induced in the receiving antenna by the transmitter, E,, can be determined by simply multiplying the receiver voltage by the transfer function: E, = Emx(Et/Em) corrected using Zantenna, Zsub and Zt.

Fig. 13 shows a block diagram of the components that act alternately in the measurement process to eliminate the influence of unwanted mutual magnetic field coupling between receiving antennas. Fig. 14 shows a more detailed view of the components that work together to make this analysis possible.

As reference is first made to fig. 13, a directional coupler 501, a directional coupler 503 and a numerically controlled oscillator 509 are specifically arranged to take into account the measurements that can be utilized to eliminate the effects of unwanted mutual magnetic field coupling between the receiving antennas 211, 213. As will be described in connection with fig. 14, directional couplers 501, 503 are connected in and out of the circuit, depending on whether normal receiving operations are desired, or whether an operation for calibration of mutual coupling is required. Receiver circuits 505, 507 are identical to the receiver circuit shown in fig. 4 and described above. This receiver circuit has a characteristic resistance R, for the receiver 505 and Rr for the receiver 507. These resistance values are approx. 50 ohms. The directional coupler 501 in fig. 14 provides at least 60 dB isolation between forward and backward traveling signals. The receiving antennas 211, 213 have an effective impedance of Zim which can change with temperature and pressure. The digital signal processor (DSP) 221 generates, or outputs, commands to the numerically controlled oscillator (NSO) 509 to provide an energizing signal that can be routed through either the directional coupler 501 to the receiving antenna 211, or through the directional coupler 503 to the receiving antenna 213. A certain portion of the energizing signal is received by the receiving antenna 211 or 213, and a part is reflected back, through the directional coupler 501 to the receiver 505 or through the directional coupler 503 to the receiver 507. The reflected signals are processed by the digital signal processor 221 and transmitted to the central processor 215. The digital signal processor 221 can simply provide a circular storage buffer for the storage of data which is then retrieved periodically by the central processor 215 for further processing. This activity is represented by the "data out" bus in fig. 13. In the preferred embodiment of the invention, each of the receiving antennas 211,213 is analyzed separately.

As a general overview, the technique of correcting a measurement made with a special receiving antenna, for the (destructive) error component due to unwanted mutual magnetic field coupling, is carried out in the present invention by making the following measurements over a pre-defined frequency interval (such as 100 Hz to 6 MHz): Direct an energy separation signal to a special receiving antenna, and measure with precision the amplitude and phase characteristics of the incident wave, measure with precision the reflected wave reflected away from the receiving antenna and back through a directional coupler; calculate the reflection coefficient p from the measurements of the incident wave and the reflected wave; use the calculated value of the reflection coefficient p and the known impedance Z0 of the directional coupler to calculate the input impedance Zinn for the particular receiving antenna; use Zitm and the known (or fixed) impedance Rr of the receiver circuit to calculate the transfer function for this particular antenna. Note that this determination is performed for all operating frequencies of interest. With particular regard to the preferred embodiment of the invention, it will be necessary to carry out measurements for 400 kHz and for 2 MHz, as these are the two operating frequencies used during logging operations. Note that the transfer function, in accordance with equation (5), provides a measure of the ratio between the voltage generated in the receiving antenna as a consequence of an interrogating electromagnetic signal (Et), and the voltage detected at the input of the receiving circuit (Emn) . In other words, the transfer function at a particular frequency is equal to E/Emn. This transfer function can be applied to measurements made during logging operations, to eliminate the influence of the decay in the detected voltage (Ej^) due to mutual magnetic field coupling and thermal (and other) drifts in antenna response. This correction can be achieved by simply multiplying a detected signal (Em,,) by the transfer function value of the receiving antenna at the interrogation frequency that senses the interrogation signal. In this way, the measurement is corrected to provide an uncorrupted signal Et for further processing. In the preferred embodiment of the invention, the mathematical operations which eliminate the destructive effect of the unwanted mutual magnetic field coupling occur in either the digital signal processor 221 or the central processor 215.

For each measurement carried out by the receiving antenna 211, in other words, the digital signal processor 221 (or the central processor 215) automatically retrieves a value that is registered in the storage for the receiving antenna 211's transfer function at the particular frequency of the interrogation signal used. The measurement carried out using the receiving antenna 211 is multiplied by the transfer function value. The resulting product is a measurement value that has been corrected for the destructive effect of unwanted mutual magnetic field coupling between the receiving antenna 211 and the receiving antenna 213. Conversely, when the receiving antenna 213 is used to measure an interrogating electromagnetic field, the digital signal processor 221 (or the central processor 215 ) the transfer function value for the particular frequency of the interrogation field, and then multiplies this value by the measurement obtained from the receiving antenna 213. The product is the measurement obtained with the receiving antenna 213 and which has been corrected for the destructive effect of unwanted mutual magnetic field coupling between the receiving antenna 213 and the receiving antenna 211. The operational details are given below in the description in connection with fig. 14.

Referring now to fig. 14, the receiving antenna 211 is shown to be optionally connected via the directional coupler 501 to the receiver circuit 505 and the digital signal processor 221. The receiving antenna 213 is also shown to be optionally connected via the directional coupler 503 to the receiving circuit 507 and the digital signal processor 221. The receiving antennas 211, 213 are optionally connected to the output of the numerically controlled oscillator 509 via power splitters 519, 521 and 523. Attenuators 511, 513, 515 and 517 are provided at selected locations in the circuit for load balancing purposes. Each damping element preferably provides a load of 60 dB. In the circuit of fig. 14, four switches are arranged, namely a switch Sl, a switch S2, a switch S3 and a switch S4. Each of these switches is under the control of the digital signal processor 221 and/or the central processor 215 (in Fig. 3). The switches Sl, S3 are three-position switches, while the switches S2, S4 are two-position switches. Each switch is under the binary control of a particular output pin of the digital signal processor 221. Changes in the binary state of the output pin of the digital signal processor 221 will toggle or toggle switches S2, S4 between open and closed positions, while switches Sl, S3 toggle between the three positions.

Fig. 14 shall now be used to describe six basic measurement operations which form the basis for and allow the technique according to the invention with the elimination of the undesirable effects of mutual magnetic field coupling between receiving antennas and phase shift due to high borehole temperatures or borehole pressures.

Step 1: In this step, switch Sl is set to position no. 2, switch S2 is closed, switch S3 is set to position no. 1, and switch S4 is left open. The numerically controlled oscillator 509 is coupled to the receiving antenna 213 via switch S2 to allow a propagating electromagnetic wave to pass between the receiving antenna 213 and the receiving antenna 211. In this particular configuration, the receiver circuit 507 is also coupled to receive and monitor the output signal from the numerically controlled oscillator 509 via the power splitter 523 and the impedance 513 while the receiving antenna 213 is energized. The receiving circuit 505 is also connected to monitor the signal coming from the receiving antenna 211 in response to the electromagnetic wave traveling from the receiving antenna 213 to the receiving antenna 211.

Step 2: This step is performed simultaneously with Step 1. The receiving circuit 505 is connected via the switch S3 to the receiving antenna 211, and monitors the response of the receiving antenna 211 to the propagating electromagnetic wave generated in the receiving antenna 213 (working as a transmitter) and received in the receiving antenna 211 (working as recipient). In Step 2, all switch positions are identical to the positions in Step 1.

The result of this simultaneous performance of these operations is that channel 1 of the digital signal processor 221 records data from the receiving antenna 211 via the receiver circuit 505, while channel 2 of the digital signal processor 221 records the output signal from the numerically controlled oscillator 509 via the receiver circuit 507.1 the preferred embodiment of the invention the numerically controlled oscillator 509 is commanded by the digital signal processor 221 to cycle through a predetermined range of frequencies. The data collected on channel 1 and channel 2 of the digital signal processor 221 thus define two data sets, namely one that records the energizing signals supplied to the receiving antenna 213 (the "incident signal"), which is operated as a transmitter, and another that records the response of the receiving antenna 211 to the energizing signal.

Fig. 15A provides a graphical representation of data recorded on channel 2 of the digital signal processor 221, a curve 601 providing an outline of the amplitude of the output signal from the numerically controlled oscillator over the predefined frequency range from fi to f2, and a curve 603 provides a record of the phase characteristics of the output signal from the numerically controlled oscillator 509 for the frequency range from f] to f2. Together, these amplitude and phase values provide a measure of the "incident signal". Fig. 15B provides an example of the type of data that can be recorded on channel 1 of the digital signal processor 221, a curve 605 representing the amplitude response of the receiving antenna 211 to the energizing electromagnetic wave provided by the receiving antenna 213, over the predefined range of frequencies from fi to f2, and as a curve 607 provides information about the phase response of the receiving antenna 211 over the same range of frequencies. The information contained in fig. 15B, similar to that contained in FIG. 9, but provides information about the operating state of the receiving antennas 211, 213. The type of data analysis discussed above in connection with fig. 9, 10A, 10B and 10C, can be performed on the receiver-to-receiver profile. In other words, the signal recorded on channel 1 provides a measure of the combined response of the receiving antenna 211 (operating as a transmitter) and the receiving antenna 213 (operating as a receiver) in combination with the effect of the borehole and formation on the signal transmission. Data sets can be produced for transmission in one direction (with the receiving antenna 213 working as a transmitter and the receiving antenna 211 working as a receiver) as well as in the other direction (with the receiving antenna 211 working as a transmitter and the receiving antenna 213 working as a receiver). The data sets compiled for these operations can be compared with profiles developed in the laboratory for normal operation. Changes or shifts in resonant frequency, antenna Q value, or response amplitude at a particular frequency can provide important information about whether the receiving antennas 211,213 are working as desired, or whether they are damaged or out of calibration.

Step 3: In this step, the switch Sl is set to position 3, and the switch S2 is closed. The positions of switch S3 and switch S4 are open and are immaterial for this operation. In this operation, the numerically controlled oscillator 509 directs an interrogation signal via the power splitter 519, the power splitter 523 and the switch S2 towards the directional coupler 503 and the receiving antenna 213. A part of the energizing signal is received by the receiving antenna 213 and represents the "incident signal", while a part is rejected by the receiving antenna 213 and represents the "reflected signal". The reflected signal is directed via the attenuator 511 and the switch Sl to the receiver circuit 507. The numerically controlled oscillator 509 is preferably stepped through a predetermined frequency range, and the receiver circuit 507 monitors the reflected signal over the particular frequency range and directs the data into channel 2 of the digital signal processor 221 Fig. 15C provides a graphical representation of the type of data recorded in channel 2 of the digital signal processor 221, with a curve 609 representing the amplitude characteristics of the reflected signal, and a curve 611 representing the phase characteristics of the reflected signal.

In Steps 4, 5 and 6, the process reverses, with the receiving antenna 211 serving as the transmitting antenna. This provides information from a different point of view.

Step 4: In this step, switch S3 is set to position 2, switch S4 is closed, switch Sl is set to position 1, and switch S2 is left open. In this configuration, the numerically controlled oscillator 509 can be stepped through a predefined frequency range, and the receiver circuit 505 can sense the amplitude and phase of the output signal from the numerically controlled oscillator 509 (the "incident signal"), and feed this to channel 1 of the digital signal processor 221. Fig. 16A provides an outline of the type of amplitude data 613 and phase data 615 that may be recorded during this operation.

Step 5: This step is carried out simultaneously with Step 4. With the same special connection configuration as in Step 1, the receiving antenna 211 is supplied with an energizing signal, so that an electromagnetic wave propagates in the direction of the receiving antenna 213. The receiving antenna 213 responds to the propagating electromagnetic signal, and this response is monitored by the receiver circuit 507 and recorded on channel 2 of the digital signal processor 221. Fig. 16B graphically presents the amplitude response curve 617 and the phase response curve 619, both over the predetermined frequency range.

Step 6: In this step, switch S3 is set to position 3, switch S4 is closed, switch Sl is set to position 1, and switch S2 is left open. In this particular coupling configuration, the energizing signal provided by the numerically controlled oscillator 509 is directed towards the receiving antenna 211. Part of the energizing signal is received by the receiving antenna 211, and part is reflected. The reflected portion is routed via attenuator 517 and switch S3, where it is monitored by receiver circuit 505, and recorded on channel 1 of digital signal processor 221. Fig. 16C provides a graphical representation of the data sets maintained on channel 1 of digital signal processor 221.

In the preferred embodiment of the invention, the data from these operations are arranged in data arrays or data tables, to allow the use of conventional data manipulation operations to detect or identify particular characteristics of the data set, such as maximum sensitivity, minimum sensitivity, rates of change of the data, and the relative position of special data properties. Diagnostic operations can be performed using . these datasets. For example, the responses that are registered in data sets that correspond to the information that is presented in graphic form in fig. 15A and 16A, are compared. Since the numerically controlled oscillator 509 has "phase coherence", the amplitude and phase measurements of the data sets of FIG. 15A and 16A be identical. The failure to find equality, or the discovery of inequality, can serve to diagnose many different mechanical problems, including broken switches, a malfunctioning receiver, or other component failure. As an alternative example, the data sets that are visually represented in fig.

15B and 16B, are compared. The curves in fig. 15B and 16B should be identical, as they represent the combined response of the receiving antennas and the borehole area between the receiving antennas.

Fig. 17 shows a flow chart representation of the preferred technique according to the invention to correct for the undesirable, destructive effect of (1) mutual magnetic field coupling between receiving antennas, and (2) any drift in antenna response. The process begins in a block 651.1 a block 653 energizes a special transmitter with a current having a special frequency to generate an electromagnetic field that propagates through the borehole and is detected in the receivers 211, 213, in accordance with a software block 655. Then , in accordance with a software block 657, the digital processor 221 or the central processor 215 obtains transfer function values for the particular operating frequencies of (a) the mutual coupling effect of the receiving antenna 211 on the receiving antenna 213, and (b) the mutual coupling effect of the receiving antenna 213 on the receiving antenna 211 Then, in accordance with a software block 659, the transfer function value of the influence of the receiving antenna 211 on the receiving antenna 213 is applied to the measurements made with the receiving antenna 213. Then the transformation value of the influence of the receiving antenna 213 on the receiving antenna 211 is applied on the measurements made with the receiving antenna 211. Then, in accordance with a software block 661, resistivity values for the formation are calculated using the corrected measurements, and the process ends in a block 663. These operations are performed for each measurement made during logging operations. The transfer functions associated with the transfer operating frequencies of 400 kHz are used to correct for mutual coupling and thermal error components present during logging operations at 400 kHz, while the transfer functions associated with 2 MHz are used to correct for the impact of mutual coupling and drift components during transmission operations at 2 MHz.

1.4 Logging Calculations

The following section illustrates how the present invention is used to derive an accurate measure of the amplitude attenuation and phase shift of the interrogating electromagnetic signal traveling through the borehole and the surrounding formation. The relationship between these amplitude and phase measurements, and their relationship to the material's resistivity, will also be shown. It should be emphasized that the resulting measure of resistivity contains a contribution from both the borehole and from the formation, and is therefore not a "final" resistivity response in the context of the preceding description. It should also be emphasized that a borehole instrument comprising two transmitters and two receivers is used to illustrate data processing methods. The derivation of formation resistivity, borehole resistivity, formation and borehole properties, and data processing using a borehole instrument comprising four transmitters and two receivers will all be discussed in later sections.

First, four transmitter-to-receiver signals are considered: (Transmitter 1[X1] to Receiver 1[R1]): Al l<e*>"

(Sender 1[X1] to Receiver 2[R2]): A^e"<12>

(Sender 2[X2] to Receiver 1[R1]): Aj^"21

(Transmitter 2[X2] to Receiver 2[R2]): A22em22

The measured amplitudes consist of:

where Xm = variation of transmitter output signal

R„ = variation of receiver sensitivity

amm = real amplitude (transmitter M to receiver N),

and the measured phases consist of:

where øxm = variation of transmitter phase (output signal)

øRn = variation of receiver phase

Øtmn = real phase (sender M to receiver N).

The previous, general equations correspond to the following more special equations:

Formation of the relationships between the different transmitter-to-receiver signals gives the following:

For Sender 1:

oe for Sender 2:

Multiplication of the above equations and taking the square root gives:

Simple algebraic manipulation of equations (9) to (11) yields:

due to the fact that all system variables fall out of the measurement.

By using two transmitters and two receivers, systematic variables can therefore be removed from both the attenuation (amplitude) terms and from the phase velocity (phase difference) terms.

Within the framework of the preferred embodiment of the invention, in which a sampled data processing device produces a signal as a function of formation resistivity based on phase representative signals, the following analysis demonstrates certain conditions relevant to the stability feature.

Consider two consecutive samples, specifically Sample A and Sample B. During Sample A, a first transmitter coil is energized to cause a wave to propagate through the formation in such a direction that the wave passes a first receive coil (RI), and later passes a second receiving coil (R2), and cause each receiving coil to produce a signal. During Sample B, a second transmitter coil is energized to cause a wave to propagate through the formation in such a direction that the wave passes a second receive coil (R2), and later passes the first receive coil (RI), causing each receiver coil to produce a signal.

Let øMR2A represent the measured phase of the signal produced by the receiver coil R2 during Sample A; let øMRlA represent the measured phase of the signal produced by the receiver coil RI during Sample A; let øMR1B represent the measured phase of the signal produced by the receiving coil RI during Sample B; and let øMR2B represent the measured phase of the signal produced by receiver coil R2 during Sample B.

The øMR2A signal depends on the phase of the wave at the location of R2, and generally has an error component attributable to various phase shifts including those introduced by the tuned receiver coil, wiring from the receiver coil to the receiver, and the receiver itself. Let øTR2A represent the real phase of the wave at the location of R2 during Sample A, and let øR2E represent the error component thus introduced:

Similarly, the øMRlA signal depends on the phase of the wave at the location of RI, and generally has its own error component. Let øTRlA represent the real phase of the wave at the location of RI under Sample A, and let øRlE represent the thus introduced error component:

During Sample A, the øMR1A signal and the øMR2A signal are processed simultaneously to produce a DeltaA signal representing the difference in phase between these two signals (ie øMR1a - øMR2A).

The component of the DeltaA signal which represents the real phase difference (øTR2A - øTR1A) is a function of the resistivity of the formation in the area between the two mc taker coils. Let F(Rapp) represent this component.

strain )t-

Similarly, the øMR2B signal and the øMR1B signal are processed simultaneously under Sample B, to produce a DeltaB signal that represents the difference in phase between these two signals (ie øMR2B - øMR1B).

The component of the DeltaB signal which represents the real phase difference (øTR1B - øTR2B) is a function of the resistivity of the formation in the area between the two receiver coils, i.e. it is equal to F(Rapp).

The DeltaA signal is recorded so that it can be found and processed with the DeltaB signal.

By adding Equations (19) and (20), we get that:

In other words, a calculated signal representing the sum of the successive samples is a function of formation resistivity, and error components, such as øRlE and øR2E, do not introduce errors into this calculated signal.

2. Parallel processing of measured data

As briefly discussed in a previous section, it is desirable to reshape or transform signals measured by the receiver or receivers into parameters of interest by simultaneously using "parallel" processing. Consider again the embodiment of the borehole logging instrument with four transmitters and two receivers shown in FIG. 2. The close distance d„ between the transmitter and receiver arrangement is denoted by the number 23, and the far distance df is denoted by the number 21. Both the close spacing distances 23 and the far spacing distances 21 are measured with respect to the center point 25 between the receivers 213 and 211 The point 25 is usually referred to as the downhole instrument's "measuring point". For a transmitter frequency ©i, the phases of the signal detected by the receivers 213 and 211 and which is written from the continuous transmission from the transmitters 209 and 205 are combined algebraically to obtain RpA|. More specifically, the algebraic mean value of a first phase shift calculated from the difference in the responses of the receivers 213 and 211 resulting from the activation of the transmitter 207, and a second phase shift calculated from the difference in the responses of the receivers 213 and 211 resulting from the activation is calculated of the transmitter 205, to give RpAt- The amplitudes of these received signals are measured simultaneously and combined, giving R^i. More specifically, the algebraic mean value of a first amplitude attenuation calculated from the ratio of the receivers 213 and 211 responses resulting from the activation of the transmitter 207 and the ratio of the receivers 213 and 211 responses resulting from the activation of the transmitter 205 is calculated to give R^i. For a transmitter frequency Gh, the phase of the signals received in the receivers 213 and 211 and which are recorded from the continuous transmission from the transmitters 209 and 203 are recombined algebraically in a similar way to obtain Rp,f,i. The amplitudes of these signals are also measured simultaneously and combined in a similar way, which gives R^i. The above sequence is repeated with a second transmitter frequency ©2, giving Rp^, R,^, Rp,^ and R^. The end result is eight apparent resistivity measurements including amplitude and phase shift which have been measured at two transmitter-receiver distances and at two transmitter frequencies.

Fig. 18 illustrates hypothetical measurements of resistivity over a thin formation layer which is denoted by the number 51, using a single transmitter and two receivers. This layer with vertical extent 56 is limited on each side by a formation which has essentially unlimited vertical extent and is denoted by the number 61. In the example, the vertical extent 56 of layer 51 is equal to 1.2 m. The real resistivity of the layer is 10 ohm-meters, as illustrated by a curve 50, and the layer is invaded to a depth of dj = 1.5 m, the resistivity of the invaded zone = 2.0 ohm-meters, as illustrated by a curve 52. The resistivity of the surrounding or shoulder formation is R^Ma = 0.5 ohm-meter, as illustrated by curve 60. The shoulder formations are not invaded by the drilling fluid. Curves 53 and 54 illustrate the apparent phase and amplitude resistivities measured across the layer boundaries with a transmitter frequency of ©i = 2 MHz. As previously defined terminology is used, the curve 53 is calculated from the difference between the two receivers and is denoted by R^, and the curve 54 is calculated from the ratio between the two receivers and is denoted by R^i. Similar curves are generated at a second frequency ©2) but are not shown. It can be realized that the maximum or peak values of the curves 53 and 54 within the zone 51, which are denoted by the numbers 58 and 57, are 2.23 and 2.07 ohm-meters respectively. Both measurements of apparent resistivity diverge greatly from the real or true resistivity of Rt = 10 ohm-meters. Fig. 19 shows a graphical representation of an algorithm for correcting apparent resistivity measurements taken at a frequency of 2 MHz for the effects of invasion in formations of unlimited vertical extent. The algorithm was derived using theoretical transmitter-receiver setup calculations which are well known in the field. Using values of dj = 1.5 meters, Rxo = 2.0 ohm-meters, and the maximum phase and amplitude values of 2.23 and 2.07 ohm-meters respectively, the resulting "corrected" value for true resistivity, = 2.09 ohm-meters, still a significant divergence from the true layer resistivity value of 10.0 ohm-meters. Lag limit corrections are applied to the maximum phase and amplitude resistivity measurements 58 and 57 using a correction algorithm which was derived from theoretical transmitter-receiver response calculations which are well known in the art and are presented graphically in fig. 20A and 20B, using a layer thickness of 1.2 m. R« denotes apparent resistivity measurement using the graphical representations. These corrected values are then serially corrected for invasion, again using the synthetic data which is presented graphically in fig. 18. After applying both layer boundary corrections and invasion corrections in series, the resulting "corrected" true resistivity value is R^ = 5.2 ohm-meters, which still shows significant deviation from the true resistivity value of 10.0 ohm-meters. It is obvious that serial or continuous corrections for the hypothetical example at a frequency of 2 MHz are completely inadequate. Similarly, the same sequence of corrections using corresponding amplitude and phase resistivities performed with U2 = 400 MHz can also be shown to be completely inadequate. Serial corrections for additional parameters (not shown) such as borehole diameters, resistivity of the drilling fluid, dielectric effects and formation anisotropy also provide insufficient corrections at one or the other transmitter frequency for real resistivity.

The present invention utilizes the eight previously defined measurements of apparent resistivity together with the comprehensive model of the borehole instrument response in a variety of different formation and borehole conditions to simultaneously determine formation and borehole parameters of interest. The process is generally defined by the matrix equation: where [R] is a 1 x 8 matrix representing eight measurements of apparent resistivity at multiple frequencies and transmitter distances as previously defined, and [X] is a 1 x 8 matrix representing eight parameters of interest to be determined. For the example considered, Rb RTO, Rskuidw, dj and the thickness of the zone 56 are included as elements of the matrix [X]. [T] is an 8 x 8 transformation matrix based on the comprehensive model of the downhole instrument response at many different wellbore and formation conditions, examples of which are shown graphically in FIG. 19, 20A and 20B. As an example, [TJ includes the borehole instrument response formations across layer boundaries, the response characteristics as a function of invasion, and response functions for all other borehole and formation parameters discussed earlier in this report. The value of the elements of [T] will depend on resistivity, and will therefore depend on the matrices [X] and [R]. As a result of this functional dependence, equation (22) is not a simple linear matrix equation. US Patent No. 5 144245 (MM. Wisler), which is assigned to the applicant in the present application, describes such a model and is hereby incorporated by reference. A non-linear regression system is used to transform equation (22), which gives

where [T] is the inversion of the response matrix [TJ. The matrices on the right-hand side of equation (23) are therefore either representative of measured quantities ([R]), or are known from theoretical calculations ([T]). Solving the equation for [X], which contains Rt as an element, yields a corrected value of R( = 10 ohm-meters for the hypothetical example shown in Fig. 18. The fact that sets of two transmitter frequencies are used in the present invention, contributes to the convergence of the measured and real formation resistivities when compared with the previous calculations that used only measurements at 2 MHz. Equally important in the transformation is that the present invention uses simultaneous inversion of the measurements at multiple frequencies and multiple distances. Thus, it is avoided the errors that are introduced at higher frequencies and that result from serial processing.

3. Determination of borehole parameters

Previous discussions defined the applications of measured borehole parameters and near-borehole parameters. The drilling fluid invasion profile is an indication of the permeability of the formation. Also, physical properties of the borehole, such as wrinkling and ellipticity, can be related to the mechanical properties of the rock mass and to the efficiency of the borehole drilling operation using the preferred MWD embodiment of the invention. Furthermore, knowledge of rock mass properties is very useful when specifying later completion activities, such as possible fracturing and even perforation programs. Finally, with knowledge of the wellbore condition, the drilling program can often be modified to increase efficiency, such as modification of drilling parameters to increase bit penetration rates.

Referring again to fig. 2, the transmitters are activated consecutively on a first frequency. The phase shift and amplitude attenuation of the induced electromagnetic signals are measured at each receiver, with respect to the transmitter output signals as previously described, yielding sixteen basic signal measurements (eight amplitude attenuation and eight phase shift measurements). The procedure is then repeated on a second transmitter frequency, yielding a further eight measurements of amplitude attenuation and eight measurements of phase shift. A total of thirty-two uncorrected "raw" measurements are therefore obtained for each cycle of transmitter activations as the borehole instrument 36 is transported along the borehole 34. Each phase shift and amplitude attenuation, being uncorrected by previously mentioned devices, is strongly influenced by the borehole and the surroundings near the borehole. These raw measurements are therefore used to determine borehole characteristics, such as borehole diameter, wrinkling and eccentricity, and also to provide a means of correcting measurements of apparent resistivity for these borehole effects. Put another way, the invention not only provides formation resistivity measurements that are corrected for disturbing effects of the borehole as previously described, but also provides means for quantifying these corrections and thus provides useful information about the physical properties of the borehole. These borehole characteristics can in turn be related to such parameters as mechanical properties of the rock mass, shallow invasion profiles, and the efficiency of the drilling program. The vertical resolution of the thirty-two measurements is usually different and varies from measurement to measurement when borehole distances vary rapidly with respect to transmitter-receiver set-up distances 21 and 23. It is necessary to apply deconvolution or deconvolution techniques to "match" or match the vertical resolution of all sixteen measurements before combining these data using the means discussed earlier. Resolution adaptation is not an independent data processing step as is often the case in the prior art, but is an integrated step in the calculation of all parameters of interest.

One must be aware that other transmitter-receiver-operating frequency combinations can be used. As an example, two transmitters and four receivers where the transmitters work on two frequencies will also give thirty-two raw measurements or unprocessed measurements. Extending the variability concept further, a setup of one receiver, working on two frequencies, and eight receivers will also give a total of thirty-two raw measurements of amplitude and phase, and so will one receiver and one transmitter working on sixteen frequencies. The transmitter-receiver frequency combination can also be varied to provide a total number of raw measurements greater or less than thirty-two, with a corresponding increase or decrease in the number of parameters of interest that can be uniquely determined.

Referring again to fig. 2, the transmitters 209, 207, 205 and 203 are activated consecutively at a given frequency ©]. The phase and amplitude of the induced electromagnetic signal is measured in each receiver-transmitter pair, giving a total of eight measurements of amplitude and eight measurements of phase which will be identified as Aj and Pj respectively where i = 1,...,8 ). The procedure is then repeated on a second transmitter frequency co2, giving a further eight measurements of amplitude and eight measurements of phase which will be identified as Aj and Pi respectively, where i = 9,..., 16. The cycle defined above is repeated as the borehole instrument is transported along the borehole. In summary, thirty-two parameters are measured as a function of instrument depth in the borehole.

The processing of measured data can best be visualized by matrix operation where the previously defined sixteen raw amplitude and sixteen raw phase measurements are multiplied by a non-quadratic matrix which transforms these thirty-two measurements into parameters of interest. The parameters of interest may be selected and varied by a user, and may include traditional formation assessment related parameters such as resistivity and dielectric constant as well as near-borehole parameters such as the radial extent of invasion of the formation by drilling fluid and the resistivity of the invaded zone. Furthermore, borehole parameters, such as borehole diameter, eccentricity and ellipticity, can be quantified as well as the resistivity of the fluid contained in the borehole. The number of parameters of interest must be limited to thirty-two or less in the preferred embodiment. In an alternative embodiment, the number of parameters of interest may be greater than the number of raw data measurements. This state or condition provides an indeterminate set of equations and requires initial calculations to be added for the number of parameters of interest that exceed the number of raw data measurements. Regression techniques are then used to minimize the discrepancy between the tool response predicted by the model and the set of measured raw data. The preferred embodiment, which uses thirty-two measured parameters, will be aimed at measuring borehole and near-borehole parameters. For illustration purposes, it will be assumed that five downhole or near-downhole parameters are to be determined. These will be denoted B„, where n = 1,...,5. The matrix operation is written as

(24) [T] x [M] = [B]

where

The matrix [T] is a transformation representing a comprehensive model of the downhole instrument response, with wellbore, near-borehole and formation states being variables. Since the elements Tg are predicted by the model, the borehole parameters to be determined, Bn (n=l,...,5), can be calculated directly from the measured parameters represented by the matrix [M]. When using the formalism according to equation (24), it is essential that the model represented by [T] provides parameters of interest (the "unknowns") as a function of the borehole instrument's response (the measured quantities).

Jian-Qun Wu and Macmillian M. Wisler ("Effects of Eccentering MWD Tool on Electromagnetic Resistivity Measurements", SPWLA, 3Ist Annual Logging Symposium, June 24-27, 1990) show a method for calculating the effects of a downhole logging tool is placed eccentrically in a borehole during resistivity measurements, and this article is hereby incorporated by reference. As an example of this work, fig. 21 the variations of apparent resistivity 75a calculated from phase shift measurements (indicated by curves 74) and amplitude ratio measurements (indicated by curves 76) as a function of logging instrument borehole eccentricity for true formation resistivity 70 of 0.2, 2.0 and 20 ohm-meters and with a borehole fluid resistivity 72 of 20 ohm-meters. The transmitter frequency is 2 MHz. A similar drawing is shown in fig. 22 for a borehole fluiohrm resistivity of 0.2 ohm-meter and where all other parameters remain the same. In these examples, functional relationships have been developed that provide apparent resistivity values 75a that will be measured by the downhole instrument 36 (the measured quantities) as a function of real or true formation resistivity 70, borehole resistivities 72 and eccentricity 75b, which are the "unknown" quantities to be determined. using means and methods according to the invention. The responses are calculated using a model developed around basic electromagnetic wave propagation principles using borehole geometry. The calculations have been verified experimentally. J.-Q. Wu, M.M. Wisler and J.F. Towle ("Effects of Arbitrarily Shaped Boreholes and Invasion on Propagation Resistivity Measurements in Drilling Horizontal Wells", Progress in Electromagnetic Research Symposium, Pasadena, California, July 14, 1993) likewise shows a device for determining the measured response of borehole instruments in terms of circular and non-circular invasion profiles and also expressed by instrument eccentricity in the borehole. Measured quantities are also expressed here by unknown parameters of interest. Put another way, the cited reference shows a device for calculating the foremost problem which, if incorporated into the comprehensive model, the present invention would set up the matrix equation (24) in the opposite direction, which would give equation (28):

Solving equation (29) with respect to [B] requires a regression system that is usually non-linear. That is, values of the parameters of interest, namely the elements of [B], are repeated until the elements of [M] calculated from equation (29) converge towards the real measured values Aj and Pj (i = 1,..., 16). It should again be emphasized that the other borehole and near-borehole parameters are included in the model. Such additional parameters may include borehole diameter and resistivity of the invaded zones. The parameters which are specified in more detail in fig. 21 and 22, are given as examples to illustrate the concepts of the data processing method. The additional characteristics of the response of the downhole instrument, obtained by means of mathematical modelling, are likewise incorporated as elements of the matrix [TJ.

4. Determination of errors associated with parameters of interest.

The present invention provides means and methods for determining errors that can be related to uncertainty associated with measured parameters of interest. Also in this case, the user of the information, or the log analyst, selects the parameters of interest, which may include the resistivity (or conductivity) of the formation, the dielectric constant of the formation, or possibly the extent to which drilling fluids invade the formation near the borehole. As previously mentioned, the analyst's primary interests are usually determination of the hydrocarbon saturation, porosity and permeability of the formations penetrated by the wellbore. It is highly desirable to perform such measurements during drilling or immediately after drilling the borehole, so that critical, economic determinations regarding the quantity and producibility of hydrocarbons at the site can be made. Based on this information, the well will either be completed or declared. The accuracy and precision of measured parameters selected to make such critical decisions is also of utmost importance. The error measurements provided by the invention can also be used to indicate equipment malfunctions of both electrical and mechanical types. Although known technology provides guidance on means and methods for measuring a wide range of geophysical parameters using electromagnetic techniques, little or no emphasis has been placed on determining the quality of the measurements. Typically, the analyst can only rely on past experience in providing, at best, qualitative estimates of the quality of the measurements obtained from the downhole instrument and associated system. Any error analysis is usually carried out long after the measurements have been carried out, and usually not at the well site. Put another way, prior art does not provide means and methods for determining the quality of electromagnetically based, geophysical measurements in real time or near real time, even if economic and operational determinations are made in real time or near real time, based on these measurements. This is particularly the case with electromagnetic measurements of formation resistivity, which weigh so heavily in the decision to complete or abandon the well. The invention provides precisely this information by providing means and methods for measuring geophysical parameters that are selected by the analyzer and at the same time provides quantitative measurements of the quality of errors associated with the measurements of the selected parameters.

Referring again to the embodiment of the invention shown in fig. 2, transmitters are activated consecutively on a first frequency. The phase and amplitude of the induced electromagnetic signal are measured, which gives four measurements of amplitude and four measurements of phase in each of the two receivers. The procedure is repeated on a second transmitter frequency, which gives a further four measurements of amplitude and four measurements of phase in each of the two receivers. Each sequence as described therefore provides thirty-two independent raw measurements. The measurement sequence is continuously repeated as the instrument is transported along the borehole. The previously mentioned mathematical model, which is based on fundamental electromagnetic wave propagation properties, describes the borehole instrument's theoretical response as a function of numerous formation and borehole parameters. Such parameters in turn include formation resistivity, invasion parameters, formation layer boundary effects, borehole conditions and the like. In this embodiment of the invention, the model contains fewer than thirty-two variable parameters, while the borehole instrument provides thirty-two measured parameters as described earlier. The system of unknown parameters is therefore "overdetermined" in the sense that there are no more measured parameters than variable or unknown parameters to be determined. It should be noted that other transmitter-receiver frequency combinations may be used, as discussed earlier. However, the number of selected parameters of interest must always be less than the number of raw data measurements, so that the resulting system of equations is overdetermined.

Non-linear inversion techniques are used to determine the set of selected unknown parameters that, using the mathematical model, predict a tool response that most accurately fits the thirty-two measured raw data points. The predicted tool response and the measured tool response will show no discrepancies only if (a) there are no errors associated with the measured data and (b) if the model without error represents the instrument response in each borehole and formation condition encountered. This is because there are more measured data points than unknown, variable parameters in the model. Any degree of mismatch or "misfit" between the model data and the measured data is a measure of inaccuracy of either the data or the model, or both the data and the model. In all cases, the determined nonconformity is treated as a quality indicator for the determined parameters of interest. In other words, an uncertainty associated with each parameter is selected by the analyst based on the goodness of fit between the model and the measured data.

Referring again to fig. 2, the transmitters 209, 207, 205 and 203 are activated consecutively on a first frequency ©j. The phase and amplitude of the induced electromagnetic signal is measured on the receiver closest to each activated transmitter, which thus gives four measurements of amplitude and four measurements of phase shift. These measured parameters will again be identified as Aj and Pj respectively, where i — 1,...,4). The procedure is repeated on a second frequency ©2, which gives a further four measurements of amplitude and four measurements of phase which are hereafter identified as Ai and Pj respectively, where i = 5,...,8. The entire procedure is then repeated for the receiver furthest from each activated transmitter, giving values of Aj and P; where i = 9,..., 16. In summary, a total of thirty-two parameters are measured using the borehole instrument 36 during each cycle as it is transported along the borehole 34. The above, combined procedure with transmission on frequencies ©1 and ©2 and recording of received signals are repeated continuously as the instrument is transported along the borehole.

Parameters of interest related to the formation, wellbore and near-borehole are selected by the analyst. These parameters can include formation resistivity, formation dielectric constant, radius of invasion for the drilling fluid, resistivity of the drilling fluid and possibly the diameter of the borehole. The selected number of parameters must be less than thirty-two, so that the system of equations described in the following section is overdetermined and thus allows the uncertainty associated with the selected parameters to be determined. For purposes of illustration, it will be assumed that the analyst selects n parameters to be determined, where n is less than thirty-two.

The processing of the data to obtain the parameters of interest, and the determination of uncertainty associated with these parameters, can best be described using matrix notation. The system is written as

The matrix [T] represents the theoretical response of the downhole instrument calculated using appropriate electromagnetic modeling techniques for a wide range of formation and wellbore conditions, the matrix [M] represents the thirty-two raw data points measured by the downhole instrument, and the matrix [X] represents the formation and wellbore parameters selected by the analyst and to be determined. Although the solution of the matrix equation (30) to obtain the desired parameters represented by the vector [X] is considered linear, in this case the elements of the matrix [T] may depend on the elements of [X]. The solution of equation (30) will therefore require a non-linear regression solution, such as a ridge regression.

Once equation (30) has been solved for [X], an inverse matrix operation is performed to produce a synthetic matrix of the measured quantities denoted by [M'], i.e.

The mismatch between the measured parameters, [M], and the synthetic values of the measured parameters, [M'], is a measure of the quality of the parameters of interest, [X]. If there is little uncertainty associated with the calculated values [X], this indicates that the quality of the measured data [M] and the model representing the instrument's response [T] are both good. If however

it can be concluded that either the measured data [M] is of poor quality (due to tool function, calibration error or similar), or the model of the tool response represented by [T] is inadequate for the conditions encountered, or both conditions have occurred Minimization of calibration, heat dissipation and errors due to mutual antenna coupling have been discussed previously. It has been determined that in many cases the response model is also very reliable and that errors in the model are only a small contributor to the observed error. It therefore follows that when [M'] [M], the source of the observed error cannot be identified. The degree of mismatch between [M'] and [M] is an indication of the magnitude of the uncertainty or error in the calculated parameters of interest, [X]. Nonlinear regression techniques suitable for use in this invention are described in the publication "Inversion of 2 MHz Propagation Resistivity Logs" by W.H. Meyer, SPWLA 33rd Annua! Logging Symposium, 14.-17. June 1992, Letter H.

5. Formation partners of interest

The transformation of radiation data measured by the sensors into apparent resistivities of the formation, near the borehole and the borehole surroundings has been discussed in previous sections. The determination of errors associated with these quantities has also been discussed. The preceding discussions also encompassed the general concepts of converting apparent resistivities and other electromagnetic properties into parameters from which "end" information, such as hydrocarbon saturation and porosity of the formation, is derived. Finally, basic problems related to the determination of hydrocarbon saturation from resistivity measurements alone, in the presence of water with low salinity or fresh water, have also been addressed. The subsequent section is devoted to the transformation of tool measurements whose accuracy and precision have been determined and optimized using previously discussed methods, into "end" parameters that include hydrocarbon saturation and porosity.

5.1 Review of physical principles

Phase shift and attenuation measurements in the low MHz frequency range depend on only three electromagnetic properties and the way in which these three properties are combined and spatially distributed near the borehole transmitter and receiver assembly. The three properties that - as an example - control the propagation of a 2 MHz electromagnetic wave are (1) magnetic permeability, (2) conductivity and (3) dielectric constant. The primary parameter of interest is conductivity (or resistivity), as this is the primary parameter used in hydrocarbon saturation calculations if the associated water is saline. In order to relate the measured phase shift and attenuation measurements taken with the borehole instrument to conductivity, assumptions must be made regarding the formation's magnetic permeability and dielectric constant.

Magnetic permeability is defined as the ability of magnetic dipoles in the formation to align themselves with an external field. Minerals and fluids that are usually found in sedimentary soil formations do not exhibit significant magnetic permeability. When calculating resistivities from measurements of amplitude and phase from a device operating in the middle kHz frequency range to the low MHz frequency range, minimal error is introduced by assuming a value of magnetic permeability equal to the value in free space, or 1 .25 x IO"<6> Henry/meter.

Conductivity is defined as a material's ability to conduct an electric charge, while dielectric constant is defined as a material's ability to store an electric charge. Dielectric constant is usually expressed by relative dielectric constant, which is the dielectric constant e of the substance in question divided by the dielectric constant in free space, Eo <=> 8.854 x IO'12.

Attention is now directed to dielectric constant and the physical principles behind the effects of this parameter on attenuation and phase signals measured in a borehole environment. In sedimentary formations, the dielectric constant arises from the ability of electric dipoles to align themselves with an alternating electromagnetic field induced by the borehole instrument. Water molecules will be used for discussion purposes. There are three phenomena that contribute to is in a porous soil formation. The first contribution is the rotation of dipolar water molecules. The water molecule has a weak positive charge on the side to which the two hydrogen atoms are bound, and a corresponding negative charge on the side of the molecule opposite the bound hydrogen atoms. In the presence of an applied electric field, the water molecule will rotate to align the positive and negative poles of the molecule with the applied electric field. In an alternating current field, such as that produced by the downhole instrument, the water molecule will rotate back and forth as the polarity of the applied field alternates. During the time period in which the water molecule is in real rotation and seeking to align with the applied field, the charge movement represents electrical charges moving in phase with the applied field and therefore conduct current and contribute to the composite formation conductivity. Once aligned with the field, the polarized water molecules represent fixed or stored charges, thus contributing to the formation's dielectric constant until the polarity of the alternating applied field is reversed. At this point, the water molecules re-rotate and again contribute to composite formation conductivity. This sequence of course repeats itself with the cycle through of the applied alternating current field. Ions that are dissolved in the formation's pore water are a second contributor to er in that they will also be set in motion by the applied alternating current field and travel in the direction of the field until they encounter a physical obstacle , such as a rock particle that forms the boundary of the pore space. As soon as the ions collide with the pore boundary and begin to accumulate, these likewise become fixed or "stored" charges, thus contributing to the dielectric constant of the formation, as described by M.A. Sherman in an article entitled "A Model for the Frequency Dependence of the Dielectric Permittivity of Rock", The Log Analyst, Vol. 29, No. 5, September-October 1988. Cations attached to cation exchange sites on the surface of certain clay minerals, is a third contributor to e, in that these can also move under the influence of an applied alternating current field. The movement of cations between different exchange sites produces effects similar to the effects of free ions in the pore water.

Complicating the issue of dielectric effects is the fact that values are dependent on the frequency of the applied field. At low frequencies, dielectric constants can be quite high, as the water molecules can easily rotate and align themselves with the field before the field's polarity reverses. Similarly, dissolved ions can migrate to the boundary of the pore space and accumulate against the pore wall long before the polarity of the field reverses. Likewise, the movement of cations may be complete before the switching of the field polarity. At low frequencies, therefore, water molecules, dissolved ions, and cations spend most of their time in a fixed orientation or position, moving for only a small fraction of the time during any given cycle of the applied alternating electromagnetic fields. At high frequencies, however, the polarity of the applied field will reverse before the three types of mobile charges come to rest. In this situation, the mobile charges spend most of their time moving in phase with the external electromagnetic field, thus increasing their conductivity and resulting in a lower dielectric constant. The phenomena of changing dielectric values and conductivity values with frequency is known as dispersion. The frequency at which the rotating molecules or mobile ions can no longer keep up with the oscillating field is known as the "relaxation frequency". The relaxation frequency, the relative dielectric constant is and the conductivity a will depend on various factors, such as porosity, average pore size, water resistivity Rw and shale mineralogy, as described in the aforementioned article by Sherman.

J. C. Sims, P.T. Cox and R.S. Simpson, "Complex Dielectric Interpretation of 20 MHz Electromagnetic Logs", Paper SPE 15486, 6Ist Annual Technical Conference and Exhibition of the Society of Petroleum Engineers, 5-8. October 1986, provides guidance on the use of a mixture recipe to interpret dielectric log data, but measurements made at only one frequency are used. US Patent No. 3,891,916 (R.A. Meador et al.) teaches the use of two frequencies, both much higher than 2 MHz, to determine dielectric constant. Meador et al. however, states the use of amplitude measurements to determine dielectric constant and resistivity, and does not address the problem of dielectric dispersion when using two frequencies with both amplitude and phase measurements. US patent no.

5 144 245 (M.M. Wisler) shows application of the Complex Refractive Index Model or CRIM model (CRIM = Complex Refractive Index Model) as a means of correcting resistivity measurements for dielectric effects, where the amplitude and phase data of the resistivity are taken at a single frequency. K.S. Cole and R.H. Cole, "Dispersion and Absorption in Dielectrics", Journal of Chemical Physics, Vol. 9. p. 341 (1941), shows a model for dielectric dispersion which can be used as a mixture model somewhat similar to the previously mentioned CRIM model and which could be used as an element in the execution of the present invention. There are many other mixing and dispersion models that could also be used.

This brief review of relevant, basic physical principles will help to give a complete account of the mediators and methods according to the invention, and progress of the present invention in relation to known technology.

Remember that a primary object of the invention is directed to the accurate measurement of the conductivity (or resistivity) of a soil formation penetrated by a borehole. As previously discussed, formation resistivity combined with formation porosity and resistivity of related water can be used to calculate hydrocarbon saturation of a porous formation. The invention is further directed to the determination of the formation's dielectric constant. This measurement is used to correct resistivity measurements carried out at certain frequencies, for the adverse effects of the formation's dielectric constant. The invention is also directed at determining the volume fraction of the formation that is saturated with water. This measurement, when combined with an independent measurement, such as a neutron porosity measurement that responds to total formation fluid (water plus liquid hydrocarbon), can be used to determine hydrocarbon saturation of the formation in either freshwater or saltwater environments. Hydrocarbon saturation cannot be determined using resistivity measurements only in fresh water environments, as the resistivity of fresh water and hydrocarbon shows little contrast.

5.2 Theoretical basis

Solutions of Maxwell's equations in homogeneous, lossy media are a function of a factor commonly referred to as the propagation constant or wave number, here defined as "A", which contains terms for conductivity, dielectric constant, and magnetic permeability. An equation for a plane wave will have the form

where

V = a field variable,

C = a constant,

e = the base of the natural logarithm,

i = the square root of -1,

x = the distance traveled, and

where

Ho = the magnetic permeability of free space,

pr = the relative permeability (which is 1.0 for free space and most soil materials), e0 = the dielectric constant of free space,

Er=the relative dielectric constant (which is 1.0 in free space),

© ^the angular frequency of the impressed field, and

a = the conductivity, which is the inverse of the resistivity.

The term k can be rewritten in terms of a complex relative dielectric constant, Ec, containing the effects of dielectric constant and conductivity, as

where

ko = the wave number in free space

A model for the soil formation is now assumed where there are two layers with different propagation constants k and different complex relative dielectric constants where the first area spans over (l-ø) units of length and the second area spans over ø units of length. A plane wave incident on the layers and passing through the layers without reflection will have the form The effective propagation constant for this model, k^ is therefore

Equation (43) is solved for the equivalent relative dielectric constant to obtain Considering all the above relations leading to equation (44), it is obvious that the effective, real relative dielectric constant is therefore corrupted by the imaginary parts of the relative dielectric constants for the two regions, and the effective conductivity is likewise distorted by the real parts of the relative dielectric constants. The model is now further related to real soil formations. The first area is set equal to related water that fills the pore space in the rock mass, the fractional volume of the water being equal to ø of the total formation volume. The second area is set equal to the rock mass, as the fractional volume of the rock mass is (l-ø) of the total formation volume. Development of equation (44) to illustrate real and imaginary components, and designation of the terms with regard to the above formation model gives where the indices w and m denote parameters linked to the water and rock components of the formation, respectively. Note that crm is equal to zero. If measurements are carried out at two known frequencies o>=(Di,<g>>2, equation (45) gives two independent, complex equations. Because both real and imaginary parts of these equations must be equal, measurements at two frequencies in reality four independent equations. The dielectric constant of water, e^, is independent of the salinity of the water and is thus a known quantity. The two frequencies are predetermined and are thus known. The quantities ecff and aeff are measured. The four independent equations can therefore be used to find a solution for the remaining three unknown quantities, namely the porosity ø, the conductivity of the water aw and the dielectric constant em of the rock. It should be noted that several transmitter-receiver-shit frequency combinations can be used in embodiments of the invention, as long as the selected combination gives four independent solutions relating aeff and eeff to aw, Sm and ø. It should also be noted that the dielectric constant of the rock mass and the dielectric constant of any hydrocarbon contained in the pore space of the rock, are essentially equal and the conductivity of each is essentially equal to zero. The calculated size ø is therefore the fraction of water inside the formation and not necessarily the effective porosity of the formation in the sense usually used in the field. To achieve effective formation porosity, it is necessary to combine the "water-filled" porosity provided by the invention with a second, independent measure of formation porosity that responds to the total fluid-filled porosity. An example of such a second measurement would be the thermal neutron "porosity" measurement that responds to the formation's hydrogen content. As the majority of hydrogen in a soil formation is in the pore space rather than in the rock mass, and as the response is essentially the same for both water and liquid hydrocarbons, the neutron porosity measure gives total liquid porosity.

5.3 Logging example

Attention is drawn to fig. 23 which illustrates logs of resistivity, which is the inverse of conductivity, measured at four different transmitter frequencies as a function of depth in feet, in a borehole. The measurements were carried out in a test well in which the formation's properties are well known from numerous studies of well log and core data, as stated in "Comparison of MWD, Wireline and Core Data from a Borehole Test Facility", Paper SPE 22735, proceedings of the Society of Petroleum Engineers 66th Annual Conference and Exhibition, pp. 741-754, (1991). These "logs" of resistivity clearly illustrate the effects of dispersion or scattering effects as a function of the frequency of the induced electromagnetic field. Attention will be focused on the zones designated by numbers 840 and 844 which are shale, and the low permeability limestone zone designated by number 846. Zone 842 is a permeable or permeable sandstone, and is therefore invaded by the drilling fluid. Radial invasion combined with different probing depths for the measurements at different frequencies mask the scattering effects. Zone 842 will therefore be ignored in this discussion. Curves 850, 852, 854 and 856 represent resistivities measured at respective frequencies of 1100 MHz, 200 MHz, 25 MHz and 2 MHz. Knowing that the zones 840, 844 and 846 are radially homogeneous (ie not invaded by the drilling fluid), it is concluded that the observed dispersion is due to dielectric effects. Fig. 24 illustrates measurement of relative dielectric constant over the same formation zones of interest, but at different frequencies where curves 870, 872, 874 and 876 represent measurements at 1100 MHz, 200 MHz, 25 MHz and 2 MHz respectively. Dielectric dispersion is again quite obvious. The phenomena of both dielectric scattering and conductivity (or resistivity) scattering and their dependence on the frequency of the induced field have been discussed in a qualitative or conceptual sense in a previous section. The phenomena can be quantified as shown in fig. 25 which illustrates generalised, theoretical dispersion curves for a pure sandstone formation. The dielectric dispersion curve 860 illustrates that ω generally decreases as frequency increases. Conversely, the conductivity curve 862 illustrates that conductivity dispersion increases with increasing frequency. Both curves 860 and 862 also clearly illustrate frequency ranges in which interfacial relaxation and molecular relaxation occur. In order to assess the extent of the variations in the relative dielectric constant that are observed in the logs on fig. 24, is really consistent with scattering effects, the four values of 8, which are plotted by curves 870, 872, 874 and 876 at a depth of 1660 feet in the limestone formation 846, in fig. 26 compared with a dispersion curve 880 which is based on published dielectric measurements (M.R. Taherain et al., "Dielectric Response of Water-Saturated Rocks", Geophysics, Vol. 55, No. 12, December 1990) performed on limestone chemical samples with resistivities of groundmass and related water (connate water) which was very similar to the limestone in Formation 846. The superimposed data points 881, 882, 883 and 884 are average readings of respective curves 876, 874, 872 and 870 taken at a depth of 1660 feet in the zone 846. The good agreement between the chemically derived dispersion curve and the log-derived measurements from these two carbonate formations suggests that the differences between the different er values from the log are really due to dispersion. Considering fig. 23,24,25 and 26 in combination, it is obvious that any model that simultaneously extracts dispersion-corrected resistivity and dielectric constant values from measurements of phase difference and amplitude ratio at varying frequencies must quantitatively include the frequency of the induced electromagnetic field.

Remember that one of the basic purposes of the invention is to determine the conductivity (or resistivity) of the formation which is free from scattering effects. A second purpose is to determine the dielectric constant of the formation which is also free of scattering effects. A third purpose is to determine effective water-filled porosity of the formation which, combined with independent measurements of total fluid-filled porosity, can be used to determine the formation's hydrocarbon saturation. A theoretical, complex refractive index model or CRIM model has been developed which relates to real formation resistivity and fulfills the aforementioned purposes of the invention. The development of the model begins with the solutions of Maxwell's equations in homogeneous, lossy media, which are a function of a factor commonly referred to as the propagation constant or wave number, here defined as "k", which contains terms regarding conductivity, dielectric constant and magnetic permeability. Reinstating Equation (39) for a solution for a plane wave for the sake of completeness, we get

where

V = a field variable,

C = a constant,

e = the base of the natural logarithm,

i = the square root of -1,

x = the distance traveled, and

where

c = speed of light = 2.999-10<8> meters/second,

Po = the magnetic permeability in free space = 4x10", -

Pt = the relative permeability (which is 1.0 for free space and most soil materials),

Eo = the dielectric constant of free space = (1/poC<2>)= 8.854 x IO"<12>,

E, = the relative dielectric constant (which is 1.0 in free space),

co the angular frequency of the applied field, and

a the conductivity.

The term k can be rewritten in terms of a complex relative dielectric constant that includes the effect of dielectric constant and conductivity, as

where

fr0 = the wavenumber in free space

Pr =1> and the complex relative dielectric constant is

+ ia(l/oos0)]

Note that k is defined so that as the conductivity a approaches zero, the complex relative dielectric constant approaches the relative dielectric constant equal to the real relative dielectric constant Er.

A model is now assumed for the soil formation where there are two layers with different propagation constants k and different complex relative dielectric constants e» where the first area spans (l-ø) length units and the second area spans ø length units. A plane wave incident on the layers and passing through the layers without reflection will have the form

where the indices 1 and 2 denote parameters linked to layer 1 and layer 2 respectively. The effective planning constant for this model, k^ is therefore or expressed by the complex dielectric constant defined above

Equation (44) is solved for the equivalent relative dielectric constant to get The model is now further related to real soil formations. The first area is set equal to related water that fills the pore space in the rock mass, the fractional volume of the water being ø of the total formation volume. The second area is set equal to the rock mass, as the fractional volume of the rock mass is (l-ø) of the total formation volume. Development of equation (45) to illustrate real and imaginary components, and specifying terms with regard to the above formation model gives where the indices w and m identify parameters linked to the water and rock mass components respectively. Note that am is equal to zero.

The effective, real dielectric constant is therefore distorted by the imaginary part of the dielectric constants in the two areas, and likewise the effective conductivity is distorted by the real parts of the relative dielectric constants, i.e.

In order to calculate the dielectric constants that one would expect to observe in rocks saturated with pure water, it will be assumed that the rocks are composed of two parts comprising the rock groundmass and the related water. The resistivity of the water and the porosity of the rock mass are varied within reasonable limits, and the dielectric constant of the combination of the two parts, which is the quantity actually sensed by the borehole instrument, is calculated by utilizing the two-component mixture relation derived above. The indices w and m denote parameters linked to the water and rock parts, respectively.

The relationship according to equation (46) can be used to graphically illustrate the functional connections between the measured quantities and the parameters that are of interest and to be determined. Fig. 27A and 27B are presented as typical illustrations of these relationships or connections. The real part 890 of the effective dielectric constant as defined by equation (46) is plotted on fig. 27A as a function of formation water resistivity, indicated on the abscissa as 892, for various porosities 894. The abscissa is logarithmic and the ordinate is linear. These records apply to a frequency ©j = 2 MHz. The real part 891 of the formation's effective conductivity is set out in fig. 27B as a function of formation water resistivity 892, again at ©j = 2 MHz and again for varying porosities 894. Both the ordinate and the abscissa are logarithmic. Similar plots can be produced for the real and imaginary components of aeff at ( 0\ = 2 MHz, and likewise plots for both the real and imaginary parts of aeff at a second frequency co2 = 400 kHz. These are graphical representations of a set of four independent equations used to determine the "unknown" formation parameters of interest, namely the effective conductivity (or resistivity), the effective dielectric constant and the water-filled porosity of the formation.

5.4 Determination of dielectric constant, resistivity and porosity

Attention is directed again to fig. 23 and 24 which show resistivity data and dielectric data respectively. Fig. 23 presents data from four borehole systems, the 2 MHz data being measured with an MWD system and the remaining data being measured with wireline systems. Fig. 24 presents dielectric data measured with the same systems. Spread of the measurements as a function of frequency is clearly shown in both logs. Based on the previously mentioned principles, the spread in the resistivity measurements would be expected to be small at 2 MHz and lower frequencies. Attention is particularly drawn to zone 846 which is known from core data to be impermeable carbonate. Scattering in this zone can only be attributed to dielectric effects. Zone 842 is a sandstone known to be permeable and therefore invaded with drilling fluids prior to driving the wireline logs. The observed scattering in this zone must be attributed, at least in part, to invasion effects as well as dielectric effects. Data from zone 846 will therefore be used to illustrate the determination of dielectric dispersion of resistivity measurements. Attention is directed again to fig. 26 which illustrates observed dielectric data superimposed on laboratory measurements of dielectric constant as a function of frequency, which measurements are published in the aforementioned article by Taherain. The illustrated curve was specially prepared using the model of Cole and Cole, to which reference has been made previously. At a depth of 1660 feet, dielectric constants measured at 2 MHz and 25 MHz are denoted by the numbers 841 and 841 respectively. 821, and the corresponding resistivities are denoted by the numbers 838 and 827. These values of 8eIr and acfr = 1/R<.ff are entered in Iilaiing (46) at the respective frequencies, the real and imaginary parts of equation (46) are set equal to each other, which gives a set of four equations, and a non-linear regression system, such as a ridge regression, is used to solve with respect to the water resistivity Rw = l/aw = 0.16, the dielectric constant of the rock mass em = 9.0, and the porosity of the formation ø = 0.05 or 5% . These are reasonable values for impermeable carbonate and agree well with core data taken in zone 846.

5.5 Borehole caliber measurement.

The ability to accurately calculate amplitude attenuation and phase shift, which is unaffected by cross-coupling and drift errors, allows for meaningful borehole gauging operations. An accurate determination of the amplitude attenuation caused by the formation alone or the wave propagation between the receiving antennas 211, 213, and an accurate measurement of the phase difference between the receiving antennas 211, 213 can be used in conjunction with a library or collection of curves or data recorded in a computer storage. Fig. 28 shows a graphical presentation of phase difference in degrees as a function of attenuation in dB. With respect to these x and y axes, a number of curves corresponding to borehole diameter in inches have been provided. In fig. 28, borehole diameters of 7", 8", 9" and 10" are graphically represented. A number of curves representing formation resistivity in ohm-meters have been produced. Fig. 28 presents formation resistivity measurements of 0.2 ohm-meter, 0.5 ohm-meter, 1.0 ohm-meter, 2.0 ohm-meter, and 200 ohm-meter. This graphic representation is accurate when the drilling mud has a resistivity of 0.05 ohm-meter (Rm). The graphic representation in fig. 28 is just an example of such a presentation. In practice, several graphical representations or data sets are provided for several mud resistivities Rm.

Provided that the formation resistivity and the mud resistivity R,,, are known, the amplitude attenuation and the phase shift of the electromagnetic interrogation field can be used to determine the diameter of the borehole in the area of the logging device. If, for example, assumed, with reference to fig. 28, that the formation resistivity is 0.5 ohm-meter and the mud resistivity Rn is 0.05 ohm-meter, a calculated amplitude attenuation of -66 dB and a phase difference of 55° indicate that the borehole has a diameter of approx. 9". In accordance with the invention, the central processor 215 and the digital signal processor 221 can be programmed to periodically or intermittently calculate the borehole diameter, and transmit it to the surface using mud pulse telemetry techniques. If the borehole diameter is increased to 10", this must be reflected in changes in amplitude attenuation and phase shift. If, on the other hand, the borehole tapers in diameter to 8", this will also be reflected in the amplitude attenuation and phase shift measurements. Borehole caliber measurement operations can only be performed if undistorted measurements of amplitude attenuation and phase shift can be obtained. As the present invention allows correction of any distorting influence of mutual magnetic coupling, or thermal or other types of drift, such measurements can be utilized for accurate determination of borehole diameter. In the preferred embodiment of the invention, several data sets are provided, each corresponding to a different mud resistivity Rm and a particular formation resistivity. These data sets are contained in the tool model matrix [ T] which was discussed in an earlier section The measurements of amplitude attenuation and phase shift are then used to determine the borehole diameter.

Claims (10)

1. Logging device for determining parameters of a borehole and a surrounding formation, comprising (a) a borehole instrument comprising at least one transmitter and at least one receiver, (b) at least one oscillator electrically coupled to the at least one transmitter to selectively energize it at least one transmitter, which has at least one digital input and one analog output, and which provides a special analog output signal from a number of available analog output signals at least partially in response to receiving a special digital command signal, (c) a control unit- device for applying the particular digital command signal from a number of available digital command signals in response to program instructions, bringing the analog output signal from said at least one oscillator to be supplied to a particular one of said at least one transmitter to thereby induce a primary electromagnetic field in the borehole and formation surroundings, using said at least one receiver to measure at least one parameter attributable to the induced primary electromagnetic field, and to calculate at least one parameter for the borehole and the formation environment, and (d) a device for transporting the borehole instrument along the borehole, characterized in that it comprises (e) a device for determining the radial position in the borehole to which the at least one parameter can be attributed the induced primary electromagnetic field is measured. 2. Device according to claim 1, characterized in that the at least one oscillator on the analog output provides an analog signal with (a) a frequency characteristic that is determined at least in part by the digital command signal on the at least one digital input, (b) a phase characteristic which is determined at least in part by the digital command signal on the at least one digital input, and (c) an amplitude characteristic which is determined at least in part by the digital command signal on the at least one digital input. 3. Device according to claim 1 or 2, characterized in that the control unit device uses a combination of a measurement of a phase property of the induced, primary electromagnetic field and a phase knowledge of the particular analog output signal to calculate the value of the at least one parameter for the borehole and the formation environment. 4. Device according to one of the preceding claims, characterized in that the control unit device uses a combination of a measurement of an amplitude characteristic of the induced, primary electromagnetic field and an amplitude knowledge of the particular analogue output signal to calculate the value of the said at least one parameter for the borehole and the for-machine surroundings. 5. Device according to one of the preceding claims, characterized in that (a) the borehole instrument is transported by means of a drill string, (b) that the said measure for at least one parameter that can be attributed to the induced, primary electromagnetic field, is transmitted to the earth's surface while the borehole instrument is located in the borehole, and (c) that the calculation of at least one parameter for the borehole and the formation environment is performed at the earth's surface. 6. Logging method for determining parameters of a borehole and a surrounding formation, the method comprising the steps of (a) providing a borehole instrument comprising at least one transmitter and at least one receiver, (b) providing at least one oscillator electrically coupled thereto at least one transmitter for selectively energizing the at least one transmitter, having at least one digital input and an analog output, and providing a particular analog output signal from among a number of available analog output signals at least partially in response to receiving a particular digital command signal, (c) providing a control unit arrangement for applying a special digital command signal from a number of available digital command signals in response to program instructions, bringing the analog output signal from the at least one oscillator to be supplied to a particular one of said at least one transmitter to thereby induce a primary electromagnetic field in the borehole and formation surroundings, using the at least one receiver to measure at least one parameter attributable to the induced primary electromagnetic field, and calculating at least one parameter for the borehole and formation environment, and (d) transporting the borehole instrument along the borehole, characterized in that it comprises the step (e) of determining the radial position in the borehole in which the at least one parameter attributable to the induced primary electromagnetic field is measured. 7. Method according to claim 6, characterized in that it comprises the further step of using the at least one oscillator to provide an analogue signal on the analogue output with (a) a frequency characteristic which is determined at least in part by the digital command signal on the at least one digital input, (b) a phase characteristic determined at least in part by the digital command signal on the at least one digital input, and (c) an amplitude characteristic determined at least partially by the digital command signal on the at least one digital input. 8. Method according to claim 6 or 7, characterized in that it comprises the step of using the control unit to combine a measurement of a phase characteristic of the induced, primary electromagnetic field and a phase knowledge of the particular analog output signal to calculate the said value for the at least one parameter for the borehole and the formation surroundings. 9. Method according to claim 6, 7 or 8, characterized in that it comprises the step of using the control unit to combine a measurement of an amplitude property of the induced, primary electromagnetic field and an amplitude knowledge of the particular analogue output signal to calculate the said value for at least one parameter for the borehole and the formation surroundings. 10. Method according to one of the claims 6-9, characterized in that it comprises the further steps (a) of transporting the borehole instrument by means of a drill string, (b) of transmitting the said measure for at least one parameter that can be attributed to the induced, primary electromagnetic fields, to the earth's surface while the borehole instrument is in the borehole, and (c) performing the calculation of the at least one parameter of the borehole and the formation environment at the earth's surface.