NO300475B1 - Borehole measurement of NMR properties in rock formations - Google Patents

Description

The present invention relates to a device and method for nuclear magnetic resonance measurements (NMR) in boreholes, and methods for determining magnetic characteristics of basic formations penetrated by a borehole.

Repeated attempts have been made to use the principles

with nuclear magnetic resonance to log oil wells for decades, with limited success. It was realized that any particles in a formation that have magnetic spin, for example atomic nuclei, protons or electrons, tend to align with a magnetic field applied to the formation. Such a magnetic field can be generated naturally, as is the case with the earth's magnetic field BE, which has an intensity of around 50/zT in areas of the earth where boreholes are usually drilled. Any given particle in a formation is additionally affected by localized magnetic fields in connection with nearby magnetic particles, other paramagnetic materials and the ionic layers that are usually found on the pore walls in certain types of formations, such as shales. These localized fields tend to be inhomogeneous, while the Earth's magnetic field is relatively homogeneous.

The hydrogen nuclei (protons) of water and hydrocarbons occurring in rock pores produce NMR signals that are different from other signals induced in other rock constituents. A mass or population of such nuclei having a net magnetization tends to align with any applied field such as BE.

When another magnetic field B1, which is transverse to BE, is applied to the protons by means of a logging probe electromagnet, the protons will align with the vector sum of BE and B1 after a sufficient polarization time tpQlhar has passed. If the polarization field Bx is switched off, the protons will tend to undergo a precession around the BE vector with a characteristic Larmor L frequency o>L which depends on the strength of the earth's field BE and the particle's gyromagnetic constant. Hydrogen nuclei precessing around a magnetic field BE of 50/zT have a characteristic frequency of about 2 kHz. If a multitude of hydrogen nuclei were brought to precess in phase, the combined magnetic fields of all the protons could generate a detectable oscillating voltage in a receiver coil. Since the magnetic moment of each proton produces field inhomogeneities, the precessing protons tend to lose their phase coherence over time, with a characteristic time constant called the transverse or spin-spin relaxation time T2. Furthermore, field inhomogeneities are also produced by other physical phenomena as mentioned above, so that the observed dephasing relaxation time T2<*> is usually shorter than T2. Borehole magnetic resonance measurements of the above type are commercially available as part of the NML<+>service of Schlumberger Technology Corporation, Houston, Texas (<+>mark of Schlumberger). This instrument is capable of measuring the free induction7weakening of hydrogen nuclei in formation fluids and providing the parameters Txog T2<*>. It does not measure the transverse relaxation time T2. A description of the basic components, operation and interpretation of the commercial logging equipment used in the NML service is given in a paper entitled "An Improved Nuclear Magnetism Logging System and its Application to Formation Evaluation", by R. C. Herrick, S. H. Couturie and D. L. Best, presented at the 54th Annual Fall Technical Conference and Exhibition of the Society of Petroleum Engineers (A.I.M.E., Dallas, Texas) in Las Vegas, Nevada, 23-26. September 1979, as this article is hereby incorporated as a reference.

Other sequences of magnetic fields can be applied to a quantity or population of protons in a formation to measure its characteristics. If, for example, a pulse of alternating current of frequency f is passed through a transmitter coil, to produce an oscillating polarization field B1 perpendicular to a static field B0, a mass of protons precessing at a Larmor frequency equal to f will tend to align at an angle to E±. At the end of the pulse when B± is removed, the aligned protons will feel a perpendicular torsional force, and precess around the B0 vector. After a characteristic time called the longitudinal or spin-lattice relaxation time T±, the protons have relaxed to thermal equilibrium, where a weighted proportion of protons are aligned in the direction of B0. Various other sequences of applied magnetic fields may be used, as discussed in T. C. Farrar and E. D. Becker, "Pulse and Fourier Transform Nuclear Magnetic Resonance", Academic Press, N.Y. (1971), Chapter 2, pages 18-33, which is hereby incorporated by reference.

Although measurements of NMR characteristics of rock samples can be made accurately in a laboratory, producing comparable measurements in a borehole can be greatly hindered by the unfavorable environment where temperatures can reach several hundreds of degrees Celsius, pressures reach tens of MPa and all the equipment must be packed into a cylindrical volume only a few inches in diameter.

One of the first NMR loggers is shown in US Patent No. 3,289,072 issued November 29, 1986 to N. A. Schuster. A powerful electromagnet is used to expose a sample of water or oil to a predetermined magnetic field. A radio frequency (RF) coil produces an oscillating second magnetic field which causes nuclear magnetic resonance of protons in the sample and resonance of similar protons in the adjacent formation. Schuster proposed the use of a multipole electromagnet handled in a sidewall pad, or alternatively a larger electromagnet mounted inside the logging probe, to produce a static magnetic field B0. Schuster has also proposed other forms of electromagnets and radio frequency detection coils, for example in US Patent No. 3,083,335 issued March 26, 1963, where the coil is placed inside a gap between two opposite poles of two bar magnets. Here the magnetic field lines of the coil intersect the field lines of the bar magnets perpendicularly, which is the optimal angle to induce nuclear magnetic precession.

A more recent US Patent No. 3,667,035 issued May 30, 1972 to C. P. Slichter, shows a similar configuration with two coaxially aligned bar magnets and a radio frequency coil placed inside the gap between opposite poles of the magnets. The term "bar magnet" is used here to denote any magnet which has only a north pole and a south pole facing in opposite directions and which can be either a permanent magnet or an electromagnet. Both the Slichter design and the Schuster design use electromagnets that require inappropriately large direct currents transmitted to a logging probe through an electrical cable that can be a thousand meters and longer.

US Patent No. 3,528,000 issued September 8, 1970 to H.F. Schwede shows a type of NMR logging apparatus in Figures 8 and 9, in which a permanent magnet produces a first magnetic field which is fixed with respect to intensity, and an inductive coil which produces a oscillating magnetic field whose frequency varies over a selected range. Since the first magnetic field is produced by two opposite magnetic poles (one N and one S) placed side by side, the field is not homogeneous, and the spatial gradient of the field is clearly different from 0 at all points in the formation. Since the first and second fields intersect not only in the formation, but also inside the borehole, it is clear that protons constituting water and or hydrocarbons in the borehole fluid contribute to signals detected by the R-coil, and must be removed either electronically or by chemical treatment of the borehole fluid, if a real formation measurement is desired.

Other NMR logging devices have been proposed that use permanent bar magnets arranged coaxially in a logging probe with a detection coil placed in the gap between the magnets, for example as shown in U.S. Patent No. 3,597,681 issued August 3, 1971 to W.B. Huckabay.

Another permanent magnet configuration has been proposed in U.S. Patent No. 4,350,955 issued September 21, 1982 to J.A. Jackson, where two permanent bar magnets are coaxially aligned so that the RF detection coil is positioned in the gap between two equal poles of the two magnets. Jackson's patent shows the use of long bar magnets, placed end to end, and with like poles facing each other to produce a static field. The resulting magnetic fields are axially symmetrical, and exit in all azimuth directions in the same way. This is an inefficient solution. Likewise, GB Patent Application Publication No. 2,141,236, published 12 December 1984, shows a similar configuration of coaxially aligned bar magnets with a detection coil placed in a gap between the magnets. This shape produces a toroidal area with a homogeneous magnetic field where nuclear resonance can be measured. However, these two devices can be adversely affected by signals from the borehole fluid in a large or sloping borehole where the device will tend to rest against a side wall in the borehole. If the apparatus is designed to produce the toroidal region far away from the probe body, the produced magnetic field becomes much weaker, resulting in a significantly weaker signal. This design further requires that the detection coil or the antenna be enclosed by a structure that does not block the oscillating electromagnetic waves for the measurement signal. For example, fiberglass or another non-metallic material is usually used; unfortunately, this structurally weaker chain weakens the structural integrity of the apparatus and makes it significantly less usable under harsh downhole conditions.

From US patent no. 4 714 881 an NMR logging probe is known where the magnetic field is directed to one side of the probe. However, a complicated arrangement of permanent magnets is used to fine-tune the shape of the magnetic field lines, but it seems obvious from what is shown in the patent that there will be a significant field gradient in the formations. It is therefore not possible to understand how the patent can achieve a relatively homogeneous field through any significant volume of the formations, and in addition it is clear from the patent that the magnetic field lines that are mapped are contrary to normal natural laws regarding electromagnetism. It is thus a question whether the device according to US 4 714881 can function as intended.

NMR measurement of particles other than hydrogen nuclei that have magnetic spin has also been proposed. U.S. Patent No. 3,430,260, issued April 15, 1969 to G.J. Benn and others, describe, for example, techniques for measuring magnetic resonance in carbon

13 cores in basic formations.

Other representative US patents that have been granted for NMR logging apparatus and techniques include the following: 3,042,855 to R.J.S Brown; 3,508,438 to R.P Alger and others; 3,483,465 to J.H. Baker Jr.; 3,505,438 to R.P Alger and others; 3,538,429 to J. H Baker Jr.; 4,035,718 to R.N. Chandler.

Each of the NMR loggers that have been proposed or constructed has had practical drawbacks. All of them have had to face the fundamental difficulties of making this type of delicate measurements under difficult conditions with regard to temperature, pressure and physical trauma that is typical of logging runs in oil wells. Furthermore, since the concentration of hydrogen nuclei in the borehole is much higher than the concentration in any rock formation, the unwanted NMR signals arising in a borehole are potentially much higher than any signals from the surrounding formations. To alleviate this difficult phenomenon, it has been known in the art to treat the borehole fluid with a "paramagnetic" component such as magnetite, and to circulate the treated fluid through the borehole before a logging run is made, so that the relaxation time of the hydrogen core in the borehole is shortened so so much so that its contribution to the NMR measurement is eliminated. Such pretreatment of borehole fluid is expensive and time-consuming. Pretreatment can also introduce the same chemical via the borehole into adjacent permeable formations and thus distort the measurements.

It has also been realized that the NMR logging devices that require powerful electromagnets tend to be unreliable because the high power currents flowing through the device inevitably tend to break down various electronic components such as switches, especially under high temperature conditions. the environment in boreholes. The earlier devices all required the probe or sidewall body to be constructed of non-metallic material such as fiberglass, synthetic rubber or Teflon to enable detection of AC signals. These materials are considerably weaker than the metal alloys normally used in the construction of other types of logging equipment. The fact that it has not been possible to use a strong metal main structure when constructing NMR logging devices has further contributed to their being relatively unpopular in the field.

Earlier NMR loggers typically required about 20-30 milliseconds, called "dead time", after a polarizing field pulse is turned off and before the transmitter coil is sufficiently damped to allow measurements to be taken. During this dead time, significant information about magnetic relaxation is irretrievably lost, and the S/N ratio is significantly reduced.

The commercially available NMR logger cannot directly measure the spin-spin relaxation time T2. Instead, the existing conventional apparatus measures the free fluid index (FFI) and the observable dephasing relaxation time T2<*>, also called the free induction decay time constant. Various techniques for log interpretation can be used to derive other useful information, as discussed in, for example, "Applications of Nuclear Magnetism Logging to Formation Evaluation" by C.H. Neuman and R.J.S. Brown, Journal of Petroleum Technology, (Dec.1982), pages 2853-2860, and in the above-mentioned article by Herrick and others.

The basic purpose of carrying out NMR measurements in boreholes is to obtain information about formation constituents that surround the borehole. Such information typically relates to the magnetic relaxation time for hydrogen nuclei in water and hydrocarbons, but it can also relate to physical parameters or other particles in the formation.

It is known that after the application and removal of a magnetic polarization field, a quantity of hydrogen nuclei or protons can undergo relaxation in several modes, as discussed in the previously cited references. As explained in Herrick et al. above, the NML apparatus applies a highly polarizing DC field Bp to the formation to align proton spins approximately perpendicular to the Earth's magnetic field BE. During normal mode operation of the apparatus, the polarization field is applied over a period of about five times Tx to polarize formation protons to saturation. A very large polarizing current (with a power of the order of 1 kilowatt) is turned off, and after the coil is completely damped, which requires about 25 milliseconds, measuring circuits are connected to the coil to detect signals induced in it by the amount of protons in the formation which now freely precesses around the earth's magnetic field BE. This free induction attenuation signal, called FID, has a frequency equal to the Larmor frequency uL in the earth's field, which is about 2 kHz, as shown in Figure 20. The basic NMR measurement is then an induced voltage in a conducting coil placed in the borehole. The amplitude, frequency and phase of this voltage signal must then be correlated with secondary parameters that tell us something about the magnetic characteristics of the measured amount of protons, namely T2, T2<*.>The secondary parameters must, in order to be used, then be connected with a interpretation method that provides the desired information, such as fluid porosity, viscosity, permeability or water content for the measured formation.

Reference is made to Figure 20 where it appears that it is previously known to measure the attenuation envelope of the free induction attenuation signal of 2 kHz, also to extrapolate the envelope to the original time T0 at which the polarization pulse Bp was switched off. The stress amplitude at T0, when multiplied by calibration constants which depend on the design parameters of the particular device, gives the free fluid index (FFI), also called the free fluid porosity (Of). The FID attenuation curve is known to be associated with the observable dephasing time constant T2<*.>

The NML apparatus can also be used in a "T-L stationary mode" where a series of non-saturated polarization pulses are applied to the formation while the apparatus remains stationary in the borehole at the measuring depth. Reference is made to Figure 21 where the free induction weakening signal is measured and a weakening envelope estimated, as before, to extrapolate the formation magnetization at the time t0 when the polarization pulse was switched off, and this is successively done for each polarization period a, b, c and d. the larger the polarization period, the more formation protons are aligned with the polarization field Bp and the higher the resulting net magnetization. These polarization pulses should be non-saturating, since the maximum magnetization M (t0) and the FID curves following the saturation pulses will be identical and redundant. The extrapolated magnetization values at the moment after turning off the polarization field, M (t0), are then plotted as a function of the polarization period to obtain a Tx build-up curve having a characteristic time constant equal to the longitudinal relaxation time 11. In previously known interpretation methods, T± was typically estimated by to fit the Tx build-up curve to an exponential attenuation function using commercially available "least squares fitting" computer programs.

Although only four points are shown in Figure 21, it is known in the art to make up to eight separate sets of FID measurements and obtain corresponding values for maximum magnetization M(t). The motivation for extracting Txer based on a desire to determine the fluid flow permeability, k, using certain known correlations between k and Tx, as discussed in the literature, for example A. Timur, "Pulsed Nuclear Magnetic Resonance Studies of Porosity, Movable Fluid and Permeability of Sand Stones", Journal of Petroleum Technology (June 1969), pages 775-786.

Because the S/N ratio for each measured T2<*-> attenuation signal is not very high in connection with the problem that the proton precession during the first 20-30 milliseconds after turning off the polarization pulse cannot be measured, it is seen that significant errors can is introduced into the estimated magnetization value at t0.. The resulting T-j^ build-up curve fitted to the data can suffer from large errors, and the extracted parameter T-l tends to be unreliable.

For many of the above reasons, the prior art logging apparatus and interpretation methods have not been able to determine formation characteristics with sufficient accuracy and reliability to be fully accepted in the field.

Accordingly, it is an object of the present invention to provide an improved apparatus and method for determining magnetic characteristics of bedrock formations more accurately and more reliably.

It is a further object of the invention to provide an apparatus and method for determining the nuclear-magnetic relaxation time, the free fluid porosity, permeability and related pore fluid characteristics in bedrock formations penetrated by a borehole.

It is also an object of the invention to provide a borehole apparatus for measuring magnetic resonance which can be constructed of strong metallic materials, which can work repeatedly under borehole conditions with high reliability, and which can accurately measure formation characteristics without requiring any pretreatment of the borehole fluid with magnetic substances.

It is a further object of the invention to provide a magnet configuration for NMR measurements which has a simple, robust construction and which is easy and convenient to test, calibrate and use when logging a borehole.

It is also an object of the invention to provide a magnetic resonance logging apparatus which directly measures the transverse relaxation time T2 for formations penetrated by a borehole.

According to another aspect of the invention, it is an object to provide improved methods for determining

the permeability and similar parameters based on measured free induction weakening signals from NMR logging devices.

It is also an object of the invention to provide improved methods for determining the magnetic relaxation times for a measured quantity or population of particles in foundation formations surrounding a borehole.

According to the invention, an apparatus is provided for examining a property of a rock formation that is penetrated by a borehole, and the apparatus is precisely defined in the attached patent claim 1. The invention also includes a method for determining a property of a rock formation that is penetrated by a borehole, and the method according to the invention is precisely defined in the attached patent claim 2. Further advantageous embodiments of the method appear from the attached independent patent claims 3-15.

By directing and configuring the combined magnetic fields from a configuration of magnets, the applicant has produced an area, distant from the magnet configuration, where the spatial field gradient is mainly around zero, thereby ensuring that the field is very homogeneous throughout the area in question. In a preferred form, the magnets are mounted inside a slide or logging pad, the static magnetic field is directed through the face of the pad into an adjacent formation, and the region of substantially homogeneous field is located in a volume of the formation behind the mud cake layer that usually covers the borehole wall. A homogeneous magnetic field several hundred times stronger than the Earth's magnetic field can thus be applied or "focused" on a volume of the formation in situ.

The RF antenna can be mounted on the outside of the metal structure of the device, so that the probe body serves as a natural shield against any signals that may be generated by resonant conditions behind the body, especially the potentially strong resonant signals from borehole fluid. In the preferred form, the antenna is designed to focus its signals radially outward from the pad surface into the formation volume which has the homogeneous field, thereby additionally reducing the distortion of measured signals due to borehole effects. As a result of this distinct feature of the invention, the logging apparatus can be constructed of strong metal alloys in contrast to previously known apparatus, and the present measurement technique actually uses the shielding effect of a metal probe to its advantage, to enhance the S/N ratio of the NMR measurement. Since borehole effects are excluded by means of the dual-focus design, it is no longer necessary to pre-treat the borehole fluid with parametric chemicals.

An elongated trough antenna may be arranged on a pad surface parallel to the borehole axis and with an elongated volume of substantially homogeneous static magnetic field in the adjacent formation. By superimposing the geometric shape of the volume of the homogeneous and static field with patterns to the RF field from the antenna, close to optimal resonance conditions can be created. The static field can be directed radially into the volume, while the RF field is directed circumferentially and thus perpendicular to the static homogeneous field inside the examination volume. The length of the trough antenna is preferably approximately equal to the length of the examination volume.

According to the present invention, methods and apparatus are provided for making rapid, pulsed measurements of magnetic resonance in basic formations surrounding a borehole, in particular direct measurement of spin-spin relaxation time T2, to determine formation characteristics.

The transmitter antenna can also be used to receive magnetic resonance signals, and special circuits are used to very quickly dampen the ringing current that occurs in the antenna after the power is switched off. The special circuit called a Q-switch attenuates the polarizing antenna current about 1000 times faster than the previous device and makes it possible to send many pulses in sequence into a formation over a short period of time.

By greatly increasing the number of measurement periods, it is possible for the logger to: (1) increase the S/N ratio of the total measured data set by either allowing a faster logging speed or continuous logging, and (2) reduce the NMR measurement time during which nuclei can diffuse into rock pores, thereby reducing the unwanted magnetic effects of such diffusion.

In connection with the invention, additional equipment can be used to pre-polarize a formation volume of interest before the main magnetic device comes close to the formation. The pre-polarization field is preferably much stronger than the field of the main magnet configuration, and serves to increase the amount of protons aligned in the BQ vector direction, thus further increasing the level of the magnetic precession signal.

Small currents can be introduced near the measuring apparatus to change the static field during part of the measurement period to destroy the signals from these localized areas. The small currents can flow through a wire which preferably has the shape of a loop that covers the antenna opening and is attached parallel to the wall contact surface of the device. This design serves to significantly reduce or eliminate any resonant signals produced by borehole mud or mud cake immediately adjacent to the antenna surface, and significantly reduce unwanted signals. The spatial extent and magnetic effects of these field inhomogeneities can be carefully controlled by choosing the distance between adjacent sectors of the wire, the current and other relevant dimensions. The wire or its equivalent can be used to produce magnetic field gradients that extend into the volume of measured resonance, enabling other beneficial magnetic measurements.

The invention allows for the interpretation of the measured data, such as free induction weakening signals, magnetization curves of the pulse sequence type and other magnetic resonance measurements, to determine the values of characteristics of formation pore fluid, such as permeability.

Due to other purposes and advantages of the invention and to provide a better understanding thereof, reference is made to the following description in connection with the cited references and the attached drawings, where: Fig. 1 is a side view of an NMR logging apparatus in a borehole to make measurements of surrounding formations, according to present invention; Fig. 2 is a diagram representing the principle of measuring the system in the apparatus of Figure 1; Fig. 3 is an enlarged cross-sectional view of a magnet array used in the preferred embodiment of the present invention shown in Fig. 1; Fig. 4 is a diagram showing the magnetic field lines, represented by arrowheads, surrounding the magnet array of Fig. 3 when placed inside a borehole; Fig. 5 is a diagram showing, in cross-section, magnetic field lines B0 of equal size for the magnet group shown in Figures 3 and 4; Fig. 6 is a diagram showing magnetic field lines for B0 with the same magnitude of 232 gauss, as in Figs. 3-5, and which also shows the survey area for the preferred embodiment shown in Fig. 1; Fig. 7 is a diagram in cross-section showing the magnetic field lines for equal size inside the examination area shown in Fig. 6; Fig. 8 is a diagram of magnetic field lines showing the vector directions and magnitude of B0 within the investigation area of Fig. 6; Fig. 9 is a perspective sketch of an antenna according to present invention; Fig. 10 is an enlarged side view in cross section of the antenna which is shown in Figure 9; Fig. 11 is an enlarged elevation of the wall in contact with the surface of the logging apparatus shown in Fig. 1, particularly cut away to show the antenna and a meander wire according to the invention; Fig. 12 is a block core of circuits which preferably located in the apparatus of Figure 1; Fig. 13 is a diagram of the ratio Bx divided by the square root of the power Px which is fed to a preferred embodiment of the antenna according to the invention, as in figure 1; Fig. 14 is a diagram showing representative signals which fed to the amplifier of Figure 9 and Figure 12; Fig. 15 is a diagram showing the pulse shape of an example of an oscillating magnetic field B-,^ produced by the antenna of Fig. 9; Fig. 16 is a circuit diagram of a Q-switch in accordance with present invention; Fig. 17 is an enlarged cross-sectional view of a pre-polarizing magnet comprising three plate magnets in accordance with an alternative embodiment of the invention; Fig. 18 is a diagram showing the magnetic field lines, represented by short arrows, within a survey area in front of the biasing magnet of Fig. 17; Fig. 19 is a diagram showing magnetic lines of equal size inside the survey area on Figure 17; Fig. 20 is a diagram showing a simplified, schematic FID signal and its attenuation envelope, in accordance with previously known interpretation methods; Fig. 21 is a diagram showing four curves representing the attenuation envelope of four sets of FID signals (not shown), plotted on a semi-logarithmic scale in accordance with prior art interpretation methods; Fig. 22 is a diagram showing a three-dimensional representation of several sets of FID signals extrapolated to their initial values and construction of a T1 build-up curve in the M(tpol) plane in accordance with previously known interpretation methods; Fig. 23 is a diagram showing eight sets of positive peak FID signals and their corresponding global fitting curves in accordance with a preferred interpretation method according to the present invention; Figs. 24A and 24B are diagrams of a T,_ build-up curve which in figure 22, but which additionally shows integration of the curve in accordance with another preferred interpretation method according to the invention; Fig. 25 is a diagram showing a series of spin echo measurements that can be made with the preferred apparatus according to the invention shown in Figures 1-15, and which further shows the integration of the curve in accordance with another preferred interpretation method according to the invention; Fig. 26 is a diagram showing laboratory measurements of T1 and T2 over relevant rock samples from different formations penetrated by, for example, an oil well, where each data point also shows a line that is representative of relative errors in the measurement of T2 due to internal magnetic inhomogeneities in the rock samples ; and Fig. 27 is a diagram showing laboratory measurements of T1 and T2 for relevant rock samples from different formations penetrated by, for example, another oil well, similar to Fig. 26.

Reference is made to the drawings and in particular to Figure 1, where a borehole 10 is shown adjacent formations 11, 12, the characteristics of which are to be determined. Inside the borehole 10 is shown a logging probe or a logging device 13 connected via a cable 8 with surface equipment 7. The device 13 preferably has a surface 14 shaped for intimate contact with the borehole wall, with minimal spaces or distances. The apparatus 13 also has a retractable arm 15 which can be activated to press the probe body 13 against the borehole wall during a logging run, with the surface 14 pressed against the surface of the borehole wall.

Although the device 13 in the preferred embodiment in Figure 1 is shown as a single body, the device can of course comprise separate components such as a sleeve, probe or slide, and the device can be combined with other logging devices as will be clear to those skilled in the art. Although the cable 8 in the preferred embodiment also forms a physical support and communication link for the invention, there are clear alternatives, and the invention can be included in, for example, a drill string using forms of telemetry that do not require a cable.

The formations 11, 12 have distinct characteristics such as formation type, porosity, permeability and oil content, which can be determined from measurements taken using the apparatus. Deposited on the borehole wall of the formation 11, 12, is typically a layer of mud cakes 16 deposited on this by natural

infiltration of borehole fluid filtrate into the formations.

In the preferred embodiment shown in figure 1, the device 13 comprises a magnet group 17 and an antenna 18 placed between the group 17 and the wall contact surface 14. The magnet group 17 produces a static magnetic field B0 in all areas surrounding the device 13. The antenna 18 produces to selected times, an oscillating magnetic field B1 which is focused into the formation 12, and is superimposed on the static field B0 in the parts of the formation which lie opposite the surface 14. The examination volume of the apparatus, which is shown by dotted lines in Figure 1, is a vertically elongated area directly in front of the apparatus surface 14 where the magnetic field produced by the magnet group 17 is essentially homogeneous and its spatial gradient is approximately equal to zero.

A biasing magnet 19, which is shown in dashed lines, may be placed directly above the array 17 in a modified embodiment of the invention which will be discussed separately.

The apparatus 13 takes a measurement by magnetically tilting the nuclear bundles of particles in the formation 12 with a pulse of the oscillating field B-^ and then detecting the precision of the tilted particles in the static, homogeneous field B0 within the examination volume over a period of time. As shown in Figure 1, this survey area does not overlap the surface of the wall contact surface 14 as in certain earlier logging devices, and does not overlap the mud cake 16 on the borehole wall.

In a pulse echo type measurement as discussed in detail in the previously cited book by Farrar and Becker, for example, a pulse of radio frequency (RF) current is passed through the antenna 18 to generate a pulse of RF field Bx, where the RF frequency is chosen to be in resonance with only hydrogen nuclei subjected to a static field strength equal to the field B0inside the survey volume. The signals induced in the antenna 18 after the RF pulse represent a measurement of nuclear magnetic precession and attenuation within the volume, and automatically exclude unwanted contributions from borehole fluid, mud cake or surrounding formations where

the field strength of B0 is different.

When constructing the preferred embodiment of the invention, the applicants have sought to optimize the signal/noise ratio (S/N ratio) of the measurement process. As those skilled in the art will appreciate, the following discussion helps to explain the main parameters considered in making the preferred embodiment of the invention.

Reference is made to Figures 2 and 3 where, in order to consider the signal strength of a nuclear magnetic resonance measurement made by the apparatus 13 in the adjacent formation 12, it is useful to treat the interaction between the antenna 18 and the magnetic moment of the formation as parts of a single circuit with four terminals , to which the reciprocity theorem can be applied. The circuit 20 having an input impedance Z0 comprises a lossless matching circuit 21 and an RF probe or antenna 22 which is simply shown as a resistance and an inductance in series. An oscillating current 1^ of frequency <■> flows through the RF probe 22, producing an oscillating magnetic field Bxi the formation, comprising the area inside a test loop 23. The voltage induced in the test loop 23 as a result of the current I-^ is given by

where Z21 is the cross-impedance between the antenna current and the voltage induced in the test loop 23. Now suppose that a current I2 is applied to the test loop, and induces a voltage V1 at the terminals of the matching circuit 20, which is where Z12 is the cross-impedance between the test loop current and the voltage induced in the antenna 22. At using the resi-prosity theorem, Z12<=Z>21, is obtained Since the magnetic moment of the loop 23 is m=I2A, the magnetization dM of a volume dV is equal to dM=I2AdV. The net signal from the entire formation can be derived from the above and represented as where the integral is taken over the volume in which the resonance condition B0=&)/y is satisfied. In order to optimize the measured signal response of the present NMR apparatus, we can assume that the volume of the NMR examination has an area AR and a length L, and that the integrand is constant within this volume. In practice, it has been shown that this assumption is a fairly good approximation. By making the substitutions o> = yBQ and M = xB0//i0in the above equation, where y is the gyromagnetic ratio, jU0 is the magnetic permeability of its space and X is the nuclear magnetic susceptibility for protons in the formation, we derive Now we wish to estimate the size of the area AR for relevant magnetic designs such as that of the magnet array 17 shown in Figure 1. As discussed in more detail below, the magnet array 17 produces a static magnetic field B0 with a saddle point at the center of a homogeneous field region denoted as volume 9 in Figure 1. The field strength can be approximated using the Taylor series evolution

Note that the resonance condition in pulse NMR technique is fulfilled when the static field's deviation from the center value B0(x,y)-B0(0, 0) is not greater than half the size of the RF field B1, so that the area of the resonance region can be deduced to be approximate

after making the simplified assumption that the area has a square cross-section. This and other approximations are made here to illustrate in simpler ways the principles underlying the invention, as it will be understood that other more accurate derivations are clearly possible. By making substitutions in the above equation (5) for the measured NMR signal, it is clear from the qualitative conditions in equation (8) that the measured NMR signal can be made better or worse by changing the various given parameters. However, the increase in the signal level is not sufficient, and it is highly desirable to keep the thermal noise level as low as possible in relation to the signal Vs. The root mean square of the thermal noise is where Z0 is the input impedance of the matching circuit 20 (nominally 50 ohms), k is Boltzman's constant and Af is the measurement bandwidth, which is matched to the bandwidth of the population of resonant particles in the formation, YBi/27r- The following ratio of peak signal to the mean square root of the noise is obtained:

In equation 10, the power fed to the antenna, P-^ has been substituted for the current by using the ratio P1=I1<2>Z0/2. By further applying the conventional definition of susceptibility according to the Curie law in MKS units,

we get the final expression for the signal/noise ratio In equation 12, the first - the expression in square brackets above depends on environmental parameters such as proton spin density N for the fluid, porosity ( f> and absolute temperature T. Some of the other expressions are Planck's constant (above 2tt) " Ti, and the nuclear spin I which has a value of 1/2 for protons. The second expression in square brackets contains design parameters that optimize device performance. It is easy to see, for example, that a high static field B0, which is included in second power, can greatly improve the S/N ratio. Furthermore, it is shown that the expression (B1/P11//2) 2^ 2 which is related to the "Q" value of the antenna should be made large. S/N- however, the ratio can undoubtedly be increased by increasing B1/P11'/2 because equations (10) and (12) hold only when the bandwidth is limited by YB1/2lt, for example when Q<B0/B1.However, when Q>B0/B1 , the bandwidth is Af=yB0/2HQ, and equation (12) becomes

For a fixed antenna geometry and measurement point, it is known that the size E1/ P11/' 2 is directly proportional to Q<1//2.> It can be seen from the above that a further reduction of the antenna losses beyond the point where Q>B0/B1 is not will increase the S/N ratio.

Reference is made to figures 1 and 3, where the magnetic assembly 17 consists of 3 permanent magnets 24, 25, 26 of samarium cobalt, which are mounted parallel to each other inside a body 27 of a metal alloy. The magnets 24, 25, 26 are elongated in the direction along the borehole, measuring 12 inches in the preferred embodiment. The magnetic poles of the magnets are not on the smallest faces of the rod or plate, which are usually considered the ends of a bar magnet; instead, the poles appear on the two opposite edges of the plate magnet and point to the left and right, respectively, in both figures 1 and 3. Inside the formation 12, the magnetic field B0, which surrounds the magnets, thus remains fairly constant along the longitudinal direction of the borehole axis.

The magnets 24, 25, 26 should be as strong as practicable and should be able to withstand physical shocks without breaking. For example, the samarium cobalt magnets that have been used are preferably enclosed in a robust brass sleeve to prevent possible explosive fragmentation in the event of magnet cracking or breakage. These magnets are commercially available and have a residual inductance of typically 10500 gauss (1.05 T). It will be clear to those skilled in the art that other magnets can be used instead of the samarium-cobalt magnets mentioned here, and the plate magnets can have different dimensions than what is shown in the preferred embodiment.

It is preferred to use elongated plate magnets to produce a static field in the formation 12 which is constant over a considerable distance L along the z-coordinate parallel to the borehole axis. A large L improves the S/Is ratio and also facilitates continuous logging along the z coordinate. However, the magnets should not be so long that they make the apparatus 13 structurally unmanageable or cause too great a distance between the surface 14 and the borehole wall in washed out zones.

The magnets 24, 26 are symmetrically mounted on the two sides of the body 27 with the north poles facing in the same direction. Magnet 25 is arranged parallel to and between the other two magnets, but with its north pole facing opposite to the magnets 24, 26. As shown in figure 3, the north poles of the magnets 24, 26 point in the direction of the surface 14 of the apparatus, while the north pole of magnet 25 points away from the surface 14, although the configuration clearly can

be reversed and still produce a similar result.

Reference is then made to figures 4-6, where it can be seen that by designing the two N-poles of the magnets 24, 26 to point towards the surface 14 and the formation 12 which lies outside this, the magnet group 17 at a great distance will act like a magnetic N-pole. However, the reversed pole positioning of the magnet 25 significantly changes the magnetic field at close and intermediate distances into the formation 12. At intermediate distances, this preferred embodiment of the magnet group 17 produces an interesting and important field irregularity within a clearly defined volume directly in front of the device surface 14. As shown in greater detail in figure 5-7, there is a well-defined volume where the magnetic field is mainly constant, and where the spatial gradient of B0 mainly disappears. This is the primary resonance area of NMR measurements and is the area of investigation shown in Figure 1.

Figure 8 shows weighted arrows following field lines within the cross-sectional area about one inch from apparatus face 14, with the length of each vector arrow proportional to the field strength and the direction of each arrow arranged in the same direction as the field lines. It can be seen that the field projects radially into the formation and that it is fairly uniform over this area, and has an essentially constant field strength of around 232 gauss.

Although the volume with the greatest field homogeneity is centered around a point approx. 4/5 inches away from the wall contact surface, this volume of essentially homogeneous field can be displaced either further or shorter into the formation, depending on the relative positioning, distance and field strength of magnet 25 relative to magnets 24, 26. It is additionally possible by means of other embodiments of the invention to provide for displacement of the magnet 25 inside the body 27 during operation of the apparatus, in order to provide a variable examination depth, depending on the circumstances. If, for example, a formation with high roughness or extremely thick mud cake is encountered, the logging operator can shift the position of the magnet 2 5 a predetermined distance to the right, as shown in figure 3, so that the survey volume 9 is shifted further into the formation, in order to avoid providing unwanted resonance signals from the sludge cake. In the preferred embodiment shown in the figures, however, the magnets 24, 25, 26 are rigidly mounted in position since the resulting positioning of the volume 9 already avoids any significant overlap with the relatively thin mud cake layer in typical boreholes.

Reference is again made to figures 5, 6 and 7 where it can be seen that the size of the examination volume 9 may depend on the nature of the measurement being taken and the strength of an RF pulse which is sent out by means of the antenna 18, as explained below .

The metal body 27 has on the front surface 14 a semi-cylindrical designed cavity or slot 28 which faces formations with which the surface 14 is in contact. The cavity 28 is arranged to receive the RF antenna 18, which will be further described below. However, one can already clearly see that the antenna 18 is placed outside the metal body 27 of the device, and is automatically shielded from electromagnetic communication with areas of the borehole that lie behind the body 27, or areas of other formations in directions cut off by the body 27. 18 thus only responds to magnetic fields that originate in front of the wall contact surface 14, for example fields that originate in the formation 12 or in the mud cake or in the mud that is in contact with the surface 14 in the vicinity of the antenna

18. By utilizing the relative geometric positioning of the antenna and the metal body 27, it is possible to minimize unwanted signal contributions that would otherwise be difficult to eliminate by means of other precautions. In the preferred embodiment, the body 27 is made of thin plates of a metal alloy rigidly attached to an internal

metal bracing, which surrounds most of the components of the apparatus apart from the antenna 18, including the circuit, the magnet group 17 and the hydraulic system of the arm 15. It is also possible to construct the body 27 from other material combinations such as

composite resins, steel, etc., as long as the overall structure is sufficiently strong and the magnetic field of the magnet group 17 can penetrate and enter the adjacent formation 12.

The antenna 18 is used both as an RF transmitter to produce a polarizing magnetic field in the formation 12, and as a receiver antenna to detect coherent magnetic signals originating from precessing protons immediately after the polarization field has ended. The antenna 18 should be constructed of one or more current-carrying loops which are very effective for generating magnetic fields in the formation. It is preferably made of a current loop which produces an oscillating field B1 inside the examination volume, which is perpendicular to B0. Other current loop orientations may be usable in other embodiments of the invention that have a static field B0 different from that of the preferred magnet array 17.

The antenna 18 is attached to the body 27 and fitted into the slot 28. Its efficiency can ideally be maximized when the current density inside the slot 28 is made uniform. In practice, optimal antenna efficiency is difficult to achieve due to various electromagnetic parasitic effects such as the "skin effect", the mutually inductive effects between distinct current loops and electrical effects inside individual conductors. The preferred antenna 18 according to the invention comprises a single current loop, in the form of a trough or a slot, as shown in Figure 9.

Reference is made to Figure 9 where the antenna 18 comprises a well-conducting semi-cylindrical cavity or trough 29, end plates 30, 31 and antenna element 32 which extends from one end plate 30 to the other end plate 31, parallel to and centered in the semi-cylindrical trough 29. The trough 29, the end plates 30, 31 and the antenna element 32 are all preferably made of thick copper which has extremely low electrical resistance. The antenna element 32 is isolated from the end plate 30 by means of a non-conductive bushing 33 and is connected to an electrical assembly 34 on the other side of the end plate 30. The antenna element 32 is attached at its other end to the other end plate 31 so that current passes freely between the trough 29 and the antenna element 32 via the end plate 31. The electrical assembly 34 is shown schematically in figure 9 as if it is connected to the circuit comprising an amplifier 35 and a detector 36. All connections in the antenna 18 are the solder or the silver solder to ensure sufficient

low resistance losses.

The RF antenna may be powered by the amplifier 35 for specified periods of time, during which it serves as an RF transmitter antenna. At other specified times, the antenna 18 can alternatively be electronically connected to the detector 36, during which times it serves as the RF receiving antenna. In certain operating modes, the antenna 18 can alternatively be used to function as a transmitter or receiver in very rapid succession. The space between the trough 29 and the antenna element 32 is preferably filled with a non-conductive material 37 which has a high magnetic permeability. In order to increase antenna sensitivity, ferrite materials are preferably used. Several tuning capacitors 3 8 are connected between the base of the antenna element 32 and the trough 29, the capacitances being chosen to provide an LC circuit, where the resonant frequency is the Larmor frequency

<=>Y<B>0-

Reference is made to Figure 10 where the relative dimensions of the antenna 18 are to be selected to maximize the antenna efficiency. The radius R of the slit element should be as large as practically possible, and the distance R-r should be maximized under the condition that r must not be so small that the antenna's impedance is increased too much. It has been found that for a twelve inch (30.5 cm) trough antenna without ferrite fill, R=0.75 inch (1.9 cm) in r=0.2 inch (0.5 cm) produces optimum efficiency. A ferrite-filled trough antenna with dimensions R=0.75 inches (1.9 cm) and R=0.3 inches (0.76 cm) has been found to be optimal. The length L of the antenna may be the same as the length of the magnet array 17, which is twelve inches (30.5 cm) in the preferred embodiment, but preferably the antenna 18 is approximately the same length as the resonant region produced by the magnet array 17 in the formation, which is

about 4 to 8 inches (10.2 to 20.3 cm) long.

The field B± produced by the antenna 18 is an oscillating magnetic field with a frequency f equal to the resonance frequency of hydrogen nuclei in the sensitive volume of the formation where the static field is around 232 gauss. Therefore, f = (yB0) / 2ir = 1.0 MHz. The strength of Bx has a direct influence on the bandwidth of precessing nuclei brought into resonance by means of B1i according to the bandwidth formula:

Since the static field B0 is about 232 gauss in the preferred embodiment and the antenna generated field strength Bx at one inch is 3 gauss, the resulting bandwidth of B0 inside the desired volume is also 3 gauss.

The strength of the Bx field in the sensitive volume also affects the S/N ratio (equation 12) in accordance with the expression B1/P11//2, where B-1 is perpendicular to the static B0 field. Figure 13 shows a plot of the magnitude of B^P<1/2> in front of a 12 inch trough antenna, where Px is the power supplied to a 50 ohm impedance matching circuit for the antenna 18 and Bx is the circularly polarized component of the radiated field. It is seen that the field strength is fairly constant equal to one inch for a longitudinal distance of about 8 inches.

Reference is now made to figures 3, 10 and 11 where the antenna 18 is fitted in the slot 28 and covered with a wear plate 39 made of non-conductive wear-resistant material to protect the ferrite material 37 and the antenna element 32. In addition, it is preferred to arrange either under or inside the wear plate 39, a thin conductive wire 40 which mainly fills the antenna opening. The wire 40 is preferably arranged in a loop with a distance S between the wire segments of about half an inch, although this dimension can be changed if it is desired to destroy magnetic resonance in a local area of greater or lesser thickness. A small direct current is passed through the wire 40 at selected intervals during the measurement cycle to generate local, inhomogeneous magnetic fields B2 which extend towards the formation 12 over a distance approximately equal to the distance S between the wire segments. Within this area of local field inhomogeneity, nuclear magnetic precession is interrupted during part of the measurement period, and any resonance states that are otherwise created by the intersection between B0 and are changed to a significant extent. The wire 40 constitutes one form of an arrangement for creating localized, inhomogeneous fields, and other embodiments are clearly possible. For example, several wires, coils or conductive grids can be used.

Destruction of the resonant field states in the mud cake regions is particularly advantageous for the preferred embodiment shown in Figures 1-8 because a typical mud cake contains a high concentration of hydrogen nuclei which can resonate strongly with an impressed RF pulse from the antenna 18. The mud cake located at the side of the antenna 18 is exposed to a stronger RF field B1 than even the examination volume 9 in the formation 12, and can therefore be strongly polarized by Bx. Furthermore, there are points of high gradient within half an inch of the surface 14 where the B0 field strength is equal

the resonance frequency of 232 gauss, as shown in figure 6-7. By applying pressure to the inhomogeneous field B2 within the sludge cake area and destroying the resonance conditions there, any unwanted NMR contributions from the sludge cake can be eliminated.

The wire 40 produces a magnetic field B2 which has a high spatial gradient dB2/dx, and can alternatively be used to produce field gradient-type NMR measurements inside the formation 12. In this case, it would be desirable to align the relevant dimensions of the wire 40 so that the area of measured NMR resonance overlaps with the gradient field B2.

It is seen that the apparatus 12 as described measures in a single direction with preferably straightening or "focusing" both the static field B0 and the oscillating field B±, to create the particular examination volume 9. By applying a further localized field B2 at areas between the volume 9 and the instrument face 14 which destroys resonance therein, the measurement effectively excludes signals originating from within the mud cake region of the borehole. Since the measuring range

(sensitivity distance) to the device 13 further is quite

limited, it is possible to enclose the apparatus within a reasonably sized calibration cell during testing or calibrating the apparatus to exclude magnetic effects from the environment. Consequently, the efficient use of the apparatus 13 for closing oil wells is facilitated.

The necessary electronics for the device 13 can be mounted in the body 27 or in a separate module or probe. The preferred circuit shown schematically in Figure 12 operates in three modes: transmit, attenuate, and receive.

In the transmitter mode, the circuit 41 must generate a large power of about 1 kilowatt at a frequency of the order of 1 MHz over a short, precisely measured period, turn off this current very quickly, within about 10 microseconds, and then isolate any signals or noise from power- the circuits from coupling with other detection circuits inside the device 13.

Reference is made to Figure 12 where the transmitter circuit comprises a 20 MHz oscillator and a synthesizer 43 which generates a sinusoidal signal with a frequency of 20 MHz plus f, where f is the desired operating frequency of the device. Both oscillators are connected to a clock 44 and kept in synchronization at all times. The output from the oscillator 42 is fed to a phase turner 45 which is controlled by a time generator 46. The phase turner 45 can produce turns of 0, 90, 180 and 270°, as desired by the operator of the apparatus, and in accordance with the needs of different measurement methods, such as The Meiboom-Gi11 sequence. The phase-shifted signal passes through a gate 47, and is then combined with the 20 MHz + f signal from the synthesizer 43 in a mixer 48. The combined signal is fed through a low-pass filter 49 which allows only the signal with frequency f to pass. Although the mixer 48 also has other frequency components at its output, these higher frequency components are filtered out. The desired operating signal of frequency f can be switched on and off at any time by suitable control of gate 47 by means of timing generator 46. Timing generator 46 is kept in precise synchronization with the clock by means of a 40 MHz synthesizer. Furthermore, the oscillators 42, 43, which have much higher frequencies, can be in operation at all times without the risk that they will adversely affect the detection circuits operating at frequency f.

The f-signal containing information about the rotated phase is fed to the amplitude modulator 50 which regulates the amplitude to change the signal to a desired pulse shape. Both the modulator 50 and the gate 40 as well as other components in the circuit 41 are controlled by means of the time generator 46 which in turn is controlled by a computer 52.

Reference is again made to figures 14-15 where a typical pulse produced by the modulator 50 and the gate 40 has a first short time interval t(l) where the amplitude has been increased by means of the modulator 50, and a second short time interval t(2) during during which the amplitude is not increased, and a third short time interval t(3) during which the amplitude is increased and the phase of the signal is reversed. The third period of phase reversal is not necessary when the shaped pulse is already sufficiently attenuated by means of the Q switch described below. The increased amplitude during t(l) helps to reduce the time it takes to ring the RF antenna 18, while the reversed phase signal during t(3) helps to remove the ringing in the antenna 18 at the end of the pulse. The resulting pulse with the magnetic field B1 that is radiated into the formation 12 is therefore more like a square pulse.

The pulse signal from the amplitude modulator 15 is amplified by means of a power amplifier 35 which is able to output about 1.2 kilowatts without distorting the signal shape. The signal then passes through an extension circuit 53 which prevents low level noise on the order of 10 volts or less from leaking out of the amplifier 35 when it is not activated, during the receive mode. The amplified pulses are then fed to the RF antenna 18 which radiates a magnetic field pulse Bx to produce nuclear spins in the formation. Between the transmitter pulses, the RF antenna receives 18 oscillating magnetic signals from nuclear spin precession.

As previously mentioned, the receiver system with the RF probe and matching circuit is designed to have a high Q to maximize the S/N ratio. In such a high Q system, the antenna tends to ring or oscillate for an undesirably long time, causing undesired magnetic spin tilting in the formation. If the antenna is allowed to ring uncontrolled, the bandwidth of the delaying magnetic field pulse can be significantly reduced. In order to minimize antenna ringing problems, a Q-switch 54 is connected to the line between the extension circuit 53 and the antenna 18 as a preferred device to suppress antenna ringing very quickly at the end of a transmitted pulse. The Q-switch 54 closes a circuit at the appropriate time, which changes the impedance of the RF probe system (including the RF antenna 18), so that the system is critically attenuated and the ringing energy is rapidly dissipated.

During the receive mode, the Q-switch 54 is turned off, and signals from precessing cores are received by the RF antenna 18 and passed through a duplexer 55 to a receiver amplifier 56. The duplexer 55 protects the receiver amplifier 56 from the high-power pulses passing from the extension circuit 53 to The RF antenna 18 during transmission and attenuation. During the receiver mode, the duplexer 55 is effectively just a 50 ohm cable connecting the antenna 18 to the receiver amplifier 56. The detected and amplified signal is then fed to a dual-phase sensitive detector 57 which also receives a reference signal which controls the sensitivity frequency of the detector 57.

The reference signal, which also has frequency f, is generated by combining the 20 MHz and 20 MHz + f outputs from the oscillator 42 and the synthesizer 43 in another mixer 58, and extracts the low-frequency component f via a low-pass filter 59. The output from low-pass filter 59 which is a sine wave form with frequency f, is used as a reference signal both for the detector 57 and a pulse generator 60. The pulse generator generates a suitable pulse form as a reaction to control and trigger signals from the computer 52, and triggers the time generator 46.

The detector 57 provides, in response to the reference signal and the formation NMR signal from the receiver amplifier 56, a measured NMR resonance signal with frequency f from the desired examination volume, and leads it to a digitizing circuit 82. The digitized signal is then passed on to the computer 52 for processing and/or formatting according to the operator's wishes.

Reference is made to Figure 16 where the Q-switch 54 comprises two symmetrical circuits 61 and 62, shown respectively at the top and bottom of the figure. The purpose of the Q-switch 54 is to introduce a resistive element in the antenna circuit in parallel with the capacitors 3 8 (see figure 9), to attenuate the circuit critically in accordance with formal Rc= 1/2 (L/C) 1/2. For example, when L=1.1X10"<7>H, C=2.3X10"<7>F and at an operating frequency of 1 MHz, the additional resistance required to critically attenuate the antenna 18, Rc=0.3 6 ohms .

Q-switch 54 uses two field-effect transistors (FETs) 63, 64 connected back-to-back to provide approximately 0.36 ohm resistance when closed. Two field effect transistors are required since each is effective in providing a resistance to a high voltage of only one polarity, which is due to an effective internal diode 67, and the ringing of the antenna 18 is a bipolar oscillating voltage. If the resistive value required to critically attenuate an antenna 18 is greater than the resistance of the field effect transistors 63, 64, further resistive elements can be inserted in series.

When the field effect transistors 63, 65 are open, the circuit is an open circuit and has no effect on the antenna circuit. Thus, the Q switch is open during the transmitter mode and during the receiver mode of the circuit (Figure 12), and closed during the attenuation mode shown in Figure 14-15 as the time period t (3).

The remaining circuit in Figure 16 comprises devices for gate-controlling the field-effect transistors 63, 64 on and off with minimal introduction of noise into the antenna circuit. Since the circuits 61, 62 are essentially identical, only one of them will be described below.

In the transmit mode, during the RF pulse, a 20 nF capacitor 65 and the collector of a transistor 66 in an intermediate stage are charged through the line comprising diodes 67, resistor 68 (51 ohms) and diode 69, diode 67 being part of the field effect transistor 64 in the lower symmetrical circuit 62. The base of the transistor 66 is connected to an optical coupler 70 which is controlled by a signal on line 71 from the timing generator 46. The optical coupler 70 is preferably used together with the NMR logging apparatus because it ensures isolation between switching - the signals and the antenna's high voltage.

The emitter of the transistor 66 in the intermediate stage is connected via the diode 77 to the gate electrode 72 of the field effect transistor 63. The gate electrode 72 is also connected to a 1 k resistor 73 and an 8.2 nF capacitor 74 which in turn is connected to the source electrode line, to form a high-pass filter in an RC combination between the gate electrode 72 and the source electrode line 75. This RC filter ensures that the voltage from the source electrode to the gate electrode never reaches excessive levels during the emission of an RF pulse, and also provides a time constant for self-turn-off. A zener diode 76 is connected in parallel with the 20 nF capacitor 65 to prevent excessive voltages from damaging the optical coupler 70.

During the damping mode, a signal from the timing generator 46 is passed via line 71 to activate the optical coupler 70 and charge the base electrode of the intermediate transistor 66. The transistor 66 is turned on, causing a voltage to be applied to the gate electrode 72 to make the field effect transistor 63 conducting, and providing attenuation of the antenna circuit.

During operation of the apparatus 13, the operator enters information into the computer 52 regarding the type of measurement sequence to be performed. The computer 52 then sets the sequence of electronic steps necessary for the equipment to realize the measurement sequence. The computer 52 controls the time generator 46 which in turn sends control signals to the various components in the circuit 41 to control the polarization pulse height, length, frequency, relative phases between successive pulses, reception mode period and frequency,

and the time management of it all.

Because the high Q antenna 18 can be quickly attenuated after sending a one kilowatt RF pulse, the apparatus 13 is able to bring a target formation 12 into resonance with many successive pulses in a short time. The dead time between a transmitted pulse and the beginning of the receive mode, about 25 microseconds, is about 1000 times shorter than the dead time of the previously commercially available logger. Using peak power of 100 watts, the pulse can have a duration of about 40 microseconds, and it is possible to have as many as 1000 pulses within a measurement cycle lasting one second.

In addition to the NMR measurements previously known to be performed using the existing commercial logging apparatus discussed in the previously cited references, a Carr-Purcell measurement can also be performed to measure the transverse relaxation time T2. This sequence is also commonly known as a 180° - 90° sequence, where the angles refer to the degree of tipping that the precise protons undergo during the measurement process. Other measurement sequences that can be made with the present apparatus include the Meiboom-Gill sequence, as described in the book by Ferrar and Becker, or a 90° - t - 90° sequence of the type described in G.G. Mc Donald and J.S. Leigh, Jr, "A New Method for Measuring Longitudinal Relaxation" Journal of Magnetic Resonance, Vol.9, pages 358-362(1973), which measures the longitudinal relaxation time Tl. It is contemplated that additional types of downhole NMR measurements may be provided in accordance with the invention to advantageously investigate the magnetic properties of basic formations.

When the apparatus 13 is used to provide continuous logs without stopping the apparatus for each measurement, an alternative embodiment may be preferred to further improve the S/N ratio beyond what has already been discussed. Reference is made to figure 1 where a pre-polarization magnet 19 is fitted in the apparatus 13 above the position of the main magnet group 13, to magnetize and polarize the formation 11 before the magnet group 17 has reached close enough for measurement. The field of the pre-polarization magnet 19 should be the same as the field from the magnet group 17 with regard to orientation, but is preferably much stronger in order to polarize a much larger number of cores. As the device is moved up through the borehole, the magnet group 17 comes close to the formation 11, and irradiates it with RF pulses. Due to the pre-polarization, however, a larger number of cores are aligned with the field B0 to the magnetic group 17 within the volume of substantially homogeneous field, and a correspondingly larger signal is produced.

The biasing magnet is preferably an assembly of magnets in a form as shown in figure 17, comprising magnets 90, 91, 92, arranged with like poles facing in the same direction to maximize the field strength produced in the formation. It is clear that other combinations of magnets can produce a similar field, and a single magnet can be used instead of an assembly as shown. Reference is made to Figures 18-19 where the magnetic field Bp of the pre-polarization magnet 19 can be significantly less homogeneous than the field of the magnet group 17 without adversely affecting the bandwidth or the S/N ratio of the NMR measurement, which only depends on the existing static field B0 at the time of the measurement.

The preferred embodiments can of course be modified in many ways without deviating from the scope of the invention, which will be clear to those skilled in the art. For example, the pre-polarization magnet need not be constructed of the type of magnets shown in figure 17, but may be a single magnet or another arrangement. Plate magnets have been used because the slim profile tends to minimize demagnetization effects, and they are relatively easy to assemble. Since they are large and have very high energy density, the ease of handling and assembly of the magnets are important considerations, and the simple form discussed here has proven to be advantageous from many points of view. Nevertheless, other magnet types can be used in accordance with the invention.

If stationary measurements are desired, there is a possibility that differential wedging and other dynamic borehole effects can cause the apparatus 13 to become wedging. If such

stationary measurements are thus to be carried out, it is preferred to provide devices for forcing the apparatus surface 14 away from the borehole wall after the completion of a measurement cycle at a certain depth. For example, two push pistons 93, 94 which

is shown in Figure 1 with dotted lines, is hydraulically activated to push the device 13 away from the borehole wall after the arm 15 has been pulled back a little.

The apparatus described above can be used to make nuclear magnetic resonance measurements in formations surrounding a borehole to determine formation characteristics such as porosity, pore size and fluid flow permeability. Various methods for interpreting NMR log data that are previously known in the field can be used with the described apparatus.

Previously known interpretation of mode NMR attenuation data has first been aimed at deriving a basic formation characteristic such as Tx, and then relating it to other formation characteristics such as permeability k. The observed attenuation time-

the constant of the previously known logging apparatus, T2<*>, could not be directly related to k because T2<*> was dependent on various magnetic interactions between the environment, the boreholes, and the apparatus which masked the true decay time constant of the hydrogen nuclei in the formation pore fluids.

Reference is made to Figure 20 where the FID waveform signal 101 represents a signal measured with the previously known apparatus in either continuous mode or stationary mode, and where the attenuation envelope 102 is obtained from the peak values of the FID signal. No signals are received during the "dead time" of about 20-30 milliseconds after the end of each polarization pulse at time t0. Four such

attenuation envelopes 102 a,b,c and d are shown in Figure 21, where the FID signals 101 are measured after non-saturating

polarization pulses with duration tpol(a) , tpol respectively

(b) , ^pole (c) °9 '-pole • Note that the envelopes 102 in Figure 21 show many zigzag points, indicating noise in the signal, while Figure 20 shows an FID envelope 102 that appears smooth because it is a simplified, schematic drawing that does not show the effects of noise. In a previously known method for determining the longitudinal relaxation time T1#, each envelope 102 is fitted to an exponential attenuation fitting curve 103 (shown in Figure 21) of the form

where tdec is the attenuation time, and A0 is the maximum amplitude of the free induction attenuation signal at the time t0 when the polarization pulse is initially turned off, and A(tdec) is the mode amplitude. - The fitting program extracts values of A0 and T2<*> that show the best fitting , and the resulting value of A0 represents the extrapolated intersection with the ordinate axis at time tdec(0) , which is shown in Figures 20-21 as points FFI. In the previously known method, a second step is required where the extrapolated values are then plotted on a curve of amplitudes A(tpol) as a function of polarization time tpol, shown in Figure 22, which produces a T-^build-up curve 104. Finally, this T-L build-up curve 104 is fitted to another exponential attenuation representation typically of the form EA0 (l-e~t/"rii) to extract values for T1.

In contrast to the previously known interpretation technique described above, a preferred method according to the present invention simultaneously adapts the measured data to a model that comprehensively describes the NMR attenuation behavior and the changes to this behavior as a result of changes in the degree of initial pre-attenuation. This preferred method provides simultaneous adaptations of the measured amplitudes A by minimizing an adaptation size of the form where the representation allows the amplitude ARE to depend on both <t>dec and tpol simultaneously. Reference is made to Figure 23 where a number of FID enclosures 102a, 102b, 102c, 102d, etc. are shown, each of which is measured as in the previous Figures 20-21, but these envelopes are not individually or separately fitted to a mathematical representation, and no attempt is made to obtain an intermediate, extrapolated value of A(t0) for each sheathing, as was done previously. Adaptation is thus performed in a single step, in contrast to the two steps in the prior art.

The parameters for the amplitude and Tl in the model that provide the best fit to the measured data are extracted and used directly for interpretation of the data. The best fit is preferably obtained using a computer program of the least-squares fit type, which performs iterative numerical minimization of the square fit size

(also known as the customization bug. A program called "ZXSSQ")

which are well known in the art and are commercially available from IMLS Company, Houston, Texas, may be used, for example. Because fits are performed simultaneously with respect to both the NMR attenuation response and the differential responses due to different initial polarizations (tpol), and in a single step (by a "global" approach), the extracted parameters A.j_ and T1± significantly more robust and less affected by signal noise.

The three examples of representations are described below, which illustrate the preferred universal method of the invention. A general form of these representations that include amplitude and T1 parameters is:

where tpoles the polarization period of the formation that tends to tip or tilt the magnetic spins of the measured

particle population, before an attenuation signal is measured, Txier is the longitudinal relaxation time of the ith type or component of measured particles, and T2i<*>is the observed relaxation time of the ith type or component.

As a first preferred representation of the universal solution according to the invention, in particular the measured amplitudes for the FID signal 101 are represented by a sum of two exponential expressions:

The two-exponential representation is based on the assumption that the formation can be considered to contain two types of protons, each type having a distinct attenuation component with maximum amplitude A0, longitudinal relaxation time Txog transverse relaxation time T2<*.>The additional subscript i=l,2 denotes two components, one component characterized by short time constants for T1#T2<*>, and the other component by long time constants. This condition results in the observed attenuation time constant T2<*> being dependent on the polarization period tpol. The global method thus realizes that T2<*> is a function of the topological envelopes 102a, 102b, 102c, 102d, etc. are not parallel and need not have the same curvature in Figure 23. By simultaneously fitting all the attenuation envelopes using the K± and Txi parameters without intermediate fitting steps (as in the prior art), the present method further increases the amount of information that contributes to the fitting , and thus provides parametric values that are significantly more robust and less affected by noise in the data.

In another preferred representation according to the invention, the six parameters in equation (D) are reduced to five by assuming that the value of each T2i<*> is related to the corresponding<T>xi through a common parameter Tinh, defined by :

The parameter Tinh is a time constant that represents an additional weakening mechanism resulting from magnetic field inhomogeneities common to both types in the representation. The representation of equation (D) is thus reduced to:

By using the five-parameter representation, it is possible to obtain relatively robust values of As, AL and T1S,<T>1L, which can then provide information about the permeability or another desired characteristic of the measured formation. In many cases, the five-parameter model fits the data as well as the first six-parameter model.

Other representations can be used with the universal fitting method, which further reduces the number of parameters and thus improves the reliability of the estimated results when processing data that has a relatively low signal-to-noise ratio. In particular, a third representation with only four fitting parameters is given by

where the four parameters A, T1#a and Tinh, are used to achieve a complete description of the NMR attenuation. This model assumes that longitudinal relaxation behavior is described by a "stretched exponential" form:

This form occurs when nuclear magnetization is composed of a distribution of a finite number of distinct exponents from as many distinct types of magnetic particles, where the assumption is made that T2i<*>and T1± are connected to each other as in the second model. The stretched exponential "representation" has the advantage that it can extract relaxation time parameters with similar accuracy to the other models in certain cases, with even greater flexibility to problems arising from low signal-to-noise ratios in the data. We have found that the stretched exponential form describes laboratory-measured rock data T1 slightly better than the two-exponential representation, despite having fewer parametric expressions.

The three preferred embodiments of the universal fit method described above have been applied to data obtained from formation samples, and the results are presented in Table 1 of the accompanying paper entitled "Compact and Consistent Representation of Rock NMR Data for Permeability Estimation," by W. E. Kenyon, P.I. Day, C. Straley and J.F. Willemsen, which is expected to be presented at the 61st Annual Technical Conference and Exhibition of the Society of Petroleum Engineers, 5-8. October 1986 in New Orleans, LA; as this article is hereby incorporated as a reference in its entirety.

After extracting values for the relaxation times T17T2 and/or T2<*>, it is usually desirable to use these values to determine other characteristics of the measured information, such as fluid permeability k. Several methods for determining k are known in the art. , and will not be discussed in detail here since they are well documented in the technical literature. For example, Seevers has proposed using an estimator for permeability of the form k a ø T<2>, where T = (Tb . T1)/(Tb-T1) and Tb is longitudinal relaxation time for the fluids in the absence of pore surface effects, Seevers, DIE. "A Nuclear Magnetic Method for Determining the Permeability of Sandstones", Society of Professional Well Log Analysts Transactions (1966), Article L, while Timur has proposed the alternative estimator k a ø£AiT<2>, Timur, A "Pulsed Nuclear Magnetic Resonance Studies of Porosity, Moveable Fluid and Permeability of Sandstones", Journal of ' Petroleum Technology, 1966, 775-786.

According to the methods in accordance with the present invention, however, the values of longitudinal relaxation time tx are preferably used in a permeability estimator of the form k a ø<mT>1;L<n,>where the exponent m is approximately 4 and n is approximately 2. Table 2 in the attached article by Kenyon et al., shows for example that the optimal estimator for the measured samples of the formation rocks is m = s2= 4.61 and n = s-l = 2.09 used in connection with the cracked exponential representation. Table 2 also shows that the universal methods according to the invention, when used in conjunction with the preferred estimator defined here, provide significantly better determination of the permeability of the measured rocks compared to previously known methods.

Another aspect of the present invention, hereinafter called the "integration method", is aimed at the determination of formation characteristics in situations where it is desirable to minimize the measurement time (for example to allow continuous logging runs). In these situations, it is preferred to minimize the number of parameters to be extracted from the available data, for reasons to be explained below. In a preferred embodiment, referring to Figure 24, the amplitude values (representing magnetization) are integrated with respect to the time axis tpol to obtain a single integrated quantity having the same unit as 4>T.

In the case of a T-L build-up curve 104 or other comparable representation of the NMR decay response, the curve 104 is integrated to obtain the area above the Top-Build s curve, which is equal to the area under the corresponding decay curve. This integral quantity having units equivalent to 4>T1 is then used in conjunction with an appropriate estimator to obtain a measure of permeability. The integrated quantity is preferably squared to provide (øT-,^<2>, and then multiplied by (øt)<m>~<2>, where øt

>is a porosity measured using another known logging apparatus, such as those commonly known as neutron porosity apparatus. Other estimators can also be used as described earlier. The integrated size is one more

robust representation of the available low S/N data because it is less dependent on the exact shape of the curve 104 and therefore less dependent on errors introduced by the mathematical fitting of NMR data which have significant levels of noise.

The integration of the curve 104 can be performed using various methods which will be obvious to those skilled in the art. Figure 24B shows an example of integration by a simple summation of separate products of the form £ Ai . Atpol. Likewise, the measured NMR attenuation signals can be integrated with respect to attenuation time to obtain an integrated quantity that contains information indicating formation characteristics, which are relatively immune to signal noise or other fine features of the NMR attenuation.

Although the figures are shown with the amplitude axis scaled as the logarithm of A, and the time axis scaled linearly, the present interpretation methods are not meant to be limited to any particular presentation of data. In alternative embodiments, the methods may be implemented with altered amplitude and time scales. For example, the time axis can be scaled as the square root of another transformation of this.

The universal adaptation method that has been described with reference to the FID signals obtained with the previously known logging apparatus can just as well be adapted to the data obtained with the pulsed NMR apparatus according to the present invention. For example, a pulsed measurement of the spin echo type, such as the Carr-Percell sequence shown in Figure 25, provides a train of pulses whose successive peaks define a T2 relaxation curve. If several such measurement sequences are carried out where each sequence begins with a different degree of initial polarization (tpol), it is possible in accordance with the present invention to determine the longitudinal relaxation time Tx. Any of the preferred representations of the universal fitting method can thus also be used to extract values of amplitude and Tx, and these extracted values can then be used to determine other characteristics of the measured formation.

Likewise, the integration method according to the invention can also be used to better interpret measured data from the new device when it is desired to minimize the measurement time. In these cases where the data set has a relatively low S/N ratio, it is preferred to integrate under the echo signals, as shown in Figure 25, and to determine the permeability in response to the area obtained in the manner already described above.

The NMR logging apparatus according to the present invention produces a static, homogeneous magnetic field within an examination volume as previously described, and superimposes oscillating pulses of RF fields that resonantly tip or tilt the spins of protons in the examination volume. By successively applying pulses in accordance with the Carr-Purcell sequence, the apparatus 13 directly measures NMR attenuation having a T2 time constant, and is thus able to directly measure the pore-fluid characteristics of this formation without the intermediate measurement of T2 <*->weakening signals, as was necessary for the previously known logging apparatus.

Because methods exist for using information about T-1 to determine other formation characteristics, it is a preferred method according to the invention to measure NMR attenuation signals having a characteristic time constant T2, converting such measurements to hypothetical values of r£1 by to apply a transformation FT, and then use the values of Tx to determine the permeability k or similar characteristics of the measured formation. Through laboratory measurements of rock samples from different wells, the applicants have found that T1=Cx(T2) where C is a constant for each well, as for example shown in figures 26-27. It is thus preferred to produce a stationary measurement of both Txog T2 at a predetermined depth in a well by, for example, using the Carr-Purcell sequence, determining the proportionality constant C and then continuously logging the rest of the borehole to obtain rapid measurements of T2. The values of T2 are transformed into T1 values by multiplying by the constant C. Finally, the T values are used in connection with one of the preferred methods according to the invention, or other comparable methods, to determine the permeability of formations at each of the corresponding depths for The T2 measurements.

The applicants have found that at low NMR frequencies the values of T± and T2 converge; thus, at sufficiently low measurement frequencies, it is preferred to adapt the measured T2 data to a hypothetical set of T1 data, and determine the permeability by applying the measured T2 data directly to T^ estimators. Furthermore, other T1- and T2-related quantities can likewise be transformed. Referring to Figure 25, for example, the integrated area of the Carr-Purcell sequence 105 is calculated and used instead of the integrated area of the T₂ build-up curve to determine permeability, as previously described.

Although the preferred methods of the invention have mostly been described with particular reference to determining permeability, it is clear that these methods can also be used to determine other useful characteristics of rock formations penetrated by a borehole, such as fluid viscosity, water saturation and porosity.

New equipment and new methods for measuring and interpreting magnetic characteristics of formations penetrated by a borehole are described and illustrated here. Those skilled in the art will realize that many variations and modifications can be made without departing from the scope of the present invention. Accordingly, it should be clear that the embodiments of the invention described above are only examples and do not limit the scope of the present invention, as defined in the appended claims.

Claims (15)

1. Apparatus for investigating a property of a rock formation penetrated by a borehole, comprising a body adapted for longitudinal movement in the borehole, which body comprises a device for generating oscillating magnetic fields focused into a significant volume of the formation and for detecting a signal representative of nuclear magnetic precession of a particle population in the formation, characterized in that the body further includes: a device for generating a static and essentially homogeneous magnetic field in the formation volume directed to one side of the body, which volume is elongated in the longitudinal direction of the borehole axis and has a significant cross-sectional extent in the plane perpendicular to the direction of the borehole axis. 2. Method for determining a property of a rock formation penetrated by a borehole, using apparatus placed inside the borehole, comprising the steps of generating oscillating magnetic fields focused into a volume of the formation, and measuring NMR signals from a particle -population in the formation, characterized by generating a static magnetic field having radially directed and substantially homogeneous field lines in said volume of the formation on one side of the apparatus, which volume is elongated in the longitudinal direction of the borehole axis and has a significant cross-sectional extent in the plane perpendicular to the direction of the borehole axis; and detection of NMR signals at the particles' Larmor frequency under the influence of the static and essentially homogeneous magnetic field inside the volume. 3. Method according to claim 2, characterized in that the step of measuring NMR signals includes measuring nuclear magnetic resonance decay signals representing transverse (T2 ) or observed (T2<*> ) magnetic relaxation of a particle population in the formation after a series of different magnetic polarization periods.; 4. Procedure according to claim 3, characterized in that it includes the following additional steps: selecting a set of values of the reference signals; comparing the set of values directly with a representation of NMR quenching that includes amplitude terms A and longitudinal relaxation time terms T1 and at the same time depends on both quenching time tdec and polarization periods Tpol assigned to these values; generating values for amplitude and Ti parameters that optimize the fit between the compared set of values and said representation; and determining the characteristic of the formation in response to the generated values of at least one of the expressions amplitude or Tx.; 5. Method according to claim 4, characterized in that the step of comparing the set of values includes comparing the selected signal values with a representation of the form ; where A(tpol ,tdec ) is the signal amplitude, tpol is the duration of a polarizing magnetic field that precedes a given measurement, tdec is the decay time at which a measurement is taken, i is the index of the type or component of magnetic resonance, AA is the signal amplitude for a given type, Tu is the longitudinal relaxation time for a given type, and T2i is the transverse relaxation time constant for a given type.; 6. Method according to claim 5, characterized in that the step of comparing the set of values further comprises comparing the measured signals with a representation of the general form: ; where the index S denotes a first component of NMR reflection, L denotes a second component of NMR quenching, and Tinh is a fitting parameter.; 7. Method according to claim 5, characterized in that the step of comparing the set of values further comprises comparing the measured signals with a representation of the form: ;where Tinh is an adaptation parameter and a is an exponential parameter.; 8. Method according to claim 2, characterized in that the step of measuring NVR signals includes measuring NMR relaxation signals representing magnetic relaxation of a particle population in the formation after a number of different magnetic polarization periods.; 9. Method according to claim 8, characterized in that it further comprises the following steps: generating, in response to the measured signals, a representation of a characteristic relaxation for the particle population, in the form of magnetization as a function of time; integrating said representation of magnetization as a function of time to obtain an integrated value; and determination of the property of the formation in response to the integrated value.; 10. Method according to claim 9, characterized in that it further includes the following steps: measurement of T2<*-> decay signals after a series of different polarization periods; determination, based on the measured signals of a Tx build-up curve for magnetization as a function of polarization period, and integration of the build-up curve to obtain the integrated value. 11. Method according to claim 8, characterized in that the step of measuring NMR signals further comprises measuring the magnetization of the particle population using a spin-echo sequence of measurements, whereby the successive peaks in the spin-echo signals occur with time constant T2 , and further comprises transformation of the integrated value to an integrated value associated with Tx relaxation, and determining the property of the formation using the integrated value associated with T^ relaxation. 12. Method according to claim 2, characterized in that the step of needling NMR signals includes measuring with a borehole tool NMR hand-eye signals representative of transverse relaxation of a population of particles in the formation exhibiting a T2 relaxation time constant. 13. Method according to claim 12 characterized in that it further comprises the following steps: generating a first representation of the signals; transforming the representation into a second representation associated with the longitudinal relaxation time constant Tx of the particle population; and determination of the formation property as a reaction to the second representation. 14. Method according to claim 2, characterized in that the step of measuring NMR signals includes measuring NMR signal signals with a borehole tool which is positioned stationary at a predetermined first depth in the borehole. 15. Method according to claim 14, characterized in that it further comprises the following steps-. generating a value representative of a longitudinal relaxation time T\ for a formation; measuring additional NMR handover signals with the tool in continuous motion at other depths in the borehole; generating additional values representing the transverse relaxation time T2 for formations at said other respective depths in response to said additional signals; and determination of a property of the formations in the other respective depths in response to both the additional values and the value representing T-j _.