1. Technical Field
This invention is related to nuclear magnetic resonance (NMR) instrumentation apparatus and methods for use in flow meters and flow controllers as well as in other analytical applications.
2. State of the Prior Art
Nuclear magnetic resonance (NMR) for use in flow measurements, dedicated flow meters, and various analytical measurements on fluids has been investigated extensively, including myriad variations in apparatus and methods of implementation, since at least as early as the 1960s (see, for example, U.S. Pat. No. 3,419,795, issued to Genthe et al.). There are a number of potential advantages of fluid flow measurement by NMR, including the following: (i) NMR does not require disturbing flow of the fluid; (ii) NMR does not require creation of a pressure drop in the flowing fluid; (iii) There are no moving parts; (iv) No instruments or sensors have to be exposed to the flowing fluid other than the inside surface of the flow channel. Therefore, deleterious effects on flow, accuracy, and flow sensor components due to deposits, clogging, abrasion, and fouling by corrosive, abrasive, viscous, or biphase fluids such as slurries can be avoided.
In general, NMR flow meters work on variations of the concept of applying a radio frequency (RF) field to a flow of materials that have a nuclear magnetic moment, usually from an odd number of protons in their atomic structure, for example, hydrogen, fluorine, chlorine, and others, to sense resonance interaction between an externally applied magnetic field and the magnetic moments of the flowing material. Since hydrogen has a large nuclear magnetic moment and is present in high number densities in nearly all fluids, NMR flow meters should be particularly well-suited to hydrogenous materials, including water, hydrocarbons, and many others. Most schemes for measuring flow with NMR principles can be categorized loosely into several groupings, including relaxation methods, time-of-flight methods, and field gradient methods.
NMR flow measurement techniques using relaxation methods generally include the fluid entering and flowing through a region of an external magnetic field for a time before entering a region of an RF coil. During travel time of the fluid in the external magnetic field, the fluid is exposed to the external magnetic field and becomes magnetized more or less according to whether the travel time, thus exposure time, is long or short compared to the time it takes for the magnetic nuclei of the fluid to come into a equilibrium in the external magnetic field (often called the relaxation time T1). Free induction decay (FID) in response to the RF excitation of the magnetized fluid in the magnetic field produces a signal in a coil, the oscillation amplitude of which is proportional to the degree of magnetization and will vary with flow velocity ν. A pervasive issue in the relaxation method, as in nearly all NMR instrumentation applications, is that the external magnetic field has to be very uniform in the region of the RF coil and FID response in order to obtain useful NMR signals, and obtaining such uniform magnetic fields is a demanding design criterion that has generally required large, heavy, and expensive magnets.
Besides the uniform field requirement, relaxation methods typically have at least two other major drawbacks: (1) They are sensitive over a relatively small flow range, because the maximum sensitivity occurs where the flow velocity ν is approximately equal to the length of travel of the fluid divided by the relaxation time T1, which is a condition that can only be changed by changing the geometry of the flow measuring system components; and (2) The sensitivity depends strongly on the relaxation time T1, so that accurate measurements depend on knowledge of the relaxation time T1 or separate calibration for each fluid.
In time-of-flight methods, a discrete portion of the fluid is tagged magnetically in some manner at a first location, and the arrival of the tagged portion at a second, downstream location is sensed. See, for example, U.S. Pat. No. 3,419,795, issued to Genthe et al. The “time-of-flight” of the tagged portion of the fluid from the first location, where it is tagged, to the second location, where the tagged portion is sensed, is related to velocity of the flow. Of course, flow rate can be determined from velocity of flow in a known flow conduit geometry (e.g., size and shape).
In some “time-of-flight” methods, the fluid enters a magnetic field region and becomes partially or fully magnetized before it reaches a first coil, where a 90° pulse suppresses the magnetization in the direction of the field. After a delay time τ, another 90° pulse in a second coil downstream from the first coil can be used to measure the magnetization there. The arrival of the tagged fluid, i.e., the portion of the fluid with the suppressed magnetization, at the second coil is manifested by a decrease in the amplitude of the NMR signal. In other words, the NMR signal amplitude from the free induction decay (FID) in the proximity of the second coil will have a minimum value indicating the suppressed magnetization, when the time τ between the first and second pulses is equal to the length L of the flow path between the two coils divided by the flow velocity ν, i.e., τ=L/ν. Consequently, the time delay τ between successive first and second pulse pairs can be varied iteratively until a minimum NMR signal amplitude is found, and that time delay τ can be used to calculation flow velocity ν by τ=L/ν.
These kinds of time-of-flight methods do not have to be calibrated for different values of T1 (relaxation time), although they become insensitive if L/ν is greater than T1, because the fluid will re-magnetize during the delay time τ, which would effectively eliminate the suppressed magnetization with which the portions of the fluid are tagged before they reach the second coil. It would also be insensitive if the time available for magnetization before the fluid reaches the first coil is substantially less than the relaxation time T1, because without sufficient pre-magnetization of the fluid, the first coil would not be able to create the tag with the RF frequency, i.e., the suppressed magnetization, in a portion of the flowing fluid.
While such time-of-flight methods have some advantages, the requirement that L/ν should be less than the relaxation time T1 is difficult to satisfy, especially for low flow rates. Also, the highly uniform magnetic field has to span both coils. Therefore, that requirement for a uniform magnetic field spanning not just one, but two coils is even more difficult to achieve and requires even larger magnets than methods that need only one coil at one location along the flow path.
In field gradient methods, the nuclear spins of the flowing fluid material are aligned using a transverse magnetic field with a linear gradient in which the strength or intensity of the magnetic field either increases or decreases along the flow path. As in other NMR instrumentation techniques, radio frequency (RF) pulses at the magnetic resonant frequency of the material are applied briefly to rotate the magnetic moments relative to the transverse magnetic field, thereby suppressing the magnetization of the fluid that is in the direction of the transverse magnetic field. Since frequency of the magnetic moments is a function of the strength of the external transverse magnetic field, and since there is a gradient in the strength of the transverse magnetic field, only a narrow slice of the flowing material will have its resonant frequency attuned to the RF pulse, i.e., that narrow slice of material that is located where the magnetic field intensity causes magnetic moment frequency that matches the frequency of the RF pulse. After the termination of the RF pulse, the time varying magnetic fields of the spins of the nuclei (FID) are detectable in the RF sensing coil, i.e., the NMR signal, for a short time as they realign to the external transverse magnetic field. However, as the excited slice of the material flows downstream into portions of the gradient external transverse magnetic field that have different magnetic field intensities, the frequencies of the signal emitted by the nuclei change proportionately as they continue to realign with the transverse magnetic field. The intensity of the NMR signal indicates the number of nuclei realigning with the transverse magnetic field, and the combination of signal time delay relative to the RF pulse and the signal frequency indicates the particle velocity. The indicated particle velocity along with the known geometry of the flow path can be used to determine fluid flow rate of the fluid.
Variations of the field gradient methods may include use of phase gradients and frequency gradients. A phase gradient is applied after RF excitation but before the NMR signal is recorded. The pulse establishes a correlation between the precession phase of a group of spins and their position along the direction of the field gradient, i.e., along the flow path. A frequency gradient is applied while the NMR signal is recorded, which establishes a correlation between the recorded precession frequency of a group of spins and their position along the direction of the field gradient, i.e., along the flow path. This information along with time can be used to establish velocity and, with flow path geometry, to establish flow rate of the fluid.
These field gradient methods for fluid flow measurement require not only accurate controls of the field gradient, but also homogeneity of the field along the gradient, which is very demanding on the external magnet characteristics. Meeting such demands generally requires the use of a large and heavy, high quality magnet, the size and cost of which is incompatible with a compact, turnkey, general purpose flow meter.
Consequently, while NMR principles are well known and myriad NMR flow meter apparatus and methods have been tried and even shown to work, the goal of compact, turnkey NMR based flow meters that have and retain accuracy and reliability over a wide range of flow rates, including very low flow rates, as commercial products has remained illusive. In spite of the potential advantages and applications of NMR to flow metering and flow controlling, such instruments are not available in the market due at least in part to the cost and complexity of suitable magnets, RF electronics, signal processing hardware, calibration issues, and other problems.
The foregoing examples of related art and limitations related therewith are intended to be illustrative and not exclusive, and they do not imply any limitations on the inventions described herein. Other limitations of the related art will become apparent to those skilled in the art upon a reading of the specification and a study of the drawings.
The accompanying drawings, which are incorporated herein and form a part of the specification, illustrate some, but not the only or exclusive, example embodiments and/or features. It is intended that the embodiments and figures disclosed herein are to be considered illustrative rather than limiting.
In the drawings:
An example NMR flow meter/controller 10 is shown in
With those understandings, references are now directed initially to
In the example flow meter 10 in
The example framework or casing 20 shown in
With reference now primarily to
An optional larger cross-section tube portion 58 can be used, if desired, in the pre-magnetizer zone 42, if longer dwell time of the fluid in the pre-magnetizer zone 42 is desired for more complete pre-magnetization of the fluid before it enters the analytical zone 46. This option may be useful, for example, in flow meters designed for measuring high flow rates in order to provide sufficient time in the pre-magnetization zone. Of course, a longer pre-magnetization zone 42 could also be used to get more complete pre-magnetization of the fluid, but a longer pre-magnetization zone 42 would require a longer pre-magnetizer magnet assembly 44, which is much more bulky and more expensive than a larger cross-section pre-magnetizer tube portion 58. Another option to increase pre-magnetization of the fluid with a given pre-magnetization field is to provide a tube 40 with a circuitous path (not shown) through the pre-magnetization zone 42 to increase dwell time of the fluid in the pre-magnetization zone 42, although a circuitous flow path may be more difficult to provide in a compact system.
As best seen in
Such coherent or nearly coherent precession of the nuclear magnetic moments of the fluid immediately after the pulse of alternating magnetic field stops, induces a detectable voltage, i.e., the NMR signal, in the coil 60 (or in any other coil in proximity to the excited fluid). However, a number of factors, including inhomogeneity of the analytical magnetic field B0, which cause different nuclear magnetic moments to precess at different angular velocities, thus less than perfectly coherent precessions of nuclear magnetic moments, result in rapid dephasing of the precessing nuclear magnetic moments. Such dephasing limits the duration of the free induction decay (FID) and causes the amplitude of the NMR signal detected in the coil 60 to decrease. The less homogenous the static field B0 is, the weaker the NMR signal will be, and the faster it will decay or disappear.
It may be helpful to mention here that the terms nuclear magnetic moments, nuclei magnetic moments, and spins are sometimes used interchangeably. Also, the NMR signals obtained from free induction decay (FID) detected by the coil 60 are also sometimes called FID signals, or just FID, and these terms may be used interchangeably when the free induction decay FID provides the NMR signal being used. However, NMR signal can also be obtained from spin-echo, which is not solely free induction decay, so, in a sense, NMR signal is a broader term in that it can be derived from FID, echo, or other nuclear magnetic resonance effects.
For the reasons mentioned above, it is important for the analytical magnetic field B0 to be as spatially uniform or homogenous as practical in order to get useful NMR signals. While a number of different magnet configurations and combinations have been used to provide uniform magnetic fields for various NMR applications and can be used with the NMR flow metering methods and techniques described herein, there are drawbacks associated with some of them. For example, iron-yoke dipole magnets, such as the iron-yoke dipole magnet assembly 66 shown diagrammatically in
Halbach magnets, such as the cylindrical Halbach magnet in
An example small, compact magnet system that provides a highly uniform analytical magnetic field B0 that is strong enough for NMR flow metering and/or analytical instrumentation for flowing fluids is shown in
M(t)=M0(1-exp(−t/T1)) (1)
where T1 is a time constant called the energy or spin-lattice relaxation time, because the nuclear magnetic moments or spins give up energy to their environment in order to come to the equilibrium at a lower energy state for the individual nuclear magnetic moments aligned with the uniform field B0. Sometimes T1 is simply called the relaxation time T1 for convenience. T1 is typically about one second or more for aqueous and other low viscosity solutions. Increasing viscosity is correlated with reduced relaxation time T1.
This relaxation of the nuclear magnetic moments to an equilibrium state is followed by the excitation of the precessing nuclear magnetic moments with the RF pulse of alternating magnetic field B1 directed orthogonal to the uniform magnetic field B0 to impose coherence, i.e., uniform phase, to the precessing nuclear magnetic moments and simultaneously to rotate them away from the relaxed equilibrium orientation to a higher energy precessing orientation in a plane orthogonal to the uniform magnetic field B0. In that more coherent, higher energy, precessing state, the combined magnetic fields of the coherently precessing nuclear magnetic moments induce the detectable NMR signal in the coil 60, as discussed above.
However, the relaxation time T1 required for the nuclear magnetic moments to give up their energy and relax to the equilibrium energy state in the direction of the uniform magnetic field B0 before the RF pulse of alternating magnetic field B1 is applied, e.g., one second or more, is a long time for the flowing fluid to have to remain in the uniform magnetic field B0. As discussed above, creating highly uniform magnetic fields is not easy, and it would require a large and complex magnet system to create a long enough, highly uniform, magnetic field B0 to expose a flowing fluid for a full second or more before the fluid is allowed to flow out of the field B0. It would have to be done with much larger, bulkier, and more expensive magnet components than is practical or needed for many NMR flow meter or analytical applications.
A very highly uniform magnetic field B0 is important for the location and proximity of the coil 60, because the precession rate (Larmor frequency fL) of the nuclear magnetic moments in the fluid is directly related to the strength of the magnetic field B0 by the relationship:
f
L=γ/2π·B0 (2)
where γ is called the gyromagnetic ratio of the magnetic moment to the magnitude of the spin angular momentum. For magnetic moments of hydrogen nuclei (protons), which are present at high concentrations in almost all liquids, the relationship between the Larmor frequency fL, (precession rate of the hydrogen nuclear magnetic moments) is:
f
L=42.58 MHz/T·B0 (3)
where megahertz (MHz) is a unit of frequency meaning 106 cycles per second, and Tesla (T) is a unit of magnetic field meaning one weber per square meter. Therefore, if the magnetic field B0 could be perfectly uniform or homogenous, all of the hydrogen nuclei in the fluid would precess at exactly the same Larmor frequency fL. On the other hand, the more inhomogeneities there are in the magnetic field B0(i.e., the less uniform the field is), the more variations there will be in the precession rates of the individual hydrogen nuclear magnetic moments, and as the precessions de-phase, the NMR signal decays and disappears, i.e., the free induction decay (FID). Therefore, the more inhomogeneities there are in the magnetic field B0, the more rapid will be the de-phasing and resulting decay and disappearance of the FID or NMR signal. As mentioned above, the terms NMR signal and FID signal or FID are sometimes used interchangeably in the art and in this description when discussing the NMR signal from free induction decay.
The interaction energy of a nuclear magnetic moment with any attainable applied magnetic field B0 is always very small compared to the thermal energy at room temperature, which disorients molecules in the fluid, so the average degree of orientation or polarization of nuclei by the magnetic field B0 is also very small. Moreover, the nuclear magnetic moment is small, about 2,000 times smaller than the electron magnetic moment responsible for ferromagnetism. Nevertheless, because of the enormous number of protons present in a typical macroscopic sample (e.g., about 1023), the RF magnetic fields generated by the precessing protons can be detected, provided they are all made to precess at nearly the same frequency and phase, which requires a very uniform magnetic field B0, as discussed above, in the vicinity where the RF coil 60 is located.
However, while a highly uniform magnetic field B0 at the location and proximity of the RF coil 60 is important, a less demanding magnetic field can be used for the initial magnetization of the fluid that orients the nuclear magnetic moments to align with the field B0. Therefore, the pre-magnetizer zone 42 (
As mentioned above, the uniform magnetic field B0 for the analytical magnet zone 46 can be provided by any of a number of magnet systems for use in NMR instrumentation and analytical systems and techniques, including those described herein, but the Helmholtz analog or pseudo-Helmholtz analytical magnet assembly 48 shown in
A conventional Helmholtz coil pair (not shown herein) is known in the art as a set of two identical, circular, co-axial coils spaced apart from each other by a distance equal to the radius of the coils and with equal current flowing through them in the same direction to produce a region of nearly uniform magnetic field at the midpoint between the coils. The magnetic field at the midpoint has linear, quadratic, and cubic dependences on the coordinates all equal to zero or nearly so. The two identical, axially magnetized, co-axial, spaced apart, cylindrical disc permanent magnets 74, 76 of the analytical magnet assembly 48, best seen in
J
S
=B
r/μ0
For a rare earth NdFeB, JS is in the range of 950 to 1,050 amps per millimeter (A/mm), depending on the grade of material used. With finite thickness disk magnets 74, 76, the first three spatial derivatives can still be made to vanish (this property stems from the high symmetry), but the optimal spacing between the two disk magnets 74, 76 is not necessarily equal to the radius and has to be found numerically or empirically. In general, a higher field B0 strength results in stronger NMR signals, and, if the disk thickness is increased at constant diameter, the central field B0 strength increases. However, while increasing the thickness of the disk magnets 74, 76 without changing diameter will increase field strength, it also makes the uniformity of the field decrease, unless the spacing between the juxtaposed inner faces 78, 80 of the disks 74, 76 is decreased. Of course, decreasing the spacing between the disk magnets 74, 76 limits the size of the sample tube 40 and coil 60 that can fit between the two disk magnets 74, 76. Consequently, in order to maintain maximized uniformity of the magnetic field B0 in a broad area at and around the midpoint where the coil 60 is positioned, a compromise may have to be taken between higher field B0 strength and keeping enough space between the disks 74, 76 for the sample volume, i.e., the sample tube 60 size, desired. This compromise leads to central magnetic field B0 values in a range of 0.25 to 0.70 T, or Larmor frequencies 10 to 30 MHz for NdFeB magnet material. Other magnet materials, for example, SmCo (comprising samarium, cobalt, and iron) can also be used, but a SmCo field would not be as high as NdFeB. However, the magnetization of SmCo varies less with temperature changes than the magnetization of the NdFeB material. Consequently, SmCo might be a better choice for a particular application and operating temperature range than NdFeB, even though it provides a lower field strength than NdFeB. The two disks 74, 76 have an attraction toward each other and can be held apart at the desired spacing, for example, by an annular shoulder 82 in the frame 20 (
As mentioned above, the pre-magnetizer magnetic field B1 does not have to be as highly homogenous or uniform as the analytical magnetic field B0. It is important, though, that the field of the pre-magnetizer magnet assembly 44, which is positioned in close proximity to the analytical zone 46, will not distort the otherwise highly uniform analytical magnetic field B0, or at least that such distortion will be minimal. Therefore, the example pre-magnetizer magnet assembly 44 shown in FIGS. 4 and 6-8 is a Halbach-cylinder-based design, albeit somewhat simplified as compared to the more complete Halbach cylinder magnets shown, for example, in
As mentioned above, the Halbach cylinder design and configuration of the pre-magnetizer assembly 44 shown in
As illustrated in FIGS. 4 and 6-8, the simplified Halbach cylinder arrangement of the pre-magnetizer magnet assembly 44 comprises four elongated bar magnets 90, 92, 94, 96 magnetized as indicated by the small arrows 91, 93, 95, 97, respectively, and assembled in a cross configuration in cross-section in order to create an approximate Halbach cylinder effect. It is helpful to position the bar magnets 90, 92, 94, 96 tightly in the cross configuration with adjacent corners of the respective bar magnets 90, 92, 94, 96 as close to touching each other as practical, given the physical constraints of a suitable mounting structure 98 (
If desired or convenient, each bar magnet 90, 92, 94, 96 can be a composite or assembly of several smaller bar magnets, as illustrated in the cross-section of
Besides being much smaller and lighter than a conventional yoked magnet assembly, the pseudo-Helmholtz configuration and design for the analytical magnet assembly 48 shown in
The shimming process can be done empirically or with the aid of a magnetic field mapping tool and a software program for computation of magnetic fields. Myriad software programs for computing magnetic fields from geometries and properties of magnets are available commercially and well-known to persons skilled in the art, for example, RADIA, available from the European Synchrotron Radiation Facility (ESRF), Grenoble, France. For example, a Hall magnetometer can be inserted into the space between the disk magnets 74, 76 (e.g., before the sample tube 40 and coil 60 are mounted) and used to measure and map the field B0 of the pseudo-Helmholtz analytical magnet assembly 48 (with or without the Halbach pre-magnetizer magnet assembly 44) and to find inhomogeneities in the analytical magnetic field B0 in the vicinity where the coil 60 is located or will be located. Various positions of the Hall magnetometer between the magnet disks 74, 76 can be recorded along with the strength of the magnetic field at each of the positions. Then, corrective shimming, which can include a variety of ferromagnetic or non-magnetic materials in shapes and sizes as needed to minimize inhomogeneties in the filed B0, for example, the steel balls 110, 112, soft iron plates (not shown), and others can be placed empirically (e.g., trial and error), or with the aid of a magnetic field computation program, as mentioned above. For example, with the map of the magnetic field B0 obtained with the Hall magnetometer, including the inhomogeneities, a magnetic field computation program or method know to persons skilled in the art can be used to choose suitable corrective shimming to minimize the inhomogeneities in the field B0. Then, with shimming in place as chosen with the aid of the computation program, the magnetic field B0 can be mapped again with the Hall magnetometer to see if the corrective shimming was sufficient, or the coil 60 can be mounted and operated to obtain an NMR signal. If necessary, the shims can be adjusted empirically to improve the uniformity of the measured field B0 or to enhance the NMR signal. When the Hall magnetometer measurements and/or the NMR signal indicate that the Field B0 is adequately uniform with the shim or shims in particular locations and/or a good NMR signal is obtained, the shims can be left or fixed in those locations. In the example shown in
Referring now primarily to
For use of the NMR apparatus 10 as a flow meter, a coil depletion method has been developed to take advantage of the single coil 60 and combination pre-magnetization and analytical magnet design described above to produce fast, accurate, and reliable flow measurements, although the relaxation method mentioned above can also be implemented with the NMR flow meter apparatus 10 described above. In this coil depletion method, the fluid flows through the sample tube 40 in the pre-magnetizer field Bp in the pre-magnetizer zone 42 created by the pre-magnetizer magnet assembly 44 to become at least partially magnetized before entering the analytical field B0 created by the analytical magnet assembly 48. The dwell time Tp spent in the pre-magnetizer zone 42 can be estimated as
T
p
=V
p
/Q
where Vp is the volume of the fluid in the sample tube portion that is in the pre-magnetizer zone 42 and Q is the volume flow rate. For adequate pre-magnetization, the time Tp should be greater than or at least comparable to the relaxation time T1, for example, in a range of about 0.5 T1 to 1.5 T1, as indicated above for many applications. However, if the signal-to-noise ratio of the NMR signal is low, it may be necessary to use a dwell time Tp of as much as 3 T1, whereas an application with a high signal-to-noise ratio may allow the dwell time Tp to be as low as 0.1 T1. Therefore, the in balancing the available signal-to-noise ratio against size and weight of the apparatus needed, the dwell time Tp may be anywhere in a range of 0.1 T1 to 3 T1, and in many applications 0.5 T1<Tp<1.5 T1 will be satisfactory.
As mentioned above, the pre-magnetizer magnetic field Bp need not be as highly uniform as the analytical field B0, and it is easier to maintain high magnetic field intensity all along the fluid flow path from the pre-magnetizer zone 42 into the analytical zone 46 if the pre-magnetizer field Bp is be oriented in the same direction as the analytical field B0. The pre-magnetizing field Bp can be, but does not have to be, larger in magnitude than the analytical field B0, or it can be weaker. However, in general, stronger magnetization of the fluid will result in better signal strength at the coil 60, so a strong pre-magnetizer field Bp has benefits.
Essentially, as indicated diagrammatically for an idealized case in
To measure the flow rate of the fluid 120 through the sample tube 40 with this coil depletion method, nuclear magnetic resonance (NMR) can be used to determine the mean velocity ν at which the fluid is flowing through the tube 40, and then, knowing the geometry and dimensions of the tube, the flow rate can be calculated from the relationship
ν=Q/A
where Q is the volume flow rate and A is the cross-sectional flow area of the sample tube 40 at the coil 60. However, as explained below, flow rate Q can also be determined with this coil depletion method directly from the ratio R of the amplitude of a second FID to the amplitude of a first FID, where the second FID results from a second excitation pulse applied after a chosen time delay τ between the first excitation pulse and the second excitation pulse. This method is distinct from the time-of-flight method mentioned above in which a magnetic tag is induced in the fluid and used to determine the time that it takes for the fluid to flow a set distance between two coils.
To determine the mean flow velocity ν, an RF pulse at the Larmor frequency is applied to the coil 60, which creates an alternating magnetic field B1 in a direction at least a component of which is transverse to the magnetic field B0 that simultaneously imposes coherency (same phase) on the precessing hydrogen nuclear magnetic moments 124 as it also rotates them to a plane that is orthogonal to the precession axes 128, as illustrated in
Referring again to
When the nuclear magnetic moments 124 are no longer in phase, as illustrated diagrammatically in
As mentioned above, there are many de-phasing influences in a physical system, one of which is slight inhomogeneities in the analytical field B0, which are impossible to eliminate completely. Such inhomogeneities or non-uniformities in the field B0 cause slight variations in the Larmor frequency (precession rate) in different regions of the sample. Those different precession rates cause different local magnetic field vectors that work against each other and over time contribute to the de-phasing of the nuclear magnetic moments. Such de-phasing induced by inhomogeneous field effects is sometimes denoted T2*, and an example is shown on
In any event, the maximum amplitude NMR signal occurs immediately after the RF pulse is terminated and the nuclear magnetic moments 124 are still precessing in phase, as illustrated in
Referring now to the idealized illustration in
Referring now to
However, the previously depleted portion of the fluid in the coil volume 142, represented diagrammatically by the volume 139 between the intermediate line of demarcation 133 and the downstream coil boundary line 134, does not produce or contribute significantly to the second NMR signal. The second 90° RF pulse applied to the nuclear magnetic moments 124, which are in random phase distribution and not recovered to any significant degree from the 90° plane 136 back toward equilibrium, does not result in any significant FID or NMR signal. In order for the RF magnetic field B1 in the direction that is orthogonal to the direction of the analytical field B0 to excite or interact with the nuclear magnetic moments 124 in a manner that imposes phase on them, there has to be a vector component of the nuclear magnetic moments 124 that is parallel to, i.e., aligned with, the analytical field B0. That condition does not exist for the nuclear magnetic moments 124 that are precessing randomly in the 90° planes 136, so they are substantially immune to the second 90° RF pulse for purposes of producing or contributing to the second NMR signal, at least not in the idealized case where it is presumed that no re-magnetization occurs in the time delay τ between the first and second pulses.
Therefore, the amplitude of the second NMR signal from the coil volume 142 after the second 90° RF pulse is proportionately less than the amplitude of the first NMR signal, because there are proportionately fewer coherently precessing nuclear magnetic moments 124 in the coil volume 142 contributing to the second NMR signal as compared to the number of nuclear magnetic moments 124 in the coil volume 142 that contributed to the first NMR signal, when the coil volume 142 was full of coherently precessing nuclear magnetic moments. Therefore, the amplitude of the second NMR signal after the second pulse is proportional to the fraction 140 of the coil volume 142 that has been refilled during the delay time τ between the first 90° RF pulse and the second 90° RF pulse. Consequently, knowing the geometry of the sample tube 60 at the coil volume 142 (e.g., the inside diameter d of the tube) and the length L of the coil 60, the full coil volume 142 between the boundary lines 32-34 can be calculated (e.g., coil volume V=L·πd2/4). Then, multiplying the coil volume V by the ratio R of the second NMR signal amplitude to the first NMR signal amplitude gives the volume V (i.e., the partial volume 140) of fluid that flowed into the coil volume 142 in the time delay τ between the first 90° RF pulse and the second 90° RF pulse. Therefore, the flow rate Q is the volume of the fluid 139 that flowed into the coil volume 142 divided by the delay time τ.
For this coil depletion method of determining flow rate, the time delay τ between the first and second 90° RF pulses has to be short enough that all of the depleted fluid 138 does not flow completely out of the coil volume 142 before the second 90° RF pulse is applied. If that condition of the depleted fluid flowing completely out of the coil volume 142 should occur, the entire coil volume 142 would be re-filled with fresh, magnetized nuclear magnetic moments, as shown in
Therefore, in general, the basic pulse sequence for measuring flow with this coil depletion method is 90°-τ-90° with NMR signals recorded immediately after each 90° pulse. Before the first 90° pulse, the fluid is magnetized throughout the coil volume 142. The first pulse suppresses the magnetization within the coil volume 142 and generates a FID or NMR signal that has maximum amplitude and can be detected with the coil 60. The delay time τ between the first and second pulses is chosen so that the depleted coil, i.e., coil volume 142 with suppressed magnetization, will be partially refilled with magnetized fluid at the time of the second pulse. The FID amplitude after the second pulse is proportional to the fraction of the coil volume that has been refilled with magnetized fluid and is a measure of the flow rate. The 90° pulse time and the FID duration are both much less than τ, so the fluid is nearly or practically stationary on these time scales.
This coil depletion method of flow measurement can be made nearly insensitive to the spin-lattice relaxation time T1 by using the ratio R of the second pulse amplitude to the first pulse amplitude of the flow-measuring parameter. When using this parameter, i.e., a ratiometric type of measurement, the inferred flow velocity does not depend strongly on the degree of pre-magnetization, because the pre-magnetization is substantially the same for both the first and the second signal, and any effect the degree of pre-magnetization has on the amplitude of the FID signals is the same in both the numerator and denominator of the ratio. Therefore, as discussed above, it is feasible for many applications to allow the dwell time that the fluid is in the pre-magnetizer zone 42 (
For example, referring again to the idealized flow illustrated in
where A1 is the FID amplitude after the first excitation pulse, A2 is the FID amplitude after the second excitation pulse, ν is the average flow velocity, τ is the delay time between the first and second pulses, L is the length of the coil 60, and T1 is the spin-lattice relaxation time in the analytical field B0. Therefore, this relationship does take into account any re-magnetization of the fluid during the delay time τ due to the analytical magnetic field B0. However, where τ is very much smaller than T1 (e.g., τ<<T1), so that τ/T1 effectively goes to zero and the exponential goes to 1 in the above relationship, thus virtually no re-magnetization, then the ratio R is:
where the resulting numerator and denominator represent the fraction of the coil length L that the fluid flows in the delay time τ. Therefore, the ratio R of the amplitude A2 of the second NMR signal to the amplitude A2 of the first NMR signal is proportional to average flow velocity ν of an idealized fluid when the delay time τ between the two pulses is very much smaller than the spin-lattice relaxation time T1. Otherwise, for a longer delay time τ, re-magnetization would begin to have an effect on the ratio R and could lead to inaccuracies in flow rate measurement. Consequently, it is desirable for the delay time τ between the pulses to be small so that re-magnetization of the depleted fluid is not a significant issue, while, of course, keeping τ long enough to allow enough partial refilling of the coil volume 142 with enough fresh magnetized fluid to get a good, useable, NMR signal. Of course, where the tube 40 has a constant diameter d and cross-sectional area A, the ratio R is also proportional to flow rate Q, as will be explained below.
The ratiometric technique used to measure flow velocity ν and/or rate Q in this method, i.e., utilizing the ratio R of the second FID amplitude A2 to the first FID amplitude A1 as the flow measuring parameter, makes the measurements relatively immune to variations of proton density in the fluid and to variations in electronic circuit characteristics. For example, if the gain of the amplifier changes or drifts due to temperature or other factors, then the apparent amplitude of both the first and second NMR signals, i.e., both the numerator and denominator in the ratio R, change by the same factor and cancel each other out.
The dependence of the NMR signal amplitude ratio R on flow velocity ν is shown in
The dimensionless sensitivity can be defined as
With this definition, a fractional change of amplitude ratio ΔR/R is related to a fractional change of flow velocity by Δν/ν by
For the idealized case represented by the broken line curve in
The solid line curve in
ν=Q/A
where Q is the volume flow rate and A is the cross-sectional area of the flow channel, e.g., sample tube 40, at the coil 60. The sensitivity Σ now depends on the flow rate Q. It reaches a maximum value Σ0≈1.2 at ν0=0.2 L/τ and R≈0.5. The sensitivity drops by less than about 20% for flow velocity within the interval
ν0/1.5<ν<ν0·1.5.
High sensitivity is thus retained for flows varying by a factor of about 1.52=2.25 (a turn-down of 2.25) for a single value of τ. Turn-down essentially means a range as expressed by the highest flow rate divided by the lowest flow rate, and for a single value of τ, the turn-down or range is not large. However, high sensitivity over a much larger region can be achieved by defining a series of overlapping flow rate ranges with different values of time delay τ, because, with this coil depletion method, the time delay τ can be varied or set to whatever value is needed to apply the second pulse before the coil volume 142 is cleared of depleted fluid, as explained above. Therefore, for higher flow rate ranges, the delay time τ can be set shorter, and for slower flow rate ranges, τ can be reset to longer times. Such switching between different values of τ for different flow rate ranges can be done manually or automatically by programming the controller to switch to a new τ when the measure flow rates approach predetermined upper and lower limits in each flow rate range. Therefore, with high sensitivity for a particular delay time τ extending over a turn-down of greater than 2.0, along with the ability to vary τ almost to whatever value is needed for high sensitivity at a particular flow rate range, the effective turn-down or range can be as high as 100 to 1, which is a large range for a flow meter.
In the explanation of the example implementations above, the RF pulse is described as a 90° pulse, and the NMR signal in the explanation above is based on the FID from a 90°pulse. Therefore, if an error is made in the duration of the pulse, i.e., a duration that causes more or less than 90° rotation of the magnetic field M0 of the fluid, the coil volume 142 will not be fully depleted of fluid magnetization after the first pulse. Such incomplete depletion of fluid magnetization after the first pulse will influence the amplitude of the FID after the second pulse, and the indicated flow rate will be in error. Therefore, while there are other pulse durations and sequences that can be used to provide a NMR signal (for example, spin echo), when 90° pulses and FID are used to get an NMR signal, errors in the pulse duration should be minimized. Consequently, it may be desirable to take reasonable measures to ensure that the time duration of the pulse is correct for rotating the field of the nuclear magnetic moments to the plane that is 90°, i.e., orthogonal, in relation to the analytical magnetic field B0. However, even when the time duration is set initially to a correct value for a 90° pulse, vagaries inherent in electronics and other systems due to temperature changes and other causes, for example, in power amplifier gain, matching network tuning, coil quality-factor and analytical field strength B0, the pulse duration can drift. Ideally, if the fluid is stationary, i.e., flow is stopped, in the sample tube 40, the second FID, thus second NMR signal, would have zero amplitude (assuming the time delay t between pulses is short enough to avoid any significant remagnetization of the fluid in the coil volume 142), because, if the fluid was stationary, all of the depleted fluid in the coil volume 142 would remain in the coil volume 142 and not get replaced. The ratio R of the second NMR signal to the first NMR signal would then also be zero. Therefore, the fluid flow in the sample tube 40 can be stopped periodically in order to “zero” the pulse duration setting to a pulse time duration for the first and second pulses that results in zero amplitude for the second FID signal.
In reality, though, the drift or variations in actual pulse duration can occur continuously or frequently, and it may not be practical to actually stop the flow in order to run tests frequently enough to ensure that the pulse durations are always set properly to produce 90° rotation of the fluid magnetization M0 with respect to the analytical field B0. However, the apparatus and coil depletion method described above can accommodate a technique for automatically “zeroing” the pulse duration setting while the fluid is flowing. To do so, the delay time τ between the first and second pulses can simply be adjusted to a very short time, so that, in ordinary flow rates, the fluid in the coil volume 142 will have hardly moved at all, e.g., an insignificant amount, during that interval between the first and second pulses. Insignificant here means that there would be not enough difference between the actual amount of flow during the time interval and no flow to be of concern in practical applications of this method or in use of the apparatus in practical applications. Therefore, the effect is as if the flow was virtually stopped during the two pulses and the resulting first and second FID signals. It is somewhat analogous to using a fast shutter speed on a camera to snap a photograph of a moving object, and the captured picture makes the object appear to have been stopped just for an instant. A delay time τ in a range of 0.1 to 2.0 milliseconds (ms) can usually be used for this purpose, depending on the characteristics and flow rates of the fluid being measured. The amplitude of the second FID signal, i.e., the NMR signal resulting from the second pulse, should be zero or as close to zero as possible. If it is not zero, the pulse duration can be changed and retried iteratively and/or by calculation or extrapolation until the ratio R converges to zero or as close to zero as practical. Persons skilled in the art know how to make pulse duration time adjustments and to make converging calculations and implementations by software, so further details of implementation are not needed for an understanding of this feature. Once the pulse duration has been zeroed, the delay time τ can then be re-set to its usual time, typically about 5 ms to 200 ms. In cases where the re-magnetization errors are too large to be ignored (for example, at low flow rates where the normal delay time τ between the first and second pulses has to be longer in order to allow enough fresh, magnetized fluid 120 to displace FID depleted fluid in the coil volume 142 to enable acquisition of a useful ratio R value), such errors can be corrected with a correction factor based on an approximate knowledge of the relaxation time T1. If necessary, T1 can be measured under stopped flow conditions.
Persons skilled in the art are generally capable of designing and making electronic circuits for creating RF pulses, driving RF coils, and receiving and processing NMR signals from coils in response to FID, and electronics packages and circuit boards for NMR applications are available commercially from a number of manufacturers and vendors, including, but not limited to, SpinCore Technologies, Inc., of Gainesville, Fla. For example, the RadioProcessor™ printed circuit board is advertised by its manufacturer, SpinCore Technologies, Inc., as a complete system console for nuclear magnetic resonance, including excitation and acquisition components, that generates completely formed RF excitation pulses and control signals and captures and digitally demodulates RF signals, as definable through software, and autonomously signal-averages the baseband data between multiple acquisitions, as well as numerous other controls and functions for NMR systems that are useful for operating the NMR apparatus and implementing the methods described herein. An example filter and switch circuit that utilizes such commercially packaged NMR electronics for driving the coil and receiving and processing signals is shown in the schematic diagram in
In
Outputs controlled by the pulse program can be output by the NMR control board 156 via a cable 158 or other communication or data link to a transmit/receive switch driver circuit 160. The NMR control board 156 and its functions are controllable by software according to documentations and instructions provided by the manufacturer or by the customization for particular applications, as is within the capabilities of persons skilled in the art. The switch driver circuit 160, which can be powered by any convenient power supply 162, responds to signals from the NMR control board 156 via the link 158 to output a voltage bias on either the output A or the output B via leads 164, 166, respectively, to the transmit/receive switch circuit 170. The transmit/receive switch 170 is actuated by the voltage biases from the switch driver circuit 160 to either direct a RF excitation signal from the transmitter circuit 172 to the coil 60 or to direct the FID signal from the coil 60 to the receiver circuit 174.
The transmitter circuit 172 receives a pulsed oscillatory signal from the NMR control board 156 at a frequency that is either set into, or determined by, the NMR control board 156, generally at or near the Larmor frequency (e.g., in a range of about 10 to 30 megahertz (MHz)), via a lead 176. The signal on the lead 176 from the NMR control board 156 is smoothed by a low pass filter 178 and then drives a power amplifier 180. The power amplifier 180 is followed by another low pass filter 182 to smooth the amplified signal and through a PIN diode isolator 184, which passes the RF signal from the transmitter circuit 172 to the coil 60. However, the PIN diode isolator 184 presents a high impedance to the probe circuit 150 when the transmitter 172 is turned off or not transmitting. Also, when the transmitter 172 is off, the PIN diode isolator 184 acts as a filter, attenuating noise from the transmitter during FID signal acquisition.
The receiver circuit 174 is basically a RF signal conditioning and pre-amplification circuit for the NMR signal acquired by the coil 60 from the FID of the excited fluid. It can comprise, for example, one or two low pass filters 186, 188 to smooth the signal, one or two pre-amplifiers 190, 192, and another low pass filter 194 to smooth the amplified signal. The pre-amplified and smoothed NMR signal is then sent via a lead 196 to the NMR control board 156 for further processing. An interface 197 can be provided for connection to the input/output board 26 (
The transmit/receive switch 170 comprises a diode bridge 198 for fast recovery to accommodate fast switching between the transmit mode, when the RF excitation pulse is transmitted to the coil 60, and the receive mode, when the NMR signal generated in the coil 60 by the FID is received by the receiver circuit 174 for pre-amplification and conditioning. The bridge diode switch 198 is controlled by the switch driver circuit 160 to be open, i.e., off, when a RF pulse signal is transmitted by the transmitter circuit 172 to the coil 60, thereby isolating the receiver circuit 174 so that the pre-amplifiers 190, 192 in the receiver circuit 174 do not get swamped or saturated by the transmitted RF pulse signal. The pre-amps 190, 192 are isolated from the transmit signal, because the high power of the transmit signal would saturate them, which would slow their recovery to a state wherein they could receive and amplify the NMR signal. The FID only lasts about 150 μs, so the switch from transmit mode to receive mode should occur very fast, and the receiver circuit 174 has to start operating very fast, for example, within about 20 μs, after the end of the RF pulse transmission in order to capture the best part of the FID signal before it decays. The diode bridge switch 198 allows for such fast switching and fast recovery. It closes, i.e., is turned on to allow signals to pass through it, by the switch driver circuit 160 as soon as the RF pulse transmission ends.
The switch driver circuit 160 responds to signals from the NMR control board 156, for example, a transistor transistor logic (TTL) signal, via the lead 158 to turn the bridge diode switch 198 on and off. Essentially, a low signal from the NMR control board 156 causes the transistors 200, 202 to be off, which allows switch output B to be positive and switch output A to be negative and thereby turning the diode bridge switch 198 on during acquisition of the NMR signal from the coil 60. A high signal from the NMR control board 156 on the lead 158 at all other times, including during RF pulse transmission, turns the transistors 200, 202 on to make the driver output A positive and driver output B negative to turn the bridge diode switch 198 off to isolate the receiver circuit 174. To avoid leakage of digital signals into the amplifiers 190, 192, the control signal from the NMR control board 156 is shown as being optically isolated by an optical coupling 208. The crossed diodes 210 to ground at the output of the diode bridge switch 198 are provided to protect the receiver circuit 174 from high power transmissions in the event a software error causes the diode bridge switch to stay on during transmission of a RF pulse to the coil 60. The trimmers 212, 214 in the switch driver circuit 160 are provided to reduce switching transient signals. As mentioned above, the NMR control board 156, if obtained from a vendor or manufacturer, such as SpinCore Technologies, Inc., usually comes with, or has available, documentation and software for programming, inputting parameters and commands, and operating all the functions associated with generating and receiving NMR signals, although other technical computing software, for example, MATLAB, available from The Mathwork, Inc., of Natick, Mass., and several open source alternatives, such as GNU Octave, FreeMat, and Scilab, can also be used. For example, control routines are available or can be set up in the software mentioned above for the desired pulse sequence and data acquisition parameters. Then a loop can be entered to repeatedly trigger the NMR control board 156, wait for data to be ready, and then collect and display data. For the example flow measurement process described above, each time the NMR control board 156 is triggered, it executes a sequence of two pulses, collecting FID data in separate memory areas after each pulse. The two-pulse sequence is repeated a number of times, called scans, and the time-domain data is averaged in the NMR control board 156. When the desired number of scans is completed, data is transferred to the computer or other processor and can be displayed, if desired, in time-domain and/or as a power spectrum. The process is then repeated a number of times, called runs. After the desired number of runs is completed, the average-over-runs of the FID amplitudes and of the ratios R of second FID amplitude to first pulse FID amplitude are calculated and can be displayed and/or stored for applications and other purposes. The standard deviations of those quantities can also be computed and stored or displayed. The data structure can be saved in memory, if desired. In a dedicated system or commercial product, such as the example flow meter/controller 10 in
In an optional variation, each 90 degree pulse can be replaced by a spin echo sequence, e.g., (90°-τ1-180°-τ1-echo)-τ-(90°-τ1-180°-τ1-echo) with τ1 being a much shorter time than τ. For example, τ1 may be about 1 millisecond. Data can be recorded during the FID that occurs right after the 90° pulses and during the spin echo. An advantage of using spin echoes for the NMR signal used in the ratio R is that the NMR signals can be recorded for a longer total time, which may yield better signal-to-noise ratio. The 90 degree pulses can also be replaced by multiple spin echo sequences, which are known to persons skilled in the art.
The amplitude of each NMR signal for use in determining the amplitude ratio R could be taken at a particular point in the NMR signal, e.g., near the start of the FID signal (see
An example of FID signals for two successive 90° RF pulses is shown in
The upper panel in
Except for the difference in amplitudes, the two FID signals in
Two FID Signals under the same conditions as Example I, except that the delay time between the first and second 90° RF pulses is only one (1) ms, are shown in
An example of dependence of FID signal amplitude ratio R on flow rate for a 25 ms time delay τ is shown in-between first and second 90° RF pulse pairs and a 0.2 second repeat time between successive 90° RF pulse pairs in
To demonstrate sensitivity and repeatability over a larger flow rate range, a set of four ranges are defined as shown in Table I, as follows:
The center-of-range volume flow rates (given in milliliters per minute) in Table I meet the condition for maximum sensitivity for the corresponding delay time τ. The repeat times are chosen long enough so that the first 90° RF pulse occurs when the coil volume 142 (
The FID signal amplitude ratio R versus flow rate Q for the overlapping flow rate ranges are shown in
From the variability of the results shown in
At flow rates above 100 ml/min, the repeatability degrades in this example, because of flow instability (incipient turbulence) in the pre-magnetizer. Flow instability causes fluctuations in transit time of fluid elements moving through the pre-magnetizer, which, in turn, will cause spatial and temporal fluctuations of the magnetization entering the coil volume 142 (
While the sensitivity of the flow rate measurement with the apparatus and method discussed above is good, it can be improved further by shaping the RF magnetic field B1 produced by the coil 16. Referring again to the idealized illustrations of the apparatus and flow measuring process in
However, because of the shape of the RF magnetic field B1 produced by a conventional coil, such as the coil 60, as illustrated diagrammatically, for example, in
While the sensitivity of the flow rate Q measurements with the apparatus and methods described above is good, it can be improved further by shaping the RF magnetic field B1 produced by the coil 60 to conform it more closely to the idealized profile in
As mentioned above, errors in the duration of the 90 degree pulses in the 90-τ-90 pulse sequence described above for the coil depletion method of measuring flow, i.e., a pulse that is too long or too short to rotate the magnetic field of the material M0 into the 90 degree plane that is orthogonal to the direction of the analytical magnetic field B0, will result in variations in the NMR signals, thus errors in the flow measurements. The zeroing, including auto-zeroing, described above is one way to minimize or eliminate those errors. An alternative method of measuring flow, which can also be performed with the apparatus and systems described above, is less sensitive to pulse duration errors. In this alternative method, sometimes referred to herein as the bridge method, flow rate is not found by the ratio R between the amplitude of the second FID signal to the amplitude of the first FID signal, as was described above for the coil depletion method. Instead, referring to
As explained above in relation to the coil depletion method, the fluid in the sample tube 40 is initially magnetized by the pre-magnetizer field BP and then by the analytical field B0 so that it is magnetized to be generally aligned with the analytical field B0, as indicated diagrammatically by the alignment of the precessing nuclear magnetic moments 124 in idealized illustration in
Then, continuing with the idealized, plug flow, i.e., assumed uniform flow velocity profile, illustration in
Therefore, when a 90 degree RF pulse from the coil 60 is applied to the fluid in the coil volume 142 at that time τ′ after the 180 degree RF pulse, the precessing nuclear magnetic moments 124 of the fresh, magnetized fluid in the first half 146 of the coil volume 142 are rotated to the 90 degree plane 126, as shown diagrammatically in
However, as also shown in
Again, as discussed above in relation to the coil depletion method of finding flow rate and/or flow velocity, in the real world, the RF magnetic field B1 does not begin and end abruptly at the ends of the coil 60 as neatly as illustrated in the idealistic figures and simplified explanation above. Therefore, the length L of the constant volume flow channel in which the fluid is influenced by the RF magnetic field B1 may not be exactly the same as the length of the coil 60, and the constant volume flow channel in which the fluid is influenced by the RF magnetic field B1 may not be exactly the same volume as the idealized coil volume 142 depicted in
As also mentioned above, in addition to the flow metering and controlling applications, the apparatus and methods described herein also have other NMR analytical applications for fluids. Three major approaches in which the apparatus and methods described herein are useful include: (i) NMR signal intensity; (ii) spin-lattice relaxation time T1; and (iii) spin-spin relaxation time T2. Some example analytical applications in which one or more of the methods and apparatus described herein are useful, either alone or in combination with other instrumentations and measurements (e.g., temperature, etc.), may include: ortho concentration in liquid hydrogen, oxygen concentration in water, oxygen concentration in organic solvents, discrimination of mesophases in liquid crystals, concentration of metal ions in water, solids content and solid surface area of slurries, fat content of oil/water emulsions, quality of cooking oil, solids content of black liquor, and many others.
The words “comprise,” ‘comprises,” “comprising,” “composed,” “composes,”, “composing,” “include,” “including,” and “includes” when used in this specification, including the claims, are intended to specify the presence of state features, integers, components, or steps, but they do not preclude the presence or addition of one or more other features, integers, components, steps, or groups thereof. Also the words “maximize” and “minimize” as used herein include increasing toward or approaching a maximum and reducing toward or approaching a minimum, respectively, even if not all the way to an absolute possible maximum or to an absolute possible minimum. The term “insignificant” means not enough to make a difference in practical applications, unless the context indicates otherwise. Also, the measurements described can be repeated any number of times by allowing enough time between measurements for the fluid affected by the RF field to clear out of the coil volume 142 and then performing the measurements again, and multiple measurements can be used, if desired, to determine flow rate or rates, average flow rates, statistical flow rates, etc. Also, while the methods described above referred to NMR measurements utilizing the spins or nuclear magnetic moments of hydrogen, these NMR measurements can also be made with nuclear magnetic moments of fluorine, chlorine, and other materials having odd numbers of protons in their atomic structures.
This application is a continuation-in-part of U.S. patent application Ser. No. 12/498,245, filed Jul. 6, 2009, which is incorporated herein by reference.
Number | Date | Country | |
---|---|---|---|
Parent | 12498245 | Jul 2009 | US |
Child | 12635697 | US |