Abstract:
Nuclear magnetic resonance spectrometer for examination of a sample under pressure has a coolant vessel containing a radio-frequency coil cooled by coolant in the vessel while located within the magnetic field of the spectrometer. A pressurizable sample holder comprises a nonmagnetic pressure retaining tube formed of electrically insulating matrix material containing electrically insulating reinforcing filaments. The spectrometer is configured to accommodate this sample holder with the axis of the pressure retaining tube transverse to the magnetic field, and the radiofrequency coil at the exterior of the pressure retaining tube. Cooling of the coil improves the signal to noise ratio and offsets the low coil filling factor which is a consequence of placing the coil outside a non-metallic pressure retaining tube. End pieces at each end of the tube are connected together and contain longitudinal pressure stress.

Description:
CROSS-REFERENCE TO RELATED APPLICATION 
       [0001]    This application claims priority to British Application No. GB1217375.3 filed 28 Sep. 2012, which is incorporated herein by reference in its entirety. 
       BACKGROUND 
       [0002]    One technology for examining properties of a solid or liquid sample is nuclear magnetic resonance (NMR) also referred to as magnetic resonance imaging (MRI). There are circumstances where a sample is examined under pressure, thus requiring a sample holder which can contain the sample under pressure while it is in the magnetic field of an NMR spectrometer. 
         [0003]    A category of samples for which examination under pressure may be required is solid and also liquid samples collected below ground. When drilling through underground rock, it is common practice to drill around a cylinder of rock, referred to as a rock core, which is subsequently brought to the surface. At the surface, rock samples from such a core may be subjected to various measurements and tests. These samples are usually cylindrical and may be referred to as a core plug. Tests which have been carried out include examination by nuclear magnetic resonance (NMR) also referred to as magnetic resonance imaging (MRI) which entails placing the core within a magnetic field and using one or more radio-frequency coils to apply radio-frequency energy to the core and receive radio-frequency signals from it. 
         [0004]    The subterranean rock formations from which such cores are taken are of course at high pressure and it can be desirable to carry out NMR measurements while the sample is under pressure. Liquid samples brought to the surface may also be subjected to NMR measurements whilst still under pressure. 
         [0005]    Design of a sample holder which can retain pressure and which can be placed in the magnetic field of an NMR spectrometer needs to address several issues, including mechanical construction for containing pressure, choice of materials to enable the core to be exposed to both magnetic field and radio-frequency, and positioning of the core holder in relation to the functional components (i.e., magnets and coils) of an NMR spectrometer. One issue is the extent to which the cross-section within the radio-frequency coil or coils is occupied by the sample. Signal to noise ratio is better if the sample occupies a high proportion of the cross-section within the coil(s). This is referred to as a high coil filling factor. 
         [0006]    There are existing designs of sample holder to contain a sample under pressure. For instance a pressurizable sample holder which is available from Ergotech Ltd, Conwy, Wales uses a tube of glass fiber reinforced composite to contain a rock sample under pressure. Compressive force applied to the ends of the tube opposes stress longitudinally relative to the pressurized tube. The radio-frequency coil and the magnets of an NMR spectrometer are positioned outside the tube in spaces between the tube and tie rods connecting the structural parts which apply compressive force to the ends of the tube. In this arrangement, where the magnets fit between the tube and the tie rods, the tie rods are spaced apart in the direction of the magnetic field and the spacing between them has to be greater than the distance between the magnets. 
         [0007]    Another sample holder intended for a sample under pressure is illustrated in US published application US2011/0030223. It has a non-magnetic metal tube to retain pressure. The radio-frequency coil required for NMR is located inside this tube, with the sample placed inside the coil. The metal tube and the end pieces screwed into it provide sufficient strength to resist both radially outward stress (hoop stress) and also longitudinal stress resulting from the internal pressure. 
       SUMMARY 
       [0008]    This summary is provided to introduce a selection of concepts that are further described below. This summary is not intended to be used as an aid in limiting the scope of the subject matter claimed. 
         [0009]    One aspect of the subject matter disclosed in this application is apparatus which comprises a nuclear magnetic resonance (NMR) spectrometer including a magnet system providing a magnetic field, at least one coolant vessel containing at least one radiofrequency coil for transmitting and/or receiving electromagnetic radiation, with the at least one coil located within the magnetic field and cooled by coolant in the vessel, and a pressurizable sample holder which comprises a nonmagnetic pressure retaining tube formed of nonmetallic electrically insulating matrix material containing electrically insulating reinforcing filaments, wherein the spectrometer is configured to accommodate the sample holder with the axis of the pressure retaining tube transverse to the magnetic field and with the at least one radiofrequency coil at the exterior of the pressure retaining tube. 
         [0010]    Retaining pressure requires mechanical strength and non-metals are usually avoided when strength is required. However, non-metals are generally electrically non-conductive and employing a non-metallic electrically insulating material for the pressure retaining tube avoids unwanted induction of eddy currents in the material of the tube when gradient coils in the NMR spectrometer are switched on and off to superimpose a temporary magnetic field gradient on the main magnetic field of the spectrometer. 
         [0011]    Positioning both the sample and pressure containing tube inwardly of the radio-frequency coil or coils gives a low coil filling factor compared to an arrangement with the radio-frequency coil inside the pressure retaining tube. The arrangement disclosed here contrasts with the customary approach of seeking to maximize the coil filling factor in order to maximize in turn the signal to noise ratio of the magnetic resonance signals. Cooling a radio-frequency coil is known to improve the signal to noise ratio and this phenomenon has been used to enhance the quality of weak signals. The arrangement disclosed here utilizes cooling of the radio-frequency coil(s) for a different reason, which is to offset a geometry leading to reduced coil filling factor. 
         [0012]    A range of nonmetallic and electrically insulating materials may be used for the pressure retaining tube. One possibility is a ceramic material. Another possibility is an electrically insulating composite comprising an electrically insulating matrix material reinforced with electrically insulating filaments. The matrix may be ceramic or may be an organic polymer. Possibilities for insulating filaments include glass fiber and fibers of poly-paraphenylene terephthalamide—marketed under the trade name Kevlar. 
         [0013]    A coolant vessel may be an annular container, for instance a vacuum flask (also termed a Dewar vessel) which is of annular shape. Such an annular container may be positioned in the magnetic field of the NMR spectrometer and encircle a space for the sample holder. The radio-frequency coil or coils cooled within the coolant vessel may be wound as at least one helical solenoid. Other forms of coil may be used: one possibility is a pair of saddle coils, one at each side of the pressure retaining tube. If the coils do not encircle the pressure resistant tube, it is possible that an annular cooling vessel is used, or that some other shape of cooling vessel or vessels is used. One possibility is a pair of saddle coils each contained in a cooling vessel which is half an annulus. 
         [0014]    A coolant vessel may simply be a container for a quantity of static coolant placed in it or there may be provisional for circulation of coolant from a supply source through the vessel, for example circulation of coolant from a cryocooler through the vessel or vessels and back to the cryocooler. A description of various types of cryocooler is provided by Radebaugh in  Journal of Phyics: Condensed Matter,  Vol. 21, 164219 (2009). 
         [0015]    The apparatus may include means to maintain the sample within the sample holder at a temperature which is higher than the temperature of the coolant. This may for instance be provision to circulate fluid through a cavity at the interior of the pressure retaining tube of the sample holder. 
         [0016]    The sample contained in a sample holder as above may possibly be a liquid, or may be a solid, such as a rock sample which may be a porous rock with liquid in its pores. 
         [0017]    In a further aspect, the disclosed subject matter provides a method of examining a sample by NMR comprising placing a sample in a pressurizable sample holder which (as above) comprises a nonmagnetic pressure retaining tube formed of nonmetallic electrically insulating matrix material containing electrically insulating reinforcing filaments; placing the sample holder in an NMR spectrometer including a magnet system providing a magnetic field, such that the axis of the pressure retaining tube is transverse to the magnetic field; providing at least one coolant vessel containing at least one radiofrequency coil at the exterior of the pressure retaining tube; cooling the at least one coil with coolant in the vessel; and applying a radio-frequency signal to a cooled coil within the vessel to induce magnetic resonance of nuclei in the sample, and using the same or another cooled coil within the vessel to receive radio-frequency emissions from the sample. 
         [0018]    A sample holder as discussed above may be provided with structural parts to contain pressure longitudinally relative to the tube, these structural parts comprising pieces to apply force longitudinally at the ends of tube and connecting structure extending between these pieces outside the tube. 
     
    
     
       BRIEF DESCRIPTION OF THE DRAWINGS 
         [0019]      FIG. 1  is a schematic cross-section showing basic parts of a sample holder in the magnetic field of an NMR spectrometer; 
           [0020]      FIG. 2  is a cross sectional view on line II-II of  FIG. 1 ; 
           [0021]      FIG. 3  is a cross sectional view similar to  FIG. 2 , but with saddle coils and circulation of coolant; and 
           [0022]      FIG. 4  is a schematic cross-section of an example of sample holder able to receive liquid under pressure. 
       
    
    
     DETAILED DESCRIPTION 
       [0023]    The sample holder shown in  FIGS. 1 and 2  has a non-metallic pressure retaining tube  10  with substantial wall thickness, indicated by double headed arrow  11 , so as to withstand hoop stress, i.e., radially outward pressure from within. Longitudinal stress from internal pressure is restrained by end pieces  12 ,  14  which are connected together by a four tie rods  16  which are in tension. Thus the tube  10  is not required to provide longitudinal strength. Both end pieces  12 ,  14  may be removable and sealed to the tube by O-rings as shown or the tube  10  could be permanently attached to one of the end pieces. 
         [0024]    A number of non-metallic materials can be used for the tube  10 . One possibility is an inorganic ceramic material. Another possibility is a fiber-reinforced composite in which elongate fibers are bound in a matrix material which may be an inorganic ceramic or may be an organic polymer. Glass reinforced polymer (GRP) is a well-known example of composite material. An organic polymer used as the matrix of a composite material may be any of a number of polymers including epoxy resin and polyetherether ketone (PEEK) which is well established as an engineering plastic. 
         [0025]    The pressure retaining tube  10  of the sample holder is encircled by a vessel  18  to contain coolant. The vessel is a vacuum flask, often referred to as a Dewar flask. It has double walls with vacuum between the two walls. This vessel  18  is annular in shape so that the space for coolant is an annulus open at its top  19  allowing coolant to be poured in. A radio-frequency coil  20  is located within this annulus and so it will be immersed in the coolant. The coolant may be liquid nitrogen so as to cool the coil  20  to 77K (−196° C.) which is the boiling temperature of nitrogen. The double walls of vessel  18  are shown in  FIG. 1 , but for the sake of simplicity,  FIG. 2  merely shows the inner and outer walls of the vessel  18 . 
         [0026]    The coil  20  is shown schematically as a single helical solenoid coil but it may be wound with multiple layers. It is possible that there could be more one coil, for example one coil as an emitter and one as an antenna with the two coils wound one on top of the other and both immersed in the coolant. 
         [0027]    The NMR spectrometer has a pair of disc shaped permanent magnets  22  facing each other but spaced apart so that a magnetic field extends in the direction indicated by the arrow B 0 . Both permanent magnets  22  may be made of rare earth compounds to give a high magnetic field. Specifically, they may possibly be neodymium iron boron (NdFeB) magnets which can be manufactured in the desired shapes or assembled from smaller blocks. 
         [0028]    Gradient coils  24  are positioned adjacent the magnets  22 . When these gradient coils  24  are energised, a magnetic field with a gradient along the length of these coils, which is the vertical direction as seen in  FIG. 1 , superimposed on the static field B 0 . This field gradient is proportional to the current in the coils  24  and its magnitude can thus be controlled. 
         [0029]    The coolant vessel  18  and the pressure retaining tube  10  of the sample holder are positioned in the magnetic field between the gradient coils  24 . As best seen from  FIG. 2 , the tie rods  16  at either side of the tube  10  are then located at positions which are spaced laterally from the axis of tube  10 . 
         [0030]      FIG. 2  shows that the geometry can be fairly compact. The four tie rods  16 , which are indicated as  16 . 1  to  16 . 4  in  FIG. 2 , are at a radial distance from the axis of tube  10  which is approximately twice the external radius of the pressure retaining tube  10  and approximately the same as the distance from the tube axis to the magnets  22 . The tie rods  16 . 1  and  16 . 2  are spaced from the axis of the tube  10  and from the tie rods  16 . 3  and  16 . 4  in directions transverse to the magnetic field B 0 . The spacing between the tie rods  16 . 1  and  16 . 3  is equal to spacing between rods  16 . 2  and  16 . 4 , and is less than double the external diameter of the tube  10 . The spacing in the direction of the magnetic field B 0  between the tie rods  16 . 1  and  16 . 2  is equal to spacing between rods  16 . 3  and  16 . 4 . It is less than the spacing between the magnets  22  and again it is less than twice the external diameter of the tube  10 . 
         [0031]    A rock sample  26  is located within the tube  10 . The end faces of the sample  26  are exposed but the cylindrical surface of the sample is enclosed and sealed by an elastomeric sleeve  28 . This sleeve  28  is urged against the cylindrical surface of the sample  26  by a liquid, referred to as confining fluid, in the space  30  between the sleeve  28  and the inside wall of tube  10 . This confining fluid may be a perfluorocarbon which does not contain hydrogen atoms and does not give any signal when NMR is used to examine resonance of hydrogen nuclei. The space  30  between the sleeve  28  and the inside wall of tube  10  is connected to inlet and outlet pipes  32 ,  34  by passages through the wall of tube  10 . 
         [0032]    Fluid to pressurize the interior of the tube  10  can be introduced along passages  36  and  38  which extend through the end members  12  and  14 . These passages can be closed by valves  40 . It is also possible to flow fluid linearly through the sample  26 , using passage  36  as an inlet for fluid under pressure while maintaining a slightly lower pressure in passage  38  as outlet. At least one spacer piece  42 , made of non-magnetic and electrically insulating material is used to keep the sample  26  in position. Such a spacer piece  42  may be made of a porous material or may incorporate apertures, to allow the end faces of the sample  26  to communicate with the passages  36 ,  38 . 
         [0033]    The confining fluid in the space  30  may be at the same pressure as fluid entering the interior of tube  10  along passage  34 , or may be at a slightly higher pressure. The confining fluid may also be circulated to control temperature, being supplied from a temperature-controlled reservoir diagrammatically indicated at  44  to inlet pipe  32 , thus maintaining the sample  26  at the temperature of the circulating confining fluid. Fluid from outlet pipe  34  flows back to the reservoir  44  by a return pipe which is not shown. 
         [0034]    The following calculation shows that cooling can offset a low coil filling factor. If the radio-frequency coil is a helical solenoid, the signal to noise ratio in an NMR measurement is given by the following equation, initially set out by Hoult and Richards in “The signal-to-noise ratio of the Nuclear Magnetic Resonance experiment,”  J. Magnetic Resonance,  vol. 24, pp. 71-85, 1976. 
         [0000]    
       
         
           
             
               
                 
                   SNR 
                   = 
                   
                     
                       
                         
                           
                             K 
                              
                             
                               ( 
                               
                                 B 
                                 1 
                               
                               ) 
                             
                           
                           xy 
                         
                          
                         
                           V 
                           s 
                         
                          
                         N 
                          
                         
                             
                         
                          
                         γ 
                          
                         
                             
                         
                          
                         
                           ℏ 
                           2 
                         
                          
                         
                           I 
                            
                           
                             ( 
                             
                               I 
                               + 
                               1 
                             
                             ) 
                           
                         
                       
                       
                         7.12 
                          
                         k 
                          
                         
                             
                         
                          
                         
                           T 
                           s 
                         
                       
                     
                     · 
                     
                       
                         ( 
                         
                           p 
                           
                             
                               FkT 
                               c 
                             
                              
                             ζΔ 
                              
                             
                                 
                             
                              
                             f 
                           
                         
                         ) 
                       
                       
                         1 
                         / 
                         2 
                       
                     
                     · 
                     
                       
                         ω 
                         0 
                         
                           7 
                           / 
                           4 
                         
                       
                       
                         
                           { 
                           
                             
                               μμ 
                               0 
                             
                              
                             
                               ρ 
                                
                               
                                 ( 
                                 
                                   T 
                                   c 
                                 
                                 ) 
                               
                             
                           
                           } 
                         
                         
                           1 
                           / 
                           4 
                         
                       
                     
                   
                 
               
               
                 
                   ( 
                   1 
                   ) 
                 
               
             
           
         
       
     
         [0035]    In this formula, fundamental constants have their usual notation, viz. 
         [0036]    h is Planck&#39;s constant divided by 2π, 
         [0037]    k is Boltzmann&#39;s constant, 
         [0038]    μ 0 =4π×10-7 Hm −1  and is the permeability of free space, 
         [0039]    γ is the magnetogyric ratio of the resonant nucleus ( 1 H in the present context) and 
         [0040]    I is the nuclear spin quantum number (I=½ for  1 H). 
         [0041]    The resonant (angular) frequency of the nucleus is denoted by ω 0 . Absolute temperatures are denoted by T S  for the sample and by T C  for the coil; note that in the present discussion these temperatures may be radically different. Characteristics of the sample are its volume V S , and the number density N of its resonant species. Properties of the spectrometer&#39;s pre-amplifier are F, the Noise Figure, and Δf, the bandwidth of the resonant circuit. Properties of the coil itself are its winding length l, the perimeter p of the wire used, its magnetic relative permeability μ, (essentially μ=1 for copper), and its electrical resistivity ρ(T C ), at the temperature T C  of the coil. A so-called “proximity” factor ζ is included which accounts for the current flowing in neighbouring coil windings when calculating the distribution of current actually flowing within the wire cross section. Finally, the overall winding geometry is implicitly included in the factor (B 1 ) xy  which denotes the magnetic field over the sample produced by unit current in the coil. Where B is inhomogeneous then this can be taken into account by the “inhomogeneity factor” K. For a solenoid, K=1 can be taken as a reasonable approximation, so this will not be considered further. 
         [0042]    The physical basis of the above formula takes into account:
       1. the induced e.m.f. by precessing nuclear magnetization;   2. the magnitude of such nuclear magnetization at thermal equilibrium;   3. the electrical noise arising from thermal reasons within the coil conductor, according to the well-known formula for “Johnson noise”; and   4. the skin depth for the r. f, current flowing in the wire of the coil.       
 
         [0047]    The coil filling factor does not appear explicitly in formula (1) above because the coil volume itself does not appear as a parameter. However, the result is consistent with the filling factor criterion in that the SNR is directly proportional to sample volume V S . 
         [0048]    The factors (B 1 ) xy  and K can both be calculated from first principles of magnetostatics (e.g., the Biot-Savart law), given the coil geometry. The result given by Hoult and Richards for the B 1  field at the centre of the sample is 
         [0000]    
       
         
           
             
               
                 
                   
                     
                       ( 
                       
                         B 
                         1 
                       
                       ) 
                     
                     xy 
                   
                   = 
                   
                     
                       
                         
                           μ 
                           0 
                         
                          
                         n 
                       
                       2 
                     
                      
                     
                       1 
                       
                         
                           [ 
                           
                             
                               a 
                               2 
                             
                             + 
                             
                               g 
                               2 
                             
                           
                           ] 
                         
                         
                           1 
                           / 
                           2 
                         
                       
                     
                   
                 
               
               
                 
                   ( 
                   2 
                   ) 
                 
               
             
           
         
       
     
         [0000]    for a solenoid of n turns, radius a and length 2g. 
         [0049]    Using these formulae we can state a ratio of the SNR values obtained from two coils at different temperatures, used for the same sample volume V S . We will assume that we detect the same resonance, with a pre-amplifier of the same Noise Figure F and receiver bandwidth Δf. Then a ratio of the respective SNR values given by formula (1) is 
         [0000]    
       
         
           
             
               
                 SNR 
                 1 
               
               
                 SNR 
                 2 
               
             
             = 
             
               
                 
                   
                     
                       ( 
                       
                         B 
                         1 
                       
                       ) 
                     
                     xy 
                   
                    
                   
                     ( 
                     1 
                     ) 
                   
                 
                 
                   
                     
                       ( 
                       
                         B 
                         1 
                       
                       ) 
                     
                     xy 
                   
                    
                   
                     ( 
                     2 
                     ) 
                   
                 
               
                
               
                 
                   ( 
                   
                     
                       
                         p 
                         1 
                       
                        
                       
                          
                         2 
                       
                        
                       
                         ζ 
                         2 
                       
                        
                       
                         T 
                         
                           c 
                            
                           
                               
                           
                            
                           2 
                         
                       
                     
                     
                       
                         p 
                         2 
                       
                        
                       
                          
                         1 
                       
                        
                       
                         ζ 
                         1 
                       
                        
                       
                         T 
                         
                           c 
                            
                           
                               
                           
                            
                           1 
                         
                       
                     
                   
                   ) 
                 
                 
                   1 
                   / 
                   2 
                 
               
                
               
                 
                   ( 
                   
                     
                       
                         ρ 
                         2 
                       
                        
                       
                         ( 
                         
                           T 
                           
                             c 
                              
                             
                                 
                             
                              
                             2 
                           
                         
                         ) 
                       
                     
                     
                       
                         ρ 
                         1 
                       
                        
                       
                         ( 
                         
                           T 
                           
                             c 
                              
                             
                                 
                             
                              
                             1 
                           
                         
                         ) 
                       
                     
                   
                   ) 
                 
                 
                   1 
                   / 
                   4 
                 
               
             
           
         
       
     
         [0050]    Employing further the solenoid field calculation in formula (2), and approximating the winding length i as 2πan where (as above) a is the coil radius and n is the number of turns, we obtain 
         [0000]    
       
         
           
             
               
                 
                   
                     
                       SNR 
                       1 
                     
                     
                       SNR 
                       2 
                     
                   
                   = 
                   
                     
                       
                         [ 
                         
                           
                             
                               a 
                               2 
                               2 
                             
                             + 
                             
                               g 
                               2 
                               2 
                             
                           
                           
                             
                               a 
                               1 
                               2 
                             
                             + 
                             
                               g 
                               1 
                               2 
                             
                           
                         
                         ] 
                       
                       
                         1 
                         / 
                         2 
                       
                     
                      
                     
                       
                         ( 
                         
                           
                             
                               p 
                               1 
                             
                              
                             
                               a 
                               2 
                             
                              
                             
                               n 
                               1 
                             
                              
                             
                               ζ 
                               2 
                             
                              
                             
                               T 
                               
                                 c 
                                  
                                 
                                     
                                 
                                  
                                 2 
                               
                             
                           
                           
                             
                               p 
                               2 
                             
                              
                             
                               a 
                               1 
                             
                              
                             
                               n 
                               2 
                             
                              
                             
                               ζ 
                               1 
                             
                              
                             
                               T 
                               
                                 c 
                                  
                                 
                                     
                                 
                                  
                                 1 
                               
                             
                           
                         
                         ) 
                       
                       
                         1 
                         / 
                         2 
                       
                     
                      
                     
                       
                         ( 
                         
                           
                             
                               ρ 
                               2 
                             
                              
                             
                               ( 
                               
                                 T 
                                 
                                   c 
                                    
                                   
                                       
                                   
                                    
                                   2 
                                 
                               
                               ) 
                             
                           
                           
                             
                               ρ 
                               1 
                             
                              
                             
                               ( 
                               
                                 T 
                                 
                                   c 
                                    
                                   
                                       
                                   
                                    
                                   1 
                                 
                               
                               ) 
                             
                           
                         
                         ) 
                       
                       
                         1 
                         / 
                         4 
                       
                     
                   
                 
               
               
                 
                   ( 
                   4 
                   ) 
                 
               
             
           
         
       
     
         [0051]    We now suppose that coil ( 1 ) is a cooled coil outside the pressure retaining tube  10  of the sample holder and coil ( 2 ) is a coil only slightly larger than a cylindrical sample, such as a coil inside a pressure retaining tube, so as to have a high coil filling factor. Such a coil will be at the sample temperature so that T c2 =T S  We also assume that the two coils have the same aspect ratio, wire diameter and number of turns of the coil, with similar proximity factors. The formula simplifies as follows: 
         [0000]    
       
         
           
             
               
                 
                   
                     
                       SNR 
                       1 
                     
                     
                       SNR 
                       2 
                     
                   
                   = 
                   
                     
                       
                         ( 
                         
                           
                             a 
                             2 
                           
                           
                             a 
                             1 
                           
                         
                         ) 
                       
                       
                         3 
                         / 
                         2 
                       
                     
                      
                     
                       
                         ( 
                         
                           
                             T 
                             s 
                           
                           
                             T 
                             c 
                           
                         
                         ) 
                       
                       
                         1 
                         / 
                         2 
                       
                     
                      
                     
                       
                         ( 
                         
                           
                             ρ 
                              
                             
                               ( 
                               
                                 T 
                                 s 
                               
                               ) 
                             
                           
                           
                             ρ 
                              
                             
                               ( 
                               
                                 T 
                                 c 
                               
                               ) 
                             
                           
                         
                         ) 
                       
                       
                         1 
                         / 
                         4 
                       
                     
                   
                 
               
               
                 
                   ( 
                   5 
                   ) 
                 
               
             
           
         
       
     
         [0052]    Copper has a linear variation of resistivity with temperature down to about 75K with a temperature coefficient of resistivity of about 0.004 deg −1 . This is consistent with the Debye model for lattice vibrational modes (phonons) which are the limiting factor in electrical conduction in metals. Because ρ(T) varies linearly with temperature down to liquid nitrogen temperatures, the formula (5) above simplifies further to a very simple estimator: 
         [0000]    
       
         
           
             
               
                 
                   
                     
                       SNR 
                       1 
                     
                     
                       SNR 
                       2 
                     
                   
                   ≈ 
                   
                     
                       
                         ( 
                         
                           
                             a 
                             2 
                           
                           
                             a 
                             1 
                           
                         
                         ) 
                       
                       
                         3 
                         / 
                         2 
                       
                     
                      
                     
                       
                         ( 
                         
                           
                             T 
                             s 
                           
                           
                             T 
                             c 
                           
                         
                         ) 
                       
                       
                         3 
                         / 
                         4 
                       
                     
                      
                     
                         
                     
                      
                     
                       { 
                       7 
                       ) 
                     
                   
                 
               
               
                 
                   ( 
                   6 
                   ) 
                 
               
             
           
         
       
     
         [0053]    In circumstances where the signal to noise ratios SNR 1  and SNR 2  are equal, the formula becomes 
         [0000]    
       
         
           
             
               
                 
                   1 
                   = 
                   
                     
                       
                         ( 
                         
                           
                             a 
                             2 
                           
                           
                             a 
                             1 
                           
                         
                         ) 
                       
                       
                         3 
                         / 
                         2 
                       
                     
                      
                     
                       
                         ( 
                         
                           
                             T 
                             s 
                           
                           
                             T 
                             c 
                           
                         
                         ) 
                       
                       
                         3 
                         / 
                         4 
                       
                     
                   
                 
               
               
                 
                   ( 
                   7 
                   ) 
                 
               
             
           
         
       
     
         [0054]    Then raising this to the power of ⅔ gives: 
         [0000]    
       
         
           
             
               
                 
                   
                     
                       a 
                       1 
                     
                     
                       a 
                       2 
                     
                   
                   = 
                   
                     
                       ( 
                       
                         
                           T 
                           s 
                         
                         
                           T 
                           c 
                         
                       
                       ) 
                     
                     
                       1 
                       / 
                       2 
                     
                   
                 
               
               
                 
                   ( 
                   8 
                   ) 
                 
               
             
           
         
       
     
         [0055]    This allows us to estimate the diameter of a coil ( 1 ) chilled to liquid nitrogen temperature which will give the same signal to noise ratio as the coil ( 2 ) above which is at ambient temperature and only slightly larger than a rock sample. Assume that coil ( 2 ) has a diameter of 40 mm (to accommodate a 38 mm core plug) and is at a sample temperature of 30° C.=303K. Assume also that the temperature of the cooled coil ( 1 ) is that of boiling nitrogen, i.e., 77K. 
         [0056]    By substituting these values in the formula above, it is found that a coil ( 1 ) at liquid nitrogen temperature with a diameter of 80 mm will give the same signal to noise ratio as a coil ( 2 ) with a diameter of 40 mm at 30° C. when the sample is the same in both cases. 
         [0057]    Of course, it is possible that a sample could be at a somewhat higher temperature, perhaps up to 130° C.=403K. It is possible also that the cooled coil could be at some other temperature, possibly lower than that of boiling nitrogen. At temperatures below that of boiling nitrogen copper displays a variation of resistivity with temperature which is no longer linear. This enhances the benefit of cooling the coil and it may therefore be beneficial to cool the radio-frequency coil(s) to around 20K (−253° C.) using helium gas from a cryocooler as the coolant. 
         [0058]      FIG. 3  shows a variation of the arrangement of  FIGS. 1 and 2 . In place of the helical solenoid as radio-frequency coil there are a pair of saddle coils  50  each in a vacuum flask  52  which is half an annulus. These vacuum flasks are closed vessels (unlike the open topped vacuum flask shown in  FIGS. 1 and 2 ) and coolant is circulated through both of them from a cryocooler diagrammatically indicated at  54 . 
         [0059]      FIG. 4  shows a sample holder for a liquid sample which is required to be kept under pressure. The general arrangement has similarity to that in  FIGS. 1 and 2 . A pressure retaining tube  10  contains hoop stress, while longitudinal stress is contained by end members  12 ,  14  connected by tie rods  16  which are in tension. Inside the pressure-retaining tube  10  there is a tube  60  made of an inorganic ceramic material. This is non-magnetic, electrically insulating and stable in contact with hydrocarbon. A suitable material is magnesia stabilized zirconia. Dynamic-Ceramic Ltd of Crewe, UK supplies this under the name Technox 300 as a raw material for fabricating ceramic articles. This tube  60  has thinner walls than the pressure retaining tube  10 . In this embodiment, the tube  10  is shaped to create an annular cavity  62  between the vessel  60  and the tube  10 . 
         [0060]    In order to admit a sample fluid under pressure, the tube  60  encloses an internal floating piston  64 . The sample fluid is admitted under pressure through valve  66  and along line  68  to the chamber  70  at one side of the piston  64  while the chamber  72  at the other side of floating piston  64  is pressurized with fluid supplied along line  74 . This fluid may be a perfluorocarbon so that it does not contain hydrogen atoms. The pressure in chamber  72  is reduced to slightly less than the pressure of the incoming sample entering through inlet  68 , so that the incoming sample slowly drives the piston  64  along the vessel  60 , expelling fluid along line  74  until vessel  60  is filled with the sample fluid. 
         [0061]    The cavity  62  is connected by passage  76  to the line  74  and hence to the chamber  72 . After the sample fluid has been admitted to chamber  70 , the fluid pressure in line  74  and cavity  62  is maintained at slightly less than the pressure in chamber  70 . Thus pressure inside the tube  60  is almost balanced by a pressure in the cavity  62  around the exterior of the tube  60  and this avoids subjecting tube  60  to too much hoop stress. The fluid in cavity  62  is kept circulating under pressure. Fluid from a temperature controlled reservoir  78  is supplied to cavity  62  along line  80  and returns to the reservoir  78  after leaving along line  74  (the return path is not shown). 
         [0062]    Within the tube  60  there are end pieces  84 ,  85  which occupy space at each end of the interior of tube  60 . When the sample has been introduced through line  68  and the floating piston  64  has been driven fully along the tube  60  so that it abuts end piece  85 , the volume occupied by the sample is in a middle part of the length of coil  20 . Consequently the liquid sample is spaced from any distortions of the radio-frequency field near the ends of the coil  20 . 
         [0063]    It will be appreciated that the example embodiments described in detail above can be modified and varied within the scope of the concepts which they exemplify. Features referred to above or shown in individual embodiments above may be used together in any combination as well as those which have been shown and described specifically. Accordingly, all such modifications are intended to be included within the scope of this disclosure as defined in the following claims.