Abstract:
A method for determining a property of a fluid includes: receiving at a computing device an admittance spectrum created by application of an excitation to a resonator contacting the fluid, the spectrum covering a first frequency range and having real and imaginary components; determining a resonant frequency of the admittance spectrum, the resonant frequency being a frequency at which a magnitude of the imaginary component is about zero; determining a bandwidth of the spectrum; and determining the property based on one or both of the resonant frequency and the bandwidth of the resonant frequency.

Description:
RELATED APPLICATION AND PRIORITY CLAIM 
       [0001]    This application claims priority under 35 U.S.C. §119 to U.S. Provisional Patent Application Ser. No. 61/454,155, filed Mar. 18, 2011, and which is incorporated herein by reference in its entirety. 
     
    
     BACKGROUND 
       [0002]    1. Field of the Invention 
         [0003]    The present invention generally relates to obtaining hydrocarbons from a hydrocarbon bearing formation in the earth and, in particular, to making density and viscosity measurements of a fluid sample from the formation. 
         [0004]    2. Description of the Related Art 
         [0005]    Boreholes are drilled into the earth for many applications such as hydrocarbon production, geothermal production and carbon dioxide sequestration. A borehole is drilled with a drill bit or other cutting tool disposed at the distal end of a drill string. A drilling rig turns the drill string and the drill bit to cut through formation rock and, thus, drill the borehole. 
         [0006]    The borehole can provide access to a hydrocarbon reservoir. A particular hydrocarbon reservoir may contain several hydrocarbon-bearing formations that may or may not be connected. 
         [0007]    As the availability of hydrocarbon deposits in the earth diminish, the cost of obtaining hydrocarbons increases. Thus, it is desirable to provide products and methods for planning when and where to pursue hydrocarbon production from a reservoir. The difficultly and costs associated with obtaining hydrocarbons from a formation is sometimes referred to as the “producibility” of a formation. The producibility is related to the density and viscosity of the fluid samples taken from the formation. As such, it is desirable to provide accurate density and viscosity measurements of the fluid sample. 
       BRIEF SUMMARY 
       [0008]    Disclosed is a method for determining a property of a fluid that includes: receiving at a computing device an admittance spectrum created by application of an excitation to a resonator contacting the fluid, the spectrum covering a first frequency range and having real and imaginary components; determining a resonant frequency of the admittance spectrum, the resonant frequency being a frequency at which a magnitude of the imaginary component is about zero; determining a bandwidth of the spectrum; and determining the property based on one or both of the resonant frequency and the bandwidth of the resonant frequency. 
         [0009]    Also disclosed is a system for determining a property of a downhole fluid that includes a downhole component including a resonator that can be immersed in the downhole fluid and a computing device in operative communication with the downhole component. The computing device is configured to: receive an admittance spectrum created by application of an excitation to the, the spectrum covering a first frequency range and having real and imaginary components; determine a resonant frequency of the admittance spectrum, the resonant frequency being a frequency at which a magnitude of the imaginary component is about zero; determine a bandwidth of the spectrum; and determine the property based on one or both of the resonant frequency and the bandwidth of the resonant frequency. 
         [0010]    Also disclosed is a method of estimating a property of a fluid downhole that includes: determining a first admittance spectrum values for a resonator immersed in a fluid down hole as a ratio of electrical output current over input voltage over a first frequency range to form a first admittance spectrum; determining a first resonant frequency and a first bandwidth for the first admittance spectrum; determining second admittance spectrum values for the resonator immersed in the fluid down hole as a ratio of electrical output current over input voltage over a second frequency range to form a second admittance spectrum, the second frequency range including the first resonant frequency and the first bandwidth; determining a second resonant frequency and a second bandwidth for the second admittance spectrum; and estimating the property for the fluid downhole from the second resonant frequency and the second bandwidth. 
         [0011]    Also disclosed is a system for determining a property of a downhole fluid that includes a downhole component including a resonator that can be immersed in the downhole fluid and a computing device in operative communication with the downhole component. The computing device is configured to: determine a first admittance spectrum values for a resonator immersed in a fluid down hole as a ratio of electrical output current over input voltage over a first frequency range to form a first admittance spectrum; determine a first resonant frequency and a first bandwidth for the first admittance spectrum; determine second admittance spectrum values for the resonator immersed in the fluid down hole as a ratio of electrical output current over input voltage over a second frequency range to form a second admittance spectrum, the second frequency range including the first resonant frequency and the first bandwidth; determine a second resonant frequency and a second bandwidth for the second admittance spectrum; and estimate the property for the fluid downhole from the second resonant frequency and the second bandwidth. 
     
    
     
       BRIEF DESCRIPTION OF THE DRAWINGS 
         [0012]    The following descriptions should not be considered limiting in any way. With reference to the accompanying drawings, like elements are numbered alike: 
           [0013]      FIG. 1  is a schematic diagram of a measurement tool deployed on a wire line in a downhole environment; 
           [0014]      FIG. 2  is a schematic diagram of a measurement tool deployed on a drill string in a monitoring-while-drilling environment; 
           [0015]      FIG. 3  is a schematic diagram of a measurement tool deployed on a flexible tubing in a downhole environment; 
           [0016]      FIG. 4  illustrates a resonator deployed in a fluid chamber; 
           [0017]      FIG. 5  is a schematic illustration of an equivalent model of a resonator deployed in a fluid chamber; 
           [0018]      FIG. 6  is a schematic illustration of a current to voltage converter provided in an illustrative embodiment to measure the admittance spectrum of the resonator; 
           [0019]      FIG. 7  is a plot of an admittance spectrum of a resonator taken when the resonator deployed in a fluid sample; 
           [0020]      FIG. 8  is a plot of an admittance spectrum of  FIG. 7  corrected to remove shunt admittance effects; 
           [0021]      FIG. 9  illustrates a method for determining certain frequencies that can be utilized to estimate a property of a fluid; and 
           [0022]      FIG. 10  illustrates another method for determining certain frequencies that can be utilized to estimate a property of a fluid. 
       
    
    
     DETAILED DESCRIPTION 
       [0023]    A detailed description of one or more embodiments of the disclosed apparatus and methods presented herein is by way of exemplification and not limitation with reference to the Figures. 
         [0024]    The viscosity and density of a reservoir fluid are useful for understanding the cost and producibility of a reservoir or formation in the earth. In an illustrative embodiment, a piezoelectric tuning fork is used as a mechanical resonator to estimate the viscosity and density of a fluid sample from the formation. It is known to use a mechanical resonator in the form of a tuning fork (e.g., a piezoelectric tuning fork) to determine viscosity and density of a reservoir fluid. It has also been established that the electrical equivalent model of a mechanical resonator is a valid model for a piezoelectric tuning fork&#39;s response to a fluid&#39;s density and viscosity. Yet, the interpretation of the fork&#39;s response to an unknown fluid in terms of density and viscosity can be problematic. Embodiments disclosed herein can be used to interpret the fork&#39;s response. It shall be understood that while a piezoelectric tuning fork has been described as the resonator, any type of resonator can be utilized in conjunction with the teachings herein. 
         [0025]      FIG. 1  is a schematic diagram of a particular illustrative embodiment deployed on a wire line in a downhole environment. As shown in  FIG. 1 , a downhole tool  10  containing a mechanical resonator  410  is deployed in a borehole  14 . The borehole is formed in formation  16 . The tool  10  is deployed via a wire line  12 . The tool  10  includes a computing device  20  that can transmit data to a surface computer  21 . The computing device  20  can include computer readable medias and embedded data structures in memory. The surface computer  21  can be part of an intelligent completion system  30 . 
         [0026]      FIG. 2  is a schematic diagram of an embodiment of another particular illustrative embodiment deployed on a drill string  15  in a monitoring while drilling environment. 
         [0027]      FIG. 3  is a schematic diagram of an embodiment of another particular illustrative embodiment deployed on a flexible tubing  13  in a downhole environment. 
         [0028]      FIG. 4  illustrates a resonator  410  as it may be utilized in any downhole tool  10  shown above or any other type of downhole tool. In operation, the downhole tool  10  includes a conduit  426 , such as pipe or other fluid transmission component, through which a fluid can travel. In  FIG. 4 , the fluid is shown as flowing in the direction shown by arrow A. When the tool  10  is deployed in a borehole  14  a pump or other urging means included in the tool  10  causes a fluid outside of the tool  10  to travel through the conduit  426 . 
         [0029]    According to one embodiment, a resonator  410  is disposed such that at least a portion of it is located within the conduit  426 . As illustrated, the resonator  410  is a mechanical resonator in the form of a tuning fork. The resonator  410  could be any type of resonator such as a bar bender, disk bender, cantilever, tuning fork, micro-machined membrane, torsion resonator, or any piezoelectric transducer. 
         [0030]    The illustrated resonator  410  includes tines  413  disposed in the conduit  426  and a base  412  from which the tines  413  extend. In this manner, the resonator  410  can be caused to contact a fluid passing through the conduit  426 . In one embodiment, the fluid is a formation fluid. In another embodiment, the fluid is water or oil based drilling mud. 
         [0031]    The resonator  410  can be excited and its response in the presence of a fluid sample can be utilized to determine fluid density, viscosity and dielectric coefficient. The fluid can be moving or static. To this end, the base  412  of the resonator  410  is illustrated coupled to a computer processor  20 . The computer processor  20  includes an exciter circuit  421  that provides an electric voltage to the resonator  410  and monitors the behavior of the resonator  410  while the voltage is applied. The behavior can be utilized to determine density, viscosity and dielectric coefficient of the fluid passing through the conduit. Of course, the exciter circuit  421  could be located in a different processor than the computer processor  20 . 
         [0032]    In one embodiment, the resonator  410  can be utilized in a flowing fluid as illustrated in  FIG. 4 . For example, the resonator  410  could be utilized when a sample of well bore or formation fluid is pumped through the tool  10  and into the well bore. In this scenario, the resonator  410  is immersed in the flowing fluid and used to determine the density, viscosity and dielectric constant for the fluid flowing in the conduit  426 . 
         [0033]    In another embodiment, the fluid sample flowing in the tool  10  is stopped from flowing while the resonator  410  is immersed in the fluid and used to determine the density, viscosity and dielectric constant for the static fluid trapped in the tool  10 . 
         [0034]    The interpretation of the response of the resonator  410  can include modeling it with an electrical equivalent model such as that shown in  FIG. 5 . In  FIG. 5 , R 0    502 , L 0    504 , and C s    506  are the equivalent series resistance, inductance, and capacitance that model the electro-mechanical resonance of a piezoelectric transducer. These parameters could also be electrical analogs of mechanical parameters for a mechanical resonator where R 0    502  represents friction, L 0    504  represents mass, and C s    506  represents compliance. C p    510  is the total parasitic capacitance that shunts current around the transducer, or it could represent anything that reduces the force applied to a resonator  410 . Together, these parameters define the motional impedance of the resonator  410 , Z m , which relates the electrical impedance of a piezoelectric transducer to the simple harmonic oscillation of a mechanical resonator as shown in equation (1) where Z f    508  represents the impedance of the fluid being sampled: 
         [0000]    
       
         
           
             
               
                 
                   
                     Z 
                     m 
                   
                   = 
                   
                     
                       R 
                       0 
                     
                     + 
                     
                       j 
                        
                       
                         ( 
                         
                           
                             ω 
                              
                             
                                 
                             
                              
                             
                               L 
                               0 
                             
                           
                           - 
                           
                             1 
                             
                               ω 
                                
                               
                                   
                               
                                
                               
                                 C 
                                 0 
                               
                             
                           
                         
                         ) 
                       
                     
                     + 
                     
                       Z 
                       f 
                     
                   
                 
               
               
                 
                   ( 
                   1 
                   ) 
                 
               
             
           
         
       
     
         [0000]    where Z f  can be modeled as shown in equation 2: 
         [0000]        Z   f   =B√{square root over (ρηω)}+(   j ( Aω+B √{square root over (ρηω))}  (2)
 
         [0000]    The A coefficient relates fluid density, ρ, to an effective increase of resonator mass when oscillating at frequency ω in the fluid. The B coefficient relates the fluid&#39;s density-viscosity product, ρω, to viscous damping of the resonator  410  by the fluid. 
         [0035]    It is convenient to describe the resonator  410  response in terms of admittance, which is the reciprocal of impedance. The total admittance of the resonator  410 , Y t , is the ratio of current flowing through the device in response to an applied voltage. It is also the sum of the motional and shunt admittances in the resonator  410 . The relationships are shown in the set of equations (3): 
         [0000]    
       
         
           
             
               
                 
                   
                     Y 
                     t 
                   
                   = 
                     
                    
                   
                     
                       I 
                       out 
                     
                     
                       V 
                       in 
                     
                   
                 
               
             
             
               
                 
                   = 
                     
                    
                   
                     
                       1 
                       
                         Z 
                         m 
                       
                     
                     + 
                     
                       jω 
                        
                       
                           
                       
                        
                       
                         C 
                         p 
                       
                     
                   
                 
               
             
             
               
                 
                   = 
                     
                    
                   
                     
                       
                         
                           ( 
                           
                             
                               R 
                               o 
                             
                             + 
                             
                               B 
                                
                               
                                 
                                   ρ 
                                    
                                   
                                       
                                   
                                    
                                   ηω 
                                 
                               
                             
                           
                           ) 
                         
                         - 
                         
                           j 
                            
                           
                             ( 
                             
                               
                                 A 
                                  
                                 
                                     
                                 
                                  
                                 ρω 
                               
                               + 
                               
                                 
                                   L 
                                   o 
                                 
                                  
                                 ω 
                               
                               + 
                               
                                 B 
                                  
                                 
                                   
                                     ρ 
                                      
                                     
                                         
                                     
                                      
                                     ηω 
                                   
                                 
                               
                               - 
                               
                                 1 
                                 
                                   ω 
                                    
                                   
                                       
                                   
                                    
                                   
                                     C 
                                     s 
                                   
                                 
                               
                             
                             ) 
                           
                         
                       
                       
                         
                           
                             ( 
                             
                               
                                 R 
                                 o 
                               
                               + 
                               
                                 B 
                                  
                                 
                                   ρηω 
                                 
                               
                             
                             ) 
                           
                           2 
                         
                         + 
                         
                           
                             ( 
                             
                               
                                 A 
                                  
                                 
                                     
                                 
                                  
                                 ρω 
                               
                               + 
                               
                                 
                                   L 
                                   o 
                                 
                                  
                                 ω 
                               
                               + 
                               
                                 B 
                                  
                                 
                                   
                                     ρ 
                                      
                                     
                                         
                                     
                                      
                                     ηω 
                                   
                                 
                               
                               - 
                               
                                 1 
                                 
                                   ω 
                                    
                                   
                                       
                                   
                                    
                                   
                                     C 
                                     s 
                                   
                                 
                               
                             
                             ) 
                           
                           2 
                         
                       
                     
                     + 
                     
                       jω 
                        
                       
                           
                       
                        
                       
                         C 
                         p 
                       
                     
                   
                 
               
             
           
         
       
     
         [0036]    The admittance of a resonator  410  can be measured with a current to voltage converter  600  as shown in  FIG. 6 . If the input voltage, V in    602 , is supplied by a swept frequency voltage source from exciter circuit  421  ( FIG. 4 ), the admittance of the resonator  410  can be measured as a function of frequency, Y .sub. (ω)=V out (ω)/(V in (ω)R f ) to form an admittance spectrum. Amplifier  604  and feed back resistor R f    606  are used to condition a current response from the resonator  410  to produce a voltage V out    508 . An admittance spectrum that shows the resonance of a resonator  410  immersed in a fluid can be used to estimate the density and viscosity of the fluid. 
         [0037]    One approach to estimating density and viscosity based on the admittance spectrum is disclosed in U.S. Pat. No. 7,844,401, which is incorporated by reference herein in its entirety. In that patent, two frequencies are determined. In particular, in that patent, the first frequency is the resonant frequency ω s  and is equal to the frequency at which the real component of the resonator&#39;s admittance is at a maximum. The second frequency is equal to the frequency at which the imaginary component of resonator&#39;s admittance is at a maximum. This frequency is referred to as ω 45  and represents the frequency where the real and imaginary components are equal, implying a 45 degree phase shift between the currents. 
         [0038]    These two frequencies can be used to estimate density and viscosity. In particular, density and viscosity can be determined based on ω s  and ω 45  according to the following relationships: 
         [0000]    
       
         
           
             ρη 
             = 
             
               [ 
               
                 
                   
                     
                       
                         ( 
                         
                           
                             ω 
                             
                               s 
                               - 
                               vac 
                             
                           
                           
                             ω 
                             45 
                           
                         
                         ) 
                       
                       2 
                     
                     - 
                     
                       
                         ( 
                         
                           
                             ω 
                             
                               s 
                               - 
                               vac 
                             
                           
                           
                             ω 
                             s 
                           
                         
                         ) 
                       
                       2 
                     
                     - 
                     
                       2 
                        
                       
                         ( 
                         
                           
                             
                               ω 
                               
                                 s 
                                 - 
                                 vac 
                               
                             
                             - 
                             
                               ω 
                               
                                 45 
                                 - 
                                 vac 
                               
                             
                           
                           
                             ω 
                             45 
                           
                         
                         ) 
                       
                     
                   
                   
                     
                       B 
                       
                         L 
                         o 
                       
                     
                      
                     
                       ( 
                       
                         
                           2 
                           
                             
                               ω 
                               45 
                             
                           
                         
                         - 
                         
                           1 
                           
                             
                               ω 
                               s 
                             
                           
                         
                       
                       ) 
                     
                   
                 
                  
                 
                   [ 
                   2 
                 
                  
                 
                   
 
                 
                  
                 
                   ρ 
                   = 
                   
                     ( 
                     
                       
                         
                           
                             ( 
                             
                               
                                 ω 
                                 
                                   s 
                                   - 
                                   vac 
                                 
                               
                               
                                 ω 
                                 s 
                               
                             
                             ) 
                           
                           2 
                         
                         - 
                         
                           
                             B 
                             
                               L 
                               o 
                             
                           
                            
                           
                             
                               ρη 
                               
                                 ω 
                                 s 
                               
                             
                           
                         
                         - 
                         1 
                       
                       
                         A 
                         
                           L 
                           o 
                         
                       
                     
                     ) 
                   
                 
               
             
           
         
       
     
         [0000]    where ω s-vac  is the resonant frequency of the resonator in a vacuum and ω 45-vac  is frequency where the real and imaginary components are equal in a vacuum. The coefficients A and B in the above relationships can be determined by measuring ω s  and ω 45  for a resonator immersed in a calibration fluid having known density and viscosity. This solution requires no a priori information about the density and viscosity being measured. Moreover, as ω s  is always larger ω 45  there is a substantially reduced possibility of an undefined result. 
         [0039]    However, it has been discovered that in some instances, it can be difficult to determine the position of maxima due to noise. The amount of noise increases as viscosity increases due to broader and weaker resonant peaks. 
         [0040]    One embodiment of the present invention includes estimating the resonance frequency based on the zero crossing of a shunt corrected imaginary admittance and estimating the 3 dB frequency as the frequency at which the real component of the admittance equals half the global maximum of the real component. In addition, a method of searching for these values is disclosed. 
         [0041]      FIG. 7  illustrates the real  702  and imaginary  704  components of the admittance of a resonator  410  in a fluid plotted versus frequency that may be observed, for example, by utilizing the converter of  FIG. 6 . The plot shown in  FIG. 7  also includes a so-called shunt admittance  706  that is due to stray capacitance (e.g., C p    510  of  FIG. 5 ). 
         [0042]    In  FIG. 8 , the shunt admittance  706  has been subtracted from the imaginary component of the admittance ( 704 ) to produce a shunt corrected imaginary admittance  705 . Because of the symmetry of the imaginary component of the admittance  704 , an estimate of the shunt admittance can be calculated as the average value thereof and as is further described in U.S. Pat. No. 7,844,401. 
         [0043]    According to one embodiment, a method for determining viscosity and density includes determining the resonance frequency (ω s ) and the (ω 45 ) frequency, respectively from the shunt corrected imaginary admittance  705  and the real component of the admittance  702 . In this embodiment, the resonance frequency is equal to the frequency of the zero crossing of the shunt corrected imaginary impedance  705 . This point is identified in  FIG. 8  by reference numeral  810 . The ω 45  frequency is equal to the 3 dB frequency of the real part of the admittance  702 . The 3 dB frequency is the frequency at which the magnitude of the amplitude of the real part of the impedance  702  is one half of the global maximum  814  of the amplitude of the real part of the impedance  702 . 
         [0044]    In another embodiment, rather than consulting the zero crossing of the imaginary impedance on a Cartesian plot, the location on a polar plot the frequency where the imaginary component of the spectrum is at 45 degrees could be utilized to determine the resonant frequency. 
         [0045]      FIG. 9  illustrates a method of determining ω s  and ω 45  according to one embodiment. At block  902  the response of a resonator disposed at least partially in a fluid sample is measured. This response is a spectrum that varies over frequency and is preferably represented in terms of admittance. The sample fluid can be moving or static. In one embodiment, the fluid is drawn from a formation under the surface of the earth. A current to voltage converter such as shown in  FIG. 6  can be used to make such measurements. As one of ordinary skill will realize, if an alternating current (AC) voltage input (V in ) is provided, the measurement will include both magnitude and phase components. Stated differently, the measurement will include real and imaginary components. 
         [0046]    At block  904  the measured admittance spectrum is corrected. This can include, for example, removing any shunt admittance due to stray capacitance from the measured admittance spectrum. The shunt admittance can be calculated, in one embodiment, as an average value of the imaginary component of the measured admittance spectrum. In block  904 , removal of the shunt admittance can include subtracting, at each sample point, the shunt admittance from the imaginary component of the measured admittance. The result of processing at block  904  provides an admittance spectrum having a real component and a shunt corrected imaginary component  705 . 
         [0047]    At block  906  the global maximum of the real component of the measured spectrum is determined. Such a maximum can be found by any now known or later developed method of determining a maximum in a spectrum. Of course, some sort of filtering can improve this determination but is not required. 
         [0048]    At block  908  the global maximum of the imaginary component of the measured spectrum is determined. As before, such a maximum can be found by any now known or later developed method of determining a maximum in a spectrum and some sort of filtering can improve this determination but is not required. 
         [0049]    At block  910 , the zero crossing of the imaginary component of the measured spectrum is determined. This can include starting a search at the frequency identified at block  908  and successively searching higher frequencies until a zero crossing is found. The result of processing at block  910  is the resonant frequency ω s . 
         [0050]    In an alternative embodiment, and due to the symmetry of the imaginary component, block  908  could include finding the global minimum of the imaginary component. In such an embodiment, block  910  includes finding the zero crossing by starting a search at the minimum value of the imaginary component and successively searching lower frequencies until a zero crossing is found. 
         [0051]    At block  912  a value that is 50% of the global maximum of the real component of the measured spectrum determined at block  906  is determined. At block  914 , beginning at the resonant frequency and successively searching lower frequencies, the frequency at which the real component equals the value determined at block  912  is determined. The frequency where this occurs is the 3 dB frequency and can be utilized as the ω 45  frequency for the calculations disclosed above. Due to symmetry, in one embodiment, the 3 dB frequency could also be found by starting at the resonant frequency and searching at successively higher frequencies. In such an embodiment, the relationships shown above may require selecting the higher of the two possible solutions for ω 45-vac . 
         [0052]    The method disclosed in  FIG. 9  can be robust even in the presence of noise because it doesn&#39;t search the frequencies of interest at a range of the spectrum where a curve representing the spectrum is nearly horizontal (i.e., at the maximum). The crossing point of a steep curve with a horizontal line is more well-defined than trying to find the maximum of a flat portion of a curve. 
         [0053]    In some cases, the quality of the determinations can be improved by performing a two-stage frequency sweep.  FIG. 10  illustrates a method of performing a two-stage frequency sweep according to one embodiment. The process begins at block  1002  where the response of a resonator disposed at least partially in a fluid sample is measured. After block  1002 , at block  1004  the measured admittance spectrum is corrected. The procedures employed at blocks  1002  and  1004  can be the same or similar to those described with respect to blocks  902  and  904 , respectively, described above. It shall be noted that processing at block  1002  can include sweeping over a first, wide range of frequencies. 
         [0054]    At block  1006 , the values of ω s  and ω 45  are determined. These values can be determined as described above or in the manner described in U.S. Pat. No. 7,844,401. Regardless of how the values of ω s  and ω 45  are determined, a frequency window that includes both ω s  and ω 45  is defined. This frequency window has a second range that is smaller than the first range and, in one embodiment is, contained entirely within the first range. 
         [0055]    At block  1008  the response of the resonator in a fluid is again measured. The measurement, however, is limited to sweeping only the second range. Using roughly the same amount of sweep data points in both sweeps, the second sweep has a higher frequency resolution than the first. The result of the second measurement is referred to herein as an auto-scaled spectrum. At block  1010  the auto-scaled spectrum is corrected to compensate for stray capacitance. In one embodiment, the correction is based on the stray capacitance values determined at block  1004  because the auto-scaled spectrum includes only frequencies surrounding the resonant frequency. 
         [0056]    Optionally, at block  1012 , a smoothing function could be applied to the corrected spectrum. The smoothing could be performed, for example, by a low-pass finite impulse response (FIR) filter. 
         [0057]    At block  1014 , ω s  and ω 45  are determined from the smooth corrected auto-scaled spectrum based on the zero crossing of the imaginary component and the 3 dB point of the real component as described above. 
         [0058]    In short, the frequencies of interest found during the first sweep are used to scale the window of interest of the second sweep. In this manner, the width of the resonance peak is auto-scaled and centered in the spectrum acquired during the second sweep. Such auto-scaling allows the use of the same noise reduction filter for all measurements, independent of the resonance characteristics which are influenced by the fluid and can, therefore, avoid the use of an adaptive filter. 
         [0059]    In one embodiment, the second frequency range is chosen such that the range from the 3 dB frequency to the resonance frequency is centered and scaled to approx. ⅓ of the window of interest. 
         [0060]    Elements of the embodiments have been introduced with either the articles “a” or “an.” The articles are intended to mean that there are one or more of the elements. The terms “including” and “having” are intended to be inclusive such that there may be additional elements other than the elements listed. The conjunction “or” when used with a list of at least two terms is intended to mean any term or combination of terms. The terms “first,” “second,” and “third” are used to distinguish elements and are not used to denote a particular order. Certain portions of the description and Figures include reference to ordered processes. It shall be appreciated that, unless specifically required by the context, the order of these processes can be varied. 
         [0061]    It will be recognized that the various components or technologies may provide certain necessary or beneficial functionality or features. Accordingly, these functions and features as may be needed in support of the appended claims and variations thereof, are recognized as being inherently included as a part of the teachings herein and a part of the invention disclosed. 
         [0062]    While the invention has been described with reference to exemplary embodiments, it will be understood that various changes may be made and equivalents may be substituted for elements thereof without departing from the scope of the invention. In addition, many modifications will be appreciated to adapt a particular instrument, situation or material to the teachings of the invention without departing from the essential scope thereof. Therefore, it is intended that the invention not be limited to the particular embodiment disclosed as the best mode contemplated for carrying out this invention, but that the invention will include all embodiments falling within the scope of the appended claims.