Abstract:
A method for characterizing wellbore response of a pulsed neutron instrument includes inserting a pulsed neutron instrument into a plurality of simulated wellbores each filled with materials representing gas and liquid and measuring response of the pulsed neutron instrument in the simulated wellbores.

Description:
CROSS-REFERENCE TO RELATED APPLICATIONS 
     Not applicable. 
     STATEMENT REGARDING FEDERALLY SPONSORED RESEARCH OR DEVELOPMENT 
     Not applicable. 
     BACKGROUND 
     This disclosure relates generally to the field of pulsed neutron well logging. More specifically, the disclosure is related to methods for determining formation hydrogen index or neutron porosity when a wellbore contains various fluids, such as oil gas and/or air in unknown quantities. 
     Subsurface formation HI (hydrogen index) measurement using high energy neutrons as a measurement source has been used in well logging since at least the 1950s. In case of no bound-water in the formation matrix (such as clean sand, carbonate formation, but not shale), hydrogen atoms only appear in the pore space (oil or water). Thus, the formation hydrogen index is typically related to formation porosity. Neutron source based porosity measurements known in the art rely on the fact that the slowing down of neutrons, and therefore the average distance traveled within the formations by the neutrons, is strongly dependent on the hydrogen content of the formation. The hydrogen content dependency is due to the fact that neutrons can incur a very large energy loss in a single elastic scattering event with a proton (a hydrogen nucleus). In its simplest form, neutron based porosity measurement can be performed using a neutron source and a detector axially spaced from the neutron source. If the axial spacing of the detector from the source is chosen appropriately, then the neutron flux at the detector location will decrease monotonically with increasing formation hydrogen content. As one possible alternative, the neutron detector can be replaced by a gamma-ray detector, since the flux of neutron induced gamma-rays is related to the neutron flux. 
     Early versions of neutron-based porosity measurement instruments included those having a single gamma-ray detector (e.g., a Geiger-Mueller counter) with a radioisotope-based neutron source (e.g.,  241 AmBe,  238 PuBe). Such instruments may be referred to as “neutron-gamma” instruments. Correspondingly, instruments using a neutron detector (e.g., a  3 He proportional counter) may be referred to as “neutron-neutron” instruments. Traditionally, the term “neutron porosity” typically means a neutron-based porosity measurement using a  241 AmBe source and “neutron-neutron” instruments. The following terms are defined in order to differentiate this work from the traditional “neutron porosity”. “Neutron-neutron porosity” may be defined as neutron porosity based on a neutron source and neutron detectors. Similarly, “neutron-gamma porosity” may be defined as neutron porosity based on a neutron source and gamma ray detectors, which is the subject of the present disclosure 
     Both neutron-neutron instrument measurements and to an even larger extent neutron-gamma instrument measurements are strongly affected by a multitude of environmental effects. Such effects include the fluid actually disposed in the wellbore at the time measurements are made. 
     It can be more difficult to measure formation HI based on gamma ray detectors as compared to using neutron detectors. In addition to other phenomena, gamma ray detectors measure the gamma rays from neutron “capture” interaction (i.e., capture of a thermal neutron by a nucleus of certain atoms having large “neutron capture cross section” and subsequent emission of a gamma ray) in the formation, wellbore or the instrument itself. Capture gamma ray measurement is therefore an indirect measurement the presence of neutrons. The physics of neutron-neutron porosity only involves neutron transport from the source to the neutron detector. The physics of neutron gamma porosity involves both neutron and gamma ray transport, so that such physics are more complex. Thus, neutron-gamma porosity may have more environmental effects which may be more difficult to interpret. 
     Notwithstanding the additional complexity in interpretation there may be advantages associated with measuring neutron-gamma porosity. The count rate of a gamma ray detector can be more than 1 order of magnitude higher than a  3 He neutron detector. The depth of investigation (lateral distance from the wellbore wall into the formation) of a neutron-gamma measurement may be deeper than that of a neutron-neutron measurement. The energy of a gamma ray from a neutron capture event is normally in the million electron volt (MeV) range, which means such gamma rays can travel a longer distance than a thermal neutron before absorption. A scintillation type gamma ray detector can also provide gamma ray spectroscopy and inelastic neutron scatter-related measurements, which a thermal or epithermal neutron detector cannot. The foregoing features make neutron-gamma porosity very appealing. 
     SUMMARY 
     A method according to one aspect for characterizing wellbore response of a pulsed neutron instrument includes inserting a pulsed neutron instrument into a plurality of simulated wellbores each filled with materials representing gas and liquid and measuring response of the pulsed neutron instrument in the simulated wellbores. 
     Other aspects and advantages will be apparent from the description and claims that follow. 
    
    
     
       BRIEF DESCRIPTION OF THE DRAWINGS 
         FIG. 1  shows an example neutron-gamma well logging instrument using a “pulsed” neutron source. 
         FIG. 1A  shows an example of conveying a well logging instrument along the interior of a wellbore. 
         FIG. 2  shows an example of source and detector timing used in some examples. 
         FIG. 3  shows an example of a ratio of numbers of capture gamma rays at two differently spaced detectors with respect to formation porosity for various fluids disposed in a wellbore. 
         FIG. 4  shows examples of TRat at standard conditions with those determined with other fluids filling the wellbore. 
         FIG. 5  shows examples of capture gamma ray count rate ratios (short by “capture ratio”) with respect to burst gamma ray count rate ratios (short by “burst ratio”) for various fluids filling the wellbore. 
         FIG. 6  shows an example of removing the HI sensitivity from a burst ratio using a capture-to-burst detector ratio. 
         FIG. 7  shows an example of characterization of the gain of the lines of the ratios in  FIG. 4  with respect to various wellbore diameters and fluids therein using. 
         FIG. 8  shows an example of characterization of the offset (zero intercept) of the lines of the ratios in  FIG. 4  with respect to various wellbore diameters and fluids therein using. 
         FIG. 8A  shows a graph of porosity determined using capture gamma ray detection ratio with respect to actual porosity for various wellbore fluids wherein the capture gamma ray detection ratio is corrected using the burst measurement. 
         FIG. 9  shows a flow chart of an example method according to the present disclosure. 
         FIG. 10  shows a graph of dispersion in the results shown in  FIG. 7  caused by the formation lithology effect in IRat. 
         FIG. 11  shows a computer system that may be used in some examples. 
         FIG. 12  shows an example tool characterization apparatus. 
         FIG. 13  shows a graph of borehole fluid density as a function of burst measurement. 
     
    
    
     DETAILED DESCRIPTION 
       FIG. 1  shows an example “neutron-gamma porosity” well logging instrument  10 . The measurement components of the instrument  10  may be disposed in a housing  12  shaped and sealed to be moved along the interior of a wellbore. The pulsed neutron well logging instrument  10  may, in a form hereof, be of a type described, for example, in U.S. Pat. No. 5,699,246. 
     The instrument housing  12  contains a pulsed neutron source  14 , and two or more gamma ray detectors  18 ,  20  at different axial spacings from the pulsed neutron source. The pulsed neutron source  14  (hereinafter “source”), when activated, will emit controlled duration “bursts” of high energy neutrons (approximately 14 MeV, and which may be emitted isotropically). One example of a pulsed neutron source is described in U.S. Pat. No. 5,293,410 issued to Chen et al. 
     Shielding  16  may be interposed between the source  14  and the axially closest detector (e.g.,  16 ) to reduce the effects of direct neutron communication between the source  14  and the detectors  18 ,  20 . The detectors  18 ,  20  may be scintillation counters each coupled to a respective counter or pulse height analyzer (not shown separately). Thus, numbers of and, with the use of a pulse height analyzer, energy of detected gamma rays may be characterized at each of a plurality of distances from the source  14 . 
     The gamma ray detectors  18 ,  20  may detect gamma rays arriving at the detector as a function of time. There are two principal mechanisms, through which a neutron-induced gamma ray can be generated. One is neutron inelastic scattering, which can be triggered only by “fast” neutrons (with energy above approximately 1 MeV, the exact energy threshold depending on the type of nucleus). The other is through neutron capture, which can be triggered primarily by thermal neutrons (with energy around 0.025 eV at room temperature) or epithermal neutrons (with energy from about 0.4 to 100 eV) being absorbed into a susceptible nucleus, as non-limiting examples, chlorine, boron and cadmium. When the source  14  is activated, the gamma rays arriving at the detectors  18 ,  20  may be generated through both mechanisms because the source keeps emitting fast neutrons which can slow down to epithermal or thermal almost instantly (relative to the acquisition system timing). When the source  14  is switched off, the gamma rays arriving at the detectors  18 ,  20  may only be generated by epithermal or thermal neutron capture because no new fast neutrons are emitted into the wellbore and formations. Thus, the measured gamma ray flux at the detectors  18 ,  20  during the source off time is an indirect measurement of epithermal and thermal neutrons. Such indirect measurement can be used to provide formation hydrogen index (HI) measurement. 
     A well logging instrument including a scintillation detector type radiation counter is shown at  210  in  FIG. 1A  as it is ordinarily used in a procedure to make measurements of properties of subsurface Earth formations penetrated by a wellbore. The wellbore  212  is drilled through the formations, shown generally at  215 . The wellbore  212  may be filled with liquid called “drilling mud”  214  during the drilling and well logging procedure, or some form of brine or other completion fluid after wellbore construction is completed. The well logging procedure includes lowering the well logging instrument  210  into the wellbore  212 . The instrument  210  may be attached to one end of an armored electrical cable  216 . The cable  216  is extended into the wellbore  212  by a winch  218  or similar spooling device to lower the instrument  210  into the wellbore  212 . The winch  218  may then be operated to withdraw the cable  216  from the wellbore while various sensors (to be further explained) in the instrument  210  make measurements of various properties of the formations  215  penetrated by the wellbore  212 . Electrical power may be transmitted along the cable  216  from the surface to operate the instrument  210 . Signals corresponding to the measurements made by the various sensors in the instrument  210  (explained above with reference to  FIG. 1 ) may be transmitted along the cable  216  for recording and/or interpretation in a recording unit  220  at the Earth&#39;s surface, or in a computer system as will be explained with reference to  FIG. 10 . 
     The present example of the well logging instrument may be an instrument that makes measurements corresponding to selected properties of the Earth formations  215  based on spectral analysis of detected gamma rays. Such instruments include a housing  210 A in which is disposed certain electronic circuitry, shown generally at E and to be further explained below. The housing  210 A may or may not include a backup pad or arm  210 B that is biased to one side of the instrument  210  to urge the other side of the instrument  210  into contact with the wall of the wellbore  212 . The other side of the instrument  210  may or may not include a tungsten or similar high density skid or pad  210 C in which is disposed a source radiation RS, which may be a pulsed neutron source as explained with reference to  FIG. 1  above. Although the example instrument shown in  FIG. 1A  includes various components disposed in a skid or pad, in other examples, the components may be disposed entirely within the instrument housing as shown in  FIG. 1 . 
     One or more radiation detectors (e.g.,  18  and  20  as explained with reference to  FIG. 1 ) including a scintillation detector crystal XTAL optically coupled to a photomultiplier PMT may be disposed in the pad  210 C. A controllable high voltage power supply HV is coupled to the photomultiplier PMT to enable photons applied thereto to be converted to voltage pulses as will be familiar to those skilled in the art. The voltage output of the high voltage power supply HV can be controlled by a controller (not shown separately in  FIG. 1A ) forming part of the circuitry E to cause the high voltage supply HV maintain a suitable voltage on the photomultiplier PMT. The example instrument shown in  FIG. 1A  is intended to illustrate an example of conveyance of an instrument in a wellbore as well as to explain examples of detector types that may be used in accordance with the present disclosure in order to obtain measurements that may be processed as will be further explained below. 
     While the example conveyance of a well logging instrument as shown in  FIG. 1A  uses armored electrical cable, the foregoing is not intended to limit the scope of instrument conveyance according to the disclosure. Any known means of conveyance may be used in other examples, including, without limitation, as part of a drill string as a logging while drilling (LWD) instrument, conveyed by coiled tubing or slickline. 
       FIG. 2  shows an example source and detector timing scheme that may be used to acquire measurements for processing as will be further explained with reference to  FIG. 9 . The source ( 14  in  FIG. 1 ) may be operated so that selected time duration “bursts” of neutrons may be emitted. This is shown in  FIG. 2  at  21 . After each burst  21 , the source may remain switched off for a selected length of time. This is shown at  22  in  FIG. 2 . A curve showing gamma rays detected by one or the other of the detectors ( 18 ,  20  in  FIG. 1 ) is shown at  24 . The detectors ( 18 ,  20  in  FIG. 1 ) may detect gamma rays resulting from inelastic collisions of high energy neutrons with nuclei in the formations ( 215  in FIG.  1 A) during the neutron bursts  21  or resulting from capture of thermal neutrons. This is shown schematically as “burst measurement” at  26 . This is a measurement during the neutron burst-on time and contains both inelastic gamma rays and capture gamma rays. During the time when the neutron source is switched off, only gamma rays resulting from capture of thermal neutrons may be detected. This is shown schematically at  28  as “capture measurement”. 
     There is a correspondence between the ratio of numbers of capture gamma rays detected at the far spacing detector ( 20  in  FIG. 1 ) with respect to the numbers detected at the near spacing detector ( 18  in  FIG. 1 ).  FIG. 3  shows a graph of the ratio of capture gamma rays detected (count rate) with respect to porosity of the formations, assuming that the pore spaces of the formations are filled with fresh water at a predetermined temperature and pressure. The various curves shown in  FIG. 3  indicate ratio of count rate, which may hereinafter be referred to as the capture ratio (or TRat) with respect to porosity for different fluids disposed in the wellbore ( 212  in  FIG. 1A ). For example, curve  30  shows the correspondence for a wellbore filled with fresh water. Curve  32  shows correspondence for a wellbore filled with “light” oil. Curves  34  and  36  show the correspondence, respectively, for a wellbore filled with methane gas having a density of 0.25 g/cm 3  and 0.1 g/cm 3 . Finally, curve  38  shows the correspondence for a wellbore filled with air. 
       FIG. 4  shows a graph of the measured count rate ratio TRat for standard conditions (fresh water filled wellbore) at line  40  with respect to the TRat measured with different fluids filling the wellbore, at lines  42 ,  44 ,  46  and  48  corresponding to the various fluids filling the wellbore as described with reference to  FIG. 3 . It has been determined through modeling experiments that the TRat for any value of porosity that would be measured at standard conditions (water filled porosity and fresh water in the wellbore) is related to the TRat that would be measured wherein various fluids fill the wellbore by a gain and offset. The value of the gain and offset are related to the type of fluid filling the wellbore. 
     One can obtain two “burst measurements” from two detectors located at two-axial distances from the source, and compute a ratio of their respective count rates as a “burst ratio” BRat, i.e. the ratio of counts acquired during the entire neutron burst or during a fraction thereof.  FIG. 5  shows the same capture ratio (TRat) vs. a burst ratio in the same borehole and formation conditions. The burst ratio has some dependence on porosity due to the presence of capture gamma rays in the burst gate, that is, the burst ratio as actually measured is contaminated by capture gamma rays. However, the burst ratio is more sensitive to the borehole fluid density variation than the formation porosity variation. Therefore, one may use the burst ratio to correct the borehole gas/oil effects in the capture ratio. 
     To illustrate the concept more clearly, one can substantially remove the porosity dependence of the burst ratio using a third ratio so that the measured burst ratio is substantially independent of the capture ratio, as shown in  FIG. 6 . In theory, one would like to have an burst ratio which is not contaminated by capture gamma rays. However, an accurate subtraction of the capture effect from the spectrum acquired during the neutron burst is difficult and may not be sufficiently accurate. The example in  FIG. 6  is based on an approximation that the number of capture gamma rays during a burst gate is proportional to the number of capture gamma rays in a capture gate right after the burst gate. The y-axis is the count rate in a capture gate of the far detector divided by the count rate in the burst gate of the near detector; the x-axis is the count rate ratio in the burst gate (Far divided by Near detector). The borehole and formation conditions in  FIG. 6  are the same as the ones in  FIG. 5 . In this example, the third ratio is a ratio between a “capture measurement” and a “burst measurement” from two detectors separately, where the capture measurement is take during a predetermined time interval after the burst with one detector and the burst measurement is taken during the entire neutron burst or a fraction thereof with a second detector. One can call this a capture/burst ratio. As can be observed in  FIG. 6 , the burst ratio is a linear function of the capture/burst ratio (the third ratio or Rat3) if the borehole conditions are the same. In different borehole conditions, the slope of the linear function does not change. Thus, the HI sensitivity of the burst ratio can be removed using a linear function of the capture/burst ratio determined in various borehole and formation conditions. 
     Such linear function may be determined as follows. Define IRat using Eq. 1. 
     
       
         
           
             
               
                 
                   
                     
                       
                         IRat 
                         = 
                           
                         ⁢ 
                         
                           BRat 
                           - 
                           
                             
                               a 
                               · 
                               Rat 
                             
                             ⁢ 
                             
                                 
                             
                             ⁢ 
                             3 
                           
                         
                       
                     
                   
                   
                     
                       
                         = 
                           
                         ⁢ 
                         
                           
                             
                               Far 
                               ⁡ 
                               
                                 ( 
                                 Burst_Gate 
                                 ) 
                               
                             
                             
                               Near 
                               ⁡ 
                               
                                 ( 
                                 Burst_Gate 
                                 ) 
                               
                             
                           
                           - 
                           
                             a 
                             · 
                             
                               
                                 Far 
                                 ⁡ 
                                 
                                   ( 
                                   Capture_Gate 
                                   ) 
                                 
                               
                               
                                 Near 
                                 ⁡ 
                                 
                                   ( 
                                   Burst_Gate 
                                   ) 
                                 
                               
                             
                           
                         
                       
                     
                   
                 
               
               
                 
                   ( 
                   1 
                   ) 
                 
               
             
           
         
       
     
     The coefficient a in Eq. 1 is a constant, which is associated with the tool design and can be characterized by laboratory experiment or by modeling so that there is no HI sensitivity in IRat. IRat is very sensitive to gas/oil present in the borehole. It still has sensitivity to formation conditions, such as gas-filled porosity and lithology, but it is relatively small compared to the borehole gas/oil effects. In International Application Publication No. WO 2012/083210 are described many other options to remove the HI sensitivity from a burst measurement. The same techniques can be applied to the present techniques as well. The following section will illustrate that the borehole gas/oil effects on the capture ratio can be estimated using IRat. 
       FIG. 7  and  FIG. 8  are plots showing the required gain and offset, which are used to correct TRat in various conditions back to the one in standard condition, as a function of IRat defined in Equation 1. The curves shown at  50 ,  52 , and  54  in  FIG. 7 , respectively, correspond to different borehole sizes, 6 inches 8 inches, and 12 inches. Corresponding borehole sizes are represented by curves  56 ,  58  and  60  in  FIG. 8 . The borehole conditions for the curves in  FIG. 7  and  FIG. 8  are the same as the ones in  FIG. 4 , which are 8-inch borehole and a casing with 5.5-inch casing size (OD) and 4.95-inch casing ID. The required gain and offset are actually the slope and offset of lines  42 ,  44 ,  46 ,  48  in  FIG. 4 , corresponding to light oil borehole, methane gas (0.25 g/cm 3 ) borehole, methane gas (0.15 g/cm 3 ) borehole and air borehole. As can be observed in  FIGS. 7 and 8 , the required gain and offset are non-linear functions of IRat. The values of the IRat shown in  FIG. 7  and  FIG. 8  are for 0-pu sandstone only. 
     In the present example, one may use second order polynomial functions to predict the required gain and offset based on the IRat, as shown in Eq. 2. The six coefficients (a1, a2, a3, b1, b2, and b3) are constants and associated with the tool design and the actual timing gates chosen for IRat and TRat. They can be characterized by laboratory experiment and/or modeling. Substituting Equation 1 in Equation 2, one will obtain Equation 3, which shows that the corrected capture ratio is essentially a second order function of three ratios, a burst ratio, a capture ratio and the third ratio. Note that Equation 3 is only one example. One can generalize Equation 3 to Equation 4 to show that the corrected capture ratio is essentially a function of three ratios.
 
 T Rat_corrected=( a   1   ·I RAT 2   +a   2   ·I RAT+ a   3 )· T Rat+( b   1   ·I RAT 2   +b   2   ·I RAT+ b   3 )  (2)
 
 T Rat_corrected= . . . [ a   1 ·( B Rat −a   0 ·Rat3) 2   +a   2 ·( B Rat −a   0 ·Rat3)+ a   3   ]·T Rat+ . . . [ b   1 ·( B Rat− a   0 ·Rat3) 2   +b   2 ·( B Rat −a   0 ·Rat3)+ b   3 ]  (3)
 
 T Rat_corrected= f ( B Rat,Rat3, T Rat)  (4)
 
       FIG. 8A  shows a graph of formation porosity determined from corrected TRat for various fluids filling the wellbore with respect to actual porosity of the formation. It may be observed in  FIG. 8A  that there is good correspondence between the porosity determined using the IRat corrected TRat for a wide range of fluid types and densities for the fluid filling the wellbore. 
       FIG. 9  shows flow chart of an example method according to the present disclosure. At  62 , measurements of inelastic gamma rays and thermal neutron capture gamma rays are made, e.g., as explained with reference to  FIG. 2 . At  64 , ratios of the foregoing count rates, capture ratio and burst ratio may be determined. Such determination, and the subsequent elements of an example method, may be performed in a computer system in the recording unit ( 220  in  FIG. 1A ) or on any other computer system as will be explained with reference to  FIG. 10 . At  66  the third ratio is determined as explained above. At  56  for the particular well logging instrument used, the gain and offset used to correct the measured TRat may be determined as explained with reference to Eq. (2) using the measured IRat. Finally, the corrected TRat may be used, at  58 , to determine formation hydrogen index (HI) or porosity. 
     In the same borehole conditions, the required gain and offset do not depend on the formation conditions. However, IRat will have some formation dependency (lithology, gas-filled porosity, etc.). Thus, the computed gain and offset based on the IRat will have some formation dependency as well. Fortunately, the lithology and gas-filled porosity effects turn out to be about 10 times smaller than the gas/oil borehole effects on the burst ratio. Therefore, the burst ratio can be used to compute the gas/oil borehole correction. 
     Some of the errors in the oil/gas borehole correction shown in  FIG. 8A  are due to the small dependence of IRat on formation lithology.  FIG. 10  shows the required gain as a function of IRat for 0-pu sandstone, limestone and dolomite. Comparing to  FIG. 7 , which is only for 0-pu sandstone, one can see some dispersion in IRat. Since the method used to predict the required gain and offset from the IRat is characterized based on 0-pu sandstone conditions, IRat will read lower in limestone or dolomite conditions, which will underestimate the gain (as shown in  FIG. 10 ) and the porosity. 
     There are several ways to improve the correction. One can remove the HI sensitivity from the burst ratio using a non-linear formula or database-search method as discussed in the above referenced International Application publication. Another way is to use a long adaptive filter on the predicted gain and offset, to average out the leftover formation sensitivity in the gain and offset. In some conditions, one can even fix the gain and offset to their average values in certain zones. 
     Note that there is a plurality of options to remove the HI sensitivity from the burst ratio. For example, instead of using the capture/burst ratio, one can use TRat itself to remove the HI sensitivity. As shown in  FIG. 5 , the HI sensitivity in the burst ratio can be removed based on a non-linear function of the capture ratio. Thus, one can compute IRat using Equation 5. Substituting Equation 5 to Equation 2, the corrected TRat can be written as a non-linear function of only a burst ratio and a capture ratio as shown in Equation 6. There is no third ratio in such example. On top of that, one can combine the steps shown at  66  and  68  in  FIG. 9 . One may separate capture and inelastic events when computing a burst ratio in order to illustrate the idea of gas/oil borehole correction clearly. Similarly, one can introduce a fourth ratio or more ratios to better remove the HI sensitivity or other formation dependency from the burst ratio, or better correct the borehole gas/oil effects on the capture ratio.
 
 I Rat= B Rat+ f ( T Rat)  (5)
 
 T Rat_corrected= f ( B Rat, T Rat)  (6)
 
     The concept of the present disclosure can also be applied to a tool design which contains at least one gamma ray detector and in which the neutron output of the generator is known. One possibility is the use of a neutron monitor such as a fast neutron (1 MeV energy and higher) detector installed proximate to the neutron source to monitor the variation of the neutron source output. Any or all the detector ratios discussed herein (either burst ratio, capture ratio or the third ratio) can be replaced by the ratio of a detected gamma ray count rate in a given timing gate and a signal indicative of the neutron output of the neutron generator. In the case of a fast neutron detector used as a neutron monitor, the number of fast neutron counts registered in the detector is directly related to the neutron output. Alternatively, the neutron output may be determined from the generator operating parameters or from the determination of radiation directly related to the neutron output of the generator and unaffected by the tool environment or a combination of a several neutron output measurements. Additionally, the concept of the present disclosure may also work for a tool equipped with more than two axially spaced apart gamma ray detectors. In such case, the detector ratios can be computed from any two detectors among the detectors in the tool. 
       FIG. 11  depicts an example computing system  100  in accordance with some embodiments. The computing system  100  may be an individual computer system  101 A or an arrangement of distributed computer systems. The computer system  101 A may include one or more analysis modules  102  that may be configured to perform various tasks according to some embodiments, such as the tasks depicted in  FIG. 9 . To perform these various tasks, analysis module  102  may execute independently, or in coordination with, one or more processors  104 , which may be connected to one or more storage media  106 . The processor(s)  104  may also be connected to a network interface  108  to allow the computer system  101 A to communicate over a data network  110  with one or more additional computer systems and/or computing systems, such as  101 B,  101 C, and/or  101 D (note that computer systems  101 B,  101 C and/or  101 D may or may not share the same architecture as computer system  101 A, and may be located in different physical locations, for example, computer systems  101 A and  101 B may be on a ship underway on the ocean or on a well drilling location, while in communication with one or more computer systems such as  101 C and/or  101 D that may be located in one or more data centers on shore, aboard ships, and/or located in varying countries on different continents). Storage media and/or processor(s) may also be disposed in the well logging tool ( 10  in  FIG. 1 ). 
     A processor can include a microprocessor, microcontroller, processor module or subsystem, programmable integrated circuit, programmable gate array, or another control or computing device. 
     The storage media  106  can be implemented as one or more computer-readable or machine-readable storage media. Note that while in the example embodiment of  FIG. 10  the storage media  106  are depicted as within computer system  101 A, in some embodiments, the storage media  106  may be distributed within and/or across multiple internal and/or external enclosures of computing system  101 A and/or additional computing systems. Storage media  106  may include one or more different forms of memory including semiconductor memory devices such as dynamic or static random access memories (DRAMs or SRAMs), erasable and programmable read-only memories (EPROMs), electrically erasable and programmable read-only memories (EEPROMs) and flash memories; magnetic disks such as fixed, floppy and removable disks; other magnetic media including tape; optical media such as compact disks (CDs) or digital video disks (DVDs); or other types of storage devices. Note that the instructions discussed above may be provided on one computer-readable or machine-readable storage medium, or alternatively, can be provided on multiple computer-readable or machine-readable storage media distributed in a large system having possibly plural nodes. Such computer-readable or machine-readable storage medium or media may be considered to be part of an article (or article of manufacture). An article or article of manufacture can refer to any manufactured single component or multiple components. The storage medium or media can be located either in the machine running the machine-readable instructions, or located at a remote site from which machine-readable instructions can be downloaded over a network for execution. 
     It should be appreciated that computing system  100  is only one example of a computing system, and that computing system  100  may have more or fewer components than shown, may combine additional components not depicted in the example embodiment of  FIG. 11 , and/or computing system  100  may have a different configuration or arrangement of the components depicted in  FIG. 11 . The various components shown in  FIG. 11  may be implemented in hardware, software, or a combination of both hardware and software, including one or more signal processing and/or application specific integrated circuits. 
     Further, the steps in the processing methods described above may be implemented by running one or more functional modules in information processing apparatus such as general purpose processors or application specific chips, such as ASICs, FPGAs, PLDs, or other appropriate devices. These modules, combinations of these modules, and/or their combination with general hardware are all included within the scope of the present disclosure. 
     In order to automatically correct the oil/gas borehole effects in real time, it is useful to characterize the tool responses in known conditions for different borehole sizes and/or casing configurations. However, oil and gas borehole conditions are difficult to reproduce in the laboratory. A pressurized vessel is used to reproduce gas borehole conditions in laboratory. This is not only expensive but also poses a danger to the operators. A diesel-filled borehole can be made practically, but the tool response is so similar to that in a water filled borehole that it does not materially assist in tool characterization. A light oil-filled borehole is not practical either due to the flammability and the rate of evaporation of most liquids that resemble light oil. 
     A novel technique which reduces safety concerns is to use plastic balls mixed with either air or water to simulate oil/gas borehole conditions. This technique is very easy to use and inexpensive. The origin of this technique is the realization that for nuclear measurements the particular chemical form of a material does not matter. The only factor affecting nuclear measurements is the volumetric number density of all the component elements.  FIG. 12  shows some plastic balls  122  and a logging tool  10  inside a transparent plastic tube  120  to illustrate the basic idea. A plastic tube (polyethylene or polypropylene) can be used as a borehole liner or a casing in the laboratory. Bottom and top caps (not shown) hold all the balls in place. Because the density of the balls may be lower than that of water, one can fill the borehole (tube  120 ) with water and the balls  122  will float up and can be collected easily. 
     The proposed technique can easily be extended to mixtures of other materials with water or other liquids. Hollow balls of any material can be used and other liquids can be substituted for the water. This allows the operator to cause the simulated borehole fluid composition to match the properties of the desired real world condition. 
     A list of techniques that extends the range of possible borehole fluids that can be modeled (e.g. including but not limited to CO 2 ) may include: (a) hollow solid particles mixed with a fluid (e.g. air or water). One can optimize the thickness and material of the hollow particles to achieve a particular element density; (b) constant stream of gas that is released at the bottom of a liquid column to create a stable (i.e. compositionally the same as a function of time) mix of gas and liquid with the desired properties while it rises; (c) a fluidized bed wherein solid particles are brought into constant motion by a fluid being pumped from below to create a stable composition as a function of time; (d) a foam, either stable or unstable (e.g. a foam temporarily stabilized by a surfactant or a more permanent foam such as polystyrene or neoprene); (e) machined or otherwise purposely structured solid (e.g. a carbon rod with a multitude of holes in it to model CO 2 ). 
     A series of measurements can be made using this technique for different formation tanks. Then the measurements can be used to characterize the borehole gas/oil correction method, which was discussed earlier. One can also use the same measurements to benchmark/validate modeling simulation and use modeling to extent the formation/borehole conditions to a wider realistic range. The characterization method is an integral part of this borehole fluid correction method due to the nonlinear behavior of the correction term between the air point and the water point. A characterization of the correction term between these two extremes dramatically improves the performance of the algorithm. 
     Beside the gas borehole correction for the porosity measurement, the burst measurement can also be used to measure borehole fluid density.  FIG. 13  shows the borehole fluid density for a 6-inch wellbore at  130 , an 8-inch wellbore at  132  and a 12.25 inch wellbore at  134  as a function of the burst measurement. The curves are a third order polynomial fit. If the borehole size in open hole conditions or the casing size is known, one may characterize the burst measurement and use it to derive the borehole fluid density. 
     While the invention has been described with respect to a limited number of embodiments, those skilled in the art, having benefit of this disclosure, will appreciate that other embodiments can be devised which do not depart from the scope of the invention as disclosed herein. Accordingly, the scope of the invention should be limited only by the attached claims.