CN116066069A

CN116066069A - Method for measuring formation porosity by using pulse neutron source and dual-function detector

Info

Publication number: CN116066069A
Application number: CN202211359134.3A
Authority: CN
Inventors: 詹晟; 杰若米·张
Original assignee: China Petroleum and Chemical Corp
Current assignee: China Petroleum and Chemical Corp
Priority date: 2021-02-11
Filing date: 2022-11-01
Publication date: 2023-05-05

Abstract

Formation porosity is measured using a logging tool having a pulsed neutron generator and a plurality of dual function detectors capable of detecting neutrons and gamma rays. The ratio of thermal neutrons, epithermal neutrons, and captured gamma rays from the plurality of detectors is utilized to obtain a plurality of neutron porosities and a plurality of gamma ray porosities at different depths of investigation. Neutron porosity and gamma-ray porosity may be further corrected by excluding peak areas attributed to hydrogen and/or chlorine to reduce shale effects and/or chlorine effects. Neutron porosity and gamma-ray porosity may be combined to provide a better assessment of porosity at different depths of investigation in the formation throughout the porosity measurement range (0-100 p.u.).

Description

Method for measuring formation porosity by using pulse neutron source and dual-function detector

Technical Field

The present disclosure provides methods and apparatus for logging a formation through a wellbore, particularly by selecting and/or combining neutron porosity and gamma-ray porosity obtained simultaneously using a plurality of dual function detectors to provide formation porosity for different depths of investigation (DOI) in the formation throughout a porosity measurement range (0-100 p.u.).

Background

Formation porosity can now be measured using a compensating neutron tool having one neutron source and two neutron detectors spaced apart from the neutron source by different distances. The neutron source may Be an isotopic neutron source (e.g., an Am-Be source). The neutron detector may detect thermal neutrons or epithermal neutrons. Fast neutrons emitted from a neutron source are moderated into thermal neutrons in the formation. Some thermal neutrons are captured by elements in the formation (i.e., thermal neutron capture) and produce gamma rays (i.e., capture gamma rays) when the excited elements decay to their ground state. Other neutrons are scattered back to the detector and detected.

The downhole formation contains water (H ₂ O), gas (CH) ₄ ) And/or oil (C) _n H _2n+2 ) All of which are rich in hydrogen. In contrast, common rocks, such as limestone (CaCO) ₃ ) Sandstone (SiO) ₂ ) Dolomite (CaMg (CO) ₃ ) ₂ ) Does not contain a large amount of hydrogen element. Because hydrogen can effectively capture thermal neutrons, the higher the formation porosity, the fewer thermal neutrons that can escape thermal capture and reach the detector. Since thermal neutrons at the far detector are higher in percentage of total neutrons than at the near detector, the neutron count rate of the far detector is affected more than that of the near detector. Thus, the ratio of the count rate of the near detector to the count rate of the far detector (near-far ratio) is positively correlated with formation porosity. That is, the higher the near-to-far ratio, the higher the formation porosity and vice versa. Furthermore, the correlation between this ratio and formation porosity is unique to a particular tool and a particular formation mineralogy (e.g., sandstone, limestone, or dolomite). A particular count rate ratio may be associated with formation porosity.

It is well known that porosity measurements can be affected by near-wellbore environmental factors such as wellbore size, tool spacing, wellbore salinity, temperature, pressure, and the like. Accordingly, various algorithms have been developed to correct these environmental factors. However, when the salinity in the wellbore, mud filtrate, or formation fluid (NaCl, KCl in the fluid) is higher, more thermal neutrons will be absorbed by the chlorine (Cl) in the high salt fluid. Therefore, the neutron count rate of the detector is reduced. Furthermore, since thermal neutrons at the far detector are a higher percentage of total neutrons than at the near detector, the neutron absorption at the far detector is more pronounced than at the near detector. Therefore, the count rate of the far detector is reduced to a greater extent than the near count rate of the near detector, so that the near-far detector count rate is increased. Thus, formation apparent porosity increases. Pseudo increases in formation apparent porosity due to high salinity are often referred to as chlorine effects.

The presence of shale in the formation can also distort apparent neutron porosity to the point that readings may be as high as 100p.u. Shale contains significant amounts of clay bound water and other minerals that affect the deceleration and absorption of neutrons, and therefore the neutron count rate in shale sand or shale is significantly reduced. Since the count rate of the far detector is more affected than the count rate of the near detector, the far-to-near ratio increases. Thus, the apparent porosity in shale sand or shale is typically read higher than the actual porosity, which is known as the shale effect. In field applications, the chlorine and shale effects may be so high that even if corrected, formation porosity measurements are unreliable.

The number of captured gamma rays is proportional to the number of thermal neutrons. Thus, formation porosity may also be measured by using a ratio of captured gamma-ray count rates. In addition, formation porosity obtained based on captured gamma rays is also affected by shale effects and chlorine effects. Gamma-ray porosity logging typically uses one pulsed neutron generator and two gamma-ray detectors. In this case, gamma rays from the thermal neutron capture reaction can be distinguished from gamma rays from inelastic scattering of fast neutrons.

Accordingly, there is a need to develop methods and tools for porosity logging that reduce or avoid chlorine effects and/or shale effects and generally improve accuracy.

Disclosure of Invention

The present disclosure provides methods and apparatus for enhanced formation porosity measurements that can cover the entire porosity measurement range (0-100 p.u.). The device has a pulsed neutron generator and a plurality of dual function detectors that detect neutrons and gamma rays. By using multiple dual function detectors, multiple neutron porosity readings and gamma ray porosity readings may be obtained simultaneously with different depths of detection for the formation. The neutron porosity and gamma-ray porosity are then corrected and/or combined to obtain one or more formation porosities with improved accuracy.

One embodiment of the present disclosure provides a method of evaluating the porosity of a downhole formation. The method includes measuring formation porosity in a wellbore using a pulsed neutron generator and a plurality of dual function detectors. By selecting and/or combining neutron porosity and gamma-ray porosity obtained simultaneously using multiple dual-function detectors, deterministic solutions can be utilized to estimate values of formation porosity at different depths of detection throughout the measurement range.

Another embodiment of the present disclosure provides an apparatus configured to evaluate the porosity of a downhole formation. The apparatus includes a pulsed neutron generator and a plurality of dual function detectors capable of detecting neutrons and gamma rays.

The present disclosure further provides a method for evaluating the porosity of a downhole formation. The method comprises the following steps: emitting neutron pulses from a pulsed neutron tool deployed in a wellbore to irradiate a formation surrounding the wellbore; detecting neutrons and gamma rays using a plurality of detectors disposed in a pulsed neutron tool; and estimating a plurality of neutron porosities and a plurality of gamma-ray porosities based on the data from the plurality of detectors. The detector in the pulsed neutron tool is a dual function detector that can be used to detect neutrons and gamma rays in the formation.

In some embodiments, neutrons detected by the plurality of detectors are selected from thermal neutrons, epithermal neutrons, or a mixture thereof, and gamma rays detected by the plurality of detectors are inelastic gamma rays, capture gamma rays, or a mixture thereof. The signals from neutrons and gamma rays detected by the detectors are distinguished by the application of pulse shape discrimination techniques.

In some other embodiments, the estimating step in the method comprises: obtaining a neutron count rate and a captured gamma-ray count rate from each of the plurality of detectors; calculating a neutron count rate ratio and a capture gamma ray count rate ratio between each two of the plurality of detectors to obtain a plurality of neutron count rate ratios and a plurality of capture gamma ray count rate ratios; and estimating a plurality of neutron porosities using the plurality of neutron count rate ratios and/or estimating a plurality of gamma-ray porosities using the plurality of gamma-ray count rate ratios.

In other embodiments, each of the plurality of neutron porosities is obtained using an algorithm, e.g., a polynomial function as shown in equation 4 of the present disclosure, having as input a corresponding neutron count rate ratio of the plurality of neutron count rate ratios. Each of the plurality of gamma-ray porosities is obtained using an algorithm, for example, a polynomial function as shown in equation 11 of the present disclosure, having as input a corresponding one of a plurality of gamma-ray count rate ratios.

In some other embodiments, each of the plurality of neutron porosities is obtained using a corrected neutron count rate ratio, wherein the corrected neutron count rate ratio is obtained by applying a correction factor to the neutron count rate ratio, the correction factor being a function of the plurality of neutron count rate ratios, e.g., according to equations 5-7 in the present disclosure.

In still other embodiments, each of the plurality of gamma-ray porosities is obtained using a corrected gamma-ray count rate ratio, wherein the corrected gamma-ray count rate ratio is obtained by applying a correction factor to the gamma-ray count rate ratio that is a function of the plurality of gamma-ray count rate ratios, e.g., according to equations 12-14 in the present disclosure.

In a specific embodiment, the method is performed using a pulsed neutron tool comprising three detectors, namely a first, a second and a third detector. The method comprises the following steps: obtaining a neutron count rate and a captured gamma ray count rate from each of the first detector, the second detector, and the third detector; calculating a first neutron count rate ratio and a first capture gamma-ray count rate ratio between the first detector and the second detector, a second neutron count rate ratio and a second capture gamma-ray count rate ratio between the second detector and the third detector, and a third neutron count rate ratio and a third capture gamma-ray count rate ratio between the first detector and the third detector; calculating three neutron porosities using the first neutron count rate ratio, the second neutron count rate ratio, and the third neutron count rate ratio, respectively; and/or calculating three capture gamma-ray porosities using the first, second, and third capture gamma-ray count rate ratios, respectively.

The method may optionally include a correction step. One example of a correction step is to correct the plurality of neutron porosities and the plurality of gamma-ray porosities by subtracting the captured gamma-ray count rate due to hydrogen, chlorine, or both, e.g., according to equations 15-20.

In a further embodiment, neutron porosity and gamma-ray porosity are evaluated and combined to provide formation porosity. In one such method, a neutron porosity value selected from a plurality of neutron porosities is compared to a value selected from a corresponding gamma-ray porosity value of a plurality of gamma-ray porosities. When the difference between the two values is less than or equal to a predetermined value, taking the value of neutron porosity as the formation porosity; when the difference between the two values is greater than a predetermined value, the value of gamma-ray porosity is taken as the formation porosity. The predetermined value may be any value in the range of 2% to 10%.

In another method, a value of a neutron porosity selected from the plurality of neutron porosities and a value of a corresponding gamma-ray porosity selected from the plurality of gamma-ray porosities are compared to a predetermined value. The formation porosity value is equal to the neutron porosity value when the neutron porosity value is less than or equal to the predetermined value, and the formation porosity value is equal to the gamma-ray porosity value when the gamma-ray porosity value is greater than the predetermined value. The predetermined value may be any value from 30p.u. to 50p.u., for example, 30p.u., 35p.u., 40p.u., 45p.u., or 50p.u.

In yet another method, the formation porosity is calculated according to a weighted function of one of the plurality of gamma-ray porosities and one of the plurality of neutron porosities, e.g., according to equation 21.

Drawings

The teachings of the present invention can be readily understood by considering the following detailed description in conjunction with the accompanying drawings.

Fig. 1A shows that the gamma ray signal recorded by the detector decays faster than the neutron signal.

Fig. 1B shows a Pulse Shape Discrimination (PSD) versus energy intersection to distinguish neutrons from gamma rays.

Fig. 2A, 2B, 2C and 2D show four exemplary configurations of a pulsed neutron logging tool having one neutron source S1 and three detectors D1, D2 and D3 arranged along the longitudinal direction of the tool housing.

FIGS. 3A, 3B, and 3C illustrate cross-sectional views of exemplary pulsed neutron logging tools having S1, D2, and D3.

Fig. 4A and 4B show cross-sectional views of an exemplary pulsed neutron logging tool having four detectors D1, D2, D31, D32 and six detectors D1, D21, D22, D31, D32, D33, respectively.

FIG. 5 illustrates a block diagram of an exemplary drilling system suitable for implementing the present disclosure.

FIG. 6 shows a schematic of inelastic and capture spectra of neutron pulses, neutron count rates, and neutron induced gamma rays.

Fig. 7 illustrates a workflow for estimating formation porosity according to an embodiment of the present disclosure.

Fig. 8 shows details of S706 to S708 in the workflow shown in fig. 7.

Fig. 9 shows how gamma ray counts from hydrogen and chlorine are separated in the spectrum of captured gamma rays from a detector to correct the overall captured gamma ray count rate.

Detailed Description

The following detailed description is provided to assist the reader in obtaining a thorough understanding of the methods, apparatus, and/or systems described herein. Reference is made to the detailed description of the disclosure, examples of which are illustrated in the accompanying drawings. Similar or like reference numbers may be used in the drawings and may indicate similar or like elements.

The features described herein may be embodied in different forms and should not be construed as limiting the embodiments set forth herein. Rather, the embodiments described herein and depicted in the drawings have been provided so that this disclosure will be thorough and complete, and will convey the full scope of the disclosure to those skilled in the art so that they may be readily appreciated from the following description: alternative embodiments exist without departing from the general principles of the present disclosure.

The scope of the invention is, therefore, defined not by the specific embodiments, but by the claims and their equivalents, and all changes within the scope of the claims and their equivalents are to be interpreted as being included in the disclosure.

In oil and gas exploration, density, porosity, mineralogy, and gas/oil saturation are important formation parameters for evaluating the total oil/gas reserves of an oilfield. Various wireline and LWD (logging while drilling) logging tools have been developed to obtain downhole formation parameters.

Formation density is obtained by measuring back-scattered gamma rays from a gamma radiation source (e.g., a Cs-137 source) received by two detectors (e.g., two sodium iodide scintillation detectors) disposed at different distances from the gamma radiation source. These two detectors are commonly referred to as a near detector and a far detector depending on their relative distance from the gamma ray source.

Neutron porosity logging tools obtain formation porosity by measuring the ratio of the neutron count rate of the near detector to the far detector after fast neutrons from an isotopic neutron source (e.g., am-Be source) are slowed down by the tool's surroundings (e.g., wellbore fluid and formation) and scattered back to the detector. This ratio is then converted to porosity in the formation mineralogy (e.g., sandstone, limestone, or dolomite) according to the particular tool. Using the count rate ratios from the two detectors can reduce the effect of changes in near-wellbore environment (wellbore fluid, wellbore size, etc.) on the porosity measurements.

Pulsed neutron logging tools employ a pulsed neutron source (e.g., a D-T neutron generator) and one, two, or three detectors that detect neutrons or neutron-induced gamma rays. The energy spectrum of neutron-induced gamma rays from each element is unique. Thus, by measuring the energy spectrum of gamma rays from inelastic scattering and/or neutron capture reactions, it is possible to identify the elements and obtain the relative percentages of gamma rays from each element in the formation, i.e., the element fractions. Inelastic scattering spectra are the basis for carbon-to-oxygen (C/O) ratio logging, but captured gamma-ray spectra may also provide information for other elements, such as magnesium (Mg), silicon (Si), calcium (Ca), iron (Fe), sulfur (S), and (Al). The captured gamma-ray energy spectrum may also provide information on many elements, such as magnesium (Mg), silicon (Si), calcium (Ca), iron (Fe), sulfur (S), titanium (Ti), potassium (K), gadolinium (Ga), hydrogen (H), and chlorine (Cl).

Since element yield logs only provide relative concentrations of elements, they are often expressed in terms of ratios such as C/O, cl/H, si/(Si+Ca), H/(Si+Ca), and Fe/(Si+Ca). These ratios are indicators of oil, salinity, mineralogy, porosity, and clay, respectively. Elemental yield logs and reaction cross sections of neutron inelastic scattering and neutron capture reactions of these elements may also be used to obtain elemental content in the formation.

In addition, by measuring the thermal neutron time decay curve or captured gamma ray time decay curve after one or more neutron pulses, a macroscopic thermal neutron absorption cross section (sigma) of the formation may be obtained, which can be used to estimate the gas/oil saturation.

In most of these applications, neutrons and gamma rays are detected by their respective detectors/sensors. For example, a He-3 gas detector is used to detect thermal neutrons. He-3 isotopes have a high thermal neutron absorption cross section. After fast neutrons emitted from the neutron source are slowed down by the formation and scattered back to the detector, the neutrons are absorbed and produce other detectable ions, such as protons (p) and tritium (T), thereby ionizing the gas. Ions and electrons multiply and drift in the electric field to form an electrical signal. Various scintillation detectors may be employed, such as NaI, csI, BGO, GSO, laBr, YAP scintillators, and photomultiplier tubes (PMTs), for detecting gamma rays. These scintillators convert the deposited energy of the gamma rays into scintillation light. PMTs convert the scintillation light into electrons and amplify them to form a current signal.

Existing nuclear logging tools typically employ a single function detector to detect neutrons or gamma rays. For example, to obtain both formation density and neutron porosity, the traditional approach has been to combine density tools and neutron porosity tools together in a tool string. The density tool may have one gamma ray source and two gamma ray detectors. The neutron porosity tool may have one neutron source and two neutron detectors. Thus, measurement of formation density and neutron porosity requires the use of two different radiation sources and four radiation detectors. A third detector may be required in order to obtain other parameters such as the saturation of the gas. Furthermore, neutron monitoring detectors may be required to monitor the source intensity of the neutron generator, as the source intensity may decrease or fluctuate over time. Thus, nuclear logging tools need to carry a variety of different types of radiation sources and detectors to measure a variety of formation parameters. Such logging tools are limited in use due to high cost, low reliability and large volume.

Recently, scintillator materials that are sensitive to both neutrons and gamma rays have been developed, such as: cs (cells) ₂ LiYCl ₆ (CLYC)、Cs ₂ LiLaBr ₆ (CLLB). By coupling crystals of this material with a scintillation photosensor, such as a photomultiplier tube (PMT), a dual-function scintillator, i.e., a dual-function detector, can be produced that is capable of detecting neutrons and gamma rays. As shown in fig. 1A and 1B, neutrons and gamma rays received by a dual function detector may be distinguished from each other using Pulse Shape Discrimination (PSD) techniques based on the fact that the electron signals from the detector due to gamma rays decay faster than the electron signals of neutrons.

Fig. 9 shows a typical energy spectrum of captured gamma rays from a detector. When the salinity is higher, there are peaks at about 1.95MeV, 5.09MeV, 5.61MeV, and 6.11MeV for gamma rays due to chlorine-captured thermal neutrons, and peaks at about 2.23MeV for gamma rays due to hydrogen-captured thermal neutrons. These peaks can be eliminated when calculating the total detector count rate for capturing gamma rays.

In this disclosure, unless otherwise indicated, a detector refers to a dual function detector that can detect neutrons and gamma rays. Such detectors employ scintillation crystals (e.g., cs ₂ LiLaBr ₆ (CLLB) and a photosensitive device (e.g., PMT)). The probe may be actively cooled or non-actively cooled as it is deployed downhole. For example, a detector using CLLB crystal and a high temperature PMT may be used at high temperature without an additional cooling device. In addition, the ratio or count rate ratio refers to a ratio between two count rates detected by two different detectors, which may be two neutron count rate ratios or two gamma ray count rate ratios.

Fig. 2A-2D are schematic illustrations (not to scale) of four exemplary configurations of a cylindrical pulsed neutron logging tool having a pulsed neutron source S1 and three dual-function detectors D1, D2, D3 disposed along a housing of the logging tool suitable for Logging While Drilling (LWD) operations. The Mud Channel (MC) is arranged along the axis of the logging tool, while the detectors are arranged eccentrically in the longitudinal direction of the logging tool. Fig. 2A also shows: a high voltage power supply (HV); electronics, such as a controller, for sending instructions, receiving and processing data from the pulsed neutron source and the detectors; and telemetry means for transmitting data between the logging tool and the surface. The high voltage power supply provides high voltage power to the detectors D1, D2, D3 and the pulsed neutron source S1. The high voltage power supply, electronics and telemetry required are not shown in figures 2B-2D for simplicity.

As shown, D1 is the near detector having the shortest distance in the longitudinal direction to the pulsed neutron source, D3 is the far detector having the longest longitudinal distance to the pulsed neutron source, and D2 is the middle detector with the longitudinal distance in between.

As shown in fig. 2A, all three detectors are located on one side of the pulsed neutron source along the logging tool. This side may be proximal or distal to the pulsed neutron source. The proximal side is the side closer to the surface when the pulsed neutron logging tool is deployed downhole, and the distal side is the side away from the surface. The high voltage power supply provides high voltage power to the detectors D1, D2, D3 and the pulsed neutron source S1. The signals from each detector are processed by electronics and the measurements/data are collected and transmitted by telemetry. As shown in fig. 2B, 2C and 2D, at least one detector is disposed on both the distal and proximal sides of the pulsed neutron source.

In wireline logging, the tool may be installed in a probe that does not contain a mud channel. The probe may be mounted along or offset from the axis of the tool body. Power and control signals may also be provided to the logging tool from the surface, and data from the logging tool may be transmitted to the surface via a cable.

The pulsed neutron source S1 in each of the logging tools depicted in fig. 2A-2D is a pulsed neutron generator. The pulsed neutron generator may be a deuterium-tritium (D-T) pulsed neutron generator that may be operated in a pulsed mode in a variety of pulse output modes (e.g., frequency, pulse duration). For example, the frequency of the neutron pulse may be about 10kHz (with a period of 100 μs), and the duration of the neutron pulse may be about 20 μs. In another embodiment, the frequency of the neutron pulse may be about 1kHz (1000 μs in period), and the neutron duration may be 50 μs. Depending on the method and measurement, the D-T neutron generator may also be operated in continuous mode. In this case, the starting frequency of the neutron generator is high enough to allow the neutrons to be emitted continuously. Neutrons from the D-T neutron generator have an initial energy of about 14.1 MeV.

The pulsed neutron source may also be a deuterium-deuterium (D-D) pulsed neutron generator, which may be operated in a pulsed mode with different pulse output modes (e.g., frequency, pulse duration). For example, the frequency of the neutron pulse may be about 20kHz (with a period of 50 μs), and the duration of the neutron pulse may be about 20 μs. Alternatively, the frequency of the neutron pulse may be about 1kHz (with a period of 1000 μs), and the duration of the neutron pulse may be 40 μs. Depending on the method and measurement, the D-D neutron generator may also be operated in continuous mode. Neutrons from the D-D neutron generator have an initial energy of about 2.5 MeV.

The neutron source S1 and the detectors D1, D2 and D3 in fig. 2A-2D only indicate their relative positions along the longitudinal direction of the housing of the logging tool, and do not indicate their positions in the radial direction in the cross section of the tool housing.

In certain embodiments, S1, D2, and D3 may be disposed in the same radial direction or different radial directions, i.e., have the same or different measured azimuth angles when deployed in the formation. FIGS. 2A, 2B, 2C and 2D show exemplary cross-sectional views in the directions A-A, B-B, C-C and D-D, respectively. S1, D2, and D3 in fig. 3A are set at the same azimuth angle. However, in fig. 3B, S1, D1, and D3 have the same azimuth angle, while D2 is at a different azimuth angle. In fig. 3C, S1 and D1 have the same azimuth angle, and each of D2 and D3 has a different azimuth angle.

Other embodiments of the logging tool may have more than three detectors. For example, fig. 4A depicts a variation of the logging tool of fig. 2A having four detectors, D1, D2, D31, and D32. D31 and D32 are approximately the same distance from S1, but are disposed at two different azimuth angles. Likewise, fig. 4B depicts another variation of the tool in fig. 2A, with six detectors, namely D1, D21, D22, D31, D32 and D33. In this embodiment, D21 and D22 are disposed opposite each other in the cross-section of the logging tool, i.e., the azimuth angles of D21 and D22 are 0 ° and 180 °, respectively. D31, D32, D33 are disposed 120 ° apart in the cross section of the logging tool, i.e. the difference in azimuth between any two of D31, D32 and D33 is 120 °. Having different azimuth angles allows the detector to preferentially receive neutrons and gamma rays of a particular angle of incidence from the formation. This embodiment also increases the detection efficiency of neutrons and gamma rays by increasing the total count rate of all detectors.

In addition, in fig. 4A, the distances of D31 and D32 from S1 are substantially the same. In fig. 4B, the distance between the middle detectors D21 and D22 and S1 is substantially the same, and the distance between the far detectors D31, D32, and D33 and S1 is substantially the same. By "substantially the same distance" is meant that the distance from S1 to the scintillator center of the detector (e.g., D31 and D32) is approximately the same. For example, the difference is less than one-half or one-quarter inch. With this arrangement, the middle detector as a whole and the far detectors as a whole have a higher count rate than when only one middle detector or only one far detector is used. Thus, the pulsed neutron source S1 may be a lower intensity source that may not be subject to the stringent regulatory constraints of higher intensity neutron sources. Furthermore, the count rate of the individual detectors can be recorded and processed separately. The differences in distance and azimuth of the various detectors may be used to obtain formation information in a particular azimuth direction.

In some embodiments, the logging tool has a plurality of shields (not shown) that can absorb neutrons and gamma rays. A shield may be placed between a neutron source and each detector in the logging tool so that the detectors receive neutrons and gamma rays from the formation instead of passing through the body of the logging tool. Alternatively, the detector may be partially shielded by providing shielding material that absorbs neutrons and gamma rays from certain directions.

The shield is made of or comprises one or more materials that are effective to attenuate thermal neutrons and gamma rays. The shielding material may comprise a material selected from the group consisting of heavy elements having a high thermal neutron absorption cross section, including metals such as gadolinium (Gd), samarium (Sm), metal oxides (e.g., gd) ₂ O ₃ 、Sm ₂ O ₃ 、B ₂ O ₃ ) Alloys containing Gd or Sm in combination with other heavy metals, e.g. Fe, pb or W, or boron-containing materials, e.g. tungsten boride (WB, WB) ₂ Etc.).

The shield may be a separate piece of metal inserted into the logging tool or may be an integral part of the sonde housing. For example, the portion of the detector housing facing the logging tool may be made of a shielding material, while the portion facing the formation is made of a material transparent to neutrons and gamma rays to form a window through which neutrons and gamma rays may pass. Thus, neutrons and gamma rays from certain angles of incidence may be absorbed by the shielding material, while those passing through the window are received by the detector. Thus, by adjusting the size and orientation of the window in the detector housing, the detector may be more sensitive to certain angles of incidence. During operation, data collected by various probes may create formation properties in a particular direction, which may be used to guide the direction of drilling.

The logging tool may be part of a wireline logging tool or included in downhole equipment as an LWD logging tool in a drilling operation. Fig. 5 is a schematic diagram of the oil drilling system 10 applied in directional drilling of a borehole 16. The oil drilling system 10 may be used for drilling on land as well as under water. A rotary drill rig including derrick 12, drill floor 14, drawworks 18, trolley 20, hook 22, rotary joint 24, kelly joint 26, and rotary table 28 is used to drill a borehole 16 into a formation. The drill string 100 includes a plurality of drill rods connected in series and secured to the bottom of the kelly joint 26 at the surface. The rotary table 28 is used to rotate the entire drill string 100, while the drawworks 18 is used to lower the drill string 100 into the wellbore 16 and apply a controlled axial compressive load. A downhole drilling assembly 150 is disposed at the distal end of the drill string 100.

Drilling fluid (also referred to as mud) is typically stored in a mud pit or mud tank 46 and delivered using a mud pump 38, the mud pump 38 forcing the drilling fluid to flow through a surge suppressor 40, then through a kelly hose 42, and through the rotary joint 24, and into the top of the drill string 100. Drilling fluid flows through the drill string 100 and into the downhole drilling assembly 150 at a rate of about 150 gallons per minute to about 600 gallons per minute. The drilling fluid then returns to the surface through the annular space between the outer surface of the drill string 100 and the borehole 16. When the drilling fluid reaches the surface, it is conveyed back to the mud tank 46 via the mud return line 44.

The pressure required to maintain drilling fluid circulation is measured by a pressure sensor 48 on the kelly hose 42. The pressure sensor detects a pressure change caused by a pressure pulse generated by the pulse generator. The amplitude of the pressure wave from the pulser can reach 500psi or higher. The measured pressure is transmitted as an electrical signal through the sensor cable 50 to the surface computer 52, and the surface computer 52 decodes and displays the transmitted information. Alternatively, the measured pressure is transmitted as an electrical signal through the sensor cable 50 to a decoder, which decodes the electrical signal and transmits the decoded signal to the surface computer 52, which surface computer 52 displays the data on a display screen.

As described above, the lower portion ("distal portion") of drill string 100 includes a downhole drilling assembly (BHA) 150 that includes a non-magnetic drill collar in which is mounted a MWD system (MWD tool or MWD tool) 160, a Logging While Drilling (LWD) tool sub 165 containing LWD tools, a downhole motor 170, a near-bit measurement sub 175, and a drill bit 180 having a drilling nozzle (not shown). The drilling fluid flows through the drill string 100 and out through the drilling nozzles of the drill bit 180. During drilling operations, the drilling system 10 may be operated in a rotary mode, wherein the drill string 100 is rotated from the surface by a motor (i.e., top drive) in the rotary table 28 or the rover 20. The drilling system 10 may also operate in a sliding mode in which the drill string 100 is not rotated from the surface, but rather the drill bit 180 is driven into rotation by the downhole motor 170. Drilling fluid is pumped from the surface through the drill string 100 to the drill bit 180 and injected into the annular space between the drill string 100 and the wall of the borehole 16. The drilling fluid carries cuttings from the wellbore 16 to the surface.

In one or more embodiments, MWD system 160 may include pulser subs, pulser drive subs, battery subs, central storage units, main boards, power subs, orientation module subs, and other sensor boards. In some embodiments, some of these devices may be located in other areas of the BHA 150. One or more of the pulser nipple and the pulser drive nipple may be in communication with a pulser 300, and the pulser 300 may be located below the MWD system 160. The MWD system 160 may transmit data to the pulse generator 300 such that the pulse generator 300 generates pressure pulses.

The non-magnetic drill collar houses a MWD system 160 that includes a set of instruments for measuring inclination, azimuth, well trajectory (wellbore trajectory), and the like. Pulsed neutron logging tools and associated electronics may be located in LWD tool sub 165. The pulsed neutron logging tool and other logging instruments may be electrically or wirelessly coupled together, powered by a battery pack or by a generator driven by the drilling fluid. All the information collected is transmitted to the surface through the mud column in the drill string in the form of pressure pulses generated by the pulser 300.

A near bit measurement joint 175 may be disposed between the downhole motor 170 and the bit 180. Pulsed neutron logging tools may alternatively be installed in the near-bit measurement nipple 175 to provide more accurate real-time formation parameters to guide directional drilling. The data may be transmitted to the MWD system 160 in the downhole drilling assembly 150 via a cable embedded in the downhole motor 170.

In one embodiment of the present disclosure, a logging tool having a D-T neutron generator and three dual function detectors is used to obtain a variety of formation parameters. FIG. 6 shows a schematic diagram of inelastic and capture energy spectra of neutron pulses, neutron count rates, and neutron induced gamma rays. The frequency of the neutron pulse is 10kHz (cycle 100 mus) and the neutron on time is 20 mus, as shown in subplot (b) of fig. 6.

Neutron count rates measured by dual function detectors, as shown in sub-graph (a) in fig. 6, are used to obtain formation porosity and other formation parameters. Neutrons from the dual function detector may be further separated depending on whether the neutron pulse is on or off, with the pulsed neutron synchronization signal being used as a coincidence or anti-coincidence signal for neutrons from the three detectors to record neutrons primarily as fast neutrons during the neutron pulse (neutron pulse on). Between neutron pulses (neutron pulse is off), neutrons are recorded as thermal neutrons. Fast neutrons and thermal neutrons recorded by the three detectors can be used to obtain a spatial distribution of fast neutrons and a spatial distribution of thermal neutrons. Neutrons from each detector may also be recorded together. In this case, all neutrons (from thermal neutrons to fast neutrons) are used to obtain a neutron spatial distribution.

The gamma rays recorded by the dual function detector may be further separated depending on whether the neutron pulse is on or off, using the pulsed neutron synchronization signal as a coincidence or anti-coincidence signal for the gamma rays from the three detectors, so that the gamma rays are recorded mainly as non-elastic energy spectra during the neutron pulse (neutron pulse on), as shown in sub-graph (c) in fig. 6. Between neutron pulses (neutron pulse is off), gamma rays are recorded as the capture energy spectrum, as shown in subplot (d) in fig. 6. The appropriate time window is selected such that most of the gamma rays measured in the capture time window are from thermal neutron capture reactions and most of the gamma rays measured in the inelastic time window are from fast neutron inelastic scattering.

The background at the detector can be measured for a period of time when the neutron generator is off and can be subtracted from the total signal of neutrons or gamma rays. The neutron background noise measured during a neutron pulse can be further subtracted by using a small portion of the neutrons measured between neutron pulses as background to obtain "pure" fast neutrons. Similarly, the gamma rays measured during a neutron pulse may be further subtracted to obtain a "pure" inelastic energy spectrum by using a small portion of the capture energy spectrum measured between neutron pulses as a background.

The captured gamma-ray count rate measured by the dual function detector after background removal can also be used to obtain formation porosity and other formation parameters.

In one exemplary embodiment, a logging tool having one neutron source and three dual detectors (i.e., a near detector, a middle detector, and a far detector) is used to measure formation porosity Φ. Fig. 2A, 2B, 2C, or 2D are examples of such logging tools. Furthermore, the neutron source may be a pulsed neutron source or an isotopic neutron source.

A logging tool is lowered into the wellbore to perform pulsed neutron logging, either in a sonde for wireline logging or as part of LWD instructions in a drill string. Each of the far, intermediate and near detectors detects neutrons and neutron-induced gamma rays. Pulse Shape Discrimination (PSD) techniques are used to separate detector signals from neutrons and gamma rays.

Then, the neutron signals from the three detectors are used to obtain the thermal neutron and epithermal neutron count rates (the total count rate CRN of the near detector _n Total count rate CRN of the middle detector _m Total count rate CRN of long detector _f ) Fast neutron count rate (count rate of near detector CRFN) _n Counting rate CRFN of the middle detector _m Gauge of long distance detectorNumber rate CRFN _f ) Thermal neutron count rate (count rate of near detector CRTN) _n Count rate CRTN of the middle detector _m Count rate CRTN of long detector _f ). During the short neutron pulse, there are fast neutrons, epithermal neutrons and thermal neutrons. Between neutron pulses, most neutrons are epithermal neutrons and thermal neutrons. However, the dual function detector is more sensitive to thermal neutrons and epithermal neutrons, so most neutrons detected by the detector are thermal neutrons and epithermal neutrons. Thus, the formation porosity may be obtained using thermal neutrons, epithermal neutrons, or the count rates of thermal neutrons and epithermal neutrons of the dual-function detector.

Thermal neutrons are neutrons with kinetic energy from about 0.025eV (at room temperature) to 0.4 eV. Epithermal neutrons are neutrons with kinetic energy from 0.4eV to 10 eV. Fast neutrons are neutrons with kinetic energies above 1 MeV.

To measure epithermal neutrons, a thin layer of thermal neutron absorber (e.g., cadmium (Cd) or gadolinium (Gd)) is used to wrap the detector so that thermal neutrons scattered back from the formation are absorbed before entering the detector.

The ratio of the three neutron count rates can be found according to equations 1-3:

Rn _m/f rn is the mid-to-far ratio _n/f Rn is the near-far ratio _n/m Is a near-to-medium ratio. Since the three detectors are arranged at different distances from the neutron source, they have different depths of Detection (DOI). Thus, the near-wellbore environment (e.g., wellbore fluid, cement, etc.) has different effects on these three ratios. Rn _m/f Is more sensitive to the stratum and Rn _n/m Is more sensitive to near-wellbore materials such as wellbore fluids.

By separately dividing three ratios Rn _n/m 、Rn _n/f And Rn _m/f Respectively applied to the ratio-to-porosity transformation (which is a polynomial function of the ratio) shown in equation 4, three neutron porosities Φ each having a different DOI can be obtained _n/m 、Φ _n/f And phi is _m/f . The coefficients a, b, c, d, e of the polynomials vary according to the different formations being explored (e.g. sandstone, limestone or dolomite). These coefficients can be obtained by fitting using data from the porosity of the core sample.

Wherein Rn is three ratios Rn of total neutron count rate _n/m 、Rn _n/f And Rn _m/f One of which.

Neutron porosity phi _n Can also be obtained by the following means: first using Rn _n/m And Rn _n/f To correct Rn _m/f Then let the corrected far-near ratio Rnc _m/f Formation porosity is obtained. Equations 5 to 7 show this algorithm.

Rnc _m/f ＝Rn _m/f +ΔR (5)

Φ _n ＝f ₁ (Rnc _m/f ) (7)

Equation (6) represents the calculation of the correction value Δr using all three total neutron count rate ratios. Adding ΔR to the mid-far ratio Rn _m/f To obtain Rnc _m/f . Finally, use Rnc _m/f To calculate neutron porosity phi _n As shown in equation (7). Alternatively, rn can be targeted _n/m Or Rn _n/f To make corrections and to calculate phi _n . It should be noted that three Φ obtained based on equations 1 to 4 or 5 to 7 _n With different DOIs.

In addition, instead of using three ratios of neutron count rates, formation porosity Φ may be calculated according to the algorithm shown in equations 8 through 11 or equations 12 through 14 by using the captured gamma-ray count rates (Rg _n/m 、Rg _n/f And Rg _m/f ) The ratio between them is performed to obtain gamma-ray porosity phi _g 。

Wherein Rg may be Rg _m/f 、Rg _n/f Or Rg _n/m . The coefficients a, B, C, D, E of the polynomials vary according to the different formations being explored (e.g. sandstone, limestone or dolomite) and can be derived by data fitting using core samples. It should be noted that three neutron porosities are calculated according to equation 4 using three different neutron count rate ratios, while three gamma-ray porosities are calculated according to equation 11 using three different gamma-ray count rate ratios. When using the same ratio of pairs of detectors, e.g. R is used _m/f When calculating, phi _n And phi is _g Can be considered to correspond to each other.

Rgc _m/f ＝Rg _m/f +ΔR (12)

ΔR＝f ₄ (Rg _m/f ，Rg _n/f ，Rg _n/m ) (13)

Φ _g ＝f ₃ (Rgc _m/f ) (14)

Equation (13) represents the calculation of the correction value Δr using all three captured gamma ray count rate ratios. Adding ΔR to the mid-far ratio Rg _m/f To obtain Rgc _m/f . Finally, use Rgc _m/f To calculate the gamma-ray porosity phi _g As shown in equation (14). Alternatively, rg can be targeted _n/m Or Rg _n/f To make corrections and to calculate phi _g . Note that each of the three neutron porosities calculated based on equations 5 through 7 can find one of the three gamma-ray porosities calculated based on equations 12 through 14 corresponding thereto.

Of the three detectors, the near detector has the shallowest DOI, the middle detector has the moderate DOI, and the far detector has the deepest DOI. Therefore, rn is used _n/m The obtained neutron porosity is the shallowest, and Rn is used _n/f And Rn _m/f The neutron porosities obtained have a moderate DOI and the deepest DOI, respectively. Also, rg was used _n/m 、Rg _n/f And Rg _m/f The DOI of the gamma-ray porosities obtained are shallowest, moderate and deepest, respectively. These different porosities, having different DOIs into the formation, may be used to evaluate near-wellbore environments, such as mud penetration in the formation.

The DOI of pulsed neutron tools depends largely on the neutron source to detector distance and formation porosity. The DOI of the near, mid, and far detectors of thermal neutron measurements may be about 8 inches, 10 inches, and 12 inches, respectively, when the formation porosity is about 20p.u. The DOIs from the near, middle and far detectors of the captured gamma ray measurement may be about 10 inches, 12 inches and 15 inches, respectively.

In the porosity measurement, Φ _n And phi is _g Can complement each other. For example, phi _n More accurate at lower formation porosities (e.g., less than 40p.u., 35p.u., or 30 p.u.), while Φ _g More accurate at higher formation porosities (e.g., greater than 40p.u., 45p.u., or 50 p.u.). Furthermore, in high salinity environments or in shale/sandstone, Φ _n Tend to be greater than phi _g It is easier to overestimate the porosity. Thus, phi _n And phi is _g Can achieve improved porosity readings over a wider range of formation porosities (e.g., 0-100 p.u.) under various wellbore and formation conditions.

FIG. 7 shows a workflow for achieving improved formation porosity using a logging tool having a pulsed neutron generator and three detectors. Fig. 8 provides details of steps S706 through S708 in the workflow. As shown in fig. 7, in S701, a fast neutron pulse emitted from a pulsed neutron generator enters a borehole and a formation. In S702, fast neutrons are slowed down as thermal neutrons by inelastic scattering (producing inelastic gamma rays) or elastic scattering with near-wellbore material and the formation. Some thermal neutrons are captured by elements in the wellbore and the formation, thereby producing captured gamma rays. At S703, some neutrons and gamma rays are scattered back to the three detectors and detected. In S704, the signal of each detector is separated according to the neutron-induced signal or the gamma-ray-induced signal. In S705, the count rate of thermal neutrons, epithermal neutrons or both thermal neutrons and epithermal neutrons for each detector, and the count rate of captured gamma rays are obtained.

Fig. 8 shows details of S706, S707, and S708 according to one of the embodiments. In S706, three ratios (Rn, i, i=1, 2, 3) between the count rates of thermal neutrons, epithermal neutrons, or both thermal neutrons and epithermal neutrons are calculated.

In S707, both neutron porosity and gamma-ray porosity are calculated from the count rate ratio. When the formation has a high shale content (clay-containing bound water H ₂ O and other minerals) or high salinity (containing NaCl and KCl), the neutron porosity and gamma-ray porosity are further corrected to obtain corrected neutron porosity (Φ) _n，t ) And corrected gamma-ray porosity (Φ) _g，t )。

FIG. 9 shows an exemplary performance spectrum of captured gamma-ray signals. Captured gamma ray Count Rate (CR) at 2.23MeV hydrogen peak above the dotted line _H ) Due to the binding of water by the clay in the shale layer, the captured gamma-rays under the 1.95MeV, 5.09MeV, 5.61MeV and 6.11MeV chlorine peaks above the dotted lineLine Count Rate (CR) _Cl ) Due to the high salinity, they all increase the gamma-ray count rate. CR (computed radiography) _H And CR (CR) _Cl Are calculated and used as inputs to an algorithm to further correct for chlorine and shale effects for neutron porosity and gamma-ray porosity, see equations 15-20.

ΔΦ _n，H ＝f ₅ (CR _H ，Φ _n ) (15)

ΔΦ _n，Cl ＝f ₆ (CR _Cl ，Φ _n ) (16)

Φ _n，t ＝Φ _n +ΔΦ _n，H +ΔΦ _n，CL (17)

ΔΦ _g，H ＝f ₇ (CR _H ，Φ _g ) (18)

ΔΦ _g，Cl ＝f ₈ (CR _Cl ，Φ _g ) (19)

Φ _g，t ＝Φ _g +ΔΦ _g，H +ΔΦ _g，CL (20)

Equation 15 provides a function that uses CR _H And neutron porosity phi _n As input to calculate a correction value corresponding to the shale effect. Also, equation 16 provides a function that uses CR _Cl And neutron porosity phi _n As input to calculate a correction value corresponding to the chlorine effect. The corrected neutron porosity Φ can be obtained according to equation 17 _n，t 。

Equations 18 and 19 calculate corrections to gamma-ray porosity due to shale effects and chlorine effects, respectively. Then, the corrected gamma-ray porosity Φ is calculated according to equation 20 _g，t 。

Although S707 provides a correction step, the correction step is optional. If the shale effect or chlorine effect is strong, one or both of these may be corrected according to the methods described above. If both shale effects and chlorine effects are weak and the accuracy of the formation porosity is not greatly affected, no correction step is required and bypass is possible.

In S708, for Φ _n，t And phi is _g，t Performing evaluationEstimated and combined to obtain formation porosity. In one embodiment, Φ _n，t And phi is _g，t Compared to one another to select a value that better represents the formation porosity. For example, if Φ _n，t And phi is _g，t The formation porosity is given as Φ if the difference between the values of (2) is less than a predetermined percentage _n，t Is a value of (2); if the difference is greater than a predetermined percentage, the formation porosity is given as Φ _g，t Is a value of (2). The predetermined percentage may be between 2% -10%, such as 2%, 3%, 5%, 7% or 10%. In another embodiment, if the porosity Φ is corrected _n，t And phi is _g，t At or below a predetermined value, the formation porosity is given as corrected porosity Φ _n，t Is a value of (2). If the porosity phi is corrected _n，t And phi is _g，t At or above a predetermined value, the formation porosity is given as phi _g，t Is a value of (2). The predetermined value may be in the range of 30p.u. to 50p.u., for example 30p.u., 35p.u., 40p.u., 45p.u., or 50p.u.

In another embodiment, the formation porosity is a weighted function of the corrected neutron porosity and the corrected gamma-ray porosity, as shown in equation 21.

Φ _t ＝w ₁ Φ _n，t +(1-w ₁ )Φ _g，t (21)

Wherein w is ₁ And (1-w) ₁ ) Is the relative weight of the corrected neutron porosity and the corrected gamma-ray porosity. w (w) ₁ May be obtained by matching the calculated porosity value with the porosity value of the core analysis. Further, all coefficients in the equations of the present disclosure may be obtained by data fitting using empirical data (e.g., data obtained from formation core analysis).

It should be noted that the methods and apparatus of the present disclosure are not limited to the examples shown. The device may have a pulsed neutron generator and more than three dual function detectors capable of detecting both neutrons and gamma rays. The method may provide improved formation porosity throughout the range from 0 to 100p.u. at different DOIs within the formation by correcting and/or combining neutron porosity and gamma-ray porosity. The porosity evaluation may be relatively immune to chlorine effects and shale effects. Further, the method may be used to obtain formation porosity by using thermal neutrons, epithermal neutrons, or both thermal and epithermal neutrons and/or the ratio of captured gamma rays. Furthermore, the method may be used in a wireline logging and logging while drilling environment.

While in the foregoing specification this disclosure has been described in relation to certain preferred embodiments thereof, and many details have been set forth for purposes of illustration, it will be apparent to those skilled in the art that the disclosure is susceptible to modification and certain other details described herein can be varied considerably without departing from the basic principles of the disclosure. Furthermore, it is to be understood that structural features or methods shown or described in any one embodiment herein may be used in other embodiments as well.

Claims

1. A method of evaluating the porosity of a downhole formation, comprising:

emitting neutron pulses by a pulsed neutron tool deployed in a wellbore to irradiate a formation surrounding the wellbore;

detecting neutrons and gamma rays using a plurality of detectors disposed in the pulsed neutron tool, wherein each detector is operable to detect neutrons and gamma rays from the formation; and

a plurality of neutron porosities and a plurality of gamma-ray porosities are estimated based on data from the plurality of detectors.

2. The method of claim 1, wherein neutrons detected by the plurality of detectors are selected from thermal neutrons, epithermal neutrons, or a mixture thereof.

3. The method of claim 1, wherein the gamma rays detected by the plurality of detectors are inelastic gamma rays, capture gamma rays, or a mixture thereof.

4. The method of claim 1, wherein two or more detectors are disposed in the pulsed neutron tool.

5. The method of claim 4, wherein the signal from neutrons and the signal from gamma rays are separated for each detector by applying a pulse shape discrimination technique.

6. The method of claim 1, wherein the estimating step comprises:

obtaining a neutron count rate and a captured gamma ray count rate from each of the plurality of detectors;

calculating a ratio of neutron count rates and a ratio of capture gamma ray count rates between each two of the plurality of detectors to obtain a plurality of neutron count rate ratios and a plurality of capture gamma ray count rate ratios;

the plurality of neutron porosities are estimated using a plurality of neutron count rate ratios and/or the plurality of gamma-ray porosities are estimated using a plurality of gamma-ray count rate ratios.

7. The method of claim 6, wherein each of the plurality of neutron porosities is obtained using an algorithm having as input a respective one of a plurality of neutron count rate ratios.

8. The method of claim 6, wherein each of the plurality of gamma-ray porosities is obtained using an algorithm having as input a respective one of a plurality of gamma-ray count rate ratios.

9. The method of claim 6, wherein each of the plurality of neutron porosities is obtained using a corrected neutron count rate ratio, wherein the corrected neutron count rate ratio is obtained by applying a correction factor to the neutron count rate ratio as a function of the plurality of neutron count rate ratios.

10. The method of claim 6, wherein each of the plurality of gamma-ray porosities is obtained using a corrected gamma-ray count rate ratio, wherein the corrected gamma-ray count rate ratio is obtained by applying a correction factor to the gamma-ray count rate ratio as a function of the plurality of gamma-ray count rate ratios.

11. The method of claim 6, wherein the estimating step comprises:

calculating a first neutron count rate ratio and a first capture gamma-ray count rate ratio between the first detector and the second detector, a second neutron count rate ratio and a second capture gamma-ray count rate ratio between the second detector and the third detector, and a third neutron count rate ratio and a third capture gamma-ray count rate ratio between the first detector and the third detector;

Estimating three neutron porosities with the first neutron count rate ratio, the second neutron count rate ratio, and the third neutron count rate ratio, respectively; and/or

The first, second and third gamma-ray count rate ratios are used to estimate a gamma-ray capture porosity, respectively.

12. The method of claim 1, wherein a first detector, a second detector, and a third detector are provided in a pulsed neutron tool, the method comprising:

obtaining a neutron count rate and a captured gamma ray count rate from each of the first detector, the second detector, and the third detector;

13. The method of claim 1, further comprising correcting the plurality of neutron porosities and the plurality of gamma-ray porosities by subtracting a captured gamma-ray count rate due to hydrogen, chlorine, or both.

14. The method of claim 1, further comprising comparing a value of neutron porosity selected from the plurality of neutron porosities with a value of corresponding gamma-ray porosity selected from the plurality of gamma-ray porosities, wherein the value of neutron porosity is designated as formation porosity when a difference between the two values is less than or equal to a predetermined value and the value of gamma-ray porosity is designated as formation porosity when the difference between the two values is greater than the predetermined value, wherein the predetermined value is in the range of 2% to 10%.

15. The method of claim 1, further comprising comparing a value of neutron porosity selected from a plurality of neutron porosities and a corresponding value of gamma-ray porosity selected from a plurality of gamma-ray porosities to a predetermined value, wherein the value of formation porosity is equal to the value of neutron porosity when the value of neutron porosity is less than or equal to the predetermined value and the value of formation porosity is equal to the value of gamma-ray porosity when the value of gamma-ray porosity is greater than the predetermined value.

16. The method of claim 15, wherein the predetermined value is between 30p.u. and 50 p.u.

17. The method of claim 1, further comprising obtaining formation porosity from a weighted function of one of a plurality of gamma-ray porosities and one of a plurality of neutron porosities.