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|page numbers = 243-287
|page numbers = 243-287
|ISBN = 978-1-55563-120-8
|ISBN = 978-1-55563-120-8
}}<br/>Nuclear logging has been used in some form since the late 1920s to provide information on lithology and rock characteristics. Continued technological advances have provided improved methods for analyzing the measurements of natural and induced nuclear readings. Even with better tool designs, the long-standing problem remains that logging tools do not directly measure the formation properties that engineers, geologists, and petrophysicists need to describe a reservoir. The goal of log analysis is to map out the downhole values of reservoir characteristics chiefly as porosity, fluid saturations, and permeability. Unfortunately, nuclear-logging tools only measure gamma ray or neutron count rates at cleverly positioned detectors. Inference, empiricism, experience, and alibis bridge these count rates to the rocks and fluids in the reservoir. Nuclear-log interpretation rests on smarter processing of these tool readings. Understanding what the tools really measure is the key to better log analysis.<br/><br/>Consider some of the limitations of the current technology. Grouping nuclear logs according to their underlying nuclear physics highlights the blurry relationship between what they measure and what we expect from them. '''Table 3D.1''' summarizes such a classification scheme. Two types of problems skew tool measurements away from their targets. First, because a nuclear tool averages over a shallow bulk volume, the borehole often represents a major part of the tool’s response. Second, even if all borehole effects can be removed, the fact remains that nuclear tools do not respond directly to reservoir properties. Sometimes, the reservoir parameter of interest does not even dominate the underlying physics of the tool. Historically, such problems have been addressed with calibrations at a few points accessible in the laboratory; these are then generalized into correction charts. Two books<ref name="r1">_</ref><ref name="r2">_</ref> serve as excellent general introductions to the convoluted physics of logging tools.<br/><br/><gallery widths="300px" heights="200px">
}}<br/>Nuclear logging has been used in some form since the late 1920s to provide information on lithology and rock characteristics. Continued technological advances have provided improved methods for analyzing the measurements of natural and induced nuclear readings. Even with better tool designs, the long-standing problem remains that logging tools do not directly measure the formation properties that engineers, geologists, and petrophysicists need to describe a reservoir. The goal of log analysis is to map out the downhole values of reservoir characteristics chiefly as porosity, fluid saturations, and permeability. Unfortunately, nuclear-logging tools only measure gamma ray or neutron count rates at cleverly positioned detectors. Inference, empiricism, experience, and alibis bridge these count rates to the rocks and fluids in the reservoir. Nuclear-log interpretation rests on smarter processing of these tool readings. Understanding what the tools really measure is the key to better log analysis.<br/><br/>Consider some of the limitations of the current technology. Grouping nuclear logs according to their underlying nuclear physics highlights the blurry relationship between what they measure and what we expect from them. '''Table 3D.1''' summarizes such a classification scheme. Two types of problems skew tool measurements away from their targets. First, because a nuclear tool averages over a shallow bulk volume, the borehole often represents a major part of the tool’s response. Second, even if all borehole effects can be removed, the fact remains that nuclear tools do not respond directly to reservoir properties. Sometimes, the reservoir parameter of interest does not even dominate the underlying physics of the tool. Historically, such problems have been addressed with calibrations at a few points accessible in the laboratory; these are then generalized into correction charts. Two books<ref name="r1">Hearst, J.R., Nelson, P.H., and Paillet, F.L. 2000. Well Logging for Physical Properties, second edition. New York City: John Wiley & Sons.</ref><ref name="r2">Ellis, D.V. 1987. Well Logging for Earth Scientists. New York City: Elsevier Science Publishing.</ref> serve as excellent general introductions to the convoluted physics of logging tools.<br/><br/><gallery widths="300px" heights="200px">
File:Vol5 Page 0244 Image 0001.png|'''Table 3D.1'''
File:Vol5 Page 0244 Image 0001.png|'''Table 3D.1'''
</gallery>
</gallery>
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=== Single-Log Interpretation-More Details ===
=== Single-Log Interpretation-More Details ===


Even though log analysts’ primary interest is only in virgin formation properties, there are at least three regions that contribute to a nuclear log measurement: the borehole (including borehole size, composition, temperature, and even the tool body), the invaded zone, and the real target, the virgin formation. The tool will respond to a weighted average of all three. For nuclear tools, the weights given to the borehole and invaded zone may be large because they are closer to the sources and detectors.<br/><br/>Log analysts typically divide the problem into three corresponding parts and attempt to handle them sequentially. First, one compensates for borehole effects by applying semiempirical environmental corrections, either from chart books or equivalent computerized correction formulas. Second, one finesses the invaded-zone problem if possible. For liquids, the density and hydrogen index of the mud filtrate may be similar enough to those of the formation fluids that the effect of invasion can be ignored, and average fluid properties can be assigned with little damage to the accuracy of the calculated porosity. If all of the potential fluid properties are not similar enough, analysts frequently assume that a log responds primarily to either the invaded zone or the deeper, uninvaded zone. The gamma-gamma scattering density log’s depth of invasion may be less than 6 in. Because of this very shallow penetration, it is usually safe to assume that the density tool responds only to the invaded zone. The neutron log is often problematic. With shallow invasion, it may primarily see the virgin formation. With deep invasion, even the neutron log may be responding only to the invaded zone. If the formation fluid is gas, the fluid density and hydrogen index differ wildly from those of a typical drilling mud. This is especially the case at shallow depths, where gas density is low. In this case, partial saturation may also feed into the solution of the log’s response. While iterative solutions for light hydrocarbons frequently work well enough, the simultaneous solution of all the log responses (including resistivity logs and saturation equations) gives the best result in these cases. While there are numerous commercial simultaneous-solver computer programs, an interesting treatment, including the effects of invasion, was given by Patchett and Wiley.<ref name="r3">_</ref><br/><br/>To put depths of investigation for nuclear tools in perspective, it is useful to introduce the concept of integrated radial geometric factors, or J -factors.<ref name="r4">_</ref> This is a method of standardizing the data from tools with different depths of investigation. The function is a measure of what fraction of a tool’s response comes from inside a certain radius, ''x'', defined by<br/><br/>[[File:Vol5 page 0250 eq 001.png|RTENOTITLE]]....................(3D.10)<br/><br/>Here, ''U''<sub>''x''</sub> refers to the tool response integrated out to some distance x into the formation, ''U''<sub>''T''</sub> is the tool’s full response out to infinity in the absence of invasion, and ''U''<sub>''i''</sub> is the tool response to a fully invaded formation. Depth of investigation is commonly defined as the radial distance into the borehole wall at which the tool response reaches 90% of the final value.<br/><br/>'''Fig. 3D.3''' compares the radial geometric response functions for the three basic nuclear logs. The radial geometric function is a quick, approximate contrivance for determining whether tool response is predominantly coming from the invaded zone or the virgin formation. The curve labeled "gr-reservoir" corresponds to a bulk density of 2.35 g/cm<sup>3</sup>. For comparison, a deep induction log does not reach its 50% response point until approximately 150 radial in. The base case shown is for a 20% porosity limestone. Obviously, the depth of investigation varies with formation composition, which is, after all, the principle on which density and neutron tools are based. The depth of investigation of a density log ranges from 4.4 in. at 5% porosity to 5.0 in. at 40%. For compensated neutron logs, depth of investigation ranges from 9.5 in. at 40% porosity limestone to 16 in. at 2.5 p.u. (porosity unit or&nbsp;% porosity). Note that increasing porosity increases the depth of investigation of the density log but decreases the depth of investigation of the neutron log. This makes sense in light of the different dominant scattering processes for neutrons (as opposed to gamma rays). A passive gamma ray response function for 100% water is shown for comparison. Even though it is stretched somewhat, as expected, the difference is not nearly as large as between nuclear measurements, and a deep induction log with a 90% response point may be deeper than 20 ft.<br/><br/><gallery widths="300px" heights="200px">
Even though log analysts’ primary interest is only in virgin formation properties, there are at least three regions that contribute to a nuclear log measurement: the borehole (including borehole size, composition, temperature, and even the tool body), the invaded zone, and the real target, the virgin formation. The tool will respond to a weighted average of all three. For nuclear tools, the weights given to the borehole and invaded zone may be large because they are closer to the sources and detectors.<br/><br/>Log analysts typically divide the problem into three corresponding parts and attempt to handle them sequentially. First, one compensates for borehole effects by applying semiempirical environmental corrections, either from chart books or equivalent computerized correction formulas. Second, one finesses the invaded-zone problem if possible. For liquids, the density and hydrogen index of the mud filtrate may be similar enough to those of the formation fluids that the effect of invasion can be ignored, and average fluid properties can be assigned with little damage to the accuracy of the calculated porosity. If all of the potential fluid properties are not similar enough, analysts frequently assume that a log responds primarily to either the invaded zone or the deeper, uninvaded zone. The gamma-gamma scattering density log’s depth of invasion may be less than 6 in. Because of this very shallow penetration, it is usually safe to assume that the density tool responds only to the invaded zone. The neutron log is often problematic. With shallow invasion, it may primarily see the virgin formation. With deep invasion, even the neutron log may be responding only to the invaded zone. If the formation fluid is gas, the fluid density and hydrogen index differ wildly from those of a typical drilling mud. This is especially the case at shallow depths, where gas density is low. In this case, partial saturation may also feed into the solution of the log’s response. While iterative solutions for light hydrocarbons frequently work well enough, the simultaneous solution of all the log responses (including resistivity logs and saturation equations) gives the best result in these cases. While there are numerous commercial simultaneous-solver computer programs, an interesting treatment, including the effects of invasion, was given by Patchett and Wiley.<ref name="r3">Patchett, J.G. and Wiley, R. 1994. Inverse Modeling Using Full Nuclear Response Functions Including Invasion Effects Plus Resistivity. Paper H presented at the 1994 SPWLA Annual Logging Symposium, Tulsa, 19–22 June.</ref><br/><br/>To put depths of investigation for nuclear tools in perspective, it is useful to introduce the concept of integrated radial geometric factors, or J -factors.<ref name="r4">Sherman, H. and Locke, S. 1975. Effect of Porosity on Depth of Investigation of Neutron and Density Sondes. Presented at the Fall Meeting of the Society of Petroleum Engineers of AIME, Dallas, Texas, 28 September-1 October 1975. SPE-5510-MS. http://dx.doi.org/10.2118/5510-MS.</ref> This is a method of standardizing the data from tools with different depths of investigation. The function is a measure of what fraction of a tool’s response comes from inside a certain radius, ''x'', defined by<br/><br/>[[File:Vol5 page 0250 eq 001.png|RTENOTITLE]]....................(3D.10)<br/><br/>Here, ''U''<sub>''x''</sub> refers to the tool response integrated out to some distance x into the formation, ''U''<sub>''T''</sub> is the tool’s full response out to infinity in the absence of invasion, and ''U''<sub>''i''</sub> is the tool response to a fully invaded formation. Depth of investigation is commonly defined as the radial distance into the borehole wall at which the tool response reaches 90% of the final value.<br/><br/>'''Fig. 3D.3''' compares the radial geometric response functions for the three basic nuclear logs. The radial geometric function is a quick, approximate contrivance for determining whether tool response is predominantly coming from the invaded zone or the virgin formation. The curve labeled "gr-reservoir" corresponds to a bulk density of 2.35 g/cm<sup>3</sup>. For comparison, a deep induction log does not reach its 50% response point until approximately 150 radial in. The base case shown is for a 20% porosity limestone. Obviously, the depth of investigation varies with formation composition, which is, after all, the principle on which density and neutron tools are based. The depth of investigation of a density log ranges from 4.4 in. at 5% porosity to 5.0 in. at 40%. For compensated neutron logs, depth of investigation ranges from 9.5 in. at 40% porosity limestone to 16 in. at 2.5 p.u. (porosity unit or&nbsp;% porosity). Note that increasing porosity increases the depth of investigation of the density log but decreases the depth of investigation of the neutron log. This makes sense in light of the different dominant scattering processes for neutrons (as opposed to gamma rays). A passive gamma ray response function for 100% water is shown for comparison. Even though it is stretched somewhat, as expected, the difference is not nearly as large as between nuclear measurements, and a deep induction log with a 90% response point may be deeper than 20 ft.<br/><br/><gallery widths="300px" heights="200px">
File:vol5 Page 0251 Image 0001.png|'''Fig. 3D.3 – Nuclear radial geometric functions: comparison of radial geometric functions for various nuclear logs in a 20-p.u. limestone.'''
File:vol5 Page 0251 Image 0001.png|'''Fig. 3D.3 – Nuclear radial geometric functions: comparison of radial geometric functions for various nuclear logs in a 20-p.u. limestone.'''
</gallery><br/>No matter what the approach, the trick is estimating the invasion diameter so that it can be compared to the tool’s depth of investigation. Invasion is a complicated function of mud weight, mud composition, formation pressure, porosity, and permeability, so a quick and dirty estimate of its extent is rarely possible. If the standard three resistivity logs with three different depths of investigation have been run, a rough estimate of the diameter of invasion can be made from so-called tornado-chart calculations. In addition to refined estimates of the true formation resistivity and the invaded-zone resistivity, a diameter of invasion also will be derived. This is based on the assumption of piston displacement of formation fluids by drilling mud, as suggested schematically in '''Fig. 3D.4'''. This step-function invasion model is far from physically correct, but at least it is a step in the right direction. As a first hurdle, this diameter of invasion can be compared to the appropriate integrated radial geometric function to confirm (or contradict) the validity of assumptions that a log’s response is predominantly from the invaded zone or the unadulterated formation. While modern array resistivity tools can produce much more detailed descriptions of the invaded zone, the response to an equivalent step-invasion profile is much more tractable. If a log’s response includes significant elements of both zones (i.e., the diameter of invasion lies somewhere between the 10 and 90% points on the ''J''-function), then its response can be weighted to the two regions. For step invasion, this is simply<br/><br/>[[File:Vol5 page 0251 eq 001.png|RTENOTITLE]]....................(3D.11)<br/><br/>where ''R'' = the tool reading, ''I'' = the tool’s bulk response in the case of complete invasion, and ''T'' = the likely bulk response to no invasion.<br/><br/><gallery widths="300px" heights="200px">
</gallery><br/>No matter what the approach, the trick is estimating the invasion diameter so that it can be compared to the tool’s depth of investigation. Invasion is a complicated function of mud weight, mud composition, formation pressure, porosity, and permeability, so a quick and dirty estimate of its extent is rarely possible. If the standard three resistivity logs with three different depths of investigation have been run, a rough estimate of the diameter of invasion can be made from so-called tornado-chart calculations. In addition to refined estimates of the true formation resistivity and the invaded-zone resistivity, a diameter of invasion also will be derived. This is based on the assumption of piston displacement of formation fluids by drilling mud, as suggested schematically in '''Fig. 3D.4'''. This step-function invasion model is far from physically correct, but at least it is a step in the right direction. As a first hurdle, this diameter of invasion can be compared to the appropriate integrated radial geometric function to confirm (or contradict) the validity of assumptions that a log’s response is predominantly from the invaded zone or the unadulterated formation. While modern array resistivity tools can produce much more detailed descriptions of the invaded zone, the response to an equivalent step-invasion profile is much more tractable. If a log’s response includes significant elements of both zones (i.e., the diameter of invasion lies somewhere between the 10 and 90% points on the ''J''-function), then its response can be weighted to the two regions. For step invasion, this is simply<br/><br/>[[File:Vol5 page 0251 eq 001.png|RTENOTITLE]]....................(3D.11)<br/><br/>where ''R'' = the tool reading, ''I'' = the tool’s bulk response in the case of complete invasion, and ''T'' = the likely bulk response to no invasion.<br/><br/><gallery widths="300px" heights="200px">
Line 79: Line 79:
</gallery><br/>There are only three radioactive elements that occur naturally: potassium, uranium, and thorium. Thorium and uranium both decay to daughters that are also radioactive, and those daughter elements in turn decay to other radioactive daughters, and so on for several generations. Most of these decays result in gamma rays. The energies of the gamma rays are characteristic of the element decaying. This leads to a characteristic pattern or spectrum of gamma ray energies for thorium and uranium, as shown in '''Fig. 3D.8'''. Potassium, for example, decays directly to a stable daughter, argon, emitting a single gamma ray with energy 1.46 MeV.<br/><br/><gallery widths="300px" heights="200px">
</gallery><br/>There are only three radioactive elements that occur naturally: potassium, uranium, and thorium. Thorium and uranium both decay to daughters that are also radioactive, and those daughter elements in turn decay to other radioactive daughters, and so on for several generations. Most of these decays result in gamma rays. The energies of the gamma rays are characteristic of the element decaying. This leads to a characteristic pattern or spectrum of gamma ray energies for thorium and uranium, as shown in '''Fig. 3D.8'''. Potassium, for example, decays directly to a stable daughter, argon, emitting a single gamma ray with energy 1.46 MeV.<br/><br/><gallery widths="300px" heights="200px">
File:vol5 Page 0257 Image 0001.png|'''Fig. 3D.8 – The spectra of gamma rays emitted by the three naturally occurring radioactive measurements (MeV) and, in the case of uranium and thorium, their daughters.'''
File:vol5 Page 0257 Image 0001.png|'''Fig. 3D.8 – The spectra of gamma rays emitted by the three naturally occurring radioactive measurements (MeV) and, in the case of uranium and thorium, their daughters.'''
</gallery><br/>Before getting into how to use the log readings, let us consider the workings of the tool. Unlike all other nuclear tools (and, in fact, all other logging measurements), it is completely passive. It emits no radiation. Instead, it simply detects incoming gamma rays from the formation and (unfortunately) the borehole. Gamma rays are electromagnetic radiation, generally in the energy range 0.1 to 100 MeV. As light, this would correspond to very short wavelengths indeed. The difference between gamma rays and X-rays is largely semantic because they overlap in energy.<br/><br/>Originally, the detector was a Geiger-Müeller tube, just as in the Geiger counter. More recently, the detectors have been switched to solid-state scintillation crystals such as NaI. When a gamma ray strikes such a crystal, it may be absorbed. If it is, the crystal produces a flash of light. This light is "seen" by a photomultiplier staring into the end of the crystal. The photomultiplier shapes the light into an electrical pulse that is counted by the tool. Hence, like all nuclear tools, the raw measured quantity in a gamma ray log is counts. As discussed above, this means that the precision of gamma ray log measurements is determined by Poisson statistics. The precision is the square root of the total number of counts recorded at a given depth. Counts recorded are basically proportional to the volume of the detector crystal times its density (which determine the probability that a gamma ray will be captured within the crystal) times the length of time counted. As with all nuclear-logging measurements, the only part of this that the logger controls is the counting time. Because log measurements are depth driven, the length of time the logger counts is inversely proportional to the logging speed.<br/><br/>Historically, gamma ray sondes have recorded the total flux of gamma radiation integrated over all energies emanating from a formation as a single count rate, the gamma ray curve. Logging tools are not uniform in their energy sensitivity. No detector responds to all the gamma rays that impinge on it. Many pass through with no effect. The sizes of a detector, the solid angle it subtends, and its thickness, as well as its composition (particularly its density), all affect its efficiency for detecting gamma rays. The tool housing around the detector, the casing, and even the density of the borehole fluid can all filter the gamma rays coming from the formation. All these factors not only lower the overall tool efficiency, they also lead to variations in efficiency for gamma rays of different energies. In short, the count rate recorded in a particular radioactive shale bed is not a unique property of the shale. It is a complex function of tool design and borehole conditions as well as the actual formation’s radioactivity. Even though gamma ray readings are generally used only in a relative sense, with reservoir (clean) and shale values determined in situ, there are advantages to a common scale. In the U.S. and most places outside the former Soviet Union, gamma ray logs are scaled in American Petroleum Inst. (API) units. This harkens back to a desire to compare logs from tools of different designs. Tools with different detector sizes and compositions will not have the same efficiency and thus will not give the same count rate even in the same hole over the same interval. To provide a common scale, API built a calibration facility at the U. of Houston. It consists of a concrete-filled pit, 4 ft in diameter, with three 8-ft beds penetrated by a 5 1/2-in. hole cased with 17-lbm casing. The top and bottom beds are composed of extremely-low-radioactivity concrete. The middle bed was made approximately twice as radioactive as a typical midcontinent U.S. shale, resulting in the zone containing 13 ppm uranium, 24 ppm thorium, and 4% potassium. The gamma ray API unit is defined as 1/200 of the difference between the count rate recorded by a logging tool in the middle of the radioactive bed and that recorded in the middle of the nonradioactive bed.<br/><br/>While it has served fairly well for more than 40 years, this is a poor way to define a fundamental unit. Different combinations of isotopes, tool designs, and hole conditions may give the same count rate, so the calibration does not transfer very far from the calibration-pit conditions. In contrast, Russian gamma ray logs are typically scaled in microroentgens (μR)/hr, which does correspond to a specific amount of radiation. Converting this to API units is a bit vaguely defined, but it is often suggested that the conversion factor is 1 μR/hr = 10 API units for Geiger tube detectors, but 15 μR/hr = 10 API for scintillation detectors. This falls in with the previous discussion of the many factors that can affect gamma ray readings. As will be seen later, the problem is further aggravated in logging-while-drilling (LWD) measurements. The API unit provides a degree of standardization, but despite the best efforts of tool designers, one cannot expect tools of different designs to read exactly the same under all conditions. Fortunately, none of this is very important because gamma ray measurements are generally used only in a relative way.<br/><br/>Because we use gamma ray logs as relative measures, precise calibration is not very important except as a visual log display feature. Environmental effects are much more important. Consider a radioactive volume of rock traversed by a borehole. Referring back to the bit of nuclear physics above, gamma rays are absorbed as they pass through the formation. For typical formations, this limits the depth of investigation to approximately 18 in. Considering only the geometry, the count rate opposite a given rock type will be much lower in a larger borehole in which the detector is effectively farther from the source of gamma rays. In an open hole, borehole size almost always has the greatest effect on the count-rate calibration. This problem can go well beyond changes in bit size. Especially if shales or sands are selectively washed out, borehole size can imprint itself of the expected gamma ray contrast between shales and sands. If the borehole is large enough, the density of the fluid filling the borehole can also impact the calibration by absorbing some of the gamma rays before they get to the tool.<br/><br/>Barite in the mud is another complication, filtering the incoming gamma rays. Thus, the gamma ray borehole size and fluid corrections are often very important and should be made if at all possible. Obviously, casing absorbs a large fraction of the gamma rays traversing it on their way to the borehole, so if the tool is run in a cased hole, casing corrections are very important. Tool design has a large impact on environmental corrections. The housing and location of the detectors all filter the incoming gamma rays. It is important to use the right environmental corrections for the tool being run. This is especially true for LWD tools that may consist of multiple detectors embedded in large, heavy drill collars that filter the incoming gamma rays in unique ways.<br/><br/>Now that we know how the tools work, we are ready to discuss how gamma ray logs are used in log analysis. While the gamma ray log traditionally has been used primarily for well-to-well correlation, it also plays a role in quantitative log analysis. As mentioned at the outset, gamma ray logs are used primarily to define and quantify productive intervals. As discussed above, there are only three naturally occurring radioactive elements—potassium, uranium, and thorium (or K, U, and Th by their elemental symbols)—and all of these tend to be associated with shales, not clean matrix minerals (e.g., quartz sand, SiO<sub>2</sub>, limestone CaCO<sub>3</sub>).<br/><br/>The most common interpretation method is the simple bulk linear mixing law presented previously.<br/><br/>[[File:Vol5 page 0259 eq 001.png|RTENOTITLE]]....................(3D.19)<br/><br/>Even though we know that the distribution of clays in shales and reservoir rocks is quite complex, to first order, log analysts frequently simplify the linear bulk mixing law to the determination of shale volume:<br/><br/>[[File:Vol5 page 0259 eq 002.png|RTENOTITLE]]....................(3D.20)<br/><br/>Standard log analysis separates the log-analysis problem into a series of sequential, independent steps. Because shale-volume determination is usually the first step in the sequential process of formation evaluation from logs, porosity and fluid volumes are not yet known. As a result, the equation is further simplified to<br/><br/>[[File:Vol5 page 0259 eq 003.png|RTENOTITLE]]....................(3D.21)<br/><br/>Adding closure,<br/><br/>[[File:Vol5 page 0259 eq 004.png|RTENOTITLE]]....................(3D.22)<br/><br/>leads to the familiar formula for calculating shale volume from a borehole-corrected gamma ray log:<br/><br/>[[File:Vol5 page 0259 eq 005.png|RTENOTITLE]]....................(3D.23)<br/><br/>where the "clean" terms represent the lumped response to the matrix grains and the fluids in the porosity. Further complications arise because the shale values are taken from overlying shale beds. The clays distributed in the reservoir rock are almost certainly not simply dispersed versions of the shales, unless they occur as thin laminations. At the very least, there will be differences between shale, made up of clay minerals, clay bound water, and silt-size particles, and the clay minerals alone distributed in the matrix. Worse, because of differences in the processes at work when the shales were laid down vs. the shaly sands, the clay minerals in the sands may not be the same as those in the matrix. To compensate for this, numerous nonlinear relationships have been proposed. These have geologically significant-sounding names like Larinov older rocks but are simply empirical and have no physical basis.<ref name="r5">_</ref> They are used to improve the correlation between gamma ray-derived shale volumes and other estimates of the shale volume, especially from core. The equations all start with the linear gamma ray index discussed above and reduce the intermediate values from there. '''Fig. 3D.9''' lists a few of the more common equations. '''Fig. 3D.10''' illustrates the degree of shale reduction that the various models afford. If one of these models must be used, select the one that best fits other available estimates of clay volume.<br/><br/><gallery widths="300px" heights="200px">
</gallery><br/>Before getting into how to use the log readings, let us consider the workings of the tool. Unlike all other nuclear tools (and, in fact, all other logging measurements), it is completely passive. It emits no radiation. Instead, it simply detects incoming gamma rays from the formation and (unfortunately) the borehole. Gamma rays are electromagnetic radiation, generally in the energy range 0.1 to 100 MeV. As light, this would correspond to very short wavelengths indeed. The difference between gamma rays and X-rays is largely semantic because they overlap in energy.<br/><br/>Originally, the detector was a Geiger-Müeller tube, just as in the Geiger counter. More recently, the detectors have been switched to solid-state scintillation crystals such as NaI. When a gamma ray strikes such a crystal, it may be absorbed. If it is, the crystal produces a flash of light. This light is "seen" by a photomultiplier staring into the end of the crystal. The photomultiplier shapes the light into an electrical pulse that is counted by the tool. Hence, like all nuclear tools, the raw measured quantity in a gamma ray log is counts. As discussed above, this means that the precision of gamma ray log measurements is determined by Poisson statistics. The precision is the square root of the total number of counts recorded at a given depth. Counts recorded are basically proportional to the volume of the detector crystal times its density (which determine the probability that a gamma ray will be captured within the crystal) times the length of time counted. As with all nuclear-logging measurements, the only part of this that the logger controls is the counting time. Because log measurements are depth driven, the length of time the logger counts is inversely proportional to the logging speed.<br/><br/>Historically, gamma ray sondes have recorded the total flux of gamma radiation integrated over all energies emanating from a formation as a single count rate, the gamma ray curve. Logging tools are not uniform in their energy sensitivity. No detector responds to all the gamma rays that impinge on it. Many pass through with no effect. The sizes of a detector, the solid angle it subtends, and its thickness, as well as its composition (particularly its density), all affect its efficiency for detecting gamma rays. The tool housing around the detector, the casing, and even the density of the borehole fluid can all filter the gamma rays coming from the formation. All these factors not only lower the overall tool efficiency, they also lead to variations in efficiency for gamma rays of different energies. In short, the count rate recorded in a particular radioactive shale bed is not a unique property of the shale. It is a complex function of tool design and borehole conditions as well as the actual formation’s radioactivity. Even though gamma ray readings are generally used only in a relative sense, with reservoir (clean) and shale values determined in situ, there are advantages to a common scale. In the U.S. and most places outside the former Soviet Union, gamma ray logs are scaled in American Petroleum Inst. (API) units. This harkens back to a desire to compare logs from tools of different designs. Tools with different detector sizes and compositions will not have the same efficiency and thus will not give the same count rate even in the same hole over the same interval. To provide a common scale, API built a calibration facility at the U. of Houston. It consists of a concrete-filled pit, 4 ft in diameter, with three 8-ft beds penetrated by a 5 1/2-in. hole cased with 17-lbm casing. The top and bottom beds are composed of extremely-low-radioactivity concrete. The middle bed was made approximately twice as radioactive as a typical midcontinent U.S. shale, resulting in the zone containing 13 ppm uranium, 24 ppm thorium, and 4% potassium. The gamma ray API unit is defined as 1/200 of the difference between the count rate recorded by a logging tool in the middle of the radioactive bed and that recorded in the middle of the nonradioactive bed.<br/><br/>While it has served fairly well for more than 40 years, this is a poor way to define a fundamental unit. Different combinations of isotopes, tool designs, and hole conditions may give the same count rate, so the calibration does not transfer very far from the calibration-pit conditions. In contrast, Russian gamma ray logs are typically scaled in microroentgens (μR)/hr, which does correspond to a specific amount of radiation. Converting this to API units is a bit vaguely defined, but it is often suggested that the conversion factor is 1 μR/hr = 10 API units for Geiger tube detectors, but 15 μR/hr = 10 API for scintillation detectors. This falls in with the previous discussion of the many factors that can affect gamma ray readings. As will be seen later, the problem is further aggravated in logging-while-drilling (LWD) measurements. The API unit provides a degree of standardization, but despite the best efforts of tool designers, one cannot expect tools of different designs to read exactly the same under all conditions. Fortunately, none of this is very important because gamma ray measurements are generally used only in a relative way.<br/><br/>Because we use gamma ray logs as relative measures, precise calibration is not very important except as a visual log display feature. Environmental effects are much more important. Consider a radioactive volume of rock traversed by a borehole. Referring back to the bit of nuclear physics above, gamma rays are absorbed as they pass through the formation. For typical formations, this limits the depth of investigation to approximately 18 in. Considering only the geometry, the count rate opposite a given rock type will be much lower in a larger borehole in which the detector is effectively farther from the source of gamma rays. In an open hole, borehole size almost always has the greatest effect on the count-rate calibration. This problem can go well beyond changes in bit size. Especially if shales or sands are selectively washed out, borehole size can imprint itself of the expected gamma ray contrast between shales and sands. If the borehole is large enough, the density of the fluid filling the borehole can also impact the calibration by absorbing some of the gamma rays before they get to the tool.<br/><br/>Barite in the mud is another complication, filtering the incoming gamma rays. Thus, the gamma ray borehole size and fluid corrections are often very important and should be made if at all possible. Obviously, casing absorbs a large fraction of the gamma rays traversing it on their way to the borehole, so if the tool is run in a cased hole, casing corrections are very important. Tool design has a large impact on environmental corrections. The housing and location of the detectors all filter the incoming gamma rays. It is important to use the right environmental corrections for the tool being run. This is especially true for LWD tools that may consist of multiple detectors embedded in large, heavy drill collars that filter the incoming gamma rays in unique ways.<br/><br/>Now that we know how the tools work, we are ready to discuss how gamma ray logs are used in log analysis. While the gamma ray log traditionally has been used primarily for well-to-well correlation, it also plays a role in quantitative log analysis. As mentioned at the outset, gamma ray logs are used primarily to define and quantify productive intervals. As discussed above, there are only three naturally occurring radioactive elements—potassium, uranium, and thorium (or K, U, and Th by their elemental symbols)—and all of these tend to be associated with shales, not clean matrix minerals (e.g., quartz sand, SiO<sub>2</sub>, limestone CaCO<sub>3</sub>).<br/><br/>The most common interpretation method is the simple bulk linear mixing law presented previously.<br/><br/>[[File:Vol5 page 0259 eq 001.png|RTENOTITLE]]....................(3D.19)<br/><br/>Even though we know that the distribution of clays in shales and reservoir rocks is quite complex, to first order, log analysts frequently simplify the linear bulk mixing law to the determination of shale volume:<br/><br/>[[File:Vol5 page 0259 eq 002.png|RTENOTITLE]]....................(3D.20)<br/><br/>Standard log analysis separates the log-analysis problem into a series of sequential, independent steps. Because shale-volume determination is usually the first step in the sequential process of formation evaluation from logs, porosity and fluid volumes are not yet known. As a result, the equation is further simplified to<br/><br/>[[File:Vol5 page 0259 eq 003.png|RTENOTITLE]]....................(3D.21)<br/><br/>Adding closure,<br/><br/>[[File:Vol5 page 0259 eq 004.png|RTENOTITLE]]....................(3D.22)<br/><br/>leads to the familiar formula for calculating shale volume from a borehole-corrected gamma ray log:<br/><br/>[[File:Vol5 page 0259 eq 005.png|RTENOTITLE]]....................(3D.23)<br/><br/>where the "clean" terms represent the lumped response to the matrix grains and the fluids in the porosity. Further complications arise because the shale values are taken from overlying shale beds. The clays distributed in the reservoir rock are almost certainly not simply dispersed versions of the shales, unless they occur as thin laminations. At the very least, there will be differences between shale, made up of clay minerals, clay bound water, and silt-size particles, and the clay minerals alone distributed in the matrix. Worse, because of differences in the processes at work when the shales were laid down vs. the shaly sands, the clay minerals in the sands may not be the same as those in the matrix. To compensate for this, numerous nonlinear relationships have been proposed. These have geologically significant-sounding names like Larinov older rocks but are simply empirical and have no physical basis.<ref name="r5">Katahara, K. 1995. Gamma Ray Log Response in Shaly Sands. The Log Analyst 36 (4): 50. http://www.onepetro.org/mslib/app/Preview.do?paperNumber=SPWLA-1995-v36n4a4&societyCode=SPWLA.</ref> They are used to improve the correlation between gamma ray-derived shale volumes and other estimates of the shale volume, especially from core. The equations all start with the linear gamma ray index discussed above and reduce the intermediate values from there. '''Fig. 3D.9''' lists a few of the more common equations. '''Fig. 3D.10''' illustrates the degree of shale reduction that the various models afford. If one of these models must be used, select the one that best fits other available estimates of clay volume.<br/><br/><gallery widths="300px" heights="200px">
File:vol5 Page 0260 Image 0001.png|'''Fig. 3D.9 – A summary of various nonlinear shale-volume models used to reduce the amount of shale below the linear, bulk mixing-law prediction.'''
File:vol5 Page 0260 Image 0001.png|'''Fig. 3D.9 – A summary of various nonlinear shale-volume models used to reduce the amount of shale below the linear, bulk mixing-law prediction.'''


Line 103: Line 103:
=== Other Applications ===
=== Other Applications ===


Gamma ray logs have a number of other niche applications. For example, injected fluids can be tagged with radioactive tracers and their progress through a field monitored with gamma ray logs in wells adjacent to the injection site.<br/><br/>Spectral natural gamma ray systems designed for K-U-Th logging have been applied to evaluate stimulations and completions.<ref name="r6">_</ref> One or more radioactive isotopes tag the various materials sent downhole. From a spectral log that separates the different isotopes, engineers establish the vertical zones of each of the different phases of the treatment. By examining peak-to-Compton-background ratios from the spectra, it is also possible to discriminate material inside the borehole from that outside the borehole. The same data yield a feeling for how far into the formation (remembering that gamma rays penetrate reservoir rocks only approximately 6 in.) the materials extend. By applying directional gamma ray detection schemes, it is also possible to infer fracture direction.
Gamma ray logs have a number of other niche applications. For example, injected fluids can be tagged with radioactive tracers and their progress through a field monitored with gamma ray logs in wells adjacent to the injection site.<br/><br/>Spectral natural gamma ray systems designed for K-U-Th logging have been applied to evaluate stimulations and completions.<ref name="r6">Gadeken, L.L. et al. 1991. The Interpretation of Radioactive Tracer Logs Using Gamma Ray Spectroscopy Measurements. The Log Analyst 32 (1): 24. http://www.onepetro.org/mslib/app/Preview.do?paperNumber=SPWLA-1991-v32n1a3&societyCode=SPWLA.</ref> One or more radioactive isotopes tag the various materials sent downhole. From a spectral log that separates the different isotopes, engineers establish the vertical zones of each of the different phases of the treatment. By examining peak-to-Compton-background ratios from the spectra, it is also possible to discriminate material inside the borehole from that outside the borehole. The same data yield a feeling for how far into the formation (remembering that gamma rays penetrate reservoir rocks only approximately 6 in.) the materials extend. By applying directional gamma ray detection schemes, it is also possible to infer fracture direction.


=== Gamma-Gamma Scattering Density Tools ===
=== Gamma-Gamma Scattering Density Tools ===
Line 157: Line 157:
'''''Fluid Effects.''''' The hydrogen index of the pore fluid (see '''Table 3D.4''') and its equivalent apparent neutron porosity ('''Table 3D.7''') can have a much bigger effect. The difference between pure water, most brines, and typical oils is small, but as the table shows, gas can have much different neutron-response properties. While the presence of gas increases the apparent porosity seen by a density log, it decreases the apparent porosity seen by the neutron log. This is the source of "gas crossover" on neutron density-log displays (see '''Fig. 3D.16'''). Moreover, the shallow-reading density log frequently is an invaded-zone measurement, completely masking the gas effect on it. Because the neutron porosity is deeper reading, it is often the only log that can be used for gas detection. Even when not completely reading the invaded zone, the neutron-porosity log probably reads a mixture of invaded and virgin formation. This leads to a very complex response equation, even in a clean reservoir:<br/><br/>[[File:Vol5 page 0273 eq 001.png|RTENOTITLE]]....................(3D.37)<br/><br/>where ''f''(''r''<sub>''i''</sub>) is the radial geometric function discussed above, ''r''<sub>''i''</sub> is the step-invasion profile approximation for the radius of invasion, ''mf'' refers to mud filtrate, ''hc'' refers to hydrocarbon, and ''w'' refers to formation water. Of course, shaly or multimineral interpretations add additional terms.<br/><br/><gallery widths="300px" heights="200px">
'''''Fluid Effects.''''' The hydrogen index of the pore fluid (see '''Table 3D.4''') and its equivalent apparent neutron porosity ('''Table 3D.7''') can have a much bigger effect. The difference between pure water, most brines, and typical oils is small, but as the table shows, gas can have much different neutron-response properties. While the presence of gas increases the apparent porosity seen by a density log, it decreases the apparent porosity seen by the neutron log. This is the source of "gas crossover" on neutron density-log displays (see '''Fig. 3D.16'''). Moreover, the shallow-reading density log frequently is an invaded-zone measurement, completely masking the gas effect on it. Because the neutron porosity is deeper reading, it is often the only log that can be used for gas detection. Even when not completely reading the invaded zone, the neutron-porosity log probably reads a mixture of invaded and virgin formation. This leads to a very complex response equation, even in a clean reservoir:<br/><br/>[[File:Vol5 page 0273 eq 001.png|RTENOTITLE]]....................(3D.37)<br/><br/>where ''f''(''r''<sub>''i''</sub>) is the radial geometric function discussed above, ''r''<sub>''i''</sub> is the step-invasion profile approximation for the radius of invasion, ''mf'' refers to mud filtrate, ''hc'' refers to hydrocarbon, and ''w'' refers to formation water. Of course, shaly or multimineral interpretations add additional terms.<br/><br/><gallery widths="300px" heights="200px">
File:vol5 Page 0274 Image 0001.png|'''Fig. 3D.16 – Schematic nuclear-log responses for some common lithologies.'''
File:vol5 Page 0274 Image 0001.png|'''Fig. 3D.16 – Schematic nuclear-log responses for some common lithologies.'''
</gallery><br/>Furthermore, the response equation becomes decidedly nonlinear when gas is introduced. To compensate for this, an additional term was introduced to the response equation. This artifact of the gas is labeled the excavation effect.<br/><br/>'''''Advanced Processing.''''' The effect of formation absorption has long been recognized. Chart-book corrections for environmental effects on the thermal neutron log are extensive but confusing. This situation reflects more on the futility of attempts to handle every downhole situation with a handful of correction charts rather than any real error by service companies or log analysts. Clearly, a new approach is needed.<br/><br/>New log-processing methods that extend laboratory benchmark data with a more detailed mathematical description of the tool’s response have been developed. Such methods replace one-size-fits-all correction charts. Effectively, log analysts using such techniques generate custom correction charts that exactly match their downhole situations. In lithologies that depart significantly from the standard limestone/sandstone/dolomite triplet, most particularly those with high capture cross-sectional minerals or fluids, the results can be dramatically different from chart-book values. With such model-based processing, corrections need not be made serially, nor are they limited to a few cases. Using laboratory benchmarked forward modeling, analysts can generate a broader range of corrections for complex lithologies and fluids. These procedures permit access to temperature and pressure regimes unattainable in laboratory formation models. This is especially important for neutron-porosity tools, whose response to porosity is both complex and tenuous ('''Fig. 3D.12''').<br/><br/>Unfortunately, this approach requires iterative, forward modeling. Logging-tool response is rarely unique; many different lithology/fluid/borehole combinations can produce the same log reading. The availability of other well information and the judgment of the analyst becomes important. Such other reservoir knowledge limits the inputs to the forward model and reduces the number of trial-and-error cycles required to interpret logs with this method.<br/><br/>For neutron tools, there is a need to rethink what the tools measure and how we parameterize the measurement. The tools measure the size of a neutron cloud, expressed as a function of a neutron macroparameter, migration length. In the past, several analysts have formulated the use of forward tool-response modeling to improve neutron-log interpretation in greater detail and include field examples. They range from mixing-law treatments<ref name="r7">_</ref> to more elaborate use of neutron transport properties.<ref name="r8">_</ref><br/><br/>There are two broad approaches to forward modeling of nuclear-tool response: macroparameters such as neutron migration length and Monte Carlo modeling. Macroparameters characterize tool response to bulk average formation composition ('''Fig. 3D.5'''), while Monte Carlo models treat geometry as well as composition ('''Fig. 3D.4''').<br/><br/>'''''Macroparameters.''''' For porosity tools, macroparameters include such things as slowing-down length (when only epithermal neutrons are considered) and migration length (when thermal neutrons are considered as well). They are averaged over composition, geometry, and energy. This approach uses simplified but physically realistic theory to calculate bulk tool response. It is important to recognize that porosity tools measure neutron migration length, not porosity. A macroparameter model calculates migration length from average porosity, matrix, and fluid types. Macroparameter methods are fast, particularly compared to Monte Carlo methods, and are tractable as part of the routine interpretation process.<ref name="r9">_</ref> Schlumberger published the SNUPAR program,<ref name="r10">_</ref> which generates macroparameters for a variety of neutron and gamma ray transport tools. Once the macroparameters are understood, it is necessary to map them into the count-rate-ratio response of a particular tool design to complete the analysis. This mapping can be accomplished by regression analysis of laboratory data taken with the particular tool.<ref name="r9">_</ref><br/><br/>'''''Monte Carlo Modeling.''''' When the detailed effects of geometry cannot be ignored, service companies (and, occasionally, even log analysts) resort to Monte Carlo modeling. It can account for borehole effects, standoff, invasion, thin beds, and tool design. All effects are calculated simultaneously as they occur physically and account for interactions and interdependencies that are ignored in the serial chart-book approach. The problem is not artificially divided into independent, noninteracting regimes, and no effects need be ignored.<br/><br/>In its most straightforward form, analog Monte Carlo modeling simulates millions of particle trajectories, tracing the progress of every particle emitted by the source. It begins with their emission at the source and follows their movement in straight-line segments. Probability distributions for interactions are accessed with random numbers generated by the computer (hence the name Monte Carlo, like a roll of the dice). These simulate particle collisions (i.e., mean distance between collisions, what the particle collides with, and its direction and speed after the collision). It is a brute-force, but fairly intuitive, approach. The models are limited primarily by the quality of the input data, particularly the nuclear cross sections of the materials involved. For real-world tools, the considerable amount of information about tool design that must be included in the model may also limit the accuracy of the Monte Carlo method.<br/><br/>The problem with analog Monte Carlo is that very few of the particles traced end up at the detector. Therefore, enormous numbers of particle histories must be followed to score enough counts at the detector to be statistically significant; even on fast computers, days of computations may be required. The answer is a mixed bag of tricks for ignoring some particles, steering others toward the detectors, and counting still others more than once. This approach can be mathematically valid but is quite tricky, especially with general-purpose codes like Los Alamos’ Monte Carlo Nuclear parameters (MCNP).<br/><br/>The biggest problem is that the models run very slowly, far too slowly to be used as the foot-by-foot forward model in an iterative interpretation process. Geometric effects are still separated from the interpretation process into the environmental-correction process. Monte Carlo modeling is generally confined to creating special-purpose correction charts. Indeed, most current service-company correction charts are generated by Monte Carlo modeling benchmarked to a few lab measurements.
</gallery><br/>Furthermore, the response equation becomes decidedly nonlinear when gas is introduced. To compensate for this, an additional term was introduced to the response equation. This artifact of the gas is labeled the excavation effect.<br/><br/>'''''Advanced Processing.''''' The effect of formation absorption has long been recognized. Chart-book corrections for environmental effects on the thermal neutron log are extensive but confusing. This situation reflects more on the futility of attempts to handle every downhole situation with a handful of correction charts rather than any real error by service companies or log analysts. Clearly, a new approach is needed.<br/><br/>New log-processing methods that extend laboratory benchmark data with a more detailed mathematical description of the tool’s response have been developed. Such methods replace one-size-fits-all correction charts. Effectively, log analysts using such techniques generate custom correction charts that exactly match their downhole situations. In lithologies that depart significantly from the standard limestone/sandstone/dolomite triplet, most particularly those with high capture cross-sectional minerals or fluids, the results can be dramatically different from chart-book values. With such model-based processing, corrections need not be made serially, nor are they limited to a few cases. Using laboratory benchmarked forward modeling, analysts can generate a broader range of corrections for complex lithologies and fluids. These procedures permit access to temperature and pressure regimes unattainable in laboratory formation models. This is especially important for neutron-porosity tools, whose response to porosity is both complex and tenuous ('''Fig. 3D.12''').<br/><br/>Unfortunately, this approach requires iterative, forward modeling. Logging-tool response is rarely unique; many different lithology/fluid/borehole combinations can produce the same log reading. The availability of other well information and the judgment of the analyst becomes important. Such other reservoir knowledge limits the inputs to the forward model and reduces the number of trial-and-error cycles required to interpret logs with this method.<br/><br/>For neutron tools, there is a need to rethink what the tools measure and how we parameterize the measurement. The tools measure the size of a neutron cloud, expressed as a function of a neutron macroparameter, migration length. In the past, several analysts have formulated the use of forward tool-response modeling to improve neutron-log interpretation in greater detail and include field examples. They range from mixing-law treatments<ref name="r7">Dahlberg, K.E. 1989. A Practical Model for Analysis of Compensated Neutron Logs in Complex Formations. Paper PP presented at the 1989 SPWLA Annual Logging Symposium, Denver, June 1989.</ref> to more elaborate use of neutron transport properties.<ref name="r8">Wiley, R. and Pachett, J.G. 1990. CNL (Compensated Neutron Log) Neutron Porosity Modeling, A Step Forward. The Log Analyst 31 (3): 133. http://www.onepetro.org/mslib/app/Preview.do?paperNumber=SPWLA-1990-v31n3a1&societyCode=SPWLA.</ref><br/><br/>There are two broad approaches to forward modeling of nuclear-tool response: macroparameters such as neutron migration length and Monte Carlo modeling. Macroparameters characterize tool response to bulk average formation composition ('''Fig. 3D.5'''), while Monte Carlo models treat geometry as well as composition ('''Fig. 3D.4''').<br/><br/>'''''Macroparameters.''''' For porosity tools, macroparameters include such things as slowing-down length (when only epithermal neutrons are considered) and migration length (when thermal neutrons are considered as well). They are averaged over composition, geometry, and energy. This approach uses simplified but physically realistic theory to calculate bulk tool response. It is important to recognize that porosity tools measure neutron migration length, not porosity. A macroparameter model calculates migration length from average porosity, matrix, and fluid types. Macroparameter methods are fast, particularly compared to Monte Carlo methods, and are tractable as part of the routine interpretation process.<ref name="r9">Tittle, C.W. 1988. Prediction of Compensated Neutron Response Using Neutron Macroparameters. Nuclear Geophysics 2 (2): 95.</ref> Schlumberger published the SNUPAR program,<ref name="r10">McKeon, D.C. and Scott, H.D. 1988. SNUPAR (Schlumberger nuclear parameters)—A nuclear parameter code for nuclear geophysics applications. Nuclear Geophysics 2 (4): 215.</ref> which generates macroparameters for a variety of neutron and gamma ray transport tools. Once the macroparameters are understood, it is necessary to map them into the count-rate-ratio response of a particular tool design to complete the analysis. This mapping can be accomplished by regression analysis of laboratory data taken with the particular tool.<ref name="r9">Tittle, C.W. 1988. Prediction of Compensated Neutron Response Using Neutron Macroparameters. Nuclear Geophysics 2 (2): 95.</ref><br/><br/>'''''Monte Carlo Modeling.''''' When the detailed effects of geometry cannot be ignored, service companies (and, occasionally, even log analysts) resort to Monte Carlo modeling. It can account for borehole effects, standoff, invasion, thin beds, and tool design. All effects are calculated simultaneously as they occur physically and account for interactions and interdependencies that are ignored in the serial chart-book approach. The problem is not artificially divided into independent, noninteracting regimes, and no effects need be ignored.<br/><br/>In its most straightforward form, analog Monte Carlo modeling simulates millions of particle trajectories, tracing the progress of every particle emitted by the source. It begins with their emission at the source and follows their movement in straight-line segments. Probability distributions for interactions are accessed with random numbers generated by the computer (hence the name Monte Carlo, like a roll of the dice). These simulate particle collisions (i.e., mean distance between collisions, what the particle collides with, and its direction and speed after the collision). It is a brute-force, but fairly intuitive, approach. The models are limited primarily by the quality of the input data, particularly the nuclear cross sections of the materials involved. For real-world tools, the considerable amount of information about tool design that must be included in the model may also limit the accuracy of the Monte Carlo method.<br/><br/>The problem with analog Monte Carlo is that very few of the particles traced end up at the detector. Therefore, enormous numbers of particle histories must be followed to score enough counts at the detector to be statistically significant; even on fast computers, days of computations may be required. The answer is a mixed bag of tricks for ignoring some particles, steering others toward the detectors, and counting still others more than once. This approach can be mathematically valid but is quite tricky, especially with general-purpose codes like Los Alamos’ Monte Carlo Nuclear parameters (MCNP).<br/><br/>The biggest problem is that the models run very slowly, far too slowly to be used as the foot-by-foot forward model in an iterative interpretation process. Geometric effects are still separated from the interpretation process into the environmental-correction process. Monte Carlo modeling is generally confined to creating special-purpose correction charts. Indeed, most current service-company correction charts are generated by Monte Carlo modeling benchmarked to a few lab measurements.


=== Pulsed-Neutron-Lifetime (PNL) Devices ===
=== Pulsed-Neutron-Lifetime (PNL) Devices ===
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=== Mechanical Integrity ===
=== Mechanical Integrity ===


Oxygen-activation flow logging may be used as a test of well integrity and zonal isolation. This is a stopwatch measurement. The neutron generator activates the oxygen in a slug of water. The time it takes the slug to move from its birthplace at the generator until it is opposite one of several remote detectors is measured. The flow velocity is just the distance from source to detector divided by the transit time. Because of the short half-life of oxygen, a particular source-to-detector spacing will be optimal only for a narrow range of flow rates. This procedure works equally well for flow inside and behind pipe. In principle, similar measurements can discern distance to the flow.<br/><br/>Boron has a very high neutron-absorption cross section that greatly reduces the neutron lifetime measured by a pulsed-neutron tool. This makes it a useful tracer when used in conjunction with pulsed-neutron logging. It has been exploited in mechanical-integrity testing by injecting borated water into a well. Any place to which the boron-tagged water finds its way will stand out on the pulsed-neutron log.<br/><br/>'''''Gravel-Pack Logs.''''' In another example, silicon activation is used to evaluate gravel-pack quality.<ref name="r11">_</ref> Gravel packs are placed in oil and gas wells to prevent the accumulation of formation material that otherwise would clog wellbores and production facilities. In the conventional logging method for gravel-pack evaluation, a nonfocused density tool detects the density contrast between packing material and completion fluid. When a pulsed-neutron log is used, it detects activation gamma rays from silicon and aluminum in the packing material that have a half-life of approximately 2.24 minutes. Of the other common downhole elements, oxygen has a much shorter half-life (7.2 seconds), and chlorine, sodium, and iron have half-lives of 30 minutes or longer. Thus, a judicious choice of logging speed can maximize sensitivity to silicon and aluminum. Because the threshold for silicon activation is high (4 to 5 MeV), the measurement is very shallow, maximizing sensitivity to the gravel-pack region.
Oxygen-activation flow logging may be used as a test of well integrity and zonal isolation. This is a stopwatch measurement. The neutron generator activates the oxygen in a slug of water. The time it takes the slug to move from its birthplace at the generator until it is opposite one of several remote detectors is measured. The flow velocity is just the distance from source to detector divided by the transit time. Because of the short half-life of oxygen, a particular source-to-detector spacing will be optimal only for a narrow range of flow rates. This procedure works equally well for flow inside and behind pipe. In principle, similar measurements can discern distance to the flow.<br/><br/>Boron has a very high neutron-absorption cross section that greatly reduces the neutron lifetime measured by a pulsed-neutron tool. This makes it a useful tracer when used in conjunction with pulsed-neutron logging. It has been exploited in mechanical-integrity testing by injecting borated water into a well. Any place to which the boron-tagged water finds its way will stand out on the pulsed-neutron log.<br/><br/>'''''Gravel-Pack Logs.''''' In another example, silicon activation is used to evaluate gravel-pack quality.<ref name="r11">Olesen, J.-R., Hudson, T.E., and Carpenter, W.W. 1989. Gravel Pack Quality Control by Neutron Activation Logging. Presented at the SPE Annual Technical Conference and Exhibition, San Antonio, Texas, 8-11 October 1989. SPE-19739-MS. http://dx.doi.org/10.2118/19739-MS.</ref> Gravel packs are placed in oil and gas wells to prevent the accumulation of formation material that otherwise would clog wellbores and production facilities. In the conventional logging method for gravel-pack evaluation, a nonfocused density tool detects the density contrast between packing material and completion fluid. When a pulsed-neutron log is used, it detects activation gamma rays from silicon and aluminum in the packing material that have a half-life of approximately 2.24 minutes. Of the other common downhole elements, oxygen has a much shorter half-life (7.2 seconds), and chlorine, sodium, and iron have half-lives of 30 minutes or longer. Thus, a judicious choice of logging speed can maximize sensitivity to silicon and aluminum. Because the threshold for silicon activation is high (4 to 5 MeV), the measurement is very shallow, maximizing sensitivity to the gravel-pack region.


=== Induced Gamma Ray Spectroscopy Tools ===
=== Induced Gamma Ray Spectroscopy Tools ===
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=== Geochemical Logs ===
=== Geochemical Logs ===


Geochemical logging is still struggling to find applications. Schlumberger’s latest incarnation is called the environmental capture sonde (ECS).<ref name="r12">_</ref> Applications lie primarily in rock and clay typing for reservoir description. The goal is to add additional elemental concentrations to the formation model. Natural gamma ray spectroscopy measurements provide potassium, uranium, and thorium data. The capture spectroscopy tool detects silicon, calcium, iron, sulfur, gadolinium, titanium, chlorine, and hydrogen.<br/><br/>In analyzing the data, elemental concentrations are derived and processed to obtain a complete mineralogical description. There are several sources of ambiguity. Most importantly, uncertainties in the measurements of the elemental concentrations are not explicitly accounted for. Because elemental concentrations derive from least-squares deconvolution of unresolved gamma ray spectra, they are not determined independently. Furthermore, sensitivities to different elements vary by orders of magnitude and often are very small, requiring large integration times. Finally, element-to-mineral mapping is not sufficiently unique. For best results, a limited suite of minerals must be selected before analyzing the data. The correct choice of a mineral suite depends on knowledge of local mineralogy from other experiences, such as core in an offset well. This arises in part from incomplete and inaccurate elemental analysis and partly from the nearly infinite variety of minerals and the small number of elements. As an example, quartz and opal contain the same elements but are quite different in their impact on a reservoir.<br/><br/>Mineralogy can in turn be related to such properties as permeability, porosity, and cation/ion-exchange capacity. Unfortunately, the minerals-to-petrophysical-properties inversion is not unique either, partly because the tool has no information about the physical configuration of the minerals (for example, grain size or fractures). Even when geochemical logging can give accurate elemental abundances, conversion of those numbers to mineralogy and petrophysical parameters such as permeability still requires a locally calibrated interpretation model. With limited goals and careful local calibration, geochemical logs do provide useful information. The logs remain tied to a local database and ''ad hoc'' knowledge to relate mineralogy to petrophysical properties.
Geochemical logging is still struggling to find applications. Schlumberger’s latest incarnation is called the environmental capture sonde (ECS).<ref name="r12">Herron, S.L. and Herron, M.M. 1996. Quantitative Lithology—An Application for Open and Cased Hole Spectroscopy. Paper E presented at the 1996 SPWLA Annual Logging Symposium.</ref> Applications lie primarily in rock and clay typing for reservoir description. The goal is to add additional elemental concentrations to the formation model. Natural gamma ray spectroscopy measurements provide potassium, uranium, and thorium data. The capture spectroscopy tool detects silicon, calcium, iron, sulfur, gadolinium, titanium, chlorine, and hydrogen.<br/><br/>In analyzing the data, elemental concentrations are derived and processed to obtain a complete mineralogical description. There are several sources of ambiguity. Most importantly, uncertainties in the measurements of the elemental concentrations are not explicitly accounted for. Because elemental concentrations derive from least-squares deconvolution of unresolved gamma ray spectra, they are not determined independently. Furthermore, sensitivities to different elements vary by orders of magnitude and often are very small, requiring large integration times. Finally, element-to-mineral mapping is not sufficiently unique. For best results, a limited suite of minerals must be selected before analyzing the data. The correct choice of a mineral suite depends on knowledge of local mineralogy from other experiences, such as core in an offset well. This arises in part from incomplete and inaccurate elemental analysis and partly from the nearly infinite variety of minerals and the small number of elements. As an example, quartz and opal contain the same elements but are quite different in their impact on a reservoir.<br/><br/>Mineralogy can in turn be related to such properties as permeability, porosity, and cation/ion-exchange capacity. Unfortunately, the minerals-to-petrophysical-properties inversion is not unique either, partly because the tool has no information about the physical configuration of the minerals (for example, grain size or fractures). Even when geochemical logging can give accurate elemental abundances, conversion of those numbers to mineralogy and petrophysical parameters such as permeability still requires a locally calibrated interpretation model. With limited goals and careful local calibration, geochemical logs do provide useful information. The logs remain tied to a local database and ''ad hoc'' knowledge to relate mineralogy to petrophysical properties.
</div></div><div class="toccolours mw-collapsible mw-collapsed">
</div></div><div class="toccolours mw-collapsible mw-collapsed">
== Multiple-Log Interpretation ==
== Multiple-Log Interpretation ==
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=== Visualization-Crossplots ===
=== Visualization-Crossplots ===


The crossplot is another method for visualizing petrophysical data. A clever crossplot can reveal even more about a formation than a standard log-depth display. In a crossplot, the analyst plots one log value on the ''x''-axis against a different log value, at the same depth, on the ''y''-axis. This is repeated for all depths of interest, creating a scatterplot such as that shown in '''Fig. 3D.15'''. With luck, the location of points on such a plot can discriminate underlying mineralogy and reveal trends such as shaliness or porosity. Each pure mineral will plot as a single point. The power to discriminate depends on the independence and uniqueness of log responses to the lithologies of interest. Crossplots frequently include calculated overlay points and lines. The points locate various lithologic endpoints of interest, while the lines track the simultaneous solution of the response equations for the two logs over a range variable such as porosity, or percentage of one mineral vs. another. These response equations are simply the linear mixing-law response equations discussed in the sections above on the individual logs. With only two variables—the two logs—only two unknowns can be extracted. For example, one could determine matrix type (and its associated endpoint-log readings) and the amount of water-filled porosity.<br/><br/>In crossplots, nuclear logs have a clear advantage over sonic or resistivity laws. As we have seen, nuclear logs generally obey simple, linear, bulk mixing laws that have a firm basis in physics. The mixing laws for sonic and resistivity measurements are not only nonlinear but also largely empirical, with only weak connections to theory. Nonlinear terms in a mixing law show up on crossplots as curved lines (the simultaneous solution for a given set of conditions corresponds to a line). In this section, the discussion will be confined to crossplots involving only nuclear logs, although many other useful combinations are possible.<br/><br/>A third variable is sometimes displayed as a ''z''-axis in the form of a color scale. In the example, the color of each point represents its gamma ray log reading according to the key along the right side. This highlights the location of shales and facilitates the selection of shale properties. This highlights the location of shales and facilitates the selection of shale properties needed in further log analysis. For example, the shale density and apparent neutron porosity of the shale can be read off the plot as the values corresponding to the cluster of shale points (in this case, approximately 2.5 g/cm<sup>3</sup> and 40 p.u.).<br/><br/>Perhaps the most useful crossplot in log analysis is an old standard, the neutron-density crossplot. An example based on the synthetic-type logs in '''Fig. 3D.16''' is shown in '''Fig. 3D.15'''. By convention (and convention is very important to quick-look, visual techniques), the neutron log, expressed in limestone porosity units, is plotted on the ''x''-axis against the density log in g/cm<sup>3</sup> on the ''y''-axis, with the scales reversed (i.e., from highest to lowest density). Ideally, because both are porosity logs, points of a given porosity in a pure lithology will fall along a diagonal line. Such a line represents the simultaneous solution of the density and neutron mixing laws as a function of varying porosity. Three such lines are generally plotted as overlays on this crossplot. They correspond to a calcite, dolomite, or quartz matrix with water-filled porosity. If the neutron log were a true hydrogen index log, the lines would extend from a y -intercept corresponding to the grain density of the particular lithology (the zero-porosity limit) to a common upper-right point corresponding to 100% water (i.e., 1.0 g/cm<sup>3</sup> density and 100% neutron porosity). While this is largely true, neutron logs are not perfect hydrogen index measures.<br/><br/>As discussed above, the most commonly run compensated neutron log actually measures neutron migration length, which is a mixture of a large hydrogen index-controlled term and a smaller term controlled by neutron capture that is matrix- and fluid-type dependent. The mix of the two terms in a given tool is design dependent. For example, epithermal neutron porosity is a nearly perfect hydrogen index log. The more commonly used thermal neutron porosity includes some capture effect. This superimposes a linear, matrix-dependent term on the neutron response and a small amount of nonlinearity when hydrogen index is low, such as in gas. Because tool design affects the relative contribution of these terms, each service company generates its own, slightly different overlays for the neutron-density crossplot. This also explains apparent differences between wireline and LWD neutron-porosity measurements.<br/><br/>Returning to the example in '''Fig. 3D.15''', the location of points on the neutron-density crossplot can be mapped to specific lithologies, a number of which are shown on the figure. Other lithology points can be plotted from their neutron- and density-log readings taken from '''Tables 3D.7''' and '''3D.5''', respectively. Edmundson and Raymer<ref name="r13">_</ref> present a more complete tabulation of pure mineral-log readings, as do most service-company chart books. Lines connecting two points on a crossplot represent the mixing of the two lithologies. Remember that water can be used as a lithology endpoint on a crossplot. This creates a porosity trend line from the pure, 0% porosity point for a given matrix to the 100% water point. Lines and points on the crossplot represent specific, simultaneous solutions of the neutron and density mixing for specific supposed lithologies. Cross-cutting lines may represent lithology trends—changes from one lithology to another or simultaneous changes in lithology and porosity. Violated assumptions can be especially revealing. A given formation thought to be a limestone may actually lie along the dolomite line, indicating that it is a dolomite or a sand plot to the lower right of the sand line and, thus, may not be as clean as hoped. The most commonly violated assumption is that the pore space is filled with a liquid (specifically water, although liquid hydrocarbons do not fall very far from the water-filled porosity line). If it were filled with gas instead, the points on the crossplot would move to the upper left, away from the water-filled porosity line. This is the same effect demonstrated by neutron-density crossover on a standard log display. More subtly, a neutron-density crossplot can flag diagenesis. For instance, dolomitization of a limestone might reveal itself as a trail of points scattering from the tight end of the limestone line to the moderate-porosity region of the dolomite one. This can be a very beneficial process, increasing the porosity of the formation. If this process were missed and the formation treated as a pure limestone, much lower porosity would be calculated, and the reservoir might be bypassed. Examination of the neutron-density crossplot should often be one of the first steps in reconnaissance log analysis. A crossplot can help the analyst identify rock types and porosity ranges and guide the selection of facies and zones.<br/><br/>By exploiting the principal of closure (the fact that the volume percentages of all the constituents of a formation must add up to exactly 1), three components can be extracted from a 2D crossplot. Consider a three-component system composed of sand, shale, and water-filled porosity. Qualitatively, the shaly sand progression beginning at a single clean-sand porosity is sketched in '''Fig. 3D.15''' as a trend line. Even if not done quantitatively, this process can indicate the direction that points would move in the presence of a change in composition. As this suggests, the neutron-density crossplot can be a useful alternative to simple gamma ray interpretation for the determination of shale volume. '''Fig. 3D.17''' is a neutron-density crossplot overlaid with a grid of lines. The grid is calculated from the density and neutron response equations, varying relative amounts of sand, water-filled porosity, and clay.<br/><br/><gallery widths="300px" heights="200px">
The crossplot is another method for visualizing petrophysical data. A clever crossplot can reveal even more about a formation than a standard log-depth display. In a crossplot, the analyst plots one log value on the ''x''-axis against a different log value, at the same depth, on the ''y''-axis. This is repeated for all depths of interest, creating a scatterplot such as that shown in '''Fig. 3D.15'''. With luck, the location of points on such a plot can discriminate underlying mineralogy and reveal trends such as shaliness or porosity. Each pure mineral will plot as a single point. The power to discriminate depends on the independence and uniqueness of log responses to the lithologies of interest. Crossplots frequently include calculated overlay points and lines. The points locate various lithologic endpoints of interest, while the lines track the simultaneous solution of the response equations for the two logs over a range variable such as porosity, or percentage of one mineral vs. another. These response equations are simply the linear mixing-law response equations discussed in the sections above on the individual logs. With only two variables—the two logs—only two unknowns can be extracted. For example, one could determine matrix type (and its associated endpoint-log readings) and the amount of water-filled porosity.<br/><br/>In crossplots, nuclear logs have a clear advantage over sonic or resistivity laws. As we have seen, nuclear logs generally obey simple, linear, bulk mixing laws that have a firm basis in physics. The mixing laws for sonic and resistivity measurements are not only nonlinear but also largely empirical, with only weak connections to theory. Nonlinear terms in a mixing law show up on crossplots as curved lines (the simultaneous solution for a given set of conditions corresponds to a line). In this section, the discussion will be confined to crossplots involving only nuclear logs, although many other useful combinations are possible.<br/><br/>A third variable is sometimes displayed as a ''z''-axis in the form of a color scale. In the example, the color of each point represents its gamma ray log reading according to the key along the right side. This highlights the location of shales and facilitates the selection of shale properties. This highlights the location of shales and facilitates the selection of shale properties needed in further log analysis. For example, the shale density and apparent neutron porosity of the shale can be read off the plot as the values corresponding to the cluster of shale points (in this case, approximately 2.5 g/cm<sup>3</sup> and 40 p.u.).<br/><br/>Perhaps the most useful crossplot in log analysis is an old standard, the neutron-density crossplot. An example based on the synthetic-type logs in '''Fig. 3D.16''' is shown in '''Fig. 3D.15'''. By convention (and convention is very important to quick-look, visual techniques), the neutron log, expressed in limestone porosity units, is plotted on the ''x''-axis against the density log in g/cm<sup>3</sup> on the ''y''-axis, with the scales reversed (i.e., from highest to lowest density). Ideally, because both are porosity logs, points of a given porosity in a pure lithology will fall along a diagonal line. Such a line represents the simultaneous solution of the density and neutron mixing laws as a function of varying porosity. Three such lines are generally plotted as overlays on this crossplot. They correspond to a calcite, dolomite, or quartz matrix with water-filled porosity. If the neutron log were a true hydrogen index log, the lines would extend from a y -intercept corresponding to the grain density of the particular lithology (the zero-porosity limit) to a common upper-right point corresponding to 100% water (i.e., 1.0 g/cm<sup>3</sup> density and 100% neutron porosity). While this is largely true, neutron logs are not perfect hydrogen index measures.<br/><br/>As discussed above, the most commonly run compensated neutron log actually measures neutron migration length, which is a mixture of a large hydrogen index-controlled term and a smaller term controlled by neutron capture that is matrix- and fluid-type dependent. The mix of the two terms in a given tool is design dependent. For example, epithermal neutron porosity is a nearly perfect hydrogen index log. The more commonly used thermal neutron porosity includes some capture effect. This superimposes a linear, matrix-dependent term on the neutron response and a small amount of nonlinearity when hydrogen index is low, such as in gas. Because tool design affects the relative contribution of these terms, each service company generates its own, slightly different overlays for the neutron-density crossplot. This also explains apparent differences between wireline and LWD neutron-porosity measurements.<br/><br/>Returning to the example in '''Fig. 3D.15''', the location of points on the neutron-density crossplot can be mapped to specific lithologies, a number of which are shown on the figure. Other lithology points can be plotted from their neutron- and density-log readings taken from '''Tables 3D.7''' and '''3D.5''', respectively. Edmundson and Raymer<ref name="r13">Edmundson, H.N. and Raymer, L.L. 1979. Radioactive Logging parameters for Common Minerals. The Log Analyst 19 (1): 38.</ref> present a more complete tabulation of pure mineral-log readings, as do most service-company chart books. Lines connecting two points on a crossplot represent the mixing of the two lithologies. Remember that water can be used as a lithology endpoint on a crossplot. This creates a porosity trend line from the pure, 0% porosity point for a given matrix to the 100% water point. Lines and points on the crossplot represent specific, simultaneous solutions of the neutron and density mixing for specific supposed lithologies. Cross-cutting lines may represent lithology trends—changes from one lithology to another or simultaneous changes in lithology and porosity. Violated assumptions can be especially revealing. A given formation thought to be a limestone may actually lie along the dolomite line, indicating that it is a dolomite or a sand plot to the lower right of the sand line and, thus, may not be as clean as hoped. The most commonly violated assumption is that the pore space is filled with a liquid (specifically water, although liquid hydrocarbons do not fall very far from the water-filled porosity line). If it were filled with gas instead, the points on the crossplot would move to the upper left, away from the water-filled porosity line. This is the same effect demonstrated by neutron-density crossover on a standard log display. More subtly, a neutron-density crossplot can flag diagenesis. For instance, dolomitization of a limestone might reveal itself as a trail of points scattering from the tight end of the limestone line to the moderate-porosity region of the dolomite one. This can be a very beneficial process, increasing the porosity of the formation. If this process were missed and the formation treated as a pure limestone, much lower porosity would be calculated, and the reservoir might be bypassed. Examination of the neutron-density crossplot should often be one of the first steps in reconnaissance log analysis. A crossplot can help the analyst identify rock types and porosity ranges and guide the selection of facies and zones.<br/><br/>By exploiting the principal of closure (the fact that the volume percentages of all the constituents of a formation must add up to exactly 1), three components can be extracted from a 2D crossplot. Consider a three-component system composed of sand, shale, and water-filled porosity. Qualitatively, the shaly sand progression beginning at a single clean-sand porosity is sketched in '''Fig. 3D.15''' as a trend line. Even if not done quantitatively, this process can indicate the direction that points would move in the presence of a change in composition. As this suggests, the neutron-density crossplot can be a useful alternative to simple gamma ray interpretation for the determination of shale volume. '''Fig. 3D.17''' is a neutron-density crossplot overlaid with a grid of lines. The grid is calculated from the density and neutron response equations, varying relative amounts of sand, water-filled porosity, and clay.<br/><br/><gallery widths="300px" heights="200px">
File:vol5 Page 0282 Image 0001.png|'''Fig. 3D.17 – The neutron-density crossplot can be used to quantify clay volume and porosity in sand/shale mixtures using simple linear mixing laws to plot lines for given bulk properties(e.g., shale volumes).'''
File:vol5 Page 0282 Image 0001.png|'''Fig. 3D.17 – The neutron-density crossplot can be used to quantify clay volume and porosity in sand/shale mixtures using simple linear mixing laws to plot lines for given bulk properties(e.g., shale volumes).'''
</gallery><br/>An example of a different, less commonly used nuclear-log crossplot is shown in '''Fig. 3D.18'''. As in the neutron-density example, the sample data from the logs in '''Fig. 3D.16''' are plotted as small squares. This display crossplots synthetic variables, not raw logs. On the ''x''-axis is the ''U'' matrix apparent. As discussed above, this transformation converts the nonlinear ''P''<sub>''e''</sub> log to ''U''<sub>ma''a''</sub>, a characteristic that obeys linear volumetric mixing. On the ''y''-axis is apparent grain density from the neutron and density logs. Somewhat simplified, this is the grain density needed to produce the neutron-log porosity from the density-log reading, assuming water-filled porosity. The blue, ternary grid shows the generic endpoints for sandstone, calcite, and dolomite. The various labels (e.g., coal and anhydrite) mark the locations at which those minerals should ideally fall on the plot. This technique, sometimes called the matrix-identification (MID) plot, is especially useful in unwinding multicomponent lithologies, as the widely separated overlay points suggest. It gets much of its power from the fact that ''P''<sub>''e''</sub> is largely porosity independent. This accounts for the near-vertical trends in much of the overlaid data from '''Fig. 3D.16'''. As in all crossplots, uncorrected environmental effects may show up as misplaced points, the hallmark of a violated assumption. For instance, because the ''P''<sub>''e''</sub> is a very shallow measurement, barite (with its high iron content) in the mud can cause a wholesale shift of the data cloud to the right.<br/><br/><gallery widths="300px" heights="200px">
</gallery><br/>An example of a different, less commonly used nuclear-log crossplot is shown in '''Fig. 3D.18'''. As in the neutron-density example, the sample data from the logs in '''Fig. 3D.16''' are plotted as small squares. This display crossplots synthetic variables, not raw logs. On the ''x''-axis is the ''U'' matrix apparent. As discussed above, this transformation converts the nonlinear ''P''<sub>''e''</sub> log to ''U''<sub>ma''a''</sub>, a characteristic that obeys linear volumetric mixing. On the ''y''-axis is apparent grain density from the neutron and density logs. Somewhat simplified, this is the grain density needed to produce the neutron-log porosity from the density-log reading, assuming water-filled porosity. The blue, ternary grid shows the generic endpoints for sandstone, calcite, and dolomite. The various labels (e.g., coal and anhydrite) mark the locations at which those minerals should ideally fall on the plot. This technique, sometimes called the matrix-identification (MID) plot, is especially useful in unwinding multicomponent lithologies, as the widely separated overlay points suggest. It gets much of its power from the fact that ''P''<sub>''e''</sub> is largely porosity independent. This accounts for the near-vertical trends in much of the overlaid data from '''Fig. 3D.16'''. As in all crossplots, uncorrected environmental effects may show up as misplaced points, the hallmark of a violated assumption. For instance, because the ''P''<sub>''e''</sub> is a very shallow measurement, barite (with its high iron content) in the mud can cause a wholesale shift of the data cloud to the right.<br/><br/><gallery widths="300px" heights="200px">
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== References ==
== References ==
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<div class="mw-collapsible-content"><references /></div><div class="mw-collapsible-content"><br/></div><div class="mw-collapsible-content"><br/></div></div>[[Category:PEH]]  [[Category:Volume V – Reservoir Engineering and Petrophysics]] [[Category:5.6.1 Open hole or cased hole log analysis]]
<br/><references />
</div></div><div class="toccolours mw-collapsible mw-collapsed">
== General References ==
<div class="mw-collapsible-content">
<br/>This is a small bibliography of papers and books that compose a basic library in nuclear well logging.<br/><br/>'''Bibliographies'''<br/>Mills, W.R., Stromswold, D.C., and Allen, L.S. 1991. Advances in Nuclear Oil Well Logging. ''Nuclear Geophysics'' '''5''' (3): 209.
 
Myers, G.D. 1992. A Review of Nuclear Logging. ''The Log Analyst'' '''33''' (3): 228.<br/><br/>'''Density Logs'''<br/>Bertozzi, W., Ellis, D.V., and Wahl, J.S. 1981. The Physical Foundations of Formation Lithology Logging with Gamma Rays. ''Geophysics'' '''46''' (10): 1439-1455. [http://dx.doi.org/10.1190/​1.1441151 http://dx.doi.org/10.1190/​1.1441151].
 
Tittman, J. and Wall, J.S. 1978. Formation Density Logging (Gamma-Gamma) Principles and Practice. ''Society of Professional Well Log Analysts; Gamma Ray, Neutron and Density Logging Reprint Volume'', SPWLA, paper D.<br/><br/>'''Gamma Ray Logs'''<br/>Wahl, J.S. 1983. Gamma ray Logging. ''Geophysics'' '''48''' (11): 1536-1550. [http://dx.doi.org/10.1190/​1.1441436 http://dx.doi.org/10.1190/​1.1441436].<br/><br/>'''General'''<br/>Ellis, D.V. 1990. Neutron and Gamma Ray Scattering Measurements for Subsurface Geochemistry. ''Science'' '''250''': 82.
 
Patchett, J.G. and Wiley, R. 1994. The Effects of Invasion on Density/Thermal Neutron Porosity Interpretation. Paper G presented at the 1994 SPWLA Annual Logging Symposium, Tulsa, 19–22 June.
 
Tingey, J.C., Nelson, R.J., and Newsham, K.E. 1995. Comprehensive Analysis of Russian Petrophysical Measurements. Paper S presented at the 1995 SPWLA Annual Logging Symposium, Paris, June 1995.
 
Tittle, C.W. 1989. A History of Nuclear Well Logging in the Oil Industry. ''Nuclear Geophysics'' '''32''' (2): 75.<br/><br/>'''Neutron-Induced Gamma Ray Logs'''<br/>Oliver, D.W., Frost, E., and Fertl, W.H. 1981. Continuous Carbon/Oxygen (C/O) Logging—Instrumentation, Interpretive Concepts and Field Applications. Paper TT presented at the 1981 SPWLA Annual Logging Symposium, Mexico City, June 1981.
 
Woodhouse, R. and Kerr, S.A. 1992. The Evaluation of Oil Saturation Through Casing Using Carbon/Oxygen Logs. ''The Log Analyst'' '''33''' (1): 1.
 
Youmans, A.H. et al. 1979. Neutron Lifetime, A New Nuclear Log. ''Society of Professional Well Log Analysts; Pulsed Neutron Logging Reprint Volume, revised edition''. SPWLA, 3.<br/><br/>'''Neutron-Porosity Logs'''<br/>Ellis, D.V. 1990. Some Insights on Neutron Measurements. ''IEEE Trans. on Nuclear Science'' '''37''' (2): 959.
 
Tittle, C.W. 1994. Porosity—An Improved Porosity Code for Processing CNL Data on Desktop Computers. ''The Log Analyst'' '''35''' (1): 27.<br/><br/>'''Textbooks'''<br/>Doveton, J.H. 1994. ''Geologic Log Analysis Using Computer Methods''. Tulsa, Oklahoma: AAPG.
 
Tittman, J. 1986. ''Geophysical Well Logging''. New York City: Academic Press.
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== SI Metric Conversion Factors ==
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{|
|-
| barns
| ×
| 1.0
| E − 24
| =
| cm<sup>2</sup>
|-
| ft
| ×
| 3.048*
| E − 01
| =
| m
|-
| in.
| ×
| 2.54*
| E + 00
| =
| cm
|-
| in.<sup>2</sup>
| ×
| 6.451 6*
| E + 00
| =
| cm<sup>2</sup>
|-
| in.<sup>3</sup>
| ×
| 1.638 706
| E + 01
| =
| cm<sup>3</sup>
|-
| psi
| ×
| 6.894 757
| E + 00
| =
| kPa
|}
 
 
<nowiki>*</nowiki>
Conversion factor is exact.</div></div>[[Category:PEH]][[Category:5.6.1 Open hole/cased hole log analysis]]
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