Petroleum Engineering Handbook
Larry W. Lake, Editor-in-Chief
Volume V – Reservoir Engineering and Petrophysics
Edward D. Holstein, Editor
Copyright 2007, Society of Petroleum Engineers
Chapter 3D - Nuclear Logging
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.
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 serve as excellent general introductions to the convoluted physics of logging tools.
Nuclear logs work because gamma rays and neutrons are penetrating radiation. Unlike visible light, they can traverse tool housings and boreholes and still sample a significant volume of the formation. They can even penetrate casing, giving them a near monopoly in cased-hole formation evaluation. They also respond to different properties than resistivity logs, which merely measure the conductivity of a formation.
To exploit a reservoir, the engineer must characterize it. That basically means building an understanding of two things: the amount and distribution of hydrocarbons and the recoverability of those hydrocarbons. Amount and distribution starts with a description of hydrocarbon volume in place. To the first order, this means bulk volume hydrocarbon:
Estimating porosity requires detailed knowledge of rock fabric, one of the primary uses of nuclear logs. Rock-fabric information runs the gamut from primary lithology (e.g., sandstone vs. limestone) to diagenesis to clay volume and distribution. Nuclear logs can provide estimates of bulk formation properties such as density and hydrogen content. With some geologic insight and simplifications, these bulk properties can be related to reservoir fabric through simple bulk mixing laws. One of the virtues of nuclear tools is that they are bulk-averaging devices. They average formation properties over a volume on the order of 1 ft3. While nuclear logs are much less sensitive to the difference between water and liquid hydrocarbons than resistivity logs, they are very sensitive to the difference between liquid- and gas-phase fluids.
The second class of reservoir properties, the actual production of hydrocarbons, is less directly accessible to nuclear measurements. Producibility depends on two broad factors: heterogeneity and permeability. At some level, log measurements can give insight into heterogeneity. Laterally, multiple wells can be correlated and overlaid on seismic cross sections to track the continuity of layers of similar properties. Logs certainly can speak to vertical continuity, at least within the limitations of their vertical resolutions. Nuclear logs do provide the best vertical resolution of any of the standard suite of log measurements (as fine as 6 in. for gamma ray-based measurements). Bedding thinner than that can be assessed only with some sort of special borehole-imaging log. In electrical logs, thin bedding may manifest itself as anisotropy, but nuclear logs’ bulk-averaging nature removes most sensitivity to the detailed internal structure of the volume they investigate. This also means that nuclear logs cannot speak directly to permeability because that does depend on the microscopic details of grain shape and size, the arrangement of the grains, clay minerals, and their distributions, nor can nuclear logs discriminate secondary porosity in vugs or fractures from primary intergranular porosity. In the end, nuclear-log interpretation is a matter of model choice as much as tool reading.
The Physics of Nuclear Logs
Nuclear Measurements and StatisticsFor logging purposes, all nuclear radiation behaves as particles, and all nuclear-log measurements are particle-counting experiments. There is randomness to the arrival of the particles, so accurate count-rate measurements need to be very long-term averages. As a result, fluctuations in radioactive logs may be statistical rather than the result of a real change in formation properties. This accounts for the apparent chatter in most nuclear logs. Because of this, nuclear logs almost always set the maximum logging speed of a simple quad-combo logging suite [i.e., a tool string with no specialty logs like borehole images, nuclear magnetic resonance (NMR), or waveform sonic].
Counting experiments obey Poisson statistics. A Poisson distribution, as Fig. 3D.1 shows, characterizes such experiments. If the expected value of the number of counts received in a given period of time is μ, then the probability of obtaining a particular number of counts, x, on a given repetition of the experiment is given by
This is the familiar bell-shaped curve, with its width or standard deviation, σ, given by
(Generally, a Poisson distribution applies to discrete events like nuclear counting experiments, while a Gaussian or normal distribution applies to continuous properties like the length of a rod; shapes and moments are nearly identical.) This means that unlike sonic- or resistivity-log measurements, nuclear-log measurements do not have a fixed precision. The precision of a nuclear measurement depends on the number of counts received. If the expected value of the nuclear counts is N, then approximately 32% of all attempts to measure N will fall outside the range . Realizing that the number of counts is simply the count rate times the integration time, to improve the precision of a nuclear-log measurement by a factor of two, one must count four times longer. Log measurements are depth-based (i.e., measurements are made approximately twice per foot). To count four times longer, one needs to log four times slower (e.g., 5 ft/min instead of 20).
Nuclear Radiation Transport
Nuclear logs are based on the interaction of nuclear radiation with matter—materials like sand, clay, water, and hydrocarbons that together make up a reservoir. For logging, the interactions are primarily particle-scattering interactions. Even though gamma rays are usually discussed as electromagnetic radiation, for nuclear logging they are treated as photons—classical particles. Even in well logging, quantum mechanics rears its head.
Well logs exploit two types of nuclear radiation: gamma rays and neutrons. Depending on the type and energy of the particle, different scattering processes predominate. Fig. 3D.2 shows a beam of particles impinging on a slab of formation from the left. Particle beams are characterized in terms of their flux, which has units of particles per unit area per unit time. The incoming flux is labeled ϕi. For scattering, the slab is characterized by the number density of potential scattering particles within it (in other words, the number of atoms per cm3). Suppose the slab in the figure has an average of Np atoms/cm3. If the slab is h cm thick, a beam of unit area will encounter and have a chance to interact with Np × h atoms as it passes through the slab. The actual probability of a given radiation particle interacting with a given atom in the slab of formation depends on a number of factors, including the nature and energy of the radiation and the characteristics of the target atom. Physicists lump these probabilities as cross sections, typically labeled σ(E), where E refers to the energy dependence of the cross section. A cross section has the units of area because it corresponds to the apparent size of the scattering target as seen by the incoming particle. Because these are atomic-scale interactions, the apparent target sizes are on the order of 10–29 cm2. Because humans relate best to numbers they can count on their fingers, a special unit of cross section, the barn, equal to 10–24 cm2, was created.
The number of particles that will be scattered out of the original beam of radiation as it passes through the slab of formation can be written as
ϕiNpσ is interpreted as a reaction rate per unit volume of formation resulting from the incident beam of radiation. Number density can be calculated from bulk density, ρb, average atomic weight, A, and Avogadro’s number, NA, according to the formula
In practice, cross sections are measured experimentally and tabulated as a function of energy for various reaction types and target nuclei. The discussion above is simplified to a slab of formation made up of a single type of atom. For real formations with a variety of atoms, the actual amount of scattering is just a volume-weighted sum of the various atoms in the formation. Many times, as Tables 3D.2 through 3D.4 show, only one type of atom will account for the vast majority of the scattering. This is in fact the basis of nuclear logging.
Integrating the differential flux equation, Eq. 3D.4, produces the unscattered flux that emerges through a thickness of formation, h, as Fig. 3D.2 shows.
This leads naturally to the concept of mean free path. The mean free path, λ, is the thickness of formation that will reduce a beam of radiation to 1/e (approximately 37%) of its original value.
It depends on the amount of material in the formation and its cross section. The mean free path of radiation in a formation determines its depth of investigation and its vertical resolution.
Density tools and neutron-porosity tools simply measure the drop-off in radiation with distance from the source of radiation. While this can be done with a single detector at an appropriate distance from a source of known strength, all modern tools use at least two detectors at different distances from the source. These designs are referred to as compensated. With a near and a far detector, it is possible for the tool designer to compensate for the borehole effects and variations in source strength.
Nuclear-logging tools exploit only two types of radiation: gamma rays and neutrons. Both follow the basic scattering principles defined above but have unique reaction types and cross sections.
Nuclear log interpretation is simply the practice of solving tool-response mixing-law equations with the judicious application of some assumptions and constraints.
The Generalized Interpretation Process
All interpretation is an approximate model. As more factors are taken into account, the interpretation usually improves, but the model becomes more complicated.
For the neutron-porosity log, the simplest interpretation model is to naively accept the raw log reading. This is acceptable in a clean, water-filled reservoir, with a single known matrix lithology:
If the reservoir is shaly, or if the fluid density is not the same as water, a hydrogen-index linear-mixing law will generally do.
This equation can be solved for ϕe given the neutron-tool response to each of the various formation components. If S w is not known and the hydrogen index of the hydrocarbon and connate water phases differ appreciably, it may be necessary to solve for porosity and fluid content simultaneously or at least iteratively.
Invasion adds the next level of complexity. Depending on the degree of invasion, the analyst may need to generate an average fluid hydrogen index, weighted by the invasion diameter and the corresponding radial geometric function for the logging tool. If the porosity is gas-filled, the simple bulk mixing law fails because the neutron response becomes nonlinear. In that case, the next level of interpretation sophistication accounts for this nonlinearity through an "excavation effect," another term added to Eq. 3D.9.
As the lithology becomes more complex, the analyst can move to a macroparameter approach characterized by a neutron migration length. Finally, if the standard environmental correction charts do not cover borehole effects, a full-blown Monte Carlo model may be needed. Fortunately, this is a very rare circumstance.
Single-Log Interpretation-More DetailsEven 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.
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.
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. 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
Here, Ux refers to the tool response integrated out to some distance x into the formation, UT is the tool’s full response out to infinity in the absence of invasion, and Ui 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.
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/cm3. 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 % 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.
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
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.
The third and final step, and the one on which the log analyst spends the most time, is the understanding of the tool’s bulk response to a formation, the T in Eq. 3D.11. Consider a small cube of formation. While the cube is heterogeneous on the microscopic scale, it can be treated as uniform on the scale of nuclear scattering. At the scale of 10 cm, the exact arrangement of crystalline rock and fluids does not matter, only the bulk average number of scattering centers of a given type. Tool response is determined by these bulk averages. Fortunately, these can be related to bulk average formation properties. Fig. 3D.5 summarizes the process. Mathematically, this bulk averaging corresponds to a linear mixing law:
where R is the bulk tool response, Vi is the fractional volume of the ith material, Ri is the response to that material only, and n is the total number of materials present. For example, if water occupies 10% of the pore space and the porosity is 20%, the fractional volume of water (also known as bulk volume water) is 0.1 × 0.2 = 0.02. For a density, log Ri is the density of the ith component. Pure water has a density of 1.0 g/cm3, so R of water is 1.0 g/cm3. The contribution of that water to the tool response is Vi × Ri = 0.02 × 1.0 = 0.02 g/cm3. Similarly, for a neutron-porosity log, Ri is the hydrogen index of material i.
More generally, the responses may not be linear, but there is still an equation or mixing law:
An example of this would be the nonlinear response of a neutron-porosity log to gas, referred to as the excavation effect or any of the numerous ad hoc, nonlinear gamma ray models.
Single-log interpretation amounts to the assumption that considering just two components (or at least only two at a time) can capture the log’s response to a formation. Examples include the determination of shale volume or total porosity from a single log curve. As an example, consider calculating shale volume from a gamma ray curve. According to the linear mixing-law equation, the gamma ray tool’s response can be written as
This seems to be one equation in two unknowns, but there is another, implicit equation, namely that the formation is composed entirely of shale and nonshale (or reservoir or clean sand); that is,
This really amounts to an assumption. Most importantly, it assumes that there is such a thing as "reservoir rock" characterized by a single bulk gamma ray response. Even in the simplest case, reservoir rock consists of matrix- and water-filled porosity.
Logs Exploting Gamma Rays and Gamma Ray Transport
Gamma Ray Interactions With FormationsGamma rays interact with formations in three different ways: photoelectric absorption, Compton scattering, and, to a limited extent, pair production. One of these will dominate depending on the energy of the gamma ray, as Fig. 3D.6 shows.
Compton Scattering. The most important interaction for logging measurements involving gamma rays is Compton scattering, which dominates in the middle energy range. The density log itself is designed to exploit Compton scattering. Compton scattering also controls the transport of natural gamma rays through a formation to the standard gamma ray tool. Compton scattering is scattering off an atomic electron. In the process, the gamma ray loses some of its energy to the electron. Compton scattering is the dominant form of gamma ray interaction with a formation, from several hundred keV (kilo electron volts, a unit of energy) all the way to 10 MeV (mega electron volts). The cross section for Compton scattering changes very little with energy. The loss of gamma rays is proportional to
where Z is the average atomic number of the formation. The attenuation law for gamma ray intensity falloff is then
For Compton scattering to be a true measure of bulk density, ρb, Z/A must be a constant. For almost all formation elements, Z/A = 1/2, and a measurement of gamma ray attenuation in the 1- to 10-MeV range can indeed be calibrated to bulk density. The notable exception is hydrogen, for which Z/A =1. Table 3D.5 lists some density values for comparison.
Photoelectric (PE) Absorption. Not surprisingly, the PE log is based on the photoelectric absorption of gamma rays, the scattering process that dominates at low energy. In this process, the incoming gamma ray is absorbed by an atomic electron, giving up all its energy to the electron in the process. If the gamma ray is energetic enough, the added energy causes the electron to break free from its atom. As another electron falls into the vacancy, a characteristic X-ray, generally less than 100 keV, is emitted. These X-rays are too low in energy to contribute to logging measurements.
The PE cross section falls off very strongly as the energy of the incoming gamma ray increases. The cross section is proportional to
It is a significant factor in gamma ray scattering only for energies less than 100 keV. This means that it is easy to separate the effects of PE absorption from those of Compton scattering by simply windowing the energies of the gamma rays detected. The same tool can make both measurements simultaneously. By examining the falloff of low-energy gamma ray flux, a logging tool can be calibrated to measure the PE factor (PEF). The PEF, in turn, is primarily sensitive to the average atomic number, Z, of the formation. Because hydrocarbons and water have very low Z values, they contribute very little to the average PE of a formation. Conversely, because the major rock matrices have very different Zs, the PE factor is a nearly porosity-independent lithology indicator.
Pair Production. The final process by which gamma rays interact with a formation needs only a passing comment because its impact on logging measurements is minimal. This process, pair production, occurs only at very high gamma ray energies. It is another absorption process, with a threshold of 1.022 MeV. The incoming gamma ray interacts with the electric field of the nucleus and is absorbed if it has enough energy. This generates an electron-positron pair. The positron (actually just an antimatter electron) is quickly annihilated, yielding two 511-keV gamma rays. This has little impact on passive gamma ray or gamma-scattering density measurements but does play a role in the appearance and analysis of gamma ray spectra from neutron-induced gamma ray logs.
Passive Gamma Ray Tools
Conceptually, the simplest tools are the passive gamma ray devices. There is no source to deal with and generally only one detector. They range from simple gross gamma ray counters used for shale and bed-boundary delineation to spectral devices used in clay typing and geochemical logging. Despite their apparent simplicity, borehole and environmental effects, such as naturally radioactive potassium in drilling mud, can easily confound them.
The gamma ray tool was the first nuclear log to come into service, around 1930 (see Fig. 3D.7). Gamma ray logs are used primarily to distinguish clean, potentially productive intervals from probable unproductive shale intervals. The measurement is used to locate shale beds and quantify shale volume. Clay minerals are formed from the decomposition of igneous rock. Because clay minerals have large cation exchange capacities, they permanently retain a portion of the radioactive minerals present in trace amounts in their parent igneous micas and feldspars. Thus, shales are usually more radioactive than sedimentary rocks. The movement of water through formations can complicate this simple model. Radioactive salts (particularly uranium salts) dissolved in the water can precipitate out in a porous formation, making otherwise clean sands appear radioactive.
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.
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.
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.
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.
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.
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.
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.
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, SiO2, limestone CaCO3).
The most common interpretation method is the simple bulk linear mixing law presented previously.
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:
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
leads to the familiar formula for calculating shale volume from a borehole-corrected gamma ray log:
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. 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.
One disadvantage of the various empirical, nonlinear models is that they generally require core data for calibration or at least justification. This is a generic problem with more complex models; they require more parameters to characterize them. To set or calibrate those parameters in turn requires more independent log or core measurements.
It is also assumed that the clean reservoir material (the sum of the pore fluids and matrix minerals) has a fixed amount of radiation associated with it. As long as the gamma ray reading associated with the clean reservoir material is small compared to the shales, this assumption is safe. As the sands become hotter (more radioactive), lumping the fluids and matrix together becomes problematic, particularly if the porosity is large.
The latest variant on the gamma ray log is the spectral gamma ray log. This starts out exactly the same as the standard gross gamma ray count log discussed above. Gamma rays from the formation are counted in a detector system. However, there is an added level of sophistication. The energy of the gamma ray captured by the detector is proportional to the brightness of the light pulse it produces, and this brightness, in turn, determines the size of the electrical pulse produced by the photomultiplier. By sorting the pulses from the photomultiplier into bins by their size, a spectrum equivalent to the energy spectrum of the incoming gamma rays is produced. As noted above, the energy of the gamma rays is determined by which element emitted them.
Spectral gamma ray measurements offer several advantages. They can help with clay typing. Variations of the relative amounts of potassium, thorium, and uranium are associated with specific shale minerals. As is so often the case in log analysis, crossplots are used to highlight these differences. Different clay minerals may (sometimes) array themselves in the pie slices of a thorium/potassium crossplot. Clays of different types also may plot in different regions on a crossplot of potassium or the thorium/potassium ratio against Pe, the PE factor. For the mathematically inclined, the same relationships may be captured in an equation of the form
For a typical shale, the coefficients are in the ratio of A:B:C=1:2:4. Uranium is more often associated with fluid movement in porous rocks than shale minerals. At the very least, the effects of uranium can be removed. In other cases, potassium may be associated with feldspar rather than shale. Differences in the ratios between the overlying reference shale and the shaly sands may highlight the problems with carrying clay properties from the overlying shale into the shaly-sand interval.
Consider briefly some details of how a standard, gross-count-rate gamma ray tool works. Most modern tools (in nuclear logging, "modern" means within the past 25 years) use a solid-state scintillator crystal (most often sodium iodide, NaI) to detect gamma rays. When a gamma ray strikes the crystal, there is some probability that it will be captured. That probability is mostly proportional to the size and density of the crystal. If it is captured, it gives off a flash of light. A photomultiplier mounted on one end of the crystal converts that light to an electrical pulse, which is then fed to an electronic pulse counter. To measure a count rate with a given precision in the laboratory, one counts until enough counts are registered to give the desired level of precision (see the discussion of counting statistics above). Then, one divides that number of counts by the time it took to get that many to obtain a count rate. Unfortunately, in a logging tool, all measurements are depth-based. To measure a count rate, the tool counts for the length of time it takes the tool to move 1/2 ft (or whatever the depth increment is), then divides by the length of time it took the tool to move that distance. This means that the precision of a nuclear-logging measurement in a given lithology is proportional to one over the square root of the logging speed. Remember that the number of counts received crossing a clean 1/2 ft will be much less than the number when crossing a shaly 1/2 ft.
The simple consideration of the discussion of radiation transport above helps clarify which environmental effects most seriously distort the gamma ray log. Imagine what happens as borehole size increases. There is less of the radiating radioactive material near the detector, and the measured count rate goes down, even though the actual level of radioactivity in the formation remains the same. Further imagine the rather typical case in which the shales are eroded and broken out while the sands remain in gauge. This would suppress the apparent gamma ray count rate in the eroded shales much more than in the sands, suppressing the gamma ray contrast between eroded shales and sands. This is typically one of the largest environmental effects on the gamma ray count rate. Again from the discussion of radiation transport, heavier materials in the path that the gamma rays must follow from the formation through the detector will absorb more gamma rays than lighter materials (as will be seen in a later section, this is the basis for the bulk density log, but that is another story and a different log). Worse yet, barite is a big absorber of gamma rays. The lesson to carry away is that borehole size and fluid corrections are almost always important when running the gamma ray log.
Spectral Gamma Ray Logs
As we saw earlier, the energy of a gamma ray depends on its source. Each of the standard naturally occurring radioactive elements (K, U, and Th) gives off a gamma ray of a unique energy when it decays. Potassium gives off only a gamma ray. The other elements give off a gamma ray, then decay to other elements called daughters, which, because they are still radioactive, give off other gamma rays, and so on. This gives rise to the pattern of gamma ray energies in Fig. 3D.8. These are called spectra of the elements and are as unique as fingerprints. It is not surprising that the brightness of a light pulse produced in a scintillator crystal is proportional to the energy of the gamma ray. The amount of current in the electrical pulse from the photomultiplier is in turn proportional to the brightness of the pulse of light. It is a simple matter to sort the pulses coming out of the photomultiplier into bins according to their pulse size before counting them. This is called pulse-height spectrum analysis and gives rise to a histogram of count rates such as those in Fig. 3D.8 instead of a single count rate. Common scintillators lack the resolution to break the gamma rays into fine enough bins to reproduce the spectra in Fig. 3D.8, so some sophisticated mathematical deconvolution is needed to infer proportions of uranium, potassium, and thorium from broadly windowed pulse-height spectra.
There are several new things that can be done once we have K, U, and Th count rates rather than just total gamma ray. The most important is that we can produce a count rate only because of potassium and thorium. This is very useful because these elements most often tag only clays, while uranium salts can be associated with moved water. These uranium salts can be precipitated out in porous reservoir rock, especially at the wellbore, where pressure changes may occur. This uranium can produce what appear to be hot sands on a gross gamma ray log. Using the uranium-free gamma ray curve from a spectral tool (CGR, in Schlumberger’s mnemonics) can circumvent this problem and improve sand/shale discrimination in such environments. Occasionally, the ratio of thorium to potassium can be exploited in clay typing. The downside of spectral gamma ray curves is reduced count rate and the accompanying reduced precision. By dividing the spectra into three components, the count rate for any one component may be less than one-third that of the total gamma ray measurement. Further errors occur in the math of deconvolution. If high-precision spectral gamma ray measurements are needed, reduced logging speed is required. The service companies have charts and computer programs that can help in the selection of logging speeds to achieve specific precisions.
LWD gamma ray tools typically embed the detector inside of a drill collar. Two to three inches of steel are interposed between the detectors and the formation. That steel acts as an energy-cutoff filter, passing high-energy gamma rays better than lower-energy ones. As a result, these tools are more sensitive to the high-energy potassium gamma rays than the lower-energy uranium and thorium. The API gamma ray unit defined in the U. of Houston facility fails to recognize that different gamma ray energy distributions (arising from different relative concentrations of potassium, uranium, and thorium in the formation, as well as different borehole conditions and detector response functions) can cause the same counting rate at the detector in the borehole. In addition, the borehole diameter of the calibration pit is too small to accommodate most measurement-while-drilling (MWD) tools. To allow direct comparison with familiar wireline gamma ray logs, MWD contractors have attempted to transfer the API unit to the new (and larger-diameter) spectral gamma ray calibration pits, also at the U. of Houston. Because of the differences in spectral response between wireline and MWD tools, there is no unambiguous way to transfer the API unit to MWD tools. This problem is not unique to MWD tools, but because of their suppressed low-energy sensitivity, it is particularly severe for them.
To offset these effects, most MWD gamma ray tools are spectral gamma ray tools that divide the spectrum into 256 channels downhole. The precise use of these windows is still evolving, but they clearly can be used for K-U-Th determination. In one case, the shielding provided by the drill collar is turned to an advantage to produce a directional gamma ray log. As the tool rotates in the hole, it looks in different directions. At a dipping bed boundary with gamma ray contrast, such as when entering or leaving a shale bed, the gamma ray reading oscillates as the tool first sees the bed on the top of the hole and then the bottom. This fact can be used to estimate the angle at which the drillstring is striking the bed and to keep drilling within a bed.
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.
Spectral natural gamma ray systems designed for K-U-Th logging have been applied to evaluate stimulations and completions. 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
A density-logging tool sends gamma rays into a formation and detects those that are scattered back. Typical logging sondes use a Cesium-137 source, which emits gamma rays of 0.66MeV. At this high energy level, Compton scattering dominates. The average electron density in the volume of formation probed by the tool controls the scattered gamma ray count rates at the detectors. As we saw above, average electron density, in turn, correlates strongly (but not perfectly) with bulk density. Because the gamma rays cannot penetrate far into the formation, the volume of investigation is small. Mudcake and tool standoff have particularly strong effects on this measurement. For less energetic gamma rays, PE absorption controls the observed count rates. Here, the average atomic number (which correlates with rock type) sets the amount of PE absorption that a formation exhibits. Again, all the bulk average effects accrue, with special problems posed by barium-weighted mud.
The depth of investigation of a density tool decreases with increasing density and never exceeds 6 in., as the pseudogeometric factor in Fig. 3D.3 shows. The log almost always measures the invaded zone, at least in porous, permeable formations. As is typical of the nuclear scattering family of measurements, the density tool uses two detectors at progressively longer distances from the source. The distance between the near and far detectors sets the vertical resolution, approximately 10 in. typically. Correction is by the spine-and-ribs technique. The spine is the normal calibrated relationship between the density measured by the near-spaced and far-spaced detectors in the absence of any gap between the tool and the borehole wall. Gaps cause departures from this spine and lead to density corrections that are applied to the density from the long-space detector. This correction is presented as a curve with the density log. Above an inch or so of standoff, the compensation fails. There is no universal correction threshold, but corrections greater than 0.05 to 0.1 g/cm3 are suspicious. Unfortunately, a low correction does not guarantee a good measurement. Connecting a particular rib back to the correct location on the spine (and, hence, to the correct bulk density) requires that the density pad be parallel to the borehole wall. Likewise, very small water-filled gaps can give rise to large corrections that are perfectly correct.
This is the one case in which the difference in design between wireline and LWD tools is significant. Wireline tools use a skid-mounted pad that is pressed directly against the borehole wall. The pad follows hole rugosity, at least at the 1- to 2-ft vertical frequency level, minimizing the tool standoff. Because this is a very shallow measurement, minimizing the thickness of the layer of mud and borehole fluid between the tool and the formation is very important. The location of the sensor in the rotating drill collar precludes pad mounting of the LWD gamma ray density sensor. Thus, direct contact with the formation is eliminated, and a large and variable mud layer is introduced into the volume of investigation. Two different approaches are used to compensate for this mud effect. One design places the source and detector in stabilizer blades. These blades displace the drilling mud, providing a nearly direct path to the formation for the probing gamma rays. Because a stabilizer can steer the bit, tool subs using them must be run several joints behind the bit to maintain directional control. The blades are also subject to wear that can affect the tool calibration. A focused source and careful detector-window design further minimize borehole effects. Measurements generally use tool rotation to correct for hole-size variations. Spectral detection of scattered gamma rays is exploited in combination with low-density windows to produce a PE measurement. In an alternate approach to solving the mud problem, multiple detectors are placed radially around the collar, and the results are averaged to remove mud effects when the mud density is known. Of course, the tool may undergo complex motion, requiring a more sophisticated algorithm. This procedure can be misled by tool precession in nearly vertical holes.
In the standard sequential interpretation process, the analyst determines porosity directly from the density log. It is conceptually the easiest of the porosity logs to interpret because, if ever a tool obeyed a linear bulk mixing law, it is the density logs.
In a simple clean reservoir, the interpretation model is:
Solved for porosity, this yields
This porosity is subscripted with a T for total porosity because it draws no distinction between pore fluid and fluid possibly bound in shales. As mentioned in the general interpretation discussion, the density log rarely sees past the invaded zone, so ρfl = ρmf, the mud-filtrate density. Even if shale is present, the interpretation merely requires an additional term:
and the corresponding shale correction to turn total porosity into effective porosity is straightforward. Again, more sophisticated formation descriptions require more parameters, which in turn require more measured data for calibration.
In known lithology, the grain density, ρma, can be chosen from a table like Table 3D.5. Sensitivity can be analyzed directly by taking the partial derivative of the response equation with respect to grain density. For a 30-p.u., water-filled sandstone, an error of 0.05 g/cm3 in the supposed grain density will only alter the calculated porosity by 2 p.u. A similar analysis of the sensitivity to fluid density shows that a variation of more than 0.1 g/cm 3 in the fluid density corresponds to a similar 2-p.u. error in the calculated porosity.
This is fortunate because fluid density within the density tool’s volume of investigation may be very difficult to estimate. As already discussed, because of its shallow depth of investigation, the density log is commonly a flushed-zone device, and the fluid density that it sees may be taken to be that of the mud filtrate. The effect of a small amount of immovable hydrocarbon or connate water can, more often than not, be ignored. If gas is present, its low density will produce an apparent increase in porosity. Here, we could have a case in which, to calculate density porosity, we must first know the average flushed-zone fluid saturation.
As discussed in the section about radiation transport, the biggest hitch in gamma-gamma scattering density evaluation is the difference between bulk density and electron density. The device measures electron density. As Table 3D.5 shows, this matters only for fluids. Knowing that the tool will be used in fluid-filled rocks, the service companies transform the electron density to a water-filled, porous limestone, calibrated bulk density. The apparent density as read by the tool is thus altered to read:
In the principal lithologies of interest, this transformed density departs less than 0.004 g/cm3 from the true bulk density. The case of a high-porosity reservoir filled with gas (and with minimal invasion) may require additional correction beginning with the removal of this "calibration." In those cases, the analyst should use the apparent density rather than the true bulk density in any mixing-law equation.
PEIn addition to gamma ray scattering, modern density tools also analyze the low-energy region of the scattered gamma ray spectrum separately. These low-energy gamma rays are subject to photoelectric absorption, which is controlled by the atomic number, Z. Z, in turn, strongly correlates with lithology (see Fig. 3D.11). The length of the lines represents a variation from 0 (top) to 40 p.u. Note how effectively the lithologies are discriminated independent of porosity.
Fig. 3D.11 - Z and, hence, the PEF measurement, discriminates lithologies, largely independent of porosity. The line lengths represent ranges of porosity from 0 to 40% in the respective lithologies. (There are three vertical lines corresponding to the porosity, ranging from 0 p.u. at the top to 40 p.u. at the bottom for each of the three common reservoir matrix lithologies. This illustrates that Z and, hence, PE is nearly porosity independent while strongly discriminating lithology. The x-axis takes on only three discrete values for each of the three lithologies).
The PE absorption cross section, in barns (10–24 cm2), is strongly dependent on the energy of the gamma rays, E, as well as the average atomic number, Z.
This means that low-energy gamma ray flux is attenuated according to
To suppress this energy dependence, the PE log is scaled as a PE index or factor:
So, in terms of Pe, the attenuation (which is what the tool actually measures) of low-energy gamma rays is simply
where ne is the electron-number density.
UUnfortunately, Pe does not obey a linear, volumetric mixing law on which log analysis thrives. To get around this, a new parameter, U, was developed.
where ρb is the formation density in g/cm3. In terms of multiple components,
which is a linear bulk mixing equation. Table 3D.6 shows typical values of PEF and U for some common formation constituents.
Neutron-Scattering Porosity ToolsBy far, the most difficult nuclear logs to interpret are those that exploit neutron scattering to estimate porosity. The log targets the average hydrogen density of the volume investigation. If all the hydrogen in the formation is in the form of porosity-filling liquid, in particular water or oil, the hydrogen index will track the porosity. A modern, compensated tool actually estimates the size of a cloud of neutrons around a source by measuring the ratio of count rates at two different distances from the source. The straight-line distance that the average neutron travels away from the source before collisions with formation atoms slow it down to thermal energy sets the size of the neutron cloud. Once a neutron slows to thermal energy and is thus in equilibrium with the rock matrix, it diffuses only very slowly away from the source. This forms the static cloud of neutrons whose size the tool measures. This characteristic distance is called the slowing-down length. Neutrons slow down through elastic, billiard-ball-type collisions. Conservation of momentum requires that they lose the most speed in collisions with nuclei of nearly their own mass (e.g., hydrogen). Obviously, collisions with other nuclei also slow neutrons, but less effectively than those with hydrogen. Table 3D.2 summarizes just how dominant hydrogen is at slowing down neutrons compared to the other common formation elements. Ideally, a porosity tool would count only epithermal neutrons because the slower thermal neutron population depends as much on the absorption cross section of the formation as it does on the slowing-down length. To get count rates high enough for statistical accuracy, logging tools typically count all neutrons, epithermal and thermal. Thus, the tool reading must be corrected for the effects of neutron capture in the formation. Fig. 3D.12 outlines the conversion from tool reading to porosity.
The neutron-porosity log first appeared in 1940. It consisted of an isotopic source, most often plutonium-beryllium, and a single detector. Many variations were produced exploiting both thermal and epithermal neutrons. In most of the early tools, neutrons were not detected directly. Instead, the tools counted gamma rays emitted when hydrogen and chlorine capture thermal neutrons. Because hydrogen has by far the greatest effect on neutron transport, the borehole effects on such a tool are large. Until recently, this type of tool was still in common use in the former Soviet Union. The now-standard compensated neutron-porosity logging (CNL) tool, in common use since the 1970s, is still a very simple tool. Like a density tool, it consists of an isotopic source (now most often americium-beryllium, although at least one tool uses an accelerator source) and two neutron detectors. The tool measures the size of the neutron cloud by characterizing the falloff of neutrons between the two detectors. Because neutrons penetrate considerably further than gamma rays, the design is much simpler than that of a density tool. It requires little collimation and does not need to be pressed against the borehole wall. The size of the fluid-filled borehole is obviously an important environmental effect that must be taken into account. As a result, even "raw" CNL porosities are reported with a borehole-size correction already applied.
LWDAs expected, some of the most interesting variations in design occur for the most troublesome measurement, the LWD tools. Although all MWD devices share the basic wireline configuration of a neutron source and two differently spaced detectors, the drillstring environment forces changes. Again, a pad-mounted tool is not possible, increasing potential borehole effects. He-3 detectors with long central wires, the standards in wireline tools, are sensitive to the effects of vibration that can cause false counts. One service company uses a new neutron detector, an Li-6 scintillator. Because this detector can respond to gamma rays as well as neutrons, spectral processing is required to strip out the gamma ray counts that show up as low-height pulses. The detector absorbs essentially all incident thermal neutrons, resulting in a high counting efficiency, but the metal hatch over the detector acts as a filter, giving a substantial epithermal character to the response, which lies somewhere between the thermal and epithermal responses of a wireline tool. In another novel approach, multiple Geiger Marsden tubes arrayed around the circumference of the collar detect capture gamma rays. In principle, most detected gamma rays come not from neutron capture in the formation, but from capture in the iron of the collar. They thus reflect the neutron population near the detector as if they were neutron detectors. In practice, this tool can exhibit lithology and salinity effects. In formations containing siderite, some correlation between porosity and grain density has been observed from this design. This indicates that some of the gamma rays recorded by the detector do indeed come from the formation. A third design takes a wireline-like approach. The primary measurement uses banks of He-3 detectors at two different spacings from an americium-beryllium source. The source is centered in the drill collar rather than near the formation. Although this makes the source separately retrievable, it also filters and lowers the neutron flux at the formation. Source-to-detector spacings are similar to wireline tools. Porosity is calculated much as it is for wireline logs. A near-to-far count-rate ratio is taken. Shop calibration factors, borehole diameter, mud weight, salinity, temperature, pressure, and matrix corrections are applied to the ratio before finally calculating porosity. This procedure is superior to correcting porosities for these effects in that it reflects perturbations on what the tool measures: neutron slowing-down length, not porosity. Because of absorption of thermal neutrons by the drill collar, the measurement has an epithermal flavor. Each bank of detectors consists of three detectors distributed radially around the circumference of the drill collar. Examining the count rates from the three detectors allows for correction for tool position in the borehole.
Like the gamma ray API unit, some historical baggage accompanies the presentation and scaling of neutron-porosity logs. The curve is presented as porosity, frequently without reference to the matrix, even though the matrix does matter. Although the curve is most often scaled as apparent limestone porosity, as we have seen earlier, it is actually a measurement of the distance required for a neutron to slow down, referred to by physicists as the slowing-down length, Ls. Neutrons produced by an americium-beryllium (Am241Be9) isotopic source have an energy of approximately 4.3 MeV, corresponding to a speed of more than 2000 cm/μs (44 million mph). Above approximately 0.1 eV (a mere 6,000 mph), neutrons slow down primarily through elastic collisions with the nuclei of atoms in the formation. Elastic collisions are like billiard-ball collisions: the nearer the nucleus struck is to the mass of the neutron, the more energy the neutron loses in the collision. This means that hydrogen, the nucleus of which has only a single proton (and which has altogether the same mass as the incoming neutron), is by far the most effective atom at slowing down a neutron (see Table 3D.2). Neutron slowing down by elastic collisions (thermalization) may be visualized as a random walk (see Fig. 3D.13). The average straight-line distance that a neutron manages to get from the source before it comes to thermal equilibrium with the reservoir is the slowing-down length, Ls. Note how much longer the slowing-down length for limestone is than for water, as shown in the figure.
Logging tools measure the size of the neutron cloud by looking at the falloff in neutron flux between two detectors. The falloff is inferred from a ratio of near-to-far neutron counting rates. As shown in the top half of Fig. 3D.14, this ratio can be uniquely related to slowing-down length. The data points in the plot represent a variety of lithologies and porosites, but all fall along the same trend line. Although it depends on details of lithology and fluid composition, conversion of slowing-down length to porosity is straightforward, as will be seen in the discussion of macroparameters later.
The standard neutron-porosity measurement counts all neutrons, not just the unthermalized or epithermal ones. They are designed this way because the epithermal count rate represents only a small fraction of the neutrons at a distance from the source. To get the count rate (and the precision) up, all available neutrons are counted. This is a textbook example of trading accuracy for precision. While elastic scattering and, thus, the hydrogen content of the formation control epithermal neutron flux, thermal neutrons can interact with the formation in other ways. In particular, they can be captured by other elements in the formation. Neutron capture is not dominated by hydrogen, as Table 3D.3 shows. This means that the standard thermal neutron porosity is contaminated by the subsequent diffusion distance, Ld, that the thermalized neutrons travel before they are finally captured. This is illustrated by the vector sum in Fig. 3D.13. This total distance the neutron travels, slowing down plus diffusion, is called the migration length, Lm. Because of the enduring confusion around the matrix assumed for a particular display of neutron porosity and the tenuous relationship between what the tool measures and porosity, values would be better reported in migration length than apparent porosity. It is as if density logs were always displayed as density porosity without always reporting the assumed matrix and fluid densities.
These problems with the interpretation of the standard compensated thermal neutron log have started a search for a new neutron-porosity tool with a more epithermal character. Accelerator neutron sources have begun to appear in commercial porosity tools. These tools take a more sophisticated approach than the simple CNL-like count-rate ratios used by current pulsed-neutron lifetime tools to obtain porosity. For example, Schlumberger has fielded a neutron generator-based porosity sonde that measures several different "neutron porosities" with both thermal and epithermal characters. These different measurements of porosity can be compared and combined to improve the final porosity estimate. While the measurement may be a better hydrogen-index porosity measurement, it is not the same as a standard compensated thermal neutron-porosity log.
Log InterpretationBecause we are stuck with values reported in apparent neutron porosity, that is how we typically interpret them. Most interpretation schemes assume that the neutron porosity is scaled in apparent limestone units; that means a limestone matrix and water-filled porosity. If the neutron matrix is not known for certain, but the actual formation matrix is, the matrix on which the neutron-porosity log was recorded can be verified by making a density-neutron crossplot. Fig. 3D.15 shows a schematic example. If the points fall along the overlay line for the actual formation matrix, the neutron log is most likely in limestone (calcite) units. If the points fall along the calcite overlay line, the log matrix is the same as the formation matrix. In particular, if the points fall along the limestone line and the reservoir is known to be sandstone, the neutron log is in sandstone units and should be transformed to limestone units before proceeding with interpretation. As the schematic shows, gas and shale can obscure these trends.
To first order, once the log has been environmentally corrected, its reading can be characterized by a linear mixing law
In the case of a purely epithermal neutron log, the approximately equal sign can be replaced by an equal sign. Because most logs encountered are thermal neutron logs, the rest of the discussion will center on thermal neutron interpretation.
The linear mixing law implies that matrix and shale effects can be handled by a simple apparent porosity of a 0-p.u. mineral. Some examples of apparent neutron porosity (on a limestone matrix) for a number of materials are given in Table 3D.7. As can be seen from the matrix overlays on the density-neutron crossplot (Fig. 3D.15), this mixing law is not quite linear, and these apparent porosities vary with true porosity. While they are correct at 0 p.u., by the time true porosity reaches 10 p.u., quartz’s apparent porosity has climbed to –4 p.u. and dolomite’s to +6 p.u. These values also can vary somewhat with tool design. In a known, single clean lithology, it is best to use the contractor’s more elaborate transforms. However, in shaly sands or dolomitized limestone, canned transforms will not exist, and the analyst falls back on the linear mixing law. In the shaly sand case, the mixing law is of the form
where ϕ app and IH are used interchangeably because both are calibrated to the apparent neutron porosity of pure water.
where f(ri) is the radial geometric function discussed above, ri 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.
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.
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.
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).
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.
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 to more elaborate use of neutron transport properties.
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).
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. Schlumberger published the SNUPAR program, 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.
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.
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.
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).
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) DevicesPNL logs measure the die-away time of a short-lived neutron pulse. They probe the formation with neutrons but detect gamma rays. Chlorine has a particularly large capture cross section for thermal neutrons. If the chlorine in the formation brine dominates the total neutron capture losses, a neutron-lifetime log will track chlorine concentration and, thus, the bulk volume of water in the formation. For constant porosity, the log will track water saturation, Sw. The neutrons are little affected by steel casing, so this is the standard cased-hole saturation tool. Like other nuclear tools, modern PNL tools incorporate two detectors for borehole compensation. These detectors also permit the calculation of a ratio porosity. This ratio porosity is similar, but not identical, to that of a compensated neutron-porosity tool. They differ because the energy of the neutrons from the pulsed accelerator source is higher than the energy from the isotopic source used in compensated neutron logging. Also, the neutron-lifetime tools detect capture gamma rays rather than direct neutrons.
The basis of operation is similar to the other nuclear radiation transport tools in that the tool infers a cross section. In this case, the tool measures the time required for a pulse of neutrons to be absorbed by a formation. The mechanism by which the neutrons disappear is primarily thermal neutron capture. The time evolution of a pulse of neutrons follows the usual exponential decay law:
where Σabs is the total neutron capture cross section of the formation expressed in capture units (c.u. = 1000 × cm2/cm3, which has units of cross-sectional area per unit volume). The total capture cross section for a formation follows the standard linear volumetric mixing law discussed above:
where Vi is the volume of a particular constituent (mineral or fluid) of a formation and Σi is the capture cross section of that constituent. Because the corrected tool reads the total capture cross of the formation, this equation forms the basis of interpretation. For example, in the case of a clean sand with a porosity that is filled with oil and water, the tool reading will be
If porosity is known either from openhole logging or the ratio porosity measured by the pulsed neutron tool itself, the various cross sections can be looked up in a table, and it is a simple matter to solve for Sw. Table 3D.8 lists the capture cross sections for several materials that commonly make up reservoirs. Several things can be observed on the basis of this table and the response equation above. First and foremost, for this measurement to be very sensitive to replacing oil by water in the pore space, the water salinity needs to be higher than 50,000 ppm NaCl. Otherwise, the oil and water capture cross sections are so similar that the measured formation cross section will not change perceptibly when one is substituted for the other. These sensitivities can be evaluated easily by setting up a simple spreadsheet and varying the values in the equation above. Eq. 3D.40 also suggests the value of running this log in a baseline monitor mode or time-lapse mode. Differences between successive logging runs will depend only on differences in fluid volumes because the terms involving the unchanging rock matrix will subtract out. In this way, no explicit knowledge of the capture cross sections of the minerals and clays is required to interpret saturation changes.
While it is rarely done, this method is particularly valuable if a baseline run is made early in the production history of the well before Sw has had a chance to change significantly.
Other Applications. Pulsed-neutron logging tools have been applied in nonconventional ways to solve several production-logging problems. Not all of these applications make use of neutron die-away time. Instead, they monitor gamma rays from neutron activation of specific elements that can be thought of as tracers. In other applications, the pulsed-neutron ratio porosity can be used for excavation-effect-style gas interpretations.
Log-Inject-Log Measurements for Residual Oil Saturation
In a variation on the baseline monitor mode of operation suggested above, residual oil saturation can be determined by a log-inject-log procedure. In this procedure, a pulsed neutron log is run over a zone of interest to get a baseline reading. Then, a brine of contrasting salinity is injected into the formation while logging pass after pass with the pulsed neutron tool. Over time, all of the movable, original formation fluids are displaced by the new brine until Sorw (residual oil saturation to waterflood) is achieved. Differences between the preinjection-pass and the final-pass formation capture cross sections give direct access to Sorw. As a bonus, changes in the capture cross-section profile over time during injection highlight permeability variations in the formation.
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.
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.
Gravel-Pack Logs. In another example, silicon activation is used to evaluate gravel-pack quality. 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
A final class of neutron logs, neutron-induced gamma ray logging, records the energy spectra of the induced gamma rays. Because elements excited by neutrons emit characteristic gamma rays, such spectra can be analyzed for elemental concentrations. Most commonly, carbon and oxygen concentrations are used to determine oil saturation, although more detailed geochemical information lies buried in the spectra.
Carbon/Oxygen (C/O) Logs
Recompletion of existing wells and the search for bypassed oil in established fields require knowledge of the current oil saturation behind pipe. In fields with connate water salinity > 20,000 ppm chlorides, PNL logs provide a convenient measurement of water saturation through tubing and casing. If the salinity is low, the neutron lifetime is not determined by the chlorine concentration in the formation. If the salinity is variable, the chlorine concentration does not track the water saturation. In both cases, a PNL log fails to give useful fluid saturations. C/O logging was developed for these situations. The tools exploit inelastic scattering of high-energy neutrons off carbon and oxygen to induce gamma rays. Spectral analysis of the resulting gamma rays yields the amounts of oxygen and carbon in the volume of investigation. Unfortunately, the carbon sensitivity of the measurement is low. The depth of investigation is extremely shallow (only a few inches into the formation). Such a small volume necessarily includes a large percentage of borehole compared to the amount of formation. It is also true that although carbon is present in oil but not in water, and oxygen is present in water but not in oil, the rock matrix (particularly carbonates) may contain significant amounts of both. Together, these result in substantial borehole and formation effects that must be accounted for in the C/O log-interpretation process. To obtain a lithology compensation, most C/O tools also record neutron capture spectra in which elements such as calcium, silicon, and iron reveal themselves. Neutron capture only occurs shortly after the neutrons have slowed down to thermal energies. Buffer timing separates inelastic C/O spectra (during the neutron burst) from capture spectra (slightly after the burst). Experience with C/O logging has been uneven at best.
Geochemical logging is still struggling to find applications. Schlumberger’s latest incarnation is called the environmental capture sonde (ECS). 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.
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.
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.
Visualization-The Multitrack Log Display
Multiple-log interpretation began with, and still revolves around, simple, quick-look visual displays. The familiar third track on a standard log display is the best example. At first glance, it may seem strange and the product of hidebound tradition. The familiar and seemingly arcane display and scales provide a great deal of information at a glance. The three principal porosity logs (density, neutron, and sonic) are scaled and placed so that they overlay and track one another in a particular clean matrix. Violated assumptions as to matrix and fluids stand out when the logs do not overlay. A particular matrix must, of course, be chosen. Most often, all logs are displayed on a limestone matrix. The standard scales are 1.95 to 2.95 g/cm3 for the density log and 0.45 to −0.15 for the neutron log. Running the density/porosity response equation presented above for water-filled limestone confirms that 1.95 g/cm 3 does indeed correspond to 0.45 porosity, and 2.95 corresponds to the curious number −0.15; 140 and 40 μs/ft also correspond, but that is the subject of another chapter.
Fig. 3D.16 shows how the various nuclear-log curves would overlay on these scales for a variety of common lithologies. Note the several porosity units (1 p.u. = 1% = 0.01 fractional) of mismatch between the density and neutron logs when the matrix is sandstone instead of limestone, as is implicit in this choice of scales. This positive crossover corresponds to the apparent density porosity being larger than the apparent neutron porosity. The word "apparent" is belabored on purpose. As discussed above, logs do not read porosity until they have been passed through an interpretation model, and that interpretation model requires assumptions about rock and fluid type. In these examples, the logs are plotted as if they were water-filled limestone. If they are not, assumptions have been violated, and logs will not overlay. The 5 to 7 p.u. of matrix crossover in sandstones plotted as if they were limestones is often mistaken for a gas effect. As the simulated logs show, gas effect is in the same direction but should result in even more crossover depending on the gas properties. In gas crossover, the violated assumptions are fluid properties. The pore space is filled with gas, not water. Gas has a lower density than water, so apparent density porosity will calculate higher than the true porosity. Neutron porosity calculates lower because gas also has a lower hydrogen index than water. Thus, apparent density and neutron porosity are "off" in opposite directions in a gas zone, resulting in large crossover in the conventional log display. As in the discussion of gas response with the individual logs, invasion often confuses the matter. The shallow penetrating density log may be reading entirely from the invaded zone, where mud filtrate (not gas) fills the porosity. With luck, the neutron log may be seeing at least some distance beyond the invasion front, so at least part of its response includes gas-filled porosity. In any case, gas crossover may be largely a neutron-log artifact, and the amount often will be less than expected. Depth (or, more precisely, pressure) also suppresses the gas crossover because gas fluid properties depend strongly on pressure.
In a known sandstone reservoir, the third track is sometimes displayed on a sandstone matrix. In this case, the density log is scaled from 1.65 to 2.65 g/cm3, and the neutron log is scaled from 60 to 0% porosity, in sandstone units. As above, 1.65 g/cm3 does indeed correspond to 60% porosity, assuming a quartz matrix density (2.65 g/cm3) and freshwater-filled porosity (fluid density equal to 1.0 g/cm3). In similar fashion to the limestone display, the curves will overlay each other exactly in clean sandstone. Generally, the neutron porosity will read to the left of the density in shales and to the right in gas-affected intervals.
Visualization-CrossplotsThe 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.
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.
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/cm3 and 40 p.u.).
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/cm3 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/cm3 density and 100% neutron porosity). While this is largely true, neutron logs are not perfect hydrogen index measures.
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.
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 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.
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.
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 Pe log to Umaa, 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 Pe 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 Pe 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.
These are but two examples of the visualizations possible with petrophysical crossplots. Other derived parameters useful in crossplotting incorporate sonic logs. These include the nlith and mlith crossplot (where mlith and nlith are derived from combining density, neutron, sonic, and PE logs) and the crossplot of apparent matrix density (from the neutron-density crossplot) vs. apparent matrix travel time (from the neutron-sonic crossplot). These procedures can reduce the simultaneous solution of more than two log responses to an x-y plot visualization. Much of this can, of course, be done mathematically by solving multiple-log response equations simultaneously. Crossplot visualizations, however, may set limits on the possible formation constituents and define the input parameters to the formation model before attempting a mathematical solution.
Despite the absence of any fundamentally new nuclear-logging measurements on the horizon, the future holds significant promise. LWD continues to mature. By getting the measurements made before significant invasion occurs, LWD mitigates one of the most serious problems of nuclear logs: their limited depths of investigation. New array resistivity measurements better map the invaded zone. This better understanding of the invaded zone should benefit nuclear-log interpretation by letting the analyst better deconvolve the invaded-zone and virgin-zone portions of the tool response. More generally, the evolution and application of simultaneous solver techniques is accelerating. It may soon be common to solve the invasion problem explicitly, simultaneously getting all the invaded and virgin formation fluids correct while interpreting porosity and ensuring consistent solution of all of the log-response equations. This is, after all, where environmental corrections, multiple-log overlays, and crossplots have been heading all along. Nuclear logging is about tools and response models, and for the foreseeable future, progress may come more from more sophisticated handling of the response models than from better measurements. Several once-promising nuclear-log measurements failed to gain traction over the last decade. The passive spectral gamma ray measurement remains a niche tool. Geochemical logging (neutron-induced gamma ray spectroscopy) failed to mature.
|e||=||natural logarithm base|
|E||=||energy dependence of the cross section|
|EGR||=||gamma ray energy|
|hV||=||vertical thickness, L2|
|IH_hc||=||hydrogen index hydrocarbon|
|IH_pf||=||hydrogen index pore fluid|
|IH_w||=||hydrogen index water|
|J||=||radial geometric function|
|Ld||=||neutron diffusion length|
|Lm||=||neutron migration length|
|Ls||=||neutron slowing-down length|
|N||=||a counting number|
|NA||=||Avogadro’s number = 6.02 × 10 23 molecules/gram molecular weight|
|Np||=||particle number density|
|Pe||=||the photoelectric factor|
|Px||=||Poisson probability distribution|
|Ri||=||tool reading for pure material|
|Sorw||=||residual oil saturation to waterflood|
|Sxo||=||flush zone water saturation|
|U||=||density-weighted F pe|
|Ui||=||tool response to flushed zone|
|Umaa||=||U matrix apparent|
|UT||=||tool response integrated to infinity|
|Ux||=||tool response integrated out to a radial distance x|
|Vbh||=||bulk volume of hydrocarbon|
|Vcn||=||volume of clean formation|
|Vf||=||volume of fluid|
|Vi||=||volume of a particular constituent (mineral or fluid) of a formation|
|Vma||=||volume fraction of matrix mineral|
|Vsh||=||volume of shale|
|x||=||particular number of counts|
|Z||=||average atomic number|
|γ||=||gamma ray tool reading in API units|
|γcn||=||gamma ray flux from 100% clean formation component|
|γf||=||gamma ray flux from 100% fluid|
|γma||=||gamma ray flux from 100% matrix|
|γns||=||gamma ray tool reading in nonshale|
|γsh||=||gamma ray tool reading in 100% shale|
|δϕ||=||a change in flux|
|λ||=||mean free path|
|μ||=||mean or expected value of a quantity|
|ρe||=||electron number density|
|ρfl||=||bulk density of fluid|
|ρma||=||bulk density of matrix mineral|
|ρmf||=||bulk density of mud filtrate|
|σ||=||standard deviation of a Poisson distribution|
|σ(E)||=||energy-(E) dependent scattering cross section|
|σco||=||Compton scattering cross section|
|Σabs||=||total neutron capture cross section|
|Σi||=||capture cross section of ith formation component|
|Σw||=||capture cross section of water|
|ϕappi||=||apparent porosity measured by a CNL in lithology i|
|ϕCNL||=||porosity measured by a compensated neutron-logging tool|
|ϕCNLx||=||apparent porosity measured by a CNL in lithology x (e.g., shale)|
|ϕi||=||initial particle flux|
|ϕma||=||apparent matrix porosity|
|ϕo||=||unscattered particle flux|
|i||=||item count or index|
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