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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. This article gives an overview of nuclear logging and how they measure the transport of radiation.
Types of nuclear logs/tools
Nuclear-logging tools exploit only two types of radiation: gamma rays and neutrons. Both follow basic scattering principles but have unique reaction types and cross sections.
- Gamma ray logs
- Neutron logs
- Nuclear logging while drilling (LWD)
- Carbon oxygen logs
- Geochemical logs
Applicability of nuclear logs
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 1 summarizes such a classification scheme. Two types of problems skew tool measurements away from their targets:
- Because a nuclear tool averages over a shallow bulk volume, the borehole often represents a major part of the tool’s response.
- 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^{[1]}^{[2]} 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 ft^{3}. 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
- 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.
Nuclear measurements and statistics
For 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, for example:
- Borehole images
- Nuclear magnetic resonance (NMR)
- Waveform sonic
Counting experiments obey Poisson statistics. A Poisson distribution, as Fig.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
- Neutrons
Depending on the type and energy of the particle, different scattering processes predominate. Fig.1 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 ϕ_{i}. For scattering, the slab is characterized by the number density of potential scattering particles within it (in other words, the number of atoms per cm^{3}). Suppose the slab in the figure has an average of N_{p} atoms/cm^{3}. If the slab is h cm thick, a beam of unit area will encounter and have a chance to interact with N_{p} × 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} cm^{2}. Because humans relate best to numbers they can count on their fingers, a special unit of cross section, the barn, equal to 10^{–24} cm^{2}, 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
ϕ_{i}N_{p}σ 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, ρ_{b}, average atomic weight, A, and Avogadro’s number, N_{A}, 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 2 through 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. 4, produces the unscattered flux that emerges through a thickness of formation, h, as Fig. 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.
Nomenclature
A | = | atomic weight |
e | = | natural logarithm base |
E | = | energy dependence of the cross section |
h | = | thickness traversed |
h_{V} | = | vertical thickness, L^{2} |
N | = | a counting number |
N_{A} | = | Avogadro’s number = 6.02 × 10 23 molecules/gram molecular weight |
N_{p} | = | particle number density |
P_{x} | = | Poisson probability distribution |
S_{w} | = | water saturation |
V_{bh} | = | bulk volume of hydrocarbon |
x | = | particular number of counts |
δϕ | = | a change in flux |
λ | = | mean free path |
μ | = | mean or expected value of a quantity |
ρ_{b} | = | bulk density |
σ | = | standard deviation of a Poisson distribution |
ϕ | = | porosity |
ϕ_{i} | = | initial particle flux |
References
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