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. 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.

Neutron-scattering porosity tools

By 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 1 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. 1 outlines the conversion from tool reading to porosity.

Fig. 1 – The nuclear-log-interpretation process can be seen as a chain of inferences, as illustrated by the neutron-porosity log.

Neutron log interpretation

Because 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. 2 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.

Fig. 2 – Neutron-density crossplot showing where the common lithologies in Fig. 2 (below) fall.

To first order, once the log has been environmentally corrected, its reading can be characterized by a linear mixing law

………………..(1)

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 1. As can be seen from the matrix overlays on the density-neutron crossplot (Fig.2), 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

………………..(2)

where ϕ app and IH are used interchangeably because both are calibrated to the apparent neutron porosity of pure water.

Fluid effects

The hydrogen index of the pore fluid (Table 2)and its equivalent apparent neutron porosity (Table 1) can have a much bigger effect. The difference between pure water, most brines, and typical oils is small, but as the table shows, gas can have much different neutron-response properties. While the presence of gas increases the apparent porosity seen by a density log, it decreases the apparent porosity seen by the neutron log. This is the source of “gas crossover” on neutron density-log displays (see Fig. 3). Moreover, the shallow-reading density log frequently is an invaded-zone measurement, completely masking the gas effect on it. Because the neutron porosity is deeper reading, it is often the only log that can be used for gas detection. Even when not completely reading the invaded zone, the neutron-porosity log probably reads a mixture of invaded and virgin formation. This leads to a very complex response equation, even in a clean reservoir:

………………..(3)

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.

Fig.3 – Schematic nuclear-log responses for some common lithologies.

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.

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, while Monte Carlo models treat geometry as well as composition.

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.

Nomenclature

IH	=	hydrogen index
IH_hc	=	hydrogen index hydrocarbon
IH_pf	=	hydrogen index pore fluid
IH_w	=	hydrogen index water
Sw	=	water saturation
Sxo	=	flush zone water saturation
Vi	=	volume of a particular constituent (mineral or fluid) of a formation
Vsh	=	volume of shale
Σi	=	capture cross section of ith formation component
ϕCNL	=	porosity measured by a compensated neutron-logging tool
ϕCNLx	=	apparent porosity measured by a CNL in lithology x (e.g., shale)
ϕe	=	effective porosity
ϕma	=	apparent matrix porosity
ϕsh	=	shale porosity
ϕappi	=	apparent porosity measured by a CNL in lithology i