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Nuclear log interpretation
Nuclear log interpretation is simply the practice of solving tool-response mixing-law equations with the judicious application of some assumptions and constraints.
Generalized single log 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.2.
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.
More advanced interpretation
Even though log analysts’ primary interest is only in virgin formation properties, there are at least three regions that contribute to a nuclear log measurement:
- The borehole that includes:
- Borehole size
- The tool body
- The invaded zone
- 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.1 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.2. 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.4. 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.3 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.
|IH_hc||=||hydrogen index hydrocarbon|
|IH_w||=||hydrogen index water|
|J||=||radial geometric function|
|Ri||=||tool reading for pure material|
|Ui||=||tool response to flushed zone|
|UT||=||tool response integrated to infinity|
|Ux||=||tool response integrated out to a radial distance x|
|Vi||=||volume of a particular constituent (mineral or fluid) of a formation|
|Vsh||=||volume of shale|
|x||=||particular number of counts|
|γ||=||gamma ray tool reading in API units|
|γns||=||gamma ray tool reading in nonshale|
|γsh||=||gamma ray tool reading in 100% shale|
|Σi||=||capture cross section of ith formation component|
|ϕCNL||=||porosity measured by a compensated neutron-logging tool|
|ϕma||=||apparent matrix porosity|
|ϕo||=||unscattered particle flux|
|i||=||item count or index|
- Patchett, J.G. and Wiley, R. 1994. Inverse Modeling Using Full Nuclear Response Functions Including Invasion Effects Plus Resistivity. Paper H presented at the 1994 SPWLA Annual Logging Symposium, Tulsa, 19–22 June.
- Sherman, H. and Locke, S. 1975. Effect of Porosity on Depth of Investigation of Neutron and Density Sondes. Presented at the Fall Meeting of the Society of Petroleum Engineers of AIME, Dallas, Texas, 28 September-1 October 1975. SPE-5510-MS. http://dx.doi.org/10.2118/5510-MS
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