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# Multiple log interpretation

Combining the information from multiple log types can provide important information, both in terms of identifying possible errors and understanding subsurface formations. The simplest and most common means of combining multiple logs is in a multitrack log display or a crossplot. Both allow the log analyst to visualize the data more effectively than looking at each log individually.

## 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/cm^{3} 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.

**Fig.1** 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. 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/cm^{3}, and the neutron log is scaled from 60 to 0% porosity, in sandstone units. As above, 1.65 g/cm^{3} does indeed correspond to 60% porosity, assuming a quartz matrix density (2.65 g/cm^{3}) and freshwater-filled porosity (fluid density equal to 1.0 g/cm^{3}). 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.

## Crossplots

The crossplot is another method for visualizing petrophysical data. A clever crossplot can reveal even more about a formation than a standard log-depth display. In a crossplot, the analyst plots one log value on the *x*-axis against a different log value, at the same depth, on the *y*-axis. This is repeated for all depths of interest, creating a scatterplot such as that shown in **Fig. 2**. 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/cm^{3} 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.1** is shown in **Fig. 2**. By convention (and convention is very important to quick-look, visual techniques), the neutron log, expressed in limestone porosity units, is plotted on the *x*-axis against the density log in g/cm^{3} on the *y*-axis, with the scales reversed (i.e., from highest to lowest density). Ideally, because both are porosity logs, points of a given porosity in a pure lithology will fall along a diagonal line. Such a line represents the simultaneous solution of the density and neutron mixing laws as a function of varying porosity. Three such lines are generally plotted as overlays on this crossplot. They correspond to a calcite, dolomite, or quartz matrix with water-filled porosity. If the neutron log were a true hydrogen index log, the lines would extend from a y -intercept corresponding to the grain density of the particular lithology (the zero-porosity limit) to a common upper-right point corresponding to 100% water (i.e., 1.0 g/cm^{3} density and 100% neutron porosity). While this is largely true, neutron logs are not perfect hydrogen index measures.

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.2**, 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 **Table 1** and **Table 2**, respectively. Edmundson and Raymer^{[1]} 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.2** 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. 3** 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. 4**. As in the neutron-density example, the sample data from the logs in **Fig.1** are plotted as small squares. This display crossplots synthetic variables, not raw logs. On the *x*-axis is the *U* matrix apparent. As discussed above, this transformation converts the nonlinear *P*_{e} log to *U*_{maa}, a characteristic that obeys linear volumetric mixing. On the *y*-axis is apparent grain density from the neutron and density logs. Somewhat simplified, this is the grain density needed to produce the neutron-log porosity from the density-log reading, assuming water-filled porosity. The blue, ternary grid shows the generic endpoints for sandstone, calcite, and dolomite. The various labels (e.g., coal and anhydrite) mark the locations at which those minerals should ideally fall on the plot. This technique, sometimes called the matrix-identification (MID) plot, is especially useful in unwinding multicomponent lithologies, as the widely separated overlay points suggest. It gets much of its power from the fact that *P*_{e} is largely porosity independent. This accounts for the near-vertical trends in much of the overlaid data from **Fig. 1**. As in all crossplots, uncorrected environmental effects may show up as misplaced points, the hallmark of a violated assumption. For instance, because the *P*_{e} 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 *n*lith and *m*lith crossplot (where *m*lith and *n*lith 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.

## References

- ↑ Edmundson, H.N. and Raymer, L.L. 1979. Radioactive Logging parameters for Common Minerals. The Log Analyst 19 (1): 38.

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