Lithology Indicators

Logs can be used to interpret lithology. The most useful logs for this purpose are

• gamma ray: natural gamma and gamma ray spectra

• density: φD and ρb

• neutron: φN

• acoustic: ∆t

In some cases, resistivity or conductivity logs can be of value.

With the exception of the photoelectric factor measurement, ρe, and the natural gamma ray spectra log, no single porosity tool measurement gives, by itself, an

indication of lithology. However, much useful information can be gathered by using combinations of porosity tool measurements.

The most useful combinations are

• crossplots such as ρb versus φN, ρe versus ∆t, and ∆t versus φN

• the M-N plot

• the MID plot

• combinations of the above with ρe and/or the gamma ray spectra measurements of K, U, and Th

In many cases, it is possible to scale porosity logs in such a way that two curves, when overlaid, give an immediate visual indication of the rock type. These methods are to be encouraged. A very good picture of a geologic column may be gained by simply color-coding an appropriately scaled combination porosity log suite. In mixed lithology it is essential to identify the rock type in order to pick correctly the parameters needed to perform other log analysis calculations for porosity and water saturation. Correct identification of lithology also assists in well-to-well correlation.

Estimating Shale Content from Gamma Ray Logs

Since it is common to find radioactive Materials associated with clay minerals that

constitute shales, it is also common practice to use the relative gamma ray deflection

as a shale volume indicator. The simplest procedure is to rescale the gamma ray

between its minimum and Maximum values (in one consistent geologic zone

consisting of both sands and shales) from 0% to 100% shale. A number of studies

have shown that this is not necessarily the best method, and alternative

relationships have been proposed. To explain these methods in detail, the gamma

ray index is defined as a linear rescaling of the OR between GRmin and GRmax such that

If this index is called X, then the alternative relationships can be stated in terms of X as follows: Relationship Equation

Linear Vshale = X

Clavier Vshale = 1.7 - (3.38 - (X + .7)2)1/2

Steiber

Bateman Vshale = X(X + GR factor) In the Bateman equation, the GR factor is a number chosen to force the result to imitate the behavior of either the Clavier or the Steiber relationship. Figure 1 illustrates the difference between these alternative relationships.

Figure 1

Gamma Ray

Figure 1 illustrates a gamma ray spectral log.

Figure 1

Note that in the left-hand track both total gamma ray activity (SGR) and a "uranium-

free" (CGR) version of the total activity are displayed. Units are in API. In the two

right-hand tracks the concentrations of U, Th, and K are displayed. Depending on the

logging service company, the units may be in counts/sec, ppm, or percentage.

Interpretation of the gamma ray spectra log is a relatively new and developing art.

One approach is to take ratios of elemental concentrations as indicators of formation properties or of formation type.

The thorium/uranium (Th/U) ratio, for example, varies with depositional

environment; it is highest for a continental, oxidizing environment and lowest for a

marine, reducing one that produces, for example, black shales. It can thus be used

in gauging the distance to ancient shorelines or the location of rapid uplift during the

time of deposition. Similarly, stratigraphic correlations of transgressions or regressions are possible using the Th/U ratio.

The uranium/potassium (U/K) ratio has been found to be a good indicator of the

potential of source rocks in argillaceous sediments. The ratio also correlates well with

vugs and natural fracture systems and, at times, with hydrocarbon shows in both clastic and carbonate reservoirs.

The thorium/potassium (Th/K) ratio has proved useful in rock typing. It is

particularly useful in clay typing, because it increases from glauconite through to

bauxite ( Figure 2 ).

Figure 2

Alternatively, the uranium versus potassium crossplot ( Figure 3 ) may be referred to

as a guide to rock type.

Figure 3

If additional data are available -- for example, the photoelectric absorption

coefficient (ρ e) -- then additional plots of the sort shown in Figure 4 and Figure 5 can be made.

Figure 4

Figure 5

Field presentations of gamma ray spectral logs can assist the analyst in the task of

mineral identification by offering curve plots with the ratios of the three components

(U, Th, and K) already computed. Figure 6 gives an example of one such

presentation.

Figure 6

The left-hand track shows total gamma ray together with a uranium-free curve. The

middle track gives three ratios: U/K, Th/U, and Th/K. The right-hand track gives a

coded display on which the coded area represents the formations with both the

highest potassium and the highest thorium content, generally the non-reservoir rocks, such as shale.

Use of Porosity Logs for Lithology Identification

Logs can be used as indicators of lithology. The most useful curves for this purpose

are

density - ρb and Pe neutron - φN acoustic - λ gamma ray - natural gamma and gamma ray spectra

With the exception of the photoelectric factor measurement, Pe, and the natural gamma ray-spectra log, no single porosity tool measurement will, by itself, give an indication of lithology. However, we can gather much useful information by using combinations of porosity tool measurements.

The most useful combinations are

• crossplots such as bulk density versus neutron porosity, bulk density versus interval transit time, and interval transit time versus neutron porosity

• the "M" and "N" plot

• the "MID" plot

• one or more of the above with Pe

In many cases it is possible to scale porosity logs in such a way that two curves, when overlaid, immediately give a visual indication of the rock type. The use of these methods is to be encouraged. A very good picture of a geologic column may be gained by simply color coding an appropriately scaled combination porosity log suite. In mixed lithology it is essential to identify the rock type to choose the correct parameters needed to perform other log analysis calculations for porosity and water saturation. Correct identification of lithology will also assist in tasks of well-to-well correlation.

Conventional Porosity Logs

The neutron-density crossplot appears in two versions. Figure 1 is to be used in the

case of fresh mud filtrates with ρf = 1.0,

Figure 1

and Figure 2 is to be used in the case of salt mud filtrates with ρf = 1.1.

Figure 2

The differences between the two are slight. The lithology is indicated by the location

of the plotted point. The positions of various nonporous minerals are shown on these

charts as points. However, the porous reservoir rocks appear as lines. Shales

typically fall in the southeast quadrant of the chart in Figure 1 .

A visual reading of a log display on compatible limestone scales yields similar

information ( Figure 3 ).

Figure 3

Note that the scale for the density log is from 2 to 3 gm/cc across Tracks 2 and 3.

The neutron, in limestone porosity units, is scaled from 42 to -18% across the same

tracks. The 0% limestone point thus coincides for both devices at four divisions from

the left of Track 3.

Where the neutron curve lies to the right of the density curve, sandstone is

indicated. This corresponds to the area to the northwest of the limestone line in

Figure 1 . When the two coincide, limestone is indicated. Large separations, such as in anhydrite, are easily recognized.

Another frequently used pair are the neutron and sonic devices. When a density log

is missing or is error prone due to bad hole effects, this plot should be used. Figure 4

illustrates the neutron-sonic crossplot.

Figure 4

It is used in much the same way as the neutron-density crossplot.

Shales typically fall near or to the right of the dolomite line.

The final combination of our trinity of porosity devices is the density-sonic crossplot (

Figure 5 ).

Figure 5

This plot is particularly useful in identifying minerals as well as reservoir rocks.

M-N Plot

Pairing of Porosity devices does not make full use of all the data when three devices

are available. If a three-dimensional graph could be built with X, Y, and Z axes

corresponding to the neutron, density, and sonic responses, then identifiable

minerals would occupy unique Points in space. Cases in which a lithologic mixture

exists could be more easily interpreted.

For example, a mixture of sand and dolomite appearing as limestone on the neutron-

density and neutron-sonic Plots would be correctly identified by the density-sonic

plot. Various attempts have been made to resolve the Problem of reducing three log

readings to a two-dimensional crossplot. One of the first, the M-N plot, requires that the two parameters M and N be defined as

where ρf is fluid density. Note that φ N needs to be in fractional units and that φ N fluid is assumed to be 1.0. Effectively, these two definitions are algebraic methods of finding the slope of a line that passes through a Plotted point and the 100% Porosity point. Since any pure reservoir rock will plot on a line on the crossplots, and the slope of this line is substantially constant, that slope is a characteristic of the rock type. Having defined M and N and determined them for a given point on the log, their values may be plotted on an M-N plot ( Figure 1 ).

Figure 1

The M-N plot has a number of shortcomings. For example, it is not truly porosity

independent in the case of dolomite since the neutron response is not linear. Another

annoying feature is that the plotted point depends on ρf, the fluid density. Finally, the actual values of M and N for common minerals and reservoir rocks are not easy to

remember and have no particular significance in themselves. Although the M-N plot

is still used by some analysts, it has largely been superseded by another plot that

accomplishes the same end result more elegantly – the MID plot.

The Matrix Identification Plot (MID)

This plot requires three porosity tools for input. Its main advantages over the M-N

plot include its independence from porosity and mud type and the fact that it uses

meaningful parameters directly related to rock properties that are easily

remembered.

The neutron and density logs are combined to define an apparent matrix density,

(ρma)a . The neutron and sonic logs are combined to define an apparent matrix travel time, (∆tma)a These two parameters are then crossplotted to define lithology mixtures.

The value of (ρma)a a can be computed from the equation

whence

Likewise,

However, in practical log evaluation, these values can be found more simply from charts. For example, Figure 2 defines (ρma)a for any ρb,

Figure 2

φ N pair and Figure 3 defines (∆tma)a for any ∆t, φ N pair.

Figure 3

Figure 4 should be used in place of Figure 3 when ρf = 1.1 (salt mud filtrate).

Figure 4

Once (ρma)a and (∆tma)a have been determined, they are crossplotted on the MID plot chart shown in Figure 5 .

Figure 5

When using either the MID plot or the M-N plot, it is useful to have available a

reference table which summarizes the values of ρ ma, ∆t ma, M and N for common minerals and reservoir rocks.

Photoelectric Factor (Pe)

In most lithologies, minerals exist in combination. Since the overall photoelectric

index is not a linear function of the Pe values of the individual components, a new

term, the volumetric photoelectric absorption index (U), has to be calculated. This index is the product of electron density and the photoelectric absorption index.

An approximation is usually made by using bulk density ρ b rather than electron density ρ e . In a complex lithology formation, the measured volumetric photoelectric absorption index is the sum of the individual volumetric photoelectric absorption indexes weighted by their relative proportions in the formation:

U = U1V1 + U2V2 + ... U1 = volumetric photoelectric absorption index of mineral 1

V1 = volumetric fraction of mineral 1 in the formation, etc.

For a porous, single-mineral, shaly formation containing hydrocarbons, a general

equation can be written as

matrix water hydrocarbon shale

term term term term Table 1 shows that the absorption coefficient, Uf, of fresh water is substantially lower than any of the matrix coefficients, Uma, and can therefore be neglected without introducing a major error.

Table 1

Only if very salty muds are used would the term need to be included. The hydrocarbon contribution can also be neglected since Uhy is less than 0.12.

If the shale content of the formation is included in the matrix, the foregoing

equations can be combined to produce the relationship

or more strictly

This equation can be solved using the nomogram shown in Figure 1 .

Figure 1

For a quick-look interpretation, the porosity φ can be taken from a density-neutron crossplot.

In complex lithology (a mixture of up to three minerals), a second physical

parameter is needed to define the individual minerals and their volume percentage in

the formation. The apparent matrix density (ρma)a derived from the density-neutron crossplot may be used or (ρma)a can be calculated using the standard formula:

where:

ρf = fluid density of the invaded zone

φf= apparent porosity from density and neutron data

Once the values of (ρma)a and (Uma)a have been calculated, they may be crossplotted

against one another to help in identifying lithology. Figure 2 shows such a crossplot,

made over a depth interval that includes anhydrite, dolomite, and shaly sand.

Figure 2

An overlay can be constructed ( Figure 3 ) which, when placed over the crossplot,

indicates the most probable mineral composition. Of course, geological knowledge

and cuttings analysis are a substantial help in selecting the main contributing

components.

Figure 3

Once the main mineral components of the formation have been identified, a plot can

be made to determine their relative proportions. Figure 4 illustrates a valid plot for a

quartz-calcite-dolomite composition, with a grid already established.

Figure 4

Continuous computation of the relative proportions of up to three minerals is possible

using this approach. Wellsite computation and display can be illustrated by an

example. A section logged with neutron, density, and Pe curves is first analyzed by a

(Uma)a versus (ρma)a crossplot ( Figure 5 ), which indicates the three main components of the formation to be magnesite, dolomite, and anhydrite.

Figure 5

The relative proportions of the three minerals at each depth are computed according

to the data points within the defined triangle. Figure 6 shows the corresponding

playback over the same interval.

Figure 6

The average grain (matrix) density (RHGA) is displayed in Track 1; the lithology in

the depth track; and the photoelectric absorption index (PEF), density porosity (DPL), average porosity (PHIA), and neutron porosity (NPL) in

Tracks 2 and 3. The porosity values are scaled in limestone units. Because of the

statistical nature of the measurements, not all data points will plot inside the

selected solution triangle defined by the three minerals. When a point falls outside

the triangle, a flag is raised on the left edge of Track 1, and only one or two minerals will be displayed.

Drilling muds loaded with barite present a burdensome problem for the lithodensity

log. If there is a high concentration of barite in the mud cake or in the drilling mud, the very high Pe value of barite can severely affect the quality of the Pe curve.

Both gas in the formation pore space and barite in the mud can be detected on a

(Uma)a versus (ρma)a crossplot ( Figure 7 ).

Figure 7

Because of its high atomic number, barite moves the (Uma)a points toward the right

(higher (Uma)a Gas influences the (ρma)a values, but has little effect on (Uma)a, and so

moves the points upward.

Chaveroo Method

A classical method of solving multimineral log problems is historically known as the

Chaveroo method. It was developed when the Chaveroo field was being actively

drilled and logged in New Mexico in the l960s. The method reduces the problem to a

simple inversion of a "response" matrix. It is most easily understood by reference to the Martini Problem.*

* I am indebted to John Doveton of the Kansas Geological Survey for the original

Martini Problem, which I have adapted slightly for the present purpose.

A log analyst, after a hard day’s work, sought comfort and deserved repose in a bar.

He ordered a martini and was immediately struck by the harmonious and mellow

proportions of its ingredients. Wishing to learn the secret of the "perfect martini," he

asked the bartender to tell him how much gin, dry vermouth, and sweet vermouth

had been used. The bartender (a geologist perhaps?) could only reply that it was

mostly made of gin "with occasional vermouthian tendencies." The analyst thereupon

set out to back-calculate the relative proportions of the mix using the alcohol and

sugar contents of the ingredients and of the mixture. He "logged" his martini to find

it had 35% alcohol and 3.4% sugar. He consulted a reference book to find the

amount of alcohol and sugar in each ingredient. Here is what he found:

Alcohol Sugar

martini 35% 3.4%

gin 47% 0%

dry vermouth 18% 3%

sweet vermouth 16% 16%

He solved the problem by setting up three simultaneous equations:

alcohol: 35 = 47 VG + 18 VDV + 16 VSV sugar: 3.4 = 3 VDV + 14 VSV material balance: 1 = VG + VDV + VSV

where VG is the fraction of gin, VDV the fraction of dry vermouth, and so on.

He then solved the three equations to find VG, VDV, and VSV, the respective

fractions of gin, dry vermouth, and sweet vermouth.

This is not a trivial example. Each logging tool can be used to set up a response

equation describing a lithology mix. If VL, VD, and VS are the bulk volumes of

limestone, dolomite, and sandstone in some lithology mixture, for example, the

density of the mixture can be expressed in terms of the relative quantities of each, and the density tool response to each:

In a similar fashion, the sonic and neutron logs can also define a response equation.

∆t = 47.5 VL + 43.5 VD + 55.5 VS + 189 φ

φΝ = 0.07 VD + (-0.03 VS) + φ

Finally, the material balance equation reveals that 1 = VL + VD + VS + φ

Elaboration of examples such as these should convince even the most mathematically inclined analyst that level-by-level solutions to matrix inversion problems using only a hand-held calculator are not recommended. Clearly, this type of processing is best left to a computer that has been fed log data in digital form.

In the last example, three independent formation measurements were combined to

solve for four unknowns: porosity and the volume fractions of limestone, dolomite,

and sandstone. Since it requires four equations to solve for four unknowns, the

material balance equation (stating that the sum of the component fractions is equal

to one) provided the missing equality. Thus, in general, given "n" independent logging measurements, a solution may be found for "n + 1" components.

For example if, in addition to neutron, density, and sonic measurements,

measurements of Pe and gamma ray were also available, then a solution could be

sought for two additional components -- anhydrite and salt, for example.

While the mathematics of the method is straightforward, its weakness lies in the

analyst’s choice of components for which the equation is intended to solve. What

happens, for example, if a heavy mineral (e.g., pyrite with Pma = 4.99 gm/cc) is

present but not specified as a component for solution in the equation? There is a

good chance that, in such a case, the point in question will fall outside the solution

polygon and result in an apparent negative amount of one of the other components meant to be solved for in the equation.

Many computer programs have been written to handle the Chaveroo approach to log

analysis in multimineral environments. Some have elegant logic to handle cases

where an unspecified component appears or a negative amount of a specified

component results. Such programs have their place and their application in situations

where either the lithology is reasonably well known (from experience, core analysis,

etc.) and where a knowledgeable analyst is employed to select both the components

and their correct end points. An example of the result obtained from this kind of

processing is shown in Figure 8 .

Figure 8

The column logged is Predominantly anhydrite and dolomite with occasional

appearances of sand and gypsum. The well was completed in the intervals shown,

acidized and fractured and put on production at 609 BOPD and 6 BWPD.

Application of the Chaveroo method generates only one answer set for a given input

set, since the system is exactly determined. Once the response equations are written

and the end points chosen for each component, one, and only one, solution can be

found for any given set of log data. What happens then if our log data are subject to

statistical variations (neutron, density, gamma ray) or our response model is

inaccurate? Logically, the answers produced will also suffer from such variations and

inaccuracies and there will be no way to assess the magnitude of the error. In

general, it can be stated that the most accurate assessment made by a Chaveroo-

type processing will be that of porosity. However, if the inaccuracies are to be properly gauged, another type of processing is called for.

Overdetermined Systems

Naturally, the interpretation model selected by the log analyst depends a great deal

on the logging program and the log responses. Ideally, the system should remain

balanced or overdetermined; in other words, the number of log inputs should not be

less than the number of unknowns. For example, with five log measurements (ρb, φ N, ∆t, Pe, and GR) a solution is sought to the relatively simple problem of finding the relative proportions of three components (sand, lime, and dolomite). Now,

instead of only one solution being possible, many are. Any three log measurements

suffice to form an exact solution subset, and in this case there are 10 different ways

to choose three logs out of five. (The reader may choose to write down all possible

combinations of any two log measurements to be omitted.) If the log measurements

are perfect and the model perfect, then all 10 possible solutions will coincide. In

practice this never happens, and the result is a set of 10 possible answers for each

component. Which one is correct? For each possible answer, a value for the original

log measurements may be back-calculated. For example, the density tool response

equation may be written

where ρ 1, ρ2 etc. are the log responses to components 1, 2, etc., and V1, V2, etc. are the volume fractions of components 1, 2, etc.

If V1,1 is the estimated value of V1 by the first of our 10 possible answer sets, then

the back-calculated value of ρ b will be

This may then be compared with the actual log reading of b and an error function defined:

If the process is repeated for all the possible solutions, the individual error function may be summed. The same procedure may then be repeated in turn for each of the logging measurements.

The problem now transforms itself into one of minimizing the error function; i.e., a

solution set in which the differences between the observed log readings and the

back-calculated log values are minimal is the most probable solution set.

This type of processing, generically referred to as global logic, may equally be

applied to any log response equation, including resistivity log responses to both the

invasion process and to water saturation variations. Figure 9 shows a generalized

flow diagram of the logical steps involved in such a processing chain.

Figure 9

Advantages of global logic processing are that places where the raw log data are

unreliable will become evident and that in zones of special interest the analyst will

have a rigidly mathematical estimate of the probability of the analysis being correct.

A major disadvantage is that the processing is so complex it requires specialists to apply it.