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18. Lithology Identification From Porosity Logs

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18 LII[THOLOGY IDENTIF'ICATION FROM POROSITY LOGS INTRODUCTION Porosity determination using the various logging devices presented in earlier chapters relies on a knowledge of the parameters related to the type of rock being investigated. In the case of the density tool, the density of the rock matrix must be known. The matrix travel time is used in interpreting the compressional wave interval transit time. In order to reflect porosity accurately, the matrix setting for the neutron tool must correspond to the rock type for the value of $,. Determining these parameters is not much of a problem if one has good geological knowledge of the formation and if the lithologies encountered are simple, such as a clean sandstone or limestone reservoir. However, what do you do when you are uncertain of the lithology, or if it is known to vary considerably in its composition, as in the case of limestone formations with variable inclusion of dolomite and anhydrite, or a sandstone with substantial calcite cementing? To address this uncertainty, this chapter considers the question of lithology identification from log responses. The logs used are those which are primarily responsive to porosity yet retain some residual sensitivity to the rock matrix type. The techniques employed are simple graphical analyses developed in the 1960s and still useful today for quick evaluations. For the graphical techniques considered, the term matrix is used to designate the principal rock types: sandstone, limestone, and dolomite. The lithological description often includes, in addition to the principal rock type, 417
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Page 1: 18. Lithology Identification From Porosity Logs

18 LII[THOLOGY IDENTIF'ICATION FROM POROSITY LOGS

INTRODUCTION

Porosity determination using the various logging devices presented in earlier chapters relies on a knowledge of the parameters related to the type of rock being investigated. In the case of the density tool, the density of the rock matrix must be known. The matrix travel time is used in interpreting the compressional wave interval transit time. In order to reflect porosity accurately, the matrix setting for the neutron tool must correspond to the rock type for the value of $,,. Determining these parameters is not much of a problem if one has good geological knowledge of the formation and if the lithologies encountered are simple, such as a clean sandstone or limestone reservoir. However, what do you do when you are uncertain of the lithology, or if it is known to vary considerably in its composition, as in the case of limestone formations with variable inclusion of dolomite and anhydrite, or a sandstone with substantial calcite cementing?

To address this uncertainty, this chapter considers the question of lithology identification from log responses. The logs used are those which are primarily responsive to porosity yet retain some residual sensitivity to the rock matrix type. The techniques employed are simple graphical analyses developed in the 1960s and still useful today for quick evaluations.

For the graphical techniques considered, the term matrix is used to designate the principal rock types: sandstone, limestone, and dolomite. The lithological description often includes, in addition to the principal rock type,

417

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the presence of several minerals often encountered in logging. These include anhydrite, halite, gypsum, and others. To geologists, this list is limited but, for the most part, it usually is sufficient to solve the question of determining porosity in a previously unknown mamx.

In more complex lithologies there can be mixtures of many different minerals. For these cases one would like to have the use of a large number of logging measurements, each with a slightly different sensitivity to the various minerals, in order to make a complete mineralogical analysis. Graphical techniques for this type of analysis are inadequate. However, the problem can be solved numerically, and several approaches are considered. The ultimate approach to this problem may be based on nuclear spectroscopy and geochemistry, which is beyond the scope of this book but is touched on in the next chapter. This chapter is confined to the complex lithology analysis which can be unscrambled using conventional logging devices. It may, at some points, resemble a ramble through the chartbook.

GRAPHICAL APPROACH FOR BINARY MIXTURES

If we consider, for a moment, the response of the three porosity tools- density, neutron and sonic- we can idealize them as follows:

P b = f (4, lithology, * - .) +,, = f (+, lithology, - - .)

At = f (+, lithology, * - a) . All three contain a dependence on porosity and a perturbation due to lithology. It seems natural to use these three measurements, two at a time, to eliminate porosity and thereby to obtain the lithology. This is precisely what is done in a number of well-known cross plotting techniques which are presented next, in order of their increasing usefulness.

The first is the density-sonic cross plot shown in Fig. 18-1. Because of the differing matrix densities and travel times for the three principal matrices, three distinct loci are traced out as water-filled porosity increases. As can be seen from the figure, there is not a great deal of contrast between the matrix endpoints. Since all the lines must join at 100% porosity, a bit of uncertainty in the measured pair (Pb, At) could cause considerable confusion in the ascribed lithology.

This is partially overcome in the next combination considered, neutron- sonic, which is shown in Fig. 18-2. In this case, the travel times are plotted as a function of the apparent limestone porosity for a thermal neutron porosity device. Due to the mamx effect of the neutron device, there is considerably more apparent separation between the three principal matrices which are shown.

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Lithology Identification from Porosity Logs 419

0 0 0)

>. tJJ C al

. 1

c .-

n Y m d a

f

At, Sonic Transit Time (ps/ft)

Figure 18-1. A density-sonic cross plot. Porosity variations of three major minerals produce trends of compressional interval transit time and bulk density. Location of measured pairs of values can help to identify the matrix mineral. Deviations from the trends can sometimes be attributed to significant portions of other minerals, some of which are also shown on the plot. From Schlumberger.'

The standard interpretation cross plot for binary mixtures, however, is the neutron-density, shown in Fig. 18-3. In this case the bulk density is plotted as a function of the apparent limestone porosity. The scale on the right is the conversion of the density to the equivalent limestone porosity for fresh-water pore fluid. To adjust this chart for other fluid densities, the density values are usually rescaled in accordance with the relation:

P b = 4% 4- (l-$)&na 9

where pfl is the density of the fluid filling the pores.

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420 Well Logging for Earth Scientists

Figure 18-2. A neutron-sonic porosity cross plot showing an apparently larger resolving power for lithology discrimination. From Schlumberger.’

As an example of the use of the neutron-density cross plot, refer to the log of Fig. 18-4. It shows two apparent porosity traces from the density and neutron devices, scaled in limestone units. At the depth indicated, 15335’, the density porosity reads about 2 PU, and the neutron 14 PU. To determine the lithology, we need only to find the intersection of these two points on Fig. 18-3. The surest way is to use the porosity scaling on the matrix curve for which the log was run. In this case it is limestone. By locating the 2-PU point on the Limestone curve, we see that the corresponding density value is about 2.68 g/cm3. Dropping a vertical line from the 14-PU point for the neutron value (to the intersection with the horizontal density value), we see

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Lithology Identification from Porosity Logs 421

+", Neutron Porosity (Limestone)(pu)

Figure 18-3. A neutron-density cross plot which is routinely used for lithology and porosity determination in simple lithologies. From Schlumberger.'

that the pair of points corresponds to a dolomite of about 8 PU, which is marked as point a in Fig. 18-3.

If the log of Fig. 18-4 had been run on a sandstone mamx and yielded the same apparent porosity values, the interpretation would be quite different. This can be seen by finding the 2-PU point on the sandstone curve in Fig. 18-3 which corresponds to a bulk density of about 2.62 g/cm3. The 14- PU sandstone porosity for the neutron is equivalent to the reading expected in a 10-PU limestone. The intersection of these two points is marked at b. This corresponds to a formation which seems to be mostly limestone but could be a mixture of dolomite and sandstone, an unlikely possibility.

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I Porosity Index I%J LS Matrix I Compensated Formation Density Porosity

Compensated Neutron Porosity I

Figure 18-4. Log of apparent limestone porosity from a neutron and density device. The logged interval includes anhydrite, dolomite, and a streak of limestone. From Dewan?

We have already seen the effect of gas on the neutron and density log presentation. Fig. 18-5 is another example which shows the evident separation in a 25' zone centered at about 1900'. The neutron reading is about 6 PU, and the density 24 PU. Both are recorded on an apparent limestone porosity scale. The location of this zone is shown as point C on the cross plot of Fig. 18-3. It is seen to be well to the left of the sandstone line. The trend of the gas effect is shown in the figure. Following this trend, the estimated porosity is found to be about 17.5 PU if the mamx is assumed to be limestone.

In the preceding example, two things are to be noted The first is that even in the case of simple lithology mixtures, if the presence of gas is admitted, there is not enough information available from the neutron and density readings alone to decide on the matrix. From the available information, one could equally conclude that the formation was a gas-bearing sandstone as well. The second is the contrast between this visual method of identifying gas and the slowing-down length approach discussed in Chapter 12.

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Lithology Identification from Porosity Logs 423

Porosity Index (%) Limestone Matri :ompensated Formation Density Poro

Compensated Neutron Porosi

I(f

Figure 18-5. Gas separation between the neutron and density complicate the lithoiogical analysis. From Dewan?

The popularity of the neutron-density log combination for gas detection must be tempered with the need for knowing the matrix. Fig. 18-6 is a good example of a false gas indication running over nearly the entire section. What we have here is a tight sandstone formation (with some gas, perhaps) which has been presented in limestone units. The crossover is purely an artifact of the presentation in limestone units. Plotting a few of the points taken from the log onto Fig. 18-3 will be convincing.

It should be apparent from the previous few examples that in the case of gas, at least, additional information concerning the lithology is necessary. It could come from the addition of the sonic measurement, for example. Another possibility is use of the P,, which can be obtained simultaneously with the density measurement. Fig. 18-7 shows an example of its use in a sequence of alternating limestones and dolomites. The first track contains the P, with sections of dolomite and limestone clearly indicated. The density and

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Gamma Ray. API Units

0 150

6 16 Caliper Diam. in Inches -------------

I 1

I Porosity Index (%) LS Matrix Compensated Formation Density Porosity I

I Compensated Neutron Porosity I

Figure 1M. A neutron and density log in a carbonate. An inappropriate matrix setting has been used which indicates the presence of gas through most of the logged interval. From Dewan?

neutron values which are presented in tracks 1 and 2 are on a scale for which water-filled limestone will show nearly perfect tracking. In the limestone zone, there is a clear separation indicating gas. However, in a short interval just below 10,000’, the density and neutron readings are nearly indistinguishable. Without additional information, this would be taken as a water-filled limestone. This can be verified by plotting the peak value of 21 PU for the neutron and 2.48 g/cm3 for the density on the cross plot of Fig. 18-3. However, with the additional knowledge of the P,, it can be seen to be a gas-bearing dolomite.

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9901

1000

Lithology Identification from Porosity Logs 425

ite

tone

Figure 18-7. The companion P, curve simplifies lithology determination in this sequence of alternating limestone and dolomites. The neutron and density information alone would not indicate gas in the lower interval. From Dewan?

COMBINING THREE POROSITY LOGS

Before the availability of the P, measurement, several methods were devised to combine the lithology information from the three porosity tools. The first approach was called the M-N cross plot. It attempts to remove the gross effect of porosity from the three measurements to deduce the matrix constants.

As indicated in Fig. 18-8 a combination of the sonic and density measurements is used to define the parameter M, which is nothing more than the slope of the At-pb curve which varies slightly between the three major

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I "f I

0 , !"ma , 4.0 3.0 2.0 1 .o

Density pb(grn/cc)

Fluid Point (100% 4)

N=(+,)f - (+,)ma 1

I I

"ma -Pf

.80 -

2 .60-

E A .40-

aY C

rn 0)

.-

.20 I e' -

0--------- I Pma

4.0 3.0 2.0 1 .o Density ~,(grn/crn~)

i Pf I

Figure 18-8. Idealized representations of density-sonic and neutron-density cross plots which define the M and N variables. Use of M and N allow two-dimensional representation of the three simultaneous logging measurements. Their definition effectively eliminates porosity from the response of each pair of measurements.

lithologies due to the matrix endpoints. The neutron-density cross plot yields a similar slope, designated as N. Once again the three matrix types produce slightly different values of N. The end product is indicated in Fig. 18-9 where the two slopes are plotted against one another. It corresponds to simultaneously viewing the two responses of Fig. 18-8 from the 100% porosity point. A number of frequently encountered minerals are shown in this manner.

M and N values can be obtained from log readings by replacing the matrix values in their definitions (see Fig. 18-8) by the appropriate log readings. If these pairs of values are plotted on the overlay of Fig. 18-9, it is possible to determine lithology, in the best of circumstances. The figure shows some spread in the matrix coordinates depending on the fluid density. Part of this is due to the nonlinearity of the neutron response, whereas the apparent values of M are determined by passing a straight line in the

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Lithology Identification from Porosity Logs 427

M

. , _ _ _ ... . - . .

1 .o

0.9

0.8

0.7

0.6

0.5

0.3 0.4 0.5 0.6 0.7 C

N

8

Figure 18-9. The M-N plot used for mineral identification. Porosity variation has nearly been eliminated, but there remains some sensitivity to the fluid density. This type of plot is frequently used to identify secondary porosity. From Schlumberger.’

appropriate space to the fluid-filled case. The location of the pivot point will change the values of M and N.

One of the best uses made of this type of presentation is to highlight the presence of secondary porosity, which causes M to change without any effect on N. This is because At remains constant for the inclusion of secondary porosity while, in the numerator of M, the density decreases. This will result in an apparent increase in M. For the case of N, both the density and neutron will change by about the same amount for the presence of secondary porosity, and thus there will be no change in its value.

The M-N plot was a first order attempt to get rid of the effects of porosity. Its successor, the MID (Matrix Identification) plot, goes one step further and tries, in a simplified way, to obtain the values of the matrix constants actually sought. The lower portion of Fig. 18-10 shows how this is done for the neutron and density values. Interpolating between the family of

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428 Well Logging for Earth Scientists

100-

90

80

-

-

70 -

60 -

50 -

40 - -

9" (PU)

Figure 18-10. A alternative to the use of M-N variables is the use of apparent matrix values for At and pb. These are obtained from the interpolated pair of cross plots using the same measurement combinations. From Schlumberger.'

curves of apparent matrix density (p,&, the location of a point defined by (pb , $,J determines the appropriate apparent matrix density. The upper half of Fig. 18-10 indicates how the apparent travel time of the matrix is determined from the neutron-sonic cross plot. Armed with these apparent matrix constants, we can enter the MID plot of Fig. 18-11. This diagram shows a considerably smaller spread of points than in the M-N plot, and the coordinates have some relationship to known physical parameters, rather than being abstract values.

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Lithology Identification from Porosity Logs 429

2.8

2.9

3.0

3.1

2.0

2.1

2.2

2.3

Salt 0

Dolomite 0

Anhydrlte 0

SChl""'hWge<

2.4

E 2.5

m 2.6

2.7

m

0 0 . 1

E Q Quartz 0

Calcite 0

Figure 18-11. The matrix identification chart obtained using the defined values of apparent matrix density and At. From Schlumberger.'

One can debate the legitimacy of the linear interpolation of the matrix values used in the preceding figures; however, this approach does represent a large improvement over the M-N plot, for two reasons. First, it gets rid of a conversion to some rather meaningless parameters and attempts instead to find the more familiar values of matrix density and travel time. The second important point is that in this procedure the actual nonlinear tool response is taken into account rather than the linear slope determination of the M-N plot.* One weakness, however, is that this still is a method for presenting only three pieces of information simultaneously. It cannot be used if you want to consider ten simultaneous measurements.

* Concerning the nonlinearity of the neutrondensity cross plot, the reader should consult Ellis and Case, who show that the curved "dolomite" line of the neutron-density cross plot represents the results of field observations, some in conditions of extreme water salinity and others in possible matrix mixtures of dolomite and anh~drite.~ A clean dolomite formation should have a linear response.

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5.5

LITHOLOGY LOGGING: INCORPORATING P,

-

Before leaving the realm of two-dimensional graphical interpretation, let us consider a final example. In the previous techniques, measurements primarily sensitive to porosity were combined to eliminate their mutual porosity dependence and to emphasize their residual lithology sensitivity. However, one common measurement, the photoelectric factor, or P,, is primarily sensitive to lithology and only mildly affected by porosity. An interesting aspect of the P, measurement is illustrated in Fig. 18-12. On the left side is the conventional neutron-density cross plot. The ordering of the three major lithologies, from top to bottom, is sandstone, limestone, and dolomite, as is the case for the other possible combinations with the sonic measurement. The adjacent figure of P, vs. P b shows a startling difference. In this figure, the upper line is for limestone, and the dolomite matrix line is between the sand and limestone lines. Because of the reordering of the lithological groups, P, adds a new dimension to the neutron-density cross plot. For this reason, use of the P, easily resolves questions of binary lithology mixtures.

1.81 I

2-8p-l 1 3.0

-.05 .05 .I5 .25 .35 .45 1.8 2.0 2.2 2.4 2.6 2.8 3.0

'b 4 (Lime)

Figure 18-12. Comparison of log data on a neutrondensity cross plot and a cross plot of P, and density. Trend lines of three matrices from 0 to 50% porosity are shown in the plot of P,. The upper lines correspond to hydrocarbon in the pores and the lower lines to water-filled porosity. The data points are from a shaly sand.

On the neutron-density cross plot, a data point falling near the limestone line might, in some extreme case, correspond to a dolomitic sand. If the P, is available, this can be immediately confirmed or disproved. If, in fact, it is a limddolomite mixture, then it will lie above the dolomite line on the P, plot and not below.

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Recall that to obtain the Pe of a mixture involves computing the U value:

U t o ~ = pe,lPe,lVl+ Pe2~e,2V2 + . * * 9

where pej, is the electron density of material i, Pqi is the photoelectric factor of material i, and Vi is the volume fraction of that material. The final value of the average & is obtained from

7 7 - utotal Pe=- - , Pe

where the average electron density index A is given by:

An interesting application of this calculation can be seen by referring to Fig. 18-12 and noting that two sets of lines have been drawn for the three matrices: one for oil-filled and the other water-filled porosity. The P, value of water is 0.36 and that of oil 0.12. One might suspect that the upper curve of the three sets would be associated with water. However, the details of the calculation (see Problem 3) show that this is not the case.

The most obvious use of the volumetric cross section U is in combination with the grain density to clearly delineate lithologies. The approach is to eliminate porosity from the density measurement and from the P, measurement to obtain the apparent grain density and the apparent value of U,. This latter parameter is conveniently found by use of the chart in Fig. 18-13. The measured bulk density and Pe values are entered into the left

2. u) c a Q

4- .-

Y m 3

Figure 18-13. Chart for determining the apparent matrix cross section U,, from a knowledge of P,, density, and apparent porosity. From Schlumberger.'

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432 Well Logging for Earth Scientists

2.2-

2.3

67 5 2.4 UJ

> ul

- c .- c 2.5 B c .- E 0 2.6 X .- L c

?. 2.7 c C F 2 2.8 P

rn

E 0

2.9

3.0

of the figure, and U, is finally extracted on the right, based on knowledge of a cross plot porosity (from a neutron-density cross plot or other source). This type of data is then plotted on the overlay of Fig. 18-14, which shows a clear triangular separation between the three principal matrices. On this plot, the volumetric analysis of complex mixtures can be done very simply, since everything scales linearly.

__

t I

Salt

K-Feldspar 0

Ouarlz

Calcite

Barite -

\ Dolomite Heavy Minerals

Kaolinite o

Anhydrite o

3.1 I

2 4 6 8 10 12 14 16

Umaa, Apparent Matrix Volumetric Cross Section (barnskc)

Figure 18-14. A matrix identification chart which uses the combination of P,, density, and another porosity device. Both density and U scale volumetrically so that mixture proportions can be easily determined. From Schlumberger.'

NUMERICAL APPROACHES TO LITHOLOGY DETERMINATION

Two-dimensional cross plots have been very useful for interpretation and will continue to provide a simple method for obtaining quick estimates of volumes of major minerals. However, other methods must be considered for cases of more complicated lithologies and for the simultaneous inclusion of multiple logging information at each depth. One way to begin is to express the log

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Lithology Identification from Porosity Logs 433

response of various tools as equations which relate the response to the volume of each of the minerals present.

Consider the simple example of two logging measurements, density and P,. First we begin with a model of the formation. We suppose the formation consists of a mixture of two minerals of relative volumes V, and V2 and with densities of p1 and p2. The photoelectric absorption properties of the two minerals are given by U1 and U2. The porosity is given by @, and it is assumed to be filled with a fluid characterized by Ufl and pfl.

The tool response equations, or mixing laws, relate the measured parameters to the formation model. The complete set for this measurement is given by:

and Pb = Pfl@ + P1"1+ P2V2

u = Ufl@ + UlV, + u,v, . The final relation necessary to solve for the three unknowns is the closure relation of the partial volumes:

l = $ + V , + V , .

The solution can most easily be seen in terms of the matrix representation of the set of simultaneous equations:

M = R V ,

where M is the vector of measurements, R is the matrix of response coefficients, and V is the vector of unknown volumes. For the balanced case of N unknowns and N-1 logging values, the solution is the inverse of the response matrix, R-'. Doveton shows a computer program for obtaining this inverse simply:

Obviously this approach can be extended to as many measurements as are available, under the condition that their responses be written as linear combinations of the volumes. Two practical problems arise. The first is relatively straightforward and concerns the problem of overdetermination, which occurs when the number of logging measurements exceeds the number of minerals in the model. One solution to this problem is to find a least- squares solution to the set of equations. In this case, a weighting matrix is used to express the confidence level associated with each measurement. The programs necessary for implementing such an approach are described by Bevington.' A commercial processing package which utilizes such an approach for computerized log interpretation, not just lithology identification, is described by Mayer and Sibbit.6

However, the more serious problem concerns the more probable Occurrence that the number of minerals in the formation will vastly outnumber the set of logging measurements. This problem has been addressed from the geological point of view by Abbot and Serra, who defined the concept of electrofacies.' This term refers to the collective set of logging

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2-

0

tool responses which allow discrimination between one bed and another. The set of N logging measurements at a particular level can be viewed as a single point in N-dimensional space. Clustering of points will indicate zones of a similar facies. A statistical approach to the problem of lithology identification uses an extensive data base for more than a hundred facies incorporating up to nine different logging tool responses.' Instead of using a two-dimensional cross plot, each mineral or electrofacies is defined in the N- dimensional space of log responses.

2 3 c - 3

Clean 20:O PU Sand - 'lean 5-20 pu Sand

10-20 PU Gas-bearing Clean 20.

2.0 Limesto- '"1 5-15 PU

I a 2.4- Clean 5-20 PU

2.6- Sand

.30 PU

2 . 8 L - ~ * . 8 * 8 0 * 2 -5.0 0 5 10 15 20 25 30 35 40 45

NPHl

RHOB

Figure 18-15. An approach to the N-dimensional space of multiple logging measurements, considering them two at a time. From Delfiner et a1.8

To implement this approach, the characteristic response of the tools is established on a two-by-two basis, as shown in Fig. 18-15. By combining all the various cross plot combinations, ellipses in N-dimensional space can be defined for the tool response to a particular type of lithology and porosity range. To identify the particular type of matrix, a given set of logging measurements is tested statistically to see in which of the many volumes it may be contained. An example of the type of display which can be produced is shown in Fig. 18-16. The results strongly resemble a core description made by a trained geologist.

These various approaches involve a practical issue of determining the model parameters as well as defining the appropriate model for a given formation and set of logging measurements. Raymer and Edmundson give

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many valuable parameters for most of the logging tools: but often one is faced with unusual minerals for which the logging tool response is unknown but can be estimated from the logging measurements. Quirein et al. describe a generalized program for lithological interpretation which permits solution of the problem in various steps." It can be used, in a first stage, to generate the electrofacies from the given set of logging measurements. If the appropriate tool responses are known, it can evaluate simultaneously up to five different models of the formation. The choice of the final model is left to the user.

I

GLOBAL I RESULTS OPEN a LITHOLOGIC r2kE lgl COLUMN

LITHOFACIES MAJOr letinitic

SRNO

sHaL CORL

SURL

SRND

5HRL

SRND

snw

CORL

ShRL

CORL

SHRL

Figure 18-16. Output of a program for automatically determining lithology from a number of predefined geological models. From DeEner et. d?

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436 Well Logging for Earth Scientists

References

Schlumberger Log Interpretation Charts, Schlumberger, New York, 1985.

Dewan, J. T., Essentials of Modern Open-hole Log Interpretation, PennWell Publishing Co., Tulsa, 1983.

Ellis. D. V., and Case, C. R., "CNT-A Dolomite Response,".Paper S, SPWLA Twenty-Fourth Annual Logging Symposium, 1983.

Doveton, J. H., Log Analysis of Subsurface Geology, Concepts and Computer Methods, John Wiley, New York, 1986.

Bevington, P. R., Data Reduction and Error Analysis for the Physical Sciences, McGraw-Hill, New York, 1969.

Mayer, C., and Sibbit, A., "Global: A New Approach to Computer- Processsed Log Interpretation," Paper SPE 9341, SPE Fifty-fifth Annual Technical Conference, 1980.

Serra, O., and Abbott, H., "The Contribution of Logging Data to Sedimentology and Stratigraphy," Paper SPE 9270, SPE Fifty-fifth Annual Technical Conference, 1980.

Delliner, P. C., Peyrat, O., and Serra, O., "Automatic Determination of Lithology from Well Logs," Paper SPE 13290, SPE Fifty-ninth Annual Technical Conference, 1984.

Edmundson, H., and Raymer, L. L., "Radioactive Logging Parameters for Common Minerals," SPWLA Twenty-third Annual Logging Symposium, 1979.

Quirein, J., Kimminau, J., Lavigne, J., Singer, J., and Wendel, F., "A Coherent Framework for Developing and Applying Multiple Formation Evaluation Models," Paper DD, SPWLA Twenty-seventh Annual Logging Symposium, 1986.

1.

2.

3.

4.

5.

6.

7.

8.

9.

10.

Problems

1. Fig. 18-4 is a log of a tight (low porosity) carbonate section. Using the neutron-density cross plot (Fig. 18-3), identify zones of the different matrix types present in this section of the well.

2. To gain some practice with the manual determination of lithology and matrix values, consider the following set of data taken from sections of a clean sandstone reservoir. Although the sandstone is free of clay, it does contain some pyrite. The question to answer is how close does the manual cross plot technique get you to the true porosity?

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The following table, which lists the values painstakingly read off the logs, is in a format which will help you to complete the task. Note the column of matrix density values, which have been determined from core analysis. Make a plot of porosity obtained from the density tool alone under two different conditions: using the core-measured grain density, and using the cross plot grain density pmn-d. For both calculations, assume that the formation fluid has a density of 1.20 g/cm3.

95 I 2.35 I 21 I I I I I I

I 9 0 I 2.40 I 19 I I 94 I 2.41 1 18 I

I I I

90 I 2.38 I 19 I

3. To verify the identification of the sets of matrix lines in the P, plot of Fig. 18-12, compute the P b and P, values for 5O%-porosity limestone, dolomite, and sandstone. Consider two cases of pore fluid, water and CH2. The appropriate values for the computations may be found in Table 10-1.

4. With reference to Figs. 18-1 through 18-3, which tool combination would you prefer to use for lithology definition in a carbonate reservoir containing limestone and dolomite? Specifically what are the maximum errors tolerable in a 5%-porous limestone so that it is not misidentified as a dolomite? For each pair of cross plots, you can evaluate the maximum tolerable error by either of the measurements or assume a simultaneous error of the two.

5. Consider a barite-loaded mud with a density of 14 lb/gal which is known to be 46% Ba!304 by weight. What is the P, of the mud? If the mud infiltrates a 2O%-porous sandstone what, P, do you expect to see?


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