CHAPTER SEVEN: CALCULATING POROSITY

Table Of Contents
7.00 Introduction To This Chapter
7.01 Definitions Of Porosity
7.02 Visual Indications Of Porosity
7.03 Scaling Logs In Porosity Units
7.04 Porosity From Compressional or Shear Sonic Log
7.05 Porosity From The Density Log
7.06 Porosity From Density Porosity Log With Matrix Offset
7.07 Porosity From Old Style Neutron Logs
7.08 Matrix Offset For Neutron Logs
7.09 Porosity From The Neutron Log
7.10 Summary Of One Log Porosity Methods
7.11 Quick Methods For Density Neutron Crossplot Calculations
7.12 Shaly Sand Crossplot (Density Neutron) With Matrix Offset
7.13 Complex Lithology Crossplot (Density Neutron)
7.14 Bulk Volume Water Crossplot (Dual Water Model)
7.15 Sonic Neutron Crossplot
7.16 Sonic Density Crossplot
7.17 Summary Of Crossplot Methods
7.18 Discussion Of Gas Correction Methods <<< New
7.19 Porosity From Microlog
7.20 Porosity From Shallow Resistivity Logs
7.21 Porosity From Deep Or Medium Resistivity Log
7.22 Summary Of Porosity From Resistivity Methods
7.23 Non-Porous Lithology Triggers
7.24 Material Balance For Porosity (Maximum Porosity)
7.25 Useful Porosity
7.26 Porosity from Nuclear Magnetic Log
7.27 Fracture Porosity
7.28 Porosity from Three-Mineral Lithology
7.29 Selection Of Porosity Method
7.30 Effective Porosity Routines
7.31 Calibrating Porosity to Core and Sample Data
7.32 Sensitivity Analysis
7.33 In Conclusion
7.34 Exercises For Chapter Seven
7.35 Bibliography For Chapter Seven

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Publication History: Originally published as Chapter Seven of the Log Analysis Handbook, Pennwell 1986. Sections 7.25 through 7.32 added for this electronic edition Feb 2001. Shear sonic porosity added to Section 7.04 Aug 2003. Simplified complex lithology model added to Section 7.11 Oct 2003. Section 7.00 revised Sept 2001 and Oct 2003.

CHAPTER SEVEN: CALCULATING POROSITY

7.00 Introduction to This Chapter
The next step in quantitative analysis, after finding shale volume, is to estimate porosity.

There are numerous porosity indicating logs, as shown in the box at left, and many flavours of each, depending on the age, design, and logging environment. Generic analysis equations, based on the Log Response Equation, for each basic tool type are contained in this Chapter. They will work for almost all available tool types. There may be rare occasions when a customized analysis model might be required.

All the porosity models require some assumptions about such things as fluid type and matrix rock properties. With the exception of the resistivity log formula, used for analysis of ancient logs, the methods involve corrections for the effects of shale.

FIGURE 7.00: The Effect of Shale on Porosity

Shale corrections are applied to porosity logs to determine effective porosity, as shown in the illustration above. Since shale contains some water, this water must be subtracted from the total porosity as measured by conventional logging tools. The mathematical method for finding shale volume is the same for all the shale distribution types, but the method for applying the shale correction to the porosity varies. This Chapter deals with clean sands or shaly sands dispersed or structural shale. Chapter Seventeen covers laminated shaly sands.

Correcting for shale is only half the battle. The other half is to correct for the mineral composition of the rocks. In most carbonate reservoirs, the lithology is usually reasonably well known from sample descriptions or can be determined from log response, so this step is relatively straightforward.

This is not true in sandstones because the mineral makeup of the sand is NOT usually described in much detail. There is a universal trend to give sandstones the physical properties of pure quartz, but this is almost universally NOT appropriate. Most sandstones contain other minerals such as mica, volcanic rock fragments, calcite, dolomite, anhydrite, and ferrous minerals, as well as the shale and clay described above. All of these minerals have different density, acoustic, and neutron properties than quartz. If a sandstone is assumed to be pure quartz when it is not, the commonly used properties of quartz will provide a pessimistic porosity answers.

Thus, authors and service company manuals that present mineral properties for “sandstone” are misleading their audience into believing these properties are constant. In more than 40 years of petrophysical analysis, I have never seen a thin section or XRD report that gave an assay of 100% quartz in any petroleum reservoir. A 100% quartz sand is very rare. If anyone doubts this statement, look at the PEF curve. If it reads more than 1.8, you have “quartz plus other things” in your sandstone.

There is a story (it may even be true) that reserves for the early North Sea discoveries were seriously underestimated because the mica in the sands was not accounted for properly. The engineers used density log porosity without correcting for the real matrix density. If true, good engineering practice would have undersized all the offshore equipment and early cash flow and rate of return on investment would have been significantly reduced. If the myth that sandstone is pure quartz is perpetuated, there will be more economic blunders of this type.

To further confuse the uninitiated, many logs show data on a "porosity" scale. These log curves are transforms of some measured physical property to an approximate porosity based on some arbitrary parameters. Examples are density, neutron, or sonic porosity on so-called Sandstone, Limestone, or Dolomite porosity scales. Porosity as defined by these transforms is only directly useful if there is no shale, the scale matches the rock mineralogy. and there are no accessory minerals. Real reservoirs are rarely this simple. DO NOT use these porosity transforms without further analysis unless all the arbitrary assumptions used to create them match exactly the rock you are analyzing.

Some people call these porosity curves an “interpretation”. They are not. They are merely a transform of the raw data to a more attractive scale. The difference between a transform and an interpretation is critical. Interpretation infers some intelligent thought went into creating and understanding the result. The service company running the log does not provide interpretations. YOU are the interpreter,

There are endless cases where a transform to an inappropriate porosity scale has caused millions in losses due to poorly informed analysts who see “gas cross over” when there is no gas, or who read porosity directly from the transform and either seriously over estimate or under estimate reservoir effective porosity.

In spite of these comments, a number of charts and tables in this Chapter and elsewhere in this Handbook show the word "sandstone' when they really should say "quartz". I have not edited the charts and tables taken from common sources, such as service company chart books, so the common usage of incorrect terminology is repeated even here.

7.01 Definitions of Porosity
Porosity is the volume of the non-solid portion of the rock filled with fluids, divided by the total volume of the rock.

Primary porosity is the porosity developed by the original sedimentation process by which the rock was created. In reports, it is often referred to in terms of percentages, while in calculations it is always a fraction.

To acquire an appreciation for the values of porosity generally encountered, assume round balls of the same size are stacked on top of each other in columns. Calculations will show a porosity of 47.6%. Spherical sand grains 1/10 the size of the balls stacked one on top of the other will have the same porosity, 47.6%.

If the same balls are packed in the closest possible arrangement in which the upper ball sits in the valley between the four lower balls, each touching, the porosity is reduced to 25.9%. Again, changing the size of the balls will not change the porosity as long as all the balls are the same size. Mixing the sizes of the balls will create lower porosity, since small ones can fit in spaces created between the larger ones.

The highest porosity normally anticipated is 47.6%. A more probable porosity is in the mid-twenties. The normal range of porosities in granular systems is 5% to 35%.

In general, porosities tend to be lower in deeper and older rocks. This decrease in porosity is primarily due to overburden pressure stresses on the rock, and cementation. There are many exceptions to this general trend, when normal overburden conditions do not prevail.

Shales closely follow the same porosity depth trend as sandstones, except that porosities are normally lower in shales. For example, in a recent mud the porosity may measure about 40%. It decreases rapidly with depth and overburden pressure until, at a depth of about 10,000 feet, normal porosities are less than 5%. Shales are plastic and therefore, compress more easily than sands.
These basic trends of porosity versus depth are not as noticeable in carbonates, where porosity is more a function of depositional environment and secondary processes, both unrelated to depth of burial.

Porosity in a real shale is not effective; that is, the water cannot move as quickly as in a sandstone with the same apparent porosity. Water in shale can be expelled over large geologic time periods, but it will not flow in the usual sense of the word.

However, many intervals that have been traditionally thought of as "shale" are really silty shales or sandy shales. These may have sufficient porosity to store hydrocarbons that might flow. This is especially true for gas, and many "gas shales" are silty shales with effective porosity. Other gas shales are mostly shale and gas is stored on the surface of fractures within the shale. This is adsorbed gas.

Secondary porosity is created by processes other than primary cementation and compaction of the sediments. An example of secondary porosity can be found in the solution of limestone or dolomite by ground waters, a process which creates vugs or caverns. Fracturing also creates secondary porosity. Dolomitisation results in the shrinking of solid rock volume as the material transforms from limestone to dolomite, giving a corresponding increase in porosity.

In most cases, secondary porosity results in much higher permeability than primary granular porosity.

The use of the term, Secondary Porosity Index (SPI), by log analysts has led to much confusion. The term means the porosity defined by the difference between porosity derived from the sonic log and the primary porosity. The primary porosity is usually defined by core analysis or the density neutron log. Depending on the shape and size of the vugs, fractures, or caverns, the SPI may or may not be a good indication of secondary porosity.

The above discussion covers the geological definitions of porosity. Petrophysicists, log analysts, and engineers use more specific terms based on the log analysis model described in Chapter Four. Here are the definitions that derive from that model.

Non-useful porosity occurs as tiny pores that do not connect to any other pores. They are almost invariably filled with immoveable water and do not contribute to useful reservoir volume or energy. Such pores occur in silt, volcanic rock fragments in sandstones, and in micritic, vuggy, or skeletal carbonates. The NMR may see some of this non-useful porosity; the jury is still out.

Porosity derived directly from a log without correction for shale content, is termed apparent or total porosity. If the zone has no shale, the total porosity equals the effective porosity. Should the zone contain shale, corrections must be applied to obtain effective porosity. DO NOT USE LOG READINGS DIRECTLY UNLESS THERE IS ZERO SHALE CONTENT.

This warning also applies to logs recorded in porosity units when the log scale does not match the actual lithology. For example, a density, neutron, or sonic log can be run on sandstone, limestone, or dolomite scales. While these scales have many valuable uses, they will give erroneous results unless the rock mineralogy exactly matches the scale definition. A log recorded on a limestone scale in a clean sandstone, shaly sandstone, or dolomite needs further data processing before it will give the correct answer.

Various methods are presented here to calculate porosity from individual or combinations of two or more logs. Two log combinations are termed crossplot methods, since the log data can be plotted on the X and Y axes of a graph.

Three or more log combinations require solution by simultaneous equations, and are usually done on a computer.


7.02 Porosity Overlay/Porosity Playback Log
All porosity logs have been recorded in such a fashion as to deflect to the left when porosity increases. This also occurs in shale zones, which creates a conflict when attempting to do a visual log interpretation since both shale content and porosity increase to the left. Use the GR and SP to discriminate shale from porous rock.

FIGURE 7.01: Porosity Playback Log for Classic Example 1

Figure 7.0l illustrates the three usual porosity logs on compatible scales, displaying that the deflection for increased porosity is always to the left.

Porosity derived from the resistivity log is also shown. This presentation is called a porosity playback log and is created in the computer, but can usually be produced by overlaying or tracing logs on compatible scales.

Non-compatible scales may be used but additional care is required.

When porosity from the resistivity log tracks the porosity curves, then the zone is probably water bearing or shaly. If the porosity from the resistivity log departs to the right of the porosity curves, the zone probably contains hydrocarbon, is tight (has no porosity) or is coal. The departure to the right was dubbed the "Mae West Effect" many years ago, but it is no longer fashionable to use this term.


7.03 Scaling Logs in Porosity Units
If logs are not recorded on porosity scales, or scales are inappropriate, it is convenient to label the required porosity scale on the log.

Table 7.0l, illustrates approximate porosity scales for a number of individual logs. These values should be memorized so that the analyst can derive approximate porosity at any time without reference to chartbooks or calculators. Porosity obtained in this manner will presumably be too high as no shale correction has been made. A mental deduction for the amount of shale, estimated from the gamma ray or SP log, should be included prior to finalizing any visual interpretation.

TABLE 7.01: Scaling Porosity Logs

Density neutron logs can be displayed on sandstone scales or limestone scales, regardless of rock type. This is a function of a switch setting in the logging truck, which allows a sandstone scale to be run in limestone rocks and vice-versa. If the scale name (e.g. sandstone) does not coincide with the rock type (e.g. limestone), the rules in Table 7.0l should be applied to derive the appropriate scale. When using charts or calculators as opposed to visual methods, use the rules pertaining to those methods, and not Table 7.0l.

TABLE 7.02: Scaling Porosity Logs

Porosity found by scaling the log in porosity units is termed the Total Porosity (PHIt), and will vary for each log, AND IS NOT THE FINAL ANSWER. NOTE: GAS AND SHALE AFFECT THE APPARENT POROSITY, SO POROSITY DETERMINED BY SCALING THE LOG IS MERELY THE FIRST STEP IN A VISUAL INTERPRETATION

The qualitative response of basic porosity logs to gas and shale are given in Table 7.02. Use these rules to modify your opinion of porosity determined by scaling the logs, or follow through with detailed hydrocarbon and shale corrections described later in this chapter.

To apply the rules in Table 7.0l, draw the scale on the log using the zero and 0.1 points listed. Label the 0.2, 0.3, 0.4 and 0.5 points by shifting an equal distance for each additional 0.1 fraction of porosity.

For example, on English units sonic logs, to create a sandstone porosity scale, mark the 0.0 porosity point at 55.5 usec/ft and the 0.1 point at 68.5 usec/ft. Add another 13 usec/ft for each 0.1 extra porosity to find the 0.2 and 0.3 porosity points. See Figure 7.02.

FIGURE 7.02: Scaling Porosity Logs

As a second example, assume a limestone unit neutron porosity scale, and convert it to a sandstone unit scale by exercising the rule "add 0.04" to get sandstone from limestone units.

The third example is the case of scaling an obsolete neutron log recorded in counts per second or other arbitrary units. The usual approach is to pick a low point on the scale, and label it as 0.25 or 0.30 porosity units. Then label a high scale point as 0.01 or 0.02 porosity units and scale logarithmically between these two points.

These three examples can be found in Figure 7.02.

The data for the sonic log for Classic Example 1 is shown with its appropriate porosity scale in the correct units for further work, as shown in Figure 7.03.

FIGURE 7.03: Scaling the Sonic Log for Classic Example 1

The density neutron log for this example is already on a porosity scale in the correct sandstone porosity units, as shown in Figure 7.01.


7.04 Porosity from the Sonic Log
The response equation for the sonic log follows the classical form:
DELT = PHIe * Sxo * DELTw (water term)
+ PHIe * (1 - Sxo) * DELTh (hydrocarbon term)
+ Vsh * DELTsh (shale term)
+ (1 - Vsh - PHIe) * Sum (Vi * DELTi) (matrix term)

WHERE
DELTh = log reading in 100% hydrocarbon
DELTi = log reading in 100% of the ith component of matrix rock
DELT = log reading
DELTsh = log reading in 100% shale
DELTw = log reading in 100% water
PHIe = effective porosity (fractional)
Sxo = water saturation in invaded zone (fractional)
Vi = volume of ith component of matrix rock
Vsh = volume of shale (fractional)

To solve for porosity from the sonic log, we assume DELTh, DELTi, DELTsh, DELTw, and Vsh are known. We also assume DELTw = DELTh and Sxo = 1.0 when no gas is present. If gas is indicated, we make assumptions about DELTh and Sxo, usually in the form of a correction factor to the gas free case. The usual result is:

PHIsc = (DELT - (1 - Vsh) * DELTMA - Vsh * DELTSH) / (DELTW - DELTMA)

The response equation is not rigorous and many exceptions are noted below.

The rules for sonic logs in Table 7.01 and 7.02, which represent simplified cases of the response equation, can be converted to calculator or computer use by the following equations. This porosity method is one of the most common calculations on older wells. The shale correction is very important and should not be ignored.

Calculate sonic compaction correction
1: CP = max (1, CDTSH / (100 + 228 * (IF DEPTHUNIT$ = "METRIC")))

Calculate total sonic porosity
2: PHIS = (DELT - DELTMA) / (DELTW - DELTMA) / CP

Correct sonic porosity for shale
3: PHISSH = (DELTSH - DELTMA) / (DELTW - DELTMA) / CP
4: PHIsc = PHIS - Vsh * PHISSH

Correct sonic porosity for gas effect
5: IF SONICGASSWITCH$ = "ON"
6: THEN PHIsc = KS * PHIS

WHERE:
CDTSH = shale travel time for compaction correction (usec/ft or usec/m)
CP = compaction factor (fractional)
DELT = sonic log reading in zone of interest (usec/ft or usec/m)
DELTMA = sonic log reading in l00% matrix rock (usec/ft or usec/m)
DELTSH = sonic log reading in l00% shale (usec/ft or usec/m)
DELTW = sonic log reading in 100% water (usec/ft or usec/m)
KS = sonic log gas correction factor
PHIS = porosity from sonic log (corrected for compaction if needed) (fractional)
PHIsc = porosity from sonic log by Wyllie method (fractional)
PHISSH = apparent sonic porosity of 100% shale after compaction correction (if needed) (fractional)
Vsh = shale volume (fractional)

COMMENTS:
Of the three "one-log" porosity methods, the sonic corrected for shale is the preferred one for wells drilled after 1957 and before 1965. However, crossplot methods or the density log corrected for shale are usually better if the log data is available.

The graphical solution for these formulae is provided in Figure 7.04. Simpler charts exist which do not include the shale or fluid correction. If any significant amount of shale exists, do not use simple charts.

FIGURE 7.04: Chart for Estimating Shale Corrected Sonic Porosity

Use the compaction correction only if CDTSH > 100 (for English units) or CDTSH > 328 (for Metric units). In western North America, this is normally required when above 3,000 - 4,000 feet (900 - l,200m).

KS is in the range 0.7 to 1.0 depending on gas density invasion and local experience. It can be derived by comparing the calculated porosity with the true porosity from cores or density neutron crossplot methods.

Use gas correction only if PHIS is too high compared to other sources, only if the zone is clean and does not need shale corrections, and if gas is known to be present. The need for this correction is rare. It is very unlikely that a gas correction will be needed in shaly sands since invasion should be relatively deep.

Another way of making gas corrections in both methods is to change DELTW to a higher value, representing the travel time of sound in a mixture of gas and water. This value depends on water saturation in the invaded zone, pressure, temperature and gas compressibility. Values in the range of 600 usec/ft (1900 usec/m) at shallow depths to 300 usec/ft (950 usec/m) at 6000 feet (2000 meters) are recommended as a starting point.

If log is in porosity units, skip Step 1 and Step 5, and read PHIS and PHISSH directly from the log. If porosity scale is in sandstone units and rock type is limestone (or vice versa), make appropriate adjustments as per Table 7.01.

CDTSH may be higher if depth is less than 3,000 ft (1,000m). Usually set CDTSH equal to DELTSH, with a minimum of 100 (English) or 328 (Metric).

CDTSH can be calculated if true porosity of a clean zone is known from core, neutron, or density log data:

CDTSH = PHIS / PHItrue * DELTSH
OR: CP = PHIS / PHItrue

WHERE:
CDTSH = shale travel time for compaction correction (usec/ft or usec/m)
CP = compaction factor (fractional) (usec/ft or usec/m)
DELTMA = sonic log reading in 100% rock matrix (usec/ft or usec/m)
DELTSH = sonic log reading in 100% shale (usec/ft or usec/m)
DELTW = sonic log reading in 100% water (usec/ft or usec/m)
PHIS = sonic log porosity in clean sand (fractional)
PHItrue = actual porosity in clean sand from core or density data (fractional)

The Hunt-Raymer method is a newer formula which is a non-linear calibration of observed porosity versus log response data. It should be used in clean sands and carbonates only, or log data may be corrected for shale first. It can be used in un-compacted sands without the compaction correction described in the Wyllie method given above. The algorithm is derived from the following empirical relationship: VELOG = VELMA * ((1 - PHIe) ^ 2) + VELW * PHIe

This can be solved for porosity in the following way:

Calculate sonic log reading corrected for shale:
1: DELTc = DELT - Vsh * (DELTSH - DELTMA)

Calculate sonic porosity
2: C = DELTMA / (2 * DELTW)
3: PHIShr = 1 - C - (C ^ 2 - DELTMA / DELTW + DELTMA / DELTc) ^ 0.5

WHERE:
C = intermediate term
DELT = sonic log reading in zone of interest (usec/ft or usec/m)
DELTc = sonic log reading corrected for shale (usec/ft or usec/m)
DELTMA = sonic log reading in l00% matrix rock (usec/ft or usec/m)
DELTSH = sonic log reading in l00% shale (usec/ft or usec/m)
DELTW = sonic log reading in 100% water (usec/ft or usec/m)
` PHIShr = porosity from sonic log by Hunt-Raymer method (fractional)
VELOG = sonic velocity log reading (ft/sec or m/sec)
VELMA = sonic velocity log reading in 100% matrix (ft/sec or m/sec)
VELW = sonic velocity log reading in 100% water (ft/sec or m/sec)
Vsh = shale volume (fractional)

COMMENTS:
A graphical solution for the Hunt-Raymer method, with no shale correction, is given in Figure 7.04A.

FIGURE 7.04A: Sonic Log Porosity from Hunt-Raymer Method (curved lines) and Wyllie Method (straight lines) - No Shale Corrections

Although the original paper does not discuss shale corrections, they are essential. Gas corrections similar to those used in the Wyllie method can be used if needed. The answer porosity will be too high in gas if the corrections are not made. The method is not universally applicable and should be tested in each area before use.

Another way of making gas corrections in both methods is to change DELTW to a higher value, representing the travel time of sound in a mixture of gas and water. This value depends on water saturation in the invaded zone, pressure, temperature and gas compressibility. Values in the range of 600 usec/ft (1900 usec/m) at shallow depths to 300 usec/ft (950 usec/m) at 6000 feet (2000 meters) are recommended as a starting point.

RECOMMENDED PARAMETERS:
See Wyllie method discussed above

NUMERICAL EXAMPLE:
1. Wyllie Method - data from Sand "D" of Classic Example 1.
DELT = 300 usec/m
DELTSH = 328 usec/m
CDTSH = 328 usec/m
DELTMA = 182 usec/m
DELTW = 616 usec/m
Vsh = 0.33

CP = 328 / 328 = 1.0
Therefore compaction correction is not needed.

PHIS = (300 - 182) / (616 - 182) / 1.0 = 0.27
PHISSH = (328 - 182) / (616 - 182) / 1.0 = 0.34
PHIsc = 0.27 - 0.33 * 0.34 = 0.16
PHIsc is not too high, and no gas is known to be present. Hence, no gas correction is made.

2. Hunt-Raymer Method - data from Sand D above.
DELTc = 300 - 0.33 * (328 - 182) = 251 usec/m
C = 182 / (2 * 616) = 0.147
PHIShr = 1 - 0.147 - (0.147 ^ 2 - 182 / 616 + 182 / 251) ^ 0.5 = 0.18

3. Wyllie Method - data from Sand "C"
DELT = 380 usec/m
DELTSH = 328 usec/m
CDTSH = 328 usec/m
DELTMA = 182 usec/m
DELTW = 616 usec/m

Vsh = 0.0
CP = 328 / 328 = 1.0
PHIS = (380 - 182) / (616 - 182) / 1.0 = 0.46
PHISSH = (328 - 182) / (616 - 182) = 0.36
PHIsc = 0.46 - 0.0 * 0.36 = 0.46
PHIsc is too high due to gas effect - assume KS = 0.75
PHIsc = 0.75 * 0.46 = 0.33

4. Hunt-Raymer Method - data from Sand C above.
DELTc = 380 - 0.00 * (328 - 182) = 380 usec/m
C = 182 / (2 * 616) = 0.147
PHIShr = 1 - 0.147 - (0.147 ^ 2 - 182 / 616 + 182 / 380) ^ 0.5 = 0.40
Porosity is too high due to gas effect - assume KS = 0.80.
PHIsc = 0.80 * 0.40 = 0.32

5. Wyllie Method - data from Sand "A"
DELT = 375 usec/m
DELTSH = 460 usec/m
CDTSH = 460 usec/m
DELTMA = 182 usec/m
DELTW = 616 usec/m

Vsh = 0.0
CP = 460 / 328 = 1.40
PHIsc = PHIS = (375 - 182) / (616 - 182) / 1.40 = 0.31
No gas correction is required.
No shale correction is required.

6. Hunt-Raymer Method - data from Sand A above.
DELTc = 375 - 0.33 * (460 - 182) = 375 usec/m
C = 182 / (2 * 616) = 0.147
PHIShr = 1 - 0.147 - (0.147 ^ 2 - 182 / 616 + 182 / 375) ^ 0.5 = 0.39

This result is a little high compared to the more conventional method.

The newer sonic logs record shear travel time as well as the compressional travel tine. The compressional data is processed as discussed above under the Wyllie and Raymer-Hunt methods. Shear travel time can be used in the Wyllie equation, using fictitious values for fluid travel time. There is very little fluid effect on shear data so there is no gas correction.

Calculate total sonic porosity
1: PHIshear1 = (DTS - DTMA_S) / (DTW_S - DTMA_S)

Correct sonic porosity for shale
2: PHISSH_S = (DTSH_S - DTMA_S) / (DTW_S - DTMA_S)
3: PHIshear = PHIshear1 - Vsh * PHISSH_S

WHERE:
DTS = shear sonic log reading in zone of interest (usec/ft or usec/m)
DTMA_S = shear sonic log reading in l00% matrix rock (usec/ft or usec/m)
DTSH_S = shear sonic log reading in l00% shale (usec/ft or usec/m)
DTW_S = (fictitious) shear sonic log reading in 100% water (usec/ft or usec/m)
PHIshear1 = porosity from shear sonic log before shale correction (fractional)
PHIshear = porosity from shear sonic log by Wyllie method (fractional)
PHISSH_S = apparent shear sonic porosity of 100% shale (fractional)
Vsh = shale volume (fractional)

COMMENTS:
Shear travel time is more sensitive to porosity than compressional data.

No gas correction is needed.

The measurement can usually be made through casing so this is a good choice for cased hole logging.

There is no record of a compaction correction being applied, but this may be needed. Comparison to core porosity or density neutron crossplot porosity will indicate when such a correction is needed.

7.05 Porosity from the Density Log
The response equation for the density log in porosity units follows the classical form:
PHID = PHIe * Sxo * PHIDw (water term)
+ PHIe * (1 - Sxo) * PHIDh (hydrocarbon term)
+ Vsh * PHIDsh (shale term)
+ (1 - Vsh - PHIe) * Sum (Vi * PHIDi) (matrix term)

WHERE:
PHIDh = log reading in 100% hydrocarbon
PHIDi = log reading in 100% of the ith component of matrix rock
PHID = log reading
PHIDsh = log reading in 100% shale PHIDw = log reading in 100% water
PHIe = effective porosity (fractional)
Sxo = water saturation in invaded zone (fractional)
Vi = volume of ith component of matrix rock
Vsh = volume of shale (fractional)

To solve for porosity from the density log, we assume PHIDh, PHIDi, PHIDsh, PHIDw, and Vsh known. We also assume PHIDw = PHIDh and Sxo = 1.0 when no gas is present. If gas is indicated, we make assumptions about PHIDh and Sxo, usually in the form of a correction factor to the gas free case, as described later.

Since PHIDi = 0 and PHIDw = 1.0, the usual result is:
PHIdc = PHID - Vsh * PHIDSH

This response equation is rigorous.

The rules for density logs in Tables 7.01 and 7.02, based on the response equation, are translated algebraically by the following formulae:

Calculate density porosity from density data.
1: PHID = (DENS - DENSMA) / (DENSW - DENSMA)

Apply density shale correction:
2: PHIDSH = (DENSH - DENSMA) / (DENSW - DENSMA)
3: PHIdc = PHID - Vsh * PHIDSH

Apply density gas correction.
4: IF DENSITYGASSWITCH$ = "ON"
5: THEN PHIdc = KD * PHIdc

WHERE:
DENS = density log reading in zone of interest (gm/cc or Kg/m3)
DENSMA = density log reading in 100% matrix rock (gm/cc or Kg/m3)
DENSSH = density log reading in 100% shale (gm/cc or Kg/m3)
DENSW = density log reading in 100% water (gm/cc or Kg/m3)
KD = density log gas correction (fractional)
PHID = porosity from uncorrected density log (fractional)
PHIdc = porosity from density log corrected for shale (fractional)
PHIDSH = apparent density log porosity of 100% shale (fractional)
Vsh = shale volume (fractional)

COMMENTS:
A graphical solution, with shale correction, is in Figure 7.05.

FIGURE 7.05: Chart for Estimating Shale Corrected Density Porosity

The density log corrected for shale is a very good approximation to porosity, but the log was not common before 1965, so sonic or neutron methods may be necessary for wells drilled before that time.

KD is in the range of 0.5 - 1.0 depending on invasion, gas density and local experience. A correction is almost always needed if gas is present.

Use gas correction only if PHIdc is too high compared to other sources and if gas is known to be present. This correction may be necessary even in shaly sands, since the depth of investigation of the density log is deep enough to see beyond the flushed zone.

If log is in porosity units, use rules in Table 7.01 to get appropriate porosity scale for the lithology being encountered or see next section. Also disregard Step 1 and Step 4, and read PHID and PHIDSH directly from the log.

If density porosity data is in percent, rather than fractional, divide the data values by 100 before Step 2 and 3 are applied.

No compaction correction is made to density log data.

RECOMMENDED PARAMETERS:
See Section 7.06.

NUMERICAL EXAMPLE:
1. Assume a zone with:
DENS = 2.15 gm/cc
DENSW = 1.00 gm/cc
DENSMA = 2.65 gm/cc
Vsh = 0.33
DENSSH = 2.60 gm/cc
PHID = (2.15 - 2.65) / (1.00 - 2.65) = 0.30
PHIDSH = (2.60 - 2.65) / (1.00 - 2.65) = 0.03
PHIdc = 0.30 - 0.33 * 0.03 = 0.29
No gas correction is required.

7.06 Porosity From Density Porosity Log With Matrix Offset
One step that is often required is to convert apparent porosity on the density log into density units, then reconstitute porosity from this value corrected for a desired matrix and fluid value. This is done by rearranging the response equation of the previous section.

The response equation for the density log in density units follows the usual form:
DENS = PHIe * Sxo * DENSw (water term)
+ PHIe * (1 - Sxo) * DENSh (hydrocarbon term)
+ Vsh * DENSsh (shale term)
+ (1 - Vsh - PHIe) * Sum (Vi * DENSi) (matrix term)

WHERE:
DENSh = log reading in 100% hydrocarbon
DENSi = log reading in 100% of the ith component of matrix rock
DENS = log reading
DENSsh = log reading in 100% shale
DENSw = log reading in 100% water
PHIe = effective porosity (fractional)
Sxo = water saturation in invaded zone (fractional)
Vi = volume of ith component of matrix rock
Vsh = volume of shale (fractional)

To solve for porosity from the density log, we assume DENSh, DENSi, DENSsh, DENSw, and Vsh are known. We also assume DENSw = DENSh and Sxo = 1.0 when no gas is present. If gas is indicated, we make assumptions about DENSh and Sxo, usually in the form of a correction factor to the gas free case, as described later.

Calculate density from density porosity.
1: DENSm = (PHID * 1.00 + (1 - PHID) * (2.65 + 0.06 * (IF LOGUNIT$ = “LIMESTONE")))
* (1 + 999 * (IF DEPTHUNIT$ = "METRIC"))

Calculate shale density.
2: DENSSHm = (PHIDSH * 1.00 + (1 - PHIDSH) * (2.65 + 0.06 * (IF LOGUNIT$ =
"LIMESTONE"))) * (1 + 999 * (IF DEPTHUNIT$ = "METRIC"))

Calculate porosity with new matrix and fluid.
3: PHIDm = (DENSm - DENSMA) / (DENSW - DENSMA)
4: PHIDSHm = (DENSSHm - DENSMA) / (DENSW - DENSMA)
5: PHIdc = PHIDm - Vsh * PHIDSHm

Apply density gas correction.
6: IF DENSITYGASSWITCH$ = "ON"
7: THEN PHIdc = KD * PHIdc

WHERE:
DENSSHm = density log reading in 100% shale reconstituted from density porosity data (gm/cc or Kg/m3)
DENSm = density value reconstituted from density porosity data (gm/cc or Kg/m3)
DENSMA = matrix density (gm/cc or Kg/m3)
DENSW = fluid density (gm/cc or Kg/m3)
PHID = porosity from uncorrected density log (fractional)
PHIdc = porosity from density log corrected for shale (fractional)
PHIDm = density porosity log reading corrected for matrix offset (fractional)
PHIDSH = density porosity log reading in 100% shale (fractional)
PHIDSHm = density porosity log reading in 100% shale corrected for matrix offset (fractional)
Vsh = volume of shale (fractional)

COMMENTS:
The graphical solution to these formulae is provided in Figure 7.05, shown in the previous section. As for the sonic log, simpler charts exist. However they should not be used if shale is present. All comments from Section 7.05 also apply.

WHERE:
DENSMA = matrix density (gm/cc or Kg/m3)
DENSW = fluid density (gm/cc or Kg/m3)
DENSSH = shale density (gm/cc or Kg/m3)

NUMERICAL EXAMPLE:
1. Data from Sand "D" in Classic Example 1
PHID = 0.12
PHIDSH = 0.03
Vsh = 0.33
Data is already in porosity units, so conversion to porosity units is not required.
No gas is known and log reading is not too high, so no gas correction is needed.
PHIdc = 0.12 - 0.33 * 0.03 = 0.11

2. Data from Sand "C" in Classic Example 1
PHID = 0.33
PHIDSH = 0.30
Vsh = 0.0
Log is already in porosity units, but porosity is too high due to gas.
PHIdc = 0.9 * 0.33 = 0.30
No shale correction is necessary.

3. Convert data to equivalent dolomite porosity with no change in fluid properties.
PHID = 0.30 (on sandstone scale)
DENSW = 1.00 gm/cc
DENSMA = 2.83 gm/cc (output units)
PHIDSH = 0.03
Vsh = 0.0
DENS = 0.30 * 1.00 + (1 - 0.30) * 2.65 = 2.15 gm/cc
DENSSH = 0.03 * 1.00 + (1 - 0.,03) * 2.65 = 2.60 gm/cc
PHIDm = (2.15 - 2.83) / (1.00 - 2.83) = 0.37
PHIDSHm = (2.60 - 2.83) / (1.00 - 2.83) = 0.12
PHIdc = 0.37 - 0.0 * 0.12 = 0.37

This value is quite high for a dolomite. Therefore, a gas correction should be considered, or else the rock is not a dolomite after all.

7.07 Porosity from Old Style Neutron Logs
For old style GRN or un-scaled neutron logs recorded in counts per second or API units, a porosity scale must be derived by the analyst. A logarithmic scale can be applied algebraically with the following formulae using the high porosity/low porosity method.

1: SLOPE = (log (PHIHI / PHILO)) / (CPSHI - CPSLO)
2: INTCPT = PHIHI / 10 ^ (CPSHI * SLOPE)
3: PHIn = INTCPT * 10 ^ (SLOPE * NCPS)

WHERE:
CPSHI = GRN counts at high porosity point (cps)
CPSLO = GRN counts at low porosity point (cps)
NCPS = neutron log reading in CPS or arbitrary units (cps)
PHIHI = high porosity point (fractional)
PHILO = low porosity point (fractional)
PHIn = apparent neutron log porosity, uncorrected for shale (fractional)

COMMENTS:
The graphical solution to this formula is given in Figure 7.06. Complete gas, shale and matrix corrections will still be required and are detailed in the following sections.

FIGURE 7.06: Chart for Estimating Porosity from Neutron Counts per Second - no shale correction

A large number of charts for specific tools, spacings, borehole conditions and rock types are available from service companies.

RECOMMENDED PARAMETERS:
PHIHI should be in the range 0.20 to 0.35.
PHILO should be in the range 0.01 to 0.05, and cannot be zero.

NUMERICAL EXAMPLE:
1. Assume an old GRN log where:
PHIHI = 0.30
PHILO = 0.01
NCPS = 2500 cps
CPSHI = 1500
CPSLO = 4500
SLOPE = (log (0.30 / 0.01)) / (1500 - 4500) = - 0.000492 (rounded to - 0.0005)
INTCPT = 0.30 / 10 ^ (1500 * (-0.0005)) = 1.6432
PHIn = 1.6432 * 10 ^ (-.0005 * 2500) = 0.096

7.08 Matrix Offset for Neutron Logs
It is often necessary to rescale a neutron log, which is already in porosity units, for lithology.

Sandstone porosity units to limestone units.
CASE 1: PHINm = PHIN - 3 - 1 * (IF NEUTRONTYPE$ = "CNL")
Limestone porosity units to sandstone units.
CASE 2: PHINm = PHIN + 3 + 1 * (IF NEUTRONTYPE$ = "CNL"
Mud cake thickness correction (SNP only).
CASE 3: PHINm = PHIN - 0.01 * max (0, CAL - BITZ) / (1 + 24.4 (IF DEPTHUNIT$ = "METRIC"))

If the log is recorded in limestone units or has been shifted to approximate limestone units, and a correction for more accurate lithology is desired, use the following formulae:

If lithology is sandstone and tool type is SNP.
CASE 4: PHINm = 0.024 + 1.021 * (PHIN ^ (-22.2 * PHIN - 1.96))
If lithology is dolomite and tool type is SNP.
CASE 5: PHINm = - 0.00434 + 0.749 * PHIN + 0.60 * (PHIN ^ 2)
If lithology is sandstone and tool type is CNL.
CASE 6: PHINm = 0.039 + 1.021 * (PHIN ^ (-22.2 * PHIN - 1.96))
If lithology is dolomite and tool type is CNL.
CASE 7: PHINm = -0.01259 + 0.389 * PHIN + 1.4 * (PHIN ^ 2)
If no lithology correction is needed.
CASE 8: PHINm = PHIN

WHERE:
BITZ = bit size (inches or mm)
CAL = caliper (inches or mm)
PHIN = original neutron log reading
PHINm = apparent neutron log porosity corrected for lithology (fractional)

COMMENTS:
These lithology adjustments are provided in graphical form in Figure 7.07.

FIGURE 7.07: Chart for Estimating Neutron Porosity - no shale correction

Shale and gas corrections are still needed after the lithology corrections have been applied, as described in the next section.

RECOMMENDED PARAMETERS:
None

7.09 Porosity From the Neutron Log
The response equation for the neutron porosity log also follows the classical form:

PHIN = PHIe * Sxo * PHINw (water term)
+ PHIe * (1 - Sxo) * PHINh (hydrocarbon term)
+ Vsh * PHINsh (shale term)
+ (1 - Vsh - PHIe) * Sum (Vi * PHINi) (matrix term)

WHERE:
PHINh = log reading in 100% hydrocarbon
PHINi = log reading in 100% of the ith component of matrix rock
PHIN = log reading
PHINsh = log reading in 100% shale
PHINw = log reading in 100% water
PHIe = effective porosity (fractional)
Sxo = water saturation in invaded zone (fractional)
Vi = volume of ith component of matrix rock
Vsh = volume of shale (fractional)

We usually assume PHINw = PHINh = 1.0, PHINi = 0.0, and that PHINsh and Vsh are known. This results in: PHInc = PHIN - Vsh * PHINSH

If PHINi is not zero, PHIN can be adjusted as in Section 7.08; then used in the response equation. If gas is present a correction factor is sometimes applied.

After converting from old style neutron logs or adjusting for lithology, the procedure is similar to that for sonic and density, namely gas correction and shale correction.

Apply neutron shale correction.
1: PHInc = PHIN - Vsh * PHINSH

Compute neutron log gas correction.
2: IF NEUTRONGASSWITCH$ = "ON"
3: THEN PHIN = KN * PHIN

WHERE:
KD = neutron gas correction factor (fractional)
PHIN = porosity from neutron log corrected for lithology or gas (fractional)
PHInc = porosity from neutron log corrected for shale (fractional)
PHINSH = apparent neutron log porosity of 100% shale (fractional)
Vsh = volume of shale (fractional)

COMMENTS:
A chart to solve this equation, along with the lithology shifts can be found in Figure 7.08.

FIGURE 7.08: Chart for Estimating Shale Corrected Neutron Porosity

KN is in the range of 1.0 to 3.0 depending on depth of invasion, gas density and logging tool type. Use local experience. Apply this correction only if gas is known to be present and log reading is still too low after lithology corrections.

The neutron log corrected for shale is one of the least accurate methods and should only be used if no other porosity data is available. This is common for wells drilled prior to 1957 or for wells logged through casing or drill pipe.

RECOMMENDED PARAMETERS:
PHINSH is in the range 0.10 to 0.40, with a default value of 0.30.

NUMERICAL EXAMPLE:
1. Assume data from Sand "D" in Classic Example 1
PHIN = 0.28
PHINSH = 0.30
Vsh = 0.33
neutron log type = CNL
CNL / FDC units = sandstone
Rescaling is not required, as log is in correct units.
No gas correction is required.

PHInc = 0.28 - 0.33 * 0.30 = 0.18

7.10 Summary of One-Log Porosity Methods
Previous sections of this Chapter have outlined several methods for calculating porosity from the individual porosity indicating logs. They are termed one-log methods, as opposed to two-log or crossplot methods, since only a single porosity indicating log is used in each case.

These methods, may be summarized in the following generalized terms:

l. Find total porosity (PHIt) in the zone of interest by scaling the log in porosity units as indicated in Table 7.01 or by using a calculator or computer with equations detailed above.

2. Apply lithology corrections if needed.

3. Estimate apparent porosity in nearby shale (PHI_SH) by observing the log response in shales, or calculating the apparent porosity of the shale from the equations.

4. Compute shale content (Vsh) from the GR, SP or density neutron crossplots as specified in Chapter Six.

5. Derive effective porosity (PHIe) by subtracting the porosity contribution of the shale.
PHIe = PHIt - Vsh * PHI_SH

6. Apply gas corrections if needed.

WHERE:
PHIe = effective porosity (fractional)
PHI_SH = shale porosity (fractional)
PHIt = total porosity (fractional)
Vsh = shale volume (fractional)

Porosity derived from any of these methods, after all corrections are applied, is called the effective porosity.

This reduction can usually be done without the aid of a calculator and allows for an accurate visual interpretation. The technique is suitable for sonic, density or neutron logs. If results from these three methods do not agree, then the analyst must find out why. Often a poor choice of shale base lines or matrix value is at fault. Calculations should be attempted again using new parameters until a satisfactory porosity result is obtained.

Note that the gas correction suggested here is extremely inaccurate, and that these methods are not recommended in gas zones, unless sufficient outside data is available for control.

The sonic method should not be attempted if the log skips excessively, unless the log can be edited confidently. The density method must not be tried in rough or large holes, as the log cannot usually be edited accurately. Use the caliper and density correction curves as a guide. None of the methods are valid in mixed lithology, unless the lithology can be zoned by use of sample descriptions. In all cases, use appropriate matrix values for reasonable results.

The answers for Classic Example 1 from the three methods described are given in Figure 7.09. The reader should verify the results before proceeding.

FIGURE 7.09: Computed Results for Shale Corrected Porosity - Classic Example 1

Plots of the computed results from all three one-log methods for the mixed lithology example are shown in Figure 7.24. These treated the zone as a shaly sandstone, so results are poor and do not match core very well where other minerals are present.

7.11 Quick Methods for Density Neutron Crossplot Calculations
Density neutron crossplot methods involve simultaneous solution of the response equations for the two logs. The response equation for the density log in porosity units follows the classical form:

PHID = PHIe * Sxo * PHIDw (water term)
+ PHIe * (1 - Sxo) * PHIDh (hydrocarbon term)
+ Vsh * PHIDsh (shale term)
+ (1 - Vsh - PHIe) * Sum (Vi * PHIDi) (matrix term)

WHERE:
PHIDh = log reading in 100% hydrocarbon
PHIDi = log reading in 100% of the ith component of matrix rock
PHID = log reading
PHIDsh = log reading in 100% shale
PHIDw = log reading in 100% water
PHIe = effective porosity (fractional)
Sxo = water saturation i