CHAPTER THIRTY: FRACTURED RESERVOIRS 3 Dual Porosity Model

Table of Contents
30.00 Introduction To This Chapter
30.01 Definition of Fractures
30.02 Basic Resistivity Concepts in Fractured Reservoirs
30.03 The Double Porosity Model in Fractured Reservoirs
30.04 Water Saturation in the Double Porosity Model
30.05 Case Histories: Fracture Analysis
30.06 In Conclusion
30.07 Exercises for Chapter Thirty
30.08: Bibliography for Chapter Thirty

Related Topics - Strongly Recommended
Chapter Twenty-Eight: Fracture Identification
Chapter Twenty-Nine: Simple Quantitative Models

Continue to Chapter Thirty-One

Publication History: This Chapter is an updated version of part of Chapter Nine of The Log Analysis Handbook Volume Two, originally self-published in 1990 as a seminar handout and workbook.

CHAPTER THIRTY: FRACTURED RESERVOIRS 3 Dual Porosity Model

30.00 Introduction To This Chapter
Natural fractures in reservoir rocks contribute significantly to productivity. Therefore, it is important to glean every scrap of information from open hole logs to locate the presence and intensity of fracturing. The use of conventional open hole logs for fracture location and fracture intensity calculations was covered in Chapter Twenty-Eight and Chapter Twenty-Nine. This Chapter deals with the dual porosity model as defined by Dr Roberto Aquilera in his original paper. Dr Aquilera has also published a hard cover textbook on the dual porosity model and fractured reservoirs in general. Students should review his material to augment this Chapter, which is briefer than the original material.

This Chapter contains some amplified or re-defined terminology that contrasts with some of Dr Aquilera’s definitions. Please be aware of these differences when reading both works.

Naturally fractured reservoirs contain secondary or induced porosity in addition to their original primary porosity. Induced porosity is formed by tension or shear stresses causing fractures in a competent or brittle formation. Fracture porosity is usually very small. Values between 0.0001 and 0.001 of rock volume are typical (0.01% to 0.1%). Fracture-related porosity, such as solution porosity in granite or carbonate reservoirs, may attain much larger values, but the porosity in the actual fracture is still very small.

Fracture analysis literature in the 1970’s suggested that fractures might contribute as much as a few to several percent porosity. More modern work using fracture aperture calculated from resistivity micro-scanner logs indicates much lower numbers. To appreciate this, consider fractures with 1 millimeter aperture spaced 1 meter apart. This gives a porosity of 0.001 fractional (0.1%). This is a very large open fracture. Most are only microns in width, so even 10 fractures of 10 microns each only give 0.0001 fractional porosity (0.01%.)

The term “secondary porosity” also includes rock-volume shrinkage due to dolomitization, porosity increase due to solution or recrystalization, and other geological processes. “Secondary porosity” should not be confused with “fracture porosity”. Secondary porosity formed in this way can be determined from modern log suites without difficulty (see Chapter Seven), except for porosity formed by fractures, which is too small to detect with conventional logs.

Fracture porosity is found accurately only by processing the formation micro-scanner curves for fracture aperture and fracture frequency (also called fracture intensity or fracture density). All other methods, including the well known “dual-porosity” model, are extremely inaccurate. These models either over-estimate fracture porosity by several orders of magnitude, or cannot be applied because the log data does not fit the model (for example when the sonic log skips, giving apparent porosity greater than the density neutron crossplot porosity - a common occurrence on older logs in fractured reservoirs).

The effect of fracture porosity on reservoir performance, however, is very large due to its enormous contribution to permeability. As a result, naturally fractured reservoirs behave differently than un-fractured reservoirs with similar porosity, due to the relative high flow capacity of the secondary porosity system. This provides high initial production rates, which can lead to extremely optimistic production forecasts and sometimes, economic failures when the small reservoir volume is not properly taken into account.

Reservoir simulation software that accounts for the fracture system is often termed a “dual porosity” model. While this is strictly true, it would be better to think of them as “dual permeability” models, since the fracture permeability fed by the matrix or reservoir permeability is far more important than the relatively small storage capacity of the fractures compared to the matrix porosity. A reservoir with only fracture porosity is quickly depleted; a decent reservoir in the matrix rock feeding into fractures will last much longer.

In order to understand the behavior of naturally fractured reservoirs, estimates must be made of hydrocarbons-in-place within both the primary (matrix rock) and secondary (fracture-only) porosity systems. To do this, we must first be able to detect the existence of fractures. Chapter Twenty-Eight covers fracture detection from the usually available conventional logs. This Chapter covers the method used to partition porosity into primary and fracture components. The effect of this partitioning on the Archie water saturation equation is also described.

30.01 Definition of Fractures
A fracture is a surface along which a loss of cohesion in the rock texture has taken place. A fracture is sometimes called a joint and, at the surface, are expressed as cracks or fissures in the rocks. Figure 30.01 shows the prominent features of a fracture. The orientation of the fracture can be anywhere from horizontal to vertical. The rough surface separates the two faces, giving rise to fracture porosity. The surfaces touch at points called asperities.

Altered rock surrounds each surface and infilling minerals may cover part or all of each surface. Minerals may fill the entire fracture, converting an open fracture to a healed or sealed fracture. The altered rock close to the fracture surfaces may contain more porosity than the unaltered host rock. Conversely, it could contain less porosity due to infilling by precipitated minerals.

FIGURE 30.01: Fracture Porosity Definitions - Note the distribution of Altered Rock that can contain “fracture-related” porosity

Fractures are caused by stress in the formation, which in turn usually derives from tectonic forces such as folds and faults. These are termed natural fractures, as opposed to induced fractures. Induced fractures are created by drilling stress or by purposely fracturing a reservoir by hydraulic pressure from surface equipment (see Chapter Twenty). Both kinds of fractures are economically important. Induced fractures may connect the wellbore to natural fractures that would otherwise not contribute to flow capacity.

Natural fractures are more common in carbonate rocks than in sandstones. Some of the best fractured reservoirs are in granite - often referred to as unconventional reservoirs. Fractures occur in preferential directions, determined by the direction of regional stress. This is usually parallel to the direction of nearby faults or folds, but in the case of overthrust faults, they may be perpendicular to the fault or there may be two orthogonal directions. Induced fractures usually have a preferential direction, often perpendicular to the natural fractures. A schematic diagram of these relationships is shown above in Figure 30.01, bottom right.

A fracture is often a high permeability path in a low permeability rock, or it may be filled with a cementing material, such as calcite, leaving the fracture with no permeability. Thus it is important to distinguish between open and healed fractures. The total volume of fractures is often small compared to the total pore volume of the reservoir.

Most natural fractures are more or less vertical. Horizontal fracture may exist for a short distance, propped open by bridging of the irregular surfaces. Most horizontal fractures, however, are sealed by overburden pressure. Both horizontal and semi-vertical fractures can be detected by various logging tools.

The vertical extent of fractures is often controlled by thin layers of plastic material, such as shale beds or laminations, or by weak layers of rock, such as stylolites in carbonate sequences. The thickness of these beds may be too small to be seen on logs, so fractures may seem to start and stop for no apparent reason.

To be an aid in production, fractures must be connected to a reasonable hydrocarbon bearing reservoir with sufficient volume to warrant exploitation. If there is no reservoir volume, a lot of fractures won’t help much unless there is sufficient fracture related solution porosity to hold an economic reserve. This can be determined by normal log analysis techniques. In reasonable non-fractured reservoirs, it is usually possible to estimate permeability, and hence productivity (see Chapter Ten), but this is not always possible in fractured reservoirs. Processing of modern resistivity micro-scanner logs ha s given us the ability to calculate both fracture porosity and permeability, but such logs are rare and cannot be run in older wells.

Although both the presence of fractures and the presence of a reservoir can be determined from logs, a production test will be needed to determine whether economic production is possible. The test must be analyzed carefully to avoid over optimistic predictions based on the flush production rates associated with the fracture system. Local correlations between fracture intensity observed on logs and production rate are also used to predict well quality.

Sometimes the primary reservoir and the fracture system may be so poorly connected that they are saturated with different fluids. Production from fractures full of hydrocarbons in a water bearing formation may initially be very good but very short lived. A more desirable scenario is a primary reservoir with appreciable hydrocarbon saturation and a fracture system that is full of water close to the borehole, showing invasion and hence good permeability, but full of hydrocarbon in the virgin formation.

Quantitative analysis of fracture aperture is possible by further processing of formation micro-imager conductivity data. The algorithm is based on the concept that higher conductivity means a larger open fracture. The fracture aperture and fracture frequency can be combined to obtain fracture porosity and fracture permeability.

Where:
KF1 = number of main fracture directions
= 1 for sub-horizontal or sub-vertical
= 2 for orthogonal sub-vertical
= 3 for chaotic or brecciated
PHIfrac = fracture porosity (fractional)
Df = fracture frequency (fractures per meter)
Wf = fracture aperture (millimeters)
Kfrac = fracture permeability (millidarcies)

Note: Equations 2, 3, and 4 give identical results.

Example 1:
Df = 1 fracture per meter
Wf = 1.0 millimeters
PHIfrac = 0.001 * 1 * 1 = 0.001 fractional (0.1%)
Kfrac = 833 * 100 * 1^3 * 1 * 1 = 83300 millidarcies

Example 2:
Df = 10 fractures per meter
Wf = 0.1 millimeters
PHIfrac = 0.001 * 10 * 0.1 = 0.001 fractional (0.1%)
Kfrac = 833 * 100 * 0.1^3 * 10 * 1 = 833 millidarcies

These examples represent well fractured reservoirs. You can see that the volume of hydrocarbon in the fractures is very small but the permeabilty is very high.

An example of a fracture aperture log from a program called Frac-View is shown in Figure 30.02. The permeability calculation was not available in this program.

FIGURE 30.02: Fracture frequency, aperture, and porosity log

30.02 Basic Resistivity Concepts in Fractured Reservoirs
Quantitative analysis of fractured reservoirs is complicated by the fact that other forms of porosity exist besides that contained by the fractures. Thus a dual porosity model has been proposed to account for both primary and secondary porosity. The theoretical principles behind the dual porosity model have been published previously in the literature by Aguilera and have been used by others with some success in Mexico, Venezuela, the United States, and Canada.

The term "dual porosity" should not be confused with the "dual water" model used for shaly formations. In addition, the fractured reservoir literature uses the phrase "total porosity" to mean the sum of effective matrix porosity plus effective fracture porosity. This is very confusing as the phrase has a different meaning in the shaly sand situation. Since there are fractured shaly reservoirs where the distinction between total and effective porosity is important, we will use the following definitions.

WHERE:
PHIe = effective porosity of dual porosity system (fractional)
PHIm = effective matrix porosity in dual porosity system (fractional)
PHIf = effective fracture porosity of dual porosity system (fractional)
PHIt = total porosity of any rock (fractional)
Vsh = shale volume (fractional)
BVWSH = bound water in 100% shale (fractional)

Some fracture literature also uses the term secondary porosity to mean fracture porosity, whereas this term has been used by others to describe the porosity not seen by the sonic log, usually some portion of the vuggy porosity. We prefer to use secondary porosity in its geological sense and use the term fracture porosity in a strictly literal sense.

To develop the dual porosity model, we invoke the basic Archie equations.

WHERE:
A = tortuosity exponent (unitless)
F = formation factor (unitless)
I = resistivity index (unitless)
M = cementation exponent (unitless)
PHIe = effective porosity of dual porosity system (fractional)
RESD = true )deep) formation resistivity (ohm-m)
RW@FT = formation water resistivity (ohm-m)

Analysis of equation 5 indicates that a crossplot of porosity vs resistivity on log-log coordinate paper will result in a straight line with a slope of -M for zones of constant water resistivity (A * RW@FT) and constant resistivity index (I). A constant resistivity index implies that the zone has constant water saturation (Sw), where Sw = (1 / I) ^ (1 / N). This plot has been called the Pickett plot and is widely used to find both A * RW@FT and M for water zones and Sw for hydrocarbon zones in conventional reservoirs.

IMPORTANT: This method is not suitable for shaly reservoirs as no shale term is included in the Pickett plot (see Figure 30.03). Therefore, be sure to exclude shale or shaly zones from a Pickett plot.

FIGURE 30.03: Porosity - resistivity crossplot (Pickett plot) identifies M

For reservoirs with fracture porosity, the value of M found from the Pickett plot is smaller than the cementation exponent, M, determined from a primary porosity sample in the laboratory, or estimated from lithological descriptions, or from an un-fractured portion of the reservoir. This is reasonable because fracture porosity results in a reduction in tortuosity and cementation. In addition, fractures can be invaded deeply by drilling fluids, thus reducing RESD and the derived value of M from the crossplot. The lower M may be compensating for invasion as much as for the fractured nature of the rock. In any case, a lower value for M decreases water saturation and this is needed whether the lower resistivity is due to invasion or to lower cementation.

Values of M from the Pickett plot in the range 1.2 to 1.7 can be expected for fractured reservoirs, as opposed to 1.8 to 2.4 for the un-fractured portion of the same rock. The laboratory measurement of M for a well-fractured rock is seldom successful, so there is not much real data to use, except in competent samples with minor micro-fractures.

We can then redefine M to reflect these differences.

Choosing Md and Mb

Normally, Md is chosen once for each fractured interval from the Pickett plot, but there is no reason to believe it is a constant because fracture intensity varies dramatically from foot to foot within the reservoir. It is clear on Figure 30.03 that every data point could have a unique value of Md, assuming all are 100% wet.

A method has been proposed by Rasmus whereby Md is calculated and used at each level, thus providing a "variable M" method throughout the zone. It is based on the sonic versus density neutron porosity:

The derivation is rather lengthy and not shown here. A fracture tortuosity term has also been omitted because it is often assumed to be 1. This presumes that PHIe >= PHIsc and PHIsc has been adequately corrected for lithology and shale. When there are no fractures, PHIsc = PHIe and Md = Mb.

In many cases, it is possible to carry out the evaluation by crossplotting (DELT - DELTMA) vs RESD, or (DENS - DENSMA) vs RESD on log-log paper instead of PHIe vs RESD. The sonic log method is not recommended if vuggy porosity exists, because the sonic log does not see all this porosity. Thus PHIsc will be too low and Md would be wrong. Likewise, if PHIsc > PHIe, the method should be abandoned.

The value of Md is determined by calculating the slope of the line drawn through the south west points in the Pickett plot, which are assumed to be water bearing levels. If no water bearing points are available because there is no water zone in the fractured interval, it is possible to make the plot by replacing RESD with RESS, the shallow resistivity, based on the assumption that the invaded zone will be more nearly 100% wet than the un-invaded zone. The constant in the equation becomes (A * RMF@FT), but this value is known as well or better than (A * RW@FT).

With the value of Md determined from the crossplot or equation 6 and Mb determined in the laboratory or estimated from lithology, it is possible to complete the evaluation to quantify primary and fracture porosities, as proposed by Aguilera.

30.03 The Dual Porosity Model in Fractured Reservoirs
The first assumption made is that matrix and fractures are connected in parallel and 100 per cent saturated with formation water:

Since it is the breakdown of PHIe into PHIm and PHIf that we are seeking, the above equation cannot help us find V directly. A useful approximation is:

This also assumes that PHIe >= PHIsc and that PHIsc is properly corrected for lithology and shale.

WHERE:
PHIe = effective porosity of dual porosity system (fractional), usually taken equal to PHIxnd from density neutron crossplot
PHIm = effective matrix porosity in dual porosity system (fractional)
PHIf = effective fracture porosity of dual porosity system (fractional)
PHIsc = sonic porosity (fractional)
Rfo = composite system resistivity at 100% Sw (ohm-m)
Ro = primary porosity resistivity at 100% Sw (ohm-m)
RW@FT = formation water resistivity at formation temperature (ohm-m)
F = formation factor for matrix rock (unitless)
Fd = formation factor for dual porosity model (unitless) Md = cementation exponent for dual porosity model, found from a Pickett plot
Mb = cementation exponent for un-fractured matrix rock, found from laboratory measurement, a Pickett plot in an un-fractured zone, or from assumption based on lithology
V = partitioning coefficient (fractional)

FIGURE 30.04: Pickett plot, partition factor, and probability graphs for Aguilera’s dual porosity model

Figure 30.04, top right, shows the graphical solution to Equation 5 for various values of Mb. If, for example, Md is 1.4, Mb = 2.0, and effective porosity (PHIe) is 0.04, then the partitioning coefficient V is 0.26; thus, the fracture (-related) porosity (PHIf) is 0.0106 and the matrix porosity (PHIm) is 0.0294.

To compare this result to core analysis, we must find matrix porosity from logs as a function of the matrix bulk volume (PHIcore), eliminating the volume of the fractures:

WHERE:
PHIcore = effective matrix porosity corrected to match core (fractional)
PHIm = effective matrix porosity in double porosity system (fractional)
PHIf = effective secondary porosity of double porosity system (fractional)

For example, if V is 0.26 and PHIe is 0.04, then fracture porosity, PHIf, is 0.0106 and PHIm is 0.0294 as before, and:
PHIcore = 0.0294 / (1 - 0.0106) = 0.0297

NOTE: If the partitioning coefficient V cannot be found from sonic versus density neutron crossplot porosity, then equation 2 and 7 must be solved iteratively.

Fracture detection methods described in Chapter Twenty-Eight require that the fractures intersect the borehole and be invaded by mud of relatively low resistivity. This is not the case with the method presented here. In some cases it has been possible to detect fractures located within the radius of investigation of the logging tools, but not intercepted by the borehole.

RECOMMENDED PARAMETERS:
Md is in the range 1.0 to 1.8
Mb is in the range 1.6 to 2.6
V is in the range 0.0 to 0.5

30.04 Water Saturation in the Dual Porosity Model
The average water saturation of the composite system is calculated using a statistical parameter, P, originally introduced to the oil industry by Porter, Pickett, and Whitman. Empirically, it has been found that P has a normal distribution for intervals which are 100 per cent saturated with water. Intervals with some hydrocarbon saturation deviate from the normal distribution.

WHERE:
DELT = sonic log reading (usec/ft or usec/m)
DELTMA = sonic matrix transit time (usec/ft or usec/m)
DENS = density log reading (g/cc or Kg/m3)
DENSMA = matrix density (g/cc or Kg/m3)
Md = cementation exponent for double porosity model, found from a Pickett plot
P = statistical parameter (unitless)
PHIe = effective porosity of double porosity system (fractional)
RESD = deep resistivity log reading (ohm-m)

Figure 30.04, bottom left, shows a schematic of P vs cumulative frequency on probability paper for a water and hydrocarbon system. The 100 per cent water saturated zones form a straight line, and the hydrocarbon intervals deviate from this line and are thus easily recognized.

Figure 30.04, bottom right, shows the same type of plot for only the water bearing intervals. The mean value of P for water zone, Pmean, is determined from this graph at a cumulative frequency of 50 per cent. An arithmetic average of the P values from the water leg is usually satisfactory, so the probability plot is not necessary.

Having the mean value of P from the water zone allows us to calculate the water saturation of the dual porosity system from the following.

WHERE:
Bo = oil formation volume factor (vol/vol)
N = water saturation exponent (unitless)
Phyd = parameter P for each hydrocarbon zone (unitless)
Pwtr = mean value of P for water bearing intervals (unitless)
Swd = water saturation for the double porosity system (fractional)
Swe = water saturation for the matrix rock (fractional)
Swf = water saturation for the fracture (fractional)
VISW = water viscosity (cp)
VISO = oil viscosity (cp)
WOR = water/oil ratio, (vol/vol)

This long evaluation process requires the reading, plotting, and crossplotting of large volumes of data, and requires a large number of calculations. This makes it an ideal computer application and hand calculation is not recommended. A solution for a gas reservoir was never published. In many cases Swf is assumed to be 0.0 (because WOR = 0)so this assumption can be used for gas wells also.

NOTE: This is essentially an "Rwa type" saturation method and relies on the presence of a water zone. In the absence of a water zone, an Archie water saturation solution (Swa) will have to suffice, giving the equivalent of Swe. Swf is not derived from log data. If parameters are unknown, start with VISW =1.0, VISO = 2.0, WOR = 0.0, and Bo = 0.8. This makes Swf = 0.0 during production, which is close to the truth.

WHERE:
A = tortuosity exponent (unitless)
Md = cementation exponent for matrix rock with fractures (unitless)
N = saturation exponent (unitless)
PHIe = effective porosity (fractional)
RESD = deep resistivity log reading (ohm-m)
RW@FT = water resistivity at formation temperature (ohm-m)
Swa = effective water saturation (fractional)

FIGURE 30.05: Dual porosity model results in a Williston Basin well

RECOMMENDED PARAMETERS:
If zone is not heavily fractured:
For sandstones:
A = 0.62
Mb = 2.15
N = 2.00

For carbonates:
A = 1.00
Mb = 2.00
N = 2.00

If zone is fractured:
Mb = 1.4 to 2.0
A = 1.00
N = 2.00

NOTE: The symbol M is used elsewhere in this book as the cementation exponent for the Archie equation. Mb is used here to indicate the use of Archie for the fractured reservoir case.

Figure 30.05 shows the computed log results for a Williston Basin Mississippian fractured zone. The contribution of fracture porosity is about 1% porosity, but water saturation is 5 to 10% lower than the analysis without the fractures. The partitioning coefficient varies and was solved by iteration.

30.05 Case Histories: Dual Porosity Fracture Analysis
**** Waiting on release of data from client

30.06 In Conclusion
Fractures are an important economic component in many reservoirs, and may be the only socially redeeming factor in most tight reservoirs. Fractures can be found in nearly all sedimentary basins and in nearly all types of traps. Many are unsuspected until an anomalous production test is run or a production history match fails on a reservoir simulator.

Most open hole logs show some indication of the fractures, although the effect may be subtle, and hard to see. Some logs show fractures better than others, and these should be run if fractures form a significant fraction of the reservoir permeability.

Even with the dual porosity model, it is difficult to quantify the log response to fractures and thus their net effect on reservoir quality is usually not well defined. The specific definitions of porosity involved in the dual porosity model should be well understood before using the method. In addition, accurate lithology and shale corrections are required before the method can be applied. Fracture porosity and permeability from resistivity micro-scanner processing may be more useful and more illuminating than the “fracture-related” porosity from the dual water model.

The mere presence of fractures, however, is usually a good sign, unless the fractures also penetrate the water leg of the pool. In this case it is difficult to stop water from being produced with the oil or gas. A good quantitative analysis of the porosity and water saturation will help prevent completions too close to the water contact.

30.07 Exercises for Chapter Thirty
Exercise 30.01: Dual Porosity Fracture Concepts
1. Define a fracture and its porosity components. Why are fractures important? (5 marks)

2. Contrast the definition of fracture porosity as used in the dual porosity model with the definition used in this book. (5 marks)

3. Describe the dual porosity/dual permeability model for fractured reservoirs. (5 marks)

4. Define the porosity partition factor V as used in this model. (5 marks)

5. How are Pickett plots used to help evaluate fractured reservoirs? (5 marks)

6. Which log can be processed to provide fracture porosity. (5 marks)

7. Given 10 fractures per meter with an average aperture of 50 microns, what is the fracture porosity and fracture permeability. (5 marks)

Exercise 30.02 - Dual Porosity Example (130 marks)
1. Using the visual log analysis procedure of The Petrophysical Pocket Pal, identify shale zones, clean zones, porous zones, and possible hydrocarbon zones. Draw bed boundaries (horizontal lines) and pick log values in each rock layer (vertical lines). Label each zone with a number, starting with your top zone.

2. Are these logs in English or Metric units?______ Is the hole in good condition?_________

3. What is the approximate porosity of the cleanest zone? ___________

4. Is there a water zone? __________What depth?____________________

5. Is there a hydrocarbon zone? ___________What depth?_________________ Based on log response and test data, identify gas/oil contact____________ and oil/water contact_________________ .

6. Pick the following values from the logs:
Shale properties: Gamma Ray clean line (GR0) ___________ _______
Gamma Ray shale line (GR100) _________ _______
Density shale line (PHIDSH) ___________ _______
Neutron shale line (PHINSH) ___________ _______
Sonic shale line (DELTSH) ___________ _______
Resistivity shale line (RSH) __________ _______

Other useful well history (if data is not provided, make rational assumptions):
Catalog water resistivity (RW) ____ @ 25'C (77'F)
Bottom hole temperature (BHT) __'C
Bottom hole depth (BHTDEP) ____ meters
Surface temperature (SUFT) __'C
Perforated interval ____ - ____ meters
Initial production ____ m3/day of ______

Sample description: dolomite, some calcite, vuggy porosity

7. Calculate shale volume from the SP and density neutron separation. Why is the GR method not used?__________

LEVEL TOP BOTTOM
NUMBER DEPTHS GR SP PHIN PHID Vshx Vshs Vshmin
___ ______ ______ _____ _____ _____ _____ _____ _____ _____ _____ _____ _____
___ ______ ______ _____ _____ _____ _____ _____ _____ _____ _____ _____ _____
___ ______ ______ _____ _____ _____ _____ _____ _____ _____ _____ _____ _____
___ ______ ______ _____ _____ _____ _____ _____ _____ _____ _____ _____ _____
___ ______ ______ _____ _____ _____ _____ _____ _____ _____ _____ _____ _____

8. Calculate effective porosity from one log sonic and density neutron crossplot. Which porosity method is best for this zone?_________ Why?___________________ How much vuggy porosity is present?

LEVEL TOP BOTTOM
NUMBER DEPTHS Vsh DELT PHIN PHID PHIsc PHInc PHIdc PHIxnd PHIsec
___ ______ ______ _____ _____ _____ _____ _____ _____ _____ _____ _____ _____
__ ______ ______ _____ _____ _____ _____ _____ _____ _____ _____ _____ _____
___ ______ ______ _____ _____ _____ _____ _____ _____ _____ _____ _____ _____
___ ______ ______ _____ _____ _____ _____ _____ _____ _____ _____ _____ _____
___ ______ ______ _____ _____ _____ _____ _____ _____ _____ _____ _____ _____

9. Calculate lithology from the photo electric method. Which two end point minerals did you use for the two mineral model?________________________ What values did you use for:
PE of shale (PESH) ______________
PE of mineral one (PE1) ______________
PE of mineral two (PE2) ______________
Can you calculate a three mineral model in each zone?_________ Why (not)? ______________________________________

LEVEL TOP BOTTOM
NUMBER DEPTHS Vsh PHIe PE V1 V2
___ ______ ______ _____ _____ _____ _____ _____ _____ _____ _____ _____ _____
___ ______ ______ _____ _____ _____ _____ _____ _____ _____ _____ _____ _____
___ ______ ______ _____ _____ _____ _____ _____ _____ _____ _____ _____ _____
___ ______ ______ _____ _____ _____ _____ _____ _____ _____ _____ _____ _____
___ ______ ______ _____ _____ _____ _____ _____ _____ _____ _____ _____ _____

10. Calculate water resistivity from the water zone, using Rwa (water zone) method. Show all data and method. Do you think this value is accurate?________ Why (not)?_ _________________________________

11. Calculate water saturation from Archie method. Is this method OK for this example?_______ What value of RW @ FT did you use?_________ RSH?_____ A?_____ M? ______ N?__________

LEVEL TOP BOTTOM
NUMBER DEPTHS Vsh PHIe RESD Rwa Swa
___ ______ ______ _____ _____ _____ _____ _____ _____ _____ _____ _____ _____
___ ______ ______ _____ _____ _____ _____ _____ _____ _____ _____ _____ _____
___ ______ ______ _____ _____ _____ _____ _____ _____ _____ _____ _____ _____
___ ______ ______ _____ _____ _____ _____ _____ _____ _____ _____ _____ _____
___ ______ ______ _____ _____ _____ _____ _____ _____ _____ _____ _____ _____

12. Make a Pickett Plot for the water zone this example. Is M constant or variable?

13. List fractured intervals and state which log curves show the fractures. Pick Md from the Pickett plot for these intervals.

LEVEL TOP BOTTOM Interval
NUMBER DEPTHS Thickness Indicator Logs Md Mb
___ ______ ______ _____ _____ _____ _____ _____ _____ _____ _____ _____ _____
___ ______ ______ _____ _____ _____ _____ _____ _____ _____ _____ _____ _____
___ ______ ______ _____ _____ _____ _____ _____ _____ _____ _____ _____ _____
___ ______ ______ _____ _____ _____ _____ _____ _____ _____ _____ _____ _____
___ ______ ______ _____ _____ _____ _____ _____ _____ _____ _____ _____ _____

14. Calculate partition factor V, fracture and matrix porosity, statistical factor P, and water saturation from the dual porosity model. What value did you choose for Pwtr? __________

LEVEL TOP BOTTOM
NUMBER DEPTHS PHIe PHIsc V PHIf PHIm P Swd Swf Swe Swa
___ ______ ______ _____ _____ _____ _____ _____ _____ _____ _____ _____ _____
___ ______ ______ _____ _____ _____ _____ _____ _____ _____ _____ _____ _____
___ ______ ______ _____ _____ _____ _____ _____ _____ _____ _____ _____ _____
___ ______ ______ _____ _____ _____ _____ _____ _____ _____ _____ _____ _____
___ ______ ______ _____ _____ _____ _____ _____ _____ _____ _____ _____ _____

15. Explain the differences between Swe and Swa.

16. If this was your well, what logs would you run in addition to those presented? _________________ Why?

Which would you omit? ________________Why?

FIGURE 30X02A: Induction log segment for Exercise 30.02

FIGURE 30X02B: Sonic waveform log segment for Exercise 30.02

FIGURE 30X02C: Density neutron log segment for Exercise 30.02

FIGURE 30X02D: Sonic log segment for Exercise 30.02

FIGURE 30X02E: Sonic amplitude log segment for Exercise 30.02

FIGURE 30X02F: Stoneley waveform log segment for Exercise 30.02

FIGURE 28X04F: Stoneley wave amplitude log segment for Exercise 30.02

FIGURE 30X02G: Lithology analysis log segment for Exercise 30.02

30.08 Bibliography for Chapter Thirty
1. Analysis of naturally fractured reservoirs from conventional well logs; Aguilera,R.; The Journal of Canadian Petroleum Technology, p. 764-772, 1976

2. Current status on the study of naturally fractured reservoirs; Aguilera,R., van Poollen,H.K.; Society of Professional Well Log Analysts: The Log Analyst, p. 3-23, 1977

3. Geologic aspects of naturally fractured reservoirs explained; Aguilera,R., van Poollen,H.K.; The Oil and Gas Journal, 13 sections, 1978

4. FCL: a computerized well log interpretation process for the evaluation of naturally fractured reservoirs; Aguilera,R., Acevedo,L.A.; The Journal of Canadian Petroleum Technology, p. 31-36, 1982

5. A variable cementation exponent, M, for fractured carbonates; Rasmus,J.C.; Society of Professional Well Log Analysts: The Log Analyst, p. 13-23, 1983

ABOUT THE AUTHOR

E. R. (Ross) Crain, P.Eng. is a Consulting Petrophysicist and a Professional Engineer with over 35 years of experience in reservoir description, petrophysical analysis, and management. He has been a specialist in the integration of well log analysis and petrophysics with geophysical, geological, engineering, and simulation phases of oil and gas exploration and exploitation, with widespread Canadian and Overseas experience.

His textbook, "Crain's Petrophysical Handbook on CD-ROM" is widely used as a reference to practical log analysis. Mr. Crain is an Honourary Member and Past President of the Canadian Well Logging Society (CWLS), a Member of Society of Petrophysicists and Well Log Analysts (SPWLA), and a Registered Professional Engineer with Alberta Professional Engineers, Geologists and Geophysicists (APEGGA)