Although wellbore image data only provide information on the apparent aperture of faults where they are intersected by a wellbore, empirical relations have been proposed that attempt to relate fault length to aperture (e.g. Gudmundsson 2000) and enable one to develop ideas about fracture networks from wellbore image data. However, it should be pointed out that the aperture at the wellbore wall is not the actual width of the fault plane. As discussed by Barton, Tessler et al. (1991), image logs are basically measuring the smoothness of the wellbore wall, such that the logs are quite sensitive to any spalling at the wellbore wall that occurs as the bit penetrates the fault plane. Thus, the apparent aperture is always going to be larger than the actual aperture. Barton, Tessler et al.
(1991) point out that it is sometimes useful to qualitatively distinguish large from small aperture faults during the analysis of image data.
One obvious limitation of imaging tools is that they will undersample fractures and faults whose planes are nearly parallel to the wellbore axis. This is most easily visualized for a vertical well – the probability of intersecting horizontal fractures in the formation is one, but the probability of intersecting vertical fractures is essentially zero. Following Hudson and Priest (1983), it is straightforward to estimate the correction to apply to a fracture population of a given dip. If we have a set of fractures of constant dip,φ, with an average separation D (measured normal to the fracture planes), the number of fractures observed along a length of wellbore, L= D/cosφ, Nobs(φ) must be corrected in order to obtain the true number of fractures that occur in the formation over a similar distance, Ntrue(φ) via
Ntrue(φ)=(cosφ)−1Nobs(φ) (5.6)
This is illustrated for densely fractured granitic rock by Barton and Zoback (1992), who also discuss sampling problems associated with truncation, the inability to detect extremely small fractures, and censoring, the fact that when an extremely large fault zone is penetrated by a wellbore, it is often difficult to identify the fault plane because the wellbore is so strongly perturbed that data quality is extremely poor.
( D I P I S P O S I T I V E TO T H E R I G H T W H E N
L O O K I N G I N T H E S T R I K E D I R E C T I O N )
U P
S O U T H
E A S T S T R I K E
( M E A S U R E D F RO M N O RT H )
S L I P R a ke
D i p D I P D I R E C T I O N ( F RO M N O RT H )
F AU LT P L A N E
Figure 5.5. Definition of strike, dip and dip direction on an arbitrarily oriented planar feature such as a fracture or fault. Rake is the direction of slip in the plane of the fault as measured from horizontal.
scratch on the footwall, resulting from relative motion of the hanging wall. The slip direction is defined by the rake angle, which is measured in the plane of the fault from horizontal.
A variety of techniques are used to represent the orientation of fractures and faults at depth. One of the most common techniques in structural geology is the use of lower hemisphere stereographic projections as illustrated in Figure 5.6 (see detailed discussions in Twiss and Moores 1992 and Pollard and Fletcher 2005). Stereographic projections show either the trace of a fracture plane (where it intersects the lower half of the hemisphere) or the intersection of fracture poles (normals to the fracture planes) and the hemisphere (Figure 5.6a). The circular diagrams (Figure 5.6b) used to represent such projections are referred to as stereonets (Schmidt equal area stereonets).
As shown in Figure 5.6b, near-horizontal fractures dipping to the northwest have poles that plot near the center of the stereonet whereas the trace of the fractures plot near the edge of the stereonet (upper left stereonet). Conversely, near-vertical fractures striking to the southeast and dipping to the southwest have poles that plot near the edge of the figure and fracture traces that cut through the stereonet near its center (lower right stereonet). The cloud of poles shown in each figure illustrates a group of fracture or fault planes with similar, but slightly different, strikes and dips. The second column
S T R I K E N 3 0o
D I P 4 0o W
N N
W
E
E
S S
Po l e 3 0o
4 0o
a. Shallow NW and SW
dipping planes E
Cluster of SW dipping planes N
N W
W E
E S
S 1
2 3
3 2
1 b.
+
+
Figure 5.6. Illustration of the display of fracture and fault data using lower hemisphere
stereographic projections. Either the intersection of the plane with the hemisphere can be shown or the pole to the plane. Planes which are sub-horizontal have poles that plot near the center of the stereonet whereas steeply dipping planes have poles which plot near the edge.
in Figure 5.1 illustrates the orientations of Mode I, normal, strike-slip and reverse faults in stereographic presentations.
Figure 5.7 shows the distribution of relatively small faults encountered in granitic rock in a geothermal area over the depth range of 6500–7000 feet that have been mapped with an electrical imaging device such as that shown in Figure 5.4. Figure 5.7a shows the data as a tadpole plot, the most common manner of portraying fracture data in the petroleum industry. The depth of each fracture is plotted as a dot with its depth along the ordinate and the amount of dip along the abscissa (ranging from 0 to 90◦). The dip direction is shown by the direction that the tail of the tadpole points. This interval is very highly fractured (almost 2000 fractures are intersected over the 500 ft interval).
The stereonet shown in Figure 5.7b illustrates the wide range of fracture orientations over the entire interval. Poles are seen at almost every location on the stereonet but the numerous poles just south of west indicate a concentration of steeply dipping fractures striking roughly north northwest and dipping steeply to the northeast. The advantages and disadvantages of the two types of representations are fairly obvious. Figure 5.7a allows one to see the exact depths at which the fractures occur as well as the dip and dip direction of individual planes, whereas Figure 5.7b provides a good overview of concentrations of fractures and faults with similar strike and dip.
Tadpole plot
N
S
E W
N
S
E W
N
S
E W
0 0.4 0.8 1.2 1.6 2 2.4 2.8 3.2 3.6 4 4.4
0 30 60 90
6500
6600
6700
6800
6900
7000
Depth (ft MD)
P O L E S TO F R AC T U R E L A N E S
K A M B C O N TO U R O F P O L E S TO P L A N E S M A X . D E N S I T Y = 4 . 7 6 s d
F R AC T U R E S T R I K E N = 1 , 9 8 7 a.
b.
c.
d.
Figure 5.7. The distribution of fault data from a geothermal well drilled into granite can be displayed in various ways. (a) A tadpole plot, where depth is shown on the ordinate and dip on the abscissa. The dip direction is shown by the direction of the tail on each dot. (b) A stereographic projection shows the wide distribution of fracture orientation. (c) A contour plot of the fracture density (after Kamb1959) to indicate statistically significant pole concentrations. (d) A rose diagram (circular histogram) indicating the distribution of fracture strikes.
In highly fractured intervals such as that shown in Figure 5.7b, it is not straightfor- ward to characterize the statistical significance of concentrations of fractures at any given orientation. Figure 5.7c illustrates the method of Kamb (1959) used to contour the difference between the concentration of fracture poles with respect to a random dis- tribution. This is expressed in terms of the number standard deviations that the observed
S a n t a B a r b a r a C h a n n e l P t . A r g u e l l o
5 0 k m
E a r t h q u a k e m a g n i t u d e :
< 2 2 - 4 4 - 6
A
B
D C B A
D
C
N
Figure 5.8. The Point Arguello area in western California is characterized by numerous
earthquakes (dots), active faults and folds (thin lines). Image data from four wells drilled into the Monterey formation (A,B,C,D) illustrate the complex distribution of faults and fractures in each as shown in the stereonets (after Finkbeiner, Barton et al.1997). AAPGC 1997 reprinted by permission of the AAPG whose permission is required for futher use.
concentration deviates from a random distribution. The areas with dark shading (>2 sd) indicate statistically significant fracture concentrations. The concentration of poles that were noted above corresponding to fractures striking north northwest and dip- ping steeply to the northeast is associated with a statistically significant concentration of poles.
Figure 5.7d shows a rose diagram (circular histogram) of fracture strikes. While the data indicate that the majority of fractures strike NNW–SSE, there are obviously many fractures with other orientations. One shortcoming of such representations is that they do not represent any information about fracture dip.
Figure 5.8 illustrates a case study in the Monterey formation in western California.
Finkbeiner, Barton et al. (1998) studied four wells penetrating the highly folded, frac- tured and faulted Monterey formation at the sites shown. As discussed further in Chapter 11, the presence of these fractures and faults in the Monterey is essential for there being sufficient permeability to produce hydrocarbons. In fact, the outcrop photograph shown
in Figure 5.2b was taken just west of well C in Figure 5.8. Numerous earthquakes occur in this region (shown by small dots), and are associated with slip on numerous reverse and strike-slip faults throughout the area. The trends of active faults and fold axes are shown on the map. The distribution of fractures and faults from analysis of ultrasonic borehole televiewer data in wells A–D are presented in the four stereonets shown. The direction of maximum horizontal compression in each well was determined from analy- sis of wellbore breakouts (explained in Chapter 6) and is northeast–southwest compres- sion (as indicated by the arrows on stereonets). Note that while the direction of maximum horizontal compression is relatively uniform (and consistent with both the trend of the active geologic structures and earthquake focal mechanisms in the region as discussed later in this chapter), the distribution of faults and fractures in each of these wells is quite different. The reason for this has to do with the geologic history of each site. The highly idealized relationships between stress directions and Mode I fractures and conjugate normal, reverse and strike-slip faults (illustrated in Figure 5.1) are not observed. Rather, complex fault and fracture distributions are often seen which reflect not only the cur- rent stress field, but deformational episodes that have occurred throughout the geologic history of the formation. Thus, the ability to actually map the distribution of fractures and faults using image logs is essential to actually knowing what features are present in situ and thus which fracture and faults are important in controlling fluid flow at depth (Chapter 11).