CRAIN'S
PETROPHYSICAL
HANDBOOK
c. 1978 - 2008 E. R. (Ross) Crain, P.Eng.
Rocky Mountain House, Alberta Canada T4T 2A2
403-845-2527 email us
Please be fair to the author - pay your Shareware Fee HERE
and receive a copy of Crain’s Petrophysical Handbook on CD-ROM
at no extra cost.
Updated 5 July 2005
CHAPTER
TWENTY:
ELASTIC
PROPERTIES
OF ROCKS Table
of Contents TABLE 20.01 Elastic Properties of Rocks Continue to Chapter Twenty-One Publication History: Portions of this Chapter were included in Chapter Ten of Volume Two of The Log Analysis Handbook, self published as course notes in 1978, updated in 1985 and 1993. Completely revised and re-organized Sep 2000 for this electronic edition. Minor updates Sep 2002 and May 2003. Major update (anisotropy) Dec 2003. CHAPTER
TWENTY:
ELASTIC
PROPERTIES
OF
ROCKS 20.00:
Introduction to This Chapter Dynamic elastic constants can also be determined in the laboratory using high frequency acoustic pulses on core samples. Static elastic constants are derived in the laboratory from tri-axial stress strain measurements (non-destructive) or the chevron notch test (destructive). Elastic constants are needed by five distinct disciplines in the petroleum industry: 1.
geophysicists interested in using logs to improve synthetic seismograms,
seismic models, and interpretation of seismic attributes, seismic
inversion, and processed seismic sections. Full coverage of the elastic properties for all five disciplines follows. Engineering applications of elastic properties are embedded in this Chapter. Further treatment of seismic petrophysics (log analysis in aid of seismic modeling and interpretation) begins in Chapter Twenty-One. Naturally fractured reservoirs are covered beginning in Chapter Twenty-Eight. A detailed discussion of sonic and density logs, which is a prerequisite to this Chapter, can be found in Chapter Nineteen. NOTE: Abbreviations used in the literature for elastic constants vary dramatically and no consistent set was found. The abbreviations used in this book reflect those used in recent Schlumberger papers. CAUTION: This book uses the abbreviation "V" for Velocity AS WELL AS for Volume, as in Vsh for volume of shale (not velocity of shale or shear velocity). Likewise the abbreviation K is used for permeability (eg Kmax, Kv, Kh, etc) as well as for compressional bulk modulus. Watch the context. IMPORTANT
NOTE: The mechanical properties theory is based on the assumption
that rocks behave elastically and are isotropic. Neither of these
assumptions are actually true in many situations. Anisotropic
behaviour is common and fractured rocks may not behave elastically.
20.01:
Elastic Constants Theory The
composite compressional bulk modulus of fluid in the pores (inverse
of fluid compressibility) is: ____1: Kf =
1/Cf = Sw / Cwtr + (1 - Sw) / Coil The pore space bulk
modulus (Kp) is derived from the porosity, fluid, and matrix
rock properties: The
composite rock/fluid compressional bulk modulus is: Compressional velocity (Vp) and shear
velocity (Vs) are defined as: Although it is not a precise solution, we often invert equations 5 and 6 to solve for Kb and N from sonic log compressional and shear travel time values. WHERE:
The Biot-Gassmann approach looks deceptively simple. However, the major
drawback to this approach is the difficulty in determining the
bulk moduli, particularly those of the empty rock frame (Kb and
N), which cannot be derived from log data. Murphy (1991)
provided equations for sandstone rocks (PHIe < 0.35) that
predict Kb and N from porosity: These can help overcome the lack of empty rock-frame data. An example of the Gassmann equation used to find sonic velocity in a gas filled rock can be found in Chapter Eighteen.
RECOMMENDED PARAMETERS: Oil
compressibility, Coil: 8.5 * 10^-10 depth 2000 ft 610 m Gas
compressibility, Cgas: 1250 * 10^-10 depth 2000 ft 610 m
20.02
Calculating Mechanical Properties Of Rocks If crossed dipole sonic data is available, anisotropic stress can be noticed by differences in the X and Y axis displays of both the compressional and shear travel times. When this occurs, all the elastic constants can be computed for both the minimum and maximum stress directions. This requires the original log to be correctly oriented with directional information, and may require extra processing in the service company computer center. There are many transforms between the elastic constants. If any two are known, all the others can be calculated. See Chapter Eighteen for these equations. Sonic and density data may need some touch-ups before use. These cases are covered below, followed by the calculation and calibration of the elastic constants.
Sonic
velocity measurements made under laboratory conditions are usually
made at 1 MHz because the core plugs are small and the high frequency
has a short enough wavelength to fully penetrate the sample. R.
A. Anderson's paper in 1984 gave graphs (Figure 20.01) of both
high and low frequency data versus Wyllie porosity. By comparing
the response of the two frequencies, we can create equations to
convert high frequency data to equivalent low frequency (logging
tool) values. Travel times taken at high frequency are too fast
(DTShi is too low). WHERE:
Use ONLY to convert lab measured high frequency (1 MHz) sonic data to equivalent low frequency sonic log data. These new values of DTS and DTC should be substituted for the original measured lab data in the following sub-sections. The correction for DTC is very small and often ignored.
In gas zones only, the density log and the compressional sonic log data must be corrected to a liquid filled state. The sonic reads too high and density too low due to the gas effect. If a full blown log analysis is available, density and sonic can be back-calculated from the porosity and lithology, provided that reasonable gas corrections were made in that analysis. Another approach is to use log data from a nearby wet or oil bearing zone in an offset well. The
following equations will also provide better data than the raw
log data in gas zones: WHERE:
These new values of DENS and DTC should be substituted for the original log data in the following sub-sections. Gas correction on DTS is very small so no correction is usually applied to DTS. These equations assume a linear relationship between gas saturation and acoustic velocity. Anderson's work (Figure 20.01) shows that it is not linear. Use Figure 20.01 when possible.
In
very slow formations, where shear travel time was impossible to
measure on older sonic logs, this formula is used to calculate
shear travel time (DTS) from Stoneley travel time: The dipole shear sonic log has reduced the need for this calculation, as it sees shear waves better than older array sonic logs. This new value of DTS should be substituted for the original log data in the following sub-sections.
This is an
empirical approximation and KS7 may be varied by calibrating to
available DTS log data..
Shear modulus is defined as the applied stress divided by the shear strain. For
rock with porosity: For
rock with no porosity: WHERE:
If the rock is anisotropic, both N and No can be calculated for the minimum and maximum stress directions by using DTSmin and DTSmax from a crossed dipole shear sonic log. Density is in gm/cc, travel time is in usec/ft, and N is in psi * 10^6 for English units. Density is in Kg/m3, travel time is in usec/m, and N is in Giga-Pascals (10^9 Pa or GPa) for Metric units. For quicklook analysis, charts may be faster than a calculator:
Poisson's Ratio is the lateral strain divided by longitudinal strain. When
shear velocity or shear travel time is available: If the rock is anisotropic, P can be calculated for the minimum and maximum stress directions by using DTSmin and DTSmax from a crossed dipole shear sonic log. PRmax comes from DTSmin and vice versa. When
shear travel time is not known, which is the case in the
vast majority of older wells, a value for Poisson's ratio
can be estimated. The usual estimate for Poisson's ratio
in shaly sands is: A table of values for other rock types is shown later in this section. If good conventional and shear seismic data are available, then Poisson's ratio can be derived continuously from seismic data. This is sometimes referred to as “seismic petrophysics”. For quicklook analysis, use this chart for Poisson’s Ratio:
A plot of Poisson's ratio versus compressional velocity, Figure 20.04, shows the effect of lithology and gas. Values for Poisson's ratio are also listed in Table 20.01 near the end of this Chapter.
In the absence of good shear sonic data, Poison's Ratio can be estimated from Figure 20.04A, based on known or assumed lithology (courtesy Barree and Associates). A high Poisson’s ratio indicates high stress level, which in turn indicates possible boundaries to a hydraulic fracture. Low Poisson’s ratio indicates weak zones which may not constrain the frac job, resulting in communication to undesired formations. Most shales constrain fractures but some may not do so. Two to three meters of rock with a Poisson's Ratio greater than 0.26 is the minimum needed to constrain a typical hydraulic fracture. Gas zones, where the sonic compressional data has not been corrected for gas, will show abnormally low Poisson's ratio. Poisson’s ratio is used to predict fracture pressure gradient in consolidated formations (Section 20.10).
Bulk Modulus is the hydrostatic pressure divided by volumetric strain. For
rock with porosity: For
rock with no porosity: WHERE:
If the rock is anisotropic, both Kb and Km can be calculated for the minimum and maximum stress directions by using DTSmin and DTSmax from a crossed dipole shear sonic log. Density is in gm/cc, travel time is in usec/ft, and Kb is in psi * 10^6 for English units. Density is in Kg/m3, travel time is in usec/m, and Kb is in Giga-Pascals (10^9 Pa or GPa) for Metric units. If you like quicklook charts, here is one for Kb:
Bulk Compressibility is the inverse of Bulk Modulus. For
rock with porosity: For
rock with no porosity: This term is called rock compressibility and abbreviated Cr in some literature. If the rock is anisotropic, both Cb and Cm can be calculated for the minimum and maximum stress directions by using DTSmin and DTSmax from a crossed dipole shear sonic log. N and Cb predict sanding (sand production) in unconsolidated formations. When log analysis shows sanding may be a problem, sand control methods (injection of plastic or resin or gravel packing) can be initiated. Sanding is not a problem when N > 0.6*10^6 psi. in oil or gas zones. High water cuts increase the likelihood of sanding. This threshold corresponds to Cb of 0.75*10^-6 psi^-1. N/Cb > 0.8*10^12 psi^2 is a more sensitive cutoff than either N or Cb cutoffs. High N/Cb ratios indicate low chance for sanding. A good cement job is also needed to reduce sanding.
Biot's Constant is the ratio of the volume change of the fluid filled porosity to the volume change of the rock when the fluid is free to move out of the rock (ie. the hydraulic pressure remains unchanged).. For
rock with porosity: For rock with no porosity, Kb = Km so ALPHA = 0. If
shear travel time is unavailable, this empirical relation may
be useful: where KS8 has the range 1 to 3, with KS8 = 1 most often used (ALPHA = PHID).
In the absence of good shear sonic data, Biot's Constant can be estimated from Figure 20.05A, based on known or assumed lithology (courtesy Barree and Associates). This graph suggests KS8 in the previous equation is greater than 2.0.
Young's Modulus is applied uni-axial stress divided by normal strain. For
rock with porosity: If the rock is anisotropic, Y can be calculated for the minimum and maximum stress directions by using DTSmin and DTSmax from a crossed dipole shear sonic log when calculating N and P. Young’s modulus is used in the fracture width (aperture) calculation in fracture design software. Here is the quicklook chart for Young’s modulus:
In the absence of good shear sonic data, Young's Modulus can be estimated from Figure 20.06A, based on known or assumed lithology (courtesy Barree and Associates). The ordinate on this graph is Young's Modulus divided by density (gm/cc), so multiply the Y axis value by density to obtain Y.
For rock with porosity, Kc = Kp + Kb + 4/3 * N. For
rock with no porosity, Kp = 0, Kb = Km, and N = No, so:
By
setting Kb = Km - 0.9 * N (empirical relation for sandstone only)
and solving for Kp: The relationships for Kb and N have not yet been published for carbonates, and may not lead to such a simple result. Interpretation
is based on the following: Kp is sometimes shown as Kf in the literature. If conventional and shear seismic data are of sufficient quality to be inverted, then these same equations can be used to detect fluid type in porous sandstones.
20.03
Calibrating Dynamic to Static Constants Unfortunately, the difference between dynamic (well log) values and static (lab) values on cores can be quite large, leading some people to dismiss the log data as wrong or useless. What makes this worse is that fracture design software has been calibrated to static (lab derived) values, so dynamic data has to be transformed to equivalent static numbers. Since the tiny core plugs used for lab work have been de-stressed and re-stressed a number of times, there is some doubt that this cycle is truly reversible, so lab measurements may not represent in-situ conditions. The difference between static and dynamic values are larger for higher porosity, which suggests that some grain bonds are easily broken by coring and subsequent testing. It might be a wise move to calibrate fracture design software to dynamic data, since this data is more readily available, and may actually have fewer inherent measurement problems. Further, the effects of reservoir anisotropy cannot be simulated in the lab, so there is no reason to expect lab data to match in-situ log results. A possible solution to this dilemma is described in later Sections.
Doug Boyd (1991) presented a summary of published Poisson's ratio data, shown at the right. FIGURE 20.07: Comparison of Poisson's Ratio As you can see, there is no direct relation between dynamic and static Poisson' ratio. Additional reasons for the mismatch might include dry rock measurements (as opposed to restored state), moisture variations in shaly samples, closing of fractures, pore shape changes, anisotropy (especially if core plugs are used instead of whole core), inconsistent (and often unknown) experimental methods, and experimental measurement error. Results of such a comparison made today might be less erratic if anisotropic effects were reduced by use of crossed dipole shear sonic data and appropriate core handling procedures. Calibration of local data seems possible, but there is no universal correction factor. When field measured closure stress is available from mini-fracs, a calibration of Poisson's ratio is fairly easy in a homogenous reservoir, but probably impractical in many cases.
Young’s modulus is also affected by differences between static and dynamic values. A transform published by Morales and Marcinew in 1993 is shown in the graph on the left and formulated as: 1: Yst = 10^(A + B * log(Ydyn))
A and B are constants that depend on porosity as shown below:
This transform was based on high frequency dynamic lab data compared to static lab data. Low frequency log data was not used so this widely used transform may have no validity.. The same paper quoted other data sets and compared their data to a transform by Eissa. Note that these transforms invoke the rock density to normalize the data; there is no physical justification for this. The equations are shown on the following graphs in Figure 20.09:
20.04
Examples of Mechanical Properties Logs
20.05:
Calculating Overburden Pressure Gradients Integrating
the density log versus depth or estimating the average rock density
profile and integrating will calculate this pressure: WHERE:
Overburden
pressure gradient is: A
literature search will turn up some relationships for (PO/D) for
specific areas, such as this one for the North Sea: In
this equation, depth is in meters.
For a real rock sequence, these values may be integrated over each lithologic interval, or can be used to replace density log data over bad hole or missing log intervals. If the density log is in porosity units, use the transforms in Chapter Nineteen to build a density log. Review density log editing hints in Chapter Five to ensure that bad data caused by bad hole conditions is not used in the integration. Figure 20.12 shows the type of editing that might be needed on a density log before integration.
20.06:
Calculating Normal Pore Pressure Gradient Formation
pore pressure gradient is: WHERE:
NOTE: All depths must be true vertical depths. Formation pore pressure (Pp) is the pore pressure used in Section 20.08 in the fracture pressure equation. The best source of pore pressure data is the drill stem test (DST) or repeat formation tester (RFT) extrapolated formation pressures from many zones in many wells, plotted versus depth. Commercial databases containing this information are available, or the data can be tabulated from well history files. The slope (Pp/D) of a series of best fit straight lines drawn through the data points will provide the pressure gradient required. The hydrocarbon content will give lower gradients: oil gives a Pp/D between 0.30 and 0.43 psi/ft (6.78 to 9.81 KPa/m). Gas zones will have gradients from 0.05 to 0.30 psi/ft (2.26 to 6.78 KPa/m). Partially depleted reservoirs may have abnormally low pore pressure if there is no active aquifer, water injection, or gas injection to support the reservoir pressure.
Some engineering problems require the initial formation pressure, before any production has occurred. The pore pressure needed for fracture pressure calculations is the current pore pressure at the time the frac is to be performed. Since reservoir pressure depends on the past history of production from all wells in the pool, local pressure anomalies may be present. The best pressure to use is the actual, measured, extrapolated shut in pressure for the zone and well to be fractured. If no measured formation pressures exist, the mud weight hydrostatic pressure can be taken as the upper limit for the pore pressure. A lower limit would be the mud weight during a gas kick.
20.07:
Calculating Abnormal Pore Pressure Gradient Some gas sands are naturally underpressured due to burial at depth with subsequent formation expansion after surface erosion. There is also some suspicion that glaciation may have pressured then relaxed these zones. Measured pressures are the only source of pressure data for such zones. Where overpressure data is sparse, a log analysis technique is sometimes helpful. It relies on fitting lines to semi-log plots of sonic travel time in shale versus depth. First,
we need to run a simplified log analysis, just to see where the
shales are: You can substitute a more sophisticated log analysis model if desired. It is used for displaying shale, porosity, and lithology on the depth plot to aid in choosing the normal shale trend line on the sonic log. Find
DELTsh points for the depth plot: Fit
a best fit or eyeball line to the DELTsh data points (ignoring
all zero or null data) above the overpressure zone - this is the
normal pressure trend line: DTSH0 is the DTnorm at zero depth and DTSH1 is the DTnorm at DEPTH1 on the best fit trend line. DTdiff is only needed for the depth plot of results. Calculate
overburden pressure gradient from an area specific transform or
by integrating the density log: NOTE: All depths must be true vertical depths. Calculate
pore pressure gradient: This equation is very sensitive to the choice of the normal trend line. The exponent 3 in the equation may also need adjustment. Expressed
as a “head of water” in meters for hydrodynamic maps: The Pp values from log analysis can be compared to DST or RFT pressures and adjustments made to the best fit lines if needed. There is no good reason to believe that the pressure in a reservoir will be equal to the pressure in the shale above it. However, if a calculated Pp in a shale is less than a measured Pp in a deeper reservoir, then we would expect the formation to leak hydrocarbons or water upward into shallower formations, or even to the surface. To
convert DST or RFT data to a head of water, rearrange equation
10 to read: An example of this technique is illustrated in Figure 20.14.
20.08:
Calculating Fracture Pressure Gradient Hydraulic fracturing may use sand to prop the fracture open, so it cannot re-seal itself due to the enormous pressure exerted by the overlying rock. Some reservoirs have natural fractures; others need to have fractures added by us. Some wells flow oil and gas at rates that make fracturing unnecessary. Fracture optimization involves designing a fracturing operation that is strong enough to penetrate the reservoir rock and yet weak enough not to break into zones where it is not wanted. In addition, a cost effective design that minimizes time and materials is needed. The extent of a hydraulic fracture is a complex relationship between the strength of the rock and the pressure difference between the rock and the fracturing pressure. The extent is defined by the fracture dimensions - height, depth of penetration (wing length or fracture length), and aperture (width or opening). One measure of a rock's strength is Poisson's Ratio. Poisson's Ratio are low (0.10 to 0.30) for most sandstones and carbonates. These rocks fracture relatively easily. Poisson's Ratio is high (0.35 to 0.45) for shale, very shaly sandstone, and coal. These rocks are more elastic and are harder to fracture. Shales are often the upper and lower barrier to the height of a fracture in a conventional sandstone. The lateral extent of a fracture is primarily determined by Young's Modulus. Stiffer rocks have higher Young's Modulus and are easier to fracture. By using radioactive tracers in the fracturing fluid, the extent of the fracture can be traced by a gamma ray log. Adequate fracture depth of penetration (fracture length) is also desired, as is fracture aperture (fracture width). These are not as easy to determine from logs as is the fracture height. Different tracer elements are used during the frac so that a spectral gamma ray log can be used to determine depth of penetration. The fracture pressure is the pressure needed to create a hydraulic fracture in a rock. It is determined by the overburden pressure (a function of depth and rock density), pore pressure, Poisson's Ratio, porosity, tectonic stresses, and anisotropy. Breakdown pressure is the sum of the fracture pressure and the friction effects of the frac fluid being delivered to the formation. Breakdown pressure can be considerably higher than fracture pressure. Closure
stress is the pressure at which the fracture closes after the
fracture pressure is relaxed. It is usually between 80 and 90%
of fracture pressure. In some literature, closure stress and fracture
pressure are used interchangeably. Rocks with high closure stress
are harder to frac (take more horsepower) than the same rocks
with lower closure stress. Shallow shaly sands have high closure
stress because they have high Poisson's Ratio. A pressure vs time diagram illustrating these pressures is given later in this Chapter as Figure 20.19. Hydraulic fractures are usually intentional, to improve the flow capacity of a reservoir. Some can be unintentional, caused by using a mud weight that is too high, resulting in rupture of the formation and lost circulation. Many technical papers and computer programs use pressure gradients instead of pressures to define the calculations. Typical pressure gradient values are: Pore
pressure - normal pressure regime Pore
pressure - abnormal pressure regime Overburden
pressure Closure
stress - typical range The average closure stress in the undisturbed part of the Western Canadian basin is 16.5 KPa/meter.
FIGURE 20.15: Stress regime - no tectonic stress (left) tectonic stress (right) CASE
1: Isotropic Reservoir (Basic Model) CASE
2: Anisotropic Reservoir (Standard Model) CASE
3: Anisotropic Reservoir (Iverson Model) CASE
4: Anisotropic Fractured Reservoir (Iverson Model) CASE
5: Total Stress Equation (Barree Model) The usual assumption is that ALPHAv = ALPHA and ALPHAh = 1.00. Poff accounts for pressure decline in the reservoir due to depletion from offset wells. STRh and Pext are still assumptions and are found by calibration to mini-fracs. WHERE:
When
formation stress is isotropic (equal in all directions),
the tectonic stress (Pext) is zero and Pfrx equals Pfry.
Some previous authors have ignored Biot’s Constant
ALPHA in their equations. Since ALPHA = 1.0 only rarely,
leaving ALPHA out of the equation is not a good idea for
real rocks when the zone is porous. Tensile strength (Ts)
of most rocks is low or zero so the term is usually ignored.
20.09:
Calibrating Fracture Pressure Gradient FIGURE 20.18: Calibrating fracture stress A common correction method is to compare log analysis stress profiles with individual results from single or multiple mini-fracs. The correction may be a linear shift of the log derived curve, such as the example in Figure 20.18. Mini-fracs or leak-off tests should be run to verify that the computed fracture pressure is close to the leak-off pressure. These tests are also called pump-in tests (Figure 20.19). If they are not equal, then there is anisotropy or tectonic stress (Pext). Alternatively, some of the data or assumptions that went into calculating Po, Pp, Pfrac, PR, or ALPHA might be wrong. The math should be iterated to obtain a good match to the mini-frac without resorting to unreasonable gradients or rock properties.
An
alternative fracture pressure approach ignores all the log derived
data. Since the calculation must be calibrated anyway, why not
calibrate directly to available mini-fracs, and ignore the log
data? Mike Cleary proposed the following equation: Where: A, B, C are constants derived from regression with pressures from mini-fracs. This approach only works when sufficient tests exist over a moderate depth range. It is of course useless where there is no test data. It also loses a lot in translation, since the underlying physics is hidden from view. Because of the major improvements in measuring shear sonic travel time that have occurred in the last 10 years or so, and the recognition and measurement of anisotropy in acoustic properties, many of Cleary's complaints about elastic properties from acoustics have disappeared. His ABC method may not need to be invoked as often as in the past. My advice is try the log analysis method first if decent modern data is available. Calibrate results to mini-fracs. Try and find the sources of errors and fix them. When there is no decent log data, use Cleary's ABC approach.
20.10:
Calculating Fracture Extent
20.11:
Gamma Ray Logging to Confirm Fracture Placement The fracture height determined from observation of the gamma ray log is used in type-curve-fit or simulation software, with the treatment placement pressure curve, to calculate fracture length (depth of penetration). The fluid plus proppant volume is used in the simulation to calculate fracture width (aperture). Some fracturing companies use a spectral gamma ray logging tool to locate different radioactive tracer elements that have been applied to different sized propping materials. The finer sized proppants will show the deepest penetration, with coarser material being deposited closer to the wellbore. The spectralog gives a 3-D image of the fracture length, height, and width (aperture). These tracers have very short half-lives (hours or days) so no permanent radioactive signature is created (Figure 20.22).
The gamma ray curve amplitude is a qualitative indicator of fracture width (aperture) since the quantity of radioactivity is proportional to the volume of proppant that carries the tracer elements. Note that after a period of production from any reservoir, there may be a permanent radioactive anomaly caused by precipitation of uranium salts. A gamma ray log run in this situation helps to identify where fluid flow is occurring. Some remedial action may be possible if flow is not as expected. Some naturally fractured reservoirs show this anomaly before production. In this case, the precipitation occurred during migration of the hydrocarbon. If a producing or naturally fractured reservoir is to be hydraulically fractured, a baseline gamma ray log should be run before the job. The post-frac tracer log should be compared to this baseline, rather than the original open hole gamma ray log.
20.12:
Determining Fracture Orientation
Many modern logs have an X and Y axis caliper, but not all of them are oriented to true north. When directional data is recorded, as with dipmeters and many modern resistivity tools, the X and Y orientations are known, Statistical plots are helpful in choosing the dominant direction (Figure 20.23B).
Natural fractures take the same directions as hydraulic fractures, indicated again by the borehole shape. In addition, the high angle dips seen on an open hole dipmeter, will also indicate this preferential direction. Since most hydraulic fracture jobs are run in casing, it is not possible to run a dipmeter or caliper survey to find the orientation of a hydraulic fracture. The preferential direction can be predicted from previous open hole data. Dipmeter and caliper data can be displayed on rose diagrams to illustrate preferential directions (Figure 20.24). If an azimuthal gamma ray log existed, the fracture orientation could be located by a tracer survey. I am not aware that such a tool exists, but it would not be difficult to design one.. The newest dipole shear sonic log is also an azimuthal tool with dipole sources set at 90 degrees to each other. The example below (Figure 20.25) shows the shear images for the X and Y directions. This log can be run in open or cased hole.
Formation microscanners and acoustic televiewer logs also provide images that will assist in locating fracture orientation before the well is cased.
20.13
Tables of Rock Properties
The elastic properties derived from sonic and density data are likewise used in a variety of applications. Geophysicists, geologists, and engineers each have specific uses for these results, so this Chapter is required reading for everyone. Fracture pressure gradient is a critical number required for a successful hydraulic fracture design. The technique described above has been used for many years. Local experience, especially in areas where bounding layers are weaker than the reservoir, must be used to temper the computed results. Logging after the job to locate the fracture extent is a necessary step in evaluation of the job. A strict post-job review of the frac job with all available data will allow you to adjust parameters in the fracture pressure gradient calculation, in the frac design parameters, and in the frac job pumping sequence before the next job is run. 20.15:
Exercises for Chapter Twenty CRAIN’S MECHANICAL PROPERTIES
EXERCISE #5: Elastic
Constants / Mechanical Properties
Assume the
following data. Calculate all results in Metric Units. | ||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||
When
lithology is known from sample descriptions or from detailed log
analysis, the shear travel time or velocity can be predicted from
the porosity, lithology, and elastic constants from tables (such
as Table 20.01), or from the following approximation:
Errors
in Poisson's ratio strongly affect calculation of in-situ closure
stress. 
FIGURE
20.08: Comparison of Young's Modulus
Because
so many assumptions are made in computing elastic constants and
pressure gradients, calibration is essential. If all the corrections
for frequency, gas, dynamic to static, anisotropy, and so on are
performed first, the correction factors may be relatively small.
The cause for error may even become apparent and the correction
might be made to Poisson's Ratio or overburden pressure. However,
the more usual case is that the cause is unknown.
A
hydraulic fracture will usually penetrate the formation in a plane
normal to minimum stress, or parallel to the plane of maximum
stress. Any stress anisotropy (tectonic stress) will cause the
fracture to be other than vertical.
