ESTIMATION OF S-WAVE VELOCITY USING OTHER TYPES OF WAVES

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Geological Setting

The CO2SINK project is aimed at a pilot CO2 storage in a gentle anticline in the northeast German Basin (NEGB) which is part of a Permian basin system. This Permian basin system extends from the southern North Sea to Poland. In the early Permian, the basin origin started with initial rifting. Subsidence followed the rifting which resulted in the deposition of Permian clastic rocks and the Upper Permian Zechstein salt. In the late Permian, a phase of accelerated subsidence started followed by relatively low subsidence rate from middle Triassic to early Jurassic (Juhlin et al., 2007). In the Triassic, Jurassic, and early Cretaceous, major rift- and wrench tectonics took place. This renewed tectonic activity resulted in the formation of local north-northeast – south-southwest directed depocenters in the NEGB. Throughout the late Cretaceous and Paleocence, the NEGB remained mainly metastable with only some local highs and marginal troughs developing (Juhlin et al., 2007).
The Ketzin site is located in the eastern part of a double anticline which formed above an elongated salt pillow situated at a depth of 1500-2000m. The axis of the anticline strikes north-northeast – south-southwest and its flanks gently dip about 15’o’ (Forster et al., 2006). Geologic formations of the Triassic (Buntsandstein, Muschelkalk, and Keuper) and Lower Jurassic form the immediate overburden above the salt pillow. Stratigraphic succession shows a first gentle uplift of the Ketzin anticline started in Early Triassic. About 140Ma ago, major uplift occurred which resulted in erosion of Lower Jurassic (Toarcian) and the Middle and Upper Jurassic formations. A second uplift occurred at 106Ma which resulted in the erosion of the previously deposited Lower Cretaceous. The total amount of eroded thickness is about 500 m (Forster et al., 2006). The Upper Cretaceous probably was never deposited in the area, which at that time was part of a structural high. Sediments of the Oligocene (Rupelton) form the first formation unaffected by anticlinal uplift resting above Jurassic sediments and these sediments are the first indicators of regional downwarping of central parts of NEGB which lasted until present (Forster et al.,2006).
Natural gas had earlier been stored at the site from the 1970s until 2000 at depths of 250 m to 400 m in Jurassic sandy layers sealed with a thick layer of Rupelian clay and interbedded mudstone (Kazemeini et al., 2009). However, the target reservoir in the CO2SINK project at the injection site is a deeper saline aquifer within the upper Stuttgart Formation of Triassic age, at a depth of 625 to 700m as shown in Figure 5 (Kazemeini et al., 2009; Forster et al., 2006).
The Stuttgart Formation contains heterogeneous lithology and is of fluvial origin (Forster et al., 2008). Sandy channel-facies rocks (good reservoir properties) deposits alternate with muddy, flood-plain facies rocks (poor reservoir quality). The sandstone interval may attain thickness from 1m to 30m where subchannels are stacked. The width of a fluvial channel-string system is from several tens of meters to several hundreds of meters (Forster et al., 2006).
Figure 5. Geology of the Ketzin anticline for selected boreholes including the injection well CO2 Ktzi 201/2007 with aquifer (light yellow) and acquitard (pink) (Forster et al., 2008).
The Weser and Arnstadt formations consisting of mudstones form an approximately 200 m thick cap rock above the Stuttgart Formation. Additional aquifer-aquitard systems are present further up, at 250m to 400m depth, in the form of Jurassic sandstone interbedded with mudstone, claystone and siltstone that form a multi aquifer system. The thickness of tertiary clay acting as caprock is from 80-90m, which covers the Jurassic sandstones. This clay plays an important role in separation of non-saline groundwater in shallow Quaternay aquifers from saline waters in the deeper aquifer. Local erosion of the Rupelton aquitard at some locations results in ascending saline waters that mix with the fresh waters of the shallow aquifers (Kazemeini et al., 2009).
The stratigraphic column based on well CO2 Ktzi 200/2007 is shown in figure 6.

Review of Acoustic Logging Method

Acoustic logging is one of the principal geophysical well logging disciplines. As formation acoustic properties (velocity and attenuation), are closely related to rock type and formation fluid such as hydrocarbons, measuring these properties can provide useful information for formation evaluation. A tool is lowered into the borehole in acoustic logging and an acoustic or sound wave is generated by a transmitter or source in the tool. The sound wave travels along the borehole and interacts with the formation (Tang et al., 2004).
The receiver picks up and records the pulse as it arrives at the receiver. The sonic log is simply a recording versus depth of time, t, required for a sound wave to traverse 1ft of formation as shown in figure 7. Interval transit time Δt or slowness, is the reciprocal of velocity of the sound wave which depends upon formation lithology and porosity. That’s why sonic logs are very useful as porosity logs (Schlumberger, 1989). The tool is pulled up or lowered by wireline cable and the measurement is made continuously along the borehole. The wireline cable supplies power from, and transmits data to, a surface control system. Such type of logging is called Wireline logging. The output of acoustic logging is an acoustic log of acoustic properties of the formation around the borehole (Tang et al., 2004).
Figure 7. A borehole device for measuring the interval transit time Δt. Ray paths of the acoustic energy refracted from the borehole into formation and back to the receiver are shown to the side (Ellis et al., 2008).
The conventional approach of acoustic logging can be used to measure the velocities of compressional and shear waves (with dipole tool) which can be further related to formation porosity and lithology. Abnormal high pore pressures and mechanical rock properties & fractures are also possible to infer and estimate from acoustic measurements (Ellis et al., 2008).
The acoustic waveform recorded with a logging device in a borehole shows the following distinct packets of energy.

Body waves:

Compressional waves:

Compressional waves are also called P-waves or longitudinal waves in which particle motion is co-linear with direction of propagation. These waves travel faster than shear waves and are recorded first on waveform data as shown in figure 8.

Shear waves:

Shear waves are also called S-waves or transverse waves in which particle motion is perpendicular to the direction of propagation (Boyer et al., 1997).
Figure 8. A typical acoustic waveform showing three distinct arrivals (Ellis et al., 2008).

Interface waves:

Pseudo-Rayleigh waves:

Pseudo-Rayleigh waves are reflected conical dispersive waves (Biot, 1952). Their phase and group velocities approach the S wave velocity of the formation at low frequency (<5kHz) while at high frequencies (>25kHz) their velocity becomes asymptotic to the compressional wave velocity of the fluid. It is only encountered in fast formations (Boyer et al., 1997).

Stoneley waves:

Stoneley waves are of large amplitude that have traveled from transmitter to receiver with a velocity less than that of the compressional wave in the borehole fluid (Boyer et al., 1997). The Stoneley wave has a lower sensitivity to the formation shear velocity and it is strongly influenced by other factors such as frequency of sound pulse, formation permeability, borehole fluid property, tool diameter, borehole radius etc, (Tang and Cheng, 1993). Stoneley waves are similar to the tube waves observed in VSP.

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Fluid waves:

Fluid waves are guided (or channel) waves, having very little scattering and they propagate through the fluid of the borehole (Boyer et al., 1997).
The waveform will contain P- and S-waves in the case of a Fast formation where shear velocity exceeds the sound velocity of the borehole fluid. In the case of slow formation, where shear velocity of the formation is less than the sound velocity of the fluid in borehole, borehole acoustic logging waveform data will consist of a compressional head wave, a direct (fluid) compressional wave of low amplitude, and a late arriving, low frequency Stoneley wave (Stevens and Day, 1986).

Types of Tools:

 Monopole tools

Monopole sonic logging tool has an axial symmetry and is equipped with multidirectional receivers as shown in figure 9.
A compressional wave is generated in fluid by transmitter in every direction, producing a P-wave and a S-wave in the surrounding formation at the critical angles of refraction (Boyer et al., 1997).
In a vertical well, the monopole tool can be used to record five types of waves:
1) refracted P-waves
2) refracted S-waves, only in fast formations
3) fluid waves
4) two dispersed tube waves, i.e. pseudo-Rayleigh and Stoneley waves (Mari et al., 1994).
Figure 9. Monopole tool showing generation of P- and S-waves (Boyer et al., 1997).
In monopole logging, borehole acoustic logging waveforms consist largely of two guided wave modes: the Stoneley and pseudo-Rayleigh waves (Toksoz and Cheng, 1981).

Dipole Tools

A dipole tool is shown in figure 10. This tool is useful in determining the S-wave velocity in slow formations (when S-wave velocity in formation is less than P-velocity in mud). In a dipole tool, sources and receivers are polarized. The emitted P-wave is polarized perpendicular to the well which generates pseudo S-waves which propagate in a parallel direction to the well (Mari et al., 1994).

Estimation of S-wave velocity using other types of waves

The waveform may consist of two main body waves propagating in a fluid-filled borehole: the P-and S-waves as in the case of Fast formations. In case of slow formations, borehole acoustic logging waveform will consist of compressional head wave, a direct (fluid) compressional wave of low amplitude, and a late arriving, low frequency Stoneley wave (Stevens and Day, 1986). This was the case in the Ktzi-201 injection well as show in figure 11. Here the P-wave and the Stoneley wave can be easily seen, but the S-wave arrivals are absent.
In this situation, the shear wave velocity can be measured from Stoneley waves recorded by a monopole tool (Cheng et al., 1983, Stevens and Day, 1986). The absence of a critical refraction means that no shear waves can be measured directly in monopole logging (Tang et al., 1995).
C = Vf (1)
1 + ρf Vf2
ρs Vs2
Where Vf is the velocity of P-wave in borehole fluid and C is Stoneley wave velocity.
Figure 11. Screen dump of Shot ID 1 showing the P-wave and the Stoneley wave.
Borehole fluid properties Vf and ρf can be measured or estimated from the type of drilling fluid used (Tang et al., 1995).
The next unknown parameter in equation (1) was the borehole fluid velocity Vf. Unfortunately; no measurement of borehole fluid velocity (Vf) was available at Ktzi-201. If we know the composition of the borehole mud and temperature & pressure, we can calculate the velocity of fluid (Batzle et al., 1992). In this case, the velocity of borehole mud (Vmud) will be same as the borehole fluid velocity (Vf). The constituents of borehole mud was mainly bentonite Be (4%) and brine water Br (96%). A simple polynomial in temperature (T), pressure (P) and salinity (S) is made to calculate the density of the brine (ρBr) (Batzle et al., 1992).
ρw = 1+10-6(-80T–3.3T2+0.00175T2+489P-2TP+0.016T2P–1.3×10-5T2P–0.333P2 – 0.002TP2), (2)  ρBr = ρw + S{0.668+0.44S+10-6[300P – 2400PS + T(80 + 3T – 3300S – 13P + 47PS)]}, (3) where ρw is the density of the water and S is the weight fraction (ppm/1000000) of sodium chloride.
The relationship for the velocity Vw of pure water to 1000C and about 100MPa is:
Vw = ∑∑wijT i P j ,
i = 0 j =0
where the coefficients of wij are given by Batzle et al., (1992).
VBr = K Br ,
ρBr
Where KBr is the bulk modulus of water and ρBr is the density of brine in g/cm3.
The equation for Vmud is given below (Poletto et al., 2002): Vmud = Kmud , (6) ρmud
Where Kmud is the bulk modulus of the mud and ρmud is the density of brine in g/cm3.
All the parameters in equation (1) are known except Vs, which can be easily calculated.

Dataset used for this study:

The full waveform sonic data in borehole Ktzi-201 (Injection well) was acquired in July, 2007. The mode of logging was monopole logging. The target was the Stuttgart Formation, saline sandstone aquifer. A total of 1210 shots were conducted and data were recorded on 13 channels. Receiver spacing was 6 inches (15.24 cm).

Software used for this study:

The data processing was done in GLOBE Claritas on a LINUX computer. In order to avoid the introduction of artifacts into processed volumes, the processing algorithm was kept simple Screen dumps of workflows and picking of wave arrivals in GLOBE Claritas are shown in Appendix A. MATLAB is used to calculate velocities and Microsoft Excel is used for plotting of velocities along depth of the borehole.

Results & Discussion:

A Full waveform sonic data were acquired in the Ktzi-201 injection well at the Ketzin CO2 storage site. The mode of logging was monopole logging. The objective was to pick P-wave & S-wave arrivals on full waveform data and calculate P-wave & S-wave velocities. On approximately all shots, P-wave was apparent and was easy to pick as shown in Appendix – A. One example of picking of P-wave arrivals at Shot ID 120 is shown in figure 12.
Figure 12. shows the waveform recorded at shot ID 120 and P-wave can be seen and easily picked.
These picked times of the P-wave arrivals were plotted in MATLAB as a function of distance to calculate P-wave velocities. A best fit line is made and the slope of the best fit line gives us P-wave velocity on that shot.
Once all the velocities of the P-wave on all shots were calculated, these P-wave velocities were plotted against depth in the Ktzi-201well as shown in figure 13.

Table of contents :

INTRODUCTION
1.1 THE SLEIPNER PROJECT
1.2 THE CO2SINK PROJECT
1.3 OBJECTIVES OF THIS STUDY
2. GEOLOGICAL SETTING
3. REVIEW OF ACOUSTIC LOGGING METHOD
3.1 BODY WAVES
3.1.1 Compressional waves
3.1.2 Shear waves
3.2 INTERFACE WAVES
3.2.1 Pseudo-Rayleigh waves
3.2.2 Stoneley waves
3.2.3 Fluid waves
3.3 TYPES OF TOOLS
3.3.1 Monopole tools
3.3.2 Dipole Tools
3.4 ESTIMATION OF S-WAVE VELOCITY USING OTHER TYPES OF WAVES
3.5 DATASET USED FOR THIS STUDY
3.6 SOFTWARE USED FOR THIS STUDY
4. RESULTS & DISCUSSION
5. CONCLUSIONS AND RECOMMENDATIONS
REFERENCE
APPENDIX – A

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