7.0 Sonic or Acoustic logs Sonic logs made simple By measuring the time taken for acoustic waves to travel from a transmitter to a receiver the sonic log determines the transit time of compressional waves in the formation (i.e. the time taken to travel through one foot of formation). Modern tools also measure the shear and Stoneley wave transit times. Primarily used by Geophysicists to determine compressional and shear wave velocities (Vp and Vs) for use in seismic interpretation, results are also used for studies of fracturing, wellbore stability and sand production, and to help determine porosity, lithology and fluid type.

= (t - tm) / (tf - tm)

where = Porosity

t = Transit time of compressional wave measured from sonic log

tm = Transit time in matrix

tf = Transit time in fluid Transit time is also called travel time or slowness. It is the reciprocal of the velocity.

t in s/ft = 106/Vp in ft/s Not the best log to calculate porosity, especially in unconsolidated formations. Transit times are high (slow) in shales and gas (even a small amount of gas can greatly increase transit time) and small (fast) in carbonates. The sonic log is used to predict overpressure. A similar log is used in cased hole to evaluate the quality of cementing. How it works A transmitter (called a transducer) creates an acoustic pulse in the 1 to 40 kHz range depending on the tool. This can be created:

By a magnetostrictive material, that changes volume when a magnetic field is applied by a coil of wire through which an electric current is pulsed (and vice versa)

By a ceramic piezoelectric material such as BaTiO2, which changes volume when an electric voltage is applied across it (and vice versa)

The detectors are the same as the transmitters except they measure current or voltage rather than apply it.

The pulses created are about 200 s long and are repeated about every 50 ms or so. The compressional pulse spreads out from the transmitter through the mud until it hits the borehole wall. On passing into the formation the wave is refracted according to Snells law; above a certain critical angle of incidence, the compressional waves are refracted parallel to the borehole wall. These refracted waves radiate compressional waves back into the mud, where the detectors pick them up. The time at which the first compressional wave arrives is used to determine the transit time. The transit time measured will be for the ray path that takes the fastest route. As

the formation has a faster compressional wave velocity than that in mud, the wave that has travelled through the formation will arrive first provided the transmitter to receiver is not too short, compared to the borehole diameter. Borehole compensation The time measured by a simple tool with one transmitter and one receiver will include the time to travel across the mud between the tool and the borehole wall. To compensate for transit through mud (at least) two receivers at different spacings are used.

TT-R1 = Tmud + ST-R1 t + Tmud

TT-R2 = Tmud + ST-R2 t + Tmud

where TT-R1 = transit time between transmitter and first receiver s ST-R1 = distance from transmitter to first receiver ft (typically 3ft)

TT-R2 = transit time between transmitter and second receiver s ST-R2 = distance from transmitter to second receiver ft (typically 5 ft)

Tmud = transit time through mud from tool to borehole wall s

t = transit time through formation in s/ft Looking at the difference between the transit time between the first and second receivers it can be seen that the transit time through mud is eliminated by subtraction.

TR2-R1 = TT-R2 - TT-R1

= ST-R2 t - ST-R1 t

t = TR2-R1 / (ST-R2 - ST-R1 ) To provide additional corrections for varying hole diameter and any tilt of the sonde a tool with two transmitters and four receivers, called the borehole compensated sonic (BHC), was the standard sonic tool from the 1960s to around 2000. Cycle skipping, Noise and Quality checks The transit time is calculated from the difference between the time at which a signal was transmitted and the arrival time when it was first detected. The arrival time was traditionally detected when the amplitude from the receiver exceeds a threshold value. If the threshold was set too low, then noise could be interpreted as an arrival giving a transit time that was too short. If it was set too high then the first arrival could be missed and the second cycle detected instead, an effect called cycle

skipping resulting in the transit time jumping by 10 to 40 s depending on whether cycle skipping occurred on one or all of the transmitter - receiver combinations. Cycle skipping and noise tend to cause spikes on the sonic. In an extreme case, it

will start reading the mud at around 200 s/ft. It is worth checking the reading in casing, which should be a steady value of around

57 s/ft.

Recent advances In recent decades there have been a number of advances including the development of LWD tools. One of the later tools developed as drilling noise made detection of wave arrivals more difficult. To minimise this, the sonic log is located above other LWD tools, as far from the bit as is practical. Stationary readings may also be used to check the log. Initially sonic logs only measured the compressional wave arrival, however there are several types of waves produced these include:

Compressional waves, the only waves detected by the older tools as they are the fastest and so arrive first. These waves propagate by moving particles in solid and fluids back and for in the direction in which they are travelling. They can travel through solids, liquids and gas; fastest in solids and slowest in gas.

Shear waves propagate by moving particles in solids in a planes perpendicular to the direction of travel. They cannot move through gas or liquids unless they are extremely viscous.

Stoneley waves are tube waves travelling through the mud and confined by the borehole walls, if the walls were completely rigid they would travel at the compressional velocity of the mud. In a borehole the Stoneley wave velocity is affected slightly by the shear velocity and density of the formation, and in permeable intervals, the amplitude is reduced (attenuated) and the velocity changes as some of the energy is lost to due to fluid movement in the formation.

A knowledge of the compressional and shear waves is used in seismic and geomechanics (wellbore stability, fracturing and sanding). To facilitate measurement of shear and Stoneley waves a number of new tools were developed.

Long spaced sonic: in shorter spaced tools the shear signal was lost in the mud or Stoneley wave arrivals so spacings such as 8 and 10ft were used for the two detectors-receiver pairs.

Array type tools: by having multiple detectors (e.g. 10 or more) at different distances from the transmitter it becomes possible to improve the signal by stacking the waveforms detected. The waveform recorded by a detector is moved in time to account for its latter arrival time and then added to the waveforms from receivers closer to the transmitter. By using say the compressional velocity to time shift the waves, all the compressional waves will be superimposed on each other giving a much bigger signal. By this means shear waves and Stoneley waves can be detected with confidence. However, in slow formations the compressional velocity in the mud is greater than the shear wave velocity and no significant shear wave is refracted along the formation-borehole interface.

Dipole tools: to overcome the problem of slow formations Dipole sonic tools were developed

Dipole tools The transmitters described previously were monopole transmitters that radiate acoustic waves of a given polarity in all directions at the same time. Dipole transmitters create a positive pulse in one direction, while transmitting a negative pulse in the opposite direction. This is achieved either by:

By a double ended piston actuated electromagnetically by coils through which a current is applied, similar to a loud speaker

A combination of monopole sources next to each other which are out of phase o With four monopole sources a Quadrupole transmitter can be created

Using a Dipole source flexural waves can be created which travel by moving the borehole walls in and out slightly. From the development of flexural waves the shear wave velocity can be obtained. Porosity calculation As compressional waves travel faster in solids then in water or gas, it is not surprising that as porosity is increased (giving more liquid or gas) the compressional velocity falls, and so the transit time increases. Sonic logs are normally plotted on a

40 to 140 s/ft scale, with the 40 on the right. Consequently an increase in Transit time can indicate higher porosity (or gas or shale), The most widely used equation for calculating porosity is by Wyllie and is called the time-average equation, as it is based on the assumption that the transit time measured by the log is the volume average of the transit times in the rock, i.e.

t = tm (1-) + tf Which gives

= (t - tm) / (tf - tm)

where = Porosity

t = Transit time s/ft = 106/Vp where Vp in ft/s

tm = Transit time in matrix s/ft

tf = Transit time in fluid s/ft Wyllies equation breaks down for unconsolidated formations and other empirical equations have been proposed including:

= (t - tm) / ( (tf - tm) Bcp ) where Bcp is greater than one. Bcp can be estimated from the transit time in adjacent shales (a measure of compaction in the area)

Bcp = tsh /100 An alternative empirical relationship is the Hunt-Raymer Transform for liquids only

= ( 1 - tm/t )/ (m - f )

where m = Density of matrix

f = Density of fluid Depth of investigation and mechanical damage near the wellbore As compressional sonic waves travel by the fastest route, which is along the borehole walls, the depth of investigation of a sonic log is very shallow and should therefore be in the invaded zone. There is an exception. The rock around the well can tend to fail if it is not very strong, the overbalance is too low or if there is some chemical interaction with the mud (e.g. swelling of clays). When failure starts to occur the sonic wave velocities start to fall. In which case the fastest path maybe deeper in the formation, around the zone of damage, up to 6 away for a traditional borehole compensated sonic log. This mainly occurs in shales. Given the risk of progressive hole deterioration and its ability to increase transit times, if sonic data is required in shales in particular, it should be obtained as soon as possible after drilling. This is one of the advantages of an LWD log. Parameters for Compressional waves Given the depth of investigation, fluid properties should be from the invaded zone, i.e. mud filtrate and any residual oil, gas or water.

Transit time s/ft Velocity ft/sec

Matrix

Sandstone 55.6 (53.8-100) 18,000 (17,390-19,030)

Limestone 47.5 (47.0 53.0) 21,000 (18,750-21,000) Dolomite 43.5 (40.0 - 45.0) 23,000 (22,222-25,000)

Shale 100 (60.0 170.0) 10,000 (5,882 16,667) Coal 115 (90.0 140.0) 8,700 (5,900 11,111) Anhydrite 50.0 20,000

Gypsum 53.0 19,000

Halite (Salt NaCl) 65.7 15,000

Fluid

Fresh water 207 4,380

Salt water 100,000 ppm NaCl, 15 psi

192.3 5,200

Salt water 200,000 ppm NaCl, 15 psi

180.5 5,540

Oil 238 4,200

Methane 15 psi 626 1,600

Drilling mud 175 - 278 3,600 - 5,700

Secondary porosity Secondary porosity consists of vugs and open fractures, typically where material, such as shells, have been dissolved since the rock was first deposited. Being more soluble carbonates such as limestone are more prone to secondary porosity. As noted the sonic waves will take the fastest route, if there are vugs (i.e. holes) in the

formation millimetres to inches across, the sonic waves detected by the log will be those travelling in some other part of the wellbore. In consequence, unlike Density or Neutron porosity, Sonic porosity should include only primary porosity. On the basis the difference between the Density and/or Neutron porosity and the Sonic porosity should be the secondary porosity. This criterion must be used with care, as the most likely cause of differences is error in the calculated porosity. In the case of an open fracture crossing the entire wellbore the above will not apply as there is no fast path for the compressional wave. Such fractures are discussed later. Gas effects Gas has a low compressional wave velocity, and can cause a significant drop in sonic velocity even at low gas saturations. For this reason even formations with residual gas can appear as gas bearing on sonic logs, but not any other logs. For quick look evaluation a fluid velocity of 2000ft/sec can be used although in reality it will be very dependent on pressure and temperature. There are means of calculating the effect of gas saturations but they are not straightforward and the density log or the density & neutron log combination are normally used in gas reservoirs. The other difficulty is that because the sonic log reads so close to the borehole, all the gas may be swept away and no gas effect may be present Shale, Compaction trends and overpressure Shales give high transit times on sonic logs due to the amount of water they contain. As shales are buried deeper into the ground the water is gradually expelled under the influence of overburden pressure, called compaction, and the transit time becomes shorter (i.e. the sonic velocity becomes faster). In addition there is an increase in sonic velocity in rocks as the effective overburden (i.e. overburden pressure minus pore pressure) increases. These effects mean that the normal trend with depth, if there is no change in lithology, is a gradual reduction in transit time. The pore pressure within the shale for a normal trend is taken as equal to hydrostatic, i.e. the pressure exerted by a column of water extending from surface to the depth in question. Overpressure is encountered when the pore pressure in rocks is higher than the hydrostatic pressure. When overpressure is encountered in shales then the normal compaction trend is reversed, instead of the transit time decreasing, it increases. Pore pressures can be calculated from various equations such as Eatons Pp = S - (S - Phyd)(tn / tlog)

3 where Pp = pore pressure

S = stress (overburden stress which can be calculated from density log) Phyd = hydrostatic pore pressure tn = transit time expected from normal trend at this depth tlog = transit time from log

The exponent is often changed so that the predictions better match pore pressures inferred from other data.

Environmental effects Sonic logs are fairly tolerant of borehole size as the time travelling across the mud is compensated for, and the wave will still take the fastest route, which is through the formation. If however the borehole gets too large (over 24) and special measures are not taken, such as eccentering the tool, the mud arrival reaches the detector before the formation Sonic logs cannot be run in gas, or gas cut mud, as the attenuation of the signal is too great Vertical resolution Typically about 2ft Using the Compressional to Shear Velocity Ratio (Vp/Vs) ratio for lithology and gas Although the Shear velocity is normally acquired for seismic or geomechanical reasons, it can also be used for log analysis. It has been suggested that the Vp/Vs ratio (or the ratio of the shear transit time to the compressional transit time) is related to lithology and gas presence. The gas effect occurs as the compressional wave velocity is reduced by gas, but the shear wave velocity is largely unaffected. A low Vp/Vs ratio will be obtained. Vp/Vs ratio is also affected by lithology as shown below (from Mason 1984), however other sources give different figures:

Vp/Vs (or ts/tc)

Sandstone 1.6 1.8 Gas bearing Sandstone 1.6

Siltstone 1.8

Limestone 1.9

Shaly Limestone 2.3

Dolomite 1.8

Shale 1.7 to 1.85

Anhydrite 2.45

Gypsum 2.45

Halite (Salt NaCl) 2.15

Vp and Vs for Geomechanical studies Geomechanical studies include:

Wellbore stability (will the borehole collapse while drilling or production?)

Hydraulic Fracturing (what is the fracture pressure, how wide will the fracture be and how high will it grow?)

Sand production (will the well produce sand?) These studies all need the Youngs modulus and Poissons ratio. They can be calculated from the Compressional and Shear velocities, which can be expressed as:

Vp2 = E (1-)

(1+)(1-2)

Vs

2 = E

2(1+) Where E = Youngs modulus

= Poissons ratio

= Density Various other parameters such as the bulk and shear modulus can also be calculated. Note however, that parameters such as Youngs modulus obtained from sonic wave data can differ from those needed for Geomechanics work as the time scale over which they act are different (microseconds in sonic waves, compared with hours in Geomechanics applications). Fast and slow shear wave orientations Shear waves propagate as a result of particle motions perpendicular to the direction of travel. If the direction of travel is z these motions can be in both the x and y directions. Crossed Dipole sonic tools have been developed with dipole sources orientated in perpendicular directions and arrays of dipole receivers. These can measure the velocity of the shear waves vibrating in both the x and the y directions. There can be anisotropy, the shear wave vibrating in one plane can have a higher velocity than the one vibrating in the perpendicular plane. The following can cause anisotropy:

Intrinsic anisotropy caused by Geologic features parallel to the well, such as shale laminations above and below a horizontal well, or parallel vertical micro fractures around a vertical well;

Stress anisotropy caused, in the case of a vertical well, by the maximum and minimum horizontal stress, often related to mountain building forces in the Earths crust such as those driving the creation of the Rockies.

Stress anisotropy data on horizontal stresses (which must be collected in vertical wells) is extremely valuable for fracturing, as it can indicate fracture orientation, and for well stability, where it can determine the direction in which a horizontal well will be most stable, i.e. least likely to collapse. The effect of frequency on Shear wave anisotropy is used to distinguish it from intrinsic anisotropy. Fractures and Stoneley waves Open fractures crossing the wellbore can greatly increase production, whether hydrocarbon or water. Sonic logs are one way of identifying them. Open fractures crossing the well should cause a loss of shear wave amplitude, as the shear waves cannot cross the fluid gap, however the best detection is from the Stoneley waves. These loose energy due to mud movement in and out of the fracture and characteristic chevrons are produced. Seismic applications Seismic measures the time a compressional (or shear) wave takes to go from the surface down to a subsurface layer and back again to a geophone. The waves are similar to those measured by a sonic log, consequently the geophysicist and petrophysicist have a close relationship.

The geophysicist needs sonic velocities to convert the two way travel times measured by seismic surveys into depths, typically a check shot or velocity survey is made. A pulse is created at surface and detected by a geophone run into the hole on wireline. From the depth and the time taken the average velocity down to that depth can be calculated. It is also possible to calculate this from sonic logs, although sonic logs are rarely run over the complete well. Check shots were extended by running a series of geophones in the well and recording the complete sonic wavetrain and not just the first arrival, to create a vertical seismic profile (VSP). Reflections off deeper formations mean it is possible to see beyond the total depth of the well. By moving the source progressively away from the well a walk away VSP is conducted which gives lateral information on the formations encountered in the well Where the well is deviated, the source is moved on surface away from the well, so it is vertically above the geophone, to give a walk above VSP. Seismic reflections need to be related to geologic formation. To do this a synthetic seismogram is created from the sonic and density logs. Seismic reflections are created at boundaries where there is a contrast between the acoustic impedance (density x compressional wave velocity) of the formation above and below the boundary. If it is gradational for example, the top of an oil reservoir may not give a sharp change in acoustic impedance and the nearest seismic reflection may come from some other boundary, it is necessary to know which. Using the sonic and density logs the shape of the synthetic seismic trace created by a section of rock can be calculated, by matching this with the actual seismic trace, the geologic features being mapped by seismic reflectors can be ascertained. AVO, or Amplitude Variation with Offset, looks at how the seismic amplitudes change as a function of the angle at which the seismic waves intersect the subsurface boundaries. If conditions are right it can be used to map oil, gas and changes in porosity and lithology from seismic surveys alone. To understand what effect the expect AVO effect is s a knowledge of shear wave and well as compressional wave velocities are needed. To calibrate the techniques and confirm it gives meaningful results, petrophysical properties from logs are essential. 4-D seismic looks at changes in seismic amplitude over time from reflections coming from the reservoir. It can be used to detect the build up of gas in oilfields, and more subtly, changes in pressures. To understand whether any changes in amplitude would be expected, data acquired from logs, and in particular the sonic log is essential.