4.2
Add v an A ancc ed Fo Forr m at atii o n Ev Eval aluu at atii o n
Sonic Measurements Ac A cquisition and Evaluation by Alain Brie Octobe Oc toberr 2012
Geo-Acoustic Measurements §
Frequency
0. 1H 1Hz
1H z
10 Hz Hz
1 00 00 Hz Hz
1k Hz Hz
f
1 0k 0k Hz Hz 1 00 00 kH kH z 1 M MH Hz
1 0M 0M Hz Hz
– Laboratory measurements are made at ultrasonic frequency, – The wavelength is a function of frequency and sound velocity,
VS P Sonic logging
Ultrasonic (laboratory) Wavelength
10 k m
1k m
10 0 ft
10 0 m
10 ft
10m
– Seismic exploration uses low frequency wave for deep penetration, – Sonic measurements are made between 1 and 20 kHz and read close to the wellbore,
Seismic ex ploration ploration
1 0 00 f t
Geo-Acoustic Measurement evaluate sound propagation in the ground.
1 ft
1m
λ 0 .1 ft
1 0 0 mm
10 1 0m m
1m m
0. 0 .1 mm
λ ft
=
1000
∆ t µ s / ft ⋅ f kHz
– Depth of investigation and vertical resolution depend on wavelength.
Geo-Acoustic Measurements §
Frequency
0. 1H 1Hz
1H z
10 Hz Hz
1 00 00 Hz Hz
1k Hz Hz
f
1 0k 0k Hz Hz 1 00 00 kH kH z 1 M MH Hz
1 0M 0M Hz Hz
– Laboratory measurements are made at ultrasonic frequency, – The wavelength is a function of frequency and sound velocity,
VS P Sonic logging
Ultrasonic (laboratory) Wavelength
10 k m
1k m
10 0 ft
10 0 m
10 ft
10m
– Seismic exploration uses low frequency wave for deep penetration, – Sonic measurements are made between 1 and 20 kHz and read close to the wellbore,
Seismic ex ploration ploration
1 0 00 f t
Geo-Acoustic Measurement evaluate sound propagation in the ground.
1 ft
1m
λ 0 .1 ft
1 0 0 mm
10 1 0m m
1m m
0. 0 .1 mm
λ ft
=
1000
∆ t µ s / ft ⋅ f kHz
– Depth of investigation and vertical resolution depend on wavelength.
First Sonic Tool
§
The first sonic measurement: – A tra transmitte itterr emits its a sound pulse lse – The arrival of the sound is detected at two receiver locations – The difference in time of arrival divided by the inter-receiver inter-receiver spacing spacing gives ∆t
∆ t =
TT 2
− TT 1
Rspac
∆t is expressed in µs/ft or µs/m This is called first motion moti on detection detection;; only the fastest arrival can be measured.
Borehole Compensated Measurement
§
Making a measurement with two transmitters on top and bottom of the receivers achieves borehole compensation. – The BHC measurement is the average of the upper and lower transmitter measurements,
∆ t BHC =
∆ t UTx + ∆ t LTx 2
– BHC corrects the effect of sonde tilt and borehole enlargement, – The The T-R T-R spacings spacings of the BHC BHC tool are 3 ft- 5 ft
Long Spacing Sonic
Short Short spacing spacing measu measurem rements ents such as as the 3 – 5 ft BHC BHC lim limit the depth of investigation and can cause adverse effects on the measurement. easurement. §
n o i t c e S w o l l a h S
n o i t c e S e t a i d e m r e t n I
– In very large boreholes the tool can read the mud ∆t instead of the formation, – In case of alteration (shale swelling) the log can read the altered zone instead of the virgin formation, – Increasing the TR Spacing increases the depth of investigation and provides a reliable measurement of the formation, – The Long Long Spaced Spaced Sonic Sonic sonde with with TR spacings of 8 –10 – 10 ft and 10 10 –12 – 12 ft was designed designed for this this purpose. purpose.
Legacy Sonic Tools
Digital Cartridge
§
Legacy Sonic Tools can be operated with a common digital cartridge that digitizes sonic waveforms downhole. – The BHC sonde has 3 - 5 ft spacing
BHC LSS
Array Sonic
UTx
– The Long Spacing Sonde has 8-10 ft and 10-12ft Spacings, – The Array Sonic has 3-5 ft, 8-10 ft spacings and an array of 8 receivers every 6 in located at 8 ft from the upper transmitter. All these measuremen ts are monopol e.
LTx UTx
UTx
LTx
LTx
Array Sonic Waveforms
Typical Array Sonic Waveforms in a fast formation. We observe 3 arrivals: §
– The Compressional Wave arrives first, – The Shear Wave next, – The Stoneley Wave last has lower frequency. – Correlation of the different arrivals across the array shows theMove-Out in time versus distance which is theSlowness in µs/ft.
Slowness-Time Coherence Computation §
The Slowness Time Coherence technique scans the waveforms for all possible times and move-out to find coherent arrivals in the waveform. – Coherence is the ratio of coherent energy along a move-out over the total energy, – Coherence of 1 is perfect correlation, – Low coherence means no correlation. – The calculated coherence for each time and slowness value is plotted on the ST Plane.
ST Plane
§
t f / s
µ
s s e n w o l S
Each point on the ST plane represents the result of a coherence computation at a certain time and move-out. – Contours a drawn around zones of equal coherence, – Low coherences are shown in blue and high coherences in red,
n e i l R T
– High coherence peaks indicate a highly correlated event propagating at this time and slowness, – The arrival time of events propagating along the borehole should be close to their slowness times the TR spacing. Time µs 0
Coherence
1
Field STC Processing Results §
This display is used to control the quality of the STC computation. – Track 3 shows the Slowness coherence projection overlaid with the resulting DT logs, – Low coherences are shown in blue and high coherences in red, – Continuous red bands indicate good quality data (good coherence), – DT logs should follow track red bands, – Result logs are shown in Track 2, – Other information is shown in Track 1.
Field STC processing for monopole P&S (DSI SAM-4).
Monopole Borehole Propagation – The transmitter sends a pressure pulse that propagate as compressional and shear body waves in the formation, – Body waves induce head waves in the formation when they are faster than the mud compressional, – Sonic receivers record the head waves, – The shear headwave only exists in fast formations – Other waves propagate in the borehole ? The pseudo-Rayleigh wave, ? The Stoneley wave, ? Normal and leaky modes (borehole arrivals).
Monopole sonic tools measure head waves, Not body waves
Compressional and Shear Waves
§
Consider a pile of disks. – If we excite a vibration by knocking vertically on the top it propagates down as a compressional wave, – With a compressional wave particle motion is parallel to the propagation direction, – If we excite a vibration by knocking the pile laterally it propagates down as a shear wave, – With a shear wave particle motion is perpendicular to the propagation direction,
Compressional (extensional)
Shear (flexural)
Monopole-Dipole Excitation
– In monopole excitation one point source sends a pressure pulse in all directions.
– With dipole excitation two point sources side-byside pulse in opposite phase creating a lateral push-pull effect.
– Quadrupole excitation uses four point sources; one diagonal pulses in phase opposition with the other diagonal.
Dipole Shear Sonic Imager §
§
The DSI, dipole shear imager tool acquires both monopole and dipole measurements. Its main features are: – Two dipole transmitters in perpendicular directions, – One monopole transmitter with high and low frequency drives, – Array of 8 receivers stations with dipole and monopole capability, – Long spacing for reading past altered zones, – Isolation joint to prevent direct wave transmission through the tool body.
DSI Tool String
Electrodynamic Dipole Transmitter There are various ways to generate dipole excitation in the borehole. Propagation
Electrodynamic Transmitter
The electrodynamic transmitter works as a loudspeaker, pushing the mud laterally,
Flexural Wave
The push excites the borehole in flexion,
Displacement
Flexural wave propagates vertically along the borehole, while particle motion is transverse; it is therefore close to a shear wave.
Dipole DSI Waveforms
Flexural
DSI – Upper Dipole (SAM-2)
Flexural Wave Dispersion
§
Inflection Point
The flexural wave is linked to the wellbore and varies with frequency. This is called frequency dispersion. – At low frequency the flexural slowness reaches the formation shear slowness, – At higher frequencies the flexural slowness increases, – The maximum amplitude of the flexural is at the inflection point, – Dispersive STC processing accounts for dispersion and outputs formation shear directly.
Flexural Dispersion Curves in 8 in. Borehole
Dipole Processing Quality Control Display
§
Quality control plot for dipole shear processing.. – ST Projection with log tracking results is presented in Track 3, – Coherence in Track 1, – Arrival frequency and filter band in Track 2, – Filtered waveform and reconstructed shear arrival time in Track 4.
Sonic Scanner Tool
§
§
§
§
The Sonic Scanner tool is the latest development in Schlumberger sonic technology. The SScan benefits from the experience acquired with the DSI-1 and DSI-2 tools and offers superior dipole as well as monopole measurement capabilities. The Sonic Scanner is modular, in the basic configuration it replaces all prior monopole tools: BHC, LSS and AS. In the full configuration it replaces the DSI and adds new capabilities for anisotropic and inhomogeneous formation analysis. The Sonic Scanner tool was designed by computer modeling, it has predictable acoustics allowing full characterization of its response and frequency behavior for high fidelity answers.
Sonic Scanner Basic Configuration §
Basic Configuration – Monopole only tool to replace old technology sondes. – True BHC with upper and lower monopole transmitters. – Large 13 receivers array provide robust measurement and multiple spacings from 1 to 7 ft. – Cement bond log (CBL) and variable density log (VDL) measurement – Improved behind casing monopole measurement with CBL/VDL simultaneous acquisition Measurements – Monopole P&S – Cement Evaluation – Altered zone evaluation
Minimum Service Sonde
Sonic Scanner Full Configuration §
Basic configuration measurements plus: – Long-spacing 10.8 to 16.8 ft monopole with MF transmitter.
Full Service Configuration
– Low frequency monopole Stoneley measurement. – Wideband dipole measurements from X and Y transmitters. – All modes including BCR acquired all the time. – Improved behind casing dipole measurement with CBL/VDL simultaneous acquisition. Measurements – Dipole X&Y and anisotropy – Monopole P&S and Stoneley – Cement Evaluation – Stress Eval – Altered zone
Sonic Scanner Waveforms
Monopole Far (MF) §
§
Dipole (XD)
High quality, high consistency waveforms; Very wideband dipole waveforms for high quality answers, especially in cased hole and new applications (formation alteration and stress evaluation).
Dipole Slowness Dispersion Analysis
§
Monopole Stoneley
Dipole XD Dipole YD MF Shear
Sonic Scanner wideband, high fidelity waveforms allow new applications from sonic waveforms. – More accurate dispersion correction, – Evaluation of formation alteration (radial velocity profiling), – Anisotropy evaluation and characterization,
MF Compressional
Sonic Wave Dispersion Analysis Plot
– Formation stress direction and stress evaluation.
Alteration Evaluation From Dipole Dispersion
§
§
Chemical or mechanical alteration of the formation near the wellbore increases the dispersion of the dipole flexural wave. Evaluation of dispersion provides: – More accurate formation shear, – Information on formation weaknesses and potential failure, – Formation stress information.
Dipole Anisotropy Radial Profiling §
Systematic acquisition of XD and YD dipole waveforms provides shear slowness in the fast and slow directions in case of anisotropy. – More accurate shear determination for formation evaluation, – Dispersion analysis further provides stress information, – This is essential information for rock mechanics evaluation.
Elastic Waves Velocities Compressional
V p
∆t =
= 304 . 8 V p
K +
4
3
Shear
⋅G
V s
ρ =
304 .8 K +
4
3
⋅G
∆ t s =
=
304 .8 V s
G ρ =
ρ
304 . 8 G ρ
¦ Sound waves are elastic waves that propagate in the ground as vibrations. ¦ In an isotropic, homogeneous (HI) medium only two moduli and thedensity are necessary to determine the velocity of the compressional and shear body waves. ¦ K is the bulk modulus, G is the shear modulus and r is the density Units: K and G in GPa ρ in g/cc V p ans V s in km/s
∆t and ∆t s in µs/ft
Elastic Waves Analogy with Spring-Mass Systems
Propagation of a vibration in a system of spring and masses.
Displacement of masses.
Spring-Mass System
Elastic Medium Velocity
Spring Stiffness
Moduli
Mass
Density Slowness
Elastic Moduli
§
Compression
Elastic moduli represent the resistance of a material to deformation. – Bulk modulus is the resistance to compression
K =
σc ε
– Shear modulus is the resistance to distortion
Shear
G =
σ s ε
Elastic Moduli
§
Young Modulus and Poisson’s ratio are often used in rock lab and rock mechanics.
Uniaxial Compression – Young Modulus is the resistance to uniaxial compression (as in a press)
E =
σu ε1
– Poisson’s ratio characterizes lateral expansion as the sample is compressed
=
ε2 ε1
=
ε3 ε1
Poisson’s Ratio is linked to Vp/Vs §
soft
Poisson’s ratio is linked to the Vp/Vs ratio. – The physical limits of Poisson’s Ratio are:
0≤υ
≤ 0. 5
– Poisson’s Ratio and Vp/Vs are linked as:
υ
−2 Vp / Vs 2 − 1
1 Vp / Vs 2
= ⋅ 2
– From which the physical limits for Vp/Vs (isotropic material) are:
2
≤ Vp / Vs ≤ ∞
Elastic Moduli Equivalence K, G
E, ν E
Bulk Modulus Shear Modulus
K G
µ
Young’s Modulus
E
Poisson’s Ratio
ν
Lame Constant
λ
-
3(1 − 2υ ) E
-
9 K µ µ + 3 K 3 K − 2µ 2( 3 K + µ )
2(1 + υ ) -
-
3 K − 2 µ
E ν
3
(1 + υ )(1 − 2υ )
λ, µ λ + 23 µ µ µ (3λ + 2µ ) λ+µ λ 2( λ + µ ) -
¦ Two elastic constants are sufficient to describe elastic properties of a HI medium (Homogeneous Isotropic), ¦ Young modulus and Poisson’s ratio are used in rock mechanics, ¦ The Lame constants λ and µ are used in theoretical physics.
Dynamic Elastic Moduli
Factors of Influence on Sonic Slowness √ Porosity √ Lithology (mineralogy) including cl ay content Pore fluid Pore shapes Micro structure Stress (pressure) and compaction Sizes of pores and grains have no influence (Sonic wavelength is much larger) ¦ Equations that do not account for all effects are approximate and limited, ¦ Most equations only account for Porosity and Lithology effects, ¦ Elastic Moduli are needed to account for fluid effect (GassmannEquation).
Wyllie Sonic Porosity In 1950 Mr Wyllie proposed a simple time-average response equationbased on a correlation of laboratory measurements to link ∆t and porosity:
∆t = φ .∆t f + (1 − φ ).∆t m The Wyllie sonic porosity is this obtained as:
∆t − ∆t m φS = ∆t f − ∆t m
In unconsolidated sands the Wyllie Porosity is larger than true porosity. A compaction factor (multiplier) is added:
∆t = Cp.φ .∆t f + (1 − Cp.φ ).∆t m
∆ t − ∆t m φS = ⋅ Cp ∆t f − ∆t m
Cp: compaction factor is 1 in well consolidated sands up to 2 in loose sands.
1
Sonic Porosity Equations Raymer-Hunt-Gardner Equation - RHG
1
=
φ
∆t ∆t f
+
(1 − φ )
2
∆t m
Velocity Equation - VelC
1
=
1
∆t ∆t m
⋅ (1 − s ⋅φ ) with
and
s = 1.45 in sandstones 1.60 in carbonates.
∆t − ∆t m φ= ( ) ∆t s 1
Sonic Porosity Chart – Por-3
Uncompacted Sandstones
s e n o t s d n a S d r e a n H o t s e e t i i m m L o l o D
s n e o t s d n a S t f o S
Porosity Evaluation from Sonic (Por-3)
V, ft/s ∆ t, µs/ft Water 5300 189 26000 38.5 Dolomite 23000 43.5 Limestone 21000 47.6 Hard Sands19500 51.3 Soft Sands 18000 55.5
Mineral End Points
End points
ρm
∆ tm
∆ ts m
Vp/Vs m
Soft sand
2.65
55.5
78.2
1.53
Hard sand
2.65
51.5
88
1.59
Limestone
2.71
47.5
88.5
1.86
Dolomite
2.87
43.5
78.5
1.8
Salt
2.16
67
116.5
1.73
An hydrite
2.98
50
92
1.84
End points for Wyllie Equation These are slightly different from mineral values.
Sound Slowness of Saline-Water Solutions
Sonic Porosity Equations In Sandstones
Slowness in Unconsolidated Sandstones
Group 1
Group 2
Group 3
Compressional slowness in shallow unconsolidated sands
Sonic Porosity Equations In Carbonates Crossplot compressional ∆t -porosity in a water-bearing limestone Secondary Porosity Index
SPI
= φ − φ S
15 PU
10.5 PU
∆t = 62 µs/ft, φSonic = 10.5 PU φND = 15 PU 62 µ s/ft
SPI = 15 – 10.5 = 4.5 PU
Porosity Evaluation from Slowness
Porosity Evaluation Recommendations
§
Well compacted sands Both Wyllie and VelC are adequate
§
§
§
Unconsolidated sands Moderate unconsolidation: VelC Substantial unconsolidation: calibrated Wyllie with Cp Carbonates VelCis a good average Can use a dual porosity model : intergranular / isolated pores Metamorphic and igneous roc ks Wyllie often gives good results for unfractured block
Vp/Vs Crossplot in Shaly Sands - Effect of Gas
Original Crossplot for Gas Sands. Brie et al. - SPE 1995
Vp/Vs vs ∆t crossplot
Updated Vp/Vs Crossplot for Sands and Carbonates
Updated Vp/Vs Crossplot Includes: - Effect of water salinity in sands, - Water and gas trends in carbonates
Vp/Vs vs ∆t crossplot Brie, SPWLA-2001
Natural Gas Properties
Live Oil Slowness
Effect of Live Oil on Vp/Vs
Live oil has an effect on ∆t and Vp/Vs. Although intuitively oil is liquid like water, it is more compressible. At high GOR the effect of live oil on sonic ∆t and Vp/Vs is comparable to that of gas.
Sands with live oil, gravity 35 API, at 200ºFand 5000 psi For different GOR
Evaluation of Gas Effect on Sonic Slowness Elastic physics govern sound propagation in materials and rocks. To understand the effect of the pore fluid, especially that of gas, on sound velocity and slowness we have to go back to the elastic properties of the rock. We have seen that sound velocity are linked to elastic moduli and density with the relations:
V p
=
K +
4
3
⋅G
and
ρ
V s
=
G ρ
Where K is the bulk modulus, G the shear modulus and ρb is the rock density. Starting from the logs K and G can be obtained with the expressions:
K = ρ bV p 2
− 4 3 ρ bV s 2
and
G
= ρ bV s
2
Gassmann Equation for Fluid Effect
2
K dry
1 − K m K = K dry + 1 − φ K dry φ + − 2 K f
G
K m
K m
= G dry
The Gassmann Equation is a physical model that relates the properties of the saturated rock to the properties of the dry frame and those of the pore fluid. It is valid at low frequency and is commonly used in seismic interpretation. It also gives good results at sonic frequencies provided the pore fluid modulus is known.
K and G are the moduli of the saturated rock Kdry and Gdry are the moduli of the dry rock-frame Km, is the bulk modulus of the mineral composing the frame Kf , is the modulus of the pore fluid andf is the porosity.
Partially Saturated Rocks In partially saturated rocks the effective fluid bulk modulus, Kfe, must be entered in the Gassmann equation. Geophysicist useWood’s Law , a compliance law to evaluate Kfe. 1− S xo S xo 1 K fe K mf K g
2.5
a P G s u l u d o M d i u l F e r o P
=
a w L i n g x i r M e w P o
’ s d o o a w W L
0 0
Liquid Saturation %
+
However Wood’s Law is too abrupt at sonic frequency where a more gradual change is observed. A realistic approximation is provided by thepower mixing law:
K fe
= (K mf − K g )⋅ S xo e + K g
100
Fluid Mixing Laws (low pressure)
The exponent e is usually around 5. Note that when saturation is less than 50% the fluid bulk modulus is practically that of gas.
Effect of Gas on Vp/Vs
In shaly sands theVp/Vs of the dry rock is constant and equal to theVp/Vs of the minerals; 1.5 to 1.58 (depending on additional minerals).
( ) =( ) = Vp 2 Vs dry
Vp 2 Vs m
K dry G
+ 43
This expression provides a link between dry bulk modulusKdry and the shear modulus G, obtained from ∆tshear . Kdry can then be used to estimate the hydrocarbon volume from ∆t, or ∆t at different saturation conditions (fluid substitution).
Effect of Gas on ∆t Slowness Light hydrocarbon effect is large in porous, unconsolidated formations.
The effect of gas on compressional ∆t is small to negligible in low porosity, compact formations.
Vp/Vs Crossplot in Tight Gas Sands - Algeria
Although the porosity is very low, the effect of gas on Vp/Vs is visible in tight sands with porosities of 10 PU or less.
Vp/Vs Crossplot in Low Porosity Oil Sand Live Oil properties: 41 deg API 1301 cuft/bbl 260°F 4500 psi
Although the effect is small, the effect of live oil on Vp/Vs is visible in tight sands with porosities of 6 to 11 PU. A quicklook method can be used to detect oil bearing intervals in the field. A polynomial correlation is adjusted to fit the Wet Sand line on the Vp/Vs crossplot
∆ t wet = a + b.∆ t s + c .∆ t s2 + d .∆ t s3 + e.∆ t s4 The wet ∆t can then be calculated from ∆tshear . In the example shown: a = -0.8482 b = 0.7665 c = -1.450 10-3 d = 1.391 10-6 e = -5.364 10-10 Chardacet al. – SPE-2003
∆t Overlay for HC Detection in Low Porosity Sands The wet ∆t calculated from ∆tshear . with the polynomial calculation is drawn with the measured ∆tlog A separation between ∆tlog and ∆twet indicate the presence of light hydrocarbon in the formation. There is good agreement with the subsequent ELAN evaluation.
Chardacet al. – SPE-2003
Vp/Vs Crossplot in Limestone Comparison of model curves with data from a clean limestone with some gas intervals. Wet Vp/Vs varies little and does not depend on spherical porosity fraction, Dry (gas bearing) Vp/Vs decreases with porosity and with decreasing spherical porosity fraction.
Generalized Dry Vp/Vs for Complex Lithology In shaly sands Vp/Vsdry is constant around 1.53, but in carbonates it changes with porosity and spherical pores fraction. A generalized equation for Vp/Vsdry is given by the expression:
(Vp / Vs ) dry
= Vp / Vs m − 3 .1(Vp / Vs m − 1 .53 )φ (1 − 0 .9 spf ) Vp/Vsm : Vp/Vs of the minerals (solids), spf : Fraction of spherical pores (molds or vugs) in the porosity
Vp/Vsm
The generalized Vp/Vsdry allows us to evaluate the hydrocarbon effect and do fluid substitution on the sonic logs in all lithologies.
