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8/18/2019 Rock Physics Coures_Lect#5
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Rock Physics: Principles and Applications
Petroleum Geophysics
Lectures and practical sessionsPGH-214-GEOPH
Lecture #5
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Lecture outcome
During this lecture, we will learn:
1. Effect of hydrocarbon on the bulk density
2. Relationship between the bulk density and P-wave velocity
3. Relationship between the P-wave and S-wave velocities
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Seismic cross section
Do you see seismic amplitude anomalies?
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Low Vp High Vp
Well A
P-wave velocity section
Well B
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Effect of hydrocarbon presence on the bulk density
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Pore fluid effect on bulk density
Gas Saturation - Rho Plot
2.05
2.1
2.15
2.2
2.25
2.3
2.35
2.4
0 20 40 60 80 100
Gas Saturation (%)
R h o ( g / c c )
ρb
ρ b
• The bulk density of the rock decreases gradually with increasing in the hydrocarbon saturation.
• There is a significant difference in the bulk density between the live gas and residual gas saturated rocks.
• The bulk density could be used to estimate the hydrocarbon saturation.
• When seismic data inverted into bulk density, then it can be used to define the hydrocarbon accumulations
Water-bearing sand
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Pore fluid effect on bulk density
Marlin Field, Gulf of Mexico
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Pore fluid effect on bulk density
Low density(gas)
High density(water)
Marlin Field, Gulf of Mexico
GR Density
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Relationship between the bulk density and P-waveseismic velocity
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Relationship between P-wave velocity and bulk density
Gardner’s equation “relation” (1974)
Gardner’s equation is applicable only for
the water-bearing reservoirs. It is not
applicable in the hydrocarbon reservoirs.
where ρb is bulk density in g/cc,
Vp is the P wave velocity in km/s,and d and f are constants.
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Relationship between P-wave velocity and bulk density
According to the following equation, the P-wave velocity has reverse relationship
with the bulk density. How can the Gardner’s equation be valid ?!
The Gardner’s equation (proportional relationship between the P-wave velocity and
bulk density) is valid as the velocity is not only controlling by the bulk density of
the rock but it is mainly affecting by the bulk and shear moduli of the rock.
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Relationship between P-wave velocity and bulk density
Castagna et al modification (1993)
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Relationship between P-wave velocity and bulk density
Castagna et al (1993) Vp-Density relationship
Ahmed Hafez et al, 2013
The constants (d and f) of the Gardner’s equation are highly depending on
the lithology . Theses constants are vary from one sedimentary basin to
another due to subsidence history and compaction diagenesis.
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Relationship between the P-wave seismic velocity and S-wave seismic velocity
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Relationship between P-wave and S-wave velocities
Castagna et al (1985)
The mudrock line also called Castagna's equation or Castagna's relation, is
an empirical linear relation between seismic P-wave velocity and S-wave velocity in brine-
saturated clastic rocks (sands, sandstones and shales).
Water point:
Vp = 1.5 km/s
Vs= 0 km/s
Quartz point:
Vp = 6.03 km/s
Vs= 4.1 km/s
Mudrock line
Where Vp and Vs in km/s
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Relationship between P-wave and S-wave velocities
Ahmed Hafez et al, 2013
The mudrock line slope is varying from one basin to another. Therefore, it
is strongly recommended to build a mudrock line for each basin per each
stratigraphic level.
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Relationship between P-wave and S-wave velocities
1
2
3
4
5
6
0
0 1 2 3 4
Vs (km/s)
V p
( k m / s )
Mudrock line
(water sand and shale)
Gas sandVp/Vs~1.5
Gas sand points are deviated from the mudrock line because the gas sand reservoirs
have lower P-wave velocity than the shale and water sand.
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Relationship between P-wave and S-wave velocities
1
2
3
4
5
6
0
0 1 2 3 4
Vs (km/s)
V p
( k m / s )
Clean gas sand
Shaly gas sand
The increasing of the shale/clay content of the sand reservoirs are resulting in increasing in
the VpVs ratio and so that the deviation from the mudrock line will decrease