Page 149 - Introduction to Petroleum Engineering

136 RESERVOIR GEOPHYSICS
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To get velocity in m/s, express K and G in Pa and density in kg/m . Hint: first
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convert GPa to Pa (1 GPa = 10 Pa and 1 Pa = 1 N/m = 1 kg/m·s ).
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7.3 A. Calculate the ratio of P‐wave velocity to S‐wave velocity (V /V ) when
S
P
V = 18 736 ft/s and V = 10 036 ft/s.
P
S
B. How long does it take a P‐wave to travel 10 000 ft?
C. How long does it take an S‐wave to travel 10 000 ft?
D. What is the difference in arrival times between the P‐wave and S‐wave
travel times in Parts B and C?
.
.
.
.
7.4 A. Suppose the correlations V P 5819 41 221 C and V S 3897 07
.
– 2.04C can be used to estimate P‐wave velocity and S‐wave velocity for
a particular sandstone. The velocities are in km/s, porosity is a fraction,
and C is clay volume fraction. Estimate P‐wave velocity for sandstone
with 20% porosity and clay volume fraction C = 0.05. Express your answer
in km/s.
B. Estimate S‐wave velocity for sandstone with 20% porosity and clay
volume fraction C = 0.05. Express your answer in km/s.
C. Use Parts A and B to calculate the ratio of velocities V /V .
P S
7.5 P‐wave velocity is V = 12 500 ft/s in a medium. What is the two‐way travel
P
(TWT) time for the P‐wave to travel vertically downward from the surface to a
depth of 10 000 ft and then back to the surface?
7.6 Young’s modulus (E) and Poisson’s ratio (ν) are related to bulk modulus (K)
and shear modulus (G) by the equations K E/( (31 2 )) and G E/(22 ).
Calculate bulk modulus (K) and shear modulus (G) when E = 4.4 × 10 psia
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and ν = 0.25.
7.7 Bulk modulus K and shear modulus G are related to Young’s modulus E and Poisson’s
ratio ν by the equations E 9 KG 3 KG) and (3K 2)/(2(3K + G)).
G
/(
Suppose bulk modulus K = 4.19×10 psia and shear modulus G = 2.28 × 10 psia.
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Calculate Young’s modulus E and Poisson’s ratio ν.
7.8 Compressibility is the reciprocal of modulus. Calculate fluid compressibility
for brine that has a modulus of 2.97 × 10 psia. Express your answer in psia .
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7.9 A. An earthquake is caused by the slippage of a fault block. The shear modulus
of the rock is 15 GPa, and the fault block slips 1 m relative to the adjacent fault
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block. The ruptured area is 2650 m . What is the seismic moment in N·m?
B. How much energy was released?
C. What is the moment magnitude of the earthquake?