Consider clean quartz sand, 100% saturated with brine with 50,000 ppm salinity at a temperature 80°C, and pressure of 300 bars with the following properties: Quartz Bulk Modulus (KO) 36 GPa
Water (brine) Bulk Modulus Kinie 3.013 GPa
Water (brinc) Density Prim 1.055 g/cm
From the wireline logs, the following properties are also measured for the sand:
Porosity 25%
P-wave velocity (pv) 2992m/s
S-wave velocity (Vs) 1309m/s
Density (o ) 2.25125 g/em
Replace 100% brine saturated fluid with 80% brine (with the same properties) and 20% gas with 1 API gravity gas under the same in-situ conditions of temperature and pressure. Using the Batzle Wang relation, the bulk modulus and the density of the gas are found to be K-0.133 GPa and 1. 0.336 g/cm
Repeat the same exercise as 1, but now replacing the pore fluid with 20% brine and 80% gas.
Calculate the P- and S-wave velocities and density of the fluid-substituted rock under both scenarios. Show the step-by-step calculations of your work along with your results.