Petrophysical properties

The background values and the geometry of the reservoir model are plotted in Figure . The reservoir is 50 m thick and the top of the reservoir is at 2 km depth. We simulate water injection wells located at 2 km and 3 km respectively. Table 1 lists the pre-flood and post-flood petrophysical properties at an injection well. The background properties both above and below the reservoir are: V_p = 2.38 km/s, V_s = 1.13 km/s, and $\rho$ = 2.1 g/cc. The relative P impedance contrast is calculated as:

 

$$\zeta_p = \frac{2( \rho^+ V_p^+ - \rho^- V_p^- )} {( \rho^+ V_p^+ + \rho^- V_p^- ) } \;,$$ (9)

and similarly for the relative S impedance contrast:

 

$$\zeta_s = \frac{2( \rho^+ V_s^+ - \rho^- V_s^- )} {( \rho^+ V_s^+ + \rho^- V_s^- ) } \;,$$ (10)

where ``+'' superscripted properties refer to the layer below the interface, and ``-'' superscripted properties refer to the layer above the interface. We note that $\zeta_p$ and $\zeta_s$ are exactly twice the normal incidence P and S plane-wave reflection coefficients R_p and R_s:

 

$$R_p = \frac{1}{2} \zeta_p \;,$$ (11)

 

$$R_s = \frac{1}{2} \zeta_s \;,$$ (12)

Figure shows the depth-dependent form of the background model and the reservoir properties at an injection well, pre- and post-flood. V_s is the left-most curve, $\rho$ in the center, and V_p to the right of each panel.

 

pre-flood post-flood

V_p 2.19 2.29

V_s 1.15 1.03

$$\rho$$ 2.05 2.09

R_p -0.055 -0.020

R_s -0.003 -0.050

 

curves12
Figure 3 Depth-dependent form of the background model and the reservoir properties at an injection well, pre- (left) and post-flood (right). V_s is the left-most curve, $\rho$ in the center, and V_p to the right within each panel. Density is nearly constant at 2.1 g/cc.