Flow Properties

The effective permeability of the rock to a phase is taken as the product of the absolute permeability times the relative permeability of the phase which is a function of saturation. Relative permeabilities used in the simulations are shown in Figure , and were taken from a North Sea data set. Relative permeabilities for water and gas are assumed to be a function of their own saturations only. The oil relative permeability is calculated from two sets of oil relative permeabilities using

$$k_{ro} = \omega_1 k_{rog} + \omega_2 k_{row} \;\;,$$ (2)

where k_rog is the relative permeability of oil in the presence of gas and connate water, k_row is the relative permeability of oil in presence of water and no gas, and $\omega_1$ and $\omega_2$ are weighting functions given by

$$\omega_1 = \frac{S_g}{S_g + S_w - S_{wc}} \;\; , \;\; \omega_2 = \frac{S_w - S_{wc}}{S_g + S_w - S_{wc}} \;\;.$$ (3)

S_g is the gas saturation, S_w is the water saturation, and S_wc is the connate water saturation. This is the default model used by Eclipse. Capillary pressure was assumed to be zero between all phases, and phase viscosities were set constant and equal to $\mu_w = 1.0\;{\rm cp}$,$\mu_o = 0.7\;{\rm cp}$, and $\mu_g = 0.02\;{\rm cp}$.

 

marcofig3
Figure 8 Relative phase permeabilities from a real North Sea data set used for the fluid-flow simulations.