Reservoir Permeability Lab Report

Relative Permeability

The permeability of a reservoir tells us something about the pressure drop required for a given fluid flow inside the reservoir. Higher permeabilities allow a lower pressure drop . We consider an oil reservoir with two fluid phases, i.e., an oil phase and an aqueous phase. The oil phase may consist of a large number of hydrocarbons, whereas the aqueous phase may contain considerable amounts of dissolved salts. Each of the phases has a given viscosity, but for the fluid flow we need to consider the permeability reduction effects due to the presence of the other phase. The permeability reduction factor is called the relative permeability and is defined by:

k_rα=k_α/k

, who matched centrifuge data to a seven parameter representation of water and oil relative permeabilities. His approximation is called the LET-type approximation and is the one used in this report. The approximation of Lomeland et al. has more parameters and thereby gives more smoother relative permeability curves. The LET stands for the 3 parameters that are L, E and T. The LET parameters are obtained from special core analysis (SCAL) experiments. SCAL experiments are flow experiments done one core plugs taken from a petroleum reservoir in order to measure the relative permeability and the capillary pressure. The LET parameters dominate different parts of the relative permeability curves. The L parameter for example dominates the part with the low relative permeability (lower part) and the T parameter dominates the part with the high relative permeability of the relative permeability curve (upper part). The E parameter dominates the part in between the L and the T parameter. From various SCAL experiments, trends were obtained for the different parameters as function of the irreducible water

The residual oil saturation (Sorw) is also a function of Swir. A typical trend model is obtained from earlier research by Lomeland et al. It can be seen that the Sorw increases with increasing Swir until a certain maximum is reached after this Sorw decreases to zero. Analysing this data gives us the following correlation between the Sorw and Swi:

S_orw=2.0698x^3-4.3857x^2+2.1741x+0.1482

The end point relative permeability also depends on Swir. [figure] As can be seen in figure[] an increased Swi leads to an low end point permeability. Lomeland et al derived the following equation which gives the end point water relative permeability (k0rw): k_rw^0=C_wko+((A_wko-Cwko)*(1-S_orw-S_wi )^Lwko)/((1-S_orw-S_wi )^Lwko+E_wko*S_orw^Twko ) (6)

All this gives the following relations for the relative permeability for oil and water:

Water: k_rw=k_rw^0 ((S_w^* )_ ^(L_w ))/((S_w^* )_ ^(L_w ) +E_w*(1-S_w^* )_ ^(T_w ) ) (7)

Oil: k_ro=k_ro^0 ((〖1-S〗_w^* )_ ^(L_0 ))/((〖1-S〗_w^* )_ ^(L_o ) +E_o*(S_w^* )_ ^(T_o ) ) (8)

With: S_w^*=(S_w-S_wir)/(1-S_orw-S_wir )