The Analysis Of Laboratory Fluid/Flow Displacement Data To Obtain Relative Permeability Curves

Relative permeability measurement methods may be broadly classified into two types: steady state and unsteady state. For the steady state method, the phases are injected at a Fixed volumetric ratio until pressure and flow equilibrium have been established. The pressure drops across the core of each phase (Δ Pa) and the flow rates of each phase (qa) are then used to calculate the relative permeabilities (k_ra) by means of the Darcy equation

Equation 1 (available in full paper) where µa is the Viscosity, k is the absolute permeability, A is the cross sectional area of the sample and L is the length of the sample. A saturation of the sample is also required, this is typically determined by weight.

The unsteady state method is based on interpreting an immiscible displacement process. This interpretation is based on one of the two approaches: application of the welge Theory (see Johnson, Bossler and Naumann¹ or Jones and Roszelle²) or numerical simulation (see Sigmund and McCafFery³).

The welge approach requires the determination of the derivative of fractional flow with saturation. These derivatives are usually found either graphically or by means of curve fitting of the data. furthermore, application of this method requires the following experimental restrictions:

1. The pressure drop across the sample must be sufficiently large so that capillary pressure effects are negligible.

2. The pressure drop restriction often necessitates the use of the flow rates much in excess of those used in the field.

3. Because graphical or point to point methods are used, a reasonable number of data points must be available after injection fluid breakthrough. for water displacing oil experiements, this is often achieved by using an oil which has a viscosity much higher than that in the field.

The second method (numerical simulation) of reducing the data, is a more direct and sophisticated means of calculating the relative permeability curves, I t is applied by assuming explicit functions to relate relative permeability and saturation. The equations most often used are referred to as Corey equations which for two phases (i and d for injected and displaced) are:

Equation 2a & 2b (available in full paper) where k_ie and k_de are the effective end point permeabilities (effective permeability when the other phase is immobile), 5_i and 5_d are the saturations, and n_i and n_d are exponents which determine the shapes of the two relative permeability curves (shape exponents).

Data reduction by the numerical 9imulatlon method can explicity take account of capillary pressure effects. Therefore, there is no need to remove these effects by means of high flow rates.