1. A method for estimating relative permeability for fractional multi-phase, multi-component fluid flow through a porous medium

comprising steps of:

(a) creating a three dimensional digital representation of a porous medium comprising scanning a sample of the porous medium

using a scanning device to make an image of the porous medium and segmenting the image to produce the three dimensional digital

representation of the porous medium;

(b) performing a first or precursor simulation over a first computational domain of the three-dimensional digital representation

of the porous medium, wherein the first computational domain extends from an inlet plane to an outlet plane and a selected

storage plane is located between the inlet and outlet planes, which comprises:

(1) setting the initial condition for the precursor simulation where the initial distribution of the fluid is single or multi-phase

flow within the volume,

(2) defining a nominal pressure at the outlet of the volume,

(3) assessing properties of the wetting fluids and non-wetting fluids,

(4) defining an inlet pressure in order to have a selected flow rate,

(5) simulating injecting of single phase fluid into the inlet plane of the sample towards the storage plane and the outlet

plane,

(6) calculating sets of variables comprising fractional flow rates, pressures, saturations, and velocities of the wetting

and non-wetting phases for all points in the porous medium within the first computational domain for successive time increments,

(7) determining if saturation at the storage plane has changed one of a preselected percentage amounts after the calculating

done at each of the time increments of step (6), and if so, storing index values for the storage plane wherein the stored

index values comprise sets of variables which comprise the saturations, and/or pressures, and/or velocities of the wetting

and/or non-wetting phases of the storage plane measured for the time increment for which the determining is done,

(8) determining after step (7) if saturation in a volume of the porous medium defined by the first computational domain is

at quasi steady state,

(9) repeating steps (5), (6), and (7) for a successive time increment if saturation in the volume is not determined to be

at quasi steady state in step (8) or ending the simulating of step (5) if quasi steady state is determined in step (8), wherein

a last set of stored index values in step (7) are designated final index values;

(c) performing a second simulation over a second computational domain of the three-dimensional digital representation of the

porous medium sample, wherein the second computational domain is defined by said storage plane which represents an inlet plane

for the second computational domain and said outlet plane used in the precursor simulation, which comprises

(i) setting the initial condition for the precursor simulation where the initial distribution of the fluid is single or multi-phase

flow within the volume,

(ii) defining a nominal pressure at the outlet of the volume,

(iii) setting inlet flow conditions of the second simulation from the storage plane of the precursor simulation, wherein a

first plane determines a first fractional flow injection of wetting and non-wetting fluid,

(iv) simulating injecting of dual phase fluids into the inlet plane of the sample of the second simulation towards the outlet

plane, wherein fractions of wetting and non-wetting phases are injected according to the saturation and pressure distribution

values stored from the precursor simulation at the storage plane, beginning with initial index values of zero for the first

couple of fractional flows stored in the precursor simulation,

(v) calculating fractional flow rates, pressures, saturations, and velocities of the wetting and non-wetting phases for all

points in the porous medium within the second computational domain for a time increment during the simulating of step (iv),

(vi) determining after step (v) if quasi steady state is reached,

(vii) repeating steps (v) and (vi) for a successive time increment if quasi steady state is not determined in step (vi),

(viii) storing the fractional flow rates, pressure, and saturations distribution calculated in step (v) if quasi steady state

is determined in step (vi),

(ix) determining if final index values stored for the variables at the storage plane in the precursor simulation have been

reached if quasi steady state is determined in step (vi),

(x) repeating steps (v), (vi), (vii), and (viii) if determined in step (ix) that the final index values stored for the storage

plane in the precursor simulation have not been reached, comprising using inflow conditions for the calculating in step (v)

which correspond to successively stored index values for the variables at the storage plane from the precursor simulation,

and

(xi) calculating relative permeability of at least one of the wetting phase and non-wetting phase if the final index values

stored for the variables at the storage plane in the precursor simulation are determined to have been reached in step (ix).