Stage 1: Preparation for drainage - core saturated with wetting phase.
Stage 2: Irreducible wetting phase (drainage) -
inject non-wetting phase until steady state, measure saturation, no wetting phase will be produced after steady state.
Stages 3-6: Inject wetting phase
Stage 3: (A) Wetting phase has not yet reached outflow face, only nonwetting phase produced at outflow face.
Stage 4: (B) Wetting phase just reaches outflow face, called breakthrough, wetting phase will be produced at outflow face.
Stage 5: (C) As injection of wetting phase continues, production of nonwetting phase decreases (unsteady state). Important to take many data points during this decrease (»cummulative nonwetting phase produced »and production rate for both phases).
Stage 6: (D) Eventually, no more nonwetting phase is produced, allowing residual nonwetting phase saturation to be determined.
linear, 1-D flow
capillary pressure neglected
cumulative nonwetting phase production,
Determine relative permeability ratio from fractional flow (production rate measured at outflow face):
4: Qtotal = Qwet + Qnonwet
5: Fwet = Qwet / Qtotal
Relative permeability ratio Fwet is related to relative permeability by the equation:
6: Fwet = 1 / (1 + (Kr_nonwet / Kr_wet)
* (MUwet / MUnonwet))
It is obvious from the above that one of Kr_nonwet or Kr_wet must be determined independently in order to find the other, using Fwet. This is done with correlation equations based on capillary pressure curves.
The process starts with calculation of effective water saturation (not to be confused with any form of water saturation from log analysis).
Pretty messy but so is the math for the lab method.
RELATIVE PERMEABILITY from MICRO
If a single fluid is present in a rock, its relative permeability is 1.0. Relative permeability allows comparison of the different abilities of fluids to flow in the presence of each other, since the presence of more than one fluid generally inhibits flow.
Key parameters that affect relative permeability include:
These parameters define the wetting (or contact) angles, which are formed at an interface between fluid and mineral. A wetting angle is larger than 90 degrees if the fluid is wetting and smaller than 90 degrees if the fluid is non-wetting.
The slow multiphase viscous flow needed for relative permeability estimates is simulated using the lattice Boltzmann method (LBM). LBM mathematically mimics the equations of multiphase viscous flow by treating the fluid as a set of particles with certain interaction rules between the particles belonging to the same fluid, different fluids, and the fluids and pore walls. LBM directly simulates static and dynamic configurations of the contacts between the fluid phases and the pore walls by taking into account surface tension and contact angles. It allows for the estimation of irreducible water and hydrocarbon saturations Source: www.ingrainrocks.com.
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