Fluid Conductivity of Steady Two-Phase Flow in a 2D Micromodel

Analysis of a Representative 2D Percolation Model

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Foams are used in reservoir engineering for enhanced oil
recovery, CO2 sequestration and environmental remediation of aquifers and
soils. One of the main mechanisms for foam generation at steady state is Roof
snap-off. In some cases, mechanistic models of Roof snap off, based on
observations from 2D micromodels are used for reservoir simulation. The main
problem with these experiments is in their 2D nature. Two-phase flow within a
2D medium requires that the fluids paths cross and compete for pore occupancy.
This virtually ensures fluctuating pore occupancy and therefore puts into
question the applicability of 2D mechanistic models for steady state foam
generation in 3D media. Two-phase flow in a micromodel is analyzed with a
lattice percolation model in order to determine under what conditions steady
two-phase flow can be achieved. The gas network is established with bond
percolation and liquid is allowed to flow across the sample with the help of
liquid bridges. These liquid bridges enable the liquid to cross gas-occupied
pore throats without snap-off. The calculated attribute for the gas and liquid
networks is equivalent resistance, ΔP/Q. For this a new unit for hydraulic
resistivity was used and is equal to the fluid viscosity divided by the pore
radius to the third power, H = μ/R3. The equivalent resistance of the gas and
liquid networks are found by applying rules from linear circuits of electrical
resistances. Solutions for the equivalent resistivity of the gas network are
calculated with the node elimination method and Kirchhoff’s solution for a
random network of resistances. The liquid network’s conductivity is calculated
as the sum of path resistances in parallel and is a theoretical maximum. The
gas and liquid conductivity of nine pre-existing 16x16 networks from
Holstvoogd(2020) are reevaluated and, in addition, twelve new samples of size
32x32 are evaluated. Functionally, the model’s behavior is as follows: gas
conductivity is inversely proportional and liquid conductivity is proportional
to the occupation threshold. It is found that the gas conductivity is a
function of tortuosity and number of parallel flow loops. Conductivity
decreases with increased tortuosity and increases with number of parallel flow
paths. The ratio of liquid and gas conductivity for the twelve 32x32 models is
calculated. When adjusted for gas viscosities of supercritical CO2 and Nitrogen
gas it is found that it is in the order of 10-3 to 10-4. Therefore, it has been
determined that it is practically impossible to achieve steady two-phase flow
without fluctuating pore occupancy.