TY - JOUR

T1 - Comparison of modified effective-medium approximation to pore-network theory for relative permeabilities

AU - Salimi, Hamidreza

AU - Bruining, Johannes

AU - Joekar-Niasar, Vahid

PY - 2020

Y1 - 2020

N2 - Pore-network models have been used to derive relative-permeability and capillary-pressure relations, which are important for oil-recovery predictions and processes. Here, we show that relative-permeability and capillary-pressure relations on large scales can be obtained much faster with the effective-medium approximation. Our approach differs from previous work in that we use various shapes of non-circular pores and combinations of different shapes. We use a finite-element approach to compute the hydraulic conductivity of arbitrarily shaped prisms, which are partly filled with oil and water. Our present interest is confined to water-wet media. Striking features of the obtained constitutive relations are that the water relative permeabilities show a marked reduction below a critical water saturation—at which there is no infinite cluster of completely filled water pores—but the water relative permeabilities continue to be finite even at very low water saturations because of corner flow. The capillary pressure remains finite even at low water saturations. Primary-drainage oil relative permeabilities are non-zero at low oil saturations, which is in line with early gas breakthrough for the solution-gas drive oil-recovery mechanism. We compare the results obtained with the effective-medium approximation to the results obtained with a pore-network model consisting of a simple-cubic lattice of prisms. The comparison shows that the pore-network generated relative-permeability curves are completely dissimilar to the effective-medium approximation derived relative-permeability curves. Furthermore, below and near the percolation threshold, the pore-network results differ significantly from one realization to another and/or from one network size to another network size. The network-model results show discontinuous behavior at the percolation threshold. This implies that pore-network results are scale dependent and the pore-network sizes up to 301 × 301 × 301 (the limitation determined by the available computer power) studied here are still far from a representative elementary volume (REV).

AB - Pore-network models have been used to derive relative-permeability and capillary-pressure relations, which are important for oil-recovery predictions and processes. Here, we show that relative-permeability and capillary-pressure relations on large scales can be obtained much faster with the effective-medium approximation. Our approach differs from previous work in that we use various shapes of non-circular pores and combinations of different shapes. We use a finite-element approach to compute the hydraulic conductivity of arbitrarily shaped prisms, which are partly filled with oil and water. Our present interest is confined to water-wet media. Striking features of the obtained constitutive relations are that the water relative permeabilities show a marked reduction below a critical water saturation—at which there is no infinite cluster of completely filled water pores—but the water relative permeabilities continue to be finite even at very low water saturations because of corner flow. The capillary pressure remains finite even at low water saturations. Primary-drainage oil relative permeabilities are non-zero at low oil saturations, which is in line with early gas breakthrough for the solution-gas drive oil-recovery mechanism. We compare the results obtained with the effective-medium approximation to the results obtained with a pore-network model consisting of a simple-cubic lattice of prisms. The comparison shows that the pore-network generated relative-permeability curves are completely dissimilar to the effective-medium approximation derived relative-permeability curves. Furthermore, below and near the percolation threshold, the pore-network results differ significantly from one realization to another and/or from one network size to another network size. The network-model results show discontinuous behavior at the percolation threshold. This implies that pore-network results are scale dependent and the pore-network sizes up to 301 × 301 × 301 (the limitation determined by the available computer power) studied here are still far from a representative elementary volume (REV).

KW - Effective-medium approximation

KW - Noncircular pore throats

KW - Percolation theory

KW - Pore-network theory

KW - Primary and secondary drainage

KW - Relative permeability

UR - http://www.scopus.com/inward/record.url?scp=85075517327&partnerID=8YFLogxK

U2 - 10.1016/j.petrol.2019.106594

DO - 10.1016/j.petrol.2019.106594

M3 - Article

AN - SCOPUS:85075517327

VL - 184

JO - Journal of Petroleum Science and Engineering

JF - Journal of Petroleum Science and Engineering

SN - 0920-4105

M1 - 106594

ER -