Premium
Pore‐Scale Modeling of Spontaneous Imbibition in Porous Media Using the Lattice Boltzmann Method
Author(s) -
Liu Haihu,
Sun Shilin,
Wu Rui,
Wei Bei,
Hou Jian
Publication year - 2021
Publication title -
water resources research
Language(s) - English
Resource type - Journals
SCImago Journal Rank - 1.863
H-Index - 217
eISSN - 1944-7973
pISSN - 0043-1397
DOI - 10.1029/2020wr029219
Subject(s) - micromodel , imbibition , wetting , lattice boltzmann methods , porous medium , mechanics , capillary action , contact angle , materials science , saturation (graph theory) , capillary pressure , viscous fingering , viscosity , surface tension , porosity , thermodynamics , composite material , mathematics , physics , germination , botany , combinatorics , biology
A new color‐gradient lattice Boltzmann model is developed to simulate spontaneous imbibition in a porous media micromodel, which needs only two‐dimensional computational cost but considers essential three‐dimensional effects. A modified periodic boundary condition is introduced to deal with inlet and outlet boundaries with great ease and effectiveness. This model is first validated against analytical solutions and micromodel experiment. It is then used to study the spontaneous imbibition process in a homogeneous micromodel for varying viscosity ratios and contact angles. Depending on the viscosity ratio ( λ ) of wetting to nonwetting fluids, three different imbibition patterns are observed, namely unstable displacement (UD), stable displacement (SD), and crossover from UD to SD, which occur at λ ≤ 0.1 , λ ≥ 10 , and 0.1 < λ < 10 , respectively. When the crossover occurs, the wetting fluid saturation at breakthrough increases between two plateaus corresponding to UD and SD, respectively. Consistent with theoretical predictions from a single capillary, the wetting fluid saturation versus time follows the relation ofS w ∝ t for λ = 1 , andS w ∝ tfor λ ≫ 1 . Due to the increased capillary valve resistance, increasing wetting phase contact angle is found to promote the flow instability, resulting in the development of preferential flow paths and thus some nonwetting fluid trapped in the flow direction. In addition, it is theoretically and numerically demonstrated that the effect of contact angle cannot be properly described by the theoretical equations derived from a single capillary because of the presence of capillary valve effect, which can be suppressed by decreasing contact angle or micromodel depth.