Solutions are investigated for 1D linear counter-current spontaneous imbibition (COUSI). The diffusion problem is scaled to depend only on a normalized coefficient Λ_n (S_n ) with mean 1 and no other parameters. A dataset of 5500 functions Λ_n was generated using combinations of (mixed-wet and strongly water-wet) relative permeabilities, capillary pressure and mobility ratios. Since the possible variation in Λ_n appears limited (mean 1, positive, zero at S_n=0, one maximum) the generated functions span most relevant cases. The scaled diffusion equation was solved for all 5500 cases and recovery profiles were analyzed in terms of time scales and early- and late time behavior. Scaled recovery falls exactly on the square root curve RF=T_n^0.5 at early time. The scaled time T_n=t/τT_ch accounts for system length L and magnitude D of the unscaled diffusion coefficient via τ=L^2/D, and T_ch accounts for Λ_n. Scaled recovery was characterized by RF_tr (highest recovery reached as T_n^0.5) and lr, a parameter controlling the decline in imbibition rate afterwards. This correlation described the 5500 recovery curves with mean R^2=0.9989. RF_tr was 0.05 to 0.2 units higher than recovery when water reached the no-flow boundary. The shape of Λ_n was quantified by three fractions z_(a,b). The parameters describing Λ_n and recovery were correlated which permitted to (1) accurately predict full recovery profiles (without solving the diffusion equation); (2) predict diffusion coefficients explaining experimental recovery; (3) explain the combined impact of interactions between wettability / saturation functions, viscosities and other input on early- and late time recovery behavior.
Effects of Brine Valency and Concentration on Oil Displacement by Spontaneous Imbibition: An Interplay between Wettability Alteration and Reduction in the Oil-Brine Interfacial Tension
Capillary rise dynamics of liquid hydrocarbons in mesoporous silica as explored by gravimetry, optical and neutron imaging: Nano-rheology and determination of pore size distributions from the shape of imbibition fronts
Flow-rate controls on trapped hydrogen redistribution in a heterogeneous sandstone: a synchrotron X-ray micro-CT study
Stanford University（斯坦福大学）；Ghent University（根特大学）；University of Edinburgh（爱丁堡大学）；University of Manchester（曼彻斯特大学）；Diamond Light Source（钻石光源）；University of Southampton（南安普顿大学）；Institute of Environmental Assessment and Water Research (IDAEA)（环境评估与水资源研究所）；Spanish Council for Scientific Research (CSIC)（西班牙科学研究委员会）
