Dynamic Effect in the Capillary Pressure–Saturation Relationship and its Impacts on Unsaturated Flow

By S. Majid Hassanizadeh, Michael A. Celia, Helge K. Dahle. 2002

445 citations recorded by the source corpus.

Capillary pressure plays a central role in the description of water flow in unsaturated soils. While capillarity is ubiquitous in unsaturated analyses, the theoretical basis and practical implications of capillarity in soils remain poorly understood. In most traditional treatments of capillary pressure, it is defined as the difference between pressures of phases, in this case air and water, and is assumed to be a function of saturation. Recent theories have indicated that capillary pressure should be given a more general thermodynamic definition, and its functional dependence should be generalized to include dynamic effects. Experimental evidence has slowly accumulated in the past decades to support a more general description of capillary pressure that includes dynamic effects. A review of these experiments shows that the coefficient arising in the theoretical analysis can be estimated from the reported data. The calculated values range from 104 to 107 kg (m s)−1 In addition, recently developed pore‐scale models that simulate interface dynamics within a network of pores can also be used to estimate the appropriate dynamic coefficients. Analyses of experiments reported in the literature, and of simulations based on pore‐scale models, indicate a range of dynamic coefficients that spans about three orders of magnitude. To examine whether these coefficients have any practical effects on larger‐scale problems, continuum‐scale simulators may be constructed in which the dynamic effects are included. These simulators may then be run to determine the range of coefficients for which discernable effects occur. Results from such simulations indicate that measured values of dynamic coefficients are within one order of magnitude of those values that produce significant effects in field simulations. This indicates that dynamic effects may be important for some field situations, and numerical simulators for unsaturated flow should generally include the additional term(s) associated with dynamic capillary pressure.

Subfields: Civil and Structural Engineering, Environmental Engineering

View Paper: https://www.semanticscholar.org/paper/9f91455d43bf1e92589df156b28d2b6e74197a7b

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Citations in the corpus

Bundle-of-Tubes Model for Calculating Dynamic Effects in the Capillary-Pressure- Saturation Relationship (2005, methodology): “For more details on the use of these ideas in conjunction with pore-scale network models, we refer to Dahle and Celia (1999) and Hassanizadeh et al. (2002).”
Linking pore-scale interfacial curvature to column-scale capillary pressure (2012, background): “More recently, dynamic effects in capillary pressure have been studied, and it is well accepted that the rate of change of saturation must be considered [9,12,14,13].”
Numerical methods for unsaturated flow with dynamic capillary pressure in heterogeneous porous media (2008, methodology): “For all FD cases, the presence of dynamic terms appears to slow down the dynamics of the flow, similarly as reported in [42].”
Quantitative Analysis of Flow Processes in a Sand Using Synchrotron‐Based X‐ray Microtomography (2005, background): “…with the theoretical development, there for example, Topp et al. (1967), Smiles et al. (1971), and has been an explosion of interest in recent years in poreothers listed in detail by Hassanizadeh et al. (2002) and scale modeling of multiphase flow in porous media, both Wildenschild et al. (2001).”
Inverse modeling of dynamic nonequilibrium in water flow with an effective approach (2012, background): “…researchers have associated such differences with a physical ‘‘nonequilibrium’’ in variably saturated water flow [Smiles et al., 1971; Vachaud et al., 1972; Plagge et al., 1999; Kneale, 1985; Schultze et al., 1999; Wildenschild et al., 2001; Hassanizadeh et al., 2002; O’Carroll et al., 2005].”
Dynamic Capillary Pressure Mechanism for Instability in Gravity-Driven Flows; Review and Extension to Very Dry Conditions (2005, methodology): “The first mathematical analysis of gravity-driven unstable flow was formulated by Raats (1973) wherein he used the Green-Ampt model of infiltration, a sharp front model, as the basis for his analysis.”
Upscaling for unsaturated flow for non‐Gaussian heterogeneous porous media (2007, methodology): “The method itself is explained, for example, by Hornung [1997]. [6] Effective parameters for the upscaled model need to be calculated from a given parameter field for a unit cell. In reality, the parameter distribution is unknown. Effective parameters can therefore only be approximated based on a gi”
Exploring dynamic effects in capillary pressure in multistep outflow experiments (2005, methodology): “The material coefficient may not be constant in a given system and may be a function of saturation [Hassanizadeh et al., 2002] or inversely proportional to the total flow rate [Kalaydjian, 1992].”
Pore‐scale displacement mechanisms as a source of hysteresis for two‐phase flow in porous media (2016, background): “…hysteresis is usually accounted for by empirical extensions to the constitutive Pc(Sw)relationship that either address the difference between drainage and imbibition [Mualem, 1974; Kool and Parker, 1987] or dynamic effects [Barenblatt et al., 2003; Hassanizadeh et al., 2002; Mitkov et al., 1998].”