An asymptotic solution for two‐phase flow in the presence of capillary forces

Vasco, D. W.

doi:10.1029/2003wr002587

Cited by 8 publications

(7 citation statements)

References 47 publications

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“…As a representative of the empirical models, the Corey model [ Corey , 1954] is expressed as Corey's model is also widely applied in the investigation of multiphase flow problems in porous media [e.g., Demond and Roberts , 1993; Pruess et al , 1999; Vasco , 2004]. The Corey model is used as another reference model to compare with the proposed model.…”

Section: Theorymentioning

confidence: 99%

A new model for predicting relative nonwetting phase permeability from soil water retention curves

Kuang¹,

Jiao²

2011

Water Resources Research

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[1] Relative permeability of the nonwetting phase in a multiphase flow in porous media is a function of phase saturation. Specific expressions of this function are commonly determined by combining soil water retention curves with relative nonwetting phase permeability models. Experimental evidence suggests that the relative permeability of the nonwetting phase can be significantly overestimated by the existing relative permeability models. A new model for the prediction of relative nonwetting phase permeability from soil water retention curves is proposed in this paper. A closed form expression can be obtained in combination with soil water retention curves. The model is mathematically simple and can easily and efficiently be implemented in numerical models of multiphase flow processes in porous media. The predicting capability of the proposed model is contrasted with wellsupported models by comparing the measured and predicted relative air permeability data for 11 soils, representing a wide range of soil textures, from sand to silty clay loam. In most of the cases the proposed model improves the agreement between the predicted relative air permeability and the measured data.Citation: Kuang, X., and J. J. Jiao (2011), A new model for predicting relative nonwetting phase permeability from soil water retention curves, Water Resour. Res., 47, W08520,

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Section: Theorymentioning

confidence: 99%

A new model for predicting relative nonwetting phase permeability from soil water retention curves

Kuang¹,

Jiao²

2011

Water Resources Research

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“…For example, the method of multiple scales has been used to model tracer transport which can vary from hyperbolic to diffusive propagation, depending on nature of the tracer and the flow conditions (Vasco & Finsterle 2004). This technique has also be used to model two‐phase flow in the subsurface, a type of non‐linear front propagation which can vary in character from hyperbolic to diffusive (Vasco 2004). Recently, the method of multiple scales has been used to model broadband electromagnetic wave propagation in the Earth (Vasco 2007).…”

Section: Introductionmentioning

confidence: 99%

Modelling quasi-static poroelastic propagation using an asymptotic approach

Vasco

2008

Geophysical Journal International

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S U M M A R YAn asymptotic technique, valid in the presence of smoothly varying flow properties, allows for the construction of a semi-analytic solution to the governing equations of quasi-static poroelasticity. In this formulation flow properties are variable while mechanical properties are constant within a specified formation. However, both mechanical and flow properties are allowed to vary discontinuously across formation boundaries. The asymptotic analysis determines that two longitudinal modes of propagation are possible: the Biot fast and slow waves. The Biot slow wave propagates as a diffusive disturbance, similar in nature to a pressure disturbance. The Biot fast wave has the characteristics of an elastic wave, and decays much more slowly with distance than does the slow wave. The Biot slow wave is found to generate elastic displacements, in the form of fast waves, as it propagates. This generation of fast waves explains the rapid onset of displacement at a remote observation point due to the injection of fluid into a poroelastic layer. A comparison of the asymptotic solution with analytic and numerical (finite-difference) solutions indicates overall agreement in both homogeneous and heterogeneous media.

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“…The generality of the method of multiple-scales has been noted by others and it has been used to model hyperbolic, dispersive, diffusive, and nonlinear phenomena (Whitham 1974;Jeffrey & Kawahara 1982;Anile et al 1993). It has proven useful in modelling fluid flow and transport when the problems are of mixed character, that is dispersive, diffusive and advective (Vasco & Finsterle 2004;Vasco 2004).…”

Section: Conc L U S I O N Smentioning

confidence: 99%

Trajectory-based modelling of broad-band electromagnetic wavefields

Vasco¹

2007

Geophysical Journal International

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SUMMARY A trajectory‐based solution of Maxwell's equations is derived using the method of multiple scales. This time‐domain technique utilizes an asymptotic expansion in terms of the ratio of the wave front length‐scale to the length‐scale of the heterogeneity. The approach provides an alternative to an expansion in terms of frequency and allows one to model electromagnetic wave propagation over a wide frequency band. At the lower end of the frequency band, the trajectory‐based solution reduces to a previously derived diffusive solution. Similarly, at higher frequencies one obtains the ‘delta‐like’ solution associated with hyperbolic wave propagation. However, the solution is also valid at intermediate frequencies which cannot be characterized as either diffusive or hyperbolic. A numerical illustration demonstrates the importance of both conduction and displacement currents at frequencies between 10 and 100 MHz. The amplitudes computed using the trajectory‐based approach compare well with analytic results for a homogeneous whole‐space. Using the technique I am able to model observations from a broad‐band (3–300 kHz) experiment at the Richmond Field Station in California. In addition, ground penetrating radar waveforms in the 5–200 MHz range, gathered at the Boise Hydrogeophysical Research Site, are matched using the results of a radar velocity tomogram.

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An asymptotic solution for two‐phase flow in the presence of capillary forces

Cited by 8 publications

References 47 publications

A new model for predicting relative nonwetting phase permeability from soil water retention curves

A new model for predicting relative nonwetting phase permeability from soil water retention curves

Modelling quasi-static poroelastic propagation using an asymptotic approach

Trajectory-based modelling of broad-band electromagnetic wavefields

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