Two-phase flow processes with dynamic effects in porous media - parameter estimation and simulation

This study contributes to the understanding of dynamic effects in the capillary pressure-saturation relationship on the local scale and macroscale as well as giving an assessment as to when these effects might need to be taken into account for the evaluation of two-phase flow processes. In a general form, the rate-dependent Pc-Sw relationship as analysed here postulates that the difference between the non-wetting and wetting phase pressure minus the equilibrium capillary pressure is a linear function of the rate of change of saturation, introducing the factor of proportionality tau. This extended Pc-Sw relationship is examined in this study under three aspects. In order to identify flow regimes where dynamic effects might be of importance, a dimensional analysis of the two-phase balance equations being closed with the extended Pc-Sw relationship is carried out. In the dimensionless equations the well-known capillary and gravitational number, Ca and Gr, evolve. Moreover, the new dimensionless number Dy appears as a factor. Dy quantifies the ratio of the 'dynamic capillary force' to the viscous force. Relating Dy to Ca or Gr yields DyC, the ratio of the dynamic to the capillary equilibrium force, and DyG, the ratio of the dynamic capillary to the gravitational force. The influence of the dynamic capillary force decreases with increasing characteristic length scale in relation to the equilibrium capillary, viscous or gravitational force. Moreover, with increasing transient flow velocity, the dynamic capillary force gains in importance. A second part of this study deals with the determination of the coefficient tau on the basis of primary drainage laboratory experiments performed by GeoDelft, The Netherlands and numerical experiments. Using the laboratory experiments tau was calculated to vary between 11.0 kPas and 154.7 kPas depending on the water saturation. The coefficient increases with decreasing water saturation. For the determination of tau using numerical experiments first homogeneous domains were considered in order to test the averaging approach. The coefficient tau was found to scale proportionally to the porosity, the (saturation-weighted average) viscosity, and the squared averaging length, as well as inversely proportional to the intrinsic permeability. Parameters that describe the equilibrium Pc-Sw relationship have a minor influence on the coefficient tau. The dependence of tau on the averaging length poses a problem as its magnitude is thus not clearly bounded, making it impossible to define an REV. As a consequence, either the averaging length should relate to a bounded property or the averaging of the phase pressures as applied in this study has to be reconsidered. Moreover, two heterogeneous domains were studied, one being a simple pattern of two fine sand lenses in a coarse sand and the other a spatially-correlated random field. An influence resulting from the simple heterogeneity pattern on the coefficient is only noticeable in case the fine sand lenses are drained. The heterogeneity stemming from the spatially-correlated random field does not affect the magnitude of the coefficient. Finally, the impact on the numerical solution of the balance equations being closed with an extended Pc-Sw relationship is assessed with simulations of imbibition processes. The dimensionless numbers Dy and DyC can be consulted to assess the impact on the solution. The front width should be applied as the characteristic length scale. It is observed that for a dominance of the dynamic capillary over the viscous force, the rate of change of saturation is dampened and thus a retardation effect with respect to the cumulative mass occurs. Locally, accelerating and slowing down of the displacement can flatten a front in comparison to a reference case. Moreover, for a high influx of wetting phase a process reversal from imbibition to drainage and back occurred. If additionally the equilibrium capillary forces are diminished, oscillations in the solution might occur for a large viscosity ratio.

Author dc:creator

• Manthey, Sabine

Advisor dc:contributor.advisor

• Helmig, Rainer (Prof. Dr.-Ing.)

Statement dc:rights

• info:eu-repo/semantics/openAccess

Language dc:language.iso

en

Identifier URI

http://elib.uni-stuttgart.de/handle/11682/270
http://dx.doi.org/10.18419/opus-253

Dc Identifier Other

263110583

OAI identifier oai:identifier

oai:elib.uni-stuttgart.de:11682/270