Search results for "Capillary pressure"
showing 8 items of 8 documents
Dimensional analysis and upscaling of two-phase flow in porous media with piecewise constant heterogeneities
2004
Dimensional analysis of the traditional equations of motion for two-phase flow in porous media allows to quantify the influence of heterogeneities. The heterogeneities are represented by position dependent capillary entry pressures and position dependent permeabilities. Dimensionless groups quantifying the influence of random heterogeneities are identified. For the case of heterogeneities with piecewise constant constitutive parameters (e.g., permeabilities, capillary pressures) we find that the upscaling ratio defined as the ratio of system size and the scale at which the constitutive parameters are known has to be smaller than the fluctuation strength of the heterogeneities defined, e.g.,…
Macroscopic equations of motion for two-phase flow in porous media
1998
The established macroscopic equations of motion for two phase immiscible displacement in porous media are known to be physically incomplete because they do not contain the surface tension and surface areas governing capillary phenomena. Therefore a more general system of macroscopic equations is derived here which incorporates the spatiotemporal variation of interfacial energies. These equations are based on the theory of mixtures in macroscopic continuum mechanics. They include wetting phenomena through surface tensions instead of the traditional use of capillary pressure functions. Relative permeabilities can be identified in this approach which exhibit a complex dependence on the state v…
Trapping and mobilization of residual fluid during capillary desaturation in porous media
1998
We discuss the problem of trapping and mobilization of nonwetting fluids during immiscible two-phase displacement processes in porous media. Capillary desaturation curves give residual saturations as a function of capillary number. Interpreting capillary numbers as the ratio of viscous to capillary forces the breakpoint in experimental curves contradicts the theoretically predicted force balance. We show that replotting the data against a novel macroscopic capillary number resolves the problem for discontinuous mode displacement.
Dimensional analysis of pore scale and field scale immiscible displacement
1996
A basic re-examination of the traditional dimensional analysis of microscopic and macroscopic multiphase flow equations in porous media is presented. We introduce a ‘macroscopic capillary number’\(\overline {Ca}\) which differs from the usual microscopic capillary number Ca in that it depends on length scale, type of porous medium and saturation history. The macroscopic capillary number\(\overline {Ca}\) is defined as the ratio between the macroscopic viscous pressure drop and the macroscopic capillary pressure.\(\overline {Ca}\) can be related to the microscopic capillary number Ca and the LeverettJ-function. Previous dimensional analyses contain a tacit assumption which amounts to setting…
WENO Schemes for Multi-Dimensional Porous Media Flow Without Capillarity
2016
In this work we derive a numerical technique based on finite-difference WENO schemes for the simulation of multi-dimensional multiphase flows in a homogeneous porous medium. The key idea is to define a compatible discretization for the fluxes of the convective term in order to maintain their divergence-free character not only in the continuous setting but also in the discrete setting, ensuring the conservation of the sum of the saturations through time evolution. The one-dimensional numerical technique is derived in detail for the case of neglected capillarity effects. Numerical results obtained with one-dimensional and two-dimensional standard tests of multiphase flow in a homogeneous poro…
Capillary pressure, hysteresis and residual saturation in porous media
2006
Abstract A macroscopic theory for capillarity in porous media is presented. The capillary pressure function in this theory is not an input parameter but an outcome. The theory is based on introducing the trapped or residual saturations as state variables. It allows to predict spatiotemporal changes in residual saturation. The theory yields process dependence and hysteresis in capillary pressure as its main result.
Capillary experiments of flow induced crystallization of HDPE
1990
Flow-induced crystallization experiments are made in a capillary apparatus modified with a downstream reservoir under pressure. Capillary length, diameter, and entrance angle are changed, as well as flow rate. The results show that the crystallization temperature is influenced both by the elongational flow at the capillary entrance and by the shear flow along the capillary. The independent effect of the pressure equals that obtained under static conditions. The effect of shear is correlated in terms of shearing work.
Macroscopic capillarity without a constitutive capillary pressure function
2006
This paper challenges the foundations of the macroscopic capillary pressure concept. The capillary pressure function, as it is traditionally assumed in the constitutive theory of two-phase immiscible displacement in porous media, relates the pressure difference between nonwetting and wetting fluid to the saturation of the wetting fluid. The traditional capillary pressure function neglects the fundamental difference between percolating and nonpercolating fluid regions as first emphasized in R. Hilfer [Macroscopic equations of motion for two phase flow in porous media, Phys. Rev. E 58 (1998) 2090]. The theoretical approach proposed here starts from residual saturations as the volume fractions…