Dynamic effects for two‐phase flow in porous media: Fluid property effects

Abstract

in Wiley InterScience (www.interscience.wiley.com).Traditional descriptions of multiphase flow in porous media rely on an extension of Darcy's law along with relationships between capillary pressure (P c ), saturation (S), and relative permeability (K r ). New theories have been proposed which suggest that P c relationships should include a dynamic coefficient (s) (Hassanizadeh and Gray, Water Resour Res. 1993;29:3389-3405) to indicate how ''quickly'' or ''slowly'' flow equilibrium is reached. While validity of these theories must be examined, it is also necessary to determine the significance of s and its range of values. In this article, we analyze the significance of s depending on fluid properties. We address the ways in which they cause nonuniqueness of dynamic two-phase flow in porous media and, hence, dynamic effect. Simulations are conducted for quasi-static and dynamic flow of perchloroethylene (PCE) in water saturated domains. The data are then fitted to the dynamic P c relationships to obtain values of s. The effects of flow directions and, viscosity and density ratios are discussed. To consider the lumped effects of various fluid properties, s-S relationships are examined for silicone oils. The results are interpreted by examining the correlation between s and a mobility coefficient, m. We discuss a scaling relationship that shows the dependence of s on fluid and material properties.The viscosity ratio has practically no effect on quasi-static P c -S relationships and only one P c -S curve is plotted.

Scale dependency of dynamic relative permeability–satuartion curves in relation with fluid viscosity and dynamic capillary pressure effect

“…Since for a saturation of 50 %, the value of mobility ratio is more than 1, the fluid fronts are considered to be stable. The trend observed here are similar to as observed by [2,13], i.e., as m decreases s increases at a given saturation.…”

“…In order to quantify effects of the stability of fluid fronts, mobility ratio (m) [2] was computed using Eq. (6) and the results are plotted to include comparison with dynamic coefficient (Figs.…”

“…But, the non-uniqueness in these relationships is well acknowledged. For example, for the P c -S w relationships and their saturation-rate dependency, depend on factors such as fluid properties like viscosity and density ratios [2][3][4][5], domain scale [6][7][8][9], media permeability [7,10,11], micro-heterogeneities [9,12], and hysteresis in P c -S w relationships [9], among others. Hou et al [13] explored the influence of measurement sensor's response on the magnitude of the dynamic capillary effects at scale of a representative elementary volume (REV) and argue that the effects may be due to the experimental measurement artifacts.…”

Experimental investigation of hysteretic dynamic effect in capillary pressure–saturation relationship for two‐phase flow in porous media

“…The dependence of the P c -S w curves on the rate of change of saturation (dS w / dt) is known as the dynamic effect in capillary pressure relationship. 7,25 The dynamic effect has been discussed significantly in the last two decades and it has been shown to be of importance, as discussed below.…”

“…In the last decade, a number of studies have discussed the significance of dynamic capillary pressure and s in different circumstances. 7,[19][20][21]23,[25][26][27][28][29][30][31][32][33][34][35][36][37][38][39][40][41][42][43] For example, hysteretic dynamic effect in the capillary pressure relationship was discussed in a theoretical study by Beliaev and Hassanizadeh 19 . Hassanizadeh et al 20 interpreted the imbibition experiments (displacement of oil by water) of Kalaydjian 44 Pa s for MI, which imply that the dynamic coefficient was found to be higher for imbibition than that for drainage by Hassanizadeh et al 21 Another study which is relevant to the current article was conducted by Sakaki et al 23 Sakaki et al conducted PD, MD, and MI experiments and measured s values for these three cases for a single porous domain of saturated hydraulic conductivity 0.016 cm/s.…”