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

Abstract

Capillary pressure-saturation-relative permeability relationships (P c -S w -K r ) are functions of importance in modeling and simulations of the hydrodynamics of two-phase flow in porous media. These relationships are found to be affected by porous medium and fluid properties but the manner in which they are affected is a topic of intense discussion. For example, reported trends in fluid viscosity and boundary conditions effects have been found to be contrary to each other in different studies. In this work, we determine the dependency of dynamic K r -S w relationships (averaged data) on domain scale in addition to investigating the effects of fluid viscosity and boundary pressure using silicone oil (i.e. 200 and 1000 cSt) and water as the respective non-wetting and wetting fluids with a view to eliminating some of the uncertainties reported in the literature. Water relative permeability, K rw , was found to increase with increasing wetting phase saturation but decreases with the increase in viscosity ratio. On the other hand, the oil relative permeability, K rnw , was found to increase with the increasing non-wetting phase saturation in addition to the increase in viscosity ratio. Also, it was found that with the increasing boundary pressure K rw decreases while K rnw increases. The influence of scale on relative permeability was slightly indicated in the non-wetting phase with K rnw decreasing as domain size increases. Effect of measurement location on dynamic relative permeability was explored which is rarely found in the literature. Comparison was also made between K r -S w relationships obtained under static and dynamic condition. Finally, mobility ratio (m) and dynamic coefficient (s) were plotted as a function of water saturation (S w ), which showed that m decreases as s increases at a given saturation, or vice versa.

Dynamic capillarity during displacement process in fractured tight reservoirs with multiple fluid viscosities

“…Relative permeability responds to the change of capillary pressure 9,11 and also reflects the stability of the displacement front. The quick decrease in the oil relative permeability demonstrates the more nonuniform front during the displacement process with the viscous oil.…”

“…Several equations have been proposed to quantitatively demonstrate the dynamic effect on the P c -S w relationship, [9][10][11] and a widely used equation has been proposed by Hassanizadeh and Gray as follows 12,13 : where P d c represents the dynamic capillary pressure, MPa, dependent on flow dynamics; P s c is the steady capillary pressure at equilibrium conditions, MPa, an intrinsic property of the porous medium-fluid system; S w ∕ t is the time derivative of the wetting fluid phase saturation, s −1 ; τ is the dynamic coefficient, Pa·s; and P w and P nw denote the wetting and nonwetting phase pressure, respectively, MPa.…”

Capillary Pressure Curve Determination Based on a 2‐D Cross‐Section Analysis Via Fractal Geometry: A Bridge Between 2‐D and 3‐D Pore Structure of Porous Media

“…As mentioned above, due to the dynamic effect of the capillary pressure, especially in the case of low permeability rocks, the intrusion pressure (capillary pressure) is related to the flow rate of mercury. Specifically, the faster the flow rate is, the greater is the capillary pressure (Abidoye, ; Goel et al, ). Thus, there is a competitive relationship between the flow rate and capillary pressure at the moment of initial displacement, causing the initial pressure to fluctuate above and below the preset pressure value P c (Abidoye & Das, ; Das et al, ).…”

“…The supercritical CO 2 ‐water system has a higher dynamic coefficient than the oil‐water system, and the time required for the system to reach equilibrium increases as the wetted saturation decreases. Additionally, this dynamic coefficient was found to be scale dependent, which can already be predicted by artificial neural network modeling (Abidoye, ; Goel et al, ). Thus, in order to ensure that the CPC can directly characterize the pore structure without being affected by fluid dynamics as mentioned above, the CPC is measured at the lab‐scale under an equilibrium or quasi‐static condition (∂ S Hg /∂ t = 0); namely, in this study, the capillary pressure P c and Hg saturation S Hg are recorded until the set P c reaches the stabilized state.…”

Upscaling of Dynamic Capillary Pressure of Two‐Phase Flow in Sandstone

“…O'Carroll et al (2005) carried out a series of multistep outflow experiments, and found that the DCP coefficient may be depended on saturation. Goel and O'Carroll (2011) and Goel et al (2016) found that the DCP coefficient was dependent on fluid viscosity. Our previous simulation results also showed a dependency of DCP coefficient on viscosity ratio (Tang et al, 2018).…”