A new unsteady-state method of determining two-phase relative permeability illustrated by CO2-brine primary drainage in berea sandstone

Relative permeability measurements are commonly fitted with the Corey and Brooks‐Corey correlations. Despite such correlations fit experimental data generally well, they are mostly of an empirical nature. Here, we propose a semiempirical model to determine relative permeabilities of the wetting and the nonwetting phases in real 3‐D porous media that accounts for pore‐scale flow regimes. The starting point is the homogenization framework proposed by Picchi and Battiato (2018, https://doi.org/10.1029/2018WR023172), where the upscaling is conducted for different spatial distributions of the flowing phases in the capillary tube setting. First, we extend the approach to realistic media by allowing pore‐scale flow regimes to coexist in a complex geometry while accounting for capillary and viscous limits in the dynamics. Then, we discuss the scaling behavior of normalized relative permeabilities in terms of the phases viscosity ratio and identify three classes which govern their scaling. We also derive an analytical expression for the fractional flow. Finally, we provide a detailed validation of the proposed model for both relative permeabilities and fractional flow against data from numerical simulations and experiments available in the literature. The data set used for validation covers a wide range of systems, ranging from brine‐CO2 to oil‐water flows. The equations derived capture well the trend of both numerical and experimental data.

Section: Discussionsupporting

confidence: 76%

Section: Discussionmentioning

confidence: 99%

Relative Permeability Scaling From Pore‐Scale Flow Regimes

Picchi

Battiato

2019

“…However, due to the non‐uniform saturation in the entrance,

Δ P^{w}

is not equal to

Δ P^{n w}

in the entrance section. Previous studies [ Chen and DiCarlo , ; Chen et al ., , ] have shown that the exit section is dominated by the capillary end effect and we do not calculate relative permeability from the exit section. In summary, CO 2 and brine relative permeabilities are calculated in each of the center three sections and only CO 2 relative permeability is calculated in the entrance section.…”

Section: Resultsmentioning

confidence: 99%

“…This study used a similar experimental method to the previous measurements of CO 2 -brine relative permeability at 208C and 10.34 MPa [Chen et al, 2014[Chen et al, , 2016a[Chen et al, , 2016bChen and DiCarlo, 2016]. The difference is that this study used heaters and thermocouples to maintain the floods at elevated temperatures.…”

Section: Methodsmentioning

confidence: 99%

Steady‐state supercritical CO₂ and brine relative permeability in Berea sandstone at different temperature and pressure conditions

Chen

Gao

Kianinejad

et al. 2017

Self Cite

We measure steady‐state two‐phase supercritical CO2‐brine relative permeabilities in a 61 cm‐long Berea sandstone core at three different conditions (40°C and 12.41 MPa, 40°C and 8.27 MPa, and 60°C and 12.41 MPa) under primary drainage. We use pressure taps to obtain pressure drops of individual sections of the core, and X‐ray Computed Tomography (CT) to obtain in situ saturation profiles, which together help to mitigate the capillary end effect. We include previously measured relative permeabilities at 20°C and 10.34 MPa, and compare all the data using both an eye‐test and a statistical test. We find no appreciable temperature and pressure dependence of CO2 relative permeability within 20–60°C and 8.27–12.41 MPa. We find slight changes in the brine relative permeability between supercritical CO2 conditions (40–60°C and 8.27–12.41 MPa) and the liquid CO2 condition (20°C and 10.34 MPa). The temperature and pressure independence of CO2 relative permeability has been previously recognized and reassured in this work using a capillary‐effect‐free method. This allows one to use a single CO2 relative permeability curve in modeling two‐phase CO2 flow within 20–60°C and 8.27–12.41 MPa.

“…Concurrent improvements of X‐ray microtomography combined with its nondestructive features have allowed direct visualization of pore‐scale structures and distribution of phases as inputs to computational models. A number of authors have investigated pore‐scale phases distribution using X‐ray microtomography and demonstrated the complexity of the nonwetting and wetting phase interface geometry (e.g., Armstrong et al, ; Blunt et al, ; X. Chen & DiCarlo, ; X. Chen et al, ; Gao et al, ; Garing et al, ; Moghadasi et al, ; Prodanovic et al, , ; Reynolds et al, ).…”

Section: Introductionmentioning

confidence: 99%

The Impact of Pore‐Scale Flow Regimes on Upscaling of Immiscible Two‐Phase Flow in Porous Media

Picchi

Battiato

2018

Empirical or theoretical extensions of Darcy's law for immiscible two‐phase flow have shown significant limitations in properly modeling the flow at the continuum scale. We tackle this problem by proposing a set of upscaled equations based on pore‐scale flow regimes, that is, the topology of flowing phases. The incompressible Navier‐Stokes equation is upscaled by means of multiple‐scale expansions and its closures derived from the mechanical energy balance for different flow regimes at the pore scale. We also derive the applicability conditions of the upscaled equations based on the order of magnitude of relevant dimensionless numbers, that is, Eotvos, Reynolds, capillary, Froude numbers, and the viscosity and density ratio of the system, as well as a set of closures valid for the basic flow regimes of low Eotvos number systems, that is, core‐annular and plug and drop traffic flows. We provide analytical expressions for the relative permeability of the wetting and nonwetting phases in different flow regimes and demonstrate that the effect of the flowing‐phases topology on the relative permeabilities is significant. Finally, we show that the classical two‐phase Darcy law is recovered for a limited range of operative conditions, while specific terms accounting for interfacial and wall interactions should be incorporated to accurately model ganglia or drop traffic flow.