The correlation of the steady-state gas/water relative permeabilities of porous media with gas and water capillary numbers

Tsakiroglou, Christos D.

doi:10.2516/ogst/2019017

Cited by 6 publications

(4 citation statements)

References 33 publications

(57 reference statements)

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“…The experimental results indicate that the proposed method can effectively characterize the relationship between rock resistivity and permeability. Tsakiroglou [14] et al converted the electrical resistances to water saturations with the aid of the Archie equation for resistivity index. Both krw and krg are regarded as power functions of water, Caw of gas and Cag of capillary numbers, the exponents of which are estimated with non-linear fitting to the experimental datasets.…”

Section: Introductionmentioning

confidence: 99%

Experimental Verification of Reservoirs with Different Wettability Using an Oil–Water Relative Permeability Model

Pei

Zhang

et al. 2022

Processes

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Oil–water relative permeability is an important parameter that affects fluid flow in porous media. It is usually obtained in a laboratory. Since rock resistivity and relative permeability are both effects of water saturation, they should theoretically have a relationship. Based on the parallel conduction principle of fluid and skeleton in porous media, the pore structure and fluid distribution can be simplified using the Kozeny–Carman permeability correction equation and the Archie formula, and the relative permeability model of the water phase can be deduced under different wetting conditions. In this study, the resistivity and relative permeability experimental data of 20 rock samples from four inspection wells were compared and verified. The results show that the proposed oil–water relative permeability model agrees well with a reservoir having a porosity range of 17.6–30.7% and an air permeability of 0.16–973 × 10−3 μm, and it may explain why the relative permeability of the water phase decreases as water saturation increases. This model could provide a new technique to construct the relative permeability curves of sandstone reservoirs.

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Section: Introductionmentioning

confidence: 99%

Experimental Verification of Reservoirs with Different Wettability Using an Oil–Water Relative Permeability Model

Pei

Zhang

et al. 2022

Processes

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“…These events lead to interruption and rearrangement of the connected pathways the respective phases flow through (Tuller and Or, 2001) and are described by a rigorous theoretical framework of pore-scale thermodynamics (Morrow, 1970). Depending on flow rate and other conditions (Avraam and Payatakes, 1995a;Lenormand and Touboul, 1998), there are different regimes that can cause fluctuations in pressure and saturation that have been systematically investigated in Avraam and Payatakes (1995a), Tsakiroglou (2019). The main regimes identified were connected pathway flow, ganglion dynamics and drop traffic.…”

Section: Introductionmentioning

confidence: 99%

The Origin of Non-thermal Fluctuations in Multiphase Flow in Porous Media

et al. 2021

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Core flooding experiments to determine multiphase flow in properties of rock such as relative permeability can show significant fluctuations in terms of pressure, saturation, and electrical conductivity. That is typically not considered in the Darcy scale interpretation but treated as noise. However, in recent years, flow regimes that exhibit spatio-temporal variations in pore scale occupancy related to fluid phase pressure changes have been identified. They are associated with topological changes in the fluid configurations caused by pore-scale instabilities such as snap-off. The common understanding of Darcy-scale flow regimes is that pore-scale phenomena and their signature should have averaged out at the scale of representative elementary volumes (REV) and above. In this work, it is demonstrated that pressure fluctuations observed in centimeter-scale experiments commonly considered Darcy-scale at fractional flow conditions, where wetting and non-wetting phases are co-injected into porous rock at small (<10−6) capillary numbers are ultimately caused by pore-scale processes, but there is also a Darcy-scale fractional flow theory aspect. We compare fluctuations in fractional flow experiments conducted on samples of few centimeters size with respective experiments and in-situ micro-CT imaging at pore-scale resolution using synchrotron-based X-ray computed micro-tomography. On that basis we can establish a systematic causality from pore to Darcy scale. At the pore scale, dynamic imaging allows to directly observe the associated breakup and coalescence processes of non-wetting phase clusters, which follow “trajectories” in a “phase diagram” defined by fractional flow and capillary number and can be used to categorize flow regimes. Connected pathway flow would be represented by a fixed point, whereas processes such as ganglion dynamics follow trajectories but are still overall capillary-dominated. That suggests that the origin of the pressure fluctuations observed in centimeter-sized fractional flow experiments are capillary effects. The energy scale of the pressure fluctuations corresponds to 105-106 times the thermal energy scale. This means the fluctuations are non-thermal. At the centimeter scale, there are non-monotonic and even oscillatory solutions permissible by the fractional flow theory, which allow the fluctuations to be visible and—depending on exact conditions—significant at centimeter scale, within the viscous limit of classical (Darcy scale) fractional flow theory. That also means that the phenomenon involves both capillary aspects from the pore or cluster scale and viscous aspects of fractional flow and occurs right at the transition, where the physical description concept changes from pore to Darcy scale.

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“…This parameter mainly alters as a function of fluid saturation. However, the dependence of relative permeability and residual saturation (S r ) on the ratio of viscous to capillary forces (denoted by the capillary number, N c ) in a microscopic/pore scale is well established in the literature (Ahmadi et al, 2019;Avraam and Payatakes, 1995;Delshad et al, 1986;Fulcher et al, 1985;Johannesen and Graue, 2007;Tsakiroglou, 2019;Tsakiroglou et al, 2007). Avraam and Payatakes (1995) have represented a pioneering work evaluating the relative permeability and flow regime behaviors during a steady-state oil-water flow in a model pore space.…”

Section: Introductionmentioning

confidence: 99%

“…The transient flow was associated with higher oil relative permeability in comparison to the steady-state regime, whereas the steady-state water relative permeability exceeded the transient one over the low N c . Tsakiroglou (2019) has also carried out a steady-state two-phase flow experiment to assess the relative permeability of the nitrogen and brine in a homogeneous sand system. He reported a robust direct relationship between the gas and water relative permeabilities and the gas and water capillary numbers, respectively.…”

Section: Introductionmentioning

confidence: 99%

A proposed capillary number dependent model for prediction of relative permeability in gas condensate reservoirs: a robust non-linear regression analysis

Mahdaviara

Helalizadeh

2020

Oil Gas Sci. Technol. – Rev. IFP Energies nouvelles

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Well deliverability reduction as a result of liquid (condensate) build up in near well regions is an important deal in the development of gas condensate reservoirs. The relative permeability is an imperative factor for characterization of the aforementioned problem. The dependence of relative permeability on the coupled effects of Interfacial Tension (IFT) and flow velocity (capillary number) together with phase saturation is well established in the literature. In gas condensate reservoirs, however, the influence of IFT and velocity on this parameter becomes more evident. The current paper aims to establish a new model for predicting the relative permeability of gas condensate reservoirs by employing the direct interpolation technique. To this end, the regression analysis was carried out using seven sets of literature published experimental data. The validity analysis was executed by utilizing statistical parameters integrated with graphical descriptions. Furthermore, a comparison was carried out between the proposed model and some literature published empirical models. The results of the examination demonstrated that the new model outperformed other correlations from the standpoints of accuracy and reliability.

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The correlation of the steady-state gas/water relative permeabilities of porous media with gas and water capillary numbers

Cited by 6 publications

References 33 publications

Experimental Verification of Reservoirs with Different Wettability Using an Oil–Water Relative Permeability Model

Experimental Verification of Reservoirs with Different Wettability Using an Oil–Water Relative Permeability Model

The Origin of Non-thermal Fluctuations in Multiphase Flow in Porous Media

A proposed capillary number dependent model for prediction of relative permeability in gas condensate reservoirs: a robust non-linear regression analysis

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