Viscous Coupling Effects Research Articles

A pore-scale investigation of viscous coupling effect on immiscible two-phase flow in porous media

Viscous coupling effect plays a significant role in immiscible two-phase flow within porous media, while its influence on relative permeability remains uncertain. In this paper, an improved MRT-based viscosity-modified multicomponent multiphase (MCMP) pseudopotential lattice Boltzmann model, capable of handling high viscosity ratio, is employed to simulate two-phase flow with different viscosities in a cross-array circular structure and a real rock structure, respectively. The applicability of this model for two-phase flow with various viscosity ratios has been verified by some typical tests. Systematically, the effects of viscosity ratio, structural configuration, and wetting condition on the relative permeability curves are investigated in conjunction with their component distributions and velocity fields at different two-phase saturations. These results indicate that due to the two-phase flow competition under different structural conditions, the viscous coupling effect has varying degrees of impacts on the mobility of thin phase and viscous phase. Further, the mechanism of two-phase lubricating effect is also discussed under different wetting conditions at Darcy flow regime.

Pore-scale insights into CO2-water two-phase flow and implications for benefits of geological carbon storage

The overall benefits of geological carbon storage (GCS) depend primarily on CO2 storability and injectability, expressed as saturation and relative permeability, respectively. The effects of GCS schemes on these two properties, the macroscopic response indicators of a two-phase seepage system, are closely related to pore-scale two-phase behaviors. However, the comprehensive effects of capillary number (Ca) and wettability (θ) on saturation and relative permeability are poorly understood. Here we proposed a digital rock physics (DRP) technique workflow for the phase field method and systematically investigated how these effects control two-phase seepage at pore scale through the high-resolution visualization results obtained. We created a Ca-θ phase diagram identified by four pore-scale displacement mechanisms, including finger-like invasion, burst, cooperative filling and coexistence of concave and convex interfaces, to illustrate the comprehensive effects of Ca and θ. We found that the relative permeability of the defending phase (water in this work) is determined by the net effect of the direct driving and viscous coupling effects. We organized comprehensive Ca-θ diagrams and revealed the favorable conditions for CO2 injectability and storability. Our results demonstrate that GCS schemes, mainly about capillary number and wettability, can significantly influence CO2 storage performance via the two-phase flow at pore scale, which should be considered carefully. This work provides valuable insights into the selection of an optimal GCS scheme and contributes to an in-depth understanding of multiphase seepage at pore scale.

Dynamic Pore Network Modeling of Imbibition in Real Porous Media with Corner Film Flow.

Wetting films can develop in the corners of pore structures during imbibition in a strongly wetting porous medium, which may significantly influence the two-phase flow dynamics. Due to the large difference in scales between main meniscus and corner film, accurate and efficient modeling of the dynamics of corner film remains elusive. In this work, we develop a novel two-pressure dynamic pore network model incorporating the interacting capillary bundle model to analyze the competition between the main meniscus and corner film flow in real porous media. A pore network with four-point star-shaped pore bodies and throat bonds is extracted from the real porous medium based on the pore shape factor and pore cross-sectional area, which is then decomposed into several layers of sub-pore networks, where the first layer of sub-pore network simulates the main meniscus flow while the upper layers characterize the corner film flow. The two-phase flow conductance of throat bonds for different layers of sub-pore networks are determined by high-resolution two-phase lattice Boltzmann modeling, thus inherently considering the viscous coupling effect. In addition, two artificial neural network models are developed to predict the two phases' flow conductance based on the shape of the throat cross section and the fluid properties. The accuracy of the developed model is validated with a lattice Boltzmann simulation of imbibition in a strongly wetting square tube. Then the model is used to simulate imbibition in a strongly wetting sandstone porous medium, and the competition between the main meniscus and the corner film flow is analyzed. The results show that with decreasing capillary number and viscosity ratio between wetting and nonwetting fluids, the development of the wetting corner film becomes more significant.

Viscous coupling effect on hydraulic conductance in a square capillary tube

Viscous coupling effect on pore-scale flow capacity and its impact on macroscopic flow properties in porous media remain subjects of ongoing debate. This study employs the Stokes equation in conjunction with the zero-velocity interface and continuity interface to investigate viscous coupling effect during two-phase flow through a square capillary tube. Our findings substantiate the significance of the viscous coupling effect in angular pore multiphase flows. Enhanced fluid conductance is linked to fluid viscosity ratios, contact angles, and wetting-film lengths at the pore scale. Proposing a novel upscaling approach, we formulate hydraulic conductance in a square capillary tube for multiphase flows by incorporating a viscous coupling term, and its validation is accomplished through comparison with results from lattice Boltzmann method simulations. Our scaling model predicts hydraulic conductance with a mean relative error of less than 1%, outperforming prior viscous coupling models with errors reaching up to 19%. The derived scaling model, incorporating the viscous coupling effect, holds potential for integration within pore-network models, offering an efficient and precise simulation method for characterizing two-phase flow through porous media at a representative scale.

Dynamic Relative Permeabilities for Partially Saturated Porous Media Accounting for Viscous Coupling Effects: An Analytical Solution

We present an analytical model to compute frequency-dependent relative permeability functions for partially saturated porous media accounting for viscous coupling effects. For this, we consider the oscillatory motion of two immiscible fluid phases and solve the Navier–Stokes equations at the pore scale using suitable interface conditions between fluids. These calculations are combined with the generalized two-phase flow Darcy equations to obtain the corresponding upscaled macroscopic fluxes. By means of an analog pore model consisting of a bundle of cylindrical capillaries in which pore fluids are distributed in a concentric manner, we find closed analytical expressions for the complex-valued and frequency- and saturation-dependent relative permeability functions. These expressions allow for a direct assessment of viscous coupling effects on oscillatory flow for all frequencies and saturations. Our results show that viscous coupling effects significantly affect flow characteristics in the viscous and inertial regimes. Dynamic relative permeabilities are affected by the pore fluid densities and viscosities. Moreover, viscous coupling effects may induce two critical frequencies in the dynamic relative permeability curves, a characteristic that cannot be addressed by extending the classic dynamic permeability definition to partially saturated scenarios using effective fluids. The theoretical derivations and results presented in this work have implications for the estimation and interpretation of seismic and seismoelectric responses of partially saturated porous media.

Co‐Current Fluid Flow Mechanisms Within a Complex Porous Structure at the Pore Level

AbstractThis study has been addressed the mechanisms of the co‐current fluid flow in a heterogeneous porous media using the lattice Boltzmann method. Since the smallest interaction between viscous and capillary forces at the interface is of great importance, the simulations are performed with the hybrid phase‐field model at the pore level. This is because the main advantage of this model is that due to its connection with the phase‐field theory, it has a solid physical basis to record interface dynamics. Model verification is followed by recording viscous coupling effects. The relative permeability curves and the velocity profiles are compared with the analytical solution, so that the observations confirm the accuracy claim of the model. In the following, the fluid flow through the heterogeneous porous structure is simulated, so that its sweep efficiency and corresponding velocity field at the breakthrough time are discussed. The results show that increasing the injection velocity reduces the displacement efficiency and increases the velocity field fluctuations due to the viscous fingering regime. Changing the wetting conditions to strong imbibition (SI) will increase the efficiency due to the role of capillary pressure and corner flow mechanism. Also, increasing the interfacial tension in the SI and the strong drainage will increase and decrease the sweep efficiency, respectively, so the rate of changes in fully immiscible flow is much higher than the near miscible flow. The velocity fluctuations in the fully immiscible flow are more significant than in the near miscible flow, which is reasonable given the flow properties.

Competition between main meniscus and corner film flow during imbibition in a strongly wetting square tube

Imbibition in a strongly wetting square tube with corner flow can be described by an interacting capillary bundle model, where the first sub-capillary describes the main meniscus flow while the others describe corner film flow. In this work, an advanced modified interacting capillary bundle model (MICBM) is developed to simulate imbibition dynamics in a strongly wetting square tube incorporating the viscous coupling effect. The flow conductances of each sub-capillary are obtained from two-phase lattice Boltzmann simulations with different viscosity ratios considering the viscous coupling effect. After verifying its accuracy, MICBM is used to analyze the imbibition dynamics of main meniscus and corner film flows under different conditions. The results show that, with increasing viscosity ratio between wetting and non-wetting fluids and increasing driving force, the wetting corner film development tends to be less significant compared with main meniscus flow. Interestingly, the corner film length first increases then decreases when the wetting fluid is less viscous than the non-wetting fluid in a long square tube. A phase diagram of dimensionless corner film length versus driving force and viscosity ratio is proposed to characterize the competition between main meniscus and corner film flow. Gravity and smaller contact angle make the corner film development more obvious. In addition, the tube length and width are shown to influence the interaction between main meniscus and corner film flow for a low viscosity ratio. The underlying physics of the above phenomena are explained in detail.

Near miscible relative permeability curves in layered porous media- investigations via diffuse interface Lattice Boltzmann method

The relative permeability of immiscible multi-phase flow in Layered 2D porous media is investigated employing the diffuse interface Lattice Boltzmann model. The interfacial tension is set to small value to mimic the near miscible condition of the fluids. The model is validated with static and dynamic analytical solutions. Three classes of porous media are examined: A high permeable porous media, a low permeable porous media, and layered dual permeable porous media. For the later case, parallel and serie conditions were considered. For each condition, three proportion of layers were studied; I– 25% of the high permeable layer, II– 50% of the high permeable layer, and III– 75% of high permeable layer. For each condition, the viscous coupling effects due to viscosity ratio, the capillary number and the effect of the fluid patterns on the relative permeability curves were investigated. The simulation results showed very small errors compare with the analytical permeability solutions of layered porous media. The findings showed that despite the dual permeable serie system, the relative permeability curve of dual permeable parallel geometry is closely matched with the analytical solution.

Effect of Hydrate on Gas/Water Relative Permeability of Hydrate-Bearing Sediments: Pore-Scale Microsimulation by the Lattice Boltzmann Method

As a clean energy source with ample reserves, natural gas hydrate is studied extensively. However, the existing hydrate production from hydrate deposits faces many challenges, especially the uncertain mechanism of complex multiphase seepage in the sediments. The relative permeability of hydrate-bearing sediments is key to evaluating gas and water production. To study such permeability, a set of pore-scale microsimulations were carried out using the Lattice Boltzmann Method. To account for the differences between hydrate saturation and hydrate pore habit, we performed a gas-water multiphase flow simulation that combines the fluids’ fundamental properties (density ratio, viscosity ratio, and wettability). Results show that the Lattice Boltzmann Method simulation is valid compared to the pore network simulation and analysis models. In gas and water multiphase flow systems, the viscous coupling effect permits water molecules to block gas flow severely due to viscosity differences. In hydrate-bearing sediments, as hydrate saturation increases, the water saturation S w between the continuous and discontinuous gas phase decreases from 0.45 to 0.30 while hydrate saturation increases from 0.2 to 0.6. Besides, the residual water and gas increased, and the capillary pressure increased. Moreover, the seepage of gas and water became more tedious, resulting in decreased relative permeability. Compared with different hydrate pore habits, pore-filling thins the pores, restricting the gas flow than the grain-coating. However, hydrate pore habit barely affects water relative permeability.

Effect of flow-independent viscosity on the propagation of Rayleigh wave in porous media

The propagation characteristics of Rayleigh wave near the surface of fluid-saturated poroviscoelastic medium are investigated in this paper. The effective stress in porous media is defined by the linear viscoelasticity theory based on Biot model and Kelvin-Voigt model. The dispersion equations of Rayleigh wave are derived analytically and then solved numerically to obtain its propagation speed and attenuation coefficient in the poroviscoelastic solid half-space. The effects of relaxation time and viscous coupling on the dispersion and attenuation of the Rayleigh wave as well as the body waves are discussed. The results indicate that the flow-independent viscosity has important influence on the propagation characteristics of Rayleigh waves, compared with the flow-dependent effect of viscous coupling between the pore fluid and solid skeleton.

Investigation of viscous coupling effects in three-phase flow by lattice Boltzmann direct simulation and machine learning technique

The momentum transfer across fluid interfaces in multi-phase flow leads to a non-negligible viscous coupling effect. In this study, we use the lattice Boltzmann method (LBM) as a direct simulator to solve the three-phase flow at pore scale. The viscous coupling effects are investigated for various fluid configurations in simple pore geometries with different conditions in terms of saturation, wettability and viscosity ratio. It is found that the viscous coupling effect can be significant for certain configurations. A parametric modification factor for conventional three-phase conductance model is then proposed to estimate the viscous coupling effect. The modification factor as a function of viscosity ratios can be easily incorporated into existing pore network model (PNM) to eliminate errors from viscous coupling effect. Moreover, an elegant approach using machine learning technique is proposed to predict the multi-phase permeability by a trained Artificial Neural Network (ANN) from the direct simulation database. Such data-driven approach can be extended to develop a more sophisticated PNM for a better prediction of transport properties taking account of the viscous coupling effects.

Application of Biot’s Poroelasticity to Seismic Analysis of Subway Stations in a Saturated Poroelastic Half-space: Effects of Viscous Coupling

ABSTRACT This paper presents a parametric investigation on the effects of viscous coupling on the seismic responses of subway stations in a saturated poroelastic half-space which is modeled as a two-phase medium by the Biot’s theory. Moreover, an equivalent single-phase model for the saturated poroelastic half-space is introduced, and comparisons between the single-phase solutions and the two-phase solutions are made. The results are obtained by a finite element-indirect boundary element coupling method. The study shows that the viscous coupling has significant influences on the seismic internal forces and deformation of the subway stations, and the single-phase approximation can cause large errors.

A compressible viscous three-phase model for porous media flow based on the theory of mixtures

In this paper we focus on a general model to describe compressible and immiscible three-phase flow in porous media. The underlying idea is to replace Darcy’s law by more general momentum balance equations. In particular, we want to account for viscous coupling effects by introducing fluid-fluid interaction terms. In [Qiao, et al. (2018) Adv Water Resour 112: 170–188] a water-oil model based on the theory of mixtures was explored. It was demonstrated how the inclusion of viscous coupling effects could allow the model to better capture flow regimes which involve a combination of co-current and counter-current flow. In this work we extend the model in different aspects: (i) account for three phases (water,oil,gas) instead of two; (ii) deal with both the compressible and incompressible case; (iii) include viscous terms that represent frictional forces within the fluid (Brinkman type). A main objective of this work is to explore this three-phase model, which appears to be more realistic than standard formulation, in the context of petroleum related applications. We first provide development of stable numerical schemes in a one-dimensional setting which can be used to explore the generalized water-oil-gas model, both for the compressible and incompressible case. Then, several numerical examples with waterflooding in a gas reservoir and water alternating gas (WAG) experiments in an oil reservoir are investigated. Differences and similarities between the compressible and incompressible model are highlighted, and the fluid-fluid interaction effect is illustrated by comparison of results from the generalized model and a conventional model formulation.

Pore-scale visualization and characterization of viscous dissipation in porous media

HypothesisThe effects of mutual transfer of momentum between two immiscible flowing fluids in porous media are not well understood nor predictable yet. From considerations at the pore-scale, it should be possible to determine whether and to what extent interfacial viscous coupling effects are significant. ExperimentsWe visualize the velocity distributions inside immobile globules of wetting phase (water) while a non-wetting phase (oil) is injected. We investigate viscous coupling effects and their relationship with the viscosity ratio and the capillary number. FindingsFour regimes of viscous dissipation are identified: (i) a regime for which the fluid-fluid interface acts as a solid wall; (ii) a regime where the wetting phase is dragged in the direction of the imposed flow; (iii) and (iv) two regimes for which the trapped globule of water shows a recirculating motion due to the shear stress at the oil/water interface. We demonstrate the significant role of the lubricating effect and of the topology of the pore space on the magnitude of viscous dissipation. Importantly, for a viscosity ratio close to one and low capillary number, we demonstrate that viscous coupling effects should be incorporated into the existing Darcy’s law formulation for two-phase flow in porous media.

Viscous Two-Phase Flow in Porous Media Driven by Source Terms: Analysis and Numerics

In this work we consider the initial-boundary value problem for a generalized, compressible, porous media two-phase model. The formulation is motivated by principles from mixture theory and involves interstitial fluid velocity $\mathbf{u}_i$ instead of Darcy type velocity $\mathbf{U}_i=\phi s_i {\mathbf{u}_i}$, where $\phi$ is porosity and $s_i$ is saturation (volume fraction) of phase $i$. The momentum balance equations account for fluid-rock resistance forces as well as fluid-fluid interaction effects, in addition to internal viscosity through a Brinkmann type viscous term. We explore a one-dimensional version of this model where we account for two-phase dynamics driven by injection and production of fluids through realistic source terms and where physically relevant capillary pressure is accounted for. Our investigations are twofold: (i) Various a priori estimates are derived that give rise to an existence result subject to a constraint on the magnitude of the viscous terms and the strength of the injection and production rate. (ii) A numerical finite difference scheme, designed for dealing effectively with the strong nonlinear coupling between the mass and momentum equations, is then used to demonstrate a variety of two-phase injection-production scenarios for a realistic reservoir setting. Different physical effects are highlighted such as the difference between compressible and incompressible flow, balance between gravity and pressure-driven flow, and effect of viscous coupling.

Cocurrent Spontaneous Imbibition In Porous Media With the Dynamics of Viscous Coupling and Capillary Backpressure

Summary This paper presents a numerical study of water displacing oil using combined cocurrent/countercurrent spontaneous imbibition (SI) of water displacing oil from a water-wet matrix block exposed to water on one side and oil on the other. Countercurrent flows can induce a stronger viscous coupling than during cocurrent flows, leading to deceleration of the phases. Even as water displaces oil cocurrently, the saturation gradient in the block induces countercurrent capillary diffusion. The extent of countercurrent flow may dominate the domain of the matrix block near the water-exposed surfaces while cocurrent imbibition may dominate the domain near the oil-exposed surfaces, implying that one unique effective relative permeability curve for each phase does not adequately represent the system. Because relative permeabilities are routinely measured cocurrently, it is an open question whether the imbibition rates in the reservoir (depending on a variety of flow regimes and parameters) will in fact be correctly predicted. We present a generalized model of two-phase flow dependent on momentum equations from mixture theory that can account dynamically for viscous coupling between the phases and the porous media because of fluid/rock interaction (friction) and fluid/fluid interaction (drag). These momentum equations effectively replace and generalize Darcy's law. The model is parameterized using experimental data from the literature. We consider a water-wet matrix block in one dimension that is exposed to oil on one side and water on the other side. This setup favors cocurrent SI. We also account for the fact that oil produced countercurrently into water must overcome the so-called capillary backpressure, which represents a resistance for oil to be produced as droplets. This parameter can thus influence the extent of countercurrent production and hence viscous coupling. This complex mixture of flow regimes implies that it is not straightforward to model the system by a single set of relative permeabilities, but rather relies on a generalized momentum-equation model that couples the two phases. In particular, directly applying cocurrently measured relative permeability curves gives significantly different predictions than the generalized model. It is seen that at high water/oil-mobility ratios, viscous coupling can lower the imbibition rate and shift the production from less countercurrent to more cocurrent compared with conventional modeling. Although the viscous-coupling effects are triggered by countercurrent flow, reducing or eliminating countercurrent production by means of the capillary backpressure does not eliminate the effects of viscous coupling that take place inside the core, which effectively lower the mobility of the system. It was further seen that viscous coupling can increase the remaining oil saturation in standard cocurrent-imbibition setups.

A novel Shan and Chen type Lattice Boltzmann two phase method to study the capillary pressure curves of an oil water pair in a porous media

Abstract In this study, an immiscible oil-water two phase flow in a typical porous media was modeled using the well-known Lattice Boltzmann method. A set of flow tests for modeling an oil-water two phase flow in the porous media were conducted to generate the capillary pressure curves for two distinctive initial conditions, namely, water and oil dispersed conditions in two domains of different resolutions. Based on the obtained results, the general trend of these curves has an acceptable agreement with the usual trend of these curves in hydrocarbon reservoirs and the capillary data are independent of the initial conditions. Also, the results showed the effect of grid resolution on capillary data which are validated quantitatively by proposing a new approach using Purcell's equation. One can see that they are compatible with the geometrical characteristics of the porous media as well as the conditions governing the tests. Finally, another set of tests for oil water pairs of higher viscosity ratio up to 4.4 was performed in a low porosity heterogeneous porous media and the viscous coupling effect on capillary data, due to viscosity ratio, was studied to strengthen the model validation.

A study to investigate viscous coupling effects on the hydraulic conductance of fluid layers in two-phase flow at the pore level

This paper examines the role of momentum transfer across fluid-fluid interfaces in two-phase flow. A volume-of-fluid finite-volume numerical method is used to solve the Navier-Stokes equations for two-phase flow at the micro-scale. The model is applied to investigate viscous coupling effects as a function of the viscosity ratio, the wetting phase saturation and the wettability, for different fluid configurations in simple pore geometries. It is shown that viscous coupling effects can be significant for certain pore geometries such as oil layers sandwiched between water in the corner of mixed wettability capillaries. A simple parametric model is then presented to estimate general mobility terms as a function of geometric properties and viscosity ratio. Finally, the model is validated by comparison with the mobilities computed using direct numerical simulation.

A mixture theory approach to model co- and counter-current two-phase flow in porous media accounting for viscous coupling

Abstract It is well known that relative permeabilities can depend on the flow configuration and they are commonly lower during counter-current flow as compared to co-current flow. Conventional models must deal with this by manually changing the relative permeability curves depending on the observed flow regime. In this paper we use a novel two-phase momentum-equation-approach based on general mixture theory to generate effective relative permeabilities where this dependence (and others) is automatically captured. In particular, this formulation includes two viscous coupling effects: (i) Viscous drag between the flowing phases and the stagnant porous rock; (ii) viscous drag caused by momentum transfer between the flowing phases. The resulting generalized model will predict that during co-current flow the faster moving fluid accelerates the slow fluid, but is itself decelerated, while for counter-current flow they are both decelerated. The implications of these mechanisms are demonstrated by investigating recovery of oil from a matrix block surrounded by water due to a combination of gravity drainage and spontaneous imbibition, a situation highly relevant for naturally fractured reservoirs. We implement relative permeability data obtained experimentally through co-current flooding experiments and then explore the model behavior for different flow cases ranging from counter-current dominated to co-current dominated. In particular, it is demonstrated how the proposed model seems to offer some possible interesting improvements over conventional modeling by providing generalized mobility functions that automatically are able to capture more correctly different flow regimes for one and the same parameter set.

An improved pore-network model including viscous coupling effects using direct simulation by the lattice Boltzmann method

Viscous coupling during simultaneous flow of different fluid phases has a significant impact on their flow through porous media. In this work, a new multiscale strategy is proposed for multiphase flow in porous media. We use the lattice Boltzmann method (LBM) to simulate two-phase flow at pore scale and obtain empirical terms for the viscous coupling inside individual pores. The empirical coupling terms are then used in a pore-network model to efficiently simulate two-phase flow through porous media at core scale. It is shown that including viscous coupling leads to better predictions of relative permeability.