Dynamic Pore Network Model Research Articles

Pore-to-Core Upscaling of Two-Phase Flow in Mixed-Wet Porous Media: Part II-A Dynamic Pore-Network Modeling Approach

Pore-to-Core Upscaling of Two-Phase Flow in Mixed-Wet Porous Media: Part II-A Dynamic Pore-Network Modeling Approach

Critical assessment of the validity of quasi-static pore network modeling in the application of underground hydrogen storage

This study explores the suitability of quasi-static pore-network modeling for simulating the transport of hydrogen in networks with box-shaped pores and square cylinder throats. The dynamic pore-network modeling results are compared with quasi-static pore-network modeling, and a good agreement is observed when the simulations reach steady-state, for a capillary number of Nc≤10−7. This finding suggests that the quasi-static approach can be used as a reliable and efficient method for studying hydrogen transport in similar networks.

Spontaneous Imbibition in Dual Permeable Media Using Dynamic Pore Network Model

AbstractUnderstanding preferential flow in porous media holds substantial theoretical significance on the design and optimization of hydrocarbon exploitation in shale reservoir. Previous researches discussed the competition of imbibition front in layered porous media while the underlining mechanism for interfacial dynamics and induced displacement efficiency of multiphase flow remains ambiguous. In this paper, we investigate the spontaneous imbibition in dual permeable media and analyze the flux exchange between the neighboring porous zones with permeability contrast using dynamic pore network model. The impact of fluid viscosity ratio and permeability contrast on the spontaneous imbibition preference have been addressed, and finally a phase diagram for displacement efficiency has been obtained. The results reveal that the dual permeable structure enhances the invasion rate of wetting fluid in the low‐permeable zone and induces unstable displacement patterns, leading to reduction of the long‐term displacement efficiency. The interfacial pattern transition from stable displacement to unstable pattern in dual permeable media could be ascribed into the flux exchange between dual permeable zones, which shows a contrary impact on the fluid flow within the low‐permeable zone under favorable and unfavorable viscosity ratios. The permeability contrast in dual permeable media intensifies this impact during spontaneous imbibition. These results help us to understand the occurrence and mutual interaction of multiphase flow in layered porous media, and provide a theoretical guidance for the hydrocarbon exploitation in shale reservoir.

A pore-network modeling perspective on the dynamics of residual trapping in geological carbon storage

This study presents the application of an efficient and robust Dynamic Pore-Network Modeling (DPNM) framework for accurate prediction of carbon dioxide (CO2) trapping behavior under the dynamic flow conditions prevalent in subsurface applications. Residual trapping of CO2 is crucial in the context of geological sequestration, serving as a constitutive relationship that controls relative permeability hysteresis and thereby determining the magnitude of CO2 trapping within formations over varying timescales. Utilizing our DPNM framework, we study the complexities of residual trapping in miniature-core-sized digital replicate of a sandstone. We systematically conduct series of two-phase flow simulations to examine the relationships between total residual CO2 amount, trapping efficiency, and initial saturations across a spectrum of capillary numbers and wettability states. Dynamic simulation results lead to a simple power-law scaling equation correlating CO2 trapping efficiency with initial saturation across various capillary numbers. Further analysis explores the morphological and topological characteristics of fluids during primary drainage and various imbibition displacements within the pore network. This work contributes an essential tool and deepens our understanding of CO2 trapping dynamics, driving progress towards more effective and safer strategies for carbon capture and storage.

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.

Disorder-induced non-linear growth of fingers in immiscible two-phase flow in porous media

Immiscible two-phase flow in porous media produces different types of patterns depending on the capillary number Ca and viscosity ratio M. At high Ca, viscous instability of the fluid–fluid interface occurs when the displaced fluid is the more viscous, and leads to viscous fingering, which is believed to exhibit the same growth behavior as the viscously-unstable fingers observed in Hele–Shaw cells by Saffman and Taylor [“The penetration of a fluid into a porous medium or Hele–Shaw cell containing a more viscous liquid,” Proc. R. Soc. London 245, 312 (1958)], or as diffusion-limited aggregates (DLA). In such Laplacian growth processes, the interface velocity depends linearly on the local gradient of the physical field that drives the growth process (for two-phase flow, the pressure field). However, a non-linear power-law dependence between the flow rate and the global pressure drop, reminiscent of what has also been observed for steady-state two-phase flow in porous media, was evidenced experimentally for the growth of viscously-unstable drainage fingers in two-dimensional porous media, 20 years ago. Here, we revisit this flow regime using dynamic pore-network modeling and explore the non-linearity in the growth properties. We characterize the previously unstudied dependencies of the statistical finger width and non-linear growth law's exponent on Ca, and discuss quantitatively, based on theoretical arguments, how disorder in the capillary barriers controls the growth process' non-linearity, and why the flow regime crosses over to Laplacian growth at sufficiently high Ca. In addition, the statistical properties of the fingering patterns are compared to those of Saffman–Taylor fingers, DLA growth patterns, and the results from the aforementioned previous experimental study.

Dynamic characterization of residual oil during long-term waterflooding experiments in heterogeneous porous structures

To improve the understanding of trapping and mobilization mechanism during multiphase flow in porous media, long-term waterflooding experiments have been performed to capture the water–oil displacement behaviors in sandstone cores with different permeability and porosity. The residual oil is therefore categorized based on force analysis and morphological characteristics. The critical values for categorization are determined by measuring differences using statistical evaluation. Simplified models of five types of residual oil are established and the dynamic variations of types and volumes of residual oil are characterized during the long-term waterflooding in the sandstone cores. The results indicate that the pore structure heterogeneity impacts the force balance and morphology of residual oil, leading to various dominant types in the sandstone cores with different permeability. Moreover, for effective mobilization of the residual oil, different strategies of enhanced oil recovery are designed controlling the force balance of residual oil. The strategies for oil mobilization are validated by the dynamic pore network modeling, and the enhanced oil recovery is up to 28 %. This study provides a new classification method of residual oil and corresponding mobilization strategies from the perspective of force balance and morphology, which is vital to enhance oil recovery in the high/ultra-high water-cut stage of the oil reservoirs.

Rapid evaluation of capillary pressure and relative permeability for oil–water flow in tight sandstone based on a physics-informed neural network

Efficient and accurate evaluation of capillary pressure and relative permeability of oil–water flow in tight sandstone with limited routinely obtainable parameters is a crucial problem in tight oil reservoir modeling and petroleum engineering. Due to the multiscale pore structure, there is complex nonlinear multiphase flow in tight sandstone. Additionally, wetting behavior caused by mineral components remarkably influences oil–water displacement in multiscale pores. All this makes predicting capillary pressure and relative permeability in tight sandstone extremely difficult. This paper proposes a physics-informed neural network, integrating five important physical models, the improved parallel genetic algorithm (PGA), and the neural network to simulate the two-phase capillary pressure and relative permeability of tight sandstone. To describe the nonlinear multiphase flow and the wettability behavior, five physical models, including the non-Darcy liquid flow rate formula, apparent permeability (AP) formula, and contact angle-capillary pressure relationship, are coupled into the neural network to improve the prediction accuracy. In addition, the input parameters and the structure of the physics-informed neural network are simplified based on analyzing the change rule of the oil–water flow with the main controlling factors, which can also save training time and improve the accuracy of the neural network. To obtain the data for training the coupled neural network, the dataset of tight sandstone in Ordos Basin is constructed with experimentally measured data and various fluid flow properties as constraints. The test results demonstrate that the estimated capillary pressure and relative permeability from the physics-informed neural network are in good agreement with the test ones. Finally, we have compared the physics-informed neural network with the quasi-static pore network model (QSPNM), dynamic pore network model (DPNM), and conventional artificial neural network (ANN). The calculation time of QSPNM and DPNM are hundreds of times longer than that of the physics-informed neural network. The coupled neural network has also performed much better than the conventional ANN. As the heterogeneity of pore spaces in tight sandstone increases, the advantages of the physics-informed neural network over ANN are more prominent. The prediction models generated in this study can estimate the capillary pressure and relative permeability based on only four routine parameters in a few seconds. Therefore, the physics-informed neural network in this paper can provide the potential parameters for large-scale reservoir simulation.

Characteristics of fluid–fluid displacement in model mixed-wet porous media: patterns, pressures and scalings

We study numerically the characteristics of fluid–fluid displacement in simple mixed-wet porous micromodels using a dynamic pore network model. The porous micromodel consists of distinct water-wet and oil-wet regions, whose fractions are varied systematically to yield a variety of displacement patterns over a wide range of capillary numbers. We find that the impact of mixed-wettability is most prominent at low capillary numbers, and it depends on the complex interplay between wettability fraction and the intrinsic contact angle of the water-wet regions. For example, the fractal dimension of the displacement pattern is a monotonically increasing function of wettability fraction in flow cells with strongly water-wet clusters, but it becomes non-monotonic with respect to wettability fraction in flow cells with weakly water-wet clusters. Additionally, mixed-wettability also manifests itself in the injection pressure signature, which exhibits fluctuations especially at low wettability fraction. Specifically, preferential filling of water-wet regions leads to reduced effective permeability and higher injection pressure, even at vanishingly small capillary numbers. Finally, we demonstrate that scaling analyses based on a weighted average description of the overall wetting state of the mixed-wet system can effectively capture the variations in observed displacement pattern morphology.

Effective rheology of immiscible two-phase flow in porous media consisting of random mixtures of grains having two types of wetting properties

We consider the effective rheology of immiscible two-phase flow in porous media consisting of random mixtures of two types of grains having different wetting properties using a dynamic pore network model under steady-state flow conditions. Two immiscible fluids, denoted by “A” and “B”, flow through the pores between these two types of grains denoted by “+” and “−”. Fluid “A” is fully wetting, and “B” is fully non-wetting with respect to “+” grains, whereas it is the opposite with “−” grains. The direction of the capillary forces in the links between two “+” grains is, therefore, opposite compared to the direction in the links between two “−” grains, whereas the capillary forces in the links between two opposite types of grains average to zero. For a window of grain occupation probability values, a percolating regime appears where there is a high probability of having connected paths with zero capillary forces. Due to these paths, no minimum threshold pressure is required to start a flow in this regime. When varying the pressure drop across the porous medium from low to high in this regime, the relation between the volumetric flow rate in the steady state and the pressure drop goes from being linear to a power law with exponent 2.56, and then to linear again. Outside the percolation regime, there is a threshold pressure necessary to start the flow and no linear regime is observed for low pressure drops. When the pressure drop is high enough for there to be a flow, we find that the flow rate depends on the excess pressure drop to a power law with exponents around 2.2–2.3. At even higher excess pressure drops, the relation becomes linear. We see no change in the exponent for the intermediate regime at the percolation critical points where the zero-capillary force paths disappear. We measure the mobility at the percolation threshold at low pressure drops so that the flow rate versus pressure drop is linear. Assuming a power law, the mobility is proportional to the difference between the occupation probability and the critical occupation probability to a power of around 5.7.

Local statistics of immiscible and incompressible two-phase flow in porous media

We consider immiscible and incompressible two-phase flow in porous media under steady-state conditions using a dynamic pore network model. We focus on the fluctuations in a Representative Elementary Area (REA), with the aim to demonstrate that the statistical distributions of the volumetric flow rate and the saturation within the REA become independent of the size of the entire model when the model is large enough. This independence is a necessary condition for developing a local statistical theory for the flow, which in turn opens for the possibility to formulate a description at scales large enough for the typical pore size to be negligible using differential equations.

Dynamic pore-scale modeling of residual fluid configurations in disordered porous media

Fluid trapping in porous media is important in many subsurface flow processes such as enhanced oil recovery and geological sequestration of carbon dioxide. To achieve optimal performance in such applications, a fundamental understanding of residual trapping mechanisms at the pore scale is necessary. In this work, we present a computational study of fluid trapping behaviors in natural porous media under different flow regimes by employing a dynamic pore-network modeling approach. The model incorporates many advanced features that have not been collectively used in previous dynamic platforms. For instance, it rigorously solves for fluid pressure fields from two-phase mass balance equations in each pore element, incorporates a detailed description of pore-scale fluid displacement dynamics of piston-like advance, snap-off, and pore-body filling, and explicitly accounts for flow through wetting layers forming in corners and rough surfaces of pore spaces. Moreover, we extend the ability of our model by including contact angle hysteresis, which is often neglected in existing dynamic models. A heavily-parallelized implementation of this platform is further advanced to achieve an efficient computational performance. We first conduct primary drainage and imbibition simulations in pore networks representing Bentheimer and Berea sandstones. We show that the predicted two-phase relative permeability curves agree well with their experimental counterparts reported in the literature. Afterwards, the validated model is used to systematically probe fluid trapping behaviors in a core-sized pore network that is constructed from high-resolution micro-computed tomography images of a Berea sandstone core sample. The effects of dynamic flow conditions and fluid properties on core-scale two-phase displacement pattern, residual-fluid configuration, and residual oil saturations are examined in detail. Fluid trapping properties such as maximum and average residual-fluid cluster size and capillary-controlled invasion selectivity at the pore scale are analyzed under both capillaryand viscous-dominated flow regimes.

Numerical studies of spontaneous imbibition in porous media: Model development and pore-scale perspectives

Spontaneous imbibition is a crucial two-phase flow process in a variety of subsurface and industrial applications. Due to the lack of an efficient and reliable pore-scale model, however, how pore-filling events in spontaneous imbibition influence average transport properties (i.e., capillary pressure and relative permeability curves) and entrapment of the nonwetting fluid has not been fully understood. In this work, we first experimentally verify an image-based dynamic pore-network model of spontaneous imbibition that is computationally efficient. Then, case studies of a Nubian sandstone are conducted. We demonstrate that average capillary pressure in cocurrent spontaneous imbibition is significantly overestimated by the widely used Young-Laplace equation. This is because the effects of dynamic pore-filling and air entrapment on average capillary pressure are not parameterized in the equation. Based on our pore-scale numerical results, we elaborate on the competition of pore-filling events under different viscosity ratios of the wetting to the nonwetting fluids. It is found that the filling mode evolves from the co-filling of neighboring pores to the preferential filling of small pores as the nonwetting viscosity increases. Our model will be a useful numerical tool for quantitatively predicting spontaneous imbibition in geological formations. Our findings will help us bridge the gap between pore-scale flow dynamics and the Darcy theory of spontaneous imbibition.

Two-phase Flow Dynamics at the Interface Between GDL and Gas Distributor Channel Using a Pore-Network Model

For improved operating conditions of a polymer electrolyte membrane (PEM) fuel cell, a sophisticated water management is crucial. Therefore, it is necessary to understand the transport mechanisms of water throughout the cell constituents especially on the cathode side, where the excess water has to be removed. Pore-scale modeling of diffusion layers and gas distributor has been established as a favorable technique to investigate the ongoing processes. Investigating the interface between the cathode layers, a particular challenge is the combination and interaction of the multi-phase flow in the porous material of the gas diffusion layer (GDL) with the free flow in the gas distributor channels. The formation, growth and detachment of water droplets on the hydrophobic, porous surface of the GDL have a major influence on the mass, momentum and energy exchange between the layers. A dynamic pore-network model is used to describe the flow through the porous GDL on the pore-scale. To capture the droplet occurrence and its influence on the flow, this dynamic two-phase pore-network model is extended to capture droplet formation and growth at the surface of the GDL as well as droplet detachment due to the gas flow in the gas distributor channels. In this article, the developed model is applied to single- and multi-tube systems to investigate the general drop behavior. These rather simple test-cases are compared to experimental and numerical data available in the literature. Finally, the model is applied to a GDL unit cell to analyze the interaction between two-phase flow through the GDL and drop formation at the interface between GDL and gas distributor channel.

A Dynamic Pore Network Model for Imbibition Simulation Considering Corner Film Flow

AbstractWetting films can develop in the corners of angular pores under strong wetting conditions. Modeling the dynamics of corner film remains elusive using direct numerical simulations because of the significant scale difference between main meniscus and corner film flow. In this paper, the modified interacting capillary bundle model (ICB), developed in our previous work to describe accurately corner film dynamics in a single square tube, is incorporated into a single‐pressure dynamic pore network model (DPNM) to simulate imbibition in strongly wetting porous media with corner film flow. The traditional pore network is decomposed into several layers of interacting subpore networks where the 0th layer of subpore network simulates the main meniscus flow and higher layers the corner film flow. The fluid flow between different layers is captured by interlayer throats. In addition, the snap‐off mechanism caused by the thickening of wetting corner film is considered. The accuracy of the developed model is validated for four cases: spontaneous imbibition in a single square tube, wetting fluid redistribution through corner films under a capillary pressure difference, snap off in a narrow throat connecting two large pores, and imbibition dynamics in a real microfluidic porous geometry. The validated model is then used to simulate both spontaneous and controlled imbibition in a pore network with random pore size distribution. The interaction between corner film and main meniscus flow in porous media is analyzed from a pore‐scale perspective.

Wicking through complex interfaces at interlacing yarns

HypothesisWicking flow in the wale direction of knit fabrics is slowed by capillary pressure minima during the transition at yarn contacts. The characteristic pore structure of yarns leads to an unfavorable free energy evolution and is the cause of these minima. ExperimentsTime-resolved synchrotron tomographic microscopy is employed to study the evolution of water configuration during wicking flow in interlacing yarns. Dynamic pore network modeling is used based on the obtained image data and distributions of delay times for pore intrusion. Good agreement is observed by comparison to the experimental data. FindingsYarn-to-yarn transition is found to coincide with slow water advance in a thin interface zone at the yarn contact. The pore spaces of the two yarns merge within this interface zone and provide a transition path. A deep capillary pressure minimum occurs while water passes through the center of the interface zone, effectively delaying the wicking flow. A pore network model considering pore intrusion delay times is expanded to include inter-yarn wicking and reproduce the observed wicking dynamics.

The Co-Moving Velocity in Immiscible Two-Phase Flow in Porous Media

We present a continuum (i.e., an effective) description of immiscible two-phase flow in porous media characterized by two fields, the pressure and the saturation. Gradients in these two fields are the driving forces that move the immiscible fluids around. The fluids are characterized by two seepage velocity fields, one for each fluid. Following Hansen et al. (Transport in Porous Media, 125, 565 (2018)), we construct a two-way transformation between the velocity couple consisting of the seepage velocity of each fluid, to a velocity couple consisting of the average seepage velocity of both fluids and a new velocity parameter, the co-moving velocity. The co-moving velocity is related but not equal to velocity difference between the two immiscible fluids. The two-way mapping, the mass conservation equation and the constitutive equations for the average seepage velocity and the co-moving velocity form a closed set of equations that determine the flow. There is growing experimental, computational and theoretical evidence that constitutive equation for the average seepage velocity has the form of a power law in the pressure gradient over a wide range of capillary numbers. Through the transformation between the two velocity couples, this constitutive equation may be taken directly into account in the equations describing the flow of each fluid. This is, e.g., not possible using relative permeability theory. By reverse engineering relative permeability data from the literature, we construct the constitutive equation for the co-moving velocity. We also calculate the co-moving constitutive equation using a dynamic pore network model over a wide range of parameters, from where the flow is viscosity dominated to where the capillary and viscous forces compete. Both the relative permeability data from the literature and the dynamic pore network model give the same very simple functional form for the constitutive equation over the whole range of parameters.

Dynamic pore network model to predict residual saturation and pressure drop in mist oleo-phobic filters

A dynamic pore network modelling (DPNM) framework is used to evaluate pressure drop and residual saturation in oleo-phobic nonwoven media in mist filters. The advanced fully-resolved VOF simulations along with μ-CT measurements are also carried out to substantiate the validity of the DPNM simulations. The results of the study show that PNM could be a beneficial and reliable tool for predicting oil saturation and pressure drop during early-stage design of oleo-phobic filters with nonwoven media. Given the considerably higher efficiency of PNM models compared to CFD-based techniques, some parametric studies were also conducted. Our findings suggest that, for a given set of operating conditions, efficiency/performance can be improved by appropriate choice of filters with optimized properties (fibre diameter, packing density, contact angle, etc.) for which the overall oil saturation and pressure drop in the filter attain minimum, may offer a self-cleaning mist filter. Finally, a correlation was developed for evaluating the performance of oleo-phobic media using the filter specifications and the data of steady state saturation and pressure drop found in open literature. The obtained correlation shows a good conformity with the experimental measurements with an average of 12.1% error for about 93% of data out of 68 data sets collected with a correlation coefficient of (R2) of 0.934.

Enhanced thermal fingering in a shear-thinning fluid flow through porous media: Dynamic pore network modeling

Thermal-viscous fingering instability in porous media is a common phenomenon in nature as well as in many scientific problems and industrial applications. Despite the importance, however, thermal transport in flow of a non-Newtonian fluid in porous media and the resulting fingering has not been studied extensively, especially if the pore space is heterogeneous. In this paper, we propose a pore network model with full graphics processing unit-parallelized acceleration to simulate thermal transport in flow through three-dimensional unstructured pore networks at centimeter scale, containing millions of pores. A thermal Meter equation is proposed to model temperature- and shear stress-dependent rheology of the non-Newtonian fluids. After comparing the simulation results with an analytical solution for the location of the thermal front in a spatially uncorrelated pore network, thermal transport in flow of both Newtonian and non-Newtonian fluids is studied in the spatially uncorrelated and correlated pore networks over a range of injection flow rates. The simulations indicate that the injection flow rate, the shear-thinning rheology, and the morphological heterogeneity of the pore space all enhance thermal-viscous fingering instability in porous media, but with distinct patterns. In spatially correlated networks, the average temperature and apparent viscosity at the breakthrough point in flow of a shear-thinning fluid exhibit non-monotonic dependence on the injection flow rate. An analysis of the fractal dimension of thermal patterns at the breakthrough point supports the conclusion. The results highlight the importance of designing optimal flow conditions for application purposes.

Dissolution and remobilization of NAPL in surfactant-enhanced aquifer remediation from microscopic scale simulations

In this paper, the dissolution and mobilization of non-aqueous phase liquid (NAPL) blobs in the Surfactant-Enhanced Aquifer Remediation (SEAR) process were upscaled using dynamic pore network modeling (PNM) of three-dimensional and unstructured networks. We considered corner flow and micro-flow mechanisms including snap-off and piston-like movement for two-phase flow. Moreover, NAPL entrapment and remobilization were evaluated using force analysis to develop the capillary desaturation curve (CDC) and predict the onset of remobilization. The corner diffusion mechanism was also applied in the modeling of interphase mass transfer to represent NAPL dissolution as the dominant mass transfer process. In addition, the effect of pore-scale heterogeneity on mass transfer rate coefficient and recovered residual NAPL was considered in the simulations. Sodium dodecyl sulfate (SDS) and Triton X-100 were used as the surfactant for the SEAR process. The results indicate that although surfactants enhance NAPL recovery during two-phase flow, surfactant-enhanced remediation of residual NAPL through dissolution is highly dependent on surfactant type. When SDS ─as a surfactant with high critical micelle concentration (CMC) and low micelle partition coefficient (Km)─ was injected into a NAPL contaminated site, the mass transfer rate coefficient decreased (due to considerable changes in interface chemical potentials) which leads to a significant reduction in NAPL recovery after the end of two-phase flow. In contrast, Triton X-100 (with low CMC and high Km) improved NAPL recovery, by enhancing solubility at surfactant concentrations greater than CMC which overcompensates the interphase mass transfer reduction.