arXiv subjects

Ryan T. Armstrong

Publications and source records attributed to Ryan T. Armstrong.

At least 19 recordsLinked to original sources

arXiv2025

From Interface Dynamics to Darcy Scale Description of Multiphase Flow in Porous Media

An outstanding characteristic of porous media, desired in many applications, is the large surface area, which facilitates solid-fluid interactions, making porous media an extreme case in colloid and interface science. In two-fluid systems, wetting and the balance of capillary and viscous forces control fluid displacement processes, leading to a wide range of complex flow regimes with rich spatio-temporal dynamics. Macroscopic two-phase flow is historically described through the phenomenological extensions of Darcy's law. Besides many other shortcomings and inconsistencies, it covers only connected pathway flow in the capillary-dominated flow regime in a rigorous manner while other flow regimes with moving interfaces and associated topological changes are entirely implicit. Given the lack of adequate descriptions, upscaling multiphase flow from pore to Darcy scale represents a long-standing challenge paving into the fields of thermodynamics, statistical mechanics and integral geometry. In this review, we compare novel concepts which have been largely motivated by experimental insights, enabled by significant advances in pore-scale imaging and modeling over the last decade.

physics.flu-dyn↗

arXiv2025

Fluctuation-dissipation theorems for multi-phase flow with memory in porous media

Recent works have reported on the collective behavior of multiphase systems under fractional flow. Such behavior has been linked to pressure and/or flux fluctuations under stationary flow conditions that occur over a broad range of resonance frequencies and associated relaxation times. However, there currently exists no theoretical development to deal with such phenomena. The aim of this paper is to develop a fundamental theory that can describe such behavior. Fluctuation-dissipation theorems for the case with memory are formulated, providing a new route to obtain frequency-dependent porous media permeability. We propose that multiphase flow systems can be explained by a multipeak Lorentzian memory function and provide supporting experimental data from the flow of decane and water in a porous medium made of glass beads. Our fluctuation dissipation theorems provide information on different types of relaxation phenomena and resonance frequencies that occur during fractional flow. We show, using experimental data, that Green-Kubo-like expressions can be formulated for two-phase fluid flow driven by a constant pressure drop. The resulting autocorrelation functions, or rather their Fourier transforms, exhibit multiple Lorentzian peak shapes. Resonances are similar to those of electric conductance. The analysis offers a new route to steady-state relative permeability measurements, including information on the relaxation times and resonance regimes that exist during fractional flow. Overall, the theory presented and supported by fractional flow experiments provides a rich set of possible directions for future developments that could fundamentally change the way multiphase flow systems are understood and studied.

physics.flu-dyn↗

arXiv2024

Fluctuation-dissipation theorems and the measurement of the Onsager coefficients for two-phase flow in porous media

We propose a new methodology for the experimental measurement of the Onsager coefficients of porous media flows by application of the fluctuation-dissipation theorem. The experimental setup consists of a steady-state flow condition in which two incompressible fluids are simultaneously injected into a modified Hele-Shaw cell. The cell is transparent and allows direct visualization of the dynamics via regular optical imaging methods. The fluctuations in the phase saturations are obtained and, by computing the temporal correlations of their time derivatives, we gain access to the Onsager coefficients. This work gives experimental grounding to recent theoretical development on the applications of the fluctuation-dissipation theorems to porous media flows.

physics.flu-dyn↗

arXiv2023

The impact of wettability on the co-moving velocity of two-fluid flow in porous media

The impact of wettability on the co-moving velocity of two-fluid flow in porous media is analyzed herein. The co-moving velocity, developed by Roy et al. (2022), is a novel representation of the flow behavior of two fluids through porous media. Our study aims to better understand the behavior of the co-moving velocity by analyzing simulation data under various wetting conditions. The simulations were conducted using the Lattice-Boltzmann color-fluid model and evaluated the relative permeability for different wetting conditions on the same rock. The analysis of the simulation data followed the methodology proposed by Roy et al. (2022) to reconstruct a constitutive equation for the co-moving velocity. Surprisingly, it was found that the coefficients of the constitutive equation were nearly the same for all wetting conditions. Based on these results, a simple approach was proposed to reconstruct the oil phase relative permeability using only the co-moving velocity relationship and water phase relative permeability. This proposed method provides new insights into the dependency of relative permeability curves, which has implications for the history matching of production data and solving the associated inverse problem. The research findings contribute to a better understanding of the impact of wettability on fluid flow in porous media and provide a practical approach for estimating relative permeability based on the co-moving velocity relationship, which has never been shown before.

physics.flu-dyn↗

arXiv2023

Effective permeability of an immiscible fluid in porous media determined from its geometric state

Based on the phenomenological extension of Darcy's law, two-fluid flow is dependent on a relative permeability function of saturation only that is process/path dependent with an underlying dependency on pore structure. For applications, fuel cells to underground $CO_2$ storage, it is imperative to determine the effective phase permeability relationships where the traditional approach is based on the inverse modelling of time-consuming experiments. The underlying reason is that the fundamental upscaling step from pore to Darcy scale, which links the pore structure of the porous medium to the continuum hydraulic conductivities, is not solved. Herein, we develop an Artificial Neural Network (ANN) that relies on fundamental geometrical relationships to determine the mechanical energy dissipation during creeping immiscible two-fluid flow. The developed ANN is based on a prescribed set of state variables based on physical insights that predicts the effective permeability of 4,500 unseen pore-scale geometrical states with $R^2 = 0.98$.

physics.flu-dyn↗

arXiv2022

DeepAngle: Fast calculation of contact angles in tomography images using deep learning

DeepAngle is a machine learning-based method to determine the contact angles of different phases in the tomography images of porous materials. Measurement of angles in 3--D needs to be done within the surface perpendicular to the angle planes, and it could become inaccurate when dealing with the discretized space of the image voxels. A computationally intensive solution is to correlate and vectorize all surfaces using an adaptable grid, and then measure the angles within the desired planes. On the contrary, the present study provides a rapid and low-cost technique powered by deep learning to estimate the interfacial angles directly from images. DeepAngle is tested on both synthetic and realistic images against the direct measurement technique and found to improve the r-squared by 5 to 16% while lowering the computational cost 20 times. This rapid method is especially applicable for processing large tomography data and time-resolved images, which is computationally intensive. The developed code and the dataset are available at an open repository on GitHub (https://www.github.com/ArashRabbani/DeepAngle).

cs.CV↗

arXiv2022

Relative permeability as a stationary process: energy fluctuations in immiscible displacement

Relative permeability is commonly used to model immiscible fluid flow through porous materials. In this work we derive the relative permeability relationship from conservation of energy, assuming that the system to be non-ergodic at large length scales and relying on averaging in both space and time to homogenize the behavior. Explicit criteria are obtained to define stationary conditions: (1) there can be no net change for extensive measures of the system state over the time averaging interval; (2) the net energy inputs into the system are zero, meaning that the net rate of work done on the system must balance with the heat removed; and (3) there is no net work performed due to the contribution of internal energy fluctuations. Results are then evaluated based on direct numerical simulation. Dynamic connectivity is observed during steady-state flow, which is quantitatively assessed based the Euler characteristic. We show that even during steady-state flow at low capillary number ($\mathsf{Ca}\sim1\times10^5$), typical flow processes will explore multiple connectivity states. The residence time for each connectivity state is captured based on the time-and-space average. The distribution for energy fluctuations is shown to be multi-modal and non-Gaussian when terms are considered independently. However, we demonstrate that their sum is zero. Given an appropriate choice of the thermodynamic driving force, we show that the conventional relative permeability relationship is sufficient to model the energy dissipation in systems with complex pore-scale dynamics that routinely alter the structure of fluid connected pathways.

physics.flu-dyn↗

arXiv2022

Deep learning of multi-resolution X-Ray micro-CT images for multi-scale modelling

Field-of-view and resolution trade-offs in X-Ray micro-computed tomography (micro-CT) imaging limit the characterization, analysis and model development of multi-scale porous systems. To this end, we developed an applied methodology utilising deep learning to enhance low resolution images over large sample sizes and create multi-scale models capable of accurately simulating experimental fluid dynamics from the pore (microns) to continuum (centimetres) scale. We develop a 3D Enhanced Deep Super Resolution (EDSR) convolutional neural network to create super resolution (SR) images from low resolution images, which alleviates common micro-CT hardware/reconstruction defects in high-resolution (HR) images. When paired with pore-network simulations and parallel computation, we can create large 3D continuum-scale models with spatially varying flow & material properties. We quantitatively validate the workflow at various scales using direct HR/SR image similarity, pore-scale material/flow simulations and continuum scale multiphase flow experiments (drainage immiscible flow pressures and 3D fluid volume fractions). The SR images and models are comparable to the HR ground truth, and generally accurate to within experimental uncertainty at the continuum scale across a range of flow rates. They are found to be significantly more accurate than their LR counterparts, especially in cases where a wide distribution of pore-sizes are encountered. The applied methodology opens up the possibility to image, model and analyse truly multi-scale heterogeneous systems that are otherwise intractable.

physics.geo-ph↗

arXiv2021

A comparative study of paired versus unpaired deep learning methods for physically enhancing digital rock image resolution

X-ray micro-computed tomography (micro-CT) has been widely leveraged to characterise pore-scale geometry in subsurface porous rock. Recent developments in super resolution (SR) methods using deep learning allow the digital enhancement of low resolution (LR) images over large spatial scales, creating SR images comparable to the high resolution (HR) ground truth. This circumvents traditional resolution and field-of-view trade-offs. An outstanding issue is the use of paired (registered) LR and HR data, which is often required in the training step of such methods but is difficult to obtain. In this work, we rigorously compare two different state-of-the-art SR deep learning techniques, using both paired and unpaired data, with like-for-like ground truth data. The first approach requires paired images to train a convolutional neural network (CNN) while the second approach uses unpaired images to train a generative adversarial network (GAN). The two approaches are compared using a micro-CT carbonate rock sample with complicated micro-porous textures. We implemented various image based and numerical verifications and experimental validation to quantitatively evaluate the physical accuracy and sensitivities of the two methods. Our quantitative results show that unpaired GAN approach can reconstruct super-resolution images as precise as paired CNN method, with comparable training times and dataset requirement. This unlocks new applications for micro-CT image enhancement using unpaired deep learning methods; image registration is no longer needed during the data processing stage. Decoupled images from data storage platforms can be exploited more efficiently to train networks for SR digital rock applications. This opens up a new pathway for various applications of multi-scale flow simulation in heterogeneous porous media.

eess.IV↗

arXiv2021

Universal description of wetting on multiscale surfaces using integral geometry

Hypothesis Emerging energy-related technologies deal with multiscale hierarchical structures, intricate surface morphology, non-axisymmetric interfaces, and complex contact lines where wetting is difficult to quantify with classical methods. We hypothesis that a universal description of wetting on multiscale surfaces can be developed by using integral geometry coupled to thermodynamic laws. The proposed approach separates the different hierarchy levels of physical description from the thermodynamic description, allowing for a universal description of wetting on multiscale surfaces. Theory and Simulations The theoretical framework is presented followed by application to limiting cases of various wetting states. The wetting states include those considered in the Wenzel, Cassie-Baxter and wicking state models. The wetting behaviour of multiscale surfaces is then explored by conducting direct simulations of a fluid droplet on a structurally rough surface and a chemically heterogeneous surface. Findings The underlying origin of the classical wetting models is shown to be rooted within the proposed theoretical framework. In addition, integral geometry provides a topological-based wetting metric that is not contingent on any type of wetting state. Being of geometrical origin the wetting metric is applicable to describe any type of wetting phenomena on complex surfaces. The proposed framework is applicable to any complex fluid topology and multiscale surface.

physics.flu-dyn↗

arXiv2021

Thermodynamics of fluctuations based on time-and-space averages

We develop non-equilibrium theory by using averages in time and space as a generalized way to upscale thermodynamics in non-ergodic systems. The approach offers a classical perspective on the energy dynamics in fluctuating systems. The rate of entropy production is shown to be explicitly scale dependent when considered in this context. We show that while any stationary process can be represented as having zero entropy production, second law constraints due to the Clausius theorem are preserved due to the fact that heat and work are related based on conservation of energy. As a demonstration we consider the energy dynamics for the Carnot cycle and for Maxwell's demon. We then consider non-stationary processes, applying time-and-space averages to characterize non-ergodic effects in heterogeneous systems where energy barriers such as compositional gradients are present. We show that the derived theory can be used to understand the origins of anomalous diffusion phenomena in systems where Fick's law applies at small length scales but not at large length scales. We then characterize fluctuations in capillary-dominated systems, which are non-stationary due to the irreversibility of cooperative events.

cond-mat.soft↗

arXiv2021

Capillary fluctuations and energy dynamics for flow in porous media

Capillary energy barriers have important consequences for immiscible fluid flow in porous media. We derive time-and-space averaging theory to account for non-equilibrium behavior and understand the role of athermal capillary fluctuations in the context of their relationship to larger scale phenomenological equations. The formulation resolves several key challenges associated with two-fluid flow in porous media: (1) geometric and thermodynamic quantities are constructed as smooth functions of time based on time-and space averages; (2) averaged thermodynamics are developed for films; (3) multi-scale fluctuation terms are identified, which account for transient behaviours of interfaces and films that occur due to pore-scale events; (4) geometric constraints are derived and imposed on the averaged thermodynamics; (5) a new constitutive model is proposed for capillary pressure dynamics that includes contributions from films; and (6) a time-and-space criterion for representative elementary volume (REV) is established based on capillary fluctuations. Capillary fluctuations are assessed quantitatively based on pore-scale simulations and experimental core-flooding data.

physics.flu-dyn↗

arXiv2020

Characterization of wetting using topological principles

Hypothesis Understanding wetting behavior is of great importance for natural systems and technological applications. The traditional concept of contact angle, a purely geometrical measure related to curvature, is often used for characterizing the wetting state of a system. It can be determined from Young's equation by applying equilibrium thermodynamics. However, whether contact angle is a representative measure of wetting for systems with significant complexity is unclear. Herein, we hypothesize that topological principles based on the Gauss-Bonnet theorem could yield a robust measure to characterize wetting. Theory and Experiments We introduce a macroscopic contact angle based on the deficit curvature of the fluid interfaces that are imposed by contacts with other immiscible phases. We perform sessile droplet simulations followed by multiphase experiments for porous sintered glass and Bentheimer sandstone to assess the sensitivity and robustness of the topological approach and compare the results to other traditional approaches. Findings We show that the presented topological principle is consistent with thermodynamics under the simplest conditions through a variational analysis. Furthermore, we elucidate that at sufficiently high image resolution the proposed topological approach and local contact angle measurements are comparable. While at lower resolutions, the proposed approach provides more accurate results being robust to resolution-based effects. Overall, the presented concepts open new pathways to characterize the wetting state of complex systems and theoretical developments to study multiphase systems.

physics.flu-dyn↗

arXiv2020

ML-LBM: Machine Learning Aided Flow Simulation in Porous Media

Simulation of fluid flow in porous media has many applications, from the micro-scale (cell membranes, filters, rocks) to macro-scale (groundwater, hydrocarbon reservoirs, and geothermal) and beyond. Direct simulation of flow in porous media requires significant computational resources to solve within reasonable timeframes. An integrated method combining predictions of fluid flow (fast, limited accuracy) with direct flow simulation (slow, high accuracy) is outlined. In the tortuous flow paths of porous media, Deep Learning techniques based on Convolutional Neural Networks (CNNs) are shown to give an accurate estimate of the steady state velocity fields (in all axes), and by extension, the macro-scale permeability. This estimate can be used as-is, or as initial conditions in direct simulation to reach a fully accurate result in a fraction of the compute time. A Gated U-Net Convolutional Neural Network is trained on a datasets of 2D and 3D porous media generated by correlated fields, with their steady state velocity fields calculated from direct LBM simulation. Sensitivity analysis indicates that network accuracy is dependent on (1) the tortuosity of the domain, (2) the size of convolution filters, (3) the use of distance maps as input, (4) the use of mass conservation loss functions. Permeability estimation from these predicted fields reaches over 90\% accuracy for 80\% of cases. It is further shown that these velocity fields are error prone when used for solute transport simulation. Using the predicted velocity fields as initial conditions is shown to accelerate direct flow simulation to physically true steady state conditions an order of magnitude less compute time. Using Deep Learning predictions (or potentially any other approximation method) to accelerate flow simulation to steady state in complex pore structures shows promise as a technique push the boundaries fluid flow modelling.

physics.flu-dyn↗

arXiv2020

Physical Accuracy of Deep Neural Networks for 2D and 3D Multi-Mineral Segmentation of Rock micro-CT Images

Segmentation of 3D micro-Computed Tomographic uCT) images of rock samples is essential for further Digital Rock Physics (DRP) analysis, however, conventional methods such as thresholding, watershed segmentation, and converging active contours are susceptible to user-bias. Deep Convolutional Neural Networks (CNNs) have produced accurate pixelwise semantic segmentation results with natural images and $μ$CT rock images, however, physical accuracy is not well documented. The performance of 4 CNN architectures is tested for 2D and 3D cases in 10 configurations. Manually segmented uCT images of Mt. Simon Sandstone are treated as ground truth and used as training and validation data, with a high voxelwise accuracy (over 99%) achieved. Downstream analysis is then used to validate physical accuracy. The topology of each segmented phase is calculated, and the absolute permeability and multiphase flow is modelled with direct simulation in single and mixed wetting cases. These physical measures of connectivity, and flow characteristics show high variance and uncertainty, with models that achieve 95\%+ in voxelwise accuracy possessing permeabilities and connectivities orders of magnitude off. A new network architecture is also introduced as a hybrid fusion of U-net and ResNet, combining short and long skip connections in a Network-in-Network configuration. The 3D implementation outperforms all other tested models in voxelwise and physical accuracy measures. The network architecture and the volume fraction in the dataset (and associated weighting), are factors that not only influence the accuracy trade-off in the voxelwise case, but is especially important in training a physically accurate model for segmentation.

eess.IV↗

arXiv2019

Linking continuum-scale state of wetting to pore-scale contact angles in porous media

Wetting phenomena play a key role in flows through porous media. Relative permeability and capillary pressure-saturation functions show a high sensitivity to wettability, which has different definitions at the continuum- and pore-scale. At the continuum-scale, the state of wetting is defined as Amott-Harvey or USBM (United States Bureau of Mines) by capillary pressure drainage and imbibition cycles. At the pore-scale, the concept of contact angle is used, which until recently was not experimentally possible to determine within an opaque porous medium. Recent progress on measurements of pore-scale contact angles by X-ray computed micro-tomography has therefore attracted significant attention in various research communities. In this work, the Gauss-Bonnet theorem is applied to provide a direct link between capillary pressure saturation $P_c(S_w)$ data and measured distributions of pore-scale contact angles. We propose that the wetting state of a porous medium can be described in terms of geometrical arguments that constrain the morphological state of immiscible fluids. The constraint describes the range of possible contact angles and interfacial curvatures that can exist for a given system. We present measurements in a tested sandstone for which the USBM index, $P_c(S_w)$, and pore-scale contact angles are measured. Additional studies are also performed using two-phase Lattice Boltzmann simulations to test a wider range of wetting conditions. We show that mean pore-scale contact angle measurements can be predicted from petrophysical data within a few differences. This provides a general framework on how continuum-scale data can be used to describe the geometrical state of fluids within porous media.

physics.flu-dyn↗

arXiv2019

Boosting Resolution and Recovering Texture of micro-CT Images with Deep Learning

Digital Rock Imaging is constrained by detector hardware, and a trade-off between the image field of view (FOV) and the image resolution must be made. This can be compensated for with super resolution (SR) techniques that take a wide FOV, low resolution (LR) image, and super resolve a high resolution (HR), high FOV image. The Enhanced Deep Super Resolution Generative Adversarial Network (EDSRGAN) is trained on the Deep Learning Digital Rock Super Resolution Dataset, a diverse compilation 12000 of raw and processed uCT images. The network shows comparable performance of 50% to 70% reduction in relative error over bicubic interpolation. GAN performance in recovering texture shows superior visual similarity compared to SRCNN and other methods. Difference maps indicate that the SRCNN section of the SRGAN network recovers large scale edge (grain boundaries) features while the GAN network regenerates perceptually indistinguishable high frequency texture. Network performance is generalised with augmentation, showing high adaptability to noise and blur. HR images are fed into the network, generating HR-SR images to extrapolate network performance to sub-resolution features present in the HR images themselves. Results show that under-resolution features such as dissolved minerals and thin fractures are regenerated despite the network operating outside of trained specifications. Comparison with Scanning Electron Microscope images shows details are consistent with the underlying geometry of the sample. Recovery of textures benefits the characterisation of digital rocks with a high proportion of under-resolution micro-porous features, such as carbonate and coal samples. Images that are normally constrained by the mineralogy of the rock (coal), by fast transient imaging (waterflooding), or by the energy of the source (microporosity), can be super resolved accurately for further analysis downstream.

eess.IV↗

arXiv2019

Geometric evolution as a source of discontinuous behavior in soft condensed matter

Geometric evolution represents a fundamental aspect of many physical phenomena. In this paper we consider the geometric evolution of structures that undergo topological changes. Topological changes occur when the shape of an object evolves such that it either breaks apart or converges back into itself to form a loop. Changes to the topology of an object are fundamentally discrete events. We consider how discontinuities arise during geometric evolution processes by characterizing the possible topological events and analyzing the associated source terms based on evolution equations for geometric invariants. We show that the discrete nature of a topological change leads to discontinuous source terms that propagate to physical variables.

cond-mat.soft↗