Network model evaluation of permeability and spatial correlation in a real random sphere packing

Flow and transport in porous media are important in many science and engineering applications such as composite materials, subsurface water contamination, packed-bed reactors, and enhanced oil recovery. The general approach to modeling such processes is at the continuum scale. Semi-empirical expressions, such as Darcy's law, are substituted for velocity in the continuity equation, which is then coupled with a momentum, mass, and energy balance. While a continuum approach is acceptable in some cases, additional modeling is required for certain non-linear flows, such as multi-phase flows, inertial flows, non-Newtonian flows, and reactive flows. Pore-scale modeling is a first-principles approach to modeling flow and transport in porous media. In this work, network models that are physically representative of specific unconsolidated media are created. The networks can be used to model a wide range of flows, but the focus here is on polymers and suspensions that exhibit non-Newtonian behavior. The network models are used to model steady flow as well as displacement by less viscous fluids. The transient displacement is used to investigate important viscous fingering patterns. While simple boundary conditions are typically imposed in network modeling (e.g. a pressure gradient in one dimension), a more general approach has been developed where boundary conditions are also imposed by direct coupling to an adjacent continuum region. Important qualitative and quantitative results are obtained from the network model for non-Newtonian fluids. Preferential flow pathways form in the network due to the inherent heterogeneity and interconnectivity in porous media. Quantitative results of Darcy velocity versus applied pressure gradient show different behavior than semi-empirical models (analogous to Darcy's law) for non-Newtonian fluids. The transient displacement patterns for non-Newtonian fluids are also different than for Newtonian fluids. If the fluid exhibits a yield stress, a steady state is reached in which some of the original non-Newtonian fluid is left trapped in the network. The displacement patterns are affected by the boundary conditions, which can be determined from direct coupling to a continuum region.

We explore the relationship between a yield stress fluid flow in a Hele-Shaw cell with irregular walls, and a non-Darcy 2D porous medium flow with limiting pressure gradient. The continuum (Hele-Shaw) flow is a much-studied simplification of a cementing displacement flow model, solved via a variational formulation that leads to a convex streamfunction minimization problem. Our interest is with the analogy between the discretization used for the numerical solution and network flows that model the associated porous media flow, i.e. via the pore-throat approach. A staggered mesh, with pressure nodes at the cell corners and streamfunction nodes at the cell center is used for the continuum problem, which naturally separates into a network representation comprising primal and dual graphs, linking streamfunction and pressure nodes, respectively. We show explicitly how the continuum model defines a network model and vice versa. We develop the variational form of the network flow, including an appropriate (discrete) streamfunction minimization and a discrete version of the principle of virtual work. Two network models are explored, based on different interpretations of the minimization problem. The network flow results are compared with analogous computed continuum flow results in 3 specific geometries. We find that our network model I, which is the most natural interpretation of the continuum model as a network flow using our discretization, generally under-predicts flow rates. This is problematic from the perspective of considering the network flow as an approximation to the porous media or Hele-Shaw flow. Network model II rectifies this situation, via a pressure interpolation method. In our examples we find that the network II flow converges to the continuum flow as the mesh and network are refined. This is not the usual comparison made, as in many pore-throat models the network is fixed according to the underlying pore-space geometry. Despite the differences, both network models have their own advantages and disadvantages. Network model I offers a more natural way of modelling the flow and is easier to apply, for example to complex meshes, e.g. unstructured triangular. Network model II gives the more accurate physical representation of the Hele-Shaw flow. Lastly, we have developed approximate algebraic relationships for the total flow rate as a function of the total applied pressure gradient, both close to the critical onset pressure and for large pressure gradients. These correlations align well with previous findings for Bingham fluid flows in porous media. • Hele-Shaw cell – porous media analogy derived for Herschel-Bulkley fluids. • Discrete pore-throat network models derived. • Discrete principle of virtual work. • Convergence as network is refined. • Improved network model that gives convergence.

Review on subsurface colloids and colloid-associated contaminant transport in saturated porous media

Prediction of imbibition from grain-scale interface movement

Semi-quantitative multiscale modelling and flow simulation in a nanoscale porous system of shale

Anomalous transport in porous media is commonly believed to be induced by the highly complex pore space geometry. However, this phenomenon is also observed in porous media with rather simple pore structure. In order to answer how ubiquitous can anomalous transport be in porous media, we in this work systematically investigate the solute transport process in a simple porous medium model with minimal structural randomness. The porosities we consider range widely from 0.30 up to 0.85, and we find by lattice Boltzmann simulations that the solute transport process can be anomalous in all cases at high Péclet numbers. We use the continuous time random walk theory to quantitatively explain the observed scaling relations of the process. A plausible hydrodynamic origin of anomalous transport in simple porous media is proposed as a complement to its widely accepted geometric origin in complex porous media. Our results, together with previous findings, provide evidence that anomalous transport is indeed ubiquitous in porous media. Consequently, attentions should be paid when modelling solute transport by the classical advection-diffusion equation, which could lead to systematic error.

We demonstrate a novel experimental arrangement for measuring wind turbulence‐induced gas transport in dry porous media under controlled conditions. This equipment was applied to assess the effect of wind turbulence on gas transport (quantified as a dispersion coefficient) as a function of distance to the surface of the porous medium exposed to wind. Two different strategies for the measurement of wind‐induced gas transport were compared. Experiments were carried out with O 2 and CO 2 as tracer gases with average vertical wind speeds of 0.02–1.06 m s −1 . Oxygen breakthrough curves as a function of distance to the wind‐exposed surface of the porous medium were analysed numerically with a finite‐difference‐based model to assess gas transport. We showed that wind turbulence‐induced gas transport is an important transport mechanism that can be 20–70 times larger than molecular diffusion‐induced transport. Wind conditions and properties of the porous medium had strong controlling effects on this relationship. Importantly, we show that even though wind‐induced gas transport is greatest near to the wind‐exposed surface, it can have marked effects on the variation in gas concentration at much greater depths. Highlights We explored the effect of atmospheric wind turbulence on gas transport in porous media. We measured the depth relation of wind‐induced dispersion in porous media for real wind conditions. Wind‐induced gas dispersion coefficients were 20–70 times larger than molecular diffusion. Wind turbulence can potentially have a considerable effect on gas transport in porous media.

Pore-scale study of effects of macroscopic pores and their distributions on reactive transport in hierarchical porous media

Electroencephalogram based communication system for locked in state person using mentally spelled tasks with optimized network model

The paper presents an image-based network model of retinal vasculature taking account of the 3D vascular distribution of the retina. Mouse retinas were prepared using flat-mount technique and vascular images were obtained using confocal microscopy. The vascular morphometric information obtained from confocal images was used for the model development. The network model developed directly represents the vascular geometry of all the large vessels of the arteriolar and venular trees and models the capillaries using uniformly distributed meshes. The vasculatures in different layers of the retina, namely the superficial, intermediate and deep layer, were modelled separately in the network and were linked through connecting vessels. The branching data of the vasculatures was recorded using the method of connectivity matrix of network (the graph theory). Such an approach is able to take into account the detailed vasculature of individual retinas concerned. Using such network model, circulation analyses to predict the spatial distribution of the pressure, flow, hematocrit, apparent viscosity and wall shear stress in the entire retinal vasculature can be carried out.KeywordsMurine retinanetwork topologymorphological datanetwork modelspatial pressureflowratevelocitywall shear stress

Random packing of equal spheres

In order to solve the problem of excessive parameters and slow computing speed of classical neural networks, this paper uses the powerful parallel computing power of quantum computing to improve the computing speed of classical neural network models, and proposes a hybrid continuous variational quantum neural network (HCVQNN) model that can be used for network intrusion detection. The continuous variable layer of the model is realized through Gaussian gate and non-Gaussian gate, in which Gaussian gate performs operations such as quantum state weight addition and offset term setting, and non-Gaussian gate performs nonlinear operations, thereby improving the overall expression ability of the network model. In addition, aiming at the unbalanced problem of UNSW-NB15 in the network intrusion dataset, this paper proposes to design the algorithm from the feature level and the algorithm level, using the ReliefF algorithm for feature selection at the feature level, and oversampling and undersampling processing at the algorithm level by combining the Borderline-SMOTE algorithm and GMM algorithm. The classification experimental results on the UNSW-NB15 network intrusion dataset show that compared with the other two network models, the HCVQNN network model obtains higher classification accuracy and lower loss function value in both binary classification and multi-classification tasks, and the classification accuracy for minority categories is also improved.

Optimization of Artificial Neural Network (ANN) model design for prediction of macroinvertebrates in the Zwalm river basin (Flanders, Belgium)

Impact of biofilm on bacterial transport and deposition in porous media

As the metaverse continues to expand, it becomes increasingly critical to have human-centric networks that are both efficient and high-performing to optimize the user experience. Network modeling plays a fundamental role in optimizing and allocating resources efficiently, and configuring networks to satisfy the demands of diverse applications and users. Recently, traditional queuing theory-based approaches to network modeling have given way to machine learning-based methods. These methods rely on vast amounts of data for building precise models. Although high-precision simulators are ubiquitous, data collection is still an expensive and time-consuming process, resulting in a data bottleneck. In this paper, we propose a weakly supervised learning approach to modeling networks for human-centric networking in the metaverse. Specifically, we identify that queuing theory-based labels can be used to design the supervision signal at a very low cost. Therefore, we propose an approach that combines the inaccurate network modeling obtained from queuing theory-based approaches with an efficient and precise network model through only a small amount of simulation data. To make it a reality, we propose a novel neural network model that combines the powerful graph neural network and transformers. Additionally, we propose several additional supervision signals and a training algorithm to build a better network model. Experimental results demonstrate that our approach reduces the burden of data collection while achieving prediction accuracy comparable to results from large amounts of expensive simulation data. Furthermore, our approach exhibits superior generalization ability.