Evaluation of Model Concepts to Describe Water Transport in Shallow Subsurface Soil and Across the Soil–Air Interface

Soil water evaporation plays a critical role in mass and energy exchanges across the land–atmosphere interface. Although much is known about this process, there is no agreement on the best modeling approaches to determine soil water evaporation due to the complexity of the numerical modeling scenarios and lack of experimental data available to validate such models. Existing studies show numerical and experimental discrepancies in the evaporation behavior and soil water distribution in soils at various scales, driving us to revisit the key process representation in subsurface soil. Therefore, the goal of this work is to test different mathematical formulations used to estimate evaporation from bare soils to critically evaluate the model formulations, assumptions and surface boundary conditions. This comparison required the development of three numerical models at the REV scale that vary in their complexity in characterizing water flow and evaporation, using the same modeling platform. The performance of the models was evaluated by comparing with experimental data generated from a soil tank/boundary layer wind tunnel experimental apparatus equipped with a sensor network to continuously monitor water–temperature–humidity variables. A series of experiments were performed in which the soil tank was packed with different soil types. Results demonstrate that the approaches vary in their ability to capture different stages of evaporation and no one approach can be deemed most appropriate for every scenario. When a proper top boundary condition and space discretization are defined, the Richards equation-based models (Richards model and Richards vapor model) can generally capture the evaporation behaviors across the entire range of soil saturations, comparing well with the experimental data. The simulation results of the non-equilibrium two-component two-phase model which considers vapor transport as an independent process generally agree well with the observations in terms of evaporation behavior and soil water dynamics. Certain differences in simulation results can be observed between equilibrium and non-equilibrium approaches. Comparisons of the models and the boundary layer formulations highlight the need to revisit key assumptions that influence evaporation behavior, highlighting the need to further understand water and vapor transport processes in soil to improve model accuracy.

     

Modeling of Langmuir Circulation: Triple Decomposition of the Craik–Leibovich Model

Turbulent shear flows on shallow continental shelves (here shallow means that the interaction with the solid, no-slip bottom is important) are of great importance because of their role in vertical mixing as well as on the transport of sediment and bioactive material. The presence of a wavefield in these areas can lead to the appearance of Langmuir circulation which is known to strongly affect the dynamics of a turbulent flow. To investigate those dynamical effects within a RANS-type modeling framework, we apply a triple decompostion to the LES results of Langmuir circulation in order to further isolate the coherent structures from fluctuating velocity field. The results are compared to the classical double-decomposition. In contrast to the double-decomposition framework, the triple-decompostion more effectively educes the coherent structure field and quantifies the need to take into account the energy exchange between the coherent and random fluctuations as well as the overall impact of the coherent structures on the turbulence dynamics.     

Poiseuille-Number-Based Kozeny–Carman Model for Computation of Pore Shape Factors on Arbitrary Cross Sections

Porous media characterization is crucial to engineering projects where the pore shape has impact on performance gains. Membrane filters, sportswear fabrics, and tertiary oil recovery are a few examples. Kozeny–Carman (K–C) models are one of the most frequently used to understand, for instance, the relation between porosity, permeability, and other small-scale parameters. However, they have limitations, such as the inability to capture the correct dependence of permeability on porosity, the imperfect handling of the linear and nonlinear effects yielded by its fundamental quantities, and the insufficiency of geometrical parameters to predict the permeability correctly. In this paper, we cope with the problem of determining shape factors for generic geometries that represent sundry porous media configurations. Specifically, we propose a method that embeds the Poiseuille number into the classical K–C equation and returns a substitute shape factor term for its original counterpart. To the best of our knowledge, the existing formulations are unable to obtain shape factors for pores whose geometry is beyond the regular ones. We apply a Galerkin-based integral (GBI) method that determines shape factors for generic cross sections of pore channels. The approach is tested on straight capillaries with arbitrary cross sections subject to steady single-phase flow under the laminar regime. We show that shape factors for basic geometries known from experimental results are replicable exactly. Besides, we provide shape factors with precision up to 4 digits for a class of geometries of interest. As a way to demonstrate the applicability of the GBI approach, we report a case study that determines shape factors for 19 generic individual pore sections of a laboratory experiment involving flow rate measurements in an industrial arrangement of a water-agar packed bed. Porosity, flow behavior, and velocity distributions determined numerically achieve a narrow agreement with experimental values. The findings of this study provide parameters that can help to design new devices or mechanisms that depend on arbitrary pore shapes, as well as to characterize fluid flows in heterogeneous porous media.

     

Analytical Modeling of Flow Behavior for Wormholes in Naturally Fractured–Vuggy Porous Media

Acidizing technology has been widely applied when developing naturally fractured–vuggy reservoirs. So testing and evaluating acidizing wells’ pressure behavior become necessary for further improving the wells’ performance. Analyzing transient pressure data can estimate some key reservoir parameters. Generally speaking, carbonate minerals are usually composed of dolomite and calcite which are easy to be dissolved by hydrochloric acid which is often used to react with the rock to create a high conductivity channel, namely wormhole. Pressure transient behavior in fractured–vuggy reservoirs has been studied for many years; however, the models of acidizing wells with wormholes were not reported in previous studies. This article presented an analytical model for wormholes in naturally fractured–vuggy carbonate reservoirs, and wormholes solutions were obtained through point sink integral method. The results were validated accurately by comparing with previous results and numerical simulation. Then in this paper, type curves were established to recognize the flow characteristics, and flow was divided into six flow regimes comprehensively. The calculative results showed that the characteristics of type curves were influenced by inter-porosity flow factor, wormhole number, fluids capacitance coefficient. We also showed that the pressure behavior was affected by the angles between wormholes, and the pressure depletion increased as the angle decreased, because the wormholes were closer, their interaction became stronger. At the end, a reservoir example was showed to demonstrate the methodology of new type curve analysis.     

Mathematical–Physical Reappraisal of Archie's First Equation on the Basis of a Statistical Network Model

Knowledge of the geometrical properties of porous rocks is crucial for the evaluation of their hydrocarbon potential. A major problem in quantitative formation evaluation is to provide a physical basis of Archie's equations first published in 1942, which are widely used in formation evaluation and are believed to reflect this knowledge empirically. Our study, a theoretical model-based approach, provides a physical basis of Archie's first equation (Archie I) and puts it up for scientific discussion. We employ the statistical network model theory of Schopper, and take sedimentation and favorable diagenetic conditions restricted to compaction into account. We find that compaction is a prominent geological feature that needs to be considered and quantified in order to establish a physical basis of Archie I. Our interpretation of Archie I – that it measures in relative terms – is in agreement with this finding, but not in line with the mainstream view, which interprets Archie I in absolute terms. Evidence suggests that compaction may also provide the overarching physical basis to address within-well integration of borehole–geophysical data (including resistivity data) as well as their integration across spatial scales from well-to-well and beyond. Although our more consistent understanding of Archie's first equation clearly helps to advance today's evaluation of resistivity logs, the gain in evaluating these logs is still not satisfactory.     

A Novel Method for Gas–Water Relative Permeability Measurement of Coal Using NMR Relaxation

Using the conventional volumetric method in unsteady-state relative permeability measurements for unconventional gas reservoirs, such as coal and gas shale, is a significant challenge because the movable water volume in coal or shale is too small to be detected. Moreover, the dead volume in the measurement system adds extra inaccuracy to the displaced water determination. In this study, a low-field nuclear magnetic resonance (NMR) spectrometer was introduced into a custom-built relative permeability measurement apparatus, and a new method was developed to accurately quantify the displaced water, avoiding the drawback of the dead volume. The changes of water in the coal matrix and cleats were monitored during the unsteady-state displacement experiments. Relative permeability curves for two Chinese anthracite and bituminous coals were obtained, matching the existing research results from the Chinese coalbed methane area. Moreover, the influences of confining pressure on the shape of the relative permeability curve were evaluated. Although uncertainties and limits exist, the NMR-based method is a practical and applicable method to evaluate the gas/water relative permeability of ultra-low permeability rocks.     

Simulation of Structure Change in Porous Media During Gas–Solid Reactions Using Cellular Automata Model

Transport in Porous Media - In some gas–solid reactions, a new solid substance is produced. The product acts as a shield and prevents the collision between gas and solid reactants which...     

Application of an Explicit Algebraic Reynolds Stress Model within a Hybrid LES–RANS Method

Large-eddy simulations (LES) still suffer from extremely large resources required for the resolution of the near-wall region, especially for high-Re flows. That is the main motivation for setting up hybrid LES–RANS methods. Meanwhile a variety of different hybrid concepts were proposed mostly relying on linear eddy-viscosity models. In the present study a hybrid approach based on an explicit algebraic Reynolds stress model (EARSM) is suggested. The model is applied in the RANS mode with the aim of accounting for the Reynolds stress anisotropy emerging especially in the near-wall region. For the implementation into a CFD code this anisotropy-resolving closure can be formally expressed in terms of a non-linear eddy-viscosity model (NLEVM). Its extra computational effort is small, still requiring solely the solution of one additional transport equation for the turbulent kinetic energy. In addition to this EARSM approach, a linear eddy-viscosity model (LEVM) is used in order to verify and emphasize the advantages of the non-linear model. In the present formulation the predefinition of RANS and LES regions is avoided and a gradual transition between both methods is assured. A dynamic interface criterion is suggested which relies on the modeled turbulent kinetic energy and the wall distance and thus automatically accounts for the characteristic properties of the flow. Furthermore, an enhanced version guaranteeing a sharp interface is proposed. The interface behavior is thoroughly investigated and it is shown how the method reacts on dynamic variations of the flow field. Both model variants, i.e. LEVM and EARSM, have been tested on the basis of the standard plane channel flow and even more detailed on the flow over a periodic arrangement of hills using fine and coarse grids.     

Modeling and simulation of a compact push–pull rubber actuator energized by an outer coil of shape memory wire

This paper introduces the concept and develops the theory for a push–pull actuator made by winding a thin shape memory wire on a solid rubber cylinder. The incompressibility of the rubber converts the thermomechanical contraction of the heated wire in twice as much axial strain available in the rubber core. The intrinsic elastic backup provided by the core allows push–pull action of the device. Based on the assumption of both material and geometric linearity, a simple theoretical model is developed, which culminates in a simple closed-form equation for the output stroke of the actuator. The theoretical predictions closely agree with refined finite element simulations, anticipating a net stroke of about 5–6% of the overall actuator length, depending on the outer load applied. The working principle of the actuator and the accuracy of the model are validated by tests on a proof-of-concept prototype.     

Numerical Simulation of Delft-Jet-in-Hot-Coflow (DJHC) Flames Using the Eddy Dissipation Concept Model for Turbulence–Chemistry Interaction

In this paper, we report results of a numerical investigation of turbulent natural gas combustion for a jet in a coflow of lean combustion products in the Delft-Jet-in-Hot-Coflow (DJHC) burner which emulates MILD (Moderate and Intense Low Oxygen Dilution) combustion behavior. The focus is on assessing the performance of the Eddy Dissipation Concept (EDC) model in combination with two-equation turbulence models and chemical kinetic schemes for about 20 species (Correa mechanism and DRM19 mechanism) by comparing predictions with experimental measurements. We study two different flame conditions corresponding to two different oxygen levels (7.6% and 10.9% by mass) in the hot coflow, and for two jet Reynolds number (Re = 4,100 and Re = 8,800). The mean velocity and turbulent kinetic energy predicted by different turbulence models are in good agreement with data without exhibiting large differences among the model predictions. The realizable k-ε model exhibits better performance in the prediction of entrainment. The EDC combustion model predicts too early ignition leading to a peak in the radial mean temperature profile at too low axial distance. However the model correctly predicts the experimentally observed decreasing trend of lift-off height with jet Reynolds number. A detailed analysis of the mean reaction rate of the EDC model is made and as possible cause for the deviations between model predictions and experiments a low turbulent Reynolds number effect is identified. Using modified EDC model constants prediction of too early ignition can be avoided. The results are weakly sensitive to the sub-model for laminar viscosity and laminar diffusion fluxes.     

Distinguishing Features of One Model of an Elastic Solid Associated with the Long–Range Interaction at the Molecular Level

A model of an elastic solid in the form of a system of elastically connected rigid elements is proposed. It is shown that the long–range interaction should be taken into account. The mathematical model proposed is, in essence, the physical model of a solid, which substantially broadens the range of its application.     

Onset of Darcy–Brinkman Ferroconvection in a Rotating Porous Layer Using a Thermal Non-Equilibrium Model: A Nonlinear Stability Analysis

This article presents a nonlinear stability analysis of a rotating thermoconvective magnetized ferrofluid layer confined between stress-free boundaries using a thermal non-equilibrium model by the energy method. The effect of interface heat transfer coefficient ( H^￠){( {{\mathcal H}^{\prime}})}, magnetic parameter (M ₃), Darcy–Brinkman number ( [^(D)]a){( {\hat{{\rm D}}{\rm a}})}, and porosity modified conductivity ratio (γ′) on the onset of convection in the presence of rotation (T_A1){({T_{{\rm A}_1}})} have been analyzed. The critical Rayleigh numbers predicted by energy method are smaller than those calculated by linear stability analysis and thus indicate the possibility of existence of subcritical instability region for ferrofluids. However, for non-ferrofluids stability and instability boundaries coincide. Asymptotic analysis for both small and large values of interface heat transfer coefficient (H^￠){({{\mathcal H}^{\prime}})} is also presented. A good agreement is found between the exact solutions and asymptotic solutions.     

Linear and Weakly Nonlinear Stability Analyses of Two-Dimensional,Steady Brinkman–Bénard Convection Using Local Thermal Non-equilibrium Model

Effect of local thermal non-equilibrium (LTNE) on onset of Brinkman–Bénard convection and on heat transport is investigated. Rigid–rigid and free–free, isothermal boundaries are considered for investigation. The assumption of LTNE leads to an ‘advanced onset’ situation compared to that predicted by the local thermal equilibrium (LTE) assumption. This results in the ‘enhanced heat transport’ situation in the problem. Asymptotic analysis for small and large values of inter-phase heat transfer coefficient is also carried out on critical Rayleigh number, critical wave number and Nusselt number. In respect of boundary influences on onset and heat transport, it is found that classical results hold even under the LTNE assumption. The other parameters’ influences on onset and heat transport are qualitatively similar in LTNE and LTE cases.     

Existence of a Weak Solution to a Nonlinear Fluid–Structure Interaction Problem Modeling the Flow of an Incompressible, Viscous Fluid in a Cylinder with Deformable Walls

We study a nonlinear, unsteady, moving boundary, fluid–structure interaction (FSI) problem arising in modeling blood flow through elastic and viscoelastic arteries. The fluid flow, which is driven by the time-dependent pressure data, is governed by two-dimensional incompressible Navier–Stokes equations, while the elastodynamics of the cylindrical wall is modeled by the one-dimensional cylindrical Koiter shell model. Two cases are considered: the linearly viscoelastic and the linearly elastic Koiter shell. The fluid and structure are fully coupled (two-way coupling) via the kinematic and dynamic lateral boundary conditions describing continuity of velocity (the no-slip condition), and the balance of contact forces at the fluid–structure interface. We prove the existence of weak solutions to the two FSI problems (the viscoelastic and the elastic case) as long as the cylinder radius is greater than zero. The proof is based on a novel semi-discrete, operator splitting numerical scheme, known as the kinematically coupled scheme, introduced in Guidoboni et al. (J Comput Phys 228(18):6916–6937, 2009) to numerically solve the underlying FSI problems. The backbone of the kinematically coupled scheme is the well-known Marchuk–Yanenko scheme, also known as the Lie splitting scheme. We effectively prove convergence of that numerical scheme to a solution of the corresponding FSI problem.     

Comparison Between Equivalent Continuum and Discrete Crack Models of Transient Radon Transport at the Soil–Building Foundation Crack Interface Using TOUGH2/EOS7Rn

In the framework of radon risk management in France, it is necessary to enhance knowledge on radon transfer from its source to exposure areas (e.g., buildings) by developing simple, accurate, numerical models for transient radon transport in three-dimensional (3D) unsaturated porous materials. The equivalent continuum model (ECM) of flow and transport at the interface between the soil and cracks (fissures) in a building foundation (e.g., slab on grade, basement) is attractive, since equivalent (effective) continuum properties assigned to model cells can represent the combined effect of individual cracks and solid matrix of the cracked concrete of the foundation (slab and blocks walls). Although the ECM approach based on the volume averaging method has been used to model flow and transport through cracks at the soil–building interface, it has never been verified numerically. Thus, the goal of the present work is to develop an ECM using this averaging method and to quantify its uncertainties based on its comparison to an accurate numerical discrete crack model (DCM) for flow and transport in the crack. As a first step, the DCM implemented in the TOUGH2/EOS7Rn module has been verified numerically through a comparison to a reference 3D steady-state numerical solution for radon transport into a house with basement under constant negative pressure. Then, 3D results of the DCM and ECM approaches were compared, under time-dependent indoor–outdoor pressure differentials conditions, for two crack line configurations in the basement slab floor and two different soil configurations with different soil permeability and radium \(^{226}\)Ra mass content values. Results of this comparison show that, for a homogeneous soil configuration, discrepancies between ECM and DCM simulated indoor radon activity concentrations decrease with the increase in soil permeability, regardless crack line configuration in the slab floor and soil radium mass content. However, ECM uncertainties were not within the range of absolute errors on measured radon concentration for the higher soil permeability \((1\times 10^{-9}, 1\times 10 ^{-8} \hbox { m}^{2})\) and the higher \(^{226}\hbox {Ra}\) mass content values (4500 \(\hbox {Bq\;kg}^{-1})\), especially for high radon pics induced by sudden increase in indoor air pressure drop. Regardless soil \(^{226}\hbox {Ra}\) mass content and crack line configuration in the slab floor, the ECM showed to be conservative for the two-layered soil configuration with the presence of aggregates beneath the slab foundation, generally practiced in buildings constructions.     

Heating and Melting of Asphalt–Paraffin Plugs in Oil‐Well Equipment Using an Electromagnetic Radiation Source Operating in a Periodic Mode

This paper considers the elimination of asphalt–paraffin plugs in wellbore equipment using a highfrequency radiation source which is energized and deenergized periodically. The dynamics of melting of plugs is analyzed numerically. The time of removal of plugs is determined with variation in the offduty ratio of the operating cycle of the highfrequency oscillator and the time of its continuous operation in a cycle.     

Stress Dependency of Permeability Represented by an Elastic Cylindrical Pore-Shell Model: Comment on Zhu et al. (Transp Porous Med (2018) 122:235–252)

Transport in Porous Media - Stress dependency of permeability of porous rocks is described by means of a theoretical elastic cylindrical pore-shell model. This model is developed based on a bundle...