Analysis of 'Investigating an extended multiphase flow model that includes specific interfacial area', Computer Methods in Applied Mechanics and Engineering, 418:116594, 2024.

Comments are provided on the recent paper by Ebadi et al. [3], which demonstrates that the formulated model that was solved contains misconceptions or errors that render the work unsuitable for describing the evolution of interfacial areas in two-fluid porous medium systems. The need for kinematic equations is described and components of a theoretically consistent approach are summarized.

Thermodynamically Constrained Averaging Theory: Principles, Model Hierarchies, and Deviation Kinetic Energy Extensions.

The thermodynamically constrained averaging theory (TCAT) is a comprehensive theory used to formulate hierarchies of multiphase, multiscale models that are closed based upon the second law of thermodynamics. The rate of entropy production is posed in terms of the product of fluxes and forces of dissipative processes. The attractive features of TCAT include consistency across disparate length scales; thermodynamic consistency across scales; the inclusion of interfaces and common curves as well as phases; the development of kinematic equations to provide closure relations for geometric extent measures; and a structured approach to model building. The elements of the TCAT approach are shown; the ways in which each of these attractive features emerge from the TCAT approach are illustrated; and a review of the hierarchies of models that have been formulated is provided. Because the TCAT approach is mathematically involved, we illustrate how this approach can be applied by leveraging existing components of the theory that can be applied to a wide range of applications. This can result in a substantial reduction in formulation effort compared to a complete derivation while yielding identical results. Lastly, we note the previous neglect of the deviation kinetic energy, which is not important in slow porous media flows, formulate the required equations to extend the theory, and comment on applications for which the new components would be especially useful. This work should serve to make TCAT more accessible for applications, thereby enabling higher fidelity models for applications such as turbulent multiphase flows.

Averaging Theory for Description of Environmental Problems: What Have We Learned?

Advances in Water Resources has been a prime archival source for implementation of averaging theories in changing the scale at which processes of importance in environmental modeling are described. Thus in celebration of the 35th year of this journal, it seems appropriate to assess what has been learned about these theories and about their utility in describing systems of interest. We review advances in understanding and use of averaging theories to describe porous medium flow and transport at the macroscale, an averaged scale that models spatial variability, and at the megascale, an integral scale that only considers time variation of system properties. We detail physical insights gained from the development and application of averaging theory for flow through porous medium systems and for the behavior of solids at the macroscale. We show the relationship between standard models that are typically applied and more rigorous models that are derived using modern averaging theory. We discuss how the results derived from averaging theory that are available can be built upon and applied broadly within the community. We highlight opportunities and needs that exist for collaborations among theorists, numerical analysts, and experimentalists to advance the new classes of models that have been derived. Lastly, we comment on averaging developments for rivers, estuaries, and watersheds.

A continuum mechanical framework for modeling tumor growth and treatment in two- and three-phase systems.

The growth and treatment of tumors is an important problem to society that involves the manifestation of cellular phenomena at length scales on the order of centimeters. Continuum mechanical approaches are being increasingly used to model tumors at the largest length scales of concern. The issue of how to best connect such descriptions to smaller-scale descriptions remains open. We formulate a framework to derive macroscale models of tumor behavior using the thermodynamically constrained averaging theory (TCAT), which provides a firm connection with the microscale and constraints on permissible forms of closure relations. We build on developments in the porous medium mechanics literature to formulate fundamental entropy inequality expressions for a general class of three-phase, compositional models at the macroscale. We use the general framework derived to formulate two classes of models, a two-phase model and a three-phase model. The general TCAT framework derived forms the basis for a wide range of potential models of varying sophistication, which can be derived, approximated, and applied to understand not only tumor growth but also the effectiveness of various treatment modalities.

TCAT Analysis of Capillary Pressure in Non-equilibrium, Two-fluid-phase, Porous Medium Systems.

Standard models of flow of two immiscible fluids in a porous medium make use of an expression for the dependence of capillary pressure on the saturation of a fluid phase. Data to support the mathematical expression is most often obtained through a sequence of equilibrium experiments. In addition to such expressions being hysteretic, recent experimental and theoretical studies have suggested that the equilibrium functional forms obtained may be inadequate for modeling dynamic systems. This situation has led to efforts to express relaxation of a system to an equilibrium capillary pressure in relation to the rate of change of saturation. Here, based on insights gained from the thermodynamically constrained averaging theory (TCAT) we propose that dynamic processes are related to changes in interfacial area between phases as well as saturation. A more complete formulation of capillary pressure dynamics is presented leading to an equation that is suitable for experimental study.

Thermodynamically Constrained Averaging Theory Approach for Modeling Flow and Transport Phenomena in Porous Medium Systems: 8. Interface and Common Curve Dynamics.

This work is the eighth in a series that develops the fundamental aspects of the thermodynamically constrained averaging theory (TCAT) that allows for a systematic increase in the scale at which multiphase transport phenomena is modeled in porous medium systems. In these systems, the explicit locations of interfaces between phases and common curves, where three or more interfaces meet, are not considered at scales above the microscale. Rather, the densities of these quantities arise as areas per volume or length per volume. Modeling of the dynamics of these measures is an important challenge for robust models of flow and transport phenomena in porous medium systems, as the extent of these regions can have important implications for mass, momentum, and energy transport between and among phases, and formulation of a capillary pressure relation with minimal hysteresis. These densities do not exist at the microscale, where the interfaces and common curves correspond to particular locations. Therefore, it is necessary for a well-developed macroscale theory to provide evolution equations that describe the dynamics of interface and common curve densities. Here we point out the challenges and pitfalls in producing such evolution equations, develop a set of such equations based on averaging theorems, and identify the terms that require particular attention in experimental and computational efforts to parameterize the equations. We use the evolution equations developed to specify a closed two-fluid-phase flow model.

Thermodynamically Constrained Averaging Theory Approach for Modeling Flow and Transport Phenomena in Porous Medium Systems: 7. Single-Phase Megascale Flow Models.

This work is the seventh in a series that introduces and employs the thermodynamically constrained averaging theory (TCAT) for modeling flow and transport in multiscale porous medium systems. This paper expands the previous analyses in the series by developing models at a scale where spatial variations within the system are not considered. Thus the time variation of variables averaged over the entire system is modeled in relation to fluxes at the boundary of the system. This implementation of TCAT makes use of conservation equations for mass, momentum, and energy as well as an entropy balance. Additionally, classical irreversible thermodynamics is assumed to hold at the microscale and is averaged to the megascale, or system scale. The fact that the local equilibrium assumption does not apply at the megascale points to the importance of obtaining closure relations that account for the large-scale manifestation of small-scale variations. Example applications built on this foundation are suggested to stimulate future work.

Thermodynamically Constrained Averaging Theory Approach for Modeling Flow and Transport Phenomena in Porous Medium Systems: 5. Single-Fluid-Phase Transport.

This work is the fifth in a series of papers on the thermodynamically constrained averaging theory (TCAT) approach for modeling flow and transport phenomena in multiscale porous medium systems. The general TCAT framework and the mathematical foundation presented in previous works are used to develop models that describe species transport and single-fluid-phase flow through a porous medium system in varying physical regimes. Classical irreversible thermodynamics formulations for species in fluids, solids, and interfaces are developed. Two different approaches are presented, one that makes use of a momentum equation for each entity along with constitutive relations for species diffusion and dispersion, and a second approach that makes use of a momentum equation for each species in an entity. The alternative models are developed by relying upon different approaches to constrain an entropy inequality using mass, momentum, and energy conservation equations. The resultant constrained entropy inequality is simplified and used to guide the development of closed models. Specific instances of dilute and non-dilute systems are examined and compared to alternative formulation approaches.

Thermodynamically Constrained Averaging Theory Approach for Modeling Flow and Transport Phenomena in Porous Medium Systems: 4. Species Transport Fundamentals.

This work is the fourth in a series of papers on the thermodynamically constrained averaging theory (TCAT) approach for modeling flow and transport phenomena in multiscale porous medium systems. The general TCAT framework and the mathematical foundation presented in previous works are built upon by formulating macroscale models for conservation of mass, momentum, and energy, and the balance of entropy for a species in a phase volume, interface, and common curve. In addition, classical irreversible thermodynamic relations for species in entities are averaged from the microscale to the macroscale. Finally, we comment on alternative approaches that can be used to connect species and entity conservation equations to a constrained system entropy inequality, which is a key component of the TCAT approach. The formulations detailed in this work can be built upon to develop models for species transport and reactions in a variety of multiphase systems.

Dental caries trends in primary teeth among third-grade children in Harris County, Texas.

PURPOSE: The purpose of this study was to assess trends in dental caries in the primary dentition of third-grade children in suburban Harris County, Texas. METHODS: The study populations for the 2 cross-sectional surveys consisted of 1,584 third-grade children in 1991 and 1,039 in 1998. Trained dentists collected data on decayed and filled tooth surfaces (dfs). Chi-square tests analyzed the differences in proportions of children with and without dental caries experience in 1991 and 1998 by demographic subgroups: (1) gender; (2) ethnicity; and (3) socioeconomic status (SES). Student's t test investigated the differences in mean dfs scores in subgroups. RESULTS: The prevalence of caries decreased significantly from 59% to 54% between 1991 and 1998 (P = .01). The caries prevalence was lower in 1998 than 1991 in certain subgroups: 1) females; 2) Caucasians; and 3) low SES. The mean dfs score decreased significantly from 4.81 to 3.16, and lower dfs scores were seen in certain demographic subgroups between the 2 studies (P < .05). Children from a low SES had high levels of untreated caries in both studies. CONCLUSIONS: Despite a decline in primary teeth caries of study participants, intergroup disparities exist, emphasizing the need for preventive strategies, especially for the low SES children.

Influence of phase connectivity on the relationship among capillary pressure, fluid saturation, and interfacial area in two-fluid-phase porous medium systems.

Multiphase flows in porous medium systems are typically modeled at the macroscale by applying the principles of continuum mechanics to develop models that describe the behavior of averaged quantities, such as fluid pressure and saturation. These models require closure relations to produce solvable forms. One of these required closure relations is an expression relating the capillary pressure to fluid saturation and, in some cases, other topological invariants such as interfacial area and the Euler characteristic (or average Gaussian curvature). The forms that are used in traditional models, which typically consider only the relationship between capillary pressure and saturation, are hysteretic. An unresolved question is whether the inclusion of additional morphological and topological measures can lead to a nonhysteretic closure relation. Relying on the lattice Boltzmann (LB) method, we develop an approach to investigate equilibrium states for a two-fluid-phase porous medium system, which includes disconnected nonwetting phase features. A set of simulations are performed within a random close pack of 1964 spheres to produce a total of 42 908 distinct equilibrium configurations. This information is evaluated using generalized additive models to quantitatively assess the degree to which functional relationships can explain the behavior of the equilibrium data. The variance of various model estimates is computed, and we conclude that, except for the limiting behavior close to a single fluid regime, capillary pressure can be expressed as a deterministic and nonhysteretic function of fluid saturation, interfacial area between the fluid phases, and the Euler characteristic. To our knowledge, this work is unique in the methods employed, the size of the data set, the resolution in space and time, the true equilibrium nature of the data, the parametrizations investigated, and the broad set of functions examined. The conclusion of essentially nonhysteretic behavior provides support for an evolving class of two-fluid-phase flow in porous medium systems models.

Stability of a fluid-fluid interface in a biconical pore segment.

Pore networks that include biconical pore segments are frequently used to model two-phase flow. In this work, we describe in detail the displacement of a fluid-fluid interface in such a pore segment. We assume sharp edges in the throat, inlet, and outlet of the pore segment to be the limiting cases of round edges, the radii of which vanish. We account for interfacial and lineal tensions that cause nonconstant contact angles. For zero lineal tension, we provide analytical solutions for flow induced by changing infinitesimally slowly either capillary pressure or the volume of one fluid. In diverging and converging cones, the common line among the two fluids and the solid phase slides while it is pinned in the throat, inlet, and outlet. We observe hysteresis within the pore segment, and drainage entry pressures deviate from prior work.

Hydrogeological research: just getting started.

This paper comments on the current state of knowledge in the field of hydrogeology and claims that fundamental understandings must be developed if creative research is to have maximum impact. Problems of great importance to society include water development and quality, waste disposal, and global cycling of resources. These problems cannot be addressed effectively unless significant advances are made in understanding of a range of challenging scientific issues including fundamental physics, the importance of scale, modeling, and chemical and biological processes. Meaningful advances in hydrogeologic research will require an increased emphasis on fundamental understanding, interdisciplinary approaches, educational reforms, and the attraction of excellent researchers to the field.

A Numerical Model Study of Ground-Water Contamination from Price's Landfill, New Jersey- I. Data Base and Flow Simulation.

Toxic waste contamination is currently threatening the Atlantic City, New Jersey public water-supply wells. The geohydrologic data for this region are presented and organized into a format suitable for a numerical model study of the contamination problem. Presentation of the data in light of numerical work reveals the importance of good estimates of boundary conditions, historical pumping records, reliable water-quality data, accurate well logs, and reasonable parameter estimates. One set of measured head data is simulated.

A Numerical Model Study of Ground-Water Contamination from Price's Landfill, New Jersey - II. Sensitivity Analysis and Contaminant Plume Simulation.

A numerical model of flow and transport in the vicinity of Price's Landfill and the Atlantic City public water-supply wells is used to estimate the extent of the existing contamination problem. Model parameters such as boundary conditions, pumping rates, permeability, and dispersivity are varied to demonstrate the sensitivity of the model to these quantities. A historical simulation of the past ten years of contamination is obtained and two schemes for remediation of the contamination problem are compared. In the light of this work, additional data requirements are revealed.