Non-equilibrium alcohol flooding model for immiscible phase remediation: 2. Model development and application

A non-equilibrium, two-phase, three-component compositional model for the simulation of alcohol flooding has been developed and tested. Inter-phase mass transfer algorithms allow for transfer of all three components at high concentrations and high mass flux rates using a two-film model. The model has been used to simulate alcohol floods where the alcohol has an affinity for either the water-rich phase, or the organic-rich phase. Calibration, using experimental effluent data from an alcohol flood which used a 2-propanol (IPA)-water-tetrachlorethene (PCE) ternary system, indicates that inter-phase mass transfer parameters can be non-unique. Sensitivity studies, completed using the non-equilibrium model for the IPA-water-PCE system, indicate that experimentally derived organic-rich phase composition data should lead to better estimates of the non-wetting phase film thickness. For alcohol flooding experiments where the primary mechanism of non-aqueous phase liquid (NAPL) removal is enhanced dissolution, near-equilibrium conditions may be achieved with NAPL recovery similar for conditions of near-equilibrium and equilibrium. However, for systems where remobilization is the primary mechanism of NAPL recovery, it is expected that although local conditions may approach equilibrium, the resulting NAPL recovery can be significantly lower than would be attained if equilibrium conditions persisted.     

Comparison of fully coupled approaches for approximating nonlinear transport and reaction problems

The purpose of this work is to evaluate the computational efficiency of fully coupled approaches for approximating a common class of nonlinear, two-phase advective–dispersive–reactive equations. The general problem considered includes homogeneous phase chemical kinetics, equilibrium interphase mass transfer, and rate-controlled interphase mass transfer––all of which may be nonlinear. Aspects of the problem investigated include discrete mass conservative formulations, temporal discretization approaches, and nonlinear equation solution methods. Their effect on computational efficiency is investigated through a series of numerical experiments using a nondimensional model problem. The effect of problem characteristics such as large sorption capacity, strong sorption nonlinearity, fast mass transfer, fast reactions, and strong diffusion is investigated. Comparisons of solution efficiency show that the optimal approach depends upon: (1) the characteristics of the problem considered, which may be described in a nondimensional form; and (2) the accuracy achieved in the solution. Results offer general guidance for selecting solution approaches for the class of problems investigated and introduce some new solution approaches to the water resources field that may be applicable to other problems.     

Dissolution of residual non-aqueous phase liquids in porous media: pore-scale mechanisms and mass transfer rates

Experiments designed to elucidate the pore-scale mechanisms of the dissolution of a residual non-aqueous phase liquid (NAPL), trapped in the form of ganglia within a porous medium, are discussed. These experiments were conducted using transparent glass micromodels with controlled pore geometry, so that the evolution of the size and shape of individual NAPL ganglia and, hence, the pore-scale mass transfer rates and mass transfer coefficients could be determined by image analysis. The micromodel design permitted reasonably accurate control of the pore water velocity, so that the mass transfer coefficients could be correlated in terms of a local (pore-scale) Peclet number. A simple mathematical model, incorporating convection and diffusion in a slit geometry was developed and used successfully to predict the observed mass transfer rates. For the case of non-wetting NAPL ganglia, water flow through the corners in the pore walls was seen to control the rate of NAPL dissolution, as recently postulated by Dillard and Blunt [Water Resour. Res. 36 (2000) 439–454]. Break-up of doublet non-wetting phase ganglia into singlet ganglia by snap-off in pore throats was also observed, confirming the interplay between capillarity and mass transfer. Additionally, the effect of wettability on dissolution mass transfer was demonstrated. Under conditions of preferential NAPL wettability, mass transfer from NAPL films covering the solid surfaces was seen to control the dissolution process. Supply of NAPL from the trapped ganglia to these films by capillary flow along pore corners was observed to result in a sequence of pore drainage events that increase the interfacial area for mass transfer. These observations provide new experimental evidence for the role of capillarity, wettability and corner flow on NAPL ganglia dissolution.     

Modeling nitrogen–carbon cycling and oxygen consumption in bottom sediments

A model framework is presented for simulating nitrogen and carbon cycling at the sediment–water interface, and predicting oxygen consumption by oxidation reactions inside the sediments. Based on conservation of mass and invoking simplifying assumptions, a coupled system of diffusive–reactive partial differential equations is formulated for two-layer conceptual model of aerobic–anaerobic sediments. Oxidation reactions are modeled as first-order rate processes and nitrate is assumed to be consumed entirely in the anoxic portion of the sediments. The sediments are delineated into a thin oxygenated surface layer whose thickness is equal to the oxygen penetration depth, and a lower, but much thicker anoxic layer. The sediments are separated from the overlying water column by a relatively thin boundary layer through which mass transfer is diffusion controlled. Transient solutions are derived using the method of Laplace transform and Green’s function, which relate pore-water concentrations of the constituents to their concentrations in the bulk water and to the flux of decomposable settling organic matter. Steady-state pore-water concentrations are also obtained including expressions for the extent of methane saturation zone and methane gas flux. A relationship relating the sediment oxygen demand (SOD) to bulk water oxygen is derived using the two-film concept, which in combination with the depth-integrated solutions forms the basis for predicting the extent of oxygen penetration in the sediment. Iterative procedure and simplification thereof are proposed to estimate the extent of methane saturation zone and thickness of the aerobic layer as functions of time. Sensitivity of steady-state solutions to key parameters illustrates sediment processes interactions and synergistic effects. Simulations indicate that for a relatively thin diffusive boundary layer, d, oxygen uptake is limited by biochemical processes inside the sediments, whereas for a thick boundary layer oxygen transfer through the diffusive boundary layer is limiting. The results show an almost linear relationship between steady-state sediment oxygen demand and bulk water oxygen. For small d methane and nitrogen fluxes are sediment controlled, whereas for large d they are controlled by diffusional transfer through the boundary layer. It is shown that the two-layer model solution converges to the one-layer model (anaerobic layer) solution as the thickness of the oxygenated layer approaches zero, and that the transient solutions approach asymptotically their corresponding steady-state solutions.     

Turbulent mechanisms in open channel sediment-laden flows

The effects of turbulence on water-sediment mixtures is a critical issue in studying sediment-laden flows. The sediment concentrations and particle inertia play a significant role in the effects of turbulence on mixtures. A two-phase mixture turbulence model was applied to investigate the turbulence mechanisms affecting sediment-laden flows. The two-phase mixture turbulence model takes into account the complicated mechanisms arising from interphase transfer of turbulent kinetic energy, particle collisions, and stratification. The turbulence in sediment-laden flows is the result of the interaction of four factors, i.e. the production, dissipation, diffusion, and inter-phase transfer of turbulent kinetic energy of mixtures. The turbulence production and dissipation are two dominant processes which balance the turbulent kinetic energy of mixtures. The turbulence production represents turbulence intensity, while the inter-phase transfer of turbulent kinetic energy denotes the effect of particles on the turbulence of sediment-laden flows. Although, the magnitude of the inter-phase interaction term is much less than that of the turbulence production and dissipation terms, due to an approximate local balance between production and dissipation of the turbulent kinetic energy, even the small order of the inter-phase interaction has a significant impact on the turbulent balance of sediment-laden flows. The presence of particles plays a duel role in the turbulence dissipation of mixtures: both promotion and suppression. An important parameter used to determine the turbulent viscosity of mixtures, which is constant in clear water, is the function of the sediment concentration and particle inertia in sediment-laden flows.     

Empirical site response evaluations: case studies in Israel

A closed-loop, time-efficient technique for site effect evaluation for seismic microzonation in urban areas is developed and implemented. It includes the following successive steps: microtremor measurements using a triangular array of three-component seismometers; estimation of the Nakamura horizontal-vertical spectral ratio, calculation of Rayleigh wave dispersion using the Aki spatial correlation method; inversion of the dispersion curve to determine a shear wave velocity model of the shallow subsurface; analytical computation of Rayleigh wave spectral ellipticity and 1-D SH transfer function for this model; and a comparison of empirical and analytical ratios and correction of the model if required. The technique has been tested at several locations in a number of towns near the active Jordan Rift valley. A reasonable agreement is obtained when comparing empirical spectral ratios and analytical transfer functions.     

Numerical model of convection in sills

The numerical model of convection in magma sills is developed. The model is based on a full system of equations of fluid dynamics and includes heat transfer, buoyancy effects and diffusion of some minor component (marker). Solidification is treated as a phase transition. The results indicate that there are some qualitative differences between very thin sills with Rayleigh number Ra = 10⁵ and thin sills with Ra = 10⁶. For a basaltic magma the first case corresponds to the thickness of the sills of approximately 30 cm and the second case corresponds to the thickness of 60 cm. In the first case mixing is inefficient and conduction is the dominant form of heat transfer. In the second case mixing is efficient and convection is the dominant form of heat transfer. Some of the results can be scaled for the more viscous magmas in thicker sills.     

A geometrical method for quantifying endmembers' fractions in three-component groundwater mixing

We present a new geometrical method capable of quantifying and illustrating the outcomes of a three-component mixing dynamics. In a three-component mixing scenario, classical algebraic equations and endmember mixing analysis (EMMA) can be used to quantify the contributions from each fraction. Three-component mixing of natural waters, either in an element–element plot or by using the EMMA mixing subspace is described by a triangular shaped distribution of sample points where each endmember is placed on an apex, while each side corresponds to the mixing function of the two endmembers placed at the apex, considering the third endmembers' contribution equal to zero. Along each side, the theoretical mixing fractions can be computed using mass balance equations. Samples with contributions from three endmembers will plot inside the triangle, while the homogeneous barycentric coordinate projections can be projected onto the three sides. The geochemistry observed in the mineralized Ferrarelle aquifer system (southern Italy) results from three-component mixing of groundwater, each with diagnostic geochemical compositions. The defined boundary conditions allow us to parameterize and validate the procedures for modelling mixing, including selection of suitable geochemical tracers.     

A time-splitting pressure-correction projection method for complete two-fluid modeling of a local scour hole

A two-dimensional vertical (2DV), Eulerian two-phase model or complete two-fluid model of the free surface flow was developed to simulate water-sediment flow in a local scour hole. In the model, the complete forms of the vertical, two-dimensional, two-fluid Navier-Stokes equations were discretized using a finite volume scheme. This discretization was done based on a standard staggered grid system using a curvilinear network system in compliance with the bed boundaries and water level. At the beginning of the computational cycle, the equations governing the fluid phase were solved based on the two-step projection method with a pressure-correction technique. In the first step, the intermediate fluid velocities were obtained by solving different phases of the momentum equations of the fluid phase using the time-splitting technique. In the second step, pressure was obtained and fluid velocities were updated. In this step a simple discretization method was applied for decreasing the computational complexity. After obtaining all the fluid phase variables at a new time step, the sediment phase momentum equations were solved using the time-splitting technique and sediment velocities were obtained. Then, at the end of the computational cycle, the sediment phase mass equation was solved and the concentrations of both phases were updated. At last, the capacity of the model for simulating of the longitudinal fluid velocity and sediment concentration in a local scour hole was evaluated. Numerical results were found to be in good agreement with experimental data.     

Earthquake response of hysteretic mass-column using non-Gaussian closure

A non-Gaussian closure scheme based on the Edgeworth expansion of the probability density function is used to study the response of a hysteretic structure under random parametric excitation. The system considered consists of a weightless mass supporting a concentrated mass and it is subjected to the vertical and horizontal components of the ground acceleration modeled as nonstationary Gaussian white noise processes. The material of the structure exhibits bilinear hysteretic behaviour. The equation governing the motion of the system is transformed into an Itô stochastic differential equation. A set of ordinary differential equations governing the response statistics are obtained. These form an infinite hierarchy of equations which must be truncated in order to solve for moments of any order. The Edgeworth expansion of the joint density is used to truncate this infinite hierarchy. Such a closure scheme appears desirable since for hysteretic systems an explicit expression of the probability density is required. A frequently used closure scheme based on Gaussian assumption underestimates the response. The non-Gaussian density can be used in reliability studies.     

Non-isothermal soil water transport and evaporation

A detailed model was formulated to describe the non-isothermal transport of water in the unsaturated soil zone. The model consists of the coupled equations of mass conservation for the liquid phase, gas phase and water vapor and the energy conservation equation. The water transport mechanisms considered are convection in the liquid phase, and convection, diffusion and dispersion of vapor in the gas phase. The boundary conditions at the soil–atmosphere interface include dynamical mass flux and energy flux that accounts for radiation transport. Comparison of numerical simulations results with published experimental data demonstrated that the present model is able to describe water and energy transport dynamics, including situations of low and moderate soil moisture contents. Analysis of field studies on soil drying suggests that that dispersion flux of the water vapor near the soil surface, which is seldom considered in soil drying models, can make a significant contribution to the total water flux.     

Thermodynamics and constitutive theory for multiphase porous-media flow considering internal geometric constraints

This paper provides the thermodynamic approach and constitutive theory for closure of the conservation equations for multiphase flow in porous media. The starting point for the analysis is the balance equations of mass, momentum, and energy for two fluid phases, a solid phase, the interfaces between the phases and the common lines where interfaces meet. These equations have been derived at the macroscale, a scale on the order of tens of pore diameters. Additionally, the entropy inequality for the multiphase system at this scale is utilized. The internal energy at the macroscale is postulated to depend thermodynamically on the extensive properties of the system. This energy is then decomposed to provide energy forms for each of the system components. To obtain constitutive information from the entropy inequality, information about the mechanical behavior of the internal geometric structure of the phase distributions must be known. This information is obtained from averaging theorems, thermodynamic analysis, and from linearization of the entropy inequality at near equilibrium conditions. The final forms of the equations developed show that capillary pressure is a function of interphase area per unit volume as well as saturation. The standard equations used to model multiphase flow are found to be very restricted forms of the general equations, and the assumptions that are needed for these equations to hold are identified.     

Predicting Soil-Water and Soil-Air Transport Properties and Their Effects on Soil-Vapor Extraction Efficiency

Accurate prediction of water and air Iran sport parameters in variably saturated soil is necessary for modeling of soil-vapor extraction (SVE) at soil sites contaminated with volatile organic chemicals (VOCs). An expression for predicting saturated water permeability (k_l,s) in undisturbed soils from the soil total porosity and the field capacity soil-water content was developed by fitting a tortuous-tube fluid flow model to measured water permeability and gas diffusivity data. The new k_l,s expression gave accurate predictions when tested against independent k_l,s data. The k_l,s expression was implemented in the Campbell relative water permeability model to yield a predictive model for water permeability in variably saturated, undisturbed soil. The water permeability model, together with recently developed predictive equations for gas permeability and gas diffusivity, was used in a two-dimensional numerical SVE model that also included non-equilibrium mass transfer of VOC from a separate phase (nonaqueous phase liquid [NAPL]) to the air phase. SVE: calculations showed that gas permeability is likely the most important factor controlling VOC migration and vapor extraction efficiency. Water permeability and gas diffusivity effects became significant at water contents near and above field capacity. The NAPL-air mass transfer coefficient also had large impacts on simulated vapor extraction efficiency. The calculations suggest that realistic SVE models need to include predictive expressions for both conveciive, diffusive. and phase-partitioning processes in natural, undisturbed soils.     

Evaluation of force components acting on gravity type quay walls during earthquakes

In the analysis of the seismic stability of gravity type quay walls, the magnitudes of force components acting on quay walls during earthquakes and the phase relationships among these force components must be properly evaluated. In general, the force components include inertia force of the wall, lateral earth force, and water force. The magnitude and the phase relationship of each force component vary with time, and are largely affected by the magnitude of excess pore pressure developed in the backfill soil of the quay wall. The dynamic thrust develops at the contact surface between the backfill soil and the wall as a result of the interaction among these force components. In this study, a simple model is proposed to evaluate the magnitude and the phase variation of the dynamic thrust on the back of the wall. The proposed model computes the dynamic thrust by using the force components calculated from existing equations. We verified the proposed model by comparing its results with those obtained from a series of shaking table tests.     

A 3D unstructured non-hydrostatic ocean model for internal waves

A 3D non-hydrostatic model is developed to compute internal waves. A novel grid arrangement is incorporated in the model. This not only ensures the homogenous Dirichlet boundary condition for the non-hydrostatic pressure can be precisely and easily imposed but also renders the model relatively simple in its discretized form. The Perot scheme is employed to discretize horizontal advection terms in the horizontal momentum equations, which is based on staggered grids and has the conservative property. Based on previous water wave models, the main works of the present paper are to (1) utilize a semi-implicit, fractional step algorithm to solve the Navier-Stokes equations (NSE); (2) develop a second-order flux-limiter method satisfying the max–min property; (3) incorporate a density equation, which is solved by a high-resolution finite volume method ensuring mass conservation and max–min property based on a vertical boundary-fitted coordinate system; and (4) validate the developed model by using four tests including two internal seiche waves, lock-exchange flow, and internal solitary wave breaking. Comparisons of numerical results with analytical solutions or experimental data or other model results show reasonably good agreement, demonstrating the model’s capability to resolve internal waves relating to complex non-hydrostatic phenomena.     

A brief theory and computing of seismic ground rotations for structural analyses

The seismic ground rotations are important with respect to spatial structural models, which are sensitive to the wave propagation. The rotational ground motion can lead to significant increasing of structural response, instability and unusual damages of buildings. Currently, the seismic analyses often take into account the rocking and torsion motions separately using artificial accelerograms. We present an exact analytical method, proposed by Nazarov [15] for computing of three rotational accelerograms simultaneously from given translational records. The method is based on spectral representation in the form of Fourier amplitude spectra of seismic waves, corresponding to the given three-component translational accelerogram. The composition, directions and properties of seismic waves are previously determined in the form of a generalized wave model of ground motion. It is supposed that seismic ground motion can be composed by superposition of P, SV, SH- and surface waves. As an example, the dynamic response analysis of 25-story building is presented. Here recorded (low-frequency) and artificial (high-frequency) accelerograms were used; each of them includes three translational and three rotational components. In this structural analysis, we have clarified primarily conditions under which rotational ground motion should be taken into account. Next, we have calculated three rotational components of seismic ground motion. Then they were taken as additional seismic loads components for further seismic analysis of the building. Note, soil–structure interaction (SSI) is not considered in this study. For computing, we use the special software for structural analyses and accelerogram processing (FEA Software STARK ES and Odyssey software, Eurosoft Co., Russia). It was developed and is used in engineering practice in the Central Research Institute of Building Constructions (TsNIISK, Moscow, Russia).     

A general approach to advective–dispersive transport with multirate mass transfer

A numerical solution that is significantly more general than other semi-analytical solutions is presented for governing equations describing advective–dispersive transport with multirate mass transfer between mobile and immobile domains. The new solution approach is general in the sense that it does not impose any restrictive assumption on the spatial or temporal variability of advective and dispersive processes in the mobile domain. A single integro-differential equation (IDE) is developed for the concentration in the mobile domain by separating the concentration in the immobile domain from the set of two partial differential equations. The solution to the IDE requires the evaluation of a temporal integral of the concentration in the mobile domain, which is a function of the Laplace transform of the distribution of the mass transfer rate coefficient. The Laplace transform is not limited to flow fields with known constant velocities. The solutions for one- and two-dimensional examples obtained using the new approach agree with those obtained by existing semi-analytical and numerical approaches.     

Substructuring of dynamical systems via the adaptive minimal control synthesis algorithm

In this paper we consider the concept of modelling dynamical systems using numerical–experimental substructuring. This type of modelling is applicable to large or complex systems, where some part of the system is difficult to model numerically. The substructured model is formed via the adaptive minimal control synthesis (MCS) algorithm. The aim of this paper is to demonstrate that substructuring can be carried out in real time, using the MCS algorithm. Thus, we reformulate the MCS algorithm into a substructuring form. We introduce the concepts of a transfer system, and carry out numerical simulations of the substructuring process using a coupled three mass example. These simulations are compared with direct simulations of a three mass system. In addition we consider the stability of the substructuring algorithm, which we discuss in detail for a class of second‐order transfer systems. A numerical–experimental system is considered, using a small‐scale experimental system, for which the substructuring algorithm is implemented in real time. Finally we discuss these results, with particular reference to the future application of this method to modelling large‐scale structures subject to earthquake excitation. Copyright © 2001 John Wiley & Sons, Ltd.