A continuum representation of fracture networks. Part II: application to the Äspö Hard Rock laboratory

A method to represent fracture networks in a continuum model is evaluated by an application to the Äspö Hard Rock Laboratory (HRL). The basic approach of the method is to first generate a fracture network, based on data from field measurements and then represent the network as grid cell conductivities, using a staggered grid arrangement. It is argued that the resulting conductivity fields capture the correlation and anisotropy structures, as well as the mean conductivity, of the rock in a realistic way. The main objective is to evaluate if the suggested method can be used in an application to a real site. The objective is formulated in three questions: ‘Can the method utilize available field data?’, ‘Can the generated fields be calibrated and conditioned?’ and ‘Are realistic distributions of pressure, flow and density obtained?’. From the application to the Äspö HRL, it is concluded that the hydraulic conductivity fields, generated by the suggested method, can utilize field data and be calibrated. It is also demonstrated that realistic distributions of pressure, flow and density can be simulated.     

Density-dependent dispersion in heterogeneous porous media Part I: A numerical study

In this paper, we describe carefully conducted numerical experiments, in which a dense salt solution vertically displaces fresh water in a stable manner. The two-dimensional porous media are weakly heterogeneous at a small scale. The purpose of these simulations, conducted for a range of density differences, is to obtain accurate concentration profiles that can be used to validate nonlinear models for high-concentration-gradient dispersion. In this part we focus on convergence of the computations, in numerical and statistical sense, to ensure that the uncertainty in the results is small enough.Concentration variances are computed, which give estimates of the uncertainty in local concentration values. These local variations decrease with increasing density contrast. For tracer transport, obtained longitudinal dispersivities are in accordance with analytical findings. In the case of high-density contrasts, stabilizing gravity forces counteract the growth of dispersive fingers, decreasing the effective width of the transition zone. For small log-permeability variances, the decrease of the apparent dispersivity that is found is in agreement with laboratory results for homogeneous columns.     

Flow and transport through two-dimensional isotropic media of binary conductivity distribution. Part 1: NUMERICAL methodology and semi-analytical solutions

Flow and transport take place in a heterogeneous medium made up from inclusions of conductivity K submerged in a matrix of conductivity K ₀. We consider two-dimensional isotropic media, with circular inclusions of uniform radii, that are placed at random and without overlap in the matrix. The system is completely characterized by the conductivity contrast =K/K ₀ and by the volume fraction n. The flow is uniform in the mean, of velocity U=const. The derivation of the velocity field is achieved by a numerical method of high accuracy, based on analytical elements. Approximate analytical solutions are derived by a few methods: composite elements, effective medium, dilute systems and first-order approximation in logconductivity variance. The latter was employed by Rubin (1995), while the dilute system approximation was used by Eames and Bush (1999) and Dagan and Lessoff (2001). Transport is solved in a Lagrangean framework, with trajectories determined numerically from the velocity field, by particle tracking. Results for the velocity variance and for the longitudinal macrodispersivity, for a few values of and n, are presented in Part 2.     

Flow and transport through two-dimensional isotropic media of binary conductivity distribution. Part 2: NUMERICAL simulations and comparison with theoretical results

In the present part the results of numerical simulations of flow and transport in media made up from circular inclusions of conductivity K that are submerged in a matrix of conductivity K ₀, subjected to uniform mean velocity, are presented. This is achieved for a few values of =K/K ₀ (0.01, 0.1 and 10) and of the volume fraction n (0.05, 0.1 and 0.2). The numerical simulations (NS) are compared with the analytical approximate models presented in Part 1: the composite elements (CEA), the effective medium (EMA), the dilute system (DSA) and the first-order in the logconductivity variance (FOA). The comparison is made for the longitudinal velocity variance and for the longitudinal macrodispersivity. This is carried out for n<0.2, for which the theoretical and simulation models represent the same structure of random and independent inclusions distribution. The main result is that transport is quite accurately modeled by the EMA and CEA for low , for which _L is large, whereas in the case of =10, the EMA matches the NS for n<0.1. The first-order approximation is quite far apart from the NS for the values of examined . This material is based upon work supported by the National Science Foundation under Grant No. 0218914. Authors also wish to thank the Center of Computational Research, University at Buffalo for assistance in running numerical simulations.     

Compressibility of porous rocks: Part I. Measurements of Hungarian reservoir rock samples

Pore volume compressibility is one of the physical properties of a reservoir that must be specified in many reservoir-engineering calculations. In the presented research, the effect of compact pressure, temperature and porosity on compressibility was investigated. A total of twenty-two different cores were tested: five limestone, one friable sandstone, fourteen medium to hard sandstone, and two very dense sandstone. Core samples were placed in the test cell and subject to compacting pressure up to 10,000 psi. Runs were made at room temperature and at 52°C for limestone samples. Although there were some publications concerning measurement and study of the effect of pressure and temperature on pore volume compressibility of reservoir rocks, nothing has been published about compressibility of Hungarian reservoir rocks, except of the work of Tóth and Bauer (1988). The present study showed pore volume compressibility data for different Hungarian fields. The result of the study at high temperature (52°C) shows that pore compressibility increases with increasing temperature.     

Significance of injection modes and heterogeneity on spatial and temporal dispersion of advecting particles in two-dimensional discrete fracture networks

We investigate the impact of injection mode (flux and resident injection) and heterogeneity in hydraulic properties on dispersion of advecting particles in two-dimensional discrete fracture network models, using a Monte Carlo method. We find that the injection mode has a significant effect on dispersion: The resident injection mode exhibits anomalous features of transport whereas the flux injection mode tends to Gaussian transport; this observation is easily understood by considering phase diagrams where a limited number of particles entering low velocity fractures greatly increase macrodispersion. In spite of a sizeable portion of negative longitudinal velocities, it is shown that multiple crossings are negligible when quantifying longitudinal macrodispersion. A simple probabilistic expression of particle mass balance is shown to predict well the spatial distribution of advecting particles.     

A joint inversion algorithm to process geoelectric and sutface wave seismic data. Part I: basic ideas1

For the exploration of near-surface structures, seismic and geoelectric methods are often applied. Usually, these two types of method give, independently of each other, a sufficiently exact model of the geological structure. However, sometimes the inversion of the seismic or geoelectric data fails. These failures can be avoided by combining various methods in one joint inversion which feads to much better parameter estimations of the model than the independent inversions. A suitable seismic method for exploring near-surface structures is the use of dispersive surface waves: the dispersive characteristics of Rayleigh and Love surface waves depend strongly on the structural and petrophysical (seismic velocities) features of the near-surface Underground. Geoelectric exploration of the structure Underground may be carried out with the well-known methods of DC resistivity sounding, such as the Schlumberger, the radial-dipole and the two-electrode arrays. The joint inversion algorithm is tested by means of synthetic data. It is demonstrated that the geoelectric joint inversion of Schlumberger, radial-dipole and two-electrode sounding data yields more reliable results than the single inversion of a single set of these data. The same holds for the seismic joint inversion of Love and Rayleigh group slowness data. The best inversion result is achieved by performing a joint inversion of both geoelectric and surface-wave data. The effect of noise on the accuracy of the solution for both Gaussian and non-Gaussian (sparsely distributed large) errors is analysed. After a comparison between least-square (LSQ) and least absolute deviation (LAD) inversion results, the LAD joint inversion is found to be an accurate and robust method.     

In situ experiments and seismic analysis of existing buildings. Part I: experimental investigations

Recent results of in situ measurements and their interest for a seismic assessment of existing buildings are presented and analysed. The present paper (Part I) is devoted to the experimental programme. The response to ambient vibrations, harmonic excitation and shock loading is recorded on intact buildings but also after their structure or their vicinity was modified. These tests aim to identify the dynamic behaviour of ordinary intact buildings built in a conventional practise. Moreover, taking advantage of their demolition, it was possible (through these tests) to determine the actual influence of the light work elements, full precast facade panels, bearing masonry walls, and the presence of neighbouring joined buildings. These experiments realized on real buildings show that information gathered from ambient measurements provide reliable and efficient data of real interest for a clear understanding of the actual building behaviour. The advantage of integrating these data in the vulnerability assessment is presented and discussed in the next paper (Part II). Copyright © 2005 John Wiley & Sons, Ltd.     

A new airborne polar Nephelometer for the measurements of optical and microphysical cloud properties. Part I: Theoretical design

A new optical sensor, the airborne Polar Nephelometer, is described. The sensor is designed to measure the optical and microphysical parameters of clouds containing either water droplets or ice crystals or a mixture of these particles ranging in size from a few micrometers to about 500 m diameter. The probe measures the scattering phase function of an ensemble of cloud particles intersecting a collimated laser beam near the focal point of a paraboloïdal mirror. The light scattered from polar angles from 3.49° to 169° is reflected onto a circular array of 33 photodiodes. The signal processing electronics and computer storage can provide one measurement of the scattering phase function every 100 ms or every 0.2 ms. The first part of the paper describes the theoretical design of a prototype version of the probe.     

Intercomparison of oceanic and atmospheric forced and coupled mesoscale simulations. Part I: Surface fluxes

A mesoscale non-hydrostatic atmospheric model has been coupled with a mesoscale oceanic model. The case study is a four-day simulation of a strong storm event observed during the SEMAPHORE experiment over a 500 × 500 km² domain. This domain encompasses a thermohaline front associated with the Azores current. In order to analyze the effect of mesoscale coupling, three simulations are compared: the first one with the atmospheric model forced by realistic sea surface temperature analyses; the second one with the ocean model forced by atmospheric fields, derived from weather forecast re-analyses; the third one with the models being coupled. For these three simulations the surface fluxes were computed with the same bulk parametrization. All three simulations succeed well in representing the main oceanic or atmospheric features observed during the storm. Comparison of surface fields with in situ observations reveals that the winds of the fine mesh atmospheric model are more realistic than those of the weather forecast re-analyses. The low-level winds simulated with the atmospheric model in the forced and coupled simulations are appreciably stronger than the re-analyzed winds. They also generate stronger fluxes. The coupled simulation has the strongest surface heat fluxes: the difference in the net heat budget with the oceanic forced simulation reaches on average 50 Wm⁻² over the simulation period. Sea surface-temperature cooling is too weak in both simulations, but is improved in the coupled run and matches better the cooling observed with drifters. The spatial distributions of sea surface-temperature cooling and surface fluxes are strongly inhomogeneous over the simulation domain. The amplitude of the flux variation is maximum in the coupled run. Moreover the weak correlation between the cooling and heat flux patterns indicates that the surface fluxes are not responsible for the whole cooling and suggests that the response of the ocean mixed layer to the atmosphere is highly non-local and enhanced in the coupled simulation.     

Inversion of near-field waveform data for earthquake source rupture process (I): Method and numerical test

In seismological study, most of the earthquake source rupture processes are inverted via matching the waveforms. The hypocenter location and fault parameters (such as strike direction, dip angle, etc.) are assumed firstly, and the fault is divided into a …     

Anisotropy and depth‐related heterogeneity of hydraulic conductivity in a bog peat. I: laboratory measurements

Anisotropy and heterogeneity of hydraulic conductivity (K) are suspected of greatly affecting rates and patterns of ground‐water seepage in peats. A new laboratory method, termed here the modified cube method, was used to measure horizontal and vertical hydraulic conductivity (K_h and K_v) of 400 samples of bog peat. The new method avoids many of the problems associated with existing field and laboratory methods, and is shown to give relatively precise measurements of K. In the majority of samples tested, K_h was much greater than K_v, indicating that the bog peat was strongly anisotropic. Log₁₀K_h, log₁₀K_v, and log₁₀ (K_h/K_v) were found to vary significantly with depth, although none of the relationships was simple. We comment on the scale dependency of our measurements. Copyright © 2002 John Wiley & Sons, Ltd.     

The role and significance of extracellular polymers in activated sludge. Part I: Literature review

In biological wastewater treatment, bacteria tend to aggregate by forming flocs, biofilms and even granules. A large part of the floc structure in activated sludge is composed of extracellular polymers. The extracellular polymeric substances (EPS) are mainly responsible for the structural and functional integrity of biofilms/flocs and they are considered to be important for the physico‐chemical properties of activated sludge. This review considers the composition of EPS and proportion between the constituents. Moreover it includes the relationship between the EPS constituents and sludge properties such as sludge retention time, hydrophobicity and surface charge.     

A marching in space and time (MAST) solver of the shallow water equations. Part I: The 1D model

A new approach is presented for the numerical solution of the complete 1D Saint-Venant equations. At each time step, the governing system of partial differential equations (PDEs) is split, using a fractional time step methodology, into a convective prediction system and a diffusive correction system. Convective prediction system is further split into a convective prediction and a convective correction system, according to a specified approximated potential. If a scalar exact potential of the flow field exists, correction vanishes and the solution of the convective correction system is the same solution of the prediction system. Both convective prediction and correction systems are shown to have at each x − t point a single characteristic line, and a corresponding eigenvalue equal to the local velocity. A marching in space and time (MAST) technique is used for the solution of the two systems. MAST solves a system of two ordinary differential equations (ODEs) in each computational cell, using for the time discretization a self-adjusting fraction of the original time step. The computational cells are ordered and solved according to the decreasing value of the potential in the convective prediction step and to the increasing value of the same potential in the convective correction step. The diffusive correction system is solved using an implicit scheme, that leads to the solution of a large linear system, with the same order of the cell number, but sparse, symmetric and well conditioned. The numerical model shows unconditional stability with regard of the Courant–Friedrichs–Levi (CFL) number, requires no special treatment of the source terms and a computational effort almost proportional to the cell number. Several tests have been carried out and results of the proposed scheme are in good agreement with analytical solutions, as well as with experimental data.     

Bridge pier failure probabilities under combined hazard effects of scour, truck and earthquake. Part I: occurrence probabilities

In many regions of the world, a bridge will experience multiple extreme hazards during its expected service life. The current American Association of State Highway and Transportation Officials (AASHTO) load and resistance factor design (LRFD) specifications are formulated based on failure probabilities, which are fully calibrated for dead load and nonextreme live loads. Design against earthquake loads is established separately. Design against scour effect is also formulated separately by using the concept of capacity reduction (or increased scour depth). Furthermore, scour effect cannot be linked directly to an LRFD limit state equation, because the latter is formulated using force-based analysis. This paper (in two parts) presents a probability-based procedure to estimate the combined hazard effects on bridges due to truck, earthquake and scour, by treating the effect of scour as an equivalent load effect so that it can be included in reliability-based bridge failure calculations. In Part I of this series, the general principle of treating the scour depth as an equivalent load effect is presented. The individual and combined partial failure probabilities due to truck, earthquake and scour effects are described. To explain the method of including non-force-based natural hazards effects, two types of common scour failures are considered. In Part II, the corresponding bridge failure probability, the occurrence of scour as well as simultaneously having both truck load and equivalent scour load are quantitatively discussed.     

Sensitivity of runoff and soil erosion to climate change in two Mediterranean watersheds. Part I: model parameterization and evaluation

Climate change is expected to effect storm runoff and erosion processes in Mediterranean watersheds at multiple spatial scales. Models are typically applied to estimate these impacts; however, the scarcity of spatially distributed data for parameterization, calibration and validation often prevents application of these models, particularly for larger catchments. This report, the first part of a two‐part article, presents an application and evaluation of the MEFIDIS model for two Mediterranean meso‐scale watersheds (115 and 290 km²) in a data‐scarce environment. A multi‐scale assessment method was used that combines quantitative validation and qualitative evaluation, consisting of three steps: (1) calibration at the small (field) scale using results from rainfall simulation experiments; (2) calibration and validation for catchment‐scale results while changing catchment‐scale parameters only (channel roughness and a parameter controlling the distribution of saturated areas); and (3) qualitative evaluation of within‐watershed erosion processes using empirical estimates of sediment delivery ratio and gully location. The results indicate that calibrating MEFIDIS at the field scale can provide reasonable results for catchment runoff and sediment export and for within‐watershed erosion processes. Copyright © 2009 John Wiley & Sons, Ltd.