This study is focused on gas‐water displacement through fracture networks. First, we investigated the flow patterns in fracture branches following a fracture intersection. Laboratory experiments were conducted to qualitatively identify the gas‐water flow patterns in intersecting fractures. A mathematical model consistent with the actual phenomena observed in the laboratory was then formulated. The mathematical model is represented by a nonlinear system of partial differential equations, which is solved by an iterative numerical method. In the second part of the study, investigations of a vertical cross section of a fracture network were conducted. Two sets of fractures were assumed to intersect orthogonally, as characteristic of some granites. The angles of the fractures with the horizontal direction were either 45° or 135°. Fracture intersection centers, fracture lengths, and fracture openings were generated according to statistical distributions. Simulations were carried out under constant pressure boundary conditions at top and bottom as might be found at offshore radioactive repositories. The present study, which accounts for a gas‐water slug, shows that the flow of water reaches quasi‐steady state with continuous gas release.

The paper presents some hydrodynamic aspects of groundwater flow as a result of location of radioactive repositories in fractured rocks formations. Such repositories are planned in Sweden in fractured granite aquifers. High and low level radioactive waste repository located in aquifers are possible sources of environment pollution.

This study originates from an accidental event of diesel oil contamination due to an overflow of a fuel storage tank. As a result of this accident, approximately 1300 m3 of diesel oil was released to the environment and freely flowed as a small stream, contaminating the loamy soil in that site. The diesel oil was concentrated especially in three ponds along the stream path, and over 10 h it completely infiltrated into the soil. The total area contaminated by the diesel oil was about 7000 m2. The maximum depth of the contamination was 5 m. The total petroleum hydrocarbon (TPH) concentration in the contaminated site was between 5000 to 50 000 mg/ kg soil, and in two locations, the TPH concentration reached about 130 000 mg/kg soil.

The problem investigated here is that of pollution due to oil spilled on the ground surface, which flows through the unsaturated zone and into the aquifer in fractured rock formations.

The penetration of light nonaqueous phase liquids (LNAPLs) in quantities that lead to an accumulation in the form of a lens above the water table is considered. First, the three-phase vertical gravity-capillary equilibrium of water, NAPL, and air above the water table is specified. The hypothesis of ‘vertical equilibrium phase distribution’ is used to derive averaged asymptotic equations describing NAPL flow as a thin lens floating above the water table. Some problems of unsteady NAPL lens movement and the development of a NAPL mound, spreading along an inclined or horizontal phreatic surface are discussed and the analytical solutions are obtained.

An investigation of natural convection in a porous medium heated from below or above, and bounded by perfectly conducting side walls, shows that a motionless solution is impossible, except for a particular side wall temperature variation. Hence, convection occurs regardless of the value of Rayleigh number and regardless of whether the fluid is heated from below or from above. Numerical solutions for identical uniform temperatures imposed on both side walls (no temperature difference between the side walls) show that when heating from below, a subcritical flow results mainly near the side walls, which amplifies and extends over the entire domain under supercritical conditions.

The results of an investigation on the effect of a weak heterogeneity of a porous medium on natural convection are presented. A medium heterogeneity is represented by spatial variations of the permeability and of the effective thermal conductivity. As a general rule the existence of horizontal thermal gradients in heterogeneous porous media provides a sufficient condition for the occurrence of natural convection. The implications of this condition are investigated for horizontal layers or rectangular domains subject to isothermal top and bottom boundary conditions. Results lead to a restriction on the classes of thermal conductivity functions which allow a motionless solution. Analytical solutions for rectangular weak heterogeneous porous domains heated from below, consistent with a basic motionless solution, are obtained by applying the weak nonlinear theory. The amplitude of the convection is obtained from an ordinary non-homogeneous differential equation, with a forcing term representative of the medium heterogeneity with respect to the effective thermal conductivity. A smooth transition through the critical Rayleigh number is obtained, thus removing a bifurcation which usually appears in homogeneous domains with perfect boundaries, at the critical value of the Rayleigh number. Within a certain range of slightly supercritical Rayleigh numbers, a symmetric thermal conductivity function is shown to reinforce a symmetrical flow while antisymmetric functions favour an antisymmetric flow. Except for the higher-order solutions, the weak heterogeneity with respect to permeability plays a relatively passive role and does not affect the solutions at the leading order. In contrast, the weak heterogeneity with respect to the effective thermal conductivity does have a significant effect on the resulting flow pattern.

The paper presents the results of an investigation of the effect of imperfectly insulated sidewalls on natural convection in porous media at slightly supercritical Rayleigh numbers. An analytical solution for a rectangular domain with imperfectly insulated sidewalls and heated from below, was obtained through the weak nonlinear theory. The solution enables the determination of the amplitude of the convection and the direction of the flow. The amplitude results from an ordinary nonhomogeneous differential equation, with a forcing term representing the heat leakage through the lateral walls. The steady state amplitude solution shows that the transition through the critical Rayleigh number is smooth, differing from the case of perfectly insulated sidewalls where a bifurcation usually appears at the critical Rayleigh number. As a result, within a certain range of slightly supercritical Rayleigh number values, the amplitude and the direction of the convection currents are uniquely determined by the heat leakage through the lateral walls and they are independent of the initial conditions. A subcritical convection occurs as a result of the imperfectly insulated sidewalls, enabling the smooth transition through the critical Rayleigh value. A three-branch bifurcation develops at a higher Rayleigh number. A stability analysis of the solutions, corresponding to these branches, shows that the amplitudes which correspond to the two highest values are stable, while the third is unstable.

A modelling study aimed at providing a better understanding of the hydrocarbon accumulations on the SW flank of the Dead Sea graben in Israel has been performed. It considers the recent geochemical finding that the source rock of the hydrocarbon occurrences in the area is the Senonian bituminous chalk and marl, buried in the central Dead Sea graben. The study investigates the effect of the regional geological and hydrogeological conditions, associated with the physical properries of the rock and fluids, on the migration and types of hydrocarbon accumulations. The investigation was performed by means of a three‐phase, two‐dimensional, numerical reservoir simulator. Typical cross‐sections, through potential anticlinal hydrocarbon traps, were considered. The study analyses possible hydrodynamic flushing in the water‐flow direction, as well as counter‐current migration in a direction opposite to the potentiometric water gradients, from the Dead Sea graben upwards. In addition to conventional hydrodynamic traps. the study includes the case of downdip entrapment due to low permeability regions. It is concluded that: (i)from the hydrodynamic point of view, the easiest oil migration path is through Paleozoic — Triassic formations: (ii) the high water salinity of these beds facilitates the up‐structure oil flow in a direction opposite to the water current movement: (iii) the Jurassic beds are probably impregnated by oil and gas coming from Triassic strata through faults: (iv) undiscovered structural traps are likely to contain mostly gas; and (v) down‐faulted blocks adjacent to sealing faults. or to low‐permeable regions (including permeable faults), are potential oil traps.

Searching for a fracture of a given hydraulic conductivity in a fractured rock, by means of observation bodies such as bore holes, is similar to a decision problem in a two-person zero-sum game with incomplete information. The searcher and the hidden fracture are considered the two players of the game. There is a finite number of moves or pure strategies in the hands of each player, that is, the former may drill a finite number of bore holes and the latter may be located or not in a certain hydraulic conductivity range of interest. A game model corresponding to this situation, taking into consideration the log-normal fracture hydraulic conductivity distribution, consistent with the occurrence in nature, is presented. The probability of finding a fracture in the jth interval of the hydraulic conductivity probability density function (PDF) graph after i drillings is taken as the payoff matrix of the game. The presented game model provides a solution for finding the number of bore holes to be drilled for intersecting a fracture within a prescribed hydraulic conductivity range. The method is exemplified for a particular data set.

A law for dispersion in fracture networks below the representative elementary volume (REV) is established by analyzing random walks in two‐dimensional fracture networks in conjunction with percolation theory. Irregular fracture networks near the percolation threshold were obtained by removing some of the fractures of a regular orthogonal network, consisting of fractures of equal length and different apertures, drawn randomly from a lognormal distribution. The random walk was directed by an exact solution of flow through the network, and Monte Carlo simulations were performed to track particles through the fracture system. The percolation theory analysis indicates a proportionality between the mean square displacement and time raised to the power 1.27, in excellent agreement with the simulations in the fracture networks, which indicate a proportionality with time raised to the power 1.3.

A stochastic approach is used for the study of flow through highly heterogeneous aquifers. The mathematical model is represented by a random partial differential equation in which the permeability and the porosity are considered to be random functions of position, defined by the average value, constant standard deviation and autocorrelation function characterized by the integral scale. The Laplace transform of the solution of the random partial differential equation is first written as a solution of a stochastic integral equation. This integral equation is solved using a Neumann series expansion. Conditions of convergence of this series are investigated and compared with the convergence of the perturbation series. For mean square convergence, the Neumann expansion method may converge for a larger range of variability in permeability and porosity than the classic perturbation method. Formal expressions for the average and for the correlation moments of the pressure are obtained. The influence of the variability of the permeability and porosity on pressure is analyzed for radial flow. The solutions presented for the pressure at the well, as function of the permeability coefficient of variation, may be of practical interest for evaluating the efficiency of well stimulation operations, such as hydraulic fracturing or acidizing methods, aimed at increasing the permeability around the well.

Microbiological denitrification in a sandy matrix was studied by means of laboratory sand columns operated at continuous and pulse feed regimes. Gas production resulting from the biological activity played a major role in modifying the hydraulic properties of the column, leading to decreases in hydraulic conductivity and porosity, higher water velocities through the column, higher dispersion and anomalies in the head difference to flow rates ratios. All of these effects were more pronounced when formate, the carbon source used, was supplied continuously: microbial activity and gas production were concentrated at the top of the column, leading to almost complete clogging. When the formate was supplied in pulses, activity and gas production were dispersed, leading to relative uniformity in the physical parameters measured and a homogeneous appearance of the column. The results suggest that in a future in situ aquifer denitrification plant, pulse application of the carbon source is prefereable to a continuous supply regime.

Many studies of flow and solute transport in fractured rocks are based on a conceptual model whereby flow occurs between parallel plates which approximate the fracture walls. Recently, it has been observed that this representation is not consistent with actual fractures. Real fractures are actually composed of a complex system of void spaces of varying aperture, and contact areas which are closed to flow. In such fractures, flow takes place through a network of channels and dead‐end regions. The present investigation analyzes and compares the behavior of solute breakthrough curves in these channels and parallel plate representations. Numerical experinents show that breakthrough curves obtained with channel models are characterized by a long tail and jumps in the solute concentration, consistent with those observed experimentally. It is concluded that the considered channel models provide a sound explanation for the behavior of real breakthrough curves, which cannot be reproduced by parallel plate models.

Positioning of a fracture within a given permeability range, under the assumption that a prospective borehole is intersected by one fracture, was modeled by Braester and Barak as a two-person zero-sum game. This paper presents two extensions of the mentioned model, one referring to the situation when more than one fracture intersects each borehole, and the other one for the case when more than one borehole are drilled simultaneously. The one-fracture game model is proved to represent a strong basis in the formalization of these complex situations.

A mathematical model is presented for the upward pulsating gas‐water displacement, from a gas source at a constant production rate or pressure at the bottom boundary to a constant pressure boundary at the top boundary. The study shows a complicated flow phenomenon caused by the unequal advance of the gas in fractures of different permeability or different inclinations. The results show that the gas breakthrough at the surface is governed by the high permeability fractures. At a constant rate of gas production the breakthrough is associated with a gas pressure drop at the bottom gas boundary. As a result, downward back flow takes place until the gas pressure builds up and reinitiates the upward displacement. It is concluded that calculations with average properties of the fracture permeability, for example, using the continuum approach, will underestimate the breakthrough time of the gas at the surface. Under constant pressure boundary conditions at the top of the cavern the average permeability will overestimate the amount of gas carried out by the fracture network. Under constant flow rate boundary conditions at the top of the cavern (i.e., bottom of the flow domain), calculations with average fracture permeability will overestimate the pressure in the cavern. The problem is of practical interest for low‐level radioactive waste repositories located in hard rock below the sea bottom.

Summary A new method of drawdown-pressure test analysis is proposed that takes into consideration the non-Darcian flow as well as the skin and borehole-storage effects. Two new correlations obtained from numerically simulated drawdown tests are used and the method of application is illustrated. The drawdown-pressure results of a synthetic numerically simulated test are used to recalculate the a priori known reservoir skin and permeability. A comparison between the obtained and the "true" reservoir skin and permeability shows an excellent agreement when the proposed method is applied. Drawdown-pressure analysis of the given examples with the conventional method shows errors > 5 % in the calculated permeability and > 50% in the calculated skin factor.

Vyredox plants are designed for in situ removal of iron and/or manganese, while Nitredox plants are designed for in situ removal of nitrates and nitrites. Both methods make use of bacteriological processes. A typical unit of a Vyredox plant comprises several injection wells, through which degassed aerated water is injected into the aquifer and a pumping well through which water, partly free of iron or manganese, is abstracted. A typical Nitredox plant comprises a number of injection-pumping wells located on the circumference of two concentric circles and a pumping well in the centre through which water, partly free of nitrates and iron and/or manganese, is produced. Water with the carbon nutrient is injected through the wells located on the outer circle, while the wells located on the inner circle play the role of the Vyredox injection wells. The Nitredox process is associated with the formation of nitrogen, which is removed through the wells located on the inner circle. Vyredox and Nitredox processes include flow phenomena, transport, chemical reactions and bacteriological processes. These phenomena are described and formulated mathematically as a first step in the mathematical modelling of such processes.