Impermeable Bed Research Articles

A mathematical model of the crustal waveguide

The two-layer model of the upper crust waveguide developed in (Karakin, 1990a; Karakin and Kambarova, 1997) is studied. The upper layer is poroelastic and the lower layer (the waveguide proper) can be in poroviscous or elastic dilatancy states. The model is based on the concept of two concurrent processes that are alternately active in the lower layer (waveguide): dilatancy and compaction. Horizontal tectonic forces displace the upper layer relative to the lower one. As a result, the porous space in the lower layer experiences dilatancy expansion, and fluids are sucked into the waveguide from upper and lower layers. The porous structure of the waveguide is then destroyed, which is accompanied by the transition of the system into the poroviscous state. The lithostatic pressure expels the fluids upward from the waveguide. This paper is devoted to the mathematical analysis of this model. A new formulation of the boundary value problem is proposed and a wave solution of the pertinent equations is given. Self excited waves in crustal waveguides are assumed to provide the driving mechanism of the vertical fluid migration in the upper crust. This migration gives rise to oil and gas deposits if the fluid flows strike impermeable anticlinal beds (traps). This model is a constituent part of the general concept of the mechanism responsible for mud volcanism. Faults cutting the traps and reaching the surface initiate the formation of mud volcanoes. Analysis of the waveguide model can provide constraints on the feeding conditions of mud volcanoes. The concept of the upper crust fluid regime proposed in the paper reconciles the hypotheses of the organic and inorganic origins of hydrocarbon accumulations. Hydrocarbon fluxes enter the crustal waveguide both from above (organic origin) and from below (inorganic origin). These fluid fluxes are reworked in the waveguide, after which they move upward. As a result, accumulated hydrocarbons display features of dierent origins.

Finite Volume Model for Nonlevel Basin Irrigation

A finite volume model for unsteady, two-dimensional, shallow water flow is developed and applied to simulate the advance and infiltration of an irrigation wave in two-dimensional basins of complex topography. The fluxes are computed with Roe's approximate Riemann solver and the monotone upstream scheme for conservation laws is used in conjunction with predictor-corrector time-stepping to provide a second-order accurate solution. Flux-limiting is implemented to eliminate spurious oscillations and the model incorporates an efficient and robust scheme to capture the wetting and drying of the soil. Model predictions are compared with experimental data for one- and two-dimensional problems involving rough, impermeable, and permeable beds, including a poorly leveled basin.

Using multiple geochemical tracers to characterize the hydrogeology of the submarine spring off Crescent Beach, Florida

A spectacular submarine spring is located about 4 km east of Crescent Beach, FL, in the Atlantic Ocean. The single vent feature of Crescent Beach Spring provides a unique opportunity to examine onshore–offshore hydrogeologic processes, as well as point source submarine ground water discharge. The Floridan aquifer system in northeastern Florida consists of Tertiary interspersed limestone and dolomite strata. Impermeable beds confine the water-bearing zones under artesian pressure. Miocene and younger confining strata have been eroded away at the vent feature, enabling direct hydrologic communication of Eocene ground water with coastal bottom waters. The spring water had a salinity of 6.02, which was immediately diluted by ambient seawater during advection/mixing. The concentration of major solutes in spring water and onshore well waters confirm a generalized easterly flow direction of artesian ground water. Nutrient concentrations were generally low in the reducing vent samples, and the majority of the total nitrogen species existed as NH 3. The submarine ground water tracers, Rn-222 (1174 dpm l −1, dpm), methane (232 nM) and barium (294.5 nM) were all highly enriched in the spring water relative to ambient seawater. The concentrations of the reverse redox elements U, V and Mo were expectedly low in the submarine waters. The strontium isotope ratio of the vent water ( 87Sr/ 86Sr=0.70798) suggests that the spring water contain an integrated signature indicative of Floridan aquifer system ground water. Additional Sr isotopic ratios from a series of surficial and Lower Floridan well samples suggest dynamic ground water mixing, and do not provide clear evidence for a single hydrogeologic water source at the spring vent. In this karst-dominated aquifer, such energetic mixing at the vent feature is expected, and would be facilitated by conduit and fractured flow. Radium isotope activities were utilized to estimate flow-path trajectories and to provide information on potential travel times between an onshore well and the spring. Using either 223Ra and 224Ra or 228Ra, and qualifying this approach with several key assumptions, estimates of water mass travel times from an upper Floridan well in Crescent Beach to the submarine vent feature (distance=4050 m) are in the order of ∼0.01–0.1 m min −1.

Response of a sloping aquifer to constant replenishment and to stream varying water level

The problem of seepage from a stream into an adjacent unconfined aquifer of semi-infinite extent, underlain by an impermeable sloping bed was considered in this study as a problem of one-dimensional unsteady-state groundwater flow. It was assumed that the water level in the stream gradually rises to a certain height, according to a known exponential function of time, while the aquifer was assumed to be replenished at a constant rate from ground surface. Applying the Laplace transformation method derived an analytical solution to an extended and linearized form of the nonhomogeneous Boussinesq equation used to describe the phreatic surface in sloping aquifers. The comparison of the analytical solution with a numerical solution obtained by applying the finite difference Mac Cormack explicit computational scheme to the nonlinear Boussinesq equation illustrates the validity of the new analytical solution and the effectiveness of the linearization. Some nondimensional diagrams are also presented to show the variation of the water table height and the seepage rate as well as their sensitivity to various sets of parameter values.

Wave Impact on a Wall Using Pressure-Impulse Theory. II: Porous Berm

Breakwaters often stand on a rubble mound or have a rubble berm in front of the structure. The pressure-impulse model for violent water-wave impact on a wall fronted by an impermeable bed is extended to include a porous region simulating a porous berm. The effect of different berm porosities on the pressure impulse is investigated. Even some large changes in porosity are found to have little effect (at most 20%) on the pressure impulse both on the wall and along the berm. However, in this study evolution toward the wall is not included.

Prediction of Subsurface Stormflow in Heterogeneous Sloping Aquifers

An ensemble-averaged prediction equation system for transient subsurface stormflow on sloping impermeable beds in heterogeneous hillslopes is derived by means of the regular perturbation method. The covariance of hydraulic conductivity and flow depth, which emerges during the derivation of the mean flow depth, causes a closure problem. To close the equation system, a second equation is derived for this covariance term. The overall set of ensemble-averaged prediction equations then is solved numerically and their validity is tested by comparing the results against those obtained from a Monte-Carlo simulation for different values of slope and variance of hydraulic conductivity. The comparison of the results suggests that the system of prediction equations gives satisfactory results for coefficient of variation of hydraulic conductivity as high as 1.12 for slopes as steep as 0.3.

Free Surface Flow over Permeable Wavy Bed

A theoretical analysis based on potential flow theory over a permeable wavy bed and a linear Darcy equation shows that the perturbations of the flow field have a phase shift relative to the wavy bed form. This phase shift results in a net form resistance on the permeable wavy surface of the bed form. The experimental results indicate that there is a phase shift between the permeable wavy bed form and the water surface profile. The theoretical results show that the phase shift and friction factors increase with the Reynolds number of the porous media flow; however, the experimental results show that the phase shift decreases with the Reynolds number of the porous media flow. This is caused by the phenomenon of flow separation on the wavy bed. The water surface profiles over the permeable wavy bed are compared with those over the impermeable wavy bed in the case of the same Froude numbers. The velocity distributions over the permeable and the impermeable wavy bed are also investigated experimentally and theoretically. The boundary wavy profiles of the permeable and the impermeable bed form vary sinusoidally.

Nature and origin of ‘carbon’ in the Archaean Witwatersrand Basin, South Africa

The nature and origin of the carbonaceous matter (‘carbon’) in the gold-bearing reefs of the Archaean Witwatersrand basin of South Africa has long been a subject of controversy and debate. The importance of the carbon results from its direct association with the gold grade. The studies reported here were directed at resolving the nature and origin of carbon. Techniques used include stope-scale (macroscopic) mapping, mesoscopic (hand specimen) examination, and microscopic studies incorporating the use of optical reflectance measurement. Macroscopic mapping has demonstrated the braided habit of carbon bodies over tens of square metres, with a close parallel to sedimentology. Mesoscopic observations, however, show the vein-like carbon seams are often cross-cutting sedimentary features, with the carbon occupying an anastomosing set of bed-parallel fractures. Microscopic observations show a globular form for the carbon and inclusions of uraninite particles. In seam carbon the globules are generally modified into elongated ‘spindles’ oriented perpendicular to bedding. Optical properties are dominated by generally high reflectance and anisotropy with a ‘swirling’ liquid crystal structure, classifying seam carbon as ‘carbonaceous mesophase’. It is this fine mesophase texture that has previously been wrongly attributed to plant (algal) morphology. Highly significantly, the optical anisotropy is bed perpendicular (rather than bed parallel as in normal sedimentary burial) indicating mesophase formation during fracture opening. Both reflectance and bireflectance of the seam mesophase show a range of values at all scales. No stratigraphic or depth trends were apparent, though geographic variation points to localization of the maximum temperature event(s). Given high anisotropies, maximum reflectance values in the 4–8% R o range and minima in the 1–2% R o range give arithmetic mean reflectance values of about 4.0% R o . Kinetic modelling equates these values with short term (50 000 years) temperature events of c. 400°C or burial temperatures of c. 280°C. Lower reflectance values of c. 2.0% R o obtained from the shales suggests thermal detachment of permeable and impermeable beds, a characteristic of pulsed hydrothermal flux. The included uraninite grains influence the orientation of the surrounding anisotropic mesophase demonstrating that uraninite predated the mesophase formation event. Regional palaeo-stress ‘frozen’ into the mesophase anisotropy indicates a NW–SE deviatoric stress. The combination of hydrocarbon, radiation and hydrothermal fluid flow marks Witwatersrand Basin pyrobitumens out as being different from conventional oil. Putative source rocks for the oil are identified in the intra-basinal Witwatersrand shale units. Lithological control in carbon seams is explained by the poro-perm and mechanical properties of the unconformity sequence of footwall, reef conglomerates and hanging wall quartzites favouring fracture along the unconformity surfaces. An overpressured oxidizing fluid created the fracture network that hosted the oil and also introduced uranium as uranyl ion. On meeting a reducing agent (oil), uraninite precipitated stabilizing the oil by polymerization. Further hotter hydrothermal flux then ‘coked’ the bitumen to often fibrous (spindle-shaped) mesophase. Continued flow deposited gold in the available pore spaces, most notably those formed by lateral contraction between mesophase spindles. The speculative role of methane in the reductive precipitation of gold is indicated by the presence of gold in any co-eval porosity largely independent of the mineral matrix.

MODELING WAVE CURRENT INTERACTION OVER AN UNEVEN SEA BOTTOM

A mathematical model is established to describe wave-current interaction over uneven sea bottoms. The basic equations of the model are obtained by vertically integrating the continuity equation and the equation of motion for flow over impermeable sea bed of mild slope. Finite difference method is utilized for numerical solutions and the results for a wave-current coexistent field over submerged mound show that the variation of the wave features is fairly significant due to the presence of the current which leads to remarkable drop of the mean water level over the mound and that the waves also affect the mean water level appreciably.

Characteristics of relict permafrost on the West Siberian Plain

Abstract The article discusses the occurrence of a zone of deep‐lying relict permafrost in the northern part of the Ket’ basin in the West Siberian Plain. It occurs at depths varying from 117 to 283 m. This permafrost is very “warm,”; its temperature being only a fraction of a degree below 0° C. It is suggested that this permafrost may not be related to atmospheric temperatures, but rather to processes occurring within the rocks; as gas compressed within permeable reservoir rocks escapes through fractures in overlying impermeable clay beds, the release of pressure may produce a reduction in temperature sufficient to initiate freezing.

Pressure and Set Down for Higher‐Order Stokes Waves on Current

The Bernoulli equation for higher‐order Stokes waves on a steady current over a horizontal, impermeable bed was analyzed, and an ambiguity was detected in the determination of the wave‐induced pressure at even‐order theories. This leads to the introduction of a new (reduced) Bernoulli constant. A simple relation between this quantity and the current‐wave set down is presented, and the set down correct to the fourth order in wave steepness is calculated. The finding of the fourth‐order current‐wave set down is a necessary step to allow calculation of the wave height for fourth‐order shoaling in the presence of a current. Finally, the difference between a wave quantity belonging to nth‐order theory and being correct to the nth order is discussed, and guidelines are offered for the determination of the former and the corresponding dispersion relation.

The Efficiency of Vertical Drains Piercing Flat-Lying Beds at Piedra Del Aguila Dam

This paper analyzes the problem of determining the pattern of flow to expect through a sequence of flat-lying beds of varying permeability which are pierced by a series of equally spaced vertical drains. A single permeable bed is assumed to be bounded by two impermeable beds from above and below and the influence of a reduction in screen efficiency is evaluated. This work arose from design work associated with the Piedra del Aguila hydroelectric project in Argentina in which the left abutment of the dam consisted of an ancient buried river channel filled with a sequence of sand and gravel sediments of varying clay content mixed with layers of volcanic tuff. The outcome of the study is that a practical limit of intercepting 80% of the flow is feasible and that this limit depends strongly upon the efficiency of the drains. All suspected aquifer beds must be drained and drain efficiency should be monitored over time.

Deep circulation of groundwater in overpressured subglacial aquifers and its geological consequences

It is generally assumed that meltwater from the base of ice sheets is discharged in a relatively thin subglacial zone. Whereas this may be true for ice sheets resting on impermeable beds, many ice sheets, such as the glacial period ice sheets of North America and Europe, flowed over extensive aquifers. A theory is developed which suggests that high rates of meltwater discharge into these aquifers would have completely reorganised their flow fields, producing intergrated patterns of glacially pressurised flow controlled by the continental-scale form of the ice sheet surface rather than the small-scale topographic basins which determine modern aquifer extent. The theory is applied to the aquifers which underlay the Saalian ice sheet in The Netherlands, where it is shown that potential gradients and groundwater flow velocities would have developed which were two orders of magnitude greater than modern values and that the dominant flow vectors would have been normal to those of the modern flow. Thus, glacial/interglacial cycling in areas which have suffered periodic glaciation during the late Cenozoic may have experienced alternating phases of greater and lesser flow energy. It represents another example of climatically-driven cyclical change in the earth. Under highly energised glacial conditions, potential gradients much larger than modern values may have produced many common features of sediment disruption, such as diapirs, liquifaction structures and pipes, and forms such as glacial ‘doughnuts’ and pock marks, which have hitherto been explained by other processes. Deep and penetrative flushing of aquifers by glacial meltwater may have left a distinctive geochemical signal in them which may be used to test the theory. Gases such as methane, generated at shallow depth, may have been trapped beneath the glacial ‘cap-rock’, and may also have played an important role in these processes.

Wave impact pressure and its effect upon bodies lying on the sea bed

This paper is concerned with the very large, sudden pressures produced by water-wave impact on a vertical wall. Numerical and theoretical models are briefly described and we show that there are significant pressure gradients along an impermeable sea bed, away from the wall. This aspect of wave impact pressure has not previously been noted. The effects of such transient pressure gradients on bodies lying on the bed are examined in the light of pressure impulse theory. Our theoretical results indicate that bodies may be displaced by these pressure gradients when ordinary fluid drag is insufficient to move them. We discuss the impulse and the speed imparted to a rigid body lying within a region of pressure impulse which has constant horizontal gradient, and we show that the impulse is related to the body's volume, and shape. Analytic results are given for a hemi-ellipsoidal “boulder”, which is free to translate in a direction perpendicular to the wall. The analysis for the hemi-ellipsoid encompasses the special cases of a semi-circular cylinder and a semi-circular disc. The case of a circular cylinder which touches the bed is also discussed, and it is shown that there is a significant vertical impulse on the body in addition to the horizontal component of the impulse.

Weichselian upper pleniglacial aeolian and ice‐cored morphology in the southern Netherlands (Noord‐Brabant, groote peel)

AbstractThe morphology of the Weichselian Late Pleniglacial land surface in the Groote Peel nature reserve (southern Netherlands) is characterized by numerous circular to oval depressions. The depressions are up to 90 m wide and 3 m deep. Some are surrounded by low (50–100 cm) ridges. Two depressions were selected for detailed study. One, of aeolian origin, is shallow (less than 1 m), the underlying sedimentary units are undisturbed and the ridge surrounding it consists of horizontally bedded aeolian sand. The second, formed by the melting of an ice core, is deeper (3 m) and dissects older units. The ice lens probably formed during the Weichselian Late Pleniglacial. Ice segregation was favoured by a low topographic gradient, impermeable beds in the subsoil and poor drainage. After partial decay of the ice core, a remnant survived during the cold, arid conditions of the Beuningen deflation phase. Final melting of the ice core occurred after deposition of Late Pleniglacial aeolian coversand, at the onset of the Late Glacial climatic amelioration. Palynological analysis indicates that infilling of the ice‐core depression started in the Late Glacial Older Dryas and possibly even during Oldest Dryas.

The Nubian Sandstone aquifer in the central and northern Negev, Israel: delineation of the hydrogeological model under conditions of scarce data

The Cl − content of ground water in the central and northern Negev ranges between 250 mg 1 −1 in the Beer Sheva area and 1600 mg 1 −1 near the Egyptian border, where the water is also thermal with high concentrations of sulphates and iron. During the last few years, groundwater resources in the heavily populated Beer Sheva area have become endangered by a continuing process of salinization. In the course of the present work, it was found that, in the study area, ground water flows through a multiple aquifer system including the Jurassic-Lower Cretaceous Kurnub Group and the Upper Cretaceous Judea Group aquifers. Because of the absence of impermeable beds at the boundary between the two groups, brackish ground water flows from the Kurnub Group into the overlying Judea Group aquifer. Moreover, numerous faults discovered in the subsurface facilitate lateral inflow of Kurnub ground water into the Judea aquifer. By interpreting new lithostratigraphic data from the Kurnub Group and seismic surveys made in the study area, it is shown that the Kurnub aquifer extends far beyond the hitherto known boundaries and contains an additional estimated volume of 51 × 10 9 m 3 of paleowater. The limiting factors of its exploitability are groundwater depth and salinity. The rational exploitation of the Kurnub paleowater may prevent salinization of the overlying Judea Group aquifer.

Overland Flow from Solitary Waves

The one‐dimensional inundation over an impermeable horizontal bed by incident solitary waves is studied both experimentally and numerically. The numerical model is based on a set of Boussinesq long‐wave equations cast in the Lagrangian frame and a finite element technique is used to effect a numerical solution. Two nonbreaking solitary waves with amplitude ratios H/d=0.14 and 0.21 were studied, and for each wave both a dry bed and a wet bed were investigated. Near the still shoreline the wave steepness is sufficiently large to require a nonhydrostatic correction to the horizontal pressure gradient, and good agreement is found between the laboratory data and the numerical results for the dry bed. The wet‐bed case could not be modeled numerically. Although the initial collapse of the wave onto the bed is not influenced significantly by viscous effects, bed friction becomes important during the subsequent inundation phase. Peak inundation front speeds are reduced 10–15% for propagation over the wet bed as compared to the dry one.

Permeability variations and aquifer development in the Dungeness shingle

The shingle of the Dungeness Foreland forms a locally important freshwater aquifer. The distribution of groundwater is largely controlled by impermeable beds of sand within the shingle. The impermeability of these beds reflects both their original texture as beach-forming sediments and the subsequent infiltration and deposition of fine-grained material. Quarrying of the Dungeness shingle is liable to breach the impermeable horizons enclosing the aquifer and has exposed it to saline intrusion. The paper is based on experience gained by the senior author (DHBR) during the commercial development of water supply from Dungeness.

Strontium Isotopic Stratigraphy Utilizing Authigenic Dolomites in Hemipelagic Sediments: ABSTRACT

Authigenic dolomites commonly occur in organic-rich, continental margin marine sediments. These dolomites play a key role in the age dating of stratigraphic sections. The dolomites often are the only lithology amenable to paleomagnetic stratigraphy; they preserve siliceous microfossils against diagenetic; recrystallization, and provide useful strontium isotopic stratigraphic ages. Several potential sources of error frequently are unique to the use of authigenic dolomites in the strontium isotope methods. (1) The dolomites occur as cements of the host lithology, hence, they are not a pure phase. Potentially important contaminants during analysis include gypsum clay minerals, feldspars, and iron and manganese oxides. Strontium may occur as a structural substituent ion in these minerals or as a surface-adsorbed ion. Various leaching techniques have been tested to isolate dolomitic strontium. Purer dolomites and strontium-enriched dolomites often can be selected to ease these problems. (2) The dolomites form after the deposition of the host sediment, therefore, they record the diagenetic age not the depositional age. The stable isotopic composition of the dolomites can aid in selection of early formed samples. (3) The dolomites record pore-water strontium isotope compositions, not seawater isotopic compositions. This problem is also minimized by choosing dolomites formed near the sediment-water interface. (4)more » The dolomites formed near the sediment-water interface originated as rotodolomites and undergo subsequent burial diagenesis, creating a potential for later strontium isotope exchange. This problem is minimized by selecting fresh samples from the interior of nearly impermeable beds and nodules. Results from the Miocene Monterey Formation of California and from the Eocene through Pliocene Pisco basin of Peru show that authigenic dolomites can provide useful strontium isotopic age estimates.« less

SOLITARY WAVES PASSING OVER SUBMERGED BREAKWATERS

A method is described for the computation of the two-dimensional unsteady motion of a solitary wave passing over submerged breakwaters. Far from the breakwater the fluid is assumed static and the sea bed is level. The fluid motion is assumed to be irrotational, incompressible and inviscid. The exact boundary conditions at the free surface and the impermeable bed are satisfied. Laplace's equation for the velocity potential is solved using a boundary integral method. Numerical results are reported which show the variety of ways in which solitary waves are distorted when they encounter submerged breakwaters.