Explicit solution of a free boundary problem for a nonlinear absorption model of mixed saturated-unsaturated flow

In wet soils, zones of saturation naturally develop in the vicinity of impermeable strata, surface ponds and subterranean cavities. Hydrology must be then concerned with transient flow through coexisting unsaturated and saturated zones. The models of advancing saturated zones necessarily involve a nonlinear free boundary problem.A closed-form analytic solution is presented for a nonlinear diffusion model under conditions of ponding at the surface. The soil water diffusivity is restricted to the special functional form D(θ) = a/(b − θ)², where θ is the water content field to be determined and a, b are positive constants. The explicit solution depends on a parameter C (determined by the data of the problem), according to two cases: 1 < C < C₁ or C ≥ C₁, where C₁ is a constant which is obtained as the unique solution of an equation. This result complements the study given in P. Broadbridge, Water Resources Research, 1990, 26, 2435–2443, in order to established when the explicit solution is available. The behavior of the bifurcation parameter C₁ as a function of the driving potential is studied with the corresponding limits for small and large values. Moreover, the sorptivity is proven to be continuously differentiable function of the variable C.     

Comparison of Galerkin-type discretization techniques for two-phase flow in heterogeneous porous media

A comparison of Standard Galerkin, Petrov-Galerkin, and Fully-Upwind Galerkin methods for the simulation of two-phase flow in heterogeneous porous media is presented. On the basis of the coupled pressure-saturation equations, a generalized formulation for all three finite element methods is derived and analysed. For flow in homogeneous media, the Petrov-Galerkin method gives excellent results. But this method fails miserably for problems with heterogeneous media. This is because it is not able to capture correctly processes that take place at interfaces when, for instance, the capillary pressure-saturation relationship after Brooks and Corey is assumed. The Fully-Upwind Galerkin method is superior to the Petrov-Galerkin approach because it is able to give correct results for flow in homogeneous and heterogeneous media for the two models of van Genuchten and Brooks-Corey. The widely used formulation which is correct for the homogeneous case cannot be used for heterogeneous media. Instead the straightforward approach of gradp_c in combination with a chord-slope technique must be utilized.     

Lithospheric Geothermal Structure in Yunnan, China

In this paper,the characteristics of the lateral variations of the deep heat flow and Hthospheric geotemperature distribution in Yunnan have been studied,and the lithospheric geothermal structure has been divided into three types,i.e.the geothermal structure in the typical modern tectonically active region,transitional geological region and stable geological region.Finally,the relationship between the geotherm and seismicitv has been discussed.     

Tectonics and Chemical Transport: The Rules of the Resource Game

The most basic solid earth resources for use by man include construction materials, energy resources, metals, ceramics, soils. With the exception of construction materials, the formation of economic mineral deposits and soils involves the thermal or gravity driven flow of various types of geofluids. The search for mineral deposits thus involves the understanding of the exact nature of fluids, their mass and flow patterns. Given the giant thermal disturbances associated with the formation and destruction of Gondwana, it must be no surprise that these regions contain very significant mineral resources on a large scale.     

Numerical simulation of NAPL flow in the subsurface

A three-dimensional, three-phase numerical model is presented for simulating the movement of immiscible fluids, including nonaqueous-phase liquids (NAPLs), through porous media. The model is designed to simulate soil flume experiments and for practical application to a wide variety of contamination scenarios involving light or dense NAPLs in heterogeneous subsurface systems. The model is derived for the three-phase flow of water, NAPL, and air in porous media. The basic governing equations are based upon the mass conservation of the constitutents within the phases. The descretization chosen to transform the governing equations into the approximating equations, although logically regular, is very general. The approximating equations are a set of simultaneous coupled nonlinear equations which are solved by the Newton-Raphson method. The linear system solutions needed for the Newton-Raphson method are obtained using a matrix of preconditioner/accelerator iterative methods. Because of the special way the governing equations are implemented, the model is capable of simulating many of the phenomena considered necessary for the sucessful simulation of field problems including entry pressure phenomena, entrapment, and preferential flow paths. The model is verified by comparing it with several exact analytic test solutions and three soil flume experiments involving the introduction and movement of light nonaqueous-phase liquid (LNAPL) or dense nonaqueous-phase liquid (DNAPL) in heterogeneous sand containing a watertable. This revised version was published online in August 2006 with corrections to the Cover Date.     

Reconstruction of natural groundwater flow paths in the multiple aquifer system of the northern Negev (Israel), based on lithological and structural evidence

 The Judea Group, a limestone and dolomite karstic aquifer of late Albian–Turonian age, is one of the most important sources of water in Israel. In the western part of the country, the Judea Group aquifer is also known as the Yarkon–Taninim basin. In the northern Negev, the Judea Group is a recipient for fresh water flowing southward from the Hebron Mountains and of brackish paleowater flowing northward from Sinai. Very little is known of the hydraulic properties of this aquifer. In order to outline assumed natural flow paths that existed in this karstic environment prior to groundwater exploitation, use was made of lithological, structural, and paleomorphological features. A detailed hydrogeological conceptual model of the Judea Group aquifer in northern Negev was established by the geological interpretation of high-resolution seismic reflection and by analysis of lithological evidence from boreholes. Isopach, isolith-contour, and isolith-ratio maps were compiled for the main lithological components. Increase in transmissivity values is inversely proportional with the cumulative thickness of argillaceous components. The lithological and hydraulic evidence provides the basis for subdividing the subsurface into distinctive permeability zones for the upper and lower sections of the aquifer; for outlining possible preferential groundwater flow paths for both subaquifers; and for improving understanding of groundwater-salinty variations that result from lithological variability, direction of groundwater flow paths, groundwater flow rates, and the duration of rock/water interactions. In an earlier conceptual model of the basin, the Judea Group aquifer was regarded as a continuous and undisturbed entity. The present study reveals an intricate groundwater flow pattern that is controlled by lithological and structural factors that create zones of preferential flow. This interpretation bears on the overall evaluation of groundwater resources and their management and exploitation. Received, December 1996 · Revised, October 1997, June 1998 · Accepted, July 1998     

Adaptive hierarchical upscaling of flow in heterogeneous reservoirs based on an a posteriori error estimate

This paper treats the upscaling of the absolute permeability in a heterogeneous reservoir. By replacing the fine scale permeability tensor with an upscaled, or effective permeability tensor, a modelling error is introduced. An a posteriori error estimate on this modelling error is formulated and tested. An implementation of the theory, based on domain decomposition coupled with a hierarchical representation of the absolute permeability field, is given. As hierarchical basis functions we have chosen the Haar system, which leads to a wavelet representation of the permeability. The wavelet representation offers a natural upscaling technique which resembles the highcut filters commonly used in signal analysis. This procedure represents an adaptive upscaling method. The numerical results show that this method conserves both the dissipation and the mean velocity in the problem fairly well. The a posteriori error estimate on the modelling error coupled with domain decomposition methods constitutes a powerful modelling tool.     

Non-linear spherical Alfvén waves

We present a one-dimensional numerical study of Alfvén waves propagating along a radial magnetic field. Neglecting losses, any spherical Alfvén wave, no matter how small its initial amplitude is, becomes non-linear at sufficiently large radii. From previous simulations of Alfvén waves in plane-parallel atmospheres we expected the waves to steepen and produce current sheets in the non-linear regime, which was confirmed by our new calculations. On the other hand we found that even the least non-linear waves were damped out almost completely before 10 R_⊙. A damping of that kind is required by models of Alfvén wave driven winds from old low-mass stars as these winds are mainly accelerated within a few stellar radii.     

Some fine-grained sedimentation phenomena in caves

Fine-grained sedimentation in caves often occurs by the parallel accretion of laminations upon the underlying bedforms. These laminations show remarkable persistence in unit thickness and grain size in a down-passage direction. A translatory flow mechanism ofdeposition is postulated which results in the rhythmic pulsing of sediment-laden water into subterranean lakes in response to variations in surface climate. The sediments are pulsed into standing water via multiple inputs, often resulting in coarser sediment being deposited on steeper slopes than on more gentle slopes. The final extension of this sediment input is the complete filling of the cave passage to the roof. The problem of sediment stability on steep slopes remains an unanswered anomaly.     

Mantle heat flow and geotherms for major tectonic units in central Europe

The results of seismic measurements along the deep seismic sounding profile VII and terrestrial heat flow measurements used for construction of heat generation models for the crust in the Paleozoic Platform region, the Sudetic Mountains (Variscan Internides) and the European Precambrian Platform show considerable differences in mantle heat flow and temperatures. At the base of the crust variations from 440–510°C in the models of Precambrian Platform to 700–820°C for the Paleozoic Platform and the Variscan Internides (Sudets) are found. These differences are associated with considerable mantle heat flow variations.The calculated models show mantle heat flow of about 8.4–12.6 mW m^–2 for the Precambrian Platform and 31 mW m^–2 to 40.2 mW m^–2 for Paleozoic orogenic areas. The heat flow contribution originating from crustal radioactivity is almost the same for the different tectonic units (from 33.5 mW m^–2 to 37.6 mW m^–2). Considerable physical differences in the lower crust and upper mantle between the Precambrian Platform and the adjacent areas, produced by lateral temperature variations, could be expected. On the basis of carbon ratio data it can be concluded that the Carboniferous paleogeothermal gradient was much lower in the Precambrian Platform area than in the Paleozoic Platform region.