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Knowledge of the geometrical properties of porous rocks is crucial for the evaluation of their hydrocarbon potential. A major problem in quantitative formation evaluation is to provide a physical basis of Archie's equations first published in 1942, which are widely used in formation evaluation and are believed to reflect this knowledge empirically. Our study, a theoretical model-based approach, provides a physical basis of Archie's first equation (Archie I) and puts it up for scientific discussion. We employ the statistical network model theory of Schopper, and take sedimentation and favorable diagenetic conditions restricted to compaction into account. We find that compaction is a prominent geological feature that needs to be considered and quantified in order to establish a physical basis of Archie I. Our interpretation of Archie I – that it measures in relative terms – is in agreement with this finding, but not in line with the mainstream view, which interprets Archie I in absolute terms. Evidence suggests that compaction may also provide the overarching physical basis to address within-well integration of borehole–geophysical data (including resistivity data) as well as their integration across spatial scales from well-to-well and beyond. Although our more consistent understanding of Archie's first equation clearly helps to advance today's evaluation of resistivity logs, the gain in evaluating these logs is still not satisfactory. more...

Spectral induced polarization as well as complex electrical measurements are used to estimate, on a non-invasive basis, hydraulic permeability in aquifers. Basic laboratory measurements on a variety of shaly sands, silts and clays showed that the main feature of their conductivity spectra in the frequency range from 10-3 to 103 Hertz is a nearly constant phase angle. Thus, a constant-phase-angle model of electrical conductivity is applied to interpret quantitatively surface and borehole spectral induced polarization measurements. The model allows for the calculation of two independent electrical parameters from only one frequency scan and a simple separation of electrical volume and interface effects. The proposed interpretation algorithm yields the true formation factor, the cation exchange capacity and the surface-area-to-porosity ratio, which corresponds to the inverse hydraulic radius. Using a Kozeny–Carman-like equation, the estimation of hydraulic permeability is possible. more...

Today's practice of interpreting Hg capillary pressure curves — a widespread method in porosimetry — is generally unsatisfactory. This has already been demonstrated by Fatt. First, the saturation branch of such a curve is interpreted using the concept of a pore space model in which essential features of a network structure are disregarded. Second, the data provided by the desaturation branch are not used. Distributions of radii of capillaries within porous materials derived by this technique are usually incorrect in that the frequencies of occurrence of the greater radii turn out too small, those of the smaller radii too large. We present a more reliable approach which constrains radii frequency ranges for the Hg saturated pore space and for both the part of the pore space that desaturates and the part that traps mercury when Hg pressure is released. The pore space may be of an arbitrary geometrical structure, the radii distribution may be continuous. Also, the Hg desaturation may enable one to distinguish experimentally between structural and contact angle hysteresis. more...

Non-linear highly energetic plasma phenomena play a key-role in the understanding of astrophysical objects. We present plasma scenarios that provide a valid description for coherent radiation emission features observed from pulsar magnetospheres and for the self-consistent magnetic field generation essential for γ-ray burst synchrotron models. For this purpose we study ultra-relativistic plasma shell collisions with ensembles of up to 109 particles. We introduce the framework of the Particle-In-Cell (PIC) approach, details of the numerical realization and performance issues on the IBM REGATTA system of the Rechenzentrum Garching and the HITACHI supercomputer of the Leibniz Rechenzentrum. A final overview on simulation results and future perspectives closes the contribution. more...

The CERN Axion Solar Telescope (CAST) searches for axions coming from photon to axion conversion in the sun's core, as stated by the Primakoff effect. Axions arise in particle physics as a consequence of the breaking of Peccei-Quinn symmetry which has been introduced as a solution to the strong CP problem. As cosmological axions they are candidates for at least some part of cold Dark Matter.They are also expected to be produced copiously in stellar interiors with energies as high as the thermal photons undergoing photon to axion conversion. In our sun the axion energy spectrum peaks at about 4.4 keV, extending up to 10 keV. CAST collected preliminary data in 2002 and data taking with its full capability will start in the beginning of 2003., NEB-X Conference on "New Developments in Gravity", May 30-June 2, 2002, Chalkidiki, GREECE. 5 pages, 2 figures more...

Magnetic reconnection is one of the most effective particle acceleration processes. Usually this process is described in a simplified analytical way. This implies a homogeneous electrical field, which has its origin in the 2-D-description of the reconnection mechanism. more...

Geophysical measurements rarely yield the target quantity, of practical interest directly. These target paramters have to be calculated from the measured quantities with the aid of petrophysical models. Examples of such target parameters are. the effectivity of rocks for advectional or diffusional transport and for sorption processes, including permeability as the advectional transport parameter, the formation factor for diffusional transport, and the specific internal surface area, measured at the due physical resolution for sorption processes. These parameters are not directly measureable with logging methods but accessible only with the help of petrophysical models from combinations of other parameters and basic generally a knowledge of complete pore size distributions. more...

A theory has been developed for calculating interlayer conductivity for natural porous systems, such as sedimentary rocks. As the materials investigated are mainly made up of silica and alumina minerals, an electrical double layer can be presumed, which carries the physical process. A new approach has been attempted by modelling the geometrical conditions. A self-similarity model has been established for describing the porous medium, the parameters of which can be derived from physical measurements. The considerations are based on the fact that the pore wall surface is structured in all orders of magnitude in such a way that the theory of fractal dimensions is applicable. Apart from the geometrical constraints, the electrochemical conditions and limitations are discussed. Experimentally, a set of sedimentary rocks were investigated for nine physical properties. A mean charge density calculated from interlayer conductivity gave a relatively high value close to that from cation-exchange capacity measurements. more...

Besides the knowledge of material constants of the homogeneous phases of a disperse system, a good understanding of its geometrical properties is necessary for describing physical processes. In order to characterize the shape of the interface between solids and pore space with respect to the irregularities in all orders of magnitude, the fractal dimension has proved to be an informative parameter. By this study the theory of fractal dimensions, in three-dimensional space originally limited to topological curves, surfaces and volumes, is extended into physical properties like specific surface, tortuosity, porosity and formation factor with “physical” dimensions −1 or 0 as an exponent of the unit of length. The typical properties of the true fractals are transferable to some of these derived parameters. This leads to power laws describing the dependence of the particular measure on the resolution length. With special models, which seem to be of widespread validity in nature, petrophysical considerations lead to further power laws for the rest of the physical parameters, dependent on discrete length parameters such as grain radius and pore radius. By determination of the exponents of such independent power laws, a better particle characterization is possible, as the fractal dimension of the surface alone may be misleading, especially when the grain size of the particles is not uniform. more...

SUMMARY Based on self organized growth, a self-similar geometrical model of rock materials is established. The structural mode of the internal surface is carried over to the three-dimensional structure of the pore space and solid phase, which can be described as a fractal network. It is characterized by the fractal dimension of surface, which can be measured by physical and stereological methods. From this, the fractal behaviour of other geometrical properties, relevant for physical processes, such as porosity, number of solid connections, tortuosity and constrictivity of the capillary system and of the solid phase can be derived. more...

In a paper presented at last year's Amsterdam meeting (viz. Geophysical Prospecting 14 (1966), 3, 301–341), J. R. Schopper derived formulas relating formation factor, permeability and porosity, by means of a statistical-network approach and by treating the electric and hydraulic resistance analogously. The model of the porous medium consists of a network of branch resistors, their values being statistically distributed about a mean Ro with a relative standard deviation (variation coefficient) s. A properly defined total resistance R of the network can be expressed by the relationship: ((1′)) Here α is a geometrical factor dependent only on the shape of the network (i.e. the number of meshes in the longitudinal and transversal direction), e is a characteristical constant dependent only on the individual mesh shape (i.e. the number of nodes and branches within a mesh). This network constant e enters the equations relating formation factor, permeability and porosity, e had been found to be in the range zero to one by calculating algebraically two special limiting network cases. However, for a better understanding of which value exactly this constant will have in actual porous media, networks with various mesh shapes have to be treated generally. Because of the basically statistical approach, the networks have to be large so that a general algebraic treatment is precluded. Hence numerical methods using digital computers must be applied. The determination of the total resistance R of any resistance network leads to the problem of solving a system of linear, inhomogeneous equations; i.e. Ohm's law written in matrix form: ((2′)) (R) is the matrix of the coefficients, composed of the individual branch resistances. (I) is the column vector, its components being fictitious circular mesh currents. (U) is the inhomogeneity column, its components being source voltages within the individual meshes. The matrix (R) has characteristic properties that depend on the mesh shape on the one hand and on the number and arrangement of the meshes on the other hand. With the regular arrangement of identical meshes investigated here, the matrix always has a banded structure and is symmetrical with respect to the main diagonal, positive definite, and non-singular. For the numerical determination of the wanted constant e the coefficients matrix is provided with values having a known distribution. Here, in particular, a computer-generated pseudorandom homogeneous distribution is used. The system, of equations is solved for R by a modified Cholesky method. Equation (1′) can then be solved fore. The main features of an ALGOL program written for this purpose and optimized with respect to storage space requirement and computer time are discussed. Networks of triangular, square and hexagonal meshes have been investigated. The results are discussed. more...

As shown previously by the author, the relations between formation factor, permeability, and porosity can be expressed in statistical parameters of the microscopic pore system. A number of other macroscopically measurable quantities depend on those same parameters. Thus, by proper combination of these quantities, it should be possible to solve for those parameters, that cannot be retrieved by direct methods. In this article, the dependencies on these statistical parameters of the capillarity with imbibition and drainage, the irreducible water saturation, the flow dispersion with miscible displacement, and quantities that are directly observable at ground surfaces or thin sections, are preliminarily studied as a preparation for possible practical measurements. (50 refs.) more...

In [50] and [51] a theory has been developed relating formation factor, permeability and porosity of porous sedimentary rock by means of statistical parameters of the pore system, and further, tying those statistical parameters to other macroscopically measurable quantities like capillarity, capillary retention, flow dispersion etc. This paper deals with experimental methods and apparatus for checking the theoretically derived relations using columns of packed loose or artificially consolidated sands or other granular matter. Some initial experiments, mainly intended for checking out equipment and methods are reported. The discussion of the results so far shows good agreement with the theory in most cases, except for the irreducible water saturation. However, for a definite statement on the general validity of the theory more data must be accumulated. ZUSAMMENFASSUNG In [50] und [51] wurde eine Theorie entwickelt zur Verknupfung von Formationsfaktor, Permeabilitat und Porositat poroser Sedimentgesteine mit Hilfe statistischer Parameter des Porensystems und ferner zur Zuruckfuhrung dieser statistischen Parameter auf andere makroskopisch messbare Grossen wie z. B. Kapillaritat, Kapillarretention, Stromungsdispersion usw. Diese Veroffentlichung hier behandelt experimentelle Methoden und eine Messapparatur zur Prufung der theoretisch abgeleiteten Beziehungen an Kolon-nen mit gepackten losen und kunstlich verfestigten Sanden und anderen granularen Materialien. Uber einige erste Experimente, die hauptsachlich der Erprobung der Appara-tur und der Messmethoden dienen sollten, wird berichtet. Die Diskussion der bisherigen Resultate zeigt in den meisten Fallen – ausgenommen fur die irreduzible Wasser-sattigung – gute Ubereinstimmung mit der Theorie. Jedoch ist fur eine bindende Aussage uber die allgemeine Gultigkeit der Theorie noch weiteres Datenmaterial notig. more...

The knowledge of hydraulic and electric properties of porous media and the relations between them is essential for the quantitative evaluation of electric well logs and the solution of other reservoir engineering problems. The state of the art in this field is not yet satisfying. Theories still show considerable discrepancies with practice due to oversimplified model approaches. Empirical relations are either too coarse, not fully determined, or valid under specific geological and geographical conditions only. This article deals with the development of a general theory of the electric and hydraulic resistance behavior of porous media on the basis of a very general statistical network model. A general solution of the relations between formation factor, permeability, and porosity is presented by means of a rigorous mathematical treatment of two limiting cases of such a network. The solution shows that the product of the formation factor and the permeability can be expressed in the expectation values and the variation coefficients of pore channel cross section and shape factor and by a network factor, that depends on the mesh texture of the network. This network factor is in the range zero to one. It is further shown that the path length increase enters both the electric and the hydraulic tortuosity by its square. more...

Motivated by the noise-boundary layer transition problem in supersonic flow, the interaction between incoming aerodynamic noise and the laminar boundary layer was studied. The noise field was modeled as a Mach wave radiation field consisting of discrete waves emanating from coherent turbulent entities moving downstream within the supersonic turbulent boundary layer. The individual disturbances are likened to miniature sonic booms and the laminar boundary layer is strafed by the waves as the sources move downstream. The mean, autocorrelation, and power spectral density of the field are expressed in terms of the wave shapes and their average arrival rates. The emphasis in the interaction analysis is on the behavior of the shocklets in the noise field. The shocklets are shown to be focused by the laminar boundary layer in its outer region. Borrowing wave-propagation terminology, this region is termed the caustic region. Using scaling laws from sonic boom work, focus factors at the caustic are estimated to vary from 2 to 6 for incoming shocklet strengths of 1 to .01 percent of the free stream pressure level. The situation regarding experimental evidence of the caustic region is reviewed. It is not clear whether the focusing effectively promotes early transition. Additional observations concerning the interaction problem are presented. more...