Stochastic geometry in petroleum geology

Many aspects of the generation, migration, trapping, and discovery of petroleum, as well as its primary and enhanced recovery, depend upon geometry. The scale of the relevant geometric features varies all the way from that of continental margins and basins down to the pores and fissures in reservoir rocks. Because the spatial complexity is so great for each of these processes, it is reasonable to describe them statistically. The primary purpose of this paper is to survey possible ways in which statistical or stochastic geometry enters and might be used in petroleum geology and engineering. While it offers some new theory, this paper does not directly suggest any specific new methods for the estimation of hydrocarbon resources or reserves. This deficiency is mainly due to the current lack of relevant data. When data are available the point of view explained herein will be fruitful. The survey ties together many topics in a novel way.     

An equation of state at subnuclear densities

An equation of state for cold matter above white dwarf densities is evaluated. The gas is considered to be a mixture of degenerate neutrons, protons and electrons combined with nuclei of one type (that is only oneA andZ value). We derive the equilibrium equations for the mixture and calculate the number densities as well as theA andZ of the nucleus. Finally we calculate an equation of state, which smoothly goes over to that of a neutron, proton electron gas mixture at a density of 5×10¹³ g/cm³.     

Pregalactic nucleosynthesis

We discuss the behavior of density fluctuations in an expanding universe and show that these should lead to the early formation of pregalactic hydrogen-helium stars of several hundred to several thousand solar masses. These stars flood the universe with radiation having a color temperature ≳10⁵ K; this terminates star formation but permits galaxy formation to continue. About 10⁻² of the mass of the galaxies is converted into heavy elements by pregalactic nucleosynthesis, with an error factor of a few.     

Distribution of Uranium in the crust of the northwestern canadian shield as shown by lake-sediment analysis

In 1972 a reconnaissance geochemical survey was carried out by the Geological Survey of Canada in the northwestern Canadian Shield. Samples of nearshore lake sediment were collected, by helicopter, from 36,000 sq. miles of the Bear and Slave Structural Provinces. Sample density was one per 10 miles. These samples have since been analyzed for 27 elements. This paper is concerned with the distribution of uranium in 1,241 samples from the western third of the survey area. This region mainly comprises the Bear Province, of Proterozoic age.The Bear Province, which is a metallogenic province for uranium, also appears to be a geochemical province for this element. Uranium is four times more abundant in lake sediments from this area (5.3 p.p.m. U) as compared to the eastern part of the Slave Province (1.3 p.p.m. U). The lake-sediment data are in agreement with analyses of composite rock samples from two parts of the survey area.Within the Bear Province the regional distribution of uranium is controlled mainly by the distribution of Proterozoic granitic rocks. Nearly all areas of 5 p.p.m. U or greater in lake sediments are underlain by Proterozoic granites, or are near to these rocks. Within the granite areas, uranium is distributed along two sets of regularly spaced linear trends. The highest contents in lake sediment, which include values up to 300 p.p.m. U, commonly occur near the intersections of the two trends. These trends correspond to a set of northeast and a set of northwest strike-slip faults and lineaments that were produced by east-west compression of the Bear Province during and after the Hudsonian Orogeny (1750 m.y.). Outside the western margin of the survey area, complex epigenetic mineralization is associated with northeasterly-trending faults. Uranium has been produced from veins of this type at Port Radium and at the Rayrock Mine. Since it is associated with faults, this type of mineralization tends to occur in topographic depressions, that often contain lakes and swamps. Lake-sediment analysis is believed to be an excellent means of detecting such mineralization, both within the survey area and possibly elsewhere in the Canadian Shield. The data obtained during 1972 provide a basis for more detailed prospecting in the region.     

The magnetic properties of Quaternary and Tertiary sediments in the southern North Sea

Cores from boreholes penetrating late Quaternary, glacial, interglacial and postglacial sediments and the underlying late Cenozoic delta complex of the southern North Sea have been examined for their magnetic properties. A magnetic polarity stratigraphy has been established as an aid to biostratigraphic dating of the sediments; the Kaena-Gauss and Gauss—Matuyama transitions and the base and top of the Olduvai subchron have been identified. The strength and stability of laboratory-induced isothermal remanent magnetisation display clear magneto-petrological variations, which match lithostratigraphic changes in the cores. Principal component analysis has picked out a basin-wide and palaeoenvironmental consistency in the magnetic data. Large, multi-domain magnetite grains predominate in the post-deltaic and fluvio-deltaic sediments, whereas smaller greigite or titanomagnetite grains are concentrated in the intertidal and marine deltaic facies. Since heavy mineral analysis indicates that most of the deltaic detritus derived from common source areas, the differences in magnetic mineralogy have probably been caused by the sediment transport processes operating within the delta complex.     

Sub-micron scale distributions of trace elements in zircon

Sub-micron scale zoning of Ti concentrations and correlations between concentrations of Ti and other trace elements (P, Ce, and Y) and cathodoluminescent (CL) banding is observed in natural zircons. Ion images were made using the Caltech Microanalysis Center’s CAMECA NanoSIMS 50L with an O⁻ primary beam focused to ~300 nm on the sample surface. The high spatial resolution of this technique allows for interrogation of chemical variations at or below the scale of CL banding in natural zircons. Images produced in this manner display two types of correlations among Ti, P, Ce, and Y (which appears to be a proxy for CL intensity): strong (correlation coefficients >0.8) and subtle (correlation coefficients ~0.15–0.4). Strongly correlated images, which display Ti variations of ca. a factor of 3 between adjacent CL bands and overall elevated trace element concentrations in CL-dark bands, were found within an oscillatory-zoned, trace element enriched sector of a CL sector-zoned zircon. Three possible causes for such correlations include: temperature-dependent equilibrium partitioning, trace element partitioning limited by diffusion in the host melt and surface-controlled, non-equilibrium growth. Comparison of our data with the expected results of these processes suggests that: (1) Ti partitioning in zircon is dependent upon non-equilibrium effects in addition to temperature and/or (2) the incorporation of elements that co-vary with Ti in zircon (e.g., Y, P and Ce) is also temperature-dependent. Sub-micron scale, high-Ti regions are also found within Proterozoic Adirondack and >4 Ga Jack Hills zircons as well as trace element enrichments (including Ti) along cracks within Jack Hills zircons.     

Measurement of Al26 in stone meteorites and its use in the derivation of orbital elements

The Al²⁶ activity has been measured by gamma-ray coincidence spectrometry in a total of 30 stony meteorites (13 bronzite, 13 hypersthene, 1 carbonaceous and 1 enstatite chondrite, and 2 achondrites). The measured Al²⁶ content has been compared with calculated values based on the method developed by Lavrukhina and Ustinova (1972a, 1972b), which takes account of the modulation of the galactic cosmic ray intensity along the meteorite orbit due to solar magnetic activity. The predictions have been modified empirically to allow for the difference in chemical composition between H- and L-chondrites. Comparison of the measured value with that predicted in the absence of solar modulation permits the estimation of the aphelion of the orbit of the meteorite. The great majority of the derived aphelia lie within the range 2.05–2.45 AU. While this result must be treated with considerable reserve owing to the uncertainties associated with the model, it is consistent with recent data from photometric observations of the asteroid belt.