Thermodynamically constrained averaging theory approach for modeling flow and transport phenomena in porous medium systems: 4. Species transport fundamentals

This work is the fourth in a series of papers on the thermodynamically constrained averaging theory (TCAT) approach for modeling flow and transport phenomena in multiscale porous medium systems. The general TCAT framework and the mathematical foundation presented in previous works are built upon by formulating macroscale models for conservation of mass, momentum, and energy, and the balance of entropy for a species in a phase volume, interface, and common curve. In addition, classical irreversible thermodynamic relations for species in entities are averaged from the microscale to the macroscale. Finally, we comment on alternative approaches that can be used to connect species and entity conservation equations to a constrained system entropy inequality, which is a key component of the TCAT approach. The formulations detailed in this work can be built upon to develop models for species transport and reactions in a variety of multiphase systems.     

Thermodynamically constrained averaging theory approach for modeling flow and transport phenomena in porous medium systems: 6. Two-fluid-phase flow

This work is the sixth in a series of papers on the thermodynamically constrained averaging theory (TCAT) approach for modeling flow and transport phenomena in multiscale porous medium systems. Building upon the general TCAT framework and the mathematical foundation presented in previous works, the limiting case of connected two-fluid-phase flow is considered. A constrained entropy inequality is developed based upon a set of primary restrictions. Formal approximations are introduced to deduce a general simplified entropy inequality (SEI). The SEI is used along with secondary restrictions and closure approximations consistent with the SEI to produce a general functional form of a two-phase-flow model. The general model is in turn simplified to yield a hierarchy of models by neglecting common curves and by neglecting both common curves and interfaces. The simplest case considered corresponds to a traditional two-phase-flow model. The more sophisticated models including interfaces and common curves are more physically realistic than traditional models. All models in the hierarchy are posed in terms of precisely defined variables that allow for a rigorous connection with the microscale. The explicit nature of the restrictions and approximations used in developing this hierarchy of models provides a clear means to both understand the limitations of traditional models and to build upon this work to produce more realistic models.     

Towed array shape estimation using Kalman filters-experimentalinvestigations

The problem of estimating the shape of a towed array instrumented with either depth sensors, compasses, or both in a discrete-time state-space formulation is treated in a companion paper by D. A. Gray et al. (to appear), in which the state-space representation is derived from a dynamical model of the propagation of tow-point-induced motion down the array. A Kalman filter is derived to recursively estimate the shape of this towed array, and solutions to the Riccati equation are used to predict the mean square error of the Kalman filter array shape estimates. The present study investigates the performance of this Kalman filter approach as an array shape estimator using both simulated examples and sea trial data. Fundamental to the Kalman filter approach is the model that describes the dynamical behavior of the towed array. The results of an experimental program that was undertaken to validate this model are also presented     

Stability considerations for one-dimensional inverse problems

Summary. We investigate the issues of stability and conditioning for the one-dimensional seismic inverse problem. We show that these issues are distinct; i.e. that numerically stable implementations of solutions to the inverse problem will not give accurate results if the problem is ill-conditioned. In addition, we identify the factors which determine the condition of the inverse problem. These are the total variation of the acoustic impedance profile being sought and the accuracy of the low-frequency content of the reflection data. We illustrate these results on implementations of two numerically stable algorithms for the inverse problem, one of which has a reputation for being unstable. A comparison shows nearly identical results for the two methods on noise-contaminated and frequency band limited reflection data. In fact, we conjecture that all of the well-known 'layer-stripping' inverse scattering methods share the same mathematical stability characteristics. On the other hand, we also show that ill-conditioning can lead to failure of such algorithms, through amplification of error due either to inaccurate data or to discretization or roundoff. Finally, we observe that appropriate smoothing of the seismic data for an ill-conditioned inverse problem (high-variation impedance profile) can cause the problem to become well-conditioned (lower-variation profile). As is typical with regularizations, the price paid for the newly-acquired ability to solve the problem is a loss of accuracy in the solution.     

Modelling OH in regions of star formation

There is a large, diverse and rapidly growing body of OH observations from regions associated with star formation, the physical conditions of which are of great interest. To interpret these observations we need to calculate the populations of the OH energy levels using as accurate a model as is feasible. We have developed a large velocity gradient (LVG) model using the lowest 48 hyperfine states of OH and including the phenomenon of far-infrared line overlap using a new theory which treats all thermal and velocity overlaps. If we use a theory of maser propagation (Field and Gray, 1988) we are then able to see how competing maser lines develop.The generic behaviour which we find is in good agreement with the extensive maser observations of Gaume and Mutel 1987 and our calculations allow us to associate general physical conditions with the four ground state maser frequencies. In addition we are able to present preliminary results of the interpretation of the OH absorption observations of Guilloteauet al. (1984) and Walmsleyet al. (1986) for the compactHII region DR21.Paper presented at the 11th European Regional Astronomical Meetings of the IAU on New Windows to the Universe, held 3–8 July, 1989, Tenerife, Canary Islands, Spain     

Nitrogen geochemistry as a tracer of fluid flow in a hydrothermal vent complex in the Karoo Basin, South Africa

We have investigated the N geochemistry of minerals and rocks from contact metamorphic aureoles and hydrothermal vent complexes (HVC) in the Karoo Basin in South Africa. The HVC formed during phreatic eruptions associated with rapid devolatilization and pressure build-up in contact aureoles around early Jurassic sill intrusions. By combining outcrop data from a HVC and core data from contact aureoles, we investigate the relationship between light element release during metamorphism and vertical fluid migration. Sandstone and breccia from the HVC contain early-diagenetic ammonium -bearing feldspar (buddingtonite) and illite. Ammonium occupies up to 95% of the A site in feldspar, corresponding to concentrations up to 5.2 wt% N. Bulk-rock N isotope data for rocks from inside and outside the hydrothermal vent complex fall into two distinct groups. Background samples have δ¹⁵N_air between +1.5‰ and +4.9‰, whereas minerals from the vent complex have δ¹⁵N in the range +7.5 to +10.6‰. The N geochemistry of contact metamorphic shale from the lower stratigraphic units of the Karoo Basin shows that the vitrinite reflectance and δ¹⁵N values are positively correlated. Shale with reflectivity values >4%Ro are enriched in ¹⁵N, with δ¹⁵N values between +6‰ and +14‰, implying the release of isotopically light N into metamorphic fluids (probably as N₂). We suggest that the relatively high δ¹⁵N values of the early-diagenetic buddingtonite in the HVC reflect exchange of buddingtonite with N-bearing fluids ascending from greater depth after their release during contact metamorphism and dehydration. We present a qualitative model whereby hydrothermal vent complexes represent fluid flow structures after their formation, focusing N-bearing metamorphic fluids sourced in deeper levels of the basin. The release of organic N from sediments at depth in volcanic basins could play a role in the geochemical cycle of N, becoming particularly important during periods of intense volcanic activity.     

Complex trajectories of aquatic and terrestrial ecosystem shifts caused by multiple human-induced environmental stresses

Large shifts in the isotopic compositions of organic matter (OM) in lake sediments, over the last few hundred years, are commonly interpreted as representing changes in photosynthetic productivity corresponding to eutrophication or in the input of terrestrial OM due to human disturbances. Based on multiple-proxy data (C:N ratio, δ¹³C and δ¹⁵N of OM, δ¹³C of calcite, lithology and fossil pollen) from a 700-year sediment core at White Lake, New Jersey (USA), we propose a new explanation that relates these large shifts in OM δ¹³C and δ¹⁵N to human-induced changes in aquatic OM producers. Combined records of geochronology, fossil pollen and lithology from White Lake reveal that the upland forest was cleared by European settlers for farmland beginning around 1745 A.D. and has gradually reforested since 1930 after the abandonment of the farmlands. For the pre-agricultural period, OM had relatively constant but extremely low δ¹³C_VPDB (−35.8 to −34.5‰) and δ¹⁵N_Air (−3.5 to −2.5‰) and high atomic C:N ratios (13.7 to 16.7), indicating a stable anoxic lake environment with prominent microbial producers. Following the human disturbance (since 1745), high OM mass accumulation rates and abundances of the green alga Pediastrum indicate an increase in aquatic photosynthetic productivity due to enhanced nutrient input from disturbed uplands. However, carbonate δ¹³C remains constant or even decreases during this period, implying that increasing productivity did not elevate the δ¹³C of dissolved inorganic carbon and thus cannot explain the observed large increase in OM δ¹³C (7.4‰) and δ¹⁵N (5.8‰) over this period. Instead, δ¹³C, δ¹⁵N and C:N ratios of OM and differences in δ¹³C between calcite and OM suggest that the large increase in OM δ¹³C and δ¹⁵N can be attributed to a human-induced ecological shift in the predominant organic source from anaerobic bacteria to autotrophic phytoplankton. During the post-agricultural period, mass accumulation rates of OM, carbonate and silicate, and the δ¹³C of OM and calcite all decreased significantly, corresponding to stabilization of the uplands. However, over the last 70 years, an intensifying aquatic stress from the deposition of ¹⁵N-enriched industrial pollutants has resulted in a steady increase of 1.9‰ in δ¹⁵N. Proxy records for lake (δ¹³C and δ¹⁵N of OM) and upland conditions (pollen and silicates) at White Lake show complex trajectories of the aquatic and terrestrial ecosystems in response to past human disturbances.