Spatial Variation Of Physical Properties Research Articles

Numerical experiments on thermal convection of highly compressible fluids with variable viscosity and thermal conductivity in 2-D cylindrical geometry: implications for mantle convection of super-Earths

SUMMARY We conduct a series of numerical experiments of thermal convection of highly compressible fluids in 2-D cylindrical annulus, in order to study the mantle convection on super-Earths. The variations in thermodynamic properties (thermal expansivity and reference density) with depth are taken to be relevant for the super-Earths with 10 times the Earth’s mass, while those in transport properties (viscosity and thermal conductivity) are modelled by an exponential dependence on temperature and/or depth. From our experiments we identified a distinct regime of convecting flow patterns induced by the interplay between the adiabatic temperature change and the spatial variations in viscosity and thermal conductivity. That is, for the cases with strong temperature-dependent viscosity and large increase in thermal conductivity with depth, a ‘deep stratosphere’ of stable thermal stratification is formed at the base of the mantle, in addition to thick stagnant lids at their top surfaces. In the ‘deep stratosphere’, the fluid motion is insignificant particularly in the vertical direction in spite of smallest viscosity owing to its strong dependence on temperature. From the comparison with the experiments with the Cartesian geometry, we also found that the occurrence of ‘deep stratosphere’ tends to be suppressed for the cases with cylindrical geometry, owing to the reduction of the surface area with depth which helps increase the temperature gradient in the lowermost mantle. Our finding may further imply that both the effects of adiabatic compression and those of spherical (or cylindrical) geometry of mantle are of crucial importance in understanding the mantle dynamics of massive super-Earths in the presence of spatial variations in physical properties.

Relaxation and relaxation exchange NMR to characterise asphaltene adsorption and wettability dynamics in siliceous systems

The fraction of asphaltenes in crude oils is among the major concerns in upstream and downstream petroleum engineering. At reservoir scale asphaltenes may cause compartmentalisation and at pore scale they may create barriers to flow, change wettability conditions and relative permeability; and as a result affect ultimate oil recovery. Rock core ageing in oil is a common step in laboratory core analysis. Where possible, crude oils relevant to the origin of cores are used, while the use of arbitrary oils, various hydrophobic chemicals and anti-wetting agents is not uncommon. Published ageing time and temperature vary broadly. This fact motivates us to evaluate the applicability of synthetic oils for studies requiring wettability alteration. We systematically study the precipitation kinetics of the heavy-end oil fraction and wettability alteration properties of mixtures comprised by various proportions of commercially available bitumen, aromatics and alkane components.Low-field NMR relaxation measurements have been applied to characterise wettability of rocks by introducing an NMR wettability index. The latter requires multiple reference measurements at end-point saturation states similar to a standard Amott-Harvey workflow. Furthermore, petrophysical interpretation of T2 relaxation data is prone to be affected by diffusional coupling effects. NMR correlation techniques have a higher prediction capacity, e.g. the T2-store-T2 (REXSY) experiment is naturally sensitive to the spatial variation of physical properties by detecting diffusion exchange between different relaxation environments. We applied a combination of relaxation and relaxation exchange techniques to study the effect of asphaltene deposition on pore-space morphology and wettability for two siliceous systems with different surface topology. The change of wettability over ageing time in different synthetic oils was tracked using T2 relaxation measurements, providing estimates of ageing dynamics useful in designing wettability-related experiments.Results show that the kinetics of asphaltene deposition and wettability alteration processes are strongly dependent on chemical composition of synthetic oils, asphaltene origin (light oil or bitumen) and solid phase morphology. Elements of the resulting deposition pattern and wetting state of the cores were inferred using the proposed approach, utilising low-field NMR T2 relaxation and T2-store-T2 relaxation exchange experiments combined with numerical simulation of relaxation responses. The knowledge of deposition pattern and dynamics obtained mainly by the mean of combination of NMR relaxation techniques contributes to the improved design of core wettability alteration steps and potentially to enhanced petrophysical application of low-field NMR technology.

Hybrid integral transforms for flow development in ducts partially filled with porous media.

A hybrid numerical-analytical solution is developed for laminar flow development in a parallel plate duct partially filled with porous media. The integral transform method is employed in combination with a single domain reformulation strategy for representing the heterogeneous media within the channel. A novel eigenfunction expansion basis is proposed, including abrupt spatial variations of physical properties due to the domain transitions. The introduction of the new basis allows for a solution with similar convergence rates as in previous applications with simpler formulations, as demonstrated through a careful convergence analysis of the expansions. The inherent automatic error control characteristic of the integral transforms approach then provides benchmark results for the developing velocity profile. Moreover, a physical analysis further verifies the consistency of both the proposed expansion and the mixed symbolic-numerical code developed. A detailed verification with a finite-element commercial code is also performed.

Two-layer heterogeneous breast phantom for photoacoustic imaging.

Photoacoustic tomography (PAT) is emerging as a potentially important aid for breast cancer detection. Well-validated tissue-simulating phantoms are needed for objective, quantitative, and physically realistic testing for system development. Prior reported PAT phantoms with homogenous structures do not incorporate the irregular layered structure of breast tissue. To assess the impact of this simplification, we design and construct two-layer breast phantoms incorporating vessel-simulating inclusions and realistic undulations at the fat/fibroglandular tissue interface. The phantoms are composed of custom poly(vinyl chloride) plastisol formulations mimicking the acoustic properties of two breast tissue types and tissue-relevant similar optical properties. Resulting PAT images demonstrate that in tissue with acoustic heterogeneity, lateral size of imaging targets is sensitive to the choice of sound speed in image reconstruction. The undulating boundary can further degrade a target's lateral size due to sound speed variation in tissue and refraction of sound waves at the interface. The extent of this degradation is also influenced by the geometric relationship between an absorber and the boundary. Results indicate that homogeneous phantom matrixes may underestimate the degradation of PAT image quality in breast tissue, whereas heterogeneous phantoms can provide more realistic testing through improved reproduction of spatial variations in physical properties.

Geophysical imaging of subsurface structures in volcanic area by seismic attenuation profiling

Geophysical imaging by using attenuation property of multichannel seismic reflection data was tested to map spatial variation of physical properties of rocks in a volcanic area. The study area is located around Miyakejima volcanic island, where an intensive earthquake swarm was observed associated with 2000 Miyakejima eruption. Seismic reflection survey was conducted five months after the swarm initiation in order to clarify crustal structure around the hypocenters of the swarm activity. However, the resulting seismic reflection profiles were unable to provide significant information of deep structures around the hypocenters. The authors newly applied a seismic attribute method that focused seismic attenuation instead of reflectivity to the volcanic area, and designed this paper to assess the applicability of this method to subsurface structural studies in poorly reflective volcanic areas. Resulting seismic attenuation profiles successfully figured out attenuation structures around the Miyakejima volcanic island. Interestingly, a remarkable high-attenuation zone was detected between Miyakejima and Kozushima islands, being well correlated with the hypocenter distribution of the earthquake swarm in 2000. The high-attenuation zone is interpreted as a fractured area that was developed by magma activity responsible for the earthquake swarms that have been repeatedly occurring there. The present study can be one example showing the applicability of seismic attenuation profiling in a volcanic area.Graphical .

Pore level modeling of imbibition in heavy oil saturated media

Heavy oil reservoirs can be found in many locations around the world, such as Canada, Venezuela, United States and Brazil. When in-situ oil viscosity is prohibitively high to allow recovery by conventional methods, additional techniques are used, such as hot water or steam injection. As water exchanges heat with the surroundings, a temperature gradient is established inside the reservoir, which results in a spatial variation of physical properties, especially viscosity. This leads to different mechanisms for fluid flow and trapping. A typical feature of heavy oil immiscible displacements is early breakthrough due to water fingering, which leads to very poor sweep efficiencies. However, physical experiments and field results have demonstrated that additional mechanisms may play a role in heavy oil immiscible displacements, such as capillary imbibition and oil stripping due to high shear flows. In this paper, a series of numerical experiments are performed to evaluate secondary imbibition at different viscosity ratios and injection rates using a Finite Volume approach to solve the Navier–Stokes equations at the pore-scale, and the Volume of Fluid method to properly capture interfaces. The simulations are performed in a 2-dimensional, water-wet, digital porous medium with complex geometry including dead end pores. The operating conditions and the associated complex topology allow evaluation of the typical pore-scale events in a secondary imbibition process, such as oil ganglion mobilization, break-up and coalescence, micro-fingering due to capillary imbibition and oil stripping in high shear flows. Thus the main production mechanisms observed in a heavy oil immiscible displacement are successfully reproduced.

Linear stability analysis on the influences of the spatial variations in thermal conductivity and expansivity on the flow patterns of thermal convection with strongly temperature-dependent viscosity

A series of linear stability analysis is carried out on the onset of thermal convection in the presence of spatial variations of viscosity, thermal conductivity and expansivity. We consider the temporal evolution of an infinitesimal perturbation superimposed to a static (motionless) and conductive state in a basally-heated planar layer. From the changes in flow patterns with increasing the amplitudes of temperature dependence of viscosity, we identified the transition into the “stagnant-lid” (ST) regime, where the convection occurs only beneath a thick and stagnant-lid of cold fluid at the top surface. Detailed analysis showed a significant increase of the aspect ratio of convection cells in ST regime induced by the spatial variations in thermal conductivity and/or expansivity: the horizontal length scale of ST convection can be enlarged by up to 50% with 10 times increase of thermal conductivity with depth. We further developed an analytical model of ST convection which successfully reproduced the mechanism of increasing horizontal length scale of ST regime convection cells for given spatial variations in physical properties. Our findings may highlight the essential roles of the spatial variation of thermal conductivity on the convection patterns in the mantle.

Influences of the depth-dependence of thermal conductivity and expansivity on thermal convection with temperature-dependent viscosity

In this paper we carried out numerical experiments of a time-dependent thermal convection in a two-dimensional Cartesian box of aspect ratio (width/height) of 6, in order to study the influences on the convecting flow patterns of the spatial variations in physical properties (viscosity η, thermal conductivity k and expansivity α). A series of calculations by systematically varying the magnitude of spatial variations in these properties showed that the strongly temperature-dependent η induces the change in flow pattern into the “stagnant lid” (ST) regime, regardless of the increase in k and/or decrease in α with depth, where the convection occurs only beneath a stagnant lid of cold fluid at the top surface. In particular, we found that the increase in thermal conductivity k with depth significantly affects the convecting flow patterns in the presence of strong temperature-dependence in η. Compared with those with uniform k, the patterns of ST convection with non-uniform k are characterized by (i) thinner top thermal boundary layers or lids and (ii) larger horizontal length scales of convection cells beneath the stagnant lid. In addition, the variation in k with depth decreases the threshold values of the temperature-dependence in η above which the ST-mode of convection takes place, which may also help stabilize the convection cells of large horizontal length scales beneath stagnant lids. Our results may highlight the potential importance of the increase in thermal conductivity with depth (or pressure) in controlling the planforms of thermal convection in the mantle of terrestrial planets.

東海地域下の三次元地震波減衰構造

Long term slow slip (LTSS) and non-volcanic low frequency earthquakes (LFEs) were reported in the central part of the Tokai district, central Japan. Such LTSS and LFE events are considered to take place at a transition zone of frictional property from stick-slip to stable sliding on the top of subducting Philippine Sea plate. To clarify the spatial variation of physical properties in this region, we estimated a three dimensional seismic attenuation structure using a joint inversion method. In the shallow depths from the surface to 5km, we found a lower Q zone located along the Median Tectonic Line which divides the southwestern Japan into two parts; an old geologic belt and a new accretionary belt. In the lower crust of the land plate at the depths of 17 to 25km, a very high Q zone (about 2000) exists just above the region where large slip rates were observed during the LTSS between 2001 and 2005. Since very few earthquakes occur in this high Q zone, that portion might consist of harder rocks than surroundings. On the contrary, the region just beneath the large slip zone has lower Q values than those of surrounding area. Comparing our results with a seismic velocity structure derived from travel time tomography, we found the high Q zone approximately coincides with a zone of relatively high velocities and the lower Q zone corresponds to a zone of relatively low velocities and high VP/VS values. A low Q zone with low velocities and high VP/VS can be interpreted as the zone which involves high-pressure fluid. Probably the high Q zone above the large slip zone works as a cap rock and prevents the fluid from moving toward the shallow part, and then the fluid pressure becomes high and it affects the occurrence of slow slip in this region.

A GEOMETRICAL HEIGHT SCALE FOR SUNSPOT PENUMBRAE

Inversions of spectropolarimetric observations of penumbral filaments deliver the stratification of different physical quantities in an optical depth scale. However, without establishing a geometrical height scale their three-dimensional geometrical structure can not be derived. This is crucial in understanding the correct spatial variation of physical properties in the penumbral atmosphere and to provide insights into the mechanism capable of explaining the observed penumbral brightness. The aim of this work is to determine a global geometrical height scale in the penumbra by minimizing the divergence of the magnetic field vector and the deviations from static equilibrium as imposed by a force balance equation that includes pressure gradients, gravity and the Lorentz force. Optical depth models are derived from the SIR inversion of spectropolarimetric data of an active region observed with SOT on-board the Hinode satellite. We use a genetic algorithm to determine the boundary condition for the inference of geometrical heights. The retrieved geometrical height scale permits the evaluation of the Wilson depression at each pixel and the correlation of physical quantities at each height. Our results fit into the uncombed penumbral scenario, i.e., a penumbra composed of flux tubes with channelled mass flow and with a weaker and more horizontal magnetic field as compared with the background field. The ascending material is hotter and denser than their surroundings. We do not find evidence of overturning convection or field free regions in the inner penumbral area analyzed. The penumbral brightness can be explained by the energy transfer of the ascending mass carried by the Evershed flow, if the physical quantities below z=-75km are extrapolated from the results of the inversion.

Thermal control of electroosmotic flow in a microchannel through temperature-dependent properties

A numerical investigation is conducted on the electroosmotic flow and associated heat transfer in a two-dimensional microchannel. The objective of this study is to explore a new conceptual idea that is control of an electroosmotic flow by using a thermal field effect through the temperature-dependent physical properties. Two exemplary problems are examined: a flow in a microchannel with a constant vertical temperature difference between two horizontal walls and a flow in a microchannel with the wall temperatures varying horizontally in a sinusoidal manner. The results of numerical computations showed that a proper control of thermal field may be a viable means to manipulate various non-plug-like flow patterns. A constant vertical temperature difference across the channel produces a shear flow. The horizontally-varying thermal condition results in spatial variation of physical properties to generate fluctuating flow patterns. The temperature variation at the wall with alternating vertical temperature gradient induces a wavy flow.

Trade-off between stability and bias in a history match problem using smoothness constraint

The history matching (HM) hydrocarbon reservoir inverse problem is ill-posed because its solution may be non-unique or unstable. Variability of acceptable solutions around local minima may be very large. Nonetheless, it is a common practice in HM to find a unique reservoir model, although there is no guarantee that this model represents the geology. Qualitative geological information is generally not considered because of difficulties to express them mathematically. Here, we incorporate ‘smoothness’ in the spatial variation of physical properties as an example of a geological qualitative constraint that can be mathematically incorporated in an objective function also honouring the data. The constraint is valid if lateral continuity exists (e.g. fluvial-deltaic siliciclastic reservoirs). We mean smoothness by conditioning the permeability and/or porosity difference between adjacent grid blocks to be small. We use a synthetic 2D water–oil model and a solution search technique allowing characterising both the optimum solution and its variability. The smoothness constraint reduces the variance of the estimates by introducing bias in the solutions still preserving good match. The key point to achieve an optimum trade-off between stability and data match is the tuning of the parameter, controlling the relative importance of the constraint in the objective function. The smoothness constraint cannot be applied to all reservoirs. However, we corroborate the idea that a ‘tool box’ of HM can be designed; each ‘tool’ can incorporate a different constraint. Therefore, the interpreter can judiciously choose a specific tool from this tool box according to the adherence of its constraint to the particular reservoir being studied.

Physical properties and stratigraphy of surface snow in western Dronning Maud Land, Antarctica

Information about the spatial variations of snow properties and of annual accumulation on ice sheets is important if we are to understand the results obtained from ice cores, satellite remote sensing data and changes in climate patterns. The layer structure and spatial variations of physical properties of surface snow in western Dronning Maud Land were analysed during the austral summers 1999/2000, 2000/01 and 2003/04 in fi ve different snow zones. The measurements were performed in shallow (1 - 2 m) snow pits along a transect extending 350 km from the seaward edge of the ice shelf to the polar plateau. These pits covered at least the last annual accumulation and ranged in elevation from near sea level to 2500 m a.s.l. The ?18O values and accumulation rates had a good linear correlation with the distance from the coast. The mean accumulation on the ice shelf was 312 ± 28 mm water equivalent (w.e.); in the coastal region it was 215 ± 43 mm w.e. and on the polar plateau it was 92 ± 25 mm w.e. The mean annual conductivity and grain size values decreased exponentially with increasing distance from the ice edge, by 48 %/100 km and 18 %/100 km respectively. The mean grain size varied between 1.5 and 1.8 mm. Depth hoar layers were a common phenomenon, especially under thin ice crusts, and were associated with low dielectric constant values.

Space and time dependence of temperature and freezing in evergreen leaves.

Infrared video thermography was used to study space and time dependence of freezing in intact, attached leaves of snow gum (Eucalyptus pauciflora Sieb. ex Spreng.) seedlings. Freezing initiated in the midvein and spread through the apoplast at 10 mm s-1. Freezing of apoplastic water was detected by a local, rapid increase in temperature, and was followed by a slower increase in leaf temperature to the equilibrium freezing temperature as symplastic water moved from cells to extracellular sites of ice formation. The duration of freezing varied with position, leaf thickness and water content. Most of the cellular water in the leaf tip and margins froze quickly, while freezing was slower near the petiole and midvein. Regions that had frozen more rapidly then began to cool more rapidly, producing steep gradients in leaf temperatures and hence also freeze-induced dehydration. Thus, spatial variation in physical properties of leaves could affect the distribution of minimum leaf temperatures, and hence, the distribution and extent of damage due to freeze-induced dehydration. These results are consistent with patterns of freezing damage in autumn when the duration of freezing may be insufficient for the whole leaf to freeze before sunrise, and may explain the general observation of increased leaf water content and thickness with altitude.

Spatial variations of the décollement/protodécollement zone and their implications: A 3‐D seismic inversion study of the northern Barbados accretionary prism

AbstractWe conducted a 3‐D seismic inversion study to investigate spatial variations of physical properties of the décollement zone (DZ) and protodécollement zone (PDZ) under the northern Barbados accretionary prism. Significant spatial variations of physical properties were observed in the PDZ seaward of the thrust front from the inversion data. The density generally increases southward with a few localized low‐density patches. A lower density commonly corresponds to a thicker PDZ, suggesting that the paleomorphology may at least partially control the variations of the physical properties. Similar low‐density patches were also found in the DZ. These features may be inherited from those of the PDZ and enhanced after subduction through localized arrested consolidation. Under the prism toe, the density of the DZ increases landward. This trend may mainly result from shear‐induced consolidation of the DZ but may also be related to landward increasing tectonic loading. Significant north–south differences in density and, thus, porosity and strength of the PDZ, are observed and these differences may continue into the DZ. A stronger DZ is likely responsible for a larger prism taper observed in the southern area of the prism toe. The larger taper, thus more horizontal shortening, coupled with a thinner sediment sheet above the PDZ in the southern area, may cause a relative retreat of the thrust front and a pronounced change in strike of the sequence thrusts south of seismic Line 690. The north–south differences may ultimately have originated in the approach of a structurally higher segment of the Tiburon Rise. The Tiburon Rise affects regional morphology and, thus, it controls the sedimentation and physical properties of the PDZ. It may also control sediment accumulation above the PDZ. Therefore, the sedimentational change induced by the structural high of the Tiburon Rise, in turn, resulted in structural change of the prism in the southern area.

Imaging the San Andreas Fault with explosion and earthquake sources

Mounting evidence suggests that fault zone heterogeneity may play a crucial role in the localization of rupture in earthquakes [Aki, 1995]. The heterogeneity can take several forms: spatial variations in physical properties (elastic properties, pore fluid pressure, etc.) or complexity in the fault surface (bends, offsets, etc.). High‐resolution, three‐dimensional models of the P and S wave velocity (Vp and Vs) structure and accurate hypocenters provide tools for studying the effects of fault zone heterogeneity on rupture localization.A dense, passive array of 48 seismic instruments was deployed south of Hollister, California, from mid‐November 1994 to late May 1995. The array obtained local‐earthquake seismograms for high‐resolution, three‐dimensional imaging of the (Vp and Vs) structure in the San Andreas fault zone. In mid‐May, anactive seismic experiment was also carried out. Figure 1 shows a 7‐km wide, 3‐ to 4‐km deep zone of very low Vp imaged during the experiment. The zone is bounded on the southwest by the San Andreas fault and the adjacent Northern Gabilan Range. The San Andreas fault appears to be approximately vertical to at least 5 km depth (the limit of good model resolution), contrary to an existing model based on gravity data.

3D seismic study of a ductile shear zone from laboratory and petrofabric data (Saint Barthélémy Massif, Northern Pyrenees, France)

ABSTRACTIn order to constrain interpretations of seismic reflection records more effectively, the seismic properties of a middle crustal section exposed in the Saint Barthélémy Massif have been determined. The massif, transected by a 200 m thick shear zone has been systematically sampled for density measurements and modal analysis has been performed in order to define the spatial variations of physical properties. Seismic velocities (Vp, VS, shear wave birefringence), have been measured on five representative samples to 600 MPa and 600°C simultaneously in the three structural directions (X, Y and Z). For two samples, the experimental data have been compared with calculated values, based on petrofabric analyses. The Lattice Preferred Orientation (LPO) is determined using universal stage, electron channelling microscopy and neutron diffraction goniometry. Using the experimental and calculated velocity data, we establish a lateral homogeneous anisotropic model.