Flow of non-Newtonian fluids in fractured porous media: Isogeometric vs standard finite element discretisation

A formulation has been derived for the flow of non-Newtonian (power-law) fluids in deformable, fractured porous media. The formulation is enhanced with a subgrid scale model to accurately represent the flow of the power-law fluids inside the cracks. The resulting equations have been discretised using standard (Lagrangian) finite element shape functions and with non-uniform rational B-splines (NURBS), which have been cast into a standard finite element datastructure using Bézier extraction. The effect of the power-law index on the velocity inside the fracture and on the total fluid flow through the porous medium has been analysed for a typical boundary-value problem. It is shown that large differences between non-Newtonian and linearised Newtonian fluids can occur for the fluid velocity inside the fracture. This can significantly influence the total fluid transport through the domain. A mesh sensitivity study has been carried out as well and shows that markedly smaller element sizes are required in order to obtain accurate results for the local flow inside the fracture, compared with the element sizes necessary for obtaining accurate results inside the porous medium away from the fracture. Moreover, a comparison has been made between the results obtained using standard Lagrange polynomials and those obtained using NURBS. It is shown that while both discretisation methods are able to accurately simulate the deformations and pressures in the porous medium, the higher interelement continuity of NURBS is mandatory for obtaining correct values of the fluid velocities inside the fracture, especially near the tips.     

Neoproterozoic evolution and Cambrian reworking of ultrahigh temperature granulites in the Eastern Ghats Province,India

The time‐scales and P–T conditions recorded by granulite facies metamorphic rocks permit inferences about the geodynamic regime in which they formed. Two compositionally heterogeneous cordierite–spinel‐bearing granulites from Vizianagaram, Eastern Ghats Province (EGP), India, were investigated to provide P–T–time constraints using petrography, phase equilibrium modelling, U–Pb geochronology, the rare earth element composition of zircon and monazite, and Ti‐in‐zircon thermometry. These ultrahigh temperature (UHT) granulites preserve discrete compositional layering in which different inferred peak assemblages are developed, including layers bearing garnet–sillimanite–spinel, and others bearing orthopyroxene–sillimanite–spinel. These mineral associations cannot be reproduced by phase equilibrium modelling of whole‐rock compositions, indicating that the samples became domainal on a scale less than that of a thin section, even at UHT conditions. Calculation of the P–T stability fields for six compositional domains within which the main rock‐forming minerals are considered to have attained equilibrium suggests peak metamorphic conditions of ~6.8–8.3 kbar at ~1,000°C. In most of these domains, the subsequent evolution resulted in the growth of cordierite and final crystallization of melt at an elevated (residual) H₂O‐undersaturated solidus, consistent with <1 kbar of decompression. Concordant U–Pb ages obtained by SHRIMP from zircon (spread 1,050–800 Ma) and monazite (spread 950–800 Ma) demonstrate that crystallization of these minerals occurred during an interval of c. 250 Ma. By combining LA‐ICP‐MS U–Pb zircon ages with Ti‐in‐zircon temperatures from the same analysis sites, we show that the crust may have remained above 900°C for a minimum of c. 120 Ma between c. 1,000 and c. 880 Ma. Overall, the results suggest that, in the interval 1,050 to 800 Ma, the evolution of the Vizianagaram granulites culminated with UHT conditions from c. 1,000 Ma to c. 880 Ma, associated with minor decompression, before further zircon crystallization at c. 880–800 Ma during cooling to the solidus. However, these rocks are adjacent to the Paderu–Anantagiri–Salur crustal block to the NW that experienced counterclockwise P–T–t paths, and records similar UHT peak metamorphic conditions (7–8 kbar, ~950°C) followed by near‐isobaric cooling, and has a similar chronology during the Neoproterozoic. The limited decompression inferred at Vizianagaram may be explained by partial exhumation due to thrusting of this crustal block over the adjacent Paderu–Anantagiri–Salur crustal block. The residual granulites in both blocks have high concentrations of heat‐producing elements and likely remained hot at mid‐crustal depths throughout a period of relative tectonic quiescence in the interval 800–550 Ma. During the Cambrian Period, the EGP was located in the hinterland of the Denman–Pinjarra–Prydz orogen. A later concordant population of zircon dated at 511 ± 6 Ma records crystallization at temperatures of ~810°C. This age may record a low‐degree of melting due to limited influx of fluid into hot, weak crust in response to convergence of the Crohn craton with a composite orogenic hinterland comprising the Rayner terrane, EGP, and cratonic India.     

Closed system behaviour of argon in osumilite records protracted high‐T metamorphism within the Rogaland–Vest Agder Sector,Norway

Here, we present results of the first ⁴⁰Ar/³⁹Ar dating of osumilite, a high‐T mineral that occurs in some volcanic and high‐grade metamorphic rocks. The metamorphic osumilite studied here is from a metapelitic rock within the Rogaland–Vest Agder Sector, Norway, an area that experienced regional granulite facies metamorphism and subsequent contact metamorphism between 1,100 Ma and 850 Ma. The large grain size (~1 cm) of osumilite in the studied rock, which preserves a nominally anhydrous assemblage, increases the potential for large portions of individual grains to have remained essentially unaffected by the effects of diffusive argon loss, potentially preserving prograde ages. Step‐heating diffusion experiments yielded a maximum activation energy of ~461 kJ/mol and a pre‐exponential factor of ~8.34 × 10⁸ cm²/s for Ar diffusion in osumilite. These parameters correspond to a relatively high closure temperature of ~620°C for a cooling rate of 10°C/Ma in an osumilite crystal with a 175 µm radius. Fragments of osumilite separated from the sample preserve a range of ages between c. 1,070 and 860 Ma. The oldest ages are inferred to date the growth of coarse‐grained osumilite during prograde granulite facies regional metamorphism, which pre‐date contact metamorphism that has historically been ascribed to the growth of osumilite in the region. The majority of fragments record ages between c. 920 and 860 Ma, inferred to reflect the growth of osumilite and/or diffusive argon loss during contact metamorphism. The retention of old ⁴⁰Ar/³⁹Ar dates was facilitated by the low diffusivity of Ar in osumilite (i.e. a closed system), large grain sizes, and anhydrous metamorphic conditions. The ability to date osumilite with the ⁴⁰Ar/³⁹Ar method provides a valuable new thermochronometer that may constrain the timing and duration of high‐T magmatic and metamorphic events.     

The partial equilibration of garnet porphyroblasts in pelitic schists and its control on prograde metamorphism,Glen Roy,Scotland

Garnet porphyroblasts in sillimanite‐bearing pelitic schists contain complex textural and compositional zoning, with considerable variation both within and between adjacent samples. The sillimanite‐bearing schists locally occur in regional Barrovian garnet zone assemblages and are indicative of a persistent lack of equilibrium during prograde metamorphism. Garnet in these Dalradian rocks from the Scottish Highlands preserves evidence of a range of metamorphic responses including initial growth and patchy coupled dissolution–reprecipitation followed by partial dissolution. Individual porphyroblasts each have a unique and variable response to prograde metamorphism and garnet with mainly flat compositional profiles co‐exists with those containing largely unmodified characteristic bell‐shaped Mn profiles. This highlights the need for caution in applying traditional interpretations of effective volume diffusion eliminating compositional variation. Cloudy garnet with abundant fluid inclusions is produced during incomplete modification of the initial porphyroblasts and these porous garnet are then particularly prone to partial replacement in sillimanite‐producing reactions. The modification of garnet via a dissolution–reprecipitation process releases Ca into the effective whole‐rock composition, displacing the pressure–temperature positions of subsequent isograd reactions. This represents the first report of internal metasomatism controlling reaction pathways. The behaviour of garnet highlights the importance of kinetic factors, especially deformation and fluids, in controlling reaction progress and how the resulting variability influences subsequent prograde history. The lack of a consistent metamorphic response, within and between adjacent schists, suggests that on both local and regional scales these rocks have largely not equilibrated at peak metamorphic conditions.     

Effect of hydrogeomorphic setting on calcareous fen hydrology

Calcareous fens are species‐rich peatlands that are dependent on minerotrophic water sources for wetland functioning, with current conceptual models suggesting the water source is ubiquitously groundwater upwelling. By quantifying the water balance and subsurface water flow paths and fluxes over 3 growing seasons for calcareous fens in 3 different hydrogeomorphic settings (Riparian, Trough, and Basin), we show evidence that challenges this conceptual model. The Riparian Fen received an order of magnitude more water inputs than the Trough or Basin Fens and was dominated by stream recharge inputs and groundwater outputs. Precipitation and evaporation dominated the water balance of the Trough Fen whereas only the Basin Fen received sizeable groundwater inputs. Indeed, subsurface water fluxes were low at all fens due to weak hydraulic gradients and low saturated hydraulic conductivity in some areas of each wetland, though variations in growing season precipitation led to subsurface flow reversals in all 3 fens. Our results demonstrate the importance of understanding landscape position, or hydrogeomorphic setting, on calcareous fen hydrology for improving conservation, management, and restoration efforts of these important ecosystems.     

Overview of analogue science activities at the McGill Arctic Research Station,Axel Heiberg Island,Canadian High Arctic

The Canadian High Arctic contains several of the highest fidelity Mars analogue sites in the world. Situated at nearly 80° north, Expedition Fjord on Axel Heiberg Island is located within a polar desert climate, with the surrounding landscape and conditions providing an invaluable opportunity to examine terrestrial processes in a cold, dry environment. Through the Canadian Space Agency's Analogue Research Network program, scientific activities based out of the McGill Arctic Research Station (M.A.R.S.) are extremely broad in scope, representing physical, biological, and technological investigations. Some of the most unique hydrogeologic features under investigation near M.A.R.S. are a series of cold saline springs that maintain liquid-state flow year round regardless of air temperature. Previous studies have examined their geomorphic relation to discharge-related formations, water chemistry, temperature monitoring, discharge rates, and combined flow/thermal modeling. Recent investigations have identified microbial communities and characterized biological activity within the springs and within permafrost sections, having direct relevance to astrobiological analogue research goals. Another main thrust of research activities based at M.A.R.S. pertains to the detection, mapping, and quantification of subsurface ice deposits. A long-term study is presently underway examining polygonal terrain, comparing surficial patterns found in the region with those identified on Mars, and using surface morphology to estimate ice wedge volumes through a combination of aerial photography interpretation and ground-based geophysical techniques. Other technological developments include the use of in situ microscopy for the detection of biomarkers and improved permafrost drilling techniques. This paper presents an overview of previous studies undertaken at M.A.R.S. over the past decades and will describe in detail both present and upcoming work.     

Mauna Kea ground-layer characterization campaign

We present the results of an 18-month study to characterize the optical turbulence in the boundary layer and in the free atmosphere above the summit of Mauna Kea in Hawaii. This survey combined the Slope-Detection and Ranging (SLODAR) and Low-Layer SCIntillation Detection And Ranging (SCIDAR) (LOLAS) instruments into a single manually operated instrument capable of measuring the integrated seeing and the optical turbulence profile within the first kilometre with spatial and temporal resolutions of 40–80 m and 1 min (SLODAR) or 10–20 m and 5 min (LOLAS). The campaign began in the fall of 2006 and observed for roughly 50–60 h per month. The optical turbulence within the boundary layer is found to be confined within an extremely thin layer (≤80 m), and the optical turbulence arising within the region from 80 to 650 m is normally very weak. Exponential fits to the SLODAR profiles give an upper limit on the exponential scaleheight of between 25 and 40 m. The thickness of this layer shows a dependence on the turbulence strength near the ground, and under median conditions the scaleheight is <28 m. The LOLAS profiles show a multiplicity of layers very close to the ground but all within the first 40 m. The free-atmosphere seeing measured by the SLODAR is 0.42 arcsec (median) at 0.5 μm and is, importantly, significantly better than the typical delivered image quality at the larger telescopes on the mountain. This suggests that the current suite of telescopes on Mauna Kea is largely dominated by a very local seeing either from internal seeing, seeing induced by the flow in/around the enclosures, or from an atmospheric layer very close to the ground. The results from our campaign suggest that ground-layer adaptive optics can be very effective in correcting this turbulence and, in principle, can provide very large corrected fields of view on Mauna Kea.     

Assessing the potential for CO2 adsorption in a subbituminous coal,Huntly Coalfield,New Zealand,using small angle scattering techniques

Small angle scattering techniques (SAXS and SANS) have been used to investigate the microstructural properties of the subbituminous coals (R_max 0.42–0.45%) from the Huntly Coalfield, New Zealand. Samples were collected from the two thick (> 5 m) coal seams in the coalfield and have been analysed for methane and carbon dioxide sorption capacity, petrography, pore size distribution, specific surface area and porosity.Specific surface area (SSA) available for carbon dioxide adsorption, extrapolated to a probe size of 4 Å, ranged from 1.25 × 10⁶ cm^? 1 to 4.26 × 10⁶ cm^? 1 with total porosity varying from 16% to 25%. Porosity was found to be predominantly composed of microporosity, which contributed the majority of the available SSA. Although considerable variation was seen between samples, the results fit well with published rank trends.Gas holding capacity at the reservoir pressure (approximately 4 MPa) ranged from 2.63 to 4.18 m³/t for methane on a dry, ash-free basis (daf) and from 22.00 to 23.72 m³/t daf for carbon dioxide. The resulting ratio of CO₂:CH₄ ranged from 5.7 to 8.6, with an average of 6.7:1.Holding capacities for both methane and carbon dioxide on a dry ash free basis (daf) were found to be correlated with sample microporosity. However, holding capacities for the two gases on an as analysed (aa) basis (that is including mineral matter and moisture), showed no such correlation. Carbon dioxide (aa) does show a negative correlation with both specific surface area and microporosity. As the coals have low inorganic matter content, the reversal is thought to be related to moisture which is likely concentrated in the pore size range 12.5–125 Å. Methane holding capacity, both daf and aa, correlates with macroporosity, thus suggesting that the holding capacity of micropores is diminished by the presence of moisture in the pores.     

Uncertainty of gas saturation estimates in a subbituminous coal seam

To assess the commercial viability of a coalbed methane prospect two of the key geological parameters measured are gas content (desorbed gas) and gas holding capacity (adsorption capacity). These two measures, together with reservoir pressure, give an estimate of the gas saturation of the reservoir. Typically gas saturation has been assessed by collecting one adsorption isotherm sample and assuming it is representative of the whole seam reservoir conditions. This study addresses that assumption.To understand the level of variation, and thus the inherent uncertainty in saturation, one core (Jasper-1) from the Huntly coalfield in New Zealand was analysed in detail. Ten samples (representing the whole coal seam) were placed into gas desorption canisters and desorbed for ten days and then analysed for adsorption capacity. Desorption analyses for total measured gas content (average in-situ basis) ranged from 2.32 to 2.89 m³/t (standard deviation (sd) = 0.18) and gas adsorptive capacity at 4 MPa (average in-situ basis) from 2.11 to 3.51 m³/t (sd = 0.38) resulting in saturations ranging from 66% to 120% (sd = 15).Determination of how many samples are required to make a realistic assessment of average reservoir properties requires a consideration of: (i) the level of accuracy desired, (ii) the limit of accuracy possible, which is governed by the magnitude of experimental error, and (iii) the innate variability of the seam. It was found that a minimum of five samples each for adsorption and desorption were required in order to significantly decrease the uncertainty in gas saturation estimates for a subbituminous coal.