Efficient block preconditioners for the coupled equations of pressure and deformation in highly discontinuous media

Large‐scale simulations of flow in deformable porous media require efficient iterative methods for solving the involved systems of linear algebraic equations. Construction of efficient iterative methods is particularly challenging in problems with large jumps in material properties, which is often the case in geological applications, such as basin evolution at regional scales. The success of iterative methods for this type of problems depends strongly on finding effective preconditioners. This paper investigates how the block‐structured matrix system arising from single‐phase flow in elastic porous media should be preconditioned, in particular for highly discontinuous permeability and significant jumps in elastic properties. The most promising preconditioner combines algebraic multigrid with a Schur complement‐based exact block decomposition. The paper compares numerous block preconditioners with the aim of providing guidelines on how to formulate efficient preconditioners. Copyright © 2010 John Wiley & Sons, Ltd.     

Electrical conductivity of H-bearing orthopyroxene single crystals measured with impedance spectroscopy

In this study, the electrical conductivity of synthetic and natural orthopyroxene single crystals containing various amounts of hydrogen and cation impurities (i.e., Al, Fe) was investigated using impedance spectroscopy. A new cell was developed to measure conductivities of submillimeter-sized oriented single crystals with impedances up to 10¹⁰?Ohm. In contrast to previous studies on olivine and orthopyroxene, results from this study do not show a simple correlation of the concentration of protons and the electrical conductivity. Instead, the electrical conductivity appears to be a complex function of iron content, hydrogen content, crystal orientation and concentration of other impurity cations and shows similar activation energies to hydrogen diffusion. Model calculations considering proton conduction rather exclude than suggest orthopyroxene as responsible phase for high-conductivity regions in the Earth’s upper mantle.     

CO2 solubility in dacitic melts equilibrated with H2O-CO2 fluids: Implications for modeling the solubility of CO2 in silicic melts

The solubility of CO₂ in dacitic melts equilibrated with H₂O-CO₂ fluids was experimentally investigated at 1250°C and 100 to 500 MPa. CO₂ is dissolved in dacitic glasses as molecular CO₂ and carbonate. The quantification of total CO₂ in the glasses by mid-infrared (MIR) spectroscopy is difficult because the weak carbonate bands at 1430 and 1530 cm⁻¹ can not be reliably separated from background features in the spectra. Furthermore, the ratio of CO_2,mol/carbonate in the quenched glasses strongly decreases with increasing water content. Due to the difficulties in quantifying CO₂ species concentrations from the MIR spectra we have measured total CO₂ contents of dacitic glasses by secondary ion mass spectrometry (SIMS).At all pressures, the dependence of CO₂ solubility in dacitic melts on x^fluid_CO2,total shows a strong positive deviation from linearity with almost constant CO₂ solubility at x_CO2fluid > 0.8 (maximum CO₂ solubility of 795 ± 41, 1376 ± 73 and 2949 ± 166 ppm at 100, 200 and 500 MPa, respectively), indicating that dissolved water strongly enhances the solubility of CO₂. A similar nonlinear variation of CO₂ solubility with x_CO2fluid has been observed for rhyolitic melts in which carbon dioxide is incorporated exclusively as molecular CO₂ (Tamic et al., 2001). We infer that water species in the melt do not only stabilize carbonate groups as has been suggested earlier but also CO₂ molecules.A thermodynamic model describing the dependence of the CO₂ solubility in hydrous rhyolitic and dacitic melts on T, P, f_CO2 and the mol fraction of water in the melt (x_water) has been developed. An exponential variation of the equilibrium constant K₁ with x_water is proposed to account for the nonlinear dependence of x_CO2,totalmelt on x_CO2fluid. The model reproduces the CO₂ solubility data for dacitic melts within ±14% relative and the data for rhyolitic melts within 10% relative in the pressure range 100-500 MPa (except for six outliers at low x_CO2fluid). Data obtained for rhyolitic melts at 75 MPa and 850°C show a stronger deviation from the model, suggesting a change in the solubility behavior of CO₂ at low pressures (a Henrian behavior of the CO₂ solubility is observed at low pressure and low H₂O concentrations in the melt). We recommend to use our model only in the pressure range 100-500 MPa and in the x_CO2fluid range 0.1-0.95. The thermodynamic modeling indicates that the partial molar volume of total CO₂ is much lower in rhyolitic melts (31.7 cm³/mol) than in dacitic melts (46.6 cm³/mol). The dissolution enthalpy for CO₂ in hydrous rhyolitic melts was found to be negligible. This result suggests that temperature is of minor importance for CO₂ solubility in silicic melts.     

Experimental palagonitization of basaltic glasses of varied composition

The rate of palagonitization of three chemically different types of basaltic glasses has been determined experimentally as a function of temperature (20–90 ° C) and time (3.5–14 months) in both fresh and saline water. Between ca. 40 ° C and 70 ° C there is a marked increase in the rate of transformation of the glasses, especially those of alkali basalt composition. The alteration process also accelerates after ca. 10 months at temperature higher than 70 ° C. These phenomena are possibly related to stepwise losses of the major elements, and minimum activation temperatures for the oxide/ion—water metasomatism.     

Formation of iron-containing colloids by the weathering of phyllite

The formation of colloids during the weathering of phyllite was investigated by exposing ground phyllite to Milli-Q water. Secondary mineral colloids of 10¹–10² nm were detected in significant concentrations. At pH of about 8.5, the solution concentration of these colloids reached up to 10 mg/L (however, acidification to pH 4.0 prevented the formation of the colloids). The mineralogical composition of the secondary mineral colloids is assumed to be a mixture of ferrihydrite, manganese oxyhydroxides, aluminosilicates, amorphous Al(OH)₃ and gibbsite with possible additions of iron silicates and␣iron-alumino silicates. The colloids were stable over longer periods of time (at least several weeks), even in the presence of suspended ground rock. Direct formation of iron-containing secondary mineral colloids at the rock–water interface by the weathering of rock material is an alternative to the well-known mechanism of iron colloid formation in the bulk of water bodies by mixing of different waters or by aeration of anoxic waters. This direct mechanism is of relevance for colloid production during the weathering of freshly crushed rock in the unsaturated zone as for instance crushed rock in mine waste rock piles. Colloids produced by this mechanism, too, can influence the transport of contaminants such as actinides because these colloids have a large specific surface area and a high sorption affinity.     

200 years of mining activities at La Paz/San Luis Potosí/Mexico - Consequences for environment and geochemical exploration

The Ag---Pb---Zn---Cu---Au mining district of Santa María de La Paz has been extensively exploited for approximately 200 years. Consequences of these activities are several deposits of tailings with high As and heavy metal concentrations, which are completely unstable. The climate is semiarid and as the dumps have no protective cover, material from the dumps is dispersed by strong winds. It is also washed out during seasonally heavy rainfalls. By these processes approximately 100 km² of surrounding have been contaminated by dump material. The As and heavy metal content of the soils was determined as well as their level in crops (Zea Maize) from agricultural lands in the vicinity of the dumps. In the direction of prevailing winds concentrations up to 1000 ppm Zn, 400 ppm Pb, 16 ppm Cd, 550 ppm Cu and 300 As have been detected in top soils. Using fuzzy cluster analysis the different contamination sources could be identified. Grains of corn from contaminated sites showed no critical concentrations, but leaves which are also used tor fodder, have As-concentrations up to 20 ppm.     

Bearing of rare earth patterns of apatites from igneous and metamorphic rocks

Twelve apatite samples from igneous and metamorphic rocks from the Black Forest and igneous rocks from the Kaiserstuhl were analysed for their REE content. The ΣREE range from 0.116 to 1.69 wt.%; the lowest values were found in the metamorphic rocks. All apatites from the various parent rocks show a general enrichment of the lighter rare earths over the heavier and their chondrite-normalized rare earth patterns exhibit a more or less pronounced negative Ce anomaly. This Ce depletion is accompanied by relatively low La and Pr values. In addition, the apatites from igneous rocks from the Black Forest show a marked negative Eu anomaly. An explanation is offered for the simultaneous occurrence of a negative Ce and a negative Eu anomaly in one investigated rock system. The negative Ce anomaly is attributed to the occurrence of phases enriched in Ce (e.g., monazite, allanite) which crystallized prior to or simultaneously with apatite. The negative Eu anomaly in these magmatic apatites most probably is caused by discrimination of Eu²⁺ from the apatite lattice. The result of this discrimination is a selective Eu enrichment in the later crystallizing feldspars, plagioclase and orthoclase. At least in this case, the positive Eu anomaly in feldspars is not a reliable indicator of low oxygen fugacity during their crystallization; the Eu depletion of the earlier crystallized apatites is preferable for this purpose.     

The relative importance of land use and climatic change in Alpine catchments

Carbon storage and catchment hydrology are influenced both by land use changes and climatic changes, but there are few studies addressing both responses under both driving forces. We investigated the relative importance of climate change vs. land use change for four Alpine catchments using the LPJ-GUESS model. Two scenarios of grassland management were calibrated based on the more detailed model PROGRASS. The simulations until 2100 show that only reforestation could lead to an increase of carbon storage under climatic change, whereby a cessation of carbon accumulation occurred in all catchments after 2050. The initial increase in carbon storage was attributable mainly to forest re-growth on abandoned land, whereas the stagnation and decline in the second half of the century was mainly driven by climate change. If land was used more intensively, i.e. as grassland, litter input to the soil decreased due to harvesting, resulting in a decline of soil carbon storage (1.2−2.9 kg C m^–2) that was larger than the climate-induced change (0.8–1.4 kg C m⁻²). Land use change influenced transpiration both directly and in interaction with climate change. The response of forested catchments diverged with climatic change (11–40 mm increase in AET), reflecting the differences in forest age, topography and water holding capacity within and between catchments. For grass-dominated catchments, however, transpiration responded in a similar manner to climate change (light management: 23–32 mm AET decrease, heavy management: 29–44 mm AET decrease), likely because grassroots are concentrated in the uppermost soil layers. Both the water and the carbon cycle were more strongly influenced by land use compared to climatic changes, as land use had not only a direct effect on carbon storage and transpiration, but also an indirect effect by modifying the climate change response of transpiration and carbon flux in the catchments. For the carbon cycle, climate change led to a cessation of the catchment response (sink/source strength is limited), whereas for the water cycle, the effect of land use change remains evident throughout the simulation period (changes in evapotranspiration do not attenuate). Thus we conclude that management will have a large potential to influence the carbon and water cycle, which needs to be considered in management planning as well as in climate and hydrological modelling.