Equilibrium and structural studies of silicon(iv) and aluminium(iii) in aqueous solution. V. Acidity constants of silicic acid and the ionic product of water in the medium range 0.05–2.0 M Na(CI) at 25°C

The apparent ionization constants for silicic acid, k₁ and k₂, and the ionic product of water, k_w, have been determined in 0.05, 0.1, 0.2, 0.4 and 2.0 M Na(CI) media at 25°C. The medium dependence of these constants was found to fit equations of the form

$\text{log}\text{k}{}_{\mathrm{i}}\text{=}\text{log}\text{K}{}_{\mathrm{i}}\text{+a}{}_{\mathrm{i}}\text{I}{}^{\mathrm{<mtext>1</mtext><mtext>2</mtext>}}\text{(1+I}{}^{\mathrm{<mtext>1</mtext><mtext>2</mtext>}}\text{)+b}{}_{\mathrm{i}}\text{I}$

where K₁ is the ionization constant in pure water, α_i and b_i are parameters of which b_i has been adjusted to present data. The following results were obtained (α_i, b_i): pK₁ = 9.84, (1.022, ?0.11); pK₂ = 13.43, (2.044, ?0.20); and pK_w = 14.01 (1.022, ?0.22). k_i values are collected in Tables I and II. Attempts have been made to explain the medium dependence of k₁ and k₂ with weak sodium silicate complexing according to the equilibria

$\text{Na}{}^{\mathrm{+}}\text{+}\text{SiO(OH)}{}^{\mathrm{?}}{}_3\text{?}\text{NaSiO(OH)}{}_3\text{;k}{}_{11}$

$\text{Na}{}^{\mathrm{+}}\text{+}\text{SiO}{}_2\text{(OH)}{}^2{}_2\text{?}\text{NaSiO}{}_2\text{(HO)}{}^{\mathrm{?}}{}_2\text{; k}{}_{21}$

giving k₁₁ = 0.37M^?1 and k₂₁= 3.0M^?1. However, these weak interactions cannot be interpreted unambiguously from potentiometric data at different 1-levels. Probably the medium dependence could equally well be expressed by variations in the activity coefficients.The measurements were performed as potentiometric titrations using a hydrogen electrode. The average number of OH^- reacted per Si(OH)₄, Z, has been varied within the limits 0 ? Z ? 1.1 and B₁, the total concentration of Si(OH)₄, between 0.001 M and 0.008 M. k₁ was evaluated from experimental data with B ? 0.003 M, and k₂ with B ? 0.008 M and Z ? 0.95.     

On the causes of pressure oscillations in low‐permeable and low‐compressible porous media

Nonphysical pressure oscillations are observed in finite element calculations of Biot's poroelastic equations in low‐permeable media. These pressure oscillations may be understood as a failure of compatibility between the finite element spaces, rather than elastic locking. We present evidence to support this view by comparing and contrasting the pressure oscillations in low‐permeable porous media with those in low‐compressible porous media. As a consequence, it is possible to use established families of stable mixed elements as candidates for choosing finite element spaces for Biot's equations. Copyright © 2011 John Wiley & Sons, Ltd.     

Quaternary denudation of southern Fennoscandia – evidence from the marine realm

Throughout the last 1.1 million years repeated glaciations have modified the southern Fennoscandian landscape and the neighbouring continental shelf into their present form. The glacigenic erosion products derived from the Fennoscandian landmasses were transported to the northern North Sea and the SE Nordic Seas continental margin. The prominent sub‐marine Norwegian Channel trough, along the south coast of Norway, was the main transport route for the erosion products between 1.1 and 0.0 Ma. Most of these erosion products were deposited in the North Sea Fan, which reaches a maximum thickness of 1500 m and has nearly 40 000 km³ of sediments. About 90% of the North Sea Fan sediments have been deposited during the last 500 000 years, in a time period when fast‐moving ice streams occupied the Norwegian Channel during each glacial stage. Back‐stripping the sediment volumes in the northern North Sea and SE Nordic Seas sink areas, including the North Sea Fan, to their assumed Fennoscandian source area gives an average vertical erosion of 164 m for the 1.1–0.0 Ma time period. The average 1.1–0.0 Ma erosion rate in the Fennoscandian source area is estimated to be 0.15 mm a^?1. We suggest, however, that large variations in erosion rates have existed through time and that the most intense Fennoscandian landscape denudation occurred during the time period of repeated shelf edge ice advances, namely from Marine Isotope Stage 12 (c. 0.5 Ma) onwards.     

Conditioning geological surfaces to horizontal wells

Computational Geosciences - Kriging is a standard method for conditioning surfaces to observations. Kriging works for vertical wells, but may produce surfaces that cross horizontal wells between...