Jonathan D. Price

Nonlinear pressure diffusion in a porous medium: Approximate solutions with applications to permeability measurements using transient pulse decay method

Transient pulse decay has been widely used to measure permeability of tight rocks and synthetic materials. When the pore fluid is a gas (e.g., dry air, Ar, or N2) as used in a gas permeameter, the pressure diffusion equation governing the pulse decay problem is nonlinear due to a pressure-dependent gas compressibility and molecular slippage effect (also known as the Klinkenberg effect). To simplify data analysis in permeability measurement using a gas permeameter, an approximate solution to the nonlinear diffusion equation was obtained using a regular perturbation method. This solution, which is similar to the original exponential solution of Brace et al. [1968] for a case when the compressibility of the pore fluid is a constant, is valid in the limit when the volume of the interconnected pore fluid is much smaller than the volume of the upstream reservoir. Applications of the approximate solution to laboratory measured pulse decay data show that the estimated sample permeability can be overestimated by as much as a factor of two if the transient gas pressure decay experiment is conducted at low pressures and if molecular slippage is not taken into account. The molecular slippage can be effectively eliminated if the pulse decay measurement is conducted at a mean pressure at least 5 times higher than the Klinkenberg slip factor, which is on the order of 1 bar for texturally equilibrated marble and quartzite used in the permeability study of Wark and Watson [1998].

Kinetics of the reaction MgO + Al2O3 → MgAl2O4 and Al-Mg interdiffusion in spinel at 1200 to 2000°C and 1.0 to 4.0 GPa

Abstract The rate of spinel (MgAl2O4) growth at the interface between MgO and Al2O3 was investigated systematically at temperatures of 1200° to ∼2000°C and pressures between 1.0 and 4.0 GPa with a solid-media, piston-cylinder apparatus. As reported in previous 1-atm studies, the thickness (ΔX) of the spinel layer increases linearly with the square root of time for experiments differing only in duration, irrespective of pressure–temperature (P-T) conditions. The reaction rate constant (k = ΔX2/2t) is log-linear in 1/T and also in pressure. The apparent activation energy of 410 kJ/mol is independent of pressure; the apparent activation volume increases systematically with increasing temperature. Electron microprobe traverses across the spinel layer reveal a significant Al excess and charge-compensating Mg deficit near the spinel/corundum interface. This nonstoichiometry is promoted by high temperatures (>1500°C), suppressed by high pressures and varies linearly across the spinel to a near-stoichiometric composition at the interface with periclase. The Al and Mg composition gradients can be used to extract interdiffusion coefficients for Al ↔ Mg exchange through the spinel, which are described by D=2.5×10−6 exp(−28200/T) m2sThese diffusivities differ substantially from the reaction rate constant k, reflecting the fact that k is a combination of the diffusivity and the reaction potential as indicated by the difference in spinel composition across the spinel layer (i.e., coexisting with corundum vs. coexisting with periclase). A simple model can be used to separate the two effects and show that the reaction potential (i.e., the MgO-Al2O3 phase diagram) is sensitive to changes in both temperature and pressure, whereas the governing diffusivity depends only on temperature.

Crystallisation of fine- and coarse-grained A-type granite sheets of the Southern Oklahoma Aulacogen, U.S.A.

A-type felsic magmatism associated with the Cambrian Southern Oklahoma Aulacogen began with eruption of voluminous rhyolite to form a thick volcanic carapace on top of an eroded layered mafic complex. This angular unconformity became a crustal magma trap and was the locus for emplacement of later subvolcanic plutons. Rising felsic magma batches ponding along this crustal magma trap crystallised first as fine-grained granite sheets and then subsequently as coarser-grained granite sheets. Aplite dykes, pegmatite dykes and porphyries are common within the younger coarser-grained granite sheets but rare to absent within the older fine-grained granite sheets. The older fine-grained granite sheets typically contain abundant granophyre. The differences between fine-grained and coarse-grained granite sheets can largely be attributed to a progressive increase in the depth of the crustal magma trap as the aulacogen evolved. At low pressures (<200MPa) a small increase in the depth of emplacement results in a dramatic increase in the solubility of H 2 O in felsic magmas. This is a direct consequence of the shape of the H 2 O-saturated granite solidus. The effect of this slight increase in total pressure on the crystallisation of felsic magmas is to delay vapour saturation, increase the H 2 O content of the residual melt fractions and further depress the solidus temperature. Higher melt H 2 O contents, and an extended temperature range over which crystallisation can proceed, both favour crystallisation of coarser-grained granites. In addition, the potential for the development of late, H 2 O-rich, melt fractions is significantly enhanced. Upon reaching vapour saturation, these late melt fractions are likely to form porphyries, aplite dykes and pegmatite dykes. For the Southern Oklahoma Aulacogen, the progressive increase in the depth of the crustal magma trap at the base of the volcanic pile appears to reflect thickening of the volcanic pile during rifting, but may also reflect emplacement of earlier granite sheets. Thus, the change in textural characteristics of granite sheets of the Wichita Granite Group may hold considerable promise as an avenue for further investigation in interpreting the history of this rifting event.

Using pegmatite geochronology to constrain temporal events in the Adirondack Mountains

U-Pb laser ablation–multicollector–inductively coupled plasma–mass spectrometry (LA-MC-ICP-MS) ages have been determined from large zircon crystals separated from pegmatites of the Adirondack Mountains, New York. Emplacement and metamorphic ages ranging from 949 ± 10 to 1222 ± 12 Ma help constrain the timing of igneous, metamorphic, and deformational history of the region, and are associated with Shawinigan, Ottawan, and Rigolet orogenesis. Geologically reasonable ages were obtained from most zircon separates despite large size, a limited number of grains, high uranium and thorium contents, dark and opaque interiors, high density of fractures, and widespread areas of metamictization and Pb loss. However, few grains show zoning or differences in composition when viewed with the backscattered mode on the scanning electron microscope. Large, clear, internally featureless, U-poor grains yield the best constrained ages. U-Th-Pb monazite ages, determined by electron probe, vary from 874 ± 27 Ma to 297 ± 62; the younger age may reflect the timing of hydrothermal fluid infiltration related to late Acadian events. This study suggests that, with appropriate care, zircons from pegmatites are a reasonable target for LA-MC-ICP-MS geochronology, widening the current arsenal of sampling targets.