Similarity solution of axisymmetric flow in porous media

Applications of the axisymmetric Boussinesq equation to groundwater hydrology and reservoir engineering have long been recognised. An archetypal example is invasion by drilling fluid into a permeable bed where there is initially no such fluid present, a circumstance of some importance in the oil industry. It is well known that the governing Boussinesq model can be reduced to a nonlinear ordinary differential equation using a similarity variable, a transformation that is valid for a certain time-dependent flux at the origin. Here, a new analytical approximation is obtained for this case. The new solution,, which has a simple form, is demonstrated to be highly accurate. (c) 2005 Elsevier Ltd. All rights reserved.

Timing and chemistry of fluid-flow events in the Lawn Hill Platform, Northern Australia

Mudrocks and carbonates of the Isa superbasin in the Lawn Hill platform in northern Australia host major base metal sulfide mineralization, including the giant strata-bound Century Zn-Pb deposit. Mineral paragenesis, stable isotope, and K-Ar dating studies demonstrate that long-lived structures such as the Termite Range fault acted as hot fluid conduits several times during the Paleoproterozoic and Mesoproterozoic in response to major tectonic events. Illite and chlorite crystallinity studies suggest the southern part of the platform has experienced higher temperatures (up to 300 degrees C) than similar stratigraphic horizons in the north. The irregular downhole variation of illite crystallinity values provides further information oil the thermal regime in the basin and shows that clay formation was controlled not only by temperature increase with depth but also by high water/rock ratios along relatively permeable zones. K-Ar dating of illite, in combination with other data, may indicate three major thermal events in the central and northern Lawn Hill platform Lit 1500, 1440 to 1400, and 1250 to 1150 Ma. This study did not detect the earlier Century base metal mineralizing event at 1575 Ma. 1500 Ma ages are recorded only in the south and correspond to the age of the Late Isan orogeny and deposition of the Lower Roper superbasin. They may reflect exhumation of a provenance region. The 1440 to 1300 Ma ages are related to fault reactivation and a thermal pulse at similar to 1440 to 1400 Ma possibly accompanied by fluid flow, with subsequent enhanced cooling possibly due to thermal relaxation or further crustal exhumation. The youngest thermal and/or fluid-flow event at 1250 to 1150 Ma is recorded mainly to the cast of the Tern-lite Range fault and may be related to the assembly of the Rodinian supercontinent. Fluids in equilibrium with illite that formed over a range of temperatures, at different times in different parts of the platform. have relatively uniform oxygen isotope compositions and more variable hydrogen isotope compositions (delta O-18 = 3.5-9.7 parts per thousand V-SMOW; delta D = -94 to -36 parts per thousand V-SMOW). The extent of the 180 enrichment and the variably depleted hydrogen isotope compositions suggest the illite interacted with deep-basin hypersaline brines that were composed of evaporated seawater and/or highly evolved meteoric water. Siderite is the most abundant iron-rich gangue phase in the Century Zn-Pb deposit, which is surrounded by all extensive ferroan carbonate alteration halo. Modeling suggests that the ore siderite formed at temperatures of 120 degrees to 150 degrees C, whereas siderite and ankerite in the alteration halo formed at temperatures of 150 degrees to 180 degrees C. The calculated isotopic compositions of the fluids are consistent with O-18-rich basinal brines and mixed inorganic and organic carbon Sources (6180 = 3-10 parts per thousand V-SMOW, delta C-13 = -7 to -3 parts per thousand V-PDB). in the northeast Lawn Hill platform carbonate-rich rocks preserve marine to early diagenetic carbon and oxygen isotope compositions, whereas ferroan carbonate cements in siltstones and shales in the Desert Creek borehole are O-18 and C-13 depleted relative to the sedimentary carbonates. The good agreement between temperature estimates from illite crystallinity and organic reflectance (160 degrees-270 degrees C) and inverse correlation with carbonate delta O-18 values indicates that organic maturation and carbonate precipitation in the northeast Lawn Hill platform resulted from interaction with the 1250 to 1150 Ma fluids. The calculated isotopic compositions of the fluid are consistent with evolved basinal brine (delta O-18 = 5.1-9.4 parts per thousand V-SMOW; delta C-13 = -13.2 to -3.7 parts per thousand V-PDB) that contained a variable organic carbon component from the oxidation and/or hydrolysis of organic matter in the host sequence. The occurrence of extensive O-18- and C-13-depleted ankerite and siderite alteration in Desert Creek is related to the high temperature of the 1250 to 1150 Ma fluid-flow event in the northeast Lawn Hill platform, in contrast to the lower temperature fluids associated with the earlier Century Zn-Pb deposit in the central Lawn Hill platform.