Computing residence times for flow towards a pumping well: nomograph solution and validity of the small draw-down approximation

A recent analytical model developed to compute the residence time of fluid flowing in an unconfined aquifer towards a single pumping well is examined. The solution is scaled and presented practically as a nomograph showing the relationship between the residence time, flow length and draw-down. In addition, a similar scaling process is undertaken for the same problem occurring in a confined aquifer so that the error introduced by approximating an unconfined system as a confined system can be understood over a wide range of conditions.

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Resumen Se examina un modelo analítico, recientemente desarrollado, para calcular el tiempo de residencia de un fluido, el cual está fluyendo dentro de un acuífero libre hacia un pozo de bombeo único. La solución después de ser ajustada, se presenta prácticamente como un nomograma, mostrando la relación entre el tiempo de residencia, la longitud del flujo y el abatimiento. Adicionalmente, un proceso similar de ajuste fue realizado para el mismo problema, pero bajo condiciones de acuífero confinado, por tanto el error causado por hacer la aproximación de un sistema libre como si fuera un sistema confinado, puede llegar a ser entendido para un rango amplio de condiciones.

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Résumé On analyse un modèle analytique récent pour calculer le temps de résidence dun fluide pendant son écoulement vers un puits de pompage dans une nappe libre. La solution a été mise-à-léchelle et présenté dune manière pratique, comme une nomogramme qui exprime la relation entre le temps de résidence, la distance de l› écoulement et le rabattement. De plus, on a utilisé un procédé similaire de mise-à-léchelle pour le même problème dans une nappe captive affin que lerreur introduite par lapproximation dune nappe libre par une nappe captive peut être interprétée pour une grande classe de conditions.

     

New U-Pb ages of zircons in the Owk Shale (Kurnool Group) with reflections on proterozoic porcellanites in India

Felsic tuff beds with some presumed sedimentary components were reported from the Owk Shale (Kurnool Group; bearing Neoproterozoic fossils) in the upper part of the sedimentary succession in the Cuddapah basin in India by Saha and Tripathy (2012a). Our optical and SEM petrographic study of three thin sections, however, indicates that the parent samples are sandy mudstones with variable amounts of a felsic volcaniclastic component. New highquality U-Pb (SHRIMP and LA-MC-ICPMS) ages of 133 detrital zircon grains from a sample show that one grain is ca. 1880 Ma, one grain is ca. 3300 Ma, and the ages of the remaining 131 grains fall between 2690 Ma and 2429 Ma, the population averaging 2522 ± 36 Ma. The data indicate that the zircons are detrital grains derived from the ca. 2.5 Ga granitic/gneissic/greenstone basement of the Dharwar cratons that also host minor older Archean enclaves. The single 1880 Ma grain could have come from a ca. 1.9 Ga LIP. In the absence of any younger magmatic zircon, the absolute age of the Owk Shale remains elusive.     

Carbon isotopic fractionation between CO2 vapour,silicate and carbonate melts: an experimental study to 30 kbar

The carbon isotopic fractionation between CO₂ vapour and sodamelilite (NaCaAlSi₂O₇) melt over a range of pressures and temperatures has been investigated using solid-media piston-cylinder high pressure apparatus. Ag₂C₂O₄ was the source of CO₂ and experimental oxygen fugacity was buffered at hematite-magnetite by the double capsule technique. The abundance and isotopic composition of carbon dissolved in sodamelilite (SM) glass were determined by stepped heating and the ¹³C of coexisting vapour was determined directly by capsule piercing. CO₂ solubility in SM displays a complex behavior with temperature. At pressures up to 10 kbars CO₂ dissolves in SM to form carbonate ion complexes and the solubility data suggest slight negative temperature dependence. Above 20 kbars CO₂ reacts with SM to form immiscible Na-rich silicate and Ca-rich carbonate melts and CO₂ solubility in Na-enriched silicate melt rises with increasing temperature above the liquidus. Measured values for carbon isotopic fractionation between CO₂ vapour and carbonate ions dissoived in sodamelilite melt at 1200°–1400° C and 5–30 kbars average 2.4±0.2, favouring¹³C enrichment in CO₂ vapour. The results are maxima and are independent of pressure and temperature. Similar values of 2 are obtained for the carbon isotopic fractionation between CO₂ vapour and carbonate melts at 1300°–1400° C and 20–30 kbars.     

Low frequency edge waves over a trench-ridge topography adjoining a straight coastline

Abstract

The possible interaction of trapped midoceanic boundary waves with a nearby coastline is examined by considering a step trench-ridge topography adjoining a semi-infinite straight coastline. The full dispersion equation, including the effect of the earth's rotation, is derived for long waves over this topography. It is shown that the presence of the coastline begins to have a significant effect on the behaviour of quasigeostrophic ridge waves whenever the wave length is greater than three times the ridge coastline separation.

As an example, the dispersion curves are presented for the topography of the Heceta Bank off the coast of Oregon and it is conjectured that the presence of this off-shore ridge may provide an explanation for the anomalous direction of propagation of the 0.1 c.p.d. shelf wave reported by Mooers and Smith (1968).     

Dynamical conditions in planets and stars

With the available data in planets, stars and galaxies, it is studied the functions of angular momentaJ(M) and amounts of actionA _c(M) (associated to the non rotational terms in the kinetic energy). The results indicate that independently of how are these functionsJ(M),A _c(M) their ratioA _c/J remains a near invariant. It is independent also from the type of angular momenta: intrinsic spins of the bodies or the total angular (orbital) momenta of the bodies forming a system; for instance, the Solar System and the planets.The relationA _c(M) for the Solar System are analogous to these in the FGK stars of the main sequence, and the relationJ(M) (also for the Solar System) is analogous to the lower possible limit for binary stars.The different types of binary stars from the short period, detached systems to contactary systems, gives a range of functionsJ(M),A _c(M) that are the same that one can expect in stars with planetary systems. According to the detection limits given for planetary companions by Campbell, Walker and Yang (1988) (masses of less than 9 Jupiter masses and orbital periods of less than 50 years) we calculate the limits forJ(M) andA _c(M) This gives a lower limitA _c/J 1 associated to stars with planetary systems as 61 Cygni and to short period detached binaries. The upper limitA _c/J 16 correspond to planetary systems as the ours and probably to cataclysmic binaries. There are reasons to suspect that systems as the ours and in range 4 A _c/J 16 (with a lower limit analogous to contactary binaries as Algols and W Ursa Majoris) must be the most common type of planetary systems. The analogies with the functionsJ(M)A _c(M) for galaxies suggest cosmogonical conditions in the stellar formation.Independently of this, one can have boundary conditions for the Jacobi problem when applied to a collapsing cloud. Namely, from the initial stage (a molecular cloud) to the final stage (a formed stellar system: binary or planetary) the angular momenta and amounts of action decayed to 10^~4 the initial values, but in such a form thatA _c(t)/J(t) remains a near invariant.     

Cesstibtantite—a geologic introduction to the inverse pyrochlores

Summary The crystal structure of cesstibtantite has been solved from diffractometer data collected on samples from Leshaia, Russia and the Tanco pegmatite, Manitoba. Cesstibtantite from the Leshaia pegmatite (type locality) hasa 10.515(2) Å, space groupFd3m, composition Cs_0.31(Sb_0.57Na_0.31Pb_0.02Bi_0.01)_O.91(Ta_1.88Nb_0.12)₂(O_5.69[OH, F]_0.31)₆(OH, F)_0.69, Z 8; its structure was refined toR 3.8,wR 4.3% using 96 observed (F > 3[F]) reflections (MoK). Cesstibtantite from the Tanco pegmatite hasa 10.496(1) Å, space groupFd3m, composition (Cs_0.22K_0.01)_0.23(Na_0.45Sb_0.39Pb_0.14· Ca_0.06Bi_0.02)_1.06(Ta_1.95Nb_0.05)₂(O_5.78[OH,F]_0.22)₆(OH,F)_0.55,Z 8; its structure was refined toR 3.9w R 3.7% using 104 observed reflections. Cesstibtantite differs from the normal pyrochlores in that it contains significant amounts of very large cations such as Cs. As these cations are too large (^VIII[r] > 1.60 Å) for the conventional [8]-coordinated A site, they occupy the [18]-coordinated site, which normally contains monovalent anions. Natural cesstibtantite samples are non-ideal in that both Cs and monovalent anions occur at the site; thus cesstibtantite is intermediate to thenormal pyrochlores (with only monovalent anions at the site) and theinverse pyrochlores (with only large cations at the site).

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Cesstibtantit—eine geologische Einfiihrung in die inversen Pyrochlore

Zusammenfassung Die Kristallstruktur von Cesstibtantit wurde auf der Basis von Diffraktometerdaten von Proben von Leshaia, Russland and dem Tanco Pegmatit, Manitoba, gelöst. Cesstibtantit aus dem Leshaia Pegmatit (Typlokalität) hat a 10.515(2) Å, RaumgruppeFd3m, die Zusammensetzung CS_0.31(Sb_0.57Na_0.31Pb_0.02Bi_0.01)_0.91(Ta_1.88Nb_0.12)₂· (O_5.69OH, F_0.31)₆(OH, F)_0.69 Z 8; die Struktur wurde aufR 3.8,wR 4.3% verfeinert unter Benützung von 96 beobachteten Reflexen. Cesstibtantit vom Tanco Pegmatit hat a 10.496(1) Å, RaumgruppeFd3m, die Zusammensetzung (Cs_0.22K_0.01)_0.23(Na_0.45· Sb_0.39Pb_0.14Ca_0.06Bi_0.02)_1.06(Ta_1.95Nb_0.05)₂(O_5.78OH,F_0.22)₆(OH,F)_0.55,Z 8; seine Struktur wurde aufR 3.9wR 3.7% auf der Basis von 104 beobachteten Rettexen verfeinert. Cesstibtantit unterscheidet sich von normalen Pyrochloren insofern, als er signifikante Mengen von sehr großen Kationen, wie z.B. Cs enthält. Da these Kationen zu groß sind (^VIII r 1.60 Å) für eine konventionelle [8]-koordinierteA Stelle, nehmen she die [18]-koordinierten Positionen ein, welche normalerweise monovalente Anionen enthalten. Natürliche Cesstibtantitproben sind nicht ideal insofern als sowohl Cs als auch monovalente Anionen in der Position vorkommen. Somit ist Cesstibtantit intermediär zu den normalen Pyrochloren (mit nur monovalenten Anionen auf der Position) and den inversen Pyrochloren (mit ausschließlichen großen Kationen an der Position).