Dynamics of wormhole formation in fractured limestones

Reactive transport in porous or fractured media often results in an evolution of highly conductive flow channels, often referred to as “wormholes”. The most spectacular wormholes are caves in fractured limestone terrains. Here, a model of their early evolution is presented. The modeling domain is a two-dimensional square net consisting of one-dimensional fractures intersecting each other in a rectangular grid. Fractures have given width b and length l, and to each fracture a constant aperture width, a (homogeneous net), or an aperture width taken from a lognormal statistical distribution (heterogeneous net) is assigned. The boundary conditions are constant head h at the input driving the water downstream to the output at h=0. Linear dissolution kinetics, controlled by surface kinetics and diffusion, are active. First we discuss the simple case of a homogeneous net. Two steps in its evolution are observed. In the first, all fractures are widened evenly and a homogeneous even dissolution front progresses slowly into the aquifer. The second step is triggered by an instability when, due to small perturbations, some of the foremost fractures gain length compared to the neighboring ones. Then, these fractures discharge flow using the parallel resistances of the net. This way they attract more fresh aggressive water and their propagation is enhanced. Several wormholes (caves) are penetrating into the aquifer but only one reaches the output, whereas the others stop growing due to the redistribution of hydraulic heads caused by the leading wormhole. The mechanisms governing the evolution of a single wormhole are explored by increasing the aperture width of one selected input fracture by Δa≪a. In this case, only one single wormhole is created and inspection of the flow rates along it reveal the mechanism of flow enhancement in detail. If one uses a heterogeneous net, the first step of evolution is suppressed because of the large perturbations, and wormholes start to grow immediately. We have also modeled the case of several competing wormholes in a homogeneous net by inserting appropriate seeds. We find that there is a critical distance between the wormholes. Within this distance only one wormhole survives, whereas there is no interaction between them when they are separated by more than the critical distance. We also answer the following question: why do wormholes in a two-dimensional model exhibit breakthrough times at least 1 order of magnitude smaller than a one-dimensional model representing the aquifer by one single plane-parallel fracture of the same dimensions? Finally, we present several scenarios with non-homogeneous distribution of initial aperture widths. In these, a uniform dissolution front does not develop and wormholes start to grow immediately, which is more likely expected in nature.</p

An extended Monod-Wyman-Changeaux-model expressed in terms of the Herzfeld-Stanley formalism applied to oxygen and carbonmonoxide binding curves of hemoglobin trout IV

An extended Monod, Wyman, Changeaux (MWC)-model, the mathematical basis of which had been formulated by Herzfeld and Stanley (J. Mol. Blol. 82:231. 1974.) was used to fit oxygen and CO-binding curves of hemoglobin trout IV measured at different pH-values between pH = 8.0 and 6.0. From this calculation one obtains that even the fully liganded molecule exhibits a R----T quaternary transition upon approaching the acid pH-region. In the case of O2-binding, the cooperativity becomes negative below pH = 6.5. This can be related to the difference between the equilibrium constants of proton binding to the alpha- and beta-subunits. Furthermore, it can be shown that the interaction between the quaternary T----R- and the tertiary t----r-transitions is different for the alpha- and beta-subunits

Dissolution influences on gypsum rock under short and long-term loading: Implications for dams

Dissolution of soluble substrates such as gypsum presents a major hazard to dams in many parts of the world. This research simulates hypothesised conditions beneath the Mosul Dam, northwest Iraq, where collapse of a karstic system associated with continuous fresh water supply from its reservoir is a recognised problem. Gypsum rocks from northern Iraq and similar rocks from Bantycock gypsum mine, UK, were analysed for short-term mechanical response following immersion (5 to 50 weeks) and long-term loading during immersion (maximum 50 weeks). New experimental devices were developed from a conventional oedometer. Cylinder samples provided a proxy for massive gypsum strata. Samples were permanently submerged at atmospheric water pressure, with groundwater recharge, flow and dissolution simulated by regular changes of water. Stress on each sample was progressively increased to a maximum of 2688 kPa. Small increases in strain were recorded by the end of each test but no failures occurred within 60 days. However, notable failure due to atmospheric water pressure and axial stress occurred over long time periods. Visible physical changes included a decrease in sample mass and volume. Similar change was recorded in ultrasonic velocities. These indicate that gypsum collapse risk beneath dams requires prolonged exposure to dissolution. The modified device performed well and was robust, and demonstrates that such a modification can provide a simple low cost system for conducting laboratory creep tests on weak rocks

Improved understanding of dynamic water and mass budgets of high‐alpine karst systems obtained from studying a well‐defined catchment area

Large areas of Europe, especially in the Alps, are covered by carbonate rocks and in many alpine regions, karst springs are important sources for drinking water supply. Because of their high variability and heterogeneity, the understanding of the hydrogeological functioning of karst aquifers is of particular importance for their protection and utilisation. Climate change and heavy rainfall events are major challenges in managing alpine karst aquifers which possess an enormous potential for future drinking water supply. In this study, we present research from a high‐alpine karst system in the UNESCO Biosphere Reserve Großes Walsertal in Austria, which has a clearly defined catchment and is drained by only one spring system. Results show that (a) the investigated system is a highly dynamic karst aquifer with distinct reactions to rainfall events in discharge and electrical conductivity; (b) the estimated transient atmospheric CO2 sink is about 270 t/a; (c) the calculated carbonate rock denudation rate is between 23 and 47 mm/1000a and (d) the rainfall‐discharge behaviour and the internal flow dynamics can be successfully simulated using the modelling package KarstMod. The modelling results indicate the relevance of matrix storage in determining the discharge behaviour of the spring, particularly during low‐flow periods. This research and the consequent results can contribute and initiate a better understanding and management of alpine karst aquifers considering climate change with more heavy rainfall events and also longer dry periods.The investigated karst system contributes to the transient atmospheric CO2 sink with about 270 t/a. Carbonate denudation rates vary between 23 and 47 mm/1000a. Rainfall‐discharge modelling results indicate the importance of matrix storage particularly during low‐flow periods. imageBundesministerium für Bildung und Forschung http://dx.doi.org/10.13039/501100002347FP7 People: Marie‐Curie Actions http://dx.doi.org/10.13039/10001126

Dual clumped isotope thermometry resolves kinetic biases in carbonate formation temperatures

© The Author(s), 2020. This article is distributed under the terms of the Creative Commons Attribution License. The definitive version was published in Bajnai, D., Guo, W., Spötl, C., Coplen, T. B., Methner, K., Löffler, N., Krsnik, E., Gischler, E., Hansen, M., Henkel, D., Price, G. D., Raddatz, J., Scholz, D., & Fiebig, J. Dual clumped isotope thermometry resolves kinetic biases in carbonate formation temperatures. Nature Communications, 11(1), (2020): 4005, doi:10.1038/s41467-020-17501-0.Surface temperature is a fundamental parameter of Earth’s climate. Its evolution through time is commonly reconstructed using the oxygen isotope and the clumped isotope compositions of carbonate archives. However, reaction kinetics involved in the precipitation of carbonates can introduce inaccuracies in the derived temperatures. Here, we show that dual clumped isotope analyses, i.e., simultaneous ∆47 and ∆48 measurements on the single carbonate phase, can identify the origin and quantify the extent of these kinetic biases. Our results verify theoretical predictions and evidence that the isotopic disequilibrium commonly observed in speleothems and scleractinian coral skeletons is inherited from the dissolved inorganic carbon pool of their parent solutions. Further, we show that dual clumped isotope thermometry can achieve reliable palaeotemperature reconstructions, devoid of kinetic bias. Analysis of a belemnite rostrum implies that it precipitated near isotopic equilibrium and confirms the warmer-than-present temperatures during the Early Cretaceous at southern high latitudes.This work became possible through DFG grant “INST 161/871-1” and the Investment in Science Fund at Woods Hole Oceanographic Institution. The authors would like to thank Sven Hofmann and Manuel Schumann for their assistance in the joint Goethe University – Senckenberg BiK-F Stable Isotope Facility at the Institute of Geosciences, Goethe University Frankfurt. K.M. acknowledges funding through “DFG ME 4955/1-1”, E.K. through “DFG MU 2845/6-1”, D.S. through “DFG SCHO 1274/8-1” and “DFG SCHO 1274/11-1”, and M.H. through “DFG HA 8694/1-1”. C.S. acknowledges funding from the University of Innsbruck. A review of the manuscript by David Evans on behalf of the USGS is acknowledged

Semi-arid zone caves:Evaporation and hydrological controls on δ¹⁸O drip water composition and implications for speleothem paleoclimate reconstructions

Oxygen isotope ratios in speleothems may be affected by external processes that are independent of climate, such as karst hydrology and kinetic fractionation. Consequently, there has been a shift towards characterising and understanding these processes through cave monitoring studies, particularly focussing on temperate zones where precipitation exceeds evapotranspiration. Here, we investigate oxygen isotope systematics at Wellington Caves in semi-arid, SE Australia, where evapotranspiration exceeds precipitation. We use a novel D2O isotopic tracer in a series of artificial irrigations, supplemented by pre-irrigation data comprised four years of drip monitoring and three years of stable isotope analysis of both drip waters and rainfall. This study reveals that: (1) evaporative processes in the unsaturated zone dominate the isotopic composition of drip waters; (2) significant soil zone ‘wetting up’ is required to overcome soil moisture deficits in order to achieve infiltration, which is highly dependent on antecedent hydro-climatic conditions; (3) lateral flow, preferential flow and sorption in the soil zone are important in redistributing subsurface zone water; (4) isotopic breakthrough curves suggest clear evidence of piston-flow at some drip sites where an older front of water discharged prior to artificial irrigation water; and (5) water residence times in a shallow vadose zone (<2 m) are highly variable and can exceed six months. Oxygen isotope speleothem records from semi-arid regions are therefore more likely to contain archives of alternating paleo-aridity and paleo-recharge, rather than paleo-rainfall e.g. the amount effect or mean annual. Speleothem-forming drip waters will be dominated by evaporative enrichment, up to ∼3‰ in the context of this study, relative to precipitation-weighted mean annual rainfall. The oxygen isotope variability of such coeval records may further be influenced by flow path and storage in the unsaturated zone that is not only drip specific but also influenced by internal cave climatic conditions, which may vary spatially in the cave

A model of karstification in the vicinity of hydraulic structures

To model the development of karst channels from primary fissures in limestone a computer simulation of solutional widening of a fracture by calcite aggressive water is suggested. The parameters defining the problem are the initial width a0 of the fracture, its length 1 and the hydraulic gradient i driving water through it. The dissolution rates of limestone determine how fast enlargement of the fractures proceeds. At a calcite concentration c far from equilibrium they follow a first order rate law F(1) = ap(ceq ~ c); close to the equilibrium concentration c a slow fourth order rate law pw = /3(c — c)4 is valid. The results show that at the time of initiation the water flow through theTcarst channels increases slowly in time until an abrupt increase occurs. After this moment of breakthrough the channel enlarges rapidly and evenly over its entire length by first order kinetics. Breakthrough times have been calculated for karstification under natural conditions for low hydraulic gradients as functions of a0 , 1 and i. Special attention is given to karstification in the vicinity of hydraulic structures where hydraulic gradients are high (\u3e 0.5) and channel lengths are below 200 m. We find that the breakthrough event will occur after less than 100 years, if (i/1) \u3e 1.1 • 10 7 a0 263 PCo2 0\u2755, 1 is in m and a0 in cm; (i/1) is given in m . PCo2 [atm] is the C02 pressure of the water entering the fracture. After this event the channels will widen to a width of about 1 cm within only 10 years, which can cause considerable leakage. Finally, we discuss critical values of the parameters i, 1, a0, which give the conditions of failure in various types of hydraulic structures