Finite element analysis of flow patterns near geological lenses in hydrodynamic and hydrothermal systems

We use theoretical and numerical methods to investigate the general pore-fluid flow patterns near geological lenses in hydrodynamic and hydrothermal systems respectively. Analytical solutions have been rigorously derived for the pore-fluid velocity, stream function and excess pore-fluid pressure near a circular lens in a hydrodynamic system. These analytical solutions provide not only a better understanding of the physics behind the problem, but also a valuable benchmark solution for validating any numerical method. Since a geological lens is surrounded by a medium of large extent in nature and the finite element method is efficient at modelling only media of finite size, the determination of the size of the computational domain of a finite element model, which is often overlooked by numerical analysts, is very important in order to ensure both the efficiency of the method and the accuracy of the numerical solution obtained. To highlight this issue, we use the derived analytical solutions to deduce a rigorous mathematical formula for designing the computational domain size of a finite element model. The proposed mathematical formula has indicated that, no matter how fine the mesh or how high the order of elements, the desired accuracy of a finite element solution for pore-fluid flow near a geological lens cannot be achieved unless the size of the finite element model is determined appropriately. Once the finite element computational model has been appropriately designed and validated in a hydrodynamic system, it is used to examine general pore-fluid flow patterns near geological lenses in hydrothermal systems. Some interesting conclusions on the behaviour of geological lenses in hydrodynamic and hydrothermal systems have been reached through the analytical and numerical analyses carried out in this paper.

Finite element analysis of heat transfer and mineralization in layered hydrothermal systems with upward throughflow

We use the finite element method to solve the coupled problem between convective pore-fluid flow, heat transfer and mineralization in layered hydrothermal systems with upward throughflow. In particular, we present the improved rock alteration index (IRAI) concept for predicting the most probable precipitation and dissolution regions of gold (Au) minerals in the systems. To validate the numerical method used in the computation, analytical solutions to a benchmark problem have been derived. After the numerical method is validated, it is used to investigate the pattern of pore-fluid Aom, the distribution of temperature and the mineralization pattern of gold minerals in a layered hydrothermal system with upward throughflow. The related numerical results have demonstrated that the present concept of IRAI is useful and applicable for predicting the most probable precipitation and dissolution regions of gold (Au) minerals in hydrothermal systems. (C) 2000 Elsevier Science S.A. All rights reserved.

Finite element modelling of rock alteration and metamorphic process in hydrothermal systems

We use the finite element method to simulate the rock alteration and metamorphic process in hydrothermal systems. In particular, we consider the fluid-rock interaction problems in pore-fluid saturated porous rocks. Since the fluid rock interaction takes place at the contact interface between the pore-fluid and solid minerals, it is governed by the chemical reaction which usually takes place very slowly at this contact interface, from the geochemical point of view. Due to the relative slowness of the rate of the chemical reaction to the velocity of the pore-fluid flow in the hydrothermal system to be considered, there exists a retardation zone, in which the conventional static theory in geochemistry does not hold true. Since this issue is often overlooked by some purely numerical modellers, it is emphasized in this paper. The related results from a typical rock alteration and metamorphic problem in a hydrothermal system have shown not only the detailed rock alteration and metamorphic process, but also the size of the retardation zone in the hydrothermal system. Copyright (C) 2001 John Wiley & Sons, Ltd.

Finite element modelling of heat transfer through permeable cracks in hydrothermal systems with upward throughflow

We use the finite element method to model the heat transfer phenomenon through permeable cracks in hydrothermal systems with upward throughflow. Since the finite element method is an approximate numerical method, the method must be validated before it is used to soh,e any new, kind of problem. However, the analytical solution, which can be used to validate the finite element method and other numerical methods, is rather limited in the literature, especially, for the problem considered here. Keeping this in mind, we have derived analytical solutions for the temperature distribution along the vertical axis of a crack in a fluid-saturated porous layer. After the finite element method is validated by comparing the numerical solution with the analytical solution for the same benchmark problem, it is used to investigate the pore-fluid flow and heat transfer in layered hydrothermal systems with vertical permeable cracks. The related analytical and numerical results have demonstrated that vertical cracks are effective and efficient members to transfer heat energy from the bottom section to the top section in hydrothermal systems with upward throughflow.

Analysis of steady-state heat transfer through mid-crustal vertical cracks with upward throughflow in hydrothermal systems

We conduct a theoretical analysis of steady-state heat transfer problems through mid-crustal vertical cracks with upward throughflow in hydrothermal systems. In particular, we derive analytical solutions for both the far field and near field of the system. In order to investigate the contribution of the forced advection to the total temperature of the system, two concepts, namely the critical Peclet number and the critical permeability of the system, have been presented and discussed in this paper. The analytical solution for the far field of the system indicates that if the pore-fluid pressure gradient in the crust is lithostatic, the critical permeability of the system can be used to determine whether or not the contribution of the forced advection to the total temperature of the system is negligible. Otherwise, the critical Peclet number should be used. For a crust of moderate thickness, the critical permeability is of the order of magnitude of 10(-20) m(2), under which heat conduction is the overwhelming mechanism to transfer heat energy, even though the pore-fluid pressure gradient in the crust is lithostatic. Furthermore, the lower bound analytical solution for the near field of the system demonstrates that the permeable vertical cracks in the middle crust can efficiently transfer heat energy from the lower crust to the upper crust of the Earth. Copyright (C) 2002 John Wiley Sons, Ltd.

Chemical and isotopic equilibrium between CO2 and CH4 in fumarolic gas discharges: Generation of CH4 in arc magmatic-hydrothermal systems

The chemical and isotopic composition of fumarolic gases emitted from Nisyros Volcano, Greece, and of a single gas sample from Vesuvio, Italy, was investigated in order to determine the origin of methane (CH,) within two subduction-related magmatic-hydrothermal environments. Apparent temperatures derived from carbon isotope partitioning between CH4 and CO2 of around 340degreesC for Nisyros and 470degreesC for Vesuvio correlate well with aquifer temperatures as measured directly and/or inferred from compositional data using the H2O-H-2-CO2-CO-CH4 geothermometer. Thermodynamic modeling reveals chemical equilibrium between CH4, CO2 and H2O implying that carbon isotope partitioning between CO2 and CH, in both systems is controlled by aquifer temperature. N-2/(3) He and CH4/(3) He ratios of Nisyros fumarolic gases are unusually low for subduction zone gases and correspond to those of midoceanic ridge environments. Accordingly, CH4 may have been primarily generated through the reduction of CO, by H, in the absence of any organic matter following a Fischer-Tropsch-type reaction. However, primary occurrence of minor amounts of thermogenic CH4 and subsequent re-equilibration with co-existing CO2 cannot be ruled out entirely- CO2/He-3 ratios and delta(13)C(CO2) values imply that the evolved CO2 either derives from a metasomatized mantle or is a mixture between two components, one outgassing from an unaltered mantle and the other released by thermal breakdown of marine carbonates. The latter may contain traces of organic matter possibly decomposing to CH4 during thermometamorphism. Copyright (C) 2004 Elsevier Ltd.

Impact of considering the effects of latent heat on caldera-hosted hydrothermal systems

To investigate the thennal effects of latent heat in hydrothennal settings, an extension was made to the existing finite-element numerical modelling software, Aquarius. The latent heat algorithm was validated using a series of column models, which analysed the effects of penneability (flow rate), thennal gradient, and position along the two-phase curve (pressure). Increasing the flow rate and pressure increases displacement of the liquid-steam boundary from an initial position detennined without accounting for latent heat while increasing the thennal gradient decreases that displacement. Application to a regional scale model of a caldera-hosted hydrothennal system based on a representative suite of calderas (e.g., Yellowstone, Creede, Valles Grande) led to oscillations in the model solution. Oscillations can be reduced or eliminated by mesh refinement, which requires greater computation effort. Results indicate that latent heat should be accounted for to accurately model phase change conditions in hydrothennal settings.

Interior point method for long-term generation scheduling of large-scale hydrothermal systems

This paper presents an interior point method for the long-term generation scheduling of large-scale hydrothermal systems. The problem is formulated as a nonlinear programming one due to the nonlinear representation of hydropower production and thermal fuel cost functions. Sparsity exploitation techniques and an heuristic procedure for computing the interior point method search directions have been developed. Numerical tests in case studies with systems of different dimensions and inflow scenarios have been carried out in order to evaluate the proposed method. Three systems were tested, with the largest being the Brazilian hydropower system with 74 hydro plants distributed in several cascades. Results show that the proposed method is an efficient and robust tool for solving the long-term generation scheduling problem.

Application of reactive fluid transport modeling to hydrothermal systems

A one-dimensional multi-component reactive fluid transport algorithm, 1DREACT (Steefel, 1993) was used to investigate different fluid-rock interaction systems. A major short coming of mass transport calculations which include mineral reactions is that solid solutions occurring in many minerals are not treated adequately. Since many thermodynamic models of solid solutions are highly non-linear, this can seriously impact on the stability and efficiency of the solution algorithms used. Phase petrology community saw itself faced with a similar predicament 10 years ago. To improve performance and reliability, phase equilibrium calculations have been using pseudo compounds. The same approach is used here in the first, using the complex plagioclase solid solution as an example. Thermodynamic properties of a varying number of intermediate plagioclase phases were calculated using ideal molecular, Al-avoidance, and non-ideal mixing models. These different mixing models can easily be incorporated into the simulations without modification of the transport code. Simulation results show that as few as nine intermediate compositions are sufficient to characterize the diffusional profile between albite and anorthite. Hence this approach is very efficient, and can be used with little effort. A subsequent chapter reports the results of reactive fluid transport modeling designed to constrain the hydrothermal alteration of Paleoproterozoic sediments of the Southern Lake Superior region. Field observations reveal that quartz-pyrophyllite (or kaolinite) bearing assemblages have been transformed into muscovite-pyrophyllite-diaspore bearing assemblages due to action of fluids migrating along permeable flow channels. Fluid-rock interaction modeling with an initial qtz-prl assemblage and a K-rich fluid simulates the formation of observed mineralogical transformation. The bulk composition of the system evolves from an SiO2-rich one to an Al2O3+K2O-rich one. Simulations show that the fluid flow was up-temperature (e.g. recharge) and that fluid was K-rich. Pseudo compound approach to include solid solutions in reactive transport models was tested in modeling hydrothermal alteration of Icelandic basalts. Solid solutions of chlorites, amphiboles and plagioclase were included as the secondary mineral phases. Saline and fresh water compositions of geothermal fluids were used to investigate the effect of salinity on alteration. Fluid-rock interaction simulations produce the observed mineral transformations. They show that roughly the same alteration minerals are formed due to reactions with both types of fluid which is in agreement with the field observations. A final application is directed towards the remediation of nitrate rich groundwaters. Removal of excess nitrate from groundwater by pyrite oxidation was modeled using the reactive fluid transport algorithm. Model results show that, when a pyrite-bearing, permeable zone is placed in the flow path, nitrate concentration in infiltrating water can be significantly lowered, in agreement with proposals from the literature. This is due to nitrogen reduction. Several simulations investigate the efficiency of systems with different mineral reactive surface areas, reactive barrier zone widths, and flow rates to identify the optimum setup.

Mineralogy and geochemistry of contrasting hydrothermal systems on the Arctic Mid Ocean Ridge (AMOR) : the Jan Mayen and Loki’s Castle vent fields

Tese de doutoramento, Ciências do Mar, Universidade de Lisboa, Faculdade de Ciências, 2016

Coupled Ge/Si and Ge isotope ratios as geochemical tracers of seafloor hydrothermal systems: Case studies at Loihi Seamount and East Pacific Rise 9°50’N

Germanium (Ge) and Silicon (Si) exhibit similar geochemical behaviour in marine environments but are variably enriched in seafloor hydrothermal fluids relative to seawater. In this study, Ge isotope and Ge/Si ratio systematics were investigated in low temperature hydrothermal vents from Loihi Seamount (Pacific Ocean, 18°54’N, 155°15’W) and results were compared to high-temperature vents from the East Pacific Rise (EPR) at 9°50’N. Loihi offers the opportunity to understand contrasting Ge and Si behaviour in low temperature seafloor hydrothermal systems characterized by abundant Fe oxyhydroxide deposition at the seafloor. The results show that both Ge/Si and δ74/70Ge in hydrothermal fluids are fractionated relative to the basaltic host rocks. The enrichment in Ge vs. Si relative to fresh basalts, together with Ge isotope fractionation (Δ74/70Ge fluid-basalt up to 1.15 ‰ at EPR 9°50’N and 1.64 ‰ at Loihi) are best explained by the precipitation of minerals (e.g. quartz and Fe-sulfides) during higher temperature seawater-rock reactions in the subsurface. The study of Fe-rich hydrothermal deposits at Loihi, largely composed of Fe-oxyhydroxides, shows that Ge isotopes are also fractionated upon mineral precipitation at the seafloor. We obtained an average Ge isotope fractionation factor between Fe-oxyhydroxide (ferrihydrite) and dissolved Ge in the fluid of -2.0 ± 0.6 ‰ (2sd), and a maximum value of -3.6 ± 0.6 ‰ (2sd), which is consistent with recent theoretical and experimental studies. The study of a hydrothermal chimney at Bio 9 vent at EPR 9°50’N also demonstrates that Ge isotopes are fractionated by approximately -5.6 ± 0.6 ‰ (2sd) during precipitation of metal sulfides under hydrothermal conditions. Using combined Ge/Si and estimated Ge isotope signatures of Ge sinks and sources in seawater, we propose a preliminary oceanic budget of Ge which reveals that an important sink, referred as the “missing Ge sink”, may correspond to Ge sequestration into authigenic Fe-oxyhydroxides in marine sediments. This study shows that combining Ge/Si and δ74/70Ge systematics provides a useful tool to trace hydrothermal Ge and Si sources in marine environments and to understand formation processes of seafloor hydrothermal deposits.

Computer simulations of coupled problems in geological and geochemical systems

The finite element method is used to simulate coupled problems, which describe the related physical and chemical processes of ore body formation and mineralization, in geological and geochemical systems. The main purpose of this paper is to illustrate some simulation results for different types of modelling problems in pore-fluid saturated rock masses. The aims of the simulation results presented in this paper are: (1) getting a better understanding of the processes and mechanisms of ore body formation and mineralization in the upper crust of the Earth; (2) demonstrating the usefulness and applicability of the finite element method in dealing with a wide range of coupled problems in geological and geochemical systems; (3) qualitatively establishing a set of showcase problems, against which any numerical method and computer package can be reasonably validated. (C) 2002 Published by Elsevier Science B.V.