High-resolution numerical simulations give clear insights into the three-dimensional structure of thermal convection associated with black-smoker hydrothermal systems. We present a series of simulations that show that, at heat fluxes expected at mid-ocean ridge spreading axes, upflow is focused in circular, pipe-like regions, with the bulk of the recharge taking place in the near-axial region. Recharging fluids have relatively warm temperatures. In this configuration, the system maximizes its heat output, which can be shown to be linked to nonlinearity in the fluid properties. Furthermore, we present a series of simulations with different permeability scenarios. These show that when permeability contrasts are moderate, convection maintains this pipe-like fluid flow structure. The permeability contrast has a dominant effect on flow patters only at early, immature, stages of convection, focussing upflow in high-permeability regions and downflow in low-permeability regions. In such early stages of convection, diffusive vent styles can emerge, which look remarkably similar to diffuse vent fields in natural systems. Finally, simulations in which permeability is defined as a function of temperature indicate that the brittle-ductile condition is likely to occur at temperatures not lower than 650°C. At lower brittle-ductile transition temperatures, the system cannot remove the heat delivered from the magma chamber and vent temperatures are substantially lower than 4000C. This result is in agreement with estimates of the brittle-ductile transition temperature from rock-mechanical studies and the occurrence of earthquakes in the oceanic lithosphère.@en

Realistic simulation of structurally complex reservoirs (SCR) is challenging in at least three ways: (1) geological structures must be represented and discretized accurately on vastly different length scales; (2) extreme ranges and discontinuous variations of material properties have to be associated with the discretized structures and accounted for in the computations; and (3) episodic, highly transient and often localized events such as well shut-in have to be resolved adequately within the overall production history, necessitating a highly adaptive resolution of time. To facilitate numerical experiments that elucidate the emergent properties, typical states and state transitions of SCRs, an application programmer interface (API) called complex systems modelling platform (CSMP ++) has been engineered in ANSI/ISO C ++. It implements a geometry and process-based SCR decomposition in space and time, and uses an algebraic multigrid solver (SAMG) for the spatio-temporal integration of the governing partial differential equations. This paper describes a new SCR simulation workflow including a two-phase fluid flow model that is compared with ECLIPSE in a single-fracture flow simulation. Geologically realistic application examples are presented for incompressible 2-phase flow, compressible 3-phase flow, and pressure-diffusion in a sector-scale model of a structurally complex reservoir.

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We present new, accurate numerical simulations of 2D models resembling hydrothermal systems active in the high-permeability axial plane of mid-ocean ridges and show that fluid flow patterns are much more irregular and convection much more unstable than reported in previous simulation studies. First, we observe the splitting of hot, rising plumes. This phenomenon is caused by the viscous instability at the interface between hot, low-viscosity fluid and cold, high-viscosity fluid. This process, known as Taylor-Saffman fingering could potentially explain the sudden extinguishing of black smokers. Second, our simulations show that for relatively moderate permeabilities, convection is unsteady resulting in transiently varying vent temperatures. The amplitude of these fluctuations typically is 40 °C with a period of decades or less, depending on the permeability. Although externally imposed events such as dike injections are possible mechanisms, they are not required to explain temperature variations observed in natural systems. Our results also offer a simple explanation of how seismic events cause fluctuating temperatures: Earthquake-induced permeability-increase shifts the hydrothermal system to the unsteady regime with accompanying fluctuating vent temperatures. We demonstrate that realistic modelling of these high-Rayleigh number convection systems does not only require the use of real fluid properties, but also the use of higher order numerical methods capable of handling high-resolution meshes. Less accurate numerical solutions smear out sharp advection fronts and thereby artificially stabilize the system.@en

We present a new finite element - finite volume (FEFV) method combined with a realistic equation of state for NaCl-H₂O to model fluid convection driven by temperature and salinity gradients. This method can deal with the nonlinear variations in fluid properties, separation of a saline fluid into a high-density, high-salinity brine phase and low-density, low-salinity vapor phase well above the critical point of pure H₂O, and geometrically complex geological structures. Similar to the well-known implicit pressure explicit saturation formulation, this approach decouples the governing equations. We formulate a fluid pressure equation that is solved using an implicit finite element method. We derive the fluid velocities from the updated pressure field and employ them in a higher-order, mass conserving finite volume formulation to solve hyperbolic parts of the conservation laws. The parabolic parts are solved by finite element methods. This FEFV method provides for geometric flexibility and numerical efficiency. The equation of state for NaCl-H₂O is valid from 0 to 750°C, 0 to 4000bar, and 0-100 wt.% NaCl. This allows the simulation of thermohaline convection in high-temperature and high-pressure environments, such as continental or oceanic hydrothermal systems where phase separation is common.

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We present the benchmarking of a new finite element - finite volume (FEFV) solution technique capable of modeling transient multiphase thermohaline convection for geological realistic p-T-X conditions. The algorithm embeds a new and accurate equation of state for the NaCl-H2O system. Benchmarks are carried out to compare the numerical results for the various component-processes of multiphase thermohaline convection. They include simulations of (i) convection driven by temperature and/or concentration gradients in a single-phase fluid (i.e., the Elder problem, thermal convection at different Rayleigh numbers, and a free thermohaline convection example), (ii) multiphase flow (i.e., the Buckley-Leverett problem), and (iii) energy transport in a pure H2O fluid at liquid, vapor, supercritical, and two-phase conditions (i.e., comparison to the U.S. Geological Survey Code HYDROTHERM). The results produced with the new FEFV technique are in good agreement with the reference solutions. We further present the application of the FEFV technique to the simulation of thermohaline convection of a 400°C hot and 10 wt.% saline fluid rising from 4 km depth. During the buoyant rise, the fluid boils and separates into a high-density, high-salinity liquid phase and a low-density, low-salinity vapor phase.@en