We present a finite element - finite volume simulation method for modelling fluid flow and solute transport accompanied by chemical reactions in experimentally obtained 3D pore geometries. The advantage of the proposed methodology with respect to other pore-scale modelling approaches is that no simplifications regarding the geometry of the porous space are required and no approximations to the flow equations are introduced. We apply this method in a proof-of-concept study of a digitised Fontainebleau sandstone sample. We use the calculated velocity profile with the finite volume procedure to simulate pore-scale transport and diffusion of the adsorbing solute. We also demonstrate how analysis of the pore geometry can be used to identify the locations of oil during the two-phase flow and couple this with the reactive transport modeling to show how this procedure can be used to estimate the potential of the enhanced oil recovery techniques.@en

We present a finite element - finite volume simulation method for modelling fluid flow and solute transport accompanied by chemical reactions in experimentally obtained 3D pore geometries. The advantage of the proposed methodology with respect to other pore-scale modelling approaches is that no simplifications regarding the geometry of the porous space are required and no approximations to the flow equations are introduced. We apply this method in a proof-of-concept study of a digitised Fontainebleau sandstone sample. We use the calculated velocity profile with the finite volume procedure to simulate pore-scale transport and diffusion of the adsorbing solute. We also demonstrate how analysis of the pore geometry can be used to identify the locations of oil during the two-phase flow and couple this with the reactive transport modeling to show how this procedure can be used to estimate the potential of the enhanced oil recovery techniques.@en

We present a finite element - finite volume simulation method for modelling fluid flow and solute transport accompanied by chemical reactions in experimentally obtained 3D pore geometries. The advantage of the proposed methodology with respect to other pore-scale modelling approaches is that no simplifications regarding the geometry of the porous space are required and no approximations to the flow equations are introduced. We apply this method in a proof-of-concept study of a digitised Fontainebleau sandstone sample. We use the calculated velocity profile with the finite volume procedure to simulate pore-scale transport and diffusion of the adsorbing solute. We also demonstrate how analysis of the pore geometry can be used to identify the locations of oil during the two-phase flow and couple this with the reactive transport modeling to show how this procedure can be used to estimate the potential of the enhanced oil recovery techniques.@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.@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.@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.@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.@en

Using X-ray computed microtomography, we have visualized and quantified the in situ structure of a trapped nonwetting phase (oil) in a highly heterogeneous carbonate rock after injecting a wetting phase (brine) at low and high capillary numbers. We imaged the process of capillary desaturation in 3D and demonstrated its impacts on the trapped nonwetting phase cluster size distribution. We have identified a previously unidentified pore-scale event during capillary desaturation. This pore-scale event, described as droplet fragmentation of the nonwetting phase, occurs in larger pores. It increases volumetric production of the nonwetting phase after capillary trapping and enlarges the fluid-fluid interface, which can enhance mass transfer between the phases. Droplet fragmentation therefore has implications for a range of multiphase flow processes in natural and engineered porous media with complex heterogeneous pore spaces.@en

Using X-ray computed microtomography, we have visualized and quantified the in situ structure of a trapped nonwetting phase (oil) in a highly heterogeneous carbonate rock after injecting a wetting phase (brine) at low and high capillary numbers. We imaged the process of capillary desaturation in 3D and demonstrated its impacts on the trapped nonwetting phase cluster size distribution. We have identified a previously unidentified pore-scale event during capillary desaturation. This pore-scale event, described as droplet fragmentation of the nonwetting phase, occurs in larger pores. It increases volumetric production of the nonwetting phase after capillary trapping and enlarges the fluid-fluid interface, which can enhance mass transfer between the phases. Droplet fragmentation therefore has implications for a range of multiphase flow processes in natural and engineered porous media with complex heterogeneous pore spaces.@en

Using X-ray computed microtomography, we have visualized and quantified the in situ structure of a trapped nonwetting phase (oil) in a highly heterogeneous carbonate rock after injecting a wetting phase (brine) at low and high capillary numbers. We imaged the process of capillary desaturation in 3D and demonstrated its impacts on the trapped nonwetting phase cluster size distribution. We have identified a previously unidentified pore-scale event during capillary desaturation. This pore-scale event, described as droplet fragmentation of the nonwetting phase, occurs in larger pores. It increases volumetric production of the nonwetting phase after capillary trapping and enlarges the fluid-fluid interface, which can enhance mass transfer between the phases. Droplet fragmentation therefore has implications for a range of multiphase flow processes in natural and engineered porous media with complex heterogeneous pore spaces.@en

Using X-ray computed microtomography, we have visualized and quantified the in situ structure of a trapped nonwetting phase (oil) in a highly heterogeneous carbonate rock after injecting a wetting phase (brine) at low and high capillary numbers. We imaged the process of capillary desaturation in 3D and demonstrated its impacts on the trapped nonwetting phase cluster size distribution. We have identified a previously unidentified pore-scale event during capillary desaturation. This pore-scale event, described as droplet fragmentation of the nonwetting phase, occurs in larger pores. It increases volumetric production of the nonwetting phase after capillary trapping and enlarges the fluid-fluid interface, which can enhance mass transfer between the phases. Droplet fragmentation therefore has implications for a range of multiphase flow processes in natural and engineered porous media with complex heterogeneous pore spaces.@en

Using X-ray computed microtomography, we have visualized and quantified the in situ structure of a trapped nonwetting phase (oil) in a highly heterogeneous carbonate rock after injecting a wetting phase (brine) at low and high capillary numbers. We imaged the process of capillary desaturation in 3D and demonstrated its impacts on the trapped nonwetting phase cluster size distribution. We have identified a previously unidentified pore-scale event during capillary desaturation. This pore-scale event, described as droplet fragmentation of the nonwetting phase, occurs in larger pores. It increases volumetric production of the nonwetting phase after capillary trapping and enlarges the fluid-fluid interface, which can enhance mass transfer between the phases. Droplet fragmentation therefore has implications for a range of multiphase flow processes in natural and engineered porous media with complex heterogeneous pore spaces.@en

Spontaneous imbibition (SI) is a key process in many petrophysical applications, ranging from the mass transfer in fractured reservoirs during a waterflood to wettability characterization of rock samples, or steam migration in geothermal reservoirs. Scaling groups are an essential tool for upscaling laboratory data and modeling and describing SI. A general form has been debated for over 90 years, and several dozen specific groups have been proposed. Here, we give the first general scaling group for arbitrary wettability state, viscosity ratios, rock type, initial water content, and boundary conditions. The result is obtained by extending recent findings for water-wet systems but otherwise arbitrary properties (Schmid and Geiger, 2012) to the mixed-wet case. The group is based on the only known exact, general solution to Darcy's equation with capillarity, and we show that this solution can be viewed as the capillary analogue to the Buckley-Leverett solution for viscous dominated flow. Our group serves as a 'master equation' that contains many of the previously obtained groups as special cases, and its generality can be used to give the first predictive theory for the validity range of specific groups. Based on the universal group, we show that SI is best characterized by the cumulative inflow of the wetting phase and not by the movement of the wetting front, as has been conjectured. Furthermore, our results give strong evidence that Darcy's equation is suitable for describing SI, contrary to what has been hypothesized. The general correlation can be fitted by an exponential model for mass transfer that closely correlates 45 published water-oil, and water-air SI experiments obtained for widely different petrophysical properties.@en

Thermohaline convection of subsurface fluids strongly influences heat and mass fluxes within the Earth's crust. The most effective hydrothermal systems develop in the vicinity of magmatic activity and can be important for geothermal energy production and ore formation. As most parts of these systems are inaccessible to direct observations, numerical simulations are necessary to understand and characterize fluid flow. Here, we present a new numerical scheme for thermohaline convection based on the control volume finite element method (CVFEM), allowing for unstructured meshes, the representation of sharp thermal and solute fronts in advection-dominated systems and phase separation of variably miscible, compressible fluids. The model is an implementation of the Complex Systems Modelling Platform CSMP++ and includes an accurate thermodynamic representation of strongly nonlinear fluid properties of salt water for magmatic-hydrothermal conditions (up to 1000°C, 500 MPa and 100 wt% NaCl). The method ensures that all fluid properties are taken as calculated on the respective node using a fully upstream-weighted approach, which greatly increases the stability of the numerical scheme. We compare results from our model with two well-established codes, HYDROTHERM and TOUGH2, by conducting benchmarks of different complexity and find good to excellent agreement in the temporal and spatial evolution of the hydrothermal systems. In a simulation with high-temperature, high-salinity conditions currently outside of the range of both HYDROTHERM and TOUGH2, we show the significance of the formation of a solid halite phase, which introduces heterogeneity. Results suggest that salt added by magmatic degassing is not easily vented or accommodated within the crust and can result in dynamic, complex hydrologies. We present a new numerical scheme for multiphase convection of salt water at magmatic-hydrothermal conditions based on the control volume finite element method. In a series of benchmarks with HYDROTHERM and TOUGH2, we find very good agreement of the simulated hydrothermal systems. Simulations at high-temperature, high-salinity conditions outside of the range of these models show the influence of solid halite on dynamic flow behavior and suggest that salt from magmatic degassing is not easily vented or accommodated within the crust.@en

Thermohaline convection of subsurface fluids strongly influences heat and mass fluxes within the Earth's crust. The most effective hydrothermal systems develop in the vicinity of magmatic activity and can be important for geothermal energy production and ore formation. As most parts of these systems are inaccessible to direct observations, numerical simulations are necessary to understand and characterize fluid flow. Here, we present a new numerical scheme for thermohaline convection based on the control volume finite element method (CVFEM), allowing for unstructured meshes, the representation of sharp thermal and solute fronts in advection-dominated systems and phase separation of variably miscible, compressible fluids. The model is an implementation of the Complex Systems Modelling Platform CSMP++ and includes an accurate thermodynamic representation of strongly nonlinear fluid properties of salt water for magmatic-hydrothermal conditions (up to 1000°C, 500 MPa and 100 wt% NaCl). The method ensures that all fluid properties are taken as calculated on the respective node using a fully upstream-weighted approach, which greatly increases the stability of the numerical scheme. We compare results from our model with two well-established codes, HYDROTHERM and TOUGH2, by conducting benchmarks of different complexity and find good to excellent agreement in the temporal and spatial evolution of the hydrothermal systems. In a simulation with high-temperature, high-salinity conditions currently outside of the range of both HYDROTHERM and TOUGH2, we show the significance of the formation of a solid halite phase, which introduces heterogeneity. Results suggest that salt added by magmatic degassing is not easily vented or accommodated within the crust and can result in dynamic, complex hydrologies. We present a new numerical scheme for multiphase convection of salt water at magmatic-hydrothermal conditions based on the control volume finite element method. In a series of benchmarks with HYDROTHERM and TOUGH2, we find very good agreement of the simulated hydrothermal systems. Simulations at high-temperature, high-salinity conditions outside of the range of these models show the influence of solid halite on dynamic flow behavior and suggest that salt from magmatic degassing is not easily vented or accommodated within the crust.@en

Thermohaline convection of subsurface fluids strongly influences heat and mass fluxes within the Earth's crust. The most effective hydrothermal systems develop in the vicinity of magmatic activity and can be important for geothermal energy production and ore formation. As most parts of these systems are inaccessible to direct observations, numerical simulations are necessary to understand and characterize fluid flow. Here, we present a new numerical scheme for thermohaline convection based on the control volume finite element method (CVFEM), allowing for unstructured meshes, the representation of sharp thermal and solute fronts in advection-dominated systems and phase separation of variably miscible, compressible fluids. The model is an implementation of the Complex Systems Modelling Platform CSMP++ and includes an accurate thermodynamic representation of strongly nonlinear fluid properties of salt water for magmatic-hydrothermal conditions (up to 1000°C, 500 MPa and 100 wt% NaCl). The method ensures that all fluid properties are taken as calculated on the respective node using a fully upstream-weighted approach, which greatly increases the stability of the numerical scheme. We compare results from our model with two well-established codes, HYDROTHERM and TOUGH2, by conducting benchmarks of different complexity and find good to excellent agreement in the temporal and spatial evolution of the hydrothermal systems. In a simulation with high-temperature, high-salinity conditions currently outside of the range of both HYDROTHERM and TOUGH2, we show the significance of the formation of a solid halite phase, which introduces heterogeneity. Results suggest that salt added by magmatic degassing is not easily vented or accommodated within the crust and can result in dynamic, complex hydrologies. We present a new numerical scheme for multiphase convection of salt water at magmatic-hydrothermal conditions based on the control volume finite element method. In a series of benchmarks with HYDROTHERM and TOUGH2, we find very good agreement of the simulated hydrothermal systems. Simulations at high-temperature, high-salinity conditions outside of the range of these models show the influence of solid halite on dynamic flow behavior and suggest that salt from magmatic degassing is not easily vented or accommodated within the crust.@en

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 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 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