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Magmatic processes in the continental crust such as crustal convection, melt ascent, magma emplacement, and batholith formation are not well understood. We solve the conservation equations for mass, momentum, and energy for two‐phase flow of melt and solid in 2D, for a thick continental crust heated from below by one or several heat pulses. A simplified binary melting model is incorporated. We systematically vary (a) the retention number, characterizing melt mobility, (b) the intensity of heat pulses applied at the bottom, and (c) the density of the solidified evolved rock. Two characteristic modes are identified: (a) in the “batholith emplacement mode,” segregation is sufficiently strong allowing melts to separate from the convective flow. This melt freezes to form buoyant SiO2‐rich layers. (b) In the “convective recycling mode,” melts are formed in the lower crust, rise together with the hot rock with little segregation, freeze at shallow depth but are partly recycled back to the lower crust where they remelt. Phase‐change‐driven convection dominates. Mode (a) is favored by high heat input, multiple heat pulses, high melt mobility, and low density of the evolved rock. Mode (b) is favored by less intense heating, less melt mobility, and denser evolved rocks. A scaling law is derived based on the thermal, melt, and compositional Rayleigh numbers and the retention number. The Altiplano‐Puna low‐velocity zone (LVZ) could represent the batholith emplacement mode with buoyant and voluminous magmas causing intense volcanism. The Tibetan LVZ is not associated with intense volcanism and might represent the convective recycling mode. Key Points Two‐phase flow models of crustal magmatic systems identify two modes: batholith emplacement versus convective recycling of evolved rock High melt mobility, multiple heating pulses, and low density of solidified evolved rock favor batholith emplacement The Altiplano‐Puna low‐velocity zone (LVZ) is in the batholith emplacement mode and the Tibetan LVZ is in the convective recycling mode

Upscaling permeability of grid blocks is crucial for groundwater models. A novel upscaling method for three-dimensional fractured porous rocks is presented. The objective of the study was to compare this method with the commonly used Oda upscaling method and the volume averaging method. First, the multiple boundary method and its computational framework were defined for three-dimensional stochastic fracture networks. Then, the different upscaling methods were compared for a set of rotated fractures, for tortuous fractures, and for two discrete fracture networks. The results computed by the multiple boundary method are comparable with those of the other two methods and fit best the analytical solution for a set of rotated fractures. The errors in flow rate of the equivalent fracture model decrease when using the multiple boundary method. Furthermore, the errors of the equivalent fracture models increase from well-connected fracture networks to poorly connected ones. Finally, the diagonal components of the equivalent permeability tensors tend to follow a normal or log-normal distribution for the well-connected fracture network model with infinite fracture size. By contrast, they exhibit a power-law distribution for the poorly connected fracture network with multiple scale fractures. The study demonstrates the accuracy and the flexibility of the multiple boundary upscaling concept. This makes it attractive for being incorporated into any existing flow-based upscaling procedures, which helps in reducing the uncertainty of groundwater models.

Salt diapirs are commonly seen in the North Sea. Below the Zechstein Group exist possibly overpressured salt-anhydrite formations. One explanation as to the salt precipitation in areas with salt diapirs is that salt cementation is thermally driven and occurs strongly in places adjacent to salt diapirs. This paper assumes that the sealing effect of the cap rock above the salt formations is compromised and overpressured fluids, carrying dissolved minerals such as anhydrite (CaSO4) and salt mineral components (NaCl of halite), flow into the porous sedimentary layers above the salt formations. Additionally, a salt-diapir-like structure is assumed to be at one side of the model. The numerical flow and heat transport simulator SHEMAT-Suite was developed and applied to calculating the concentrations of species, and dissolution and precipitation amounts. Results show that the overpressured salt-anhydrite formations have higher pressure heads and the species elements sodium and chlorite are transported into porous sediment rocks through water influx (saturated brine). Halite can precipitate as brine with sodium and chlorite ions flows to the cooler environment. Salt cementation of reservoir rocks leads to decreasing porosity and permeability near salt domes, and cementation of reservoir formations decreases with growing distance to the salt diapir. The proposed approach in this paper can also be used to evaluate precipitation relevant to scaling problems in geothermal engineering.

Granitoid intrusions are the primary heat source of many deep geothermal reservoirs in Tuscany. The depth and shape of these plutons, characterised in this study by a prominent seismic reflector (the K horizon), may vary significantly within the spatial scale of interest. In an exploration field, simulations reveal the mechanisms by which such a heat source influences temperature distribution. A simple analysis quantifies the sensitivity of potentially measurable indicators (i.e. vertical temperature profiles and surface heat flow) to variations in depth, temperature, and shape of the heat source within given ranges of uncertainty.

During geothermal reservoir development, drilling deep boreholes turns out to be extremely expensive and risky. Thus, it is of great importance to work out the details of suitable borehole locations in advance. Here, given a set of existing boreholes, we demonstrate how a sophisticated numerical technique called optimal experimental design helps to find a location of an additional exploratory borehole that reduces risk and, ultimately, saves cost. More precisely, the approach minimizes the uncertainty when deducing the effective permeability of a buried reservoir layer from a temperature profile measured in this exploratory borehole. In this paper, we (1) outline the mathematical formulation in terms of an optimization problem, (2) describe the numerical implementation involving various software components, and (3) apply the method to a 3D numerical simulation model representing a real geothermal reservoir in northern Italy. Our results show that optimal experimental design is conceptually and computationally feasible for industrial-scale applications. For the particular reservoir and the estimation of permeability from temperature, the optimal location of the additional borehole coincides with regions of high flow rates and large deviations from the mean temperature of the reservoir layer in question. Finally, the presentation shows that, methodologically, the optimization method can be generalized from estimating permeability to finding any other reservoir properties.

The Ensemble Kalman Filter (EnKF) is a popular estimation technique in the geosciences. It is used as a numerical tool for state vector prognosis and parameter estimation. The EnKF can, for example, help to evaluate the geothermal potential of an aquifer. In such applications, the EnKF is often used with small or medium ensemble sizes. It is therefore of interest to characterize the EnKF behavior for these ensemble sizes. For seven ensemble sizes (50, 70, 100, 250, 500, 1000, 2000) and seven EnKF-variants (Damped, Iterative, Local, Hybrid, Dual, Normal Score and Classical EnKF), we computed 1000 synthetic parameter estimation experiments for two set-ups: a 2D tracer transport problem and a 2D flow problem with one injection well. For each model, the only difference among synthetic experiments was the generated set of random permeability fields. The 1000 synthetic experiments allow to calculate the pdf of the RMSE of the characterization of the permeability field. Comparing mean RMSEs for different EnKF-variants, ensemble sizes and flow/transport set-ups suggests that multiple synthetic experiments are needed for a solid performance comparison. In this work, 10 synthetic experiments were needed to correctly distinguish RMSE differences between EnKF-variants smaller than 10%. For detecting RMSE differences smaller than 2%, 100 synthetic experiments were needed for ensemble sizes 50, 70, 100 and 250. The overall ranking of the EnKF-variants is strongly dependent on the physical model set-up and the ensemble size.