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- Borehole heat exchanger (1)
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We present an effective finite difference formulation for implementing and modeling multiple borehole heat exchangers (BHE) in the general 3-D coupled heat and flow transport code SHEMAT. The BHE with arbitrary length can be either coaxial or double U-shaped. It is particularly suitable for modeling deep BHEs which contain varying pipe diameters and materials.
Usually, in numerical simulations, a fine discretization of the BHE assemblage is required, due to the large geometric aspect ratios involved. This yields large models and long simulation times. The approach avoids this problem by considering heat transport between fluid and the soil through pipes and grout via thermal resistances. Therefore, the simulation time can be significantly reduced.
The coupling with SHEMAT is realized by introducing an effective heat generation. Due to this connection, it is possible to consider heterogeneous geological models, as well as the influence of groundwater flow. This is particularly interesting when studying the long term behavior of a single BHE or a BHE field. Heating and cooling loads can enter the model with an arbitrary interval, e.g. from hourly to monthly values. When dealing with large BHE fields, computing times can be further significantly reduced by focusing on the temperature field around the BHEs, without explicitly modeling inlet and outlet temperatures. This allows to determine the possible migration of cold and warm plumes due to groundwater flow, which is of particular importance in urban areas with a high BHE installation density.
The model is validated against the existing BHE modeling codes EWS and EED. A comparison with monitoring data from a deep BHE in Switzerland shows a good agreement. Synthetic examples demonstrate the field of application of this model.
Modeling contribution to risk assessment of thermal production power for geothermal reservoirs
(2013)
Numerische Simulation des Gefrierprozesses bei der Baugrundvereisung im durchströmten Untergrund
(2008)
Quantifying and minimizing uncertainty is vital for simulating technically and economically successful geothermal reservoirs. To this end, we apply a stochastic modelling sequence, a Monte Carlo study, based on (i) creating an ensemble of possible realizations of a reservoir model, (ii) forward simulation of fluid flow and heat transport, and (iii) constraining post-processing using observed state variables. To generate the ensemble, we use the stochastic algorithm of Sequential Gaussian Simulation and test its potential fitting rock properties, such as thermal conductivity and permeability, of a synthetic reference model and—performing a corresponding forward simulation—state variables such as temperature. The ensemble yields probability distributions of rock properties and state variables at any location inside the reservoir. In addition, we perform a constraining post-processing in order to minimize the uncertainty of the obtained distributions by conditioning the ensemble to observed state variables, in this case temperature. This constraining post-processing works particularly well on systems dominated by fluid flow. The stochastic modelling sequence is applied to a large, steady-state 3-D heat flow model of a reservoir in The Hague, Netherlands. The spatial thermal conductivity distribution is simulated stochastically based on available logging data. Errors of bottom-hole temperatures provide thresholds for the constraining technique performed afterwards. This reduce the temperature uncertainty for the proposed target location significantly from 25 to 12 K (full distribution width) in a depth of 2300 m. Assuming a Gaussian shape of the temperature distribution, the standard deviation is 1.8 K. To allow a more comprehensive approach to quantify uncertainty, we also implement the stochastic simulation of boundary conditions and demonstrate this for the basal specific heat flow in the reservoir of The Hague. As expected, this results in a larger distribution width and hence, a larger, but more realistic uncertainty estimate. However, applying the constraining post-processing the uncertainty is again reduced to the level of the post-processing without stochastic boundary simulation. Thus, constraining post-processing is a suitable tool for reducing uncertainty estimates by observed state variables.
SHEMAT-Suite: An open-source code for simulating flow, heat and species transport in porous media
(2020)
SHEMAT-Suite is a finite-difference open-source code for simulating coupled flow, heat and species transport in porous media. The code, written in Fortran-95, originates from geoscientific research in the fields of geothermics and hydrogeology. It comprises: (1) a versatile handling of input and output, (2) a modular framework for subsurface parameter modeling, (3) a multi-level OpenMP parallelization, (4) parameter estimation and data assimilation by stochastic approaches (Monte Carlo, Ensemble Kalman filter) and by deterministic Bayesian approaches based on automatic differentiation for calculating exact (truncation error-free) derivatives of the forward code.