Reservoir-scale transdimensional fracture network inversion

The Waiwera aquifer hosts a structurally complex geothermal groundwater system, where a localized thermal anomaly feeds the thermal reservoir. The temperature anomaly is formed by the mixing of waters from three different sources: fresh cold groundwater, cold seawater and warm geothermal water. The stratified reservoir rock has been tilted, folded, faulted, and fractured by tectonic movement, providing the pathways for the groundwater. Characterization of such systems is challenging, due to the resulting complex hydraulic and thermal conditions which cannot be represented by a continuous porous matrix. By using discrete fracture network models (DFNs) the discrete aquifer features can be modelled, and the main geological structures can be identified. A major limitation of this modelling approach is that the results are strongly dependent on the parametrization of the chosen initial solution. Classic inversion techniques require to define the number of fractures before any interpretation is done. In this research we apply the transdimensional DFN inversion methodology that overcome this limitation by keeping fracture numbers flexible and gives a good estimation on fracture locations. This stochastic inversion method uses the reversible-jump Markov chain Monte Carlo algorithm and was originally developed for tomographic experiments. In contrast to such applications, this study is limited to the use of steady-state borehole temperature profiles – with significantly less data. This is mitigated by using a strongly simplified DFN model of the reservoir, constructed according to available geological information. We present a synthetic example to prove the viability of the concept, then use the algorithm on field observations for the first time. The fit of the reconstructed temperature fields cannot compete yet with complex three-dimensional continuum models, but indicate areas of the aquifer where fracturing plays a big role. This could not be resolved before with continuum modelling. It is for the first time that the transdimensional DFN inversion was used on field data and on borehole temperature logs as input.DFG, 318763901, SFB 1294, Data Assimilation - The seamless integration of data and models, Assimilating data with different degrees of uncertainty into statistical models for earthquake occurrence (B04)TU Berlin, Open-Access-Mittel - 201

Upscaling of a dual-permeability Monte Carlo simulation model for contaminant transport in fractured networks by genetic algorithm parameter identification

International audienceThe transport of radionuclides in fractured media plays a fundamental role in determining the level of risk offered by a radioactive waste repository in terms of expected doses. Discrete Fracture Networks (DFN) methods can provide detailed solutions to the problem of modeling the contaminant transport in fractured media. However, within the framework of the performance assessment (PA) of radioactive waste repositories, the computational efforts required are not compatible with the repeated calculations that need to be performed for the probabilistic uncertainty and sensitivity analyses of PA. In this paper, we present a novel upscaling approach, which consists in computing the detailed numerical fractured flow and transport solutions on a small scale and use the results to derive the equivalent continuum parameters of a lean, one-dimensional Dual-Permeability, Monte Carlo Simulation (DPMCS) model by means of a Genetic Algorithm search. The proposed upscaling procedure is illustrated with reference to a realistic case study of migration taken from literature

Uncertainty quantification in Discrete Fracture Network models: stochastic geometry

We consider the problem of uncertainty quantification analysis of the output of underground flow simulations. We consider in particular fractured media described via the discrete fracture network model; within this framework, we address the relevant case of networks in which the geometry of the fractures is described by stochastic parameters. In this context, due to a possible lack of smoothness in the quantity of interest with respect to the stochastic parameters, well assessed techniques such as stochastic collocation may fail in providing reliable estimates of first-order moments of the quantity of interest. In this paper, we overcome this issue by applying the Multilevel Monte Carlo method, using as underlying solver an extremely robust method

Anomalous transport in disordered fracture networks: Spatial Markov model for dispersion with variable injection modes

We investigate tracer transport on random discrete fracture networks that are characterized by the statistics of the fracture geometry and hydraulic conductivity. While it is well known that tracer transport through fractured media can be anomalous and particle injection modes can have major impact on dispersion, the incorporation of injection modes into effective transport modeling has remained an open issue. The fundamental reason behind this challenge is that-even if the Eulerian fluid velocity is steady-the Lagrangian velocity distribution experienced by tracer particles evolves with time from its initial distribution, which is dictated by the injection mode, to a stationary velocity distribution. We quantify this evolution by a Markov model for particle velocities that are equidistantly sampled along trajectories. This stochastic approach allows for the systematic incorporation of the initial velocity distribution and quantifies the interplay between velocity distribution and spatial and temporal correlation. The proposed spatial Markov model is characterized by the initial velocity distribution, which is determined by the particle injection mode, the stationary Lagrangian velocity distribution, which is derived from the Eulerian velocity distribution, and the spatial velocity correlation length, which is related to the characteristic fracture length. This effective model leads to a time-domain random walk for the evolution of particle positions and velocities, whose joint distribution follows a Boltzmann equation. Finally, we demonstrate that the proposed model can successfully predict anomalous transport through discrete fracture networks with different levels of heterogeneity and arbitrary tracer injection modes. © 2017 Elsevier Ltd.PKK and SL acknowledge a grant (16AWMP- B066761-04) from the AWMP Program funded by the Ministry of Land, Infrastructure and Transport of the Korean government and the support from Future Research Program (2E27030) funded by the Korea Institute of Science and Technology (KIST). PKK and RJ acknowledge a MISTI Global Seed Funds award. MD acknowledges the support of the European Research Council (ERC) through the project MHetScale (617511). TLB acknowledges the support of European Research Council (ERC) through the project Re- activeFronts (648377). RJ acknowledges the support of the US Department of Energy through a DOE Early Career Award (grant DE-SC0009286). The data to reproduce the work can be obtained from the corresponding author.N

Finite element method for coupled thermo-hydro-mechanical processes in discretely fractured and non-fractured porous media

Numerical analysis of multi-field problems in porous and fractured media is an important subject for various geotechnical engineering tasks such as the management of geo-resources (e.g. engineering of geothermal, oil and gas reservoirs) as well as waste management. For practical usage, e.g. for geothermal, simulation tools are required which take into account both coupled thermo-hydro-mechanical (THM) processes and the uncertainty of geological data, i.e. the model parametrization. For modeling fractured rocks, equivalent porous medium or multiple continuum model approaches are often only the way currently due to difficulty to handle geomechanical discontinuities. However, they are not applicable for prediction of flow and transport in subsurface systems where a few fractures dominates the system behavior. Thus modeling coupled problems in discretely fractured porous media is desirable for more precise analysis. The subject of this work is developing a framework of the finite element method (FEM) for modeling coupled THM problems in discretely fractured and non-fractured porous media including thermal water flow, advective-diffusive heat transport, and thermoporoelasticity. Pre-existing fractures are considered. Systems of discretely fractured porous media can be considered as a problem of interacted multiple domains, i.e. porous medium domain and discrete fracture domain, for hydraulic and transport processes, and a discontinuous problem for mechanical processes. The FEM is required to take into account both kinds of the problems. In addition, this work includes developing a methodology for the data uncertainty using the FEM model and investigating the uncertainty impacts on evaluating coupled THM processes. All the necessary code developments in this work has been carried out with a scientific open source project OpenGeoSys (OGS). In this work, fluid flow and heat transport problems in interactive multiple domains are solved assuming continuity of filed variables (pressure and temperature) over the two domains. The assumption is reasonable if there are no infill materials in fractures. The method has been successfully applied for several numerical examples, e.g. modeling three-dimensional coupled flow and heat transport processes in discretely fractured porous media at the Gross Schoenebck geothermal site (Germany), and three-dimensional coupled THM processes in porous media at the Urach Spa geothermal site (Germany). To solve the mechanically discontinuous problems, lower-dimensional interface elements (LIEs) with local enrichments have been developed for coupled problems in a domain including pre-existing fractures. The method permits the possibility of using existing flow simulators and having an identical mesh for both processes. It enables us to formulate the coupled problems in monolithic scheme for robust computation. Moreover, it gives an advantage in practice that one can use existing standard FEM codes for groundwater flow and easily make a coupling computation between mechanical and hydraulic processes. Example of a 2D fluid injection problem into a single fracture demonstrated that the proposed method can produce results in strong agreement with semi-analytical solutions. An uncertainty analysis of THM coupled processes has been studied for a typical geothermal reservoir in crystalline rock based on the Monte-Carlo method. Fracture and matrix are treated conceptually as an equivalent porous medium, and the model is applied to available data from the Urach Spa and Falkenberg sites (Germany). Reservoir parameters are considered as spatially random variables and their realizations are generated using conditional Gaussian simulation. Two reservoir modes (undisturbed and stimulated) are considered to construct a stochastic model for permeability distribution. We found that the most significant factors in the analysis are permeability and heat capacity. The study demonstrates the importance of taking parameter uncertainties into account for geothermal reservoir evaluation in order to assess the viability of numerical modeling