Development of the submodelling workflow

The large-scale Germany model (Ahlers et al., 2021, 2022) developed within the SpannEnD project integrates available stress information and provides a first-order prognosis on the 3D stress state in the subsurface of whole Germany. In the course of analysing the geomechanical suitability of particular regions of Germany or of specific candidate sites for a repository for nuclear waste it is advantageous to use the results from the Germany model as stress data are generally sparse. This implies that stress from a larger-scale model needs to be transferred to a smaller-scale model, and the technique to accomplish this task is called submodelling.

Development of modeling techniques to adapt mechanical properties to the model scale

A key problem in geomechanical modelling is that at local scales of a few 10s of kilometer stress magnitude for model calibration are seldom available. A solution to this problem is to create two successively calibrated models – one large-scale model with coarse resolution (root model ) and one local model with fine resolution (branch model). The large-scale root model is calibrated with stress magnitude data and delivers either displacement boundary conditions for the local-scale high resolution model (branch model) or synthetic calibration data that can be used for the calibration of the local-scale branch model. Tests with generic models show that both ways lead to similar results, but using synthetic calibration data is slightly better. A comparison with a truth model shows that using displacement boundary conditions results in a difference to the truth model of 2.3% whereas using synthetic calibration data results in a deviation of 1.9%. A prerequisite is that the elastic rock properties at the location of synthetic data points have to be identical in root and branch model.

Development of modeling techniques to adapt mechanical properties to the model scale

in progress

Preparation of the geomechanical model for sub-area 001

Submodelling is used to transfer the stress state from the global Germany-model to a regional scale model of a siting area. This regional-scale siting area model addresses clay as host rock. The research area is located between Baden-Württemberg and Bavaria, in the Swabian Alb and Molasse basin, covering Teilgebiet 001 (001_00TG_032_01IG_T_f_jmOPT), focusing on the middle Jurassic Opalinus clay, up to 300 meters thickness (see figure a). The geological history involves sedimentation, tectonic subsidence, and uplift from the Triassic to the Cenozoic , overlying a Permo-Carboniferous basement of gneisses and Variscan granites exposed in the Black Forest and Bohemian Massif. The Opalinus clay, which is a target formation for potential nuclear waste repository, deposited during the middle Jurassic time and consist of sandy to silty claystone with thin intercalated carbonate-rich layers (Nagra, 2002).

Preparation of the geomechanical model for sub-area 009

Submodelling is used to transfer the stress state from the global Germany-model to a regional scale model of a siting area. This regional-scale siting area model addresses crystalline host rock. As a contribution to method developments, the model is focused on a part of siting area 009 (Teilgebiet 009_00TG_194_00IG_K_g_SO). Due to the vast area of siting area 009, the model area does not cover the entire region (see figure). The model area is chosen in a way to contain the German Continental Deep Drilling Programme (German: Kontinentales Tiefbohrprogramm der Bundesrepublik Deutschland, KTB) site with a unique set of geoscientific data that is available. Furthermore, the model is extended towards the northeast in order to incorporate an existing geological model of the Ore Mountains (Erzgebirge). Details of the model geometry are presented in the interim project report.

The result from the model scenario that uses synthetic calibration data taken from the Germany model and using the multi-scale submodelling approach deviate from the model scenarios that use data from the KTB and the Falkenberg well for the model calibration. However, this is not a deficit of the submodelling technique, but due to the poor coverage with calibration data. Furthermore, the data from Falkenberg are very shallow data which does not fit very well to the vertical model resolution. This highlights the importance of choosing suitable calibration data.

Scale dependency of stress and rock properties

In the first place stresses in rock depend on acting forces and on elastic rock properties. Measured stresses as well as elastic properties are a matter of scale. This is because natural rock is composed of spatially variable fractions of mineral types, it can comprise inclusions of variable size or variable porosity, it can exhibit fractures of different orientation and frictional properties or alternating layers of differing rock type. Typical measurement methods of both stress and elastic properties require a certain minimum scale to derive a value (e.g. ~1 m for hyrofrac tests and some ten centimetres for static compression tests) and often measurements are conducted at locations suitable for the measurement method (e.g. hydrofrac tests in stiff rock units more likely allow development of proper fractures than in pre-damaged sections or in units of low strength and intact rock facilitates rock sample preparation and permits reproducible results). Thus, measurements of stress and elastic properties generally represent an integrated value over the measurement scale or are biased due to the specific location chosen for the measurements. Several approaches have been used to assess the impact of inhomogeneous rock properties on stress.

A) Statistical distribution of rock stiffness in space

Young’s modulus is defined statistically distributed in a rock layer following a chi square distribution centered around a mean value. The resulting horizontal stress along a vertical profile fluctuates around the stress path derived for a homogeneous Young’s modulus of the mean value of the distribution. The amount of deviation reaches up to 7% in the tested cases but is on average much lower. The deviation depends on element size with larger elements yielding larger deviations.

B) Statistical distribution of rock stiffness in layered stratigraphy

A succession of horizontally layered units is considered in which rock stiffness is statistically assigned to the individual layers according to a chi square distribution centered around a mean value. A maximum deviation of 21 % in the magnitude of maximum horizontal stress was derived with respect to the stress in a homogenous rock column. Grouping neighbouring layers with a stiffness corresponding to their mean value results a reduction of deviation with respect to the stress in homogeneous rock column but may lead to deviations with respect to data the model was originally calibrated to taking into account the detailed stratigraphy.

C) Mixing laws for effective elastic media

The self-consistent method is used to calculate effective elastic constants for inclusions of variable shape, volume ratio and stiffness deviation between the inclusion material and the matrix material. In an example the Young’s modulus decreases by 45 % if a consolidated sandstone includes 5 % flat clay lenses of low stiffness.

D) Multiscale material model

The mean-field homogenization approach is used to numerically compute the mechanical behaviour of composite materials. Assuming a spherical porosity of 10 % the maximum horizontal stress magnitude reduces by up to 8 % compared to if the rock is without porosity. Cleavages represented by penny shaped voids of very low aspect ratios can play a greater role, particularly for the minimum horizontal stress. Depending on the orientation of the cleavages relative to the acting far-field forces the maximum horizontal stress decreases by up to 36 % and the minimum horizontal stress by 20 % relative to the case with no cleavages. The minimum horizontal stress can also increase with other orientations. A random orientation of the cleavages still reduces the maximum horizontal stress by 15 % in the tested example. These numbers refer to the mean field where strain and stress are averaged over the composite material. Stress on the micro-level in the individual constituents of the material can differ more.

E) Jointed Material

The jointed material model is used to capture the effect of fractured rock on the stress state depending on the orientation and frictional properties of the fractures. In a test case the minimum horizontal stress is increased by 8 % and the maximum horizontal stress is decreased by 3 % relative to the case without fractures. In a trial-and-error approach it was inferred that this corresponds to a reduction of Young‘s modulus by 10 % relative to the intact rock without fractures.

References:

Ahlers, S., Henk, A., Hergert, T., Reiter, K., Müller, B., Röckel, L., Heidbach, O., Morawietz, S., Scheck-Wenderoth, M., and Anikiev, D.: 3D crustal stress state of Germany according to a data-calibrated geomechanical model, Solid Earth, 12, 1777–1799, https://doi.org/10.5194/se-12-1777-2021, 2021.

Ahlers, S., Röckel, L., Hergert, T., Reiter, K., Heidbach, O., Henk, A., Müller, B., Morawietz, S., Scheck-Wenderoth, M., and Anikiev, D.: The crustal stress field of Germany: a refined prediction, Geothermal Energy, 10, https://doi.org/10.1186/s40517-022-00222-6, 2022.

BGE: Zwischenbericht Teilgebiete gemäß § 13 StandAG: Stand 28.09.2020, 443 pp., 2020.

Nagra: Projekt Opalinuston – Synthese der geowissenschaftlichen Untersuchungsergebnisse: Entsorgungsnachweis für abgebrannte Brennelemente, verglaste hochaktive sowie langlebige mittelaktive Abfälle, NTB, 02-03, 659 pp., 2002.