Abstract
This report is a part of SKB Task Force on Modelling of Groundwater Flow and Transport of Solutes and focuses on Task 10.2.2c. In the task, the objective was to predict flow rates in a natural fracture between two rock parts which were compressed together with different normal loads. In the experiment carried out within the POST project, the rock samples were prepared and the first hydro-mechanical tests were conducted while the rock fracture remained unopened. After the tests, the fracture was opened, and the fracture surfaces scanned with high-precision instruments. Further flow tests were performed in the same fracture after the rock parts were re-emplaced together.
Using the fracture surface scan data and information on the placement of the rock parts in the experiment, different modelling teams conducted the blind prediction exercise where the flow ratesunder different normal loads were predicted. The experimental flow rate results were only provided after the predictions had been made. Our modelling team selected a modelling approach, where the rock-mechanical deformation was simulated with contact modelling followed by fluid flow modelling in the deformed fracture void space. Both the contact and fluid flow numerical modelling were conducted with COMSOL Multiphysics.
Preliminary analytical and numerical models were created to better understand the model uncertainties including fracture scan precision and placement of the top fracture surface with respect to the bottom one. These preliminary models showed that the scan precision is important when modelling slow flow, and that the fracture surface placement deviations especially in z- but also x- and y-directions are statistically significant factors affecting the flow rate.
The preliminary models were followed by converting the experimental fracture surface scan data into a model geometry which consists of the two rock parts separated by the fracture. The rock parts were virtually compressed against each other, and the contact of the fracture surfaces and the deformation of the linear elastic assumed rock were simulated with two different approaches, Nearing Contact Model and Departing Contact Model. With the first model, a normal load of 1 MPa was considered while with the latter normal loads of 0, 1, 2, 4, 6 and 8 MPa were studied. Even though the contact formulations aimed to prevent geometrical overlap of the fracture surfaces, this was not achieved perfectly. Thus, a contact offset value was used in the contact modelling to prevent the overlap, which was important for the subsequent flow modelling. The contact offset, however, added error to fracture geometry and, therefore, to the flow model, and a balance between modelling error and preventing the overlap had to be sought.
The resulting stress distribution from both contact modelling approaches showed that the uniaxial compressive strength was exceeded in some areas on the surfaces and possible breaking of the rock could occur. This indicates that the assumption of linear elastic deformation induced uncertainty to the model. On the other hand, the simulated displacements between the top and bottom rock parts showed a somewhat similar trend with high normal loads (over 2 MPa) as the measured LVDT data, which gives some confidence in the only elastic model.
The deformed fracture void space between the two rock parts that resulted from the contact modelling was converted into a flow channel geometry where the water flow driven by pressure difference was simulated. Very slow flow rate was assumed, leading to the use of the Navier-Stokes equations without the inertial term. The predicted flow rates significantly overestimated the experimentally measured flow rate with both approaches and with the different normal loads. The flow rates also varied depending on the contact approach and the contact offset value.
Using the fracture surface scan data and information on the placement of the rock parts in the experiment, different modelling teams conducted the blind prediction exercise where the flow ratesunder different normal loads were predicted. The experimental flow rate results were only provided after the predictions had been made. Our modelling team selected a modelling approach, where the rock-mechanical deformation was simulated with contact modelling followed by fluid flow modelling in the deformed fracture void space. Both the contact and fluid flow numerical modelling were conducted with COMSOL Multiphysics.
Preliminary analytical and numerical models were created to better understand the model uncertainties including fracture scan precision and placement of the top fracture surface with respect to the bottom one. These preliminary models showed that the scan precision is important when modelling slow flow, and that the fracture surface placement deviations especially in z- but also x- and y-directions are statistically significant factors affecting the flow rate.
The preliminary models were followed by converting the experimental fracture surface scan data into a model geometry which consists of the two rock parts separated by the fracture. The rock parts were virtually compressed against each other, and the contact of the fracture surfaces and the deformation of the linear elastic assumed rock were simulated with two different approaches, Nearing Contact Model and Departing Contact Model. With the first model, a normal load of 1 MPa was considered while with the latter normal loads of 0, 1, 2, 4, 6 and 8 MPa were studied. Even though the contact formulations aimed to prevent geometrical overlap of the fracture surfaces, this was not achieved perfectly. Thus, a contact offset value was used in the contact modelling to prevent the overlap, which was important for the subsequent flow modelling. The contact offset, however, added error to fracture geometry and, therefore, to the flow model, and a balance between modelling error and preventing the overlap had to be sought.
The resulting stress distribution from both contact modelling approaches showed that the uniaxial compressive strength was exceeded in some areas on the surfaces and possible breaking of the rock could occur. This indicates that the assumption of linear elastic deformation induced uncertainty to the model. On the other hand, the simulated displacements between the top and bottom rock parts showed a somewhat similar trend with high normal loads (over 2 MPa) as the measured LVDT data, which gives some confidence in the only elastic model.
The deformed fracture void space between the two rock parts that resulted from the contact modelling was converted into a flow channel geometry where the water flow driven by pressure difference was simulated. Very slow flow rate was assumed, leading to the use of the Navier-Stokes equations without the inertial term. The predicted flow rates significantly overestimated the experimentally measured flow rate with both approaches and with the different normal loads. The flow rates also varied depending on the contact approach and the contact offset value.
| Original language | English |
|---|---|
| Publisher | Svensk Kärnbränslehantering AB (SKB) |
| Number of pages | 60 |
| Publication status | Published - 2025 |
| MoE publication type | D4 Published development or research report or study |
Publication series
| Series | SKB rapport |
|---|---|
| Number | R-23-15 |
| ISSN | 1402-3091 |