#### WP 2: Pathways through pressure-driven percolation

## News

At CAU Kiel, three samples under different stress boundary conditions undergo the fracking process using the true triaxial apparatus. According to the pre-existing mechanical stress distribution, the fracking pattern under applied hydraulic pressure is unique for each stress distribution.

IfG is exploring the opportunities presented by new software techniques to model the desiccation processes of clay.

#### CAU Kiel

The fluid-driven percolation experiments on cubical clay and salt samples with dimensions of 43 x 43 x 43 mm are conducted under laboratory conditions at CAU Kiel. The hydraulic pump filled with hydraulic oil can reach a pressure of up to 700 bar. The pressure-controlled technique is considered, and the corresponding flow rates are stored. Three samples under different stress boundary conditions undergo the fracking process using the true triaxial apparatus. The existing P and S-wave ultrasonic sensors on pistons are used to measure the material property change using the analytical relation existing in literature. According to the pre-existing mechanical stress distribution, the fracking pattern under applied hydraulic pressure is unique for each stress distribution. In order to visualize the fracking path, X-Ray computed tomography (XRCT) scans are made at the University of Stuttgart from samples before and after fracking. To keep the cracks open, a mixture of metal powder with a maximum particle dimension of 30 micrometers is added to the fluid mixture.

#### IfG

**Modelling: Shrinking of clay and crack opening due to desiccation**

When clay is exposed to air, for example on the surface of walls of drifts, it tends to develop cracks because its water content evaporates. The pore pressure in the material is reduced, leading to tensile stresses which eventually open up cracks. Recently, Itasca added a feature of bulk pore pressure to its 3DEC program in addition to the usual discrete element fluid knot feature, which could open up the possibility to model and analyze such processes. We are currently exploring the possibility by simulating a block of saturated clay with a constant evaporation rate at the top. As expected, we see the creation of cracks:

Up to now, only qualitative results have been obtained. It remains to be explored whether the model is also able to function with more realistic parameter sets.

At CAU Kiel, the gas and fluid pressure-driven percolation in clay and salt stones are experimentally and numerically investigated. Using the true triaxial device in the laboratory of CAU Kiel, a fluid-driven percolation test on a cubic sample is carried out. By controlling the three principal stresses individually, the frack paths and change of flow rate are determined.

The crack initiation and propagation, change of permeability, change of flow rate upon cracking and during the healing process and developed frack paths are all captured with the hydro-mechanical dual lattice model (Grassi 2009). The conduct elements are the fluid pathways throughout the discretized medium.

P. Grassl (2009). A lattice approach to model flow in cracked concrete. Cement & Concrete Composites 31 (2009) 454–460.

#### Experiments on Pressure-driven Percolation and Sealing/Healing of cracks

Up to now, three experiments have been carried out to study the sealing and healing of cracks in rock salt. Boreholes were drilled to the center of cylindrical samples and fitted with a metal pipe so that gas pressure could be applied to a small area at the center.

Initially, all samples were placed under isostatic stress of 50 MPa for one day to consolidate them. For the actual experiments, the isostatic stresses were then changed to 10 MPa, 30 MPa, and 50 MPa, respectively. A gas pressure at the center of the samples was then applied and increased in small steps until a gas flow was detected. In all three cases, a gas flow was detected before the percolation threshold was reached (usually a few bar below), which indicates that the samples suffered micro-fractures during preparation. After the last increase of the pressure, the flow rate was monitored for 24 to 60 hours under constant conditions. The corresponding permeabilities were:

In all three cases, a reduction of the permeability was observed, showing a narrowing of the pathways due to creep.

Further analysis and a numerical model for WP 2.2 (see following article: Numerical Model of Fractures) are work in progress.

#### Numerical Modeling of Fractures

The IfG worked on several Model Exercises (ME) that were agreed on between the project partners of GeomInt.

The first ME was a simple three-point bending test to compare how the various methods employed at the different institutions describe fracture mechanics. We used the discrete element method 3DEC (Itasca Consulting Group) to set up two models of a granite bar:

For each, the force and the crack mouth opening displacement (CMOD) were recorded as well as the acoustic emissions.

The results agree very well with an experiment done by Tarokh et al. (Int. J. Fract. 204, p 191 (2017)).

In a second ME, pressure-driven percolation in a cubic sample of rock salt in an anisotropic true-triaxial stress state was simulated. The purpose was to study the orientation of the resulting fractures as a function of the stress state and to compare the performance of the various methods employed by the project partners. Here again we used 3DEC:

#### IfG

Development of numerical methods: Quantitative treatment of pressure driven percolation and the difference between liquids and gas

Pressure-driven percolation in a cylindrical sample: In a homogeneous sample and stress state, the fluid expands in an isotropic pattern.

#### BGR

BGR has tested the implementation of the new implemented X-FEM LIE approach in OGS-6. With this approach, it is possible to simulate the hydraulic stimulated deformation behavior of an existing crack. This includes opening and closing, shear deformation and change of crack permeability.

In order to determine the flow pathways through pressure-driven percolation, the experimental result provided from our project partner IfG Leipzig is used. In their provided test a cylindrical sample is under radial confinement pressure of 50 MPa and gas pressure is gradually increased till the gas flow rate initiated in the medium (Figure 1).

With application of lattice element method (LEM) and using the dual lattice method to define the conduct elements as flow paths (L_{ij}), the hydro model is coupled with previously developed mechanical model.

The gas flow rate change with developed pressures and fracture aperture is determined using,

where k_{L} is the permeability, e_{i’j’} is the aperture width in 2D lattice model, L_{ij} is the conduct element length, *μ* is the viscosity and P_{i} and P_{j} are the gas pressure in i and j conduct points.

According to the differential equation of the non-stationary flow problems, the flow in a single conduct element (i,j) is,

where k_{M} and C_{M} are the conductivity and capacity matrix, respectively and P is the pressure potential with two degrees of freedom.

With solving the aforementioned equation the applied forces on conduct points (i,j) as well as lattice points (i‘,j‘) are determined and inserted in mechanical model. The change of aperture width, e_{i’j’}, with crack opening is determined and transferred to flow model. The LEM boundary condition is shown in figure 3. The generated lattice model has 20,000 Voronoi cells and randomness factor of 0.5. The model has around 50,000 elements. The fracture flow path in the tip of the hole is shown in Figure 4. In general, the fracture pathway is in horizontal direction.

The comparison of experimental results from IfG Leipzig and LEM simulation results from CAU Kiel is shown in Figure 5. The fracture initiation is at gas pressure of 39.6 MPa, which corresponds to propagation of gas flow into medium. In LEM, the gas pressure is gradually increased, 0.1 MPa steps, till 45 MPa. The healing of the fractures is not captured with LEM, which need to be investigated.

The IfG set up a three-dimensional model to test several approaches for the propagation of fluids by pressure driven percolation. Pressure driven percolation is defined as the opening of intercrystalline grain boundaries, caused by fluid pressure, that leads to the creation of interconnected flow paths. A library of subroutines has been set up, with several numerical functions that can describe the advancement of the fluid front. Currently numerical simulations are under way to study the influence of the compressibility of the fluid, with a focus on the difference between gases and liquids.

Within AP2, the UFZ team implemented cohesive zone models for hydraulically stimulated fracturing as well as specific hydraulic fracture flow laws into numerical methods in OpenGeoSys using enriched finite element spaces. Simultaneously, a phase field model for pressure driven pathway generation has been implemented and is being tested.

Currently, comparisons between both methods are ongoing regarding the quantification of key physical quantities such as fracture volume or percolation/fracture initiation pressure.

The flow path in salt stones is due to pre-existing or developed discontinuities in the microstructure. The mechanical loads can result in new flow paths as well as propagation of pre-existing microcracks and eventually increase of the hydraulic conductivity of the salt stones. In this regard, in CAU Kiel laboratory, extensive experimental tests under coupled thermo-hydro-mechanical (THM) conditions will be conducted. The aim is to investigate the change of THM property of salt stones due to developed microcracks. Besides the laboratory tests, the numerical study is also conducted. While using in-house developed Lattice Element Method (LEM) and the experimental results, a new numerical method for determining the change of hydraulic conductivity under THM processes will be developed. According to our research results in CAU Kiel, the developed LEM is able to capture the developed fracture path and it‘s effect on mechanical and thermal properties of the rock samples.

**References:**

[1] A. S. Sattari, Z. H. Rizvi, H. B. Motra, F. Wuttke (2017). Meso-scale modeling of heat transport in a heterogeneous cemented geomaterial by lattice element method. Granular Matter. 19:66. (DOI 10.1007/s10035-017-0751-4).

[2] Zarghaam H. Rizvi, Amir S. Sattari, Hem B. Motra, Frank Wuttke (2017). Effective parameter evaluation in heterogeneous cemented geomaterials subjected to high temperature, pressure and constrained deformations, Second International Symposium on Coupled Phenomena in Environmental Geotechnics, University of Leeds, UK.