**2. Materials and methods**

#### **2.1. Sample material**

To investigate the influence of rock properties on tensile test methods, six different rock types were tested. Bebertal sandstone, a medium grained Permian sandstone from a quarry near Magdeburg, Germany. Ruhrsandstone, a fine-grained and massive Carboniferous arcose from the Ruhr area in Germany. A medium to coarse grained, jointed Permian andesite from the Doenstedt Eiche quarry near Doenstedt, Germany. A medium grained, highly jointed Permian rhyolite from the Holzmuehlental quarry near Flechtingen, Germany. A micritic Jurassic limestone from a quarry near Treuchtlingen, Germany and a coarse grained marble from Carrara, Italy. The rocks' petrophysical properties, namely bulk density, grain density, compressional wave speed, porosity, permeability, cohesion and friction angle are listed in Table 1.

#### **2.2. Petrophysical characterization**

Dry densities are calculated geometrically based on geometrical properties, grain densities are measured according to DIN 18124. Compressional wave velocities are measured at each core with a Geotron USG 40/UST 50-12 at room temperature and in dry condition. Porosities are derived from the difference between grain density and geometrical density of the oven-dried samples. Permeabilities are evaluated via a constant head test on the hollow cylinder samples used for the MF tests [7]. Bebertal-sandstones are permeable enough to use a simple axial flowthrough test with a maximum pressure difference of up to 3 bars. The samples are sealed off with rubber jackets to minimize water-flow along the sample surface. Unconfined compressive strengths and static moduli of elasticity are measured by uniaxial compressive tests [8].


**Table 1.** Averaged values of petrophysical properties of the rock samples. ρd dry bulk density, ρs grain density, vp compressional wave velocity, Φ porosity, k permeability, c cohesion, φ friction angle.

#### **2.3. Testing procedure of the tensile strength tests**

tests are taken to be size independent when used as input parameter for numerical studies

We compare the results of 3 different, easily applicable laboratory tests for tensile strength of rocks. The sample set comprises a micritic limestone, a coarse-grained marble, a fine-grained Ruhr-Sandstone, a medium-grained rhyolite, a medium- /coarse-grained andesite and a medium grained sandstone. All tested rocks were characterized petrographically as well as by ultrasonic velocities, density, porosity, permeability, static, dynamic elastic moduli and compressive strength. In order to determine the effects of specimen size on test results, we carried out BDT according to ISRM [4] with disc diameters of 30, 40, 50, 62, 75 and 84 mm, respectively. The recently presented MTT [5] was used as a tensile strength test with an approximately uniform tensile stress distribution. Hydraulic tensile strength was evaluated by MF experiments (core diameter 40 and 62 mm; borehole/diameter ratio 1:10) under uniaxial compression [6]. MF pressurization was performed with a constant fluid volume rate of 0.1 ml/s representing a stress rate of 0.3 MPa/s. In all tests relevant acoustic emission (AE) values

To investigate the influence of rock properties on tensile test methods, six different rock types were tested. Bebertal sandstone, a medium grained Permian sandstone from a quarry near Magdeburg, Germany. Ruhrsandstone, a fine-grained and massive Carboniferous arcose from the Ruhr area in Germany. A medium to coarse grained, jointed Permian andesite from the Doenstedt Eiche quarry near Doenstedt, Germany. A medium grained, highly jointed Permian rhyolite from the Holzmuehlental quarry near Flechtingen, Germany. A micritic Jurassic limestone from a quarry near Treuchtlingen, Germany and a coarse grained marble from Carrara, Italy. The rocks' petrophysical properties, namely bulk density, grain density, compressional wave speed, porosity, permeability, cohesion and friction angle are listed in

Dry densities are calculated geometrically based on geometrical properties, grain densities are measured according to DIN 18124. Compressional wave velocities are measured at each core with a Geotron USG 40/UST 50-12 at room temperature and in dry condition. Porosities are derived from the difference between grain density and geometrical density of the oven-dried samples. Permeabilities are evaluated via a constant head test on the hollow cylinder samples used for the MF tests [7]. Bebertal-sandstones are permeable enough to use a simple axial flowthrough test with a maximum pressure difference of up to 3 bars. The samples are sealed off with rubber jackets to minimize water-flow along the sample surface. Unconfined compressive strengths and static moduli of elasticity are measured by uniaxial compressive tests [8].

have been evaluated to get additional information on the failure processes.

at different spatial sizes.

982 Effective and Sustainable Hydraulic Fracturing

**2. Materials and methods**

**2.2. Petrophysical characterization**

**2.1. Sample material**

Table 1.

All experiments are performed in a stiff servo-hydraulic loading frame from Material Testing Systems (MTS) with a load capacity of 4000 kN. For further details on the technical specifica‐ tions see Table 2.


**Table 2.** Technical specifications of the measurement system.

Acoustic Emission (AE) signals are acquired with an AMSY-5 Acoustic Emission Measurement System (Vallen Systeme GmbH, Germany) equipped with up to 6 Sensors of type VS150-M. The Sensors are sensitive in a frequency range of 100-450 kHz with a resonance frequency of 150 kHz and a preamplification of 34 dBAE. Due to machine noise in the range below 100 kHz incoming signals are filtered by a digital bandpass-filter in a frequency range of 95-850 kHz. AE data are sampled by a sampling rate of 10 kHz. The sensors are fixed using hot-melt adhesive to ensure best coupling characteristics. Pencil-break tests (Hsu-Nielsen source) and sensor pulsing runs (active acoustic emission by one sensor) are used to ensure good sensor coupling of the sensor on the sample.

#### *2.3.1. Hydraulic fracturing core experiments (MF) procedure*

Minifrac experiments are carried out mainly on 40 mm cores with a borehole diameter of 4mm. Furthermore some 62 mm cores with a borehole of 6 mm diameter are tested. The samples are loaded axially up to 5 MPa to ensure that the packer mechanism is tight and seals off the borehole openings at the top and at the bottom. The borehole pressure was raised servo controlled with a fixed volume rate of 0.1 ml/s that results in a pressure rate of approximately 0.3 MPa/s. All MF tests are monitored by Acoustic Emissions with four sensors glued directly to the samples and a fifth sensor placed at the incoming hydraulic line.

#### *2.3.2. Brazilian Disc Tests (BDT) procedure*

All Brazilian disc tests are carried out following the ISRM suggested method [4] at a load rate of 200 N/s. Disc diameters used are 30, 40, 50, 62, 75 and 84 mm, whereas the length to diameter ratio (L/D) was constant at 0.5. All tests are monitored by one AE-sensor glued directly in the middle of the disc specimen. The size dependency is tested with discs from Ruhrsandstone, marble, rhyolite and limestone.

#### *2.3.3. Modified Tension Test (MTT) procedure*

The MTT tests are driven load controlled at a rate of 200 N/s that corresponds to a stress rate of 0.02 MPa/s. The axial force is applied from the top (Figure 1). MTT test samples are observed by up to 6 AE-Sensors glued directly to the specimen. The samples were overcored with 62 mm and 30 mm diameters where the overlapping height is 1/3 of the total sample height (Figure 1). The centralizing of the drills was achieved by using a former plate to adjust the sample before drilling. Despite assiduously arrangement the eccentricity of the overcoring was in the range of up to 3 mm due to the imprecise vertical guidance of a standard drilling machine. In order to test the influence of eccentricity we also prepared samples with an eccentricity of 14 mm.
