Marcel Frehner

Finite-element simulations of Stoneley guided-wave reflection and scattering at the tips of fluid-filled fractures

The reflection and scattering of Stoneley guided waves at the tip of a crack filled with a viscous fluid was studied numerically intwodimensionsusingthefinite-elementmethod.Therocksurrounding the crack is fully elastic and thefluidfilling the crack is elastic in its bulk deformation behavior and viscous in its shear deformation behavior. The crack geometry, especially the crack tip, is resolved in detail by the unstructured finite-element mesh. Atthetipofthecrack,theStoneleyguidedwaveisreflected.The amplitude ratio between reflected and incident Stoneley guided wave is calculated from numerical simulations, which provide valuesrangingbetween43%andcloseto100%dependingonthe type of fluid filling the crack water, oil or hydrocarbon gas, the crack geometry elliptical or rectangular, and the presence of a small gas cap at the cracktip.The interference of incident and reflectedStoneleyguidedwavesleadstoanodezeroamplitudeat the tip of the crack.At other positions along the crack, this interferenceincreasestheamplitude.However,theexponentialdecay awayfromthecrackmakestheStoneleyguidedwavedifficultto detectatarelativelyshortdistanceawayfromthecrack.Thepart oftheStoneleyguidedwavethatisnotreflectedisscatteredatthe crack tip and emitted into the surrounding elastic rock as body waves. For fully saturated cracks, the radiation pattern of these elastic body waves points in every direction from the crack tip. TheemittedelasticbodywavescanallowthedetectionofStoneley guided wave-related resonant signals at distances away from thecrackwheretheamplitudeoftheStoneleyguidedwaveitself istoosmalltobedetected.

Synchrotron-based X-ray tomographic microscopy for rock physics investigations

ABSTRACTSynchrotron radiation X-ray tomographic microscopy is a nondestructive method providing ultra-high-resolution 3D digital images of rock microstructures. We describe this method and, to demonstrate its wide applicability, we present 3D images of very different rock types: Berea sandstone, Fontainebleau sandstone, dolomite, calcitic dolomite, and three-phase magmatic glasses. For some samples, full and partial saturation scenarios are considered using oil, water, and air. The rock images precisely reveal the 3D rock microstructure, the pore space morphology, and the interfaces between fluids saturating the same pore. We provide the raw image data sets as online supplementary material, along with laboratory data describing the rock properties. By making these data sets available to other research groups, we aim to stimulate work based on digital rock images of high quality and high resolution. We also discuss and suggest possible applications and research directions that can be pursued on the basis o...

Integrated numerical and laboratory rock physics applied to seismic characterization of reservoir rocks

A good understanding of the effect of rock and pore-fluid properties on seismic waves is necessary for the characterization of a subsurface hydrocarbon reservoir from a seismic data set. Information about the rock and fluids in the reservoir can be obtained, for example, through well logging and laboratory tests with samples cored from the wellbore. Together with seismic data, this information can be extrapolated for the entire dimension of the reservoir to provide valuable quantitative estimates for production. Additionally, this information can be extrapolated in time for monitoring the spatial redistribution of fluids during production. Making such space and time extrapolations more accurate using seismic data is the main goal of rock physics. For that, identifying and understanding the physical processes taking place in a reservoir rock at different scales is an important step and the subject of our article.

The Alpstein in three dimensions: fold-and-thrust belt visualization in the Helvetic zone, eastern Switzerland

To investigate the geometrical relationships between folding and thrust faulting, we built a 3D geological model of the Helvetic fold-and-thrust belt in eastern Switzerland from several existing and two newly drawn cross-sections in the Säntis area. We partly redrew existing cross-sections and validated them by checking for line length balance; to fill areas with no data we drew additional cross-sections. The model was built based on surface interpolation of the formation interfaces and thrusts between the cross-sections, which allowed generating eight main surfaces. In addition, we used cave data to validate the final model in depth. The main structural elements in the Säntis area, the Säntis Thrust and the Sax-Schwende Fault, are also implemented in the model. The result is a 3D structural model of the area, which provides an intuitive way for examining a portion of a complex structural nappe. The 3D model highlights the shapes of the main anticline-syncline pairs and how these fold trains vary laterally in amplitude and wavelength. It shows how lateral variations in fold style correlate with regional shortening gradients as determined from line-length balancing. The model also clearly shows the lateral extension, the trend, and the variation in displacement along the principal faults. The reconstruction of horizons in 3D allows the investigation of cross-sections in any given direction. The 3D model is useful for developing and understanding how the internal nappe structures, namely folds and thrust faults, change along strike due to palaeogeographic and stratigraphic variations. Lateral stratigraphy variations correlate with different deformation responses of the nappe. Changes can occur either abruptly across transverse faults or in a more gradual manner.

A novel EBSD‐based finite‐element wave propagation model for investigating seismic anisotropy: Application to Finero Peridotite, Ivrea‐Verbano Zone, Northern Italy

A novel electron backscatter diffraction (EBSD) -based finite-element (FE) wave propagation simulation is presented and applied to investigate seismic anisotropy of peridotite samples. The FE model simulates the dynamic propagation of seismic waves along any chosen direction through representative 2D EBSD sections. The numerical model allows separation of the effects of crystallographic preferred orientation (CPO) and shape preferred orientation (SPO). The obtained seismic velocities with respect to specimen orientation are compared with Voigt-Reuss-Hill estimates and with laboratory measurements. The results of these three independent methods testify that CPO is the dominant factor controlling seismic anisotropy. Fracture fillings and minor minerals like hornblende only influence the seismic anisotropy if their volume proportion is sufficiently large (up to 23%). The SPO influence is minor compared to the other factors. The presented FE model is discussed with regard to its potential in simulating seismic wave propagation using EBSD data representing natural rock petrofabrics.

Waves in Residual-Saturated Porous Media

We present a three-phase model describing wave propagation phenomena in residual-saturated porous media. The model consists of a continuous non-wetting phase and a discontinuous wetting phase and is an extension of classical biphasic (Biot-type) models. The model includes resonance effects of single liquid bridges or liquid clusters with miscellaneous eigenfrequencies taking into account a visco-elastic restoring force (pinned oscillations and/or sliding motion of the contact line). For the quasi-static limit case, i.e., ω ↦0, the results of the model are identical with the phase velocity obtained with the well-known Gassmann–Wood limit.

Interpretation of Hydrocarbon Microtremors as Nonlinear Oscillations Driven by Oceanic Background Waves

Summary Hydrocarbon Microtremor Analysis (HyMAS) identifies the presence of hydrocarbon containing geological structures by analyzing low frequency seismic background wave signals. A possible interpretation of this reproducibly observable phenomenon is the excitation of hydrocarbon related resonances. Synthetic spectra produced by basic linear and non-linear one-dimensional models of an oscillating liquid filled porous medium show characteristic features of measured HyMAS spectra when oceanic background waves around 0.1-0.2Hz are assumed to be the external driving force.

The not-so-simple effects of boundary conditions on models of simple shear

Analog modeling of geological processes, such as folding instabilities or the behavior of inclusions in a matrix, often employs a linear simple-shear rig. In theory, a homogeneous plane-strain flow is prescribed at the boundaries of such deformation rigs but, in practice, the resulting internal deformation of the analog material (commonly paraffin wax or silicone putties) often deviates strongly from the intended homogeneous strain field. This can easily lead to misinterpretation of such analog experiments. We present a numerical finite-element approach to quantify the influence of imperfect simple-shear boundary conditions on the internal deformation of a homogeneous viscous analog material. The results demonstrate that imperfect boundary conditions in the vorticity-normal plane can cause the heterogeneous strain observed in some analog experiments. However, in other experiments, the analog material lies on top of a weak lubricating material or is sandwiched between two such materials. These layers lead to a viscous drag force acting on the analog material, resulting in imperfect simple-shear boundary conditions in the third dimension. For this experimental configuration, the numerical results show that the lubricating layers are responsible for the heterogeneous strain observed in analog models. The resulting errors in internal strain can be as high as 100%, and these difficult-to-avoid boundary effects must be considered when interpreting analog simple-shear experiments.

Hydrocarbon Microtremors Interpreted as Oscillations Driven by Oceanic Background Waves

Hydrocarbon Microtremor Analysis (HyMAS) is an innovative technology for identifying the presence of hydrocarbon containing geological structures by analyzing low frequency background wave signals. A possible interpretation of this reproducibly observable phenomenon is the excitation of hydrocarbon related resonances. Synthetic spectra produced by basic linear and non-linear one-dimensional models of an oscillating liquid filled porous medium show characteristic features of measured HyMAS spectra when oceanic background waves around 0.1-0.2Hz are assumed to be the external driving force.

Strain and foliation refraction patterns around buckle folds

Abstract Axial plane foliation associated with geological folds may exhibit a divergent or convergent fan. Commonly, the foliation is assumed to reflect the major principal finite strain orientation. Here, the strain orientation around numerically simulated single-layer buckle folds is analysed in detail. Four different strain measures are considered: (1) finite strain, (2) infinitesimal strain, (3) incremental strain (recording the strain history from a certain shortening value until the end), and (4) initially layer-perpendicular passive marker lines. In the matrix at the outer arc of the fold, all strain measures result in similar divergent fan patterns. Therefore, divergent foliation fans around natural folds cannot readily be associated with the finite strain orientation as they may reflect other strain measures. In the simulated folds, the convergent fans in the stronger layer show differences between the different strain measures, which are associated with a 90°-switch of the major principal strain from a layer-perpendicular to a layer-parallel orientation at the outer arc. A similar observation is made in one of three studied natural folds (near Ribadeo and Luarca, NW Spain). It is suggested that the convergent foliation fan pattern inside a fold is better suited for strain estimates than the divergent fan around a fold.