NP7.1

We propose a mesoscopic thermodynamics approach for coupling multiphysics processes across scales in porous or multiphase media. In this multiscale reaction-diffusion formalism interactions of discrete phenomena at the local scale are seen as being subject to a larger scale Thermo-Hydro-Mechano-Chemical (THMC) thermodynamic force. When local interactions are incompatible with the large-scale thermodynamic stress field incompatibilities can arise which trigger accelerations resulting in meso-scale generalized thermodynamic fluxes of another (THMC) kind. The classical acoustic tensor localization criterion in plasticity theory is here understood as a standing wave solution of such acceleration waves. These classical zero-speed acceleration wave solutions are solitary waves, also known as solitons, and are interpreted in the reaction-diffusion formalism as self-diffusion dominated by harvesting all available energy from the cross-diffusional tails.

The more general case of non-zero traveling wave speed solutions is related to the cross-diffusion coefficients between different macro- and meso-scale thermodynamic THMC forces and fluxes. These cross-diffusion terms in the 4 x 4 THMC diffusion matrix are shown to lead to multiple diffusional P- and S-wave equations as THMC coupled, time-resolved dynamic solutions of the equation of motion. We show that the off-diagonal cross-diffusivities can give rise to a new class of waves also known as cross-diffusion waves or quasi-solitons. Their unique property is that for critical conditions cross-diffusion waves can funnel wave energy into a soliton wave focus.

Mathematically these solutions can be compared to events in ocean waves and optical fibers known as 'rogue waves' or 'high energy pulses of light' in lasers. In the context of hydromechanical coupling, a rogue wave would appear as a sudden fluid pressure spike on the future fault plane. This hydromechanically coupled fluid pressure P-wave instability is here interpreted as a trigger for the S-wave seismic moment release of a double couple dominated earthquake event. The proposed multiscale cascade of wave energy may apply to many other material instabilities.

How to cite: Regenauer-Lieb, K., Hu, M., Sun, Q., and Schrank, C.: Quasi-solitary multiscale cross-diffusion waves as a precursor to Earth instabilities, EGU General Assembly 2021, online, 19–30 Apr 2021, EGU21-3584, https://doi.org/10.5194/egusphere-egu21-3584, 2021.

Coupled Thermo-Hydro-Mechano-Chemical (THMC) patterns are ubiquitous in nature yet their origin is not yet fully understood. We propose a generic framework for pattern formation in terms of quasi-solitary wave instabilities that are triggered by cross-scale THMC-feedbacks considering a general topology of saturated porous media [1]. We identify the important aspect of cross-diffusion terms and present a linear stability analysis of the governing partial differential equations (pde’s). Multiple transient wave instabilities are found as solutions of the coupled THMC pde’s and in the standing wave limit (infinite time scale) these waves form the solitary wave patterns frozen into the geosystems at various scales.

Cross diffusion in a complex system is defined by the phenomenon that a gradient of one generalised thermodynamic force drives a generalised thermodynamic flux of another kind. Thermodynamic forces and fluxes in a THMC-system are defined as follows. Thermodynamic forces are the gradients of the THMC-system. The flux (T) represents Fourier’s law where thermal conductivity represents its characteristic diffusivity. The flux (H) describes Darcy’s law, where the diffusivity depends on the intrinsic permeability of the porous structure and the viscosity of saturating fluid. The flux (M) represents the incremental change in the solid-phase overstress adopting a Representative Elementary Volume (REV) formalism. The fluid phase within the REV, as an immediate environment surrounding the solid matrix, synchronously feels the pressure change, and vice versa. The flux (C) is Fick’s law, where chemical reaction and transport processes occur predominantly at/around the solid-fluid interfacial areas.

In order to express the THMC feedback we write the governing reaction diffusion equations as coupled HM equations with generalized source terms depending on temperature, concentration, fluid pressure and solid overstress and further consider the cross-diffusion terms as a generic framework:

where h₁>0, h₂>0, h₁+h₂>0 are the cross-diffusion coefficients [2] triggering wave instabilities from solid-fluid interaction at the microscale. The capital D../Dt denotes the material derivative. In the case that h₁=h₂=0 the classical conservation laws are recovered, and no stationary waves are obtained. Propagating waves recorded in laboratory experiments and possible field applications are interpreted with this new approach.

How to cite: Hu, M., Sun, Q., Schrank, C., and Regenauer-Lieb, K.: Cross-Diffusion Triggered Multiphysics Wave Instabilities, EGU General Assembly 2021, online, 19–30 Apr 2021, EGU21-8133, https://doi.org/10.5194/egusphere-egu21-8133, 2021.

The Cosserat model generalises an elastic material taking into account the possible microstructure of the elements of the material continuum. In particular, within the Cosserat model the structured material point is rigid and can only experience microrotations, which is also known as micropolar elasticity. The propagation of elastic waves in such a medium is studied and we find two classes of waves, transversal rotational waves and longitudinal rotational waves, both of which are solutions of the nonlinear partial differential equations. For certain parameter choices, the transversal wave velocity can be greater than the longitudinal wave velocity.  We couple the rotational waves to linear elastic waves to study the behaviour of the coupled system and find wave-like solutions with differing wave speeds. In addition we also consider the so-called Cosserat coupling term. In this setting we seek soliton type solutions assuming small elastic displacements, however, we allow the material points to experience full rotations which are not assumed to be small.

How to cite: Boehmer, C.: Wave-like solutions in Cosserat micropolar elasticity, EGU General Assembly 2021, online, 19–30 Apr 2021, EGU21-5241, https://doi.org/10.5194/egusphere-egu21-5241, 2021.

We designed and modified an experimental method to simultaneously measure the stress-strain (static moduli) and stress dependence of S and P-wave velocities of rocks (sandstone) under hydrostatic pressure by a Hoek’s cell. Dynamic moduli were calculated from the direct measurement of ultrasonic P- and S-wave velocities at a central dominant frequency of 1 MHz, while static moduli was recorded by strain gauges. The hydrostatic pressure was applied with a fixed rate at 1MPa/minute. We observed that the dynamic bulk moduli can be up to 44% higher than the static moduli in sandstones with porosity ranging from 8% to 24%. The results are in agreement with the existing empirical equations for soft rocks. Our experimental results demonstrate that the dynamic bulk’s modulus ranges from 4-13GPa, while the static bulk modulus ranges from 2-11GPa. We measured dynamic Young’s modulus and Poisson’s ratio at four different time periods (before applying the stress, right after the unloading, 20 days, and 60 days after the experiment) to investigate the effect of time on stress relaxation and eventually on the properties of the sandstones. All the samples showed an increase of Young’s modulus right after the stress application and then a gradual decrease of this value over time because of this relaxation; however, most of the samples could not reach the original state due to irreversible deformation at micro-level. Dynamic moduli show greater sensitivity to the irreversible deformations as compared to static moduli (even within the elastic limits). Dynamic moduli of porous material are also more sensitive to the microstructure than the static ones. Independent P and S-wave measurement for this study showed that the estimation of the S-wave velocity from the recorded P-wave velocity is not an accurate procedure and introduces a big error in the final calculation of the dynamic moduli. It also confirmed that by registering an accurate P-wave velocity the UCS (Unconfined Compressive Strength) value can be accurately estimated for sandstones. This demonstrates the great potential of dynamic studies as a non-destructive method to estimate this value for porous materials.

How to cite: Nourifard, N., Pasternak, E., and Lebedev, M.: Improved estimation method for dynamic bulk moduli of sandstones subjected to hydrostatic stress., EGU General Assembly 2021, online, 19–30 Apr 2021, EGU21-3588, https://doi.org/10.5194/egusphere-egu21-3588, 2021.

Seismicity associated with fluid injection into the subsurface is one of the most important issues worldwide. Fluid injection into or near a fault could lead to the fault sliding and to moderate or even hazardous seismic events. In the presented research, we study the single fault behavior under action of a single well injection near the fault. Various cases of initial conditions, system geometry, and friction properties of the fault are considered. To describe the friction on the fault we use two-parameter rate-and-state law. The fault has zones characterized by velocity-weakening and velocity-strengthening friction behavior. We analyze how location and size of the velocity-weakening zone and parameters of the friction law influence the fault sliding dynamics. We also consider how the fault sliding is changed when taking into account the rock poroelastic effects. As the result, we get conditions that are favorable for the occurrence of noticeable seismicity.

How to cite: Riga, V. and Sergey, T.: Numerical study of fault sliding under fluid injection, EGU General Assembly 2021, online, 19–30 Apr 2021, EGU21-2542, https://doi.org/10.5194/egusphere-egu21-2542, 2021.

Acoustic transmission data obtained in laboratory experiment were used to estimate main stages of hydraulic fracture onset, growth and filling by fracturing fluid. Laboratory setup consists of two horizontal disks with a diameter of 750 mm, and a sidewall with an internal diameter of 430 mm. The disks and the sidewall form a pressure chamber with a diameter of 430 mm at a height of 70 mm. There are a number of holes in the disks and the sidewall that are used for mounting ultrasonic transducers, pressure sensors, as well as for fluid injections. As a model material, a mixture of gypsum with cement was used, which was poured into the chamber. The sample was saturated with water gypsum solution and loaded with vertical and two horizontal stresses using special chambers. The fracture was created by viscous fluid (mineral oil with viscosity 0.1 Pa*s) injection with a constant rate 0.2 cm³/s through a cased borehole (diameter 12 mm) with a horizontal slot, which was preliminary located in the center of the sample. Hydraulic fracturing monitoring was carried out by recording of ultrasonic pulses passing through the sample during fracturing. To separate the ultrasonic pulses, the frequency of their sending was used. After that, the envelope of each record fragment was constructed using the Hilbert transformation and its maximum was found. Comparison of the ultrasonic pulse amplitude variations and injection pressure led to the following observations. Initial decrease in the pulse amplitudes began before the maximum pressure was reached, which may indicate the hydraulic fracturing onset at a pressure less than the maximum. The amplitude decline occurs smoothly, so it is difficult to identify any characteristic point on these curves and, accordingly, it is difficult to establish an accurate time of the fracturing onset and the fracture rate. The fracture rate was estimated by different methods previously as ≈130 mm/s. After the decline, the pulse amplitudes started to increase, that was related with the injection fluid front propagation in the fracture. In contrast to the decline, the beginning of the amplitude growth was clearly detected. Taking into account the spatial locations of the ultrasonic pulse source, receivers, and fracture, it is possible to estimate the propagation velocity of the fracturing fluid front as ≈35 mm/s. After the increase, the ultrasonic pulse amplitudes started to decrease significantly (up to 3 times), which is probably due to the further expansion of the fracture aperture. On the transducers located closer to the well, this decline is maximum. When the injection is stopped, the ultrasonic pulse amplitudes began to grow again, which indicates the fracture closure as the injection pressure decrease. In the experiments on the fracture re-opening under various stress applied to the sample, a linear relationship between the fracture re-opening pressure and applied vertical stress was found. This type of relationship should be expected, but values of the relation parameters declined from the values suggested in theoretical research, which was explained by taken into account back-stresses and non-linear behavior of the sample material.

How to cite: Turuntaev, S., Zenchenko, E., Zenchenko, P., Trimonova, M., and Baryshnikov, N.: Dynamics of hydraulic fracture development according to acoustic transmission data, EGU General Assembly 2021, online, 19–30 Apr 2021, EGU21-8858, https://doi.org/10.5194/egusphere-egu21-8858, 2021.

An important issue in rapid brittle fracture is the limiting speed of crack propagation. It is widely believed that brittle mode I crack cannot propagate faster than the Rayleigh wave speed, or the speed of sound on a solid surface. Mode II cracks are also limited by longitudinal speed wave. The origin for this belief stems from the predictions of continuum mechanics. Once the crack speed reaches a theoretical upper limit in a material, which is most often larger than one fifth of the Rayleigh wave velocity, branching of a propagating crack occurs. To verify this hypothesis, this paper presents the results of an experimental program aimed at disclosing the size effect on the crack velocity in the Splitting Tensile Strength indirect test (i.e. the Brazilian Test) using high-speed photography techniques. Over 100 Brazilian tests with more than 10 different rock types at various diameters were prepared and tested according to the ASTM standard recommendations using either a servo hydraulic machine or an electromechanical load frame at a wide ranges of load/displacement rates. By adopting a high frame rate of above 100,000 frames per second (fps), crack initiation, propagation, and coalescence were captured to study the size effect on the crack speed and failure mode on the Brazilian test results.

How to cite: Serati, M.: Tensile Crack Speed in Brittle Rocks, EGU General Assembly 2021, online, 19–30 Apr 2021, EGU21-13894, https://doi.org/10.5194/egusphere-egu21-13894, 2021.

Improved efficiency of hydraulic fracturing (HF) operations in complex reservoir rocks requires producing an extensive network of secondary fractures alongside the main fractures. The goal of the presented research is to find optimal stress-strain conditions yielding the most extensive network of secondary fractures at the microscale. The scope includes integrating results of microstructural characterization of tight gas reservoir rock samples and geomechanics. The study addresses the problem of hydraulic fracture optimization by suggesting stress-strain conditions to maximize fracture branching and, therefore, to optimize the drainage zone. We use a multidisciplinary approach including experimental data obtaining and numerical simulations. The first step is preparing a consistent set of 2D and 3D digital rock (DR) microscale models describing the experimental geometry, mineral composition and spatial distribution of mechanical properties of real rock samples. Geomechanical and petrophysical laboratory testing provide calibration/validation data for the DR models. Lab experiments include compressive and tensile strength testing coupled with digital image correlation, and X-ray computed tomography, 2D scanning electron microscopy coupled with mineralogy mapping. The preparation of DR models involves advanced 2D-to-3D and 3D-to-3D image registration techniques. The second step is a simulation of stress-strain states and fracture propagation in the models. We build simulation grids based on the mineral model and use a commercial mechanical simulator to simulate the fracture propagation at a microscale at given stress conditions. We applied the above approach to one of the most promising gas formations located in West Siberia, Russia. The reservoir rock features low permeability and pore dimensions down to tens of nanometers. Simulations delivered fracture networks for different loading conditions at the microscale. Simulation of typical geomechanical conditions allowed choosing reasonable stress-strain conditions that sustain the highest degree of formation fracturing. The research results may be applied to unconventional plays by increasing the efficiency of HF operation and maximizing production from isolated pore systems via establishing voids connectivity in the near-wellbore zone. The knowledge of the optimal stress-strain state for a near-wellbore zone will set the goal for HF propagation modeling at a wellbore scale. Using the approach, a geomechanical modeler would focus on designing main fractures, sustaining required stress-strain conditions in its vicinity, and thus producing the maximal amount of secondary microfractures. The results novelty is related with the simulation of 3D fracture propagation in highly heterogeneous reservoirs rocks taking into account its void space structure and fabric in geometry closest to real conditions.

How to cite: Nachev, V. and Turuntaev, S.: 3D Numerical Mineral Mechanical Modeling of Fracture Propagation in Complex Reservoirs Rocks at Microscale, EGU General Assembly 2021, online, 19–30 Apr 2021, EGU21-14958, https://doi.org/10.5194/egusphere-egu21-14958, 2021.

Currently, a number of studies showing that the injection of fluid into the formation can cause induced seismicity. Usually, it is associated with a change in the stress-strain state of the reservoir during the pore pressure front propagation. Modeling this process requires knowledge of the features of the filtration properties of reservoir rocks. Many researchers note the fact that the measured permeability of rock samples decreases at low pressure gradients. Among other things, this may be due to the formation of boundary adhesion layers with altered properties at the interfaces between the liquid and solid phases. The characteristic thickness of such layer can be fractions of a micron, and the effect becomes significant when filtering the fluid in rocks with a comparable characteristic pore size. The purpose of this work was to study the filtration properties of rock samples with low permeability at low flow rates. Laboratory modeling of such processes is associated with significant technical difficulties, primarily with the accuracy limit of measuring instruments when approaching zero speed values. The technique used by us to conduct the experiment and data processing allows us to study the dependence of the apparent permeability on the pore pressure gradient in the range of 0.01 MPa/m, which is comparable to the characteristic pressure gradients during the development of oil fields. In the course of the study, we carried out laboratory experiments on limestone core samples, during which the dependencies of their apparent permeability on the pore pressure gradient were obtained. We observed a significant decrease in their permeability at low flow rates. In the course of analyzing the experimental results, we proposed that a decrease in apparent permeability may occur due to the effect of even a small amount of residual gas in the pore space of the samples. This has been confirmed by additional experiments. The possibility of clogging of core sample pore space must be considered when conducting when conducting laboratory studies of the core apparent permeability.

How to cite: Baryshnikov, N., Zenchenko, E., and Turuntaev, S.: Possible Reason of the Dependence of an Apparent Permeability on the Pressure Gradient at low Flow Rates in Laboratory Study, EGU General Assembly 2021, online, 19–30 Apr 2021, EGU21-2491, https://doi.org/10.5194/egusphere-egu21-2491, 2021.