A Time-Continuation Solver for Hydraulic Fracture Propagation

We present an efficient time-continuation scheme for fluid-driven fracture propagation problems in the frame-work of the extended finite element method (XFEM). The fully coupled, fully implicit hydro-mechanical system is solved in conjunction with the linear elastic fracture propagation criterion by the Newton-Raphson method. Therefore, at the end of each time-step solve, the model ensures the energy release rate of weakest fracture tips within the equilibrium propagation regime. Besides, an initialization procedure for newly created fracture space as well as a priori estimate of stress intensity factor (SIF) growth rates are also developed to further improve the solver performance. We validate the model by the analytical solution and extend the problem to the multiple fracture propagation where stress shadow phenomenon occur.

Lactococcus lactis Mutants Obtained From Laboratory Evolution Showed Elevated Vitamin K2 Content and Enhanced Resistance to Oxidative Stress

Vitamin K2 is an important vitamin for human health. Vitamin K2 enrichment in the human diet is possible by using vitamin K2-producing bacteria such as Lactococcus lactis in food fermentations. Based on previous observations that aerated cultivation conditions improved vitamin K2 content in L. lactis, we performed laboratory evolution on L. lactis MG1363 by cultivating this strain in a shake flask in a sequential propagation regime with transfers to a fresh medium every 72h. After 100 generations of propagation, we selected three evolved strains that showed improved stationary phase survival in oxygenated conditions. In comparison to the original strain MG1363, the evolved strains showed 50–110% increased vitamin K2 content and exhibited high resistance against hydrogen peroxide-induced oxidative stress. Genome sequencing of the evolved strains revealed common mutations in the genes ldh and gapB. Proteomics analysis revealed overproduction of glyceraldehyde 3-phosphate dehydrogenase (GapA), universal stress protein A2 (UspA2), and formamidopyrimidine-DNA glycosylase (MutM) under aerated conditions in evolved strains, proteins with putative functions in redox reactions, universal stress response, and DNA damage repair, all of which could contribute to the enhanced oxidative stress resistance. The mechanisms underlying elevated vitamin K2 content in the evolved strains remain to be elucidated. Two out of the three evolved strains performed similar to the original strain MG1363 in terms of growth and acidification of culture media. In conclusion, this study demonstrated a natural selection approach without genetic manipulations to obtain vitamin K2 overproducers that are highly relevant for food applications and contributed to the understanding of oxidative stress resistance in L. lactis.

R-Curve Characterization of Crumb Rubber Modified Asphalt Mixtures Incorporating Warm Mix Additive at Low Temperatures

In a previous research by authors, a methodology was developed to derive J-R curves for Hot Mix Asphalt (HMA) mixtures using an elastic-plastic approach where a comprehensive understanding of crack propagation regime could be achieved. In this research, the effect of crumb rubber modification of HMA binder is studied in terms of R-curves and crack propagation at low temperatures. Mode I Single edge notched beam (SE(B)) fracture tests were conducted in temperature levels of 0 °C, -10 °C, and -20 °C. PG58-22 and PG64-22 binders were used in the fabrication of HMA samples. Modified specimens consist of 20% crumb rubber along with the incorporation of 3% warm mix admixture. Crack growth resistance curves were obtained in SE(B) tests by means of image processing and recording of the progressive crack length. Elastic-plastic J-R curves revealed that crumb rubber modified mixtures exhibit higher crack growth resistance for each bitumen performance grade. As well, increased ductility and cohesive energy can be observed according to the R-curves as the mixtures are modified by crumb rubber.

Non steady-state intersonic cracks in elastomer membranes under large static strain

International audience Dynamic crack propagation in elastomer membranes is investigated; the focus is laid on cracks reaching the speed of shear waves in the material. The specific experimental setup developed to measure crack speed is presented in details. The protocol consists in (1) stretching an elastomer membrane under planar tension loading conditions, then (2) initiating a small crack on one side of the membrane. The crack speed is measured all along the crack path in both reference and actual configurations, including both acceleration and deceleration phases, i.e. non steady-state crack propagation phases. The influence of the prescribed stretch ratio on crack speed is analysed in the light of both these new experiments and the few previously published studies. Conclusions previously drawn for steady-state crack growth are extended to non steady-state conditions: stretch perpendicular to the crack path governs crack speed in intersonic crack propagation regime, and the role of the stretch in crack direction is minor.

Modelling hydraulic fracturing with the J-integral

<p>Hydraulic fracturing plays a central role in engineering fractured reservoirs. To simulate the propagation of “dry” fractures, the J-integral has been a standard technique. Its superior accuracy at coarser resolutions make it particularly attractive, especially for reservoir-scale simulations. However, the extension of the J-integral to hydro-mechanical simulations of fluid-driven fracturing has not received the same attention or success. In particular, while several studies have highlighted the capacity of the method in simulating viscosity-dominated propagation, detailed investigations into the performance of the method are still missing. In this work, we find that the extent of hydraulic fracturing is typically overestimated by the J-integral in the viscosity-dominated propagation regime.<span>  </span>A finite element analysis is conducted which sheds light on the source of the error. The case is put forward that the inaccurate numerical solution for fluid pressure is <em>exclusively</em> responsible for the loss in accuracy of the J-integral. With this new understanding, the J-integral is reformulated to minimise its dependence on inaccurate fluid pressures, bypassing the aforementioned sources of error. The reformulation, termed the J<sub>V</sub>-integral, is both simple to implement, and general to the numerical method. Within the framework of finite elements, a propagation algorithm using the novel J<sub>V</sub>-integral is subsequently constructed with two distinct abilities compared to the original J-integral. The first is an increased ability to capture the viscosity-dominated regime of propagation at significantly coarser resolutions. Finite element simulations conducted at various levels of refinement detail the promising results relevant to hydro-mechanical simulations at reservoir scale.<span>  </span>The ability of the method in simulating the toughness regime remains as performant as the original J-integral.<span>  </span>The second, is the ability of the J<sub>V</sub>-integral in extracting the propagation velocity of the fracture; a feature particular to methods arising from hydraulic fracture mechanics. Consequently, the method demonstrates an inherent advantage when converging on the fracture length, requiring significantly fewer iterations compared to the original formulation. Fundamentally, the velocity obtained via the J<sub>V</sub>-integral has the potential to be used in combination with front-tracking schemes like the implicit level set method. As a result, the J<sub>V</sub>-integral appears to be a promising method when simulating hydraulic fracturing in geoenergy applications and beyond.<span> </span></p>

Transition from Diffusion to Wave Propagation in Fractional Jeffreys-Type Heat Conduction Equation

The heat conduction equation with a fractional Jeffreys-type constitutive law is studied. Depending on the value of a characteristic parameter, two fundamentally different types of behavior are established: diffusion regime and propagation regime. In the first case, the considered equation is a generalized diffusion equation, while in the second it is a generalized wave equation. The corresponding memory kernels are expressed in both cases in terms of Mittag–Leffler functions. Explicit representations for the one-dimensional fundamental solution and the mean squared displacement are provided and analyzed analytically and numerically. The one-dimensional fundamental solution is shown to be a spatial probability density function evolving in time, which is unimodal in the diffusion regime and bimodal in the propagation regime. The multi-dimensional fundamental solutions are probability densities only in the diffusion case, while in the propagation case they can have negative values. In addition, two different types of subordination principles are formulated for the two regimes. The Bernstein functions technique is extensively employed in the theoretical proofs.

Filament simulations in regions of highly-varying parallel connection length

The island divertor topology of the Wendelstein 7-X (W7-X) scrape-off-layer exhibits regions of highly varying connection length. Here, we present drift-plane simulations of seeded filaments in regions of sharp transitions in parallel connection length – a parameter which dictates the propagation regime for plasma blobs. It is determined that a transition in parallel connection length alters the trajectory of filaments; filaments which enter regions of lower connection length are decelerated, and vice versa. It is also determined that if the lobes of a potential dipole created by diamagnetic drifts within the filament exist in two regions of distinct parallel connection length, the filament is then steered towards the region of higher connection length. The extreme case of a narrow region of varying connection length can also alter the trajectory of a filament, depending on the extent of this region. Finally, simulations mimicking the view from the W7-X gas puff imaging (GPI) diagnostic view plane are presented. It is determined that filaments in the view of the W7-X GPI diagnostic exhibit a predominantly poloidal propagation due to the radial electric field, since the radial velocity is relatively small.