Effects of varying injection rate on dynamic slip nucleation along a frictional weakening fault

2021 ◽  
Author(s):  
Federico Ciardo ◽  
Antonio Pio Rinaldi ◽  
Stefan Wiemer
Keyword(s):  
Boundary Element ◽  
Shear Crack ◽  
Fractured Reservoirs ◽  
Injection Rate ◽  
Numerical Results ◽  
Small Scale ◽  
Rate Variation ◽  
Injection Strategy ◽  
Seismicity Rates ◽  
Dynamic Slip

<div> <p><span>Anthropogenic injection of fluid into tight fractured reservoirs is known to alter the stress state of the Earth`s crust,  inducing micro-seismicity and eventually significant earthquakes. The injection scenario, in terms of injection pressure or injection rate, is one of the key controlling parameters for injection-induced seismicity. Although a number of studies have been carried out on understanding the effects of injection strategy on seismicity rates, less is known about its effect on the nucleation of dynamic slip on a pressurized fault, especially for non-stationary injection protocols.</span></p> </div><div> <p><span>In this contribution we study the effects of injection rate variation on the transition between aseismic and seismic slip along a frictional weakenig fault. Notably, we parametrize the injection strategy by assuming an initial linear increase of injection rate in time, up to a value after which it remains constant. We perform a scalying analysis and identify the governing parameters that control the fault response. We solve numerically the coupled hydro-mechanical problem using a fast boundary element solver for localized inelastic deformations [1]. Upon benchmarking the numerical results with the semi-analytical ones of Garagash and Germanovich [2] for the specific case of constant injection rate, we investigate the effect of injection rate variation on critically stressed and marginally pressurized faults. We derive analytical expressions for nucleation time and we confirm them via numerical results. Furthermore, we present a small scale yielding solution for marginallly pressurized faults and investigate the influence of injection scenario on shear crack run-out distances (when occuring).</span></p> </div><div> <p><span> </span></p> </div><div> <p><strong><span>References   </span></strong></p> </div><div> <p><span>[1] Ciardo, F., Lecampion, B., Fayard, F., and Chaillat, S. (2020), A fast boundary element based solver for localized inelastic deformations, </span><em>Int J Numer Methods Eng</em>. 2020; 1–23.</p> </div><div> <p><span>[2] Garagash, D., and L. N. Germanovich (2012), Nucleation and arrest of dynamic slip on a pressurized fault, <em>J. Geophys. Res</em>., 117, </span>B10310<span>.</span></p> </div>

Barotropic theory for the velocity profile of Jupiter’s turbulent jets: an example for an exact turbulent closure

2018 ◽  
Vol 860 ◽  
pp. 577-607
Author(s):  
E. Woillez ◽  
F. Bouchet
Keyword(s):  
Velocity Profile ◽  
Turbulent Jets ◽  
Equilibrium Structure ◽  
Injection Rate ◽  
Velocity Shear ◽  
Small Scale ◽  
Reynolds Stresses ◽  
Zonal Jets ◽  
Time Scale Separation ◽  
Turbulent Closure

We model the dynamics of Jupiter’s jets by the stochastic barotropic $\unicode[STIX]{x1D6FD}$-plane model. In this simple framework, by analytic computation of the averaged effect of eddies, we obtain three new explicit results about the equilibrium structure of jets. First we obtain a very simple explicit relation between the Reynolds stresses, the energy injection rate and the averaged velocity shear. This predicts the averaged velocity profile far from the jet edges (extrema of zonal velocity). Our approach takes advantage of a time-scale separation between the inertial dynamics on one hand, and the spin-up (or spin-down) time on the other. Second, a specific asymptotic expansion close to the eastward jet extremum explains the formation of a cusp at the scale of energy injection, characterized by a curvature that is independent of the forcing spectrum. Finally, we derive equations that describe the evolution of the westward tip of the jets. The analysis of these equations is consistent with the previously discussed picture of barotropic adjustment, explaining the relation between the westward jet curvature and the $\unicode[STIX]{x1D6FD}$-effect. Our results give a consistent overall theory of the stationary velocity profile of inertial barotropic zonal jets, in the limit of small-scale forcing.

An Integrated Approach for History Matching of Multiscale-Fracture Reservoirs

SPE Journal ◽  
2019 ◽  
Vol 24 (04) ◽  
pp. 1508-1525
Author(s):  
Mengbi Yao ◽  
Haibin Chang ◽  
Xiang Li ◽  
Dongxiao Zhang
Keyword(s):  
History Matching ◽  
Large Scale ◽  
Fractured Reservoirs ◽  
Integrated Approach ◽  
Small Scale ◽  
Gaussian Field ◽  
Limited Information ◽  
Fractured Reservoir ◽  
Discrete Fracture Model ◽  
Single Scale

Summary Naturally or hydraulically fractured reservoirs usually contain fractures at various scales. Among these fractures, large-scale fractures might strongly affect fluid flow, making them essential for production behavior. Areas with densely populated small-scale fractures might also affect the flow capacity of the region and contribute to production. However, because of limited information, locating each small-scale fracture individually is impossible. The coexistence of different fracture scales also constitutes a great challenge for history matching. In this work, an integrated approach is proposed to inverse model multiscale fractures hierarchically using dynamic production data. In the proposed method, a hybrid of an embedded discrete fracture model (EDFM) and a dual-porosity/dual-permeability (DPDP) model is devised to parameterize multiscale fractures. The large-scale fractures are explicitly modeled by EDFM with Hough-transform-based parameterization to maintain their geometrical details. For the area with densely populated small-scale fractures, a truncated Gaussian field is applied to capture its spatial distribution, and then the DPDP model is used to model this fracture area. After the parameterization, an iterative history-matching method is used to inversely model the flow in a fractured reservoir. Several synthetic cases, including one case with single-scale fractures and three cases with multiscale fractures, are designed to test the performance of the proposed approach.

Needle Displacement Visualization With Simultaneous Measurement of Injection Rate for CR Diesel Injector: A Novel Experimental Technique

2019 ◽  
Author(s):  
Giancarlo Chiatti ◽  
Ornella Chiavola ◽  
Fulvio Palmieri
Keyword(s):  
Experimental Technique ◽  
Optical Sensors ◽  
Digital Imaging ◽  
Measurement Techniques ◽  
Combustion Process ◽  
Injection Rate ◽  
The Other ◽  
Pollutant Emissions ◽  
Injection System ◽  
Injection Strategy

Abstract The control of combustion is a key topic for diesel engine development in terms of performance and pollutant emissions. The combustion process is piloted through the proper injection strategy, which depends on the features of the injection system. Mechanical-hydraulic models of high-pressure injection systems often support the accurate tuning of the injection strategy. The higher is the accuracy in the modeling of the electro-injector behavior, the deeper is the role of the simulation. Under such a viewpoint, the validation of the models is undoubtedly fundamental. One of the most crucial information characterizing the injector relies on the measurement of the needle displacement. Needle displacement affects rate, timing and quantity of injected fuel; it also influences the flow features within the nozzle, which are then reflected by the primary atomization process. Needle is considered hardly-accessible due to the injector architecture itself, making difficult the measurement of displacement. Nevertheless, the problem has been handled in different ways and three measurement techniques have been proposed. On one side, there is the measurement based on eddy-current transducers; on the other side, there are two alternative procedures, based on the use of optical sensors. However, in all cases, the needle is traced indirectly, since the position of the control plunger of the needle is observed. The current contribution presents a novel experimental technique for the measurement of needle displacement. The method is based on the direct visualization of the needle, allowing for the detailed definition of its law of motion through digital imaging, when the injector is characterized on a test-rig under transient conditions. The paper describes the details of the diagnostic scheme, the experimental facility and the digital imaging set-up. The main features and the capabilities of the method are discussed, in comparison with the other available techniques.

Boundary Element Algorithm for Nonlinear Modeling and Simulation of Three-Temperature Anisotropic Generalized Micropolar Piezothermoelasticity with Memory-Dependent Derivative

2020 ◽  
Vol 12 (03) ◽  
pp. 2050027 ◽  
Author(s):  
Mohamed Abdelsabour Fahmy
Keyword(s):  
Boundary Element ◽  
Smart Materials ◽  
Nonlinear Modeling ◽  
Computation Time ◽  
Industrial Applications ◽  
Numerical Results ◽  
Element Formulation ◽  
Adaptive Smoothing ◽  
Nonlinear Properties ◽  
Element Algorithm

The main aim of this paper is to introduce a new memory-dependent derivative theory to contribute for increasing development of technological and industrial applications of anisotropic smart materials. This theory is called three-temperature anisotropic generalized micropolar piezothermoelasticity. The governing equations of the proposed theory are very difficult to solve analytically because of material anisotropy and its nonlinear properties. Therefore, we propose a new boundary element formulation for solving such equations. The efficiency of our proposed technique has been developed by using an adaptive smoothing and prolongation algebraic multigrid (aSP-AMG) preconditioner to reduce the computation time. The numerical results are presented highlighting the effects of the kernel function and time delay on the temperature and displacements. The numerical results also verify the validity and accuracy of the proposed methodology. It can be concluded from the numerical results of our current complex and general study that some well-known uncoupled, coupled and generalized theories of anisotropic micropolar piezothermoelasticity can be connected with the three-temperature radiative heat conduction to characterize the deformation of anisotropicmicropolar piezothermoelasticstructures in the context of memory-dependent derivative.

scholarly journals Prediction of a Small-Scale Pool Fire with FireFoam

2017 ◽  
Vol 2017 ◽  
pp. 1-12 ◽  
Author(s):  
Camilo Andrés Sedano ◽  
Omar Darío López ◽  
Alexander Ladino ◽  
Felipe Muñoz
Keyword(s):  
Numerical Results ◽  
Pool Fire ◽  
Flame Height ◽  
Combustion Model ◽  
Small Scale ◽  
Average Temperature ◽  
Eddy Simulation ◽  
Fire Experiment ◽  
Large Eddy ◽  
Good Agreement

A computational model using Large Eddy Simulation (LES) for turbulence modelling was implemented, by means of the Eddy Dissipation Concept (EDC) combustion model using the fireFoam solver. A small methanol pool fire experiment was simulated in order to validate and compare the numerical results, hence trying to validate the effectiveness of the solver. A detailed convergence analysis is performed showing that a mesh of approximately two million elements is sufficient to achieve satisfactory numerical results (including chemical kinetics). A good agreement was achieved with some of the experimental and previous computational results, especially in the prediction of the flame height and the average temperature contours.

scholarly journals Dynamic faulting studied by a finite difference method

1982 ◽  
Vol 72 (2) ◽  
pp. 345-369
Author(s):  
Jean Virieux ◽  
Raul Madariaga
Keyword(s):  
Finite Difference ◽  
Finite Difference Method ◽  
Difference Method ◽  
Maximum Stress ◽  
Numerical Solutions ◽  
Shear Crack ◽  
Numerical Results ◽  
Three Dimensions ◽  
Shear Cracks ◽  
Stress Criterion

Abstract We have developed a finite difference method that is especially adapted to the study of dynamic shear cracks. We studied a number of simple earthquake source models in two and three dimensions with special emphasis on the modeling of the stress field. We compared our numerical results for semi-infinite and self-similar shear cracks with the few exact solutions that are available in the literature. We then studied spontaneous rupture propagation with the help of a maximum stress criterion. From dimensional arguments and a few simple examples, we showed that the maximum stress criterion depended on the physical dimensions of the fault. For a given maximum stress intensity, the finer the numerical mesh, the higher the maximum stress that had to be adopted. A study of in-plane cracks showed that at high rupture velocities, the numerical results did not resolve the stress concentration due to the rupture front from the stress peak associated with the shear wave propagating in front of the crack. We suggest that this is the reason why transonic rupture velocities are found in the numerical solutions of in-plane faulting when the rupture resistance is rather low. Finally, we studied the spontaneous propagation of an initially circular rupture. Two distinct modes of nucleation of the rupture were studied. In the first, a plane circular shear crack was formed instantaneously in a uniformly prestressed medium. After a while, once stress concentrations had developed around the crack edge, the rupture started to grow. In the second type of nucleation, a preexisting circular crack became unstable at time t = 0 and started to grow. The latter model appeared to us as a more realistic simulation of earthquake triggering. In this case, the initial stress was nonuniform and was the static field of the preexisting fault.

scholarly journals A Novel MDD-Based BEM Model for Transient 3T Nonlinear Thermal Stresses in FGA Smart Structures

2020 ◽  
Author(s):  
Mohamed Abdelsabour Fahmy
Keyword(s):  
Thermal Stress ◽  
Boundary Element ◽  
Thermal Stresses ◽  
Smart Structures ◽  
Industrial Applications ◽  
Functionally Graded ◽  
Numerical Results ◽  
Stress Distributions ◽  
Proposed Model ◽  
Further Development

The main objective of this chapter is to introduce a novel memory-dependent derivative (MDD) model based on the boundary element method (BEM) for solving transient three-temperature (3T) nonlinear thermal stress problems in functionally graded anisotropic (FGA) smart structures. The governing equations of the considered study are nonlinear and very difficult if not impossible to solve analytically. Therefore, we develop a new boundary element scheme for solving such equations. The numerical results are presented highlighting the effects of the MDD on the temperatures and nonlinear thermal stress distributions and also the effect of anisotropy on the nonlinear thermal stress distributions in FGA smart structures. The numerical results also verify the validity and accuracy of the proposed methodology. The computing performance of the proposed model has been performed using communication-avoiding Arnoldi procedure. We can conclude that the results of this chapter contribute to increase our understanding on the FGA smart structures. Consequently, the results also contribute to the further development of technological and industrial applications of FGA smart structures of various characteristics.

scholarly journals Fluid Flow Characterization Framework for Naturally Fractured Reservoirs Using Small-Scale Fully Explicit Models

2020 ◽  
Vol 134 (2) ◽  
pp. 399-434
Author(s):  
Daniel Lorng Yon Wong ◽  
Florian Doster ◽  
Sebastian Geiger ◽  
Eddy Francot ◽  
François Gouth
Keyword(s):  
Fluid Flow ◽  
Fractured Reservoirs ◽  
Naturally Fractured Reservoirs ◽  
Small Scale ◽  
Flow Characterization ◽  
Naturally Fractured

Viscous Oil Recovery and In Situ Deasphalting in Fractured Reservoirs: Part 1. The Effect of Solvent Injection Rate

2018 ◽  
Vol 32 (1) ◽  
pp. 360-372 ◽  
Author(s):  
Chao-Yu Sie ◽  
Bradley Nguyen ◽  
Marco Verlaan ◽  
Orlando Castellanos-Diaz ◽  
Kelli Adiaheno ◽  
...  
Keyword(s):  
Oil Recovery ◽  
Fractured Reservoirs ◽  
Injection Rate ◽  
Solvent Injection ◽  
Effect Of Solvent ◽  
Viscous Oil

First Successful Proppant Frac in a Water Injection Field Strategy, West Qurna-1, South Iraq

2022 ◽  
Author(s):  
Erfan Mustafa Al lawe ◽  
Adnan Humaidan ◽  
Afolabi Amodu ◽  
Mike Parker ◽  
Oscar Alvarado ◽  
...  
Keyword(s):  
Water Injection ◽  
Injection Rate ◽  
Fracture Model ◽  
Productivity Index ◽  
Base Line ◽  
Reservoir Pressure ◽  
Injection Strategy ◽  
Injection Test ◽  
Step Rate ◽  
Step Down

Abstract Zubair formation in West Qurna field, is one of the largest prolific reservoirs comprising of oil bearing sandstone layers interbedded with shale sequences. An average productivity index of 6 STB/D/psi is observed without any types of stimulation treatment. As the reservoir pressure declines from production, a peripheral water injection strategy was planned in both flanks of the reservoir to enhance the existing wells production deliverability. The peripheral injection program was initiated by drilling several injectors in the west flank. Well A1 was the first injector drilled and its reservoir pressure indicated good communication with the up-dip production wells. An injection test was conducted, revealing an estimated injectivity index of 0.06 STB//D/psi. Candidate well was then re-perforated and stimulated with HF/HCl mud acid, however no significant improvement in injectivity was observed due to the complex reservoir mineralogy and heterogeneity associated to the different targeted layers. An extended high-pressure injection test was performed achieving an injectivity index of 0.29 STB/D/psi at 4500 psi. As this performance was sub-optimal, a proppant fracture was proposed to achieve an optimal injection rate. A reservoir-centric fracture model was built, using the petrophysical and geo-mechanical properties from the Zubair formation, with the objective of optimizing the perforation cluster, fracture placement and injectivity performance. A wellhead isolation tool was utilized as wellhead rating was not able to withstand the fracture model surface pressure; downhole gauges were also installed to provide an accurate analysis of the pressure trends. The job commenced with a brine injection test to determine the base-line injectivity profile. The tubing volume was then displaced with a linear gel to perform a step-rate / step-down test. The analysis of the step-rate test revealed the fracture extension pressure, which was set as the maximum allowable injection pressure when the well is put on continuous injection. The step-down test showed significant near wellbore tortuosity with negligible perforation friction. A fracture fluid calibration test was then performed to validate the integrated model leak-off profile, fracture gradient and young’s modulus; via a coupled pressure fall-off and temperature log analysis. Based on the fluid efficiency, the pad volume was adjusted to achieve a tip screen-out. The job was successfully pumped and tip screen-out was achieved after pumping over ~90% of the planned proppant volume. A 7 days post-frac extended injection test was then conducted, achieving an injection rate of 12.5 KBWD at 1300 psi with an injectivity index of 4.2 STB/D/psi. These results proved that the implementation of a reservoir-centric Proppant Fracture treatment, can drastically improve the water injection strategy and field deliverability performance even in good quality rock formations. This first integrated fracture model and water injection field strategy, represents a building platform for further field development optimization plans in Southern Iraq.

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