Checking Static Properties Using Conservative SAT Approximations for Reachability

2017 ◽  
pp. 233-250 ◽  
Author(s):  
Pedro Antonino ◽  
Thomas Gibson-Robinson ◽  
A. W. Roscoe
Keyword(s):  
Static Properties

Umbilics : static properties and shear-induced displacements

1973 ◽  
Vol 34 (7) ◽  
pp. 629-633 ◽  
Author(s):  
A. Rapini
Keyword(s):  
Static Properties

Static properties of a random one-dimensional magnet

1975 ◽  
Vol 36 (12) ◽  
pp. 1177-1181 ◽  
Author(s):  
M. F. Thorpe
Keyword(s):  
Static Properties ◽  
One Dimensional

scholarly journals Validation of Digital Rock Physics Algorithms

Minerals ◽  
2019 ◽  
Vol 9 (11) ◽  
pp. 669
Author(s):  
Rongrong Lin ◽  
Leon Thomsen
Keyword(s):  
Rock Physics ◽  
Image Resolution ◽  
Staggered Grid ◽  
Static Properties ◽  
Shear Moduli ◽  
Digital Rock Physics ◽  
Digital Rock ◽  
Saturated Rock ◽  
Theoretical Predictions ◽  
Theoretical Test

With a detailed microscopic image of a rock sample, one can determine the corresponding 3-D grain geometry, forming a basis to calculate the elastic properties numerically. The issues which arise in such a calculation include those associated with image resolution, the registration of the digital numerical grid with the digital image, and grain anisotropy. Further, there is a need to validate the numerical calculation via experiment or theory. Because of the geometrical complexity of the rock, the best theoretical test employs the Hashin–Shtrikman result that, for an aggregate of two isotropic components with equal shear moduli, the bulk modulus is uniquely determined, independent of the micro-geometry. Similarly, for an aggregate of two isotropic components with a certain combination of elastic moduli defined herein, the Hashin–Shtrikman formulae give a unique result for the shear modulus, independent of the micro-geometry. For a porous, saturated rock, the solid incompressibility may be calculated via an “unjacketed” test, independent of the micro-geometry. Any numerical algorithm proposed for digital rock physics computation should be validated by successfully confirming these theoretical predictions. Using these tests, we validate a previously published staggered-grid finite difference damped time-stepping algorithm to calculate the static properties of digital rock models.

scholarly journals DISSIPATIVE QUANTUM DISORDERED MODELS

2006 ◽  
Vol 20 (19) ◽  
pp. 2795-2804 ◽  
Author(s):  
LETICIA F. CUGLIANDOLO
Keyword(s):  
Glassy Phase ◽  
Quantum Critical Point ◽  
Mean Field ◽  
Static Properties ◽  
One Dimensional ◽  
Time Dynamics ◽  
Long Range Interactions ◽  
Disordered Models ◽  
Different Types ◽  
Dissipative Environments

This article reviews recent studies of mean-field and one dimensional quantum disordered spin systems coupled to different types of dissipative environments. The main issues discussed are: (i) The real-time dynamics in the glassy phase and how they compare to the behaviour of the same models in their classical limit. (ii) The phase transition separating the ordered – glassy – phase from the disordered phase that, for some long-range interactions, is of second order at high temperatures and of first order close to the quantum critical point (similarly to what has been observed in random dipolar magnets). (iii) The static properties of the Griffiths phase in random king chains. (iv) The dependence of all these properties on the environment. The analytic and numeric techniques used to derive these results are briefly mentioned.

A Proxy Flow Modelling Workflow to Estimate Gridded Dynamic Properties and Well Production Rates by Deep Learning Algorithms

2021 ◽  
Author(s):  
Soumi Chaki ◽  
Yevgeniy Zagayevskiy ◽  
Terry Wong
Keyword(s):  
Neural Network ◽  
Deep Learning ◽  
Dynamic Properties ◽  
Reservoir Management ◽  
Flow Modeling ◽  
Static Properties ◽  
Production Rates ◽  
Reservoir Properties ◽  
Well Production ◽  
Reservoir Simulator

Abstract This paper proposes a deep learning-based framework for proxy flow modeling to predict gridded dynamic petroleum reservoir properties (like pressure and saturation) and production rates for wells in a single framework. It approximates the solution of a full physics-based numerical reservoir simulator, but runs much more rapidly, allowing users to generate results for a much wider range of scenarios in a given time than could be done with a full physics simulator. The proxy can be used for reservoir management tasks like history matching, uncertainty quantification, and field development optimization. A deep-learning based methodology for accurate proxy-flow modeling is presented which combines U-Net (a variant of convolutional neural network) to predict gridded dynamic properties and deep neural network (DNN) models to forecast well production rates. First, gridded dynamic properties, such as reservoir pressure and phase saturations, are predicted from static properties like reservoir rock porosity and absolute permeability using a U-Net. Then, the static properties and the dynamic properties predicted by the U-Net are input to a DNN to predict production rates at the well perforations. The inclusion of U-net predicted pressure and saturations improves the quality of the well rate predictions. The proposed methodology is presented with the synthetic Brugge reservoir discretized into grid blocks. The U-Net input consists of three properties: dynamic gridded reservoir properties (such as pressure or fluid saturation) at the current state, static gridded porosity, and static gridded permeability. The U-Net has only one output property, the target gridded property (such as pressure or saturation) at the next time step. Training and testing datasets are generated by running 13 full physics flow simulations and dividing them in a 12:1 ratio. Nine U-Net models are calibrated to predict pressures/saturations, one for each of the nine grid layers present in the Brugge model. These outputs are then concatenated to obtain the complete pressure/saturation model for all nine layers. The constructed U-Net models match the distributions of generated pressures/saturations of the numerical reservoir simulator with a correlation coefficient value of approximately 0.99 and above 95% accuracy. The DNN models approximate well production rates accurately from U-Net predicted pressures and saturations along with static properties like transmissibility and horizontal permeability. For each well and each well perforation, the production rate is predicted with the DNN model. The use of the constructed proxy flow model generates reservoir predictions within a few minutes compared to the hours or days typically taken by a full physics flow simulator. The direct connection that is established between the gridded static and dynamic properties of the reservoir and well production rates using U-Net and DNN models has not been presented previously. Using only a small number of runs for its training, the workflow matches the numerical reservoir simulator results with reduced computational effort. This helps reservoir engineers make informed decisions more quickly, resulting in more efficient reservoir management.

Investigation on a two-stage platform of large stroke for broadband vertical vibration isolation

2018 ◽  
Vol 25 (6) ◽  
pp. 1233-1245 ◽  
Author(s):  
Xiling Xie ◽  
Mingke Ren ◽  
Hongbo Zheng ◽  
Zhiyi Zhang
Keyword(s):  
Vibration Isolation ◽  
Vertical Vibration ◽  
Optical Switches ◽  
Static Properties ◽  
Two Stage ◽  
Maximum Displacement ◽  
Primary Stage ◽  
Low Frequencies ◽  
Attenuation Rate ◽  
Secondary Stage

For the purpose of preventing vibration-sensitive optical switches from malfunction caused by broadband vertical vibration, a novel two-stage vibration isolation platform is proposed. The primary stage is a bellows-type isolator of large stroke and low isolation frequency, and the secondary stage is a small-stroke hybrid isolator composed of bellows and voice-coil actuators. In the primary stage, two pre-compressed horizontal bellows and one vertical bellows are used to counter the weight of the switch and to reduce the total height of the isolator. The static properties of the primary stage are analyzed, and the vibration isolation of the platform is investigated. Numerical results indicate that the two-stage platform is effective in isolating vertical vibration. Experiments are also conducted to verify the performance of the platform. It is exhibited that the transmissibility is less than 0 dB over 2 Hz, and the attenuation rate reaches −35 dB/dec at high frequencies. The frequency range of test is 2–200 Hz, and the maximum displacement is 10 mm at 2 Hz. In the secondary stage, the actuators can substantially suppress the resonance peak, and promote isolation performance at low frequencies.

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