Direct simulation of non-additive variables on unstructured grids : the case of permeability

2021 ◽  
Author(s):  
◽  
Pauline Mourlanette
Keyword(s):  
Unstructured Grids ◽  
Computational Cost ◽  
Simulation Method ◽  
Breakthrough Curves ◽  
Tracer Experiment ◽  
Conventional Approach ◽  
Geostatistical Simulation ◽  
Permeability Heterogeneity ◽  
Research Perspectives ◽  
Parameters Selection

Uncertainties related to permeability heterogeneity can be estimated using geostatistical simulation methods. Usually, these methods are applied on regular grids with cells of constant size, whereas unstructured grids are more flexible to honor geological structures and offer local refinements for fluid-flow simulations. However, cells of different sizes require to account for the support dependency of permeability statistics (support effect). This work presents a novel workflow based on the power averaging technique. The averaging exponent ω is estimated using a response surface calibrated from numerical upscaling experiments. Using spectral turning bands, permeability is simulated on points in each unstructured cell, and later averaged with a local value of ω that depends on the cell size and shape, but also on the proportion of each facies inside the cell. The method is first illustrated on a synthetic case, with a single facies. The simulation of a tracer experiment is used to compare this novel geostatistical simulation method with a conventional approach based on a fine scale Cartesian grid. The results show the consistency of both the simulated permeability fields and the tracer breakthrough curves. The application to an industrial case with two facies is then presented and shows both consistent permeability fields and computational costs acceptable for the industry. Indeed, the computational cost for several realizations is much lower than the conventional approach based on a pressure-solver upscaling. The method works for the presented cases, but its theoretical ro-bustness can still be improved. A discussion on pressure solver upscal-ing parameters selection and power averaging limits is available in the conclusion, as well as a few research perspectives on multiple facies and non stationary proportions inclusion, the management of anisotropy and the extension to multiphase flow.

scholarly journals A geostatistical extreme-value framework for fast simulation of natural hazard events

2016 ◽  
Vol 472 (2189) ◽  
pp. 20150855 ◽  
Author(s):  
Benjamin D. Youngman ◽  
David B. Stephenson
Keyword(s):  
Natural Hazard ◽  
Computational Cost ◽  
Additive Model ◽  
Simulation Method ◽  
Value Theory ◽  
Extreme Value ◽  
Wind Gust ◽  
Continuous Space ◽  
Statistical Framework ◽  
Distribution Parameters

We develop a statistical framework for simulating natural hazard events that combines extreme value theory and geostatistics. Robust generalized additive model forms represent generalized Pareto marginal distribution parameters while a Student’s t -process captures spatial dependence and gives a continuous-space framework for natural hazard event simulations. Efficiency of the simulation method allows many years of data (typically over 10 000) to be obtained at relatively little computational cost. This makes the model viable for forming the hazard module of a catastrophe model. We illustrate the framework by simulating maximum wind gusts for European windstorms, which are found to have realistic marginal and spatial properties, and validate well against wind gust measurements.

Comparison of Various Discretization Schemes for Simulation of Large Field Case Reservoirs Using Unstructured Grids

2021 ◽  
Author(s):  
Samier Pierre ◽  
Raguenel Margaux ◽  
Darche Gilles
Keyword(s):  
Large Scale ◽  
Unstructured Grids ◽  
Computational Cost ◽  
Large Field ◽  
Real Field ◽  
Test Case ◽  
Generation Task ◽  
Field Case ◽  
Flux Approximation ◽  
Discretization Schemes

Abstract Solving the equations governing multiphase flow in geological formations involves the generation of a mesh that faithfully represents the structure of the porous medium. This challenging mesh generation task can be greatly simplified by the use of unstructured (tetrahedral) grids that conform to the complex geometric features present in the subsurface. However, running a million-cell simulation problem using an unstructured grid on a real, faulted field case remains a challenge for two main reasons. First, the workflow typically used to construct and run the simulation problems has been developed for structured grids and needs to be adapted to the unstructured case. Second, the use of unstructured grids that do not satisfy the K-orthogonality property may require advanced numerical schemes that preserve the accuracy of the results and reduce potential grid orientation effects. These two challenges are at the center of the present paper. We describe in detail the steps of our workflow to prepare and run a large-scale unstructured simulation of a real field case with faults. We perform the simulation using four different discretization schemes, including the cell-centered Two-Point and Multi-Point Flux Approximation (respectively, TPFA and MPFA) schemes, the cell- and vertex-centered Vertex Approximate Gradient (VAG) scheme, and the cell- and face-centered hybrid Mimetic Finite Difference (MFD) scheme. We compare the results in terms of accuracy, robustness, and computational cost to determine which scheme offers the best compromise for the test case considered here.

scholarly journals Numerical studies of higher order tau-leaping methods

2021 ◽  
Author(s):  
Anuj Dhoj Thapa
Keyword(s):  
Stochastic Simulation ◽  
Computational Cost ◽  
Practical Interest ◽  
Stochastic Simulation Algorithm ◽  
Simulation Method ◽  
Equation Model ◽  
Fast Reactions ◽  
Biochemical Systems ◽  
Computationally Intensive ◽  
Reacting Systems

Gillespie's algorithm, also known as the Stochastic Simulation Algorithm (SSA), is an exact simulation method for the Chemical Master Equation model of well-stirred biochemical systems. However, this method is computationally intensive when some fast reactions are present in the system. The tau-leap scheme developed by Gillespie can speed up the stochastic simulation of these biochemically reacting systems with negligible loss in accuracy. A number of tau-leaping methods were proposed, including the explicit tau-leaping and the implicit tau-leaping strategies. Nonetheless, these schemes have low order of accuracy. In this thesis, we investigate tau-leap strategies which achieve high accuracy at reduced computational cost. These strategies are tested on several biochemical systems of practical interest.

scholarly journals Density effects on salt tracer breakthrough curves from constructed wetland ponds

2004 ◽  
Vol 35 (3) ◽  
pp. 237-250 ◽  
Author(s):  
Bernhard H. Schmid ◽  
Michael A. Hengl ◽  
Ursula Stephan
Keyword(s):  
Constructed Wetland ◽  
Laboratory Experiments ◽  
Reynolds Numbers ◽  
Breakthrough Curves ◽  
Tracer Experiment ◽  
Potential Density ◽  
Planning Stage ◽  
Low Reynolds Numbers ◽  
Density Effects ◽  
Tracer Experiments

Salt tracer experiments are a convenient method to determine travel time distributions in constructed wetland ponds. Typically, these flows are characterized by low Reynolds numbers at times even within the laminar flow regime. In this environment the injection of salt may cause strong density effects, thereby jeopardizing the usefulness of the recorded breakthrough curves. After a tracer experiment has been completed, an indication of potential density stratification in the field may be noticed in the form of surprisingly small recovery rates of a tracer considered as nearly conservative. To provide a tool that permits the intended experiment to be judged at the planning stage already, criteria have been developed that yield approximate maximum concentrations, not to be exceeded if density effects shall be avoided. Laboratory experiments were carried out and the newly derived relationships applied with success. The criteria may in future be useful, too, in the planning of tracer experiments in slowly flowing rivers and streams.

scholarly journals A Fast and Effective Method for Unsupervised Segmentation Evaluation of Remote Sensing Images

2020 ◽  
Vol 12 (18) ◽  
pp. 3005
Author(s):  
Maofan Zhao ◽  
Qingyan Meng ◽  
Linlin Zhang ◽  
Die Hu ◽  
Ying Zhang ◽  
...  
Keyword(s):  
Remote Sensing ◽  
Computational Cost ◽  
Visual Interpretation ◽  
Remote Sensing Images ◽  
Unsupervised Segmentation ◽  
Segmentation Evaluation ◽  
Parameters Selection ◽  
Object Based ◽  
Geographic Object ◽  
The Difference

The segmentation of remote sensing images with high spatial resolution is important and fundamental in geographic object-based image analysis (GEOBIA), so evaluating segmentation results without prior knowledge is an essential part in segmentation algorithms comparison, segmentation parameters selection, and optimization. In this study, we proposed a fast and effective unsupervised evaluation (UE) method using the area-weighted variance (WV) as intra-segment homogeneity and the difference to neighbor pixels (DTNP) as inter-segment heterogeneity. Then these two measures were combined into a fast-global score (FGS) to evaluate the segmentation. The effectiveness of DTNP and FGS was demonstrated by visual interpretation as qualitative analysis and supervised evaluation (SE) as quantitative analysis. For this experiment, the ‘‘Multi-resolution Segmentation’’ algorithm in eCognition was adopted in the segmentation and four typical study areas of GF-2 images were used as test data. The effectiveness analysis of DTNP shows that it can keep stability and remain sensitive to both over-segmentation and under-segmentation compared to two existing inter-segment heterogeneity measures. The effectiveness and computational cost analysis of FGS compared with two existing UE methods revealed that FGS can effectively evaluate segmentation results with the lowest computational cost.

Effect of Grid Deviation on Flow Solutions

SPE Journal ◽  
2009 ◽  
Vol 14 (01) ◽  
pp. 67-77 ◽  
Author(s):  
Xiao-Hui Wu ◽  
Rossen Parashkevov
Keyword(s):  
Corner Point ◽  
Unstructured Grids ◽  
Numerical Study ◽  
Computational Cost ◽  
Flow Equation ◽  
Attractive Alternative ◽  
Anisotropic Permeability ◽  
Voronoi Grid ◽  
Coordinate Lines ◽  
Volume Method

Summary The two-point flux finite-volume method (2P-FVM) is the most widely used method for solving the flow equation in reservoir simulations. For 2P-FVM to be consistent, the simulation grid needs to be orthogonal (or k-orthogonal if the permeability field is anisotropic). It is well known that corner-point grids can introduce large errors in the flow solutions because of the lack of orthogonality in general. Multipoint flux formulations that do not rely on grid orthogonality have been proposed, but these methods add significant computational cost to solving the flow equation. Recently, 2.5D unstructured grids that combine 2D Voronoi areal grids with vertical projections along deviated coordinate lines have become an attractive alternative to corner-point gridding. The Voronoi grid helps maintain orthogonality areally and can mitigate grid orientation effects. However, experience with these grids is limited. In this paper, we present an analytical and numerical study of these 2.5D unstructured grids. We focus on the effect of grid deviation on flow solutions in homogeneous, but anisotropic, permeability fields. In particular, we consider the grid deviation that results from gridding to sloping faults. We show that 2P-FVM does not converge to the correct solution as the grid refines. We further quantify the errors for some simple flow scenarios using a technique that combines numerical analysis and asymptotic expansions. Analytical error estimates are obtained. We find that the errors are highly flow dependent and that they can be global with no strong correlation with local nonorthogonality measures. Numerical tests are presented to confirm the analytical findings and to show the applicability of our conclusions to more-general flow scenarios.

scholarly journals A fast direct numerical simulation method for characterising hydraulic roughness

2015 ◽  
Vol 773 ◽  
pp. 418-431 ◽  
Author(s):  
D. Chung ◽  
L. Chan ◽  
M. MacDonald ◽  
N. Hutchins ◽  
A. Ooi
Keyword(s):  
Numerical Simulation ◽  
Direct Numerical Simulation ◽  
Computational Cost ◽  
Simulation Method ◽  
Reynolds Numbers ◽  
Proof Of Concept ◽  
Hydraulic Roughness ◽  
Velocity Shift ◽  
High Reynolds ◽  
Reynolds Number Flows

We describe a fast direct numerical simulation (DNS) method that promises to directly characterise the hydraulic roughness of any given rough surface, from the hydraulically smooth to the fully rough regime. The method circumvents the unfavourable computational cost associated with simulating high-Reynolds-number flows by employing minimal-span channels (Jiménez & Moin, J. Fluid Mech., vol. 225, 1991, pp. 213–240). Proof-of-concept simulations demonstrate that flows in minimal-span channels are sufficient for capturing the downward velocity shift, that is, the Hama roughness function, predicted by flows in full-span channels. We consider two sets of simulations, first with modelled roughness imposed by body forces, and second with explicit roughness described by roughness-conforming grids. Owing to the minimal cost, we are able to conduct direct numerical simulations with increasing roughness Reynolds numbers while maintaining a fixed blockage ratio, as is typical in full-scale applications. The present method promises a practical, fast and accurate tool for characterising hydraulic resistance directly from profilometry data of rough surfaces.

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