The Use of the Monte Carlo Method for Solving Large-Scale Problems in Neutronics

1972 ◽  
Vol 135 (1) ◽  
pp. 16 ◽  
Author(s):  
J. B. Parker
Keyword(s):  
Monte Carlo ◽  
Monte Carlo Method ◽  
Large Scale ◽  
Large Scale Problems ◽  
The Monte Carlo Method

Accurate, Efficient Quantification of Uncertainty for Flow in Heterogeneous Reservoirs Using the KLME Approach

SPE Journal ◽  
2006 ◽  
Vol 11 (02) ◽  
pp. 239-247 ◽  
Author(s):  
Zhiming Lu ◽  
Dongxiao Zhang
Keyword(s):  
Monte Carlo ◽  
Monte Carlo Method ◽  
Large Scale ◽  
Moment Equation ◽  
Reservoir Properties ◽  
Flow And Transport ◽  
Heterogeneous Reservoirs ◽  
Flow Problems ◽  
The Monte Carlo Method ◽  
The Moment

Summary Accurate modeling of flow in oil/gas reservoirs requires a detailed description of reservoir properties such as permeability and porosity. However, such reservoirs are inherently heterogeneous and exhibit a high degree of spatial variability in medium properties. Significant spatial heterogeneity and a limited number of measurements lead to uncertainty in characterization of reservoir properties and thus to uncertainty in predicting flow in the reservoirs. As a result, the equations that govern flow in such reservoirs are treated as stochastic partial differential equations. The current industrial practice is to tackle the problem of uncertainty quantification by Monte Carlo simulations (MCS). This entails generating a large number of equally likely random realizations of the reservoir fields with parameter statistics derived from sampling, solving deterministic flow equations for each realization, and post-processing the results over all realizations to obtain sample moments of the solution. This approach has the advantages of applying to a broad range of both linear and nonlinear flow problems, but it has a number of potential drawbacks. To properly resolve high-frequency space-time fluctuations in random parameters, it is necessary to employ fine numerical grids in space-time. Therefore, the computational effort for each realization is usually large, especially for large-scale reservoirs. As a result, a detailed assessment of the uncertainty associated with flow-performance predictions is rarely performed. In this work, we develop an accurate yet efficient approach for solving flow problems in heterogeneous reservoirs. We do so by obtaining higher-order solutions of the prediction and the associated uncertainty of reservoir flow quantities using the moment-equation approach based on Karhunen-Loéve decomposition (KLME). The KLME approach is developed on the basis of the Karhunen-Loéve (KL) decomposition, polynomial expansion, and perturbation methods. We conduct MCS and compare these results against different orders of approximations from the KLME method. The 3D computational examples demonstrate that this KLME method is computationally more efficient than both Monte Carlo simulations and the conventional moment-equation method. The KLME approach allows us to evaluate higher-order terms that are needed for highly heterogeneous reservoirs. In addition, like the Monte Carlo method, the KLME approach can be implemented with existing simulators in a straightforward manner, and they are inherently parallel. The efficiency of the KLME method makes it possible to simulate fluid flow in large-scale heterogeneous reservoirs. Introduction Owing to the heterogeneity of geological formations and the incomplete knowledge of medium properties, the medium properties may be treated as random functions, and the equations describing flow and transport in these formations become stochastic. Stochastic approaches to flow and transport in heterogeneous porous media have been extensively studied in the last 2 decades, and many stochastic models have been developed (Dagan 1989; Gelhar 1993; Zhang 2002). Two commonly used approaches for solving stochastic equations are MCS and the moment-equation method. A major disadvantage of the Monte Carlo method, among others, is the requirement for large computational efforts. An alternative to MCS is an approach based on moment equations, the essence of which is to derive a system of deterministic partial differential equations governing the statistical moments [usually the first two moments (i.e., mean and covariance)], and then solve them analytically or numerically.

scholarly journals Sensitivity of Radiocarbon Sum Calibration

2020 ◽  
Author(s):  
Martin Hinz
Keyword(s):  
Monte Carlo ◽  
Monte Carlo Method ◽  
False Positive ◽  
Large Scale ◽  
Simulation Approach ◽  
The Monte Carlo Method ◽  
Standard Tool ◽  
Data Density ◽  
Detection Probabilities ◽  
Positive Results

Sum calibration has become a standard tool for demographic studies, even though the methodology itself is far from uncontroversial. In addition to fundamental methodological criticism, questions are frequently raised about the sample size and data density required to detect large-scale changes in past populations. This article uses a simulation approach to determine the detection probabilities for events of varying intensity and with varying data density. At the same time, the effectiveness of Monte Carlo-based confidence envelopes as a countermeasure against false-positive results is tested. The results show that the detection of such events is not unlikely and that the Monte Carlo method is well suited to separate signal and noise. However, the nature of the events already observed in this way demands further assessment.

scholarly journals Assessment of Geothermal Resources in the North Jiangsu Basin, East China, Using Monte Carlo Simulation

Energies ◽  
2021 ◽  
Vol 14 (2) ◽  
pp. 259
Author(s):  
Yibo Wang ◽  
Lijuan Wang ◽  
Yang Bai ◽  
Zhuting Wang ◽  
Jie Hu ◽  
...  
Keyword(s):  
Monte Carlo ◽  
Monte Carlo Method ◽  
Large Scale ◽  
Plate Boundary ◽  
Yangtze Craton ◽  
Geothermal Resources ◽  
Late Mesozoic ◽  
Thermal Reservoir ◽  
The North ◽  
The Monte Carlo Method

Geothermal energy has been recognized as an important clean renewable energy. Accurate assessment of geothermal resources is an essential foundation for their development and utilization. The North Jiangsu Basin (NJB), located in the Lower Yangtze Craton, is shaped like a wedge block of an ancient plate boundary and large-scale carbonate thermal reservoirs are developed in the deep NJB. Moreover, the NJB exhibits a high heat flow background because of its extensive extension since the Late Mesozoic. In this study, we used the Monte Carlo method to evaluate the geothermal resources of the main reservoir shallower than 10 km in the NJB. Compared with the volumetric method, the Monte Carlo method takes into account the variation mode and uncertainties of the input parameters. The simulation results show that the geothermal resources of the sandstone thermal reservoir in the shallow NJB are very rich, with capacities of (6.6–12) × 1020 J (mean 8.6 × 1020 J), (5.1–16) × 1020 J (mean 9.1 × 1020 J), and (3.2–11) × 1020 J (mean 6.6 × 1020 J) for the Yancheng, Sanduo and Dai’nan sandstone reservoir, respectively. In addition, the capacity of the geothermal resource of the carbonate thermal reservoir in the deep NJB is far greater than the former, reaching (9.9–15) × 1021 J (mean 12 × 1021 J). The results indicate capacities of a range value of (1.2–1.7) × 1021 J (mean 1.4 × 1022 J) for the whole NJB (<10 km).

UGR CALCULATION BASED ON THE LUMINANCE SPATIAL-ANGULAR DISTRIBUTION

2020 ◽  
Vol 2020 (4) ◽  
pp. 25-32
Author(s):  
Viktor Zheltov ◽  
Viktor Chembaev
Keyword(s):  
Monte Carlo ◽  
Angular Distribution ◽  
Monte Carlo Method ◽  
Visual Task ◽  
New Method ◽  
Lighting System ◽  
Preliminary Assessment ◽  
System A ◽  
The Monte Carlo Method

The article has considered the calculation of the unified glare rating (UGR) based on the luminance spatial-angular distribution (LSAD). The method of local estimations of the Monte Carlo method is proposed as a method for modeling LSAD. On the basis of LSAD, it becomes possible to evaluate the quality of lighting by many criteria, including the generally accepted UGR. UGR allows preliminary assessment of the level of comfort for performing a visual task in a lighting system. A new method of "pixel-by-pixel" calculation of UGR based on LSAD is proposed.

PSHA software review based on the Monte Carlo method

2020 ◽  
pp. 14-24
Author(s):  
V.A. Mironov ◽  
S.A. Peretokin ◽  
K.V. Simonov
Keyword(s):  
Monte Carlo ◽  
Monte Carlo Method ◽  
Seismic Hazard ◽  
Hazard Analysis ◽  
Software Review ◽  
Seismic Hazard Analysis ◽  
Probabilistic Seismic Hazard ◽  
Test Calculation ◽  
Seismic Surveys ◽  
The Monte Carlo Method

The article is a continuation of the software research to perform probabilistic seismic hazard analysis (PSHA) as one of the main stages in engineering seismic surveys. The article provides an overview of modern software for PSHA based on the Monte Carlo method, describes in detail the work of foreign programs OpenQuake Engine and EqHaz. A test calculation of seismic hazard was carried out to compare the functionality of domestic and foreign software.

Application of the Monte Carlo Method for the Prediction of Behavior of Peptides

2019 ◽  
Vol 20 (12) ◽  
pp. 1151-1157 ◽  
Author(s):  
Alla P. Toropova ◽  
Andrey A. Toropov
Keyword(s):  
Monte Carlo ◽  
Monte Carlo Method ◽  
Natural Sciences ◽  
Monte Carlo Technique ◽  
Quantitative Structure ◽  
Structure Property ◽  
The Monte Carlo Method ◽  
Modern Natural

Prediction of physicochemical and biochemical behavior of peptides is an important and attractive task of the modern natural sciences, since these substances have a key role in life processes. The Monte Carlo technique is a possible way to solve the above task. The Monte Carlo method is a tool with different applications relative to the study of peptides: (i) analysis of the 3D configurations (conformers); (ii) establishment of quantitative structure – property / activity relationships (QSPRs/QSARs); and (iii) development of databases on the biopolymers. Current ideas related to application of the Monte Carlo technique for studying peptides and biopolymers have been discussed in this review.

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