Using Inflow Records to Approximate Solutions to Statistical Moment Equations of an Explicit Stochastic Reservoir Optimization Method

2021 ◽  
Vol 147 (7) ◽  
Author(s):  
Alcigeimes B. Celeste ◽  
José Ítalo Porto Siqueira ◽  
Ximing Cai
Keyword(s):  
Approximate Solutions ◽  
Optimization Method ◽  
Statistical Moment ◽  
Moment Equations ◽  
Reservoir Optimization

Conditional Statistical Moment Equations for Dynamic Data Integration in Heterogeneous Reservoirs

2006 ◽  
Vol 9 (03) ◽  
pp. 280-288 ◽  
Author(s):  
Liyong Li ◽  
Hamdi A. Tchelepi
Keyword(s):  
Statistical Moment ◽  
Limited Data ◽  
Pressure Data ◽  
Moment Equations ◽  
Reservoir Properties ◽  
Incomplete Knowledge ◽  
Heterogeneous Reservoirs ◽  
Knowledge Uncertainty ◽  
Available Information ◽  
Permeability Field

Summary An inversion method for the integration of dynamic (pressure) data directly into statistical moment equations (SMEs) is presented. The method is demonstrated for incompressible flow in heterogeneous reservoirs. In addition to information about the mean, variance, and correlation structure of the permeability, few permeability measurements are assumed available. Moreover, few measurements of the dependent variable are available. The first two statistical moments of the dependent variable (pressure) are conditioned on all available information directly. An iterative inversion scheme is used to integrate the pressure data into the conditional statistical moment equations (CSMEs). That is, the available information is used to condition, or improve the estimates of, the first two moments of permeability, pressure, and velocity directly. This is different from Monte Carlo (MC) -based geostatistical inversion techniques, where conditioning on dynamic data is performed for one realization of the permeability field at a time. In the MC approach, estimates of the prediction uncertainty are obtained from statistical post-processing of a large number of inversions, one per realization. Several examples of flow in heterogeneous domains in a quarter-five-spot setting are used to demonstrate the CSME-based method. We found that as the number of pressure measurements increases, the conditional mean pressure becomes more spatially variable, while the conditional pressure variance gets smaller. Iteration of the CSME inversion loop is necessary only when the number of pressure measurements is large. Use of the CSME simulator to assess the value of information in terms of its impact on prediction uncertainty is also presented. Introduction The properties of natural geologic formations (e.g., permeability) rarely display uniformity or smoothness. Instead, they usually show significant variability and complex patterns of correlation. The detailed spatial distributions of reservoir properties, such as permeability, are needed to make performance predictions using numerical reservoir simulation. Unfortunately, only limited data are available for the construction of these detailed reservoir-description models. Consequently, our incomplete knowledge (uncertainty) about the property distributions in these highly complex natural geologic systems means that significant uncertainty accompanies predictions of reservoir flow performance. To deal with the problem of characterizing reservoir properties that exhibit such variability and complexity of spatial correlation patterns when only limited data are available, a probabilistic framework is commonly used. In this framework, the reservoir properties (e.g., permeability) are assumed to be a random space function. As a result, flow-related properties such as pressure, velocity, and saturations are random functions. We assume that the available information about the permeability field includes a few measurements in addition to the spatial correlation structure, which we take here as the two-point covariance. This incomplete knowledge (uncertainty) about the detailed spatial distribution of permeability is the only source of uncertainty in our problem. Uncertainty about the detailed distribution of the permeability field in the reservoir leads to uncertainty in the computed predictions of the flow field (e.g., pressure).

scholarly journals Optimization of TIG Welding Parameters Using a Hybrid Nelder Mead-Evolutionary Algorithms Method

2020 ◽  
Vol 4 (1) ◽  
pp. 10 ◽  
Author(s):  
Rohit Kshirsagar ◽  
Steve Jones ◽  
Jonathan Lawrence ◽  
Jim Tabor
Keyword(s):  
Evolutionary Algorithms ◽  
Global Minimum ◽  
Error Function ◽  
Approximate Solutions ◽  
Optimization Method ◽  
Computational Effort ◽  
Welding Parameters ◽  
Additional Function ◽  
Effort Function ◽  
Better Than

A number of evolutionary algorithms such as genetic algorithms, simulated annealing, particle swarm optimization, etc., have been used by researchers in order to optimize different manufacturing processes. In many cases these algorithms are either incapable of reaching global minimum or the time and computational effort (function evaluations) required makes the application of these algorithms impractical. However, if the Nelder Mead optimization method is applied to approximate solutions cheaply obtained from these algorithms, the solution can be further refined to obtain near global minimum of a given error function within only a few additional function evaluations. The initial solutions (vertices) required for the application of Nelder-Mead optimization can be obtained through multiple evolutionary algorithms. The results obtained using this hybrid method are better than that obtained from individual algorithms and also show a significant reduction in the computation effort.

scholarly journals Approximate solutions for coupled moment equations

1982 ◽  
Vol 24 (1) ◽  
pp. 86-97
Author(s):  
Graham Winley ◽  
Keith Tognetti
Keyword(s):  
Stochastic Process ◽  
Differential Equations ◽  
Approximate Solutions ◽  
The Other ◽  
Main Concern ◽  
Higher Moments ◽  
System Of Equations ◽  
Moment Equations ◽  
Second Moments ◽  
A New Technique

AbstractIn studying the coupled differential equations for the moments of a stochastic process it is often found that the equation for the j th moment involves higher moments. The usual methods of “decoupling” such a system of equations to obtain estimates of the moments are surveyed and shown generally to result in a system of nonlinear simultaneous differential equations which may be readily solved by numerical methods.Often, estimates of the first and second moments are the main concern. In this case, two further assumptions reported in the literature can be used to simplify the system and avoid the expense of solving the nonlinear equations. These two techniques are evaluated and compared with a new technique. Two processes are analysed, one representing a chemical reaction and the other population growth.

scholarly journals Parallel genetic algorithms on the graphics processing units using island model and simulated annealing

2017 ◽  
Vol 9 (7) ◽  
pp. 168781401770741 ◽  
Author(s):  
Cheng-Chieh Li ◽  
Chu-Hsing Lin ◽  
Jung-Chun Liu
Keyword(s):  
Genetic Algorithm ◽  
Genetic Algorithms ◽  
Simulated Annealing ◽  
Graphics Processing Units ◽  
Optimal Solution ◽  
Approximate Solutions ◽  
Optimization Method ◽  
Approximate Algorithm ◽  
Parallel Genetic Algorithms ◽  
Graphics Processing

To solve a non-deterministic polynomial-hard problem, we can adopt an approximate algorithm for finding the near-optimal solution to reduce the execution time. Although this approach can come up with solutions much faster than brute-force methods, the downside of it is that only approximate solutions are found in most situations. The genetic algorithm is a global search heuristic and optimization method. Initially, genetic algorithms have many shortcomings, such as premature convergence and the tendency to converge toward local optimal solutions; hence, many parallel genetic algorithms are proposed to solve these problems. Currently, there exist many literatures on parallel genetic algorithms. Also, a variety of parallel genetic algorithms have been derived. This study mainly uses the advantages of graphics processing units, which has a large number of cores, and identifies optimized algorithms suitable for computation in single instruction, multiple data architecture of graphics processing units. Furthermore, the parallel simulated annealing method and spheroidizing annealing are also used to enhance performance of the parallel genetic algorithm.

Multiple scattering of electromagnetic waves by a collection of plasma drift turbulent vortices

1995 ◽  
Vol 53 (3) ◽  
pp. 365-372
Author(s):  
David Resendes
Keyword(s):  
Multiple Scattering ◽  
Cross Section ◽  
Electromagnetic Waves ◽  
Incoherent Scattering ◽  
Statistical Moment ◽  
Moment Equations ◽  
Single Vortex ◽  
Plasma Drift ◽  
Vortex Solution ◽  
Self Consistent

An application of the self-consistent multiple-scattering theory of electromagnetic waves to drift turbulent vortices is presented. Using the known single-vortex solution, the integral equation describing the scattering from a finite density of drift turbulent vortices is obtained. Rather than solving this equation and then averaging, the averaging operation is taken first to obtain statistical moment equations, from which the coherent and incoherent scattering follow. These results are expressed in a Fourier basis, and the cross-section is evaluated. Limiting forms of the theory and straightforward generalizations are discussed.

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