Characterizing heterogeneous permeable media with spatial statistics and tracer data using sequential simulated annealing

Datta‐Gupta, Akhil; Lake, Larry W.; Pope, Gary A.

doi:10.1007/bf02273537

Cited by 43 publications

(14 citation statements)

References 20 publications

(16 reference statements)

Supporting

Mentioning

Contrasting

Order By: Relevance

“…A simple technique is simulated annealing which was investigated in [126] and [41]. Using a fast simulator such as a streamline method (fast by virtue of the IMPES approximation and the one-dimensional approximation along the streamlines) or a coarse grid simulator, this might be practical.…”

Section: Derivative-free Methodsmentioning

confidence: 99%

Geological Modelling and Reservoir Simulation

Farmer

2005

Mathematics in Industry

View full text Add to dashboard Cite

Summary.The main mathematical techniques used in building geological models for input to fluid flow simulation are reviewed. The subject matter concerns the entire geological and reservoir simulation modelling workflow relating to the subsurface. To provide a realistic illustration of a complete fluid flow model, a short outline of two-phase incompressible flow through porous media is given. The mathematics of model building is discussed in a context of seismic acquisition, processing and interpretation, well logging and geology. Grid generation, geometric modelling and spatial statistics are covered in considerable detail. A few new results in the area of geostatistics are proved. In particular the equivalence of radial basis functions, general forms of kriging and minimum curvature methods is shown. A Bayesian formulation of uncertainty assessment is outlined. The theory of inverse problems is discussed in a general way, from both deterministic and statistical points of view. There is a brief discussion of upscaling. A case for multiscale geological modelling is made and the outstanding research problems to be solved in building multiscale models from many types of data are discussed.

show abstract

Section: Derivative-free Methodsmentioning

confidence: 99%

Geological Modelling and Reservoir Simulation

Farmer

2005

Mathematics in Industry

View full text Add to dashboard Cite

show abstract

“…While the log permeability is approximately normal for many porous media, the Monte Carlo method does not assume a Gaussian field, and is thus more general. See also [13]. In [58], genetic algorithms are compared to simulated annealing for solution of the inverse problem, while in [53], MCMC methods are studied.…”

Section: Flow In Porous Mediamentioning

confidence: 99%

Stochastic methods for the prediction of complex multiscale phenomena

Glimm¹,

Sharp²

1998

Quart. Appl. Math.

View full text Add to dashboard Cite

Abstract.The purpose of this paper is to develop a general framework for the prediction of complex multiscale phenomena and to illustrate this framework through comparison to two examples of current interest to the authors.Prediction involves a two-step process of inverse prediction to describe the system, given observations of its behavior, and forward prediction, to specify system behavior, given its description. Introduction.This paper is concerned with methods for the analysis and prediction of complex phenomena. The complexity of systems considered here results from the interaction of a number of subsystems, or within a single subsystem from the interaction of phenomena occurring on a number of length and/or time scales.The analysis and prediction problem divides into two components, the forward problem and the inverse problem. The forward problem is to determine the solution describing system behavior, given the governing equations and initial data. The inverse problem is to determine the governing equations and initial data, given observations of the system. These two problems are linked in usage as the inverse problem, on the basis of current observations, and give the governing equations and data needed to solve the forward problem, which in turn makes predictions going beyond current observations. Forward prediction is very different from inverse prediction by statistical inference. Forward prediction assumes complete data and gives a complete answer. Even in the stochastic case, the data and the answer for forward prediction are complete within a probabilistic framework. For statistical inference, to solve the inverse prediction problem,

show abstract

“…Many inverse methods have been developed to effectively address the inverse modeling problem (e.g., [30,5,7,32,6,8,17] among the others). This inverse modeling problem is often cast as an optimization problem: an objective function is first defined by the mismatch between the observations and the simulations computed from an initial model, then the objective function is minimized by tuning the initial model parameters using some optimization subroutines (either stochastic or deterministic).…”

Section: Introductionmentioning

confidence: 99%

A multiscale method for subsurface inverse modeling: Single-phase transient flow

Caers

2011

Advances in Water Resources

View full text Add to dashboard Cite

Characterizing heterogeneous permeable media with spatial statistics and tracer data using sequential simulated annealing

Cited by 43 publications

References 20 publications

Geological Modelling and Reservoir Simulation

Geological Modelling and Reservoir Simulation

Stochastic methods for the prediction of complex multiscale phenomena

A multiscale method for subsurface inverse modeling: Single-phase transient flow

Contact Info

Product

Resources

About