Plurigau: a computer program for simulating spatial facies using the truncated plurigaussian method

Truncated plurigaussian simulation is a useful method for simulating spatial categorical variables, such as facies, in a geological context. The method is an extension of the truncated Gaussian method that retains the main advantages of the latter (mainly that it produces permissible sets of indicator semi-variograms and cross-semi-variograms) but overcomes its limitations (the truncated Gaussian method only reproduces sequentially ranked categories). The method is based on the truncation of two Gaussian random functions that may, or may not, be correlated. PLURIGAU is an ANSI Fortran-77 computer program for performing conditional or unconditional truncated plurigaussian simulations of spatial categories. The number of facies, spatial relations between the facies, proportions of each facies, indicator semi-variograms and indicator cross-semi-variograms must be known or estimated from experimental data. The program calculates the four thresholds for each of the facies (two for each of the Gaussian random functions) and the covariance models for the two Gaussian random functions.The simulation of the Gaussian random functions may be done using any of the methods available. Conditioning has been implemented by a simple acceptance–rejection technique embedded within sequential Gaussian simulation algorithm. A case study is provided so that the implementation of the programs can be checked and the results are discussed.     

A nonsmooth nonlinear conjugate gradient method for interactive contact force problems

Interactive rigid body simulation is important for robot simulation and virtual design. A vital part of the simulation is the computation of contact forces. This paper addresses the contact force problem, as used in interactive simulation. The contact force problem can be formulated in the form of a nonlinear complementarity problem (NCP), which can be solved using an iterative splitting method, such as the projected Gauss–Seidel (PGS) method. We present a novel method for solving the NCP problem by applying a Fletcher–Reeves type nonlinear nonsmooth conjugate gradient (NNCG) type method. We analyze and present experimental convergence behavior and properties of the new method. Our results show that the NNCG method has at least the same convergence rate as PGS, and in many cases better.     

A geostatistical algorithm to reproduce lateral gradual facies transitions: Description and implementation

Valid representations of geological heterogeneity are fundamental inputs for quantitative models used in managing subsurface activities. Consequently, the simulation of realistic facies distributions is a significant aim. Realistic facies distributions are typically obtained by pixel-based, object-based or process-based methods. This work presents a pixel-based geostatistical algorithm suitable for reproducing lateral gradual facies transitions (LGFT) between two adjacent sedimentary bodies. Lateral contact (i.e. interfingering) between distinct depositional facies is a widespread geometric relationship that occurs at different scales in any depositional system. The algorithm is based on the truncation of the sum of a linear expectation trend and a random Gaussian field, and can be conditioned to well data. The implementation introduced herein also includes subroutines to clean and geometrically characterize the obtained LGFT. The cleaned sedimentary body transition provides a more appropriate and realistic facies distribution for some depositional settings. The geometric measures of the LGFT yield an intuitive measure of the morphology of the sedimentary body boundary, which can be compared to analogue data. An example of a LGFT obtained by the algorithm presented herein is also flow simulated, quantitatively demonstrating the importance of realistically reproducing them in subsurface models, if further flow-related accurate predictions are to be made.     

A computer method of constructing geological histories from field surveys and maps

A computer method has been designed to analyze binary relations between geological events. It interprets the relations in a form which allows construction of a multinodal network of relationships (of which tree-form networks are a special situation).The method is a form of data management which does not require the names to be ranked or the relations between names to be specified in advance, as do other geological systems. The data within the file may be added to as new information is collected, and the relationships determined from the data on file at any time. The method therefore is suited particularly to studies in which data accumulate progressively. Data structures which are more complex than a multinodal network are detected as “contradictions” or “contradictory rings”.The method has been used successfully in constructing explanations for geological maps from the field evidence recorded on the face of the map. It provides a means of assembling historical data from many maps as well as from supplementary information, such as radiometric or paleontological dates, and synthesizing a history for a region. The method therefore may be useful in tectonic analysis.     

Hierarchical stochastic modeling and optimization for petroleum field development under geological uncertainty

Real-world simulation optimization (SO) problems entail complex system modeling and expensive stochastic simulation. Existing SO algorithms may not be applicable for such SO problems because they often evaluate a large number of solutions with many simulation calls. We propose an integrated solution method for practical SO problems based on a hierarchical stochastic modeling and optimization (HSMO) approach. This method models and optimizes the studied system at increasing levels of accuracy by hierarchical sampling with a selected set of principal parameters. We demonstrate the efficiency of HSMO using the example problem of Brugge oil field development under geological uncertainty.     

Wire frame: A reliable approach to build sealed engineering geological models

The technique of 3D geological modeling (3DGM) is an effective tool for representing complex geological objects. In order to improve the accuracy of geological models applied in numerical simulation methods such as finite elements and finite differences, we can use 3DGM as a modeling tool. To do this, however, 3DGM must provide the ability to model geological and artificial objects in a unified way, and its geological model must be seamless for mesh generation. We present the concept of a sealed engineering geological model (SEGM), and describe its topological representation. Three kinds of conditions: geometric continuity, topological consistency and geological consistency, which must be satisfied by SEGM, are discussed in detail. A new method for constructing an SEGM based on a wire frame is proposed. It includes three main components: wire frame construction, interface modification and reconstruction, and block tracing. Building a unitary wire frame, which is composed of many simple arcs and connects all interfaces seamlessly, is the key of this method. An algorithm, involving two intersections computations and partition of simple arcs, is proposed for building a wire frame. Additionally, we also propose a local iterative algorithm for computing fault traces. As an example, we build an SEGM for the dam area of a hydraulic engineering project in the HuNan province of China.     

A simple method for representing some univariate frequency distributions, with particular application in Monte Carlo-based simulation

Introduced in this paper is a simple yet effective method for representing some of the types of univariate frequency distribution that commonly are required in Monte Carlo-based simulation. To use the method, an appropriate parent distribution is first chosen; then this distribution is modified by blending a constant value into the density function; the particular value used is the ordinate of the density function at its mode. The advantages of the method are (1) that a wide variety of forms of distribution can be represented, (2) that the number of parameters is low, (3) that the parameters can be varied continuously to let sets of systematically related distributions be constructed, and (4) that the resulting distribution functions are straightforward to invert numerically, thereby letting random deviates be generated quickly and efficiently. The method is potentially of particular value in Monte Carlo-based simulation, because it allows distributions of greatly differing forms to be represented within a single, flexible framework. The paper describes the method, provides the necessary equations for parameter estimation, and gives an example of a simulation exercise in which the method proved valuable. A demonstration program is provided that allows experimentation with the method.     

Local Bases for Model-reduced Smoke Simulations

We present a flexible model reduction method for simulating incompressible fluids. We derive a novel vector field basis composed of localized basis flows which have simple analytic forms and can be tiled on regular lattices, avoiding the use of complicated data structures or neighborhood queries. Local basis flow interactions can be precomputed and reused to simulate fluid dynamics on any simulation domain without additional overhead. We introduce heuristic simulation dynamics tailored to our basis and derived from a projection of the Navier-Stokes equations to produce physically plausible motion, exposing intuitive parameters to control energy distribution across scales. Our basis can adapt to curved simulation boundaries, can be coupled with dynamic obstacles, and offers simple adjustable trade-offs between speed and visual resolution.     

INDUCTIVE LEARNING FOR PARAMETER OPTIMIZATION

Optimization of simulation model output is one of the most important tasks in a simulation study of a complex system. Efficacy of an optimization approach is expressed in the accuracy of locating a global extremum, as well as in the number of investigated search points. The approach Machine Learning Optimization (ML-Opt), presented in this article, explores functional dependencies between search points in order to reduce the number of evaluations. Functional relations between search points are determined by an inductive learning algorithm, which generates a classifier used as a control structure in the optimization process. The classifier approximates the structure of the unknown goal function given by a simulation model and affects the generation of new search points. A discussion of a numerical example concludes the paper.     

A paris-model approach to modular simulation

The development of complex models can be greatly facilitated by the utilization of libraries of reusable model components. In this paper we describe an object-oriented module specification formalism (MSF) for implementing archivable modules in support of continuous spatial modeling. This declarative formalism provides the high level of abstraction necessary for maximum generality, provides enough detail to allow a dynamic simulation to be generated automatically, and avoids the “hard-coded” implementation of space-time dynamics that makes procedural specifications of limited usefulness for specifying archivable modules. A set of these MSF modules can be hierarchically linked to create a parsimonious model specification, or “parsi-model”. The parsi-model exists within the context of a modeling environment (an integrated set of software tools which provide the computer services necessary for simulation development and execution), which can offer simulation services that are not possible in a loosely-coupled “federated” environment, such as graphical module development and configuration, automatic differentiation of model equations, run-time visualization of the data and dynamics of any variable in the simulation, transparent distributed computing within each module, and fully configurable space-time representations. We believe this approach has great potential for bringing the power of modular model development into the collaborative simulation arena.