Representation Of Faults Research Articles

Virtual Elements for Representation of Faults, Cracks and Hydraulic Fractures in Dynamic Flow Simulations

Representation of discrete faults at reservoir scale in numerical modelling is a sophisticated task, since discretization has to be in agreement with grid convergence criteria of the numerical simulator applied. An accurate spatial representation of faults and fractures in dynamic flow simulations is essential for an assessment of fluid flow in faults. In the context of the present study the Virtual Element concept for discrete fault integration into regional-scale dynamic models was developed taking into account variable fault geometries without modifying the initial gridding scheme. Coupled multi-phase flow simulations were successfully undertaken to validate the implementation of the developed concept.

Analogue and Mixed-Signal Production Test Speed-Up by Means of Fault List Compression

Accurate test effectiveness estimation for analogue and mixed-signal Systems on a Chip (SoCs) is currently prohibitive in the design environment. One of the factors that sky rockets fault simulation costs is the number of structural faults which need to be simulated at circuit-level. The purpose of this paper is to propose a novel fault list compression technique by defining a stratified fault list, build with a set of “representative” faults, one per stratum. Criteria to partition the fault list in strata, and to identify representative faults are presented and discussed. A fault representativeness metric is proposed, based on an error probability. The proposed methodology allows different tradeoffs between fault list compression and fault representation accuracy. These tradeoffs may be optimized for each test preparation phase. The fault representativeness vs. fault list compression tradeoff is evaluated with an industrial case study—a DC-DC (switched buck converter). Although the methodology is presented in this paper using a very simple fault model, it may be easily extended to be used with more elaborate fault models. The proposed technique is a significant contribution to make mixed-signal fault simulation cost-effective as part of the production test preparation.

Reliable stabilization of switched system with average dwell-time approach

This paper presents an average dwell-time approach for reliable stabilization of a class of switched nonlinear systems. Due to the nature of average dwell-time techniques and the representation of actuator faults, this paper has the following features compared with the existing methods in the literature: (1) the proposed method is independent of arbitrary switching policies provided that switching is on-the-average slow enough; (2) the proposed controller exponentially stabilizes this class of nonlinear systems with actuator faults and its nominal (i.e., without actuator faults) systems without necessarily changing any structures and/or parameters of the proposed controllers; and (3) the proposed method treats all actuators in a unified way without necessarily classifying all actuators into faulty actuators and healthy ones. A numerical example is given to show the effectiveness of the proposed method.

Kinematics of Tertiary to Quaternary intracontinental deformation of upper crust in the Eastern Cordillera, southern Central Andes, NW Argentina

To elucidate factors controlling the geometry of, and kinematics associated with, prominent upper‐crustal structures in the Eastern Cordillera of NW Argentina, structural analyses of key areas were complemented by fault slip analysis, remote sensing and 3D representation of prominent faults. The analyses revealed that deformation during Tertiary to Quaternary times was accomplished mostly by prominent orogen‐parallel reverse faults, the geometry of which was significantly influenced by Paleozoic and Cretaceous planar structures. Locally, this deformation was preceded by kilometer‐scale doming of upper‐crustal rocks. Analysis of 767 brittle faults at 67 stations in the studied areas indicates that local upper‐crustal doming and orogen‐parallel reverse faults formed chiefly under NW‐SE and E‐W shortening. Shortening directions inferred from fault slip data portray the kinematics of first‐order faults and folds. More specifically, shortening directions are mostly uniform with respect to first‐order structures. Age and kinematics of deformation inferred from brittle fault analysis in the study areas is consistent with equivalent data compiled from other parts of the Eastern Cordillera, Puna and Pampean Ranges. Collectively, the data is at variance with hypotheses relating late Tertiary to Quaternary deformation in the Eastern Cordillera to plate (boundary) kinematics. The kinematics of intracontinental deformation in the southern Central Andes points to deformation partitioning of upper crust as a consequence of bulk E‐W shortening. We, therefore, caution the usage of brittle fault‐kinematics in continental interiors as an indication for plate‐kinematic changes.

Model-based fault diagnosis for aerospace systems: a survey

This survey of model-based fault diagnosis focuses on those methods that are applicable to aerospace systems. To highlight the characteristics of aerospace models, generic non-linear dynamical modelling from flight mechanics is recalled and a unifying representation of sensor and actuator faults is presented. An extensive bibliographical review supports a description of the key points of fault detection methods that rely on analytical redundancy. The approaches that best suit the constraints of the field are emphasized and recommendations for future developments in in-flight fault diagnosis are provided.

Discussion on fault Diagnosis methods of Discrete Event Systems

Fault Diagnosis of Discrete Event Systems has become an active research area in recent years. The research activity in this area is driven by the needs of many different application domains such as manufacturing, process control, control systems, transportation, communication networks, software engineering, and others. The aim of this plenary address is to review the state-of the art on methods and techniques for fault diagnosis of discrete event systems. Theoretical and practical issues related to model description tools, diagnosis processing structure, sensor selection, fault representation and inference will be discussed. Some criteria to choose methods to achieve fault diagnosis and future research directions will be investigated.

Three dimensional modelling of fractured and faulted reservoirs: Framework and implementation

Modelling of coupled physical processes in fractured and faulted media is a major challenge for the geoscience community. Due to the complexity related to the geometry of real fracture networks and fault systems, modelling studies have been mainly restricted either to two dimensional cases or to simplified orthogonal fracture systems consisting of vertical and horizontal fractures. An approach to generate three dimensional meshes for realistic fault geometries is presented. The method enables representation of faults in an arbitrary incline as two dimensional planes within a three dimensional, stratified porous matrix of a generic geometry. Based on a structural geological model, the method creates three dimensional unstructured tetrahedral meshes. These meshes can be used for finite element and finite volume numerical simulations. A simulation of a coupled fluid flow and heat transport problem for a two layered porous medium cut by two crossing faults is presented to test the reliability of the method.

Assisted history matching for the characterization of fractured reservoirs

Methodologies and numerical tools are available (1) to construct geologically realistic models of fracture networks and (2) to turn these models into simplified conceptual models usable for field-scale simulations of multiphase production methods. A critical step remains however, that of characterizing the flow properties of the geological fracture network. The multiscale nature of fracture networks and the associated modeling cost impose a scale-dependent characterization: (1) multiscale fractures that may be characterized in local dynamic test areas, e.g., drainage areas involved in well tests, through the calibration of geologically realistic discrete fracture network (DFN) models and accurate local flow-test simulations; and (2) large-scale faults that are characterized through reservoir-scale production history simulations that involve upscaled flow models with an explicit fault representation. However, field data are commonly insufficient to fully characterize the multiscale fracture properties. Therefore, efficient inversion methodologies are necessary to sample wide ranges of property values and to characterize a variety of solutions, i.e., fracture models that are consistent with dynamic data. This article presents an inversion methodology to facilitate the characterization of fracture properties from well-test data. A genetic optimization algorithm has been developed and coupled with a three-dimensional DFN flow simulator to perform the simultaneous calibration of well-test data. As a first step, the calibration data result from interpreted well tests, i.e., data are equivalent transmissivities. Applications are presented on a geologically realistic fractured reservoir model having three facies, two fracture sets, and three wells. The characterized fracture properties are mean length, mean conductivity, orientation dispersion factors, and facies-dependent properties such as fracture density. The effectiveness of this inversion methodology to characterize physically meaningful and data-consistent fracture properties is discussed.

Fault-tolerant Internal Model Control with Application to a Diesel Engine

The paper proposes a new structure for fault-tolerant control of nonlinear systems subject to persistent faults. The principle of Internal Model Control (IMC) is extended to ensure fault tolerance with respect to faults that do not affect the plant stability. The method is based on a representation of sensor, actuator and plant faults as parameter changes of the plant model, which is part of the IMC control law. It is proved that the IMC control loop, which is extended by a diagnostic unit, tolerates substantial faults and ensures the nominal loop performance unless the fault changes the structure of the nonlinear plant. These results are illustrated for the air path of a Diesel engine.

Comparison of Fault Representation Methods in Finite Difference Simulations of Dynamic Rupture

Assessing accuracy of numerical methods for spontaneous rupture simulation is challenging because we lack analytical solutions for reference. Previous comparison of a boundary integral method (bi) and finite-difference method (called dfm) that explicitly incorporates the fault discontinuity at velocity nodes (traction- at-split-node scheme) shows that both converge to a common, grid-independent solution and exhibit nearly identical power-law convergence rates with respect to grid spacing Δ x . We use this solution as a reference for assessing two other proposed finite-difference methods, the thick fault (tf) and stress glut (sg) methods, both of which approximate the fault-jump conditions through inelastic increments to the stress components (inelastic-zone schemes). The tf solution fails to match the qualitative rupture behavior of the reference solution and has quantitative misfits in root- mean-square rupture time of ∼30% for the smallest computationally feasible Δ x (with ∼9 grid-point resolution of cohesive zone, denoted N c = 9). For sufficiently small values of Δ x , the sg method reproduces the qualitative features of the reference solution, but rupture velocity remains systematically low for sg relative to the reference solution, and sg lacks the well-defined power-law convergence seen for bi and dfm. The rupture-time error for sg, with N c ∼ 9, remains well above uncertainty in the reference solution, and the split-node method attains comparable accuracy with N c 1/4 as large (and computation timescales as ( N c ) 4 ). Thus, accuracy is highly sensitive to the formulation of the fault-jump conditions: The split-node method attains power-law convergence. The sg inelastic-zone method achieves solutions that are qualitatively meaningful and quantitatively reliable to within a few percent, but convergence is uncertain, and sg is computationally inefficient relative to the split-node approach. The tf inelastic-zone method does not achieve qualitatively meaningful solutions to the 3D test problem and is sufficiently computationally inefficient that it is not feasible to explore convergence quantitatively.

Design verification by test vectors and arithmetic transform Universal Test Set

We investigate methodology for simulation-based verification under a fault model. Since it is currently not feasible to describe a comprehensive explicit model of design errors, we propose an implicit fault model. The model is based on the arithmetic transform (AT) spectral representation of faults. The verification of circuits under the small errors in spectral domain is then performed by the universal test set (UTS) approach to test vector generation. The major result shows that, for errors whose AT has at most t nonzero coefficients, there exist the UTS test vector set of size O(n/sub 2//sup log t/). Consequently, verification confidence can be parameterized by the size of the error t, where at most O(n/sub 2//sup log t/) verification vectors are simulated to verify the absence of faults belonging to such an implicitly defined fault class. The experimental confirmation of the feasibility of verification using such UTS is presented, together with the relations between the arithmetic and Walsh-Hadamard spectra that bound the AT error spectrum and show that a class of small error circuits has small error spectrum. The proposed approach has the advantage of compatibility with formal verification and testing methods.

Modelling of Conductive Faults with a Multiscale Approach

Some of the most productive oil and gas reservoirs are found in formations crossed by multiscale fractures/faults. Among them, conductive faults may closely control reservoir performance. However, their modelling encounters numerical and physical difficulties linked with: - the necessity to keep an explicit representation of faults through small-size gridblocks; - the modelling of multiphase flow exchanges between the fault and the neighbouring medium. In the present work, a physically representative and numerically efficient modelling approach is proposed to incorporate subvertical conductive faults in single- and dual-porosity simulators. To validate our approach and demonstrate its efficiency, simulation results of multiphase displacements in representative field sector models are presented.

Direct seismic energy modeling and application to the 1979 Imperial Valley earthquake

The seismic energy associated with an earthquake has two representations: the work of the seismic waves done against a distant surface or a fault representation. For a fault subject to slip‐weakening friction, the energy density is the difference between an elastostatic work and a work density spent in fracture and relaxation. We apply this to a dynamic simulation of the 1979 Imperial Valley earthquake, whose initial conditions are inspired by previous kinematic studies. A large area of the fault has a negative energy density, and the emission of energy is roughly confined to small parts of the fault with large positive energy density. We compute the work of the seismic waves against the surface of a sphere enclosing the source, and we find the same amount of energy. We produce a map of energy directivity that shows that 40% of the energy passes through only 6.5% of the sphere.

Fault Classification Using Pseudomodal Energies and Neural Networks

A new fault identie cation method is introduced that uses pseudomodal energies to train neural networks. The proposed procedure is tested on a simulated cantilevered beam and a population of 20 cylindrical shells, and its performance is compared to that of the procedure that uses modal properties to train neural networks. Both the cantilevered beam and cylindrical shells are divided into three substructures, and faults are introduced into these substructures. The cylinder is excited using modal hammer, and acceleration is measured using an accelerometer. Each fault case is assigned a fault identity with the presence of fault represented by a 1, whereas the absence of fault is represented by a 0. Following this fault representation scheme, a fault located in substructure 1 would have an identity of [1 0 0], with two zeros indicating the absence of faults in substructures 2 and 3. The neural network used is a multilayer perceptron trained using scaled conjugatemethod. The statistical overlap factor and principal component analysis are used to reduce the size of the input data. For both examples the pseudomodal-energytrained neural networks provide better classie cation of faults than the networks trained using the conventional modal properties. Nomenclature aq = lower frequency bounds for qth pseudomodal energy bq = upper frequency bounds for qth pseudomodal energy [C] = damping matrix d[≤]

Representation and scaling of faults in fluid flow models

Fault representation and scaling in flow models are examined with respect to fault zone properties, the accuracy with which they can be determined, and how these variables and fault geometries can be incorporated realistically in to flow models. Outcrop data show that fault displacement/thickness ratios and permeability vary widely. For simple single fault models, results for numerical models are compared with analytical and statistical methods. Representation of a fault as a transmissibility surface conflates the effects of four variables--fault zone thickness and permeability, grid-block size and matrix (host-rock) cell permeability. Random spatial variation of transmissibility factor values is well represented by a uniform transmissibility factor which is the arithmetic mean of the values representing log-normally distributed permeability and thicknesses. Realistic ranges of fault zone thicknesses can be represented without grid-block refinement by an upscaling method based on simple transformation of transmissibility factor curves derived from a range of coarse grid-block models. Sub-seismic faults have significant effects on effective permeability of model volumes at kilometre scales only when the faults are assigned a permeability less than c. 0.001 of the matrix permeability.

Locating bridging faults using dynamically computed stuck-at fault dictionaries

Novel algorithms for locating bridging faults, based on the voting and wired models, in combinational circuits are presented. The algorithm uses small portions of the stuck-at fault dictionary, not the bridge fault dictionary, computed during fault location. This, along with an implicit representation of bridging faults, contributes significantly to the efficiency of the algorithm. Experimental evaluation of the algorithm on ISCAS circuits is presented.

A general model for representing arbitrary unsymmetries in various types of network analysis

When dealing with unsymmetric faults various proposals have been put forward. In general they have been characterized by specific treatment of the single fault in accordance with the structure and impedances involved. The model presented is based on node equations and was originally developed for transient stability studies in order to allow for an arbitrary fault representation as seen from the positive sequence network. The method results in impedances -or admittances-combining the negative sequence and zero sequence representation for the symmetrical network with the structure and electrical constants of the unsymmetry involving one or more buses. These impedances are introduced in the positive sequence network in the nodes involved in the unsymmetrical conditions. In addition the model can be used for static fault current analysis and presents also in this connection a general method of solution; the method is easy to use since the task of user is limited to establishing the node admittance matrix of the unsymmetry expressed in phase coordinates. The paper is completed with two examples showing the application of the method, one fault for which a well known representation exists and one complicated fault situation which has not been treated before for traditional transient stability analysis.

An algebra of multiple faults in RAMs

Cell array faults in random-access memories (RAMs) are usually represented by Mealy automata. In such a model, multiple faults should also be representable by automata; in fact, it should be possible to compute the automaton representing a multiple fault from the automata representing the single faults that make up the multiple fault. In this paper we study properties of binary composition operations on automata that are appropriate for the representation of multiple faults in RAMs. First, we derive a set of generic conditions that every composition operation must satisfy. Second, we develop a set of physical conditions that the composition must satisfy in order to apply to stuck-at, transition and coupling faults in RAMs. Third, we represent the transition table rules used by van de Goor and Smit by a composition operation and prove that this operation satisfies both the generic and physical conditions. Fourth, we point out that in some circumstances, it is appropriate to use a different composition operation (defined by us in a previous paper) to permit a different handling of coupling faults in the presence of stuck-at or transition faults. We compare and relate the properties of the two algebras.

NON-LINEAR FAULT BEHAVIOUR NEAR UNDERGROUND EXCAVATIONS — A BOUNDARY ELEMENT APPROACH

A boundary element model for stress/stability analysis of underground excavations in the vicinity of faults is presented. The boundary element formulation adopts the fictitious stress method for the simulation of excavation boundaries and the displacement discontinuity method for the representation of faults. The numerical model employs the Barton–Bandis non-linear joint model for the modelling of the fault behaviour and linear elastic behaviour for the rock. An incremental-iterative in situ stress relaxation algorithm is implemented for the non-linear analysis of the faults. Both deformation and peak strength models of Barton–Bandis are incorporated for modelling the mechanical behaviour of the fault. The non-linear deformation of fault considers the effects of coupling between shear and normal stresses and displacement, joint closure, joint separation, hardening followed by post-peak or residual behaviour. The peak strength model employs a mobilized non-linear shear strength envelope. The differences between linear and non-linear simulation of the fault models are discussed. A comparison of model predictions with the classical Mohr–Coulomb peak strength model with constant joint stiffness is presented. The numerical model is used for a case study of Canadian hard rock underground mine. The shear and normal displacements along the fault during four mining sequences with backfill simulation are presented and discussed.

Representation of normal slant faults in a 2D burial history model

ABSTRACTA discussion is given of the impact of normal slant faults on basinal structure, compaction, fluid overpressure development, and thermal effects in sedimentary basins. Faults which are hydraulically closed or open to fluid flow are examined in a dynamical two‐dimensional fluid/ flow compaction model.From this numerical investigation three dominant factors characterize the effects of single and multiple faults with open or closed hydraulic behaviours: (i) there is a difference in excess pressure for fault planes with open or shut hydraulic conditions, but the neighbourhood where the effect of the fault is dominant is fairly localized (to within about half a kilometre or so laterally from the fault plane); (ii) the lateral and vertical motion of sediments between faulted blocks induces a thermal difference prior to, during, and post‐faulting, which can play a role in influencing hydrocarbon generation, migration, and accumulation; (iii) porosity retention and permeability modification by fault development could influence hydrocarbon exploration decisions regarding sealing, migration pathways, and fluid retention.The general patterns of slant fault effects described here should prevail in most geological situations, because the numerical experiments are designed to illuminate sharply the dominant response characteristics within the framework of simplified situations.