Characterization and Simulation of Discrete Fracture Networks in Unconventional Shale Reservoirs

Fracture characterization and simulation of complex fracture networks are investigated with the emphasis on better and faster approaches to generate fractures by conforming to available data resources, and on accurate, robust, and efficient techniques to grid and discretize complex fracture networks. Three fracture characterization techniques such as fractal-based, microseismic-constrained, and outcrop-based are presented. Natural fractures are generated either stochastically from fractal-based theory, or constrained by microseismic information, or from outcrop maps. Hydraulic fractures are computed from a fast proxy model for fracture propagation that incooperates material balance and lab-measured conductivity data. Then, optimization-based unstructured gridding and discretization technique is developed to handle complex fracture networks with extensively fracture clustering, nonorthogonal and low-angle fracture intersections, and nonuniform fracture aperture distributions. Moreover, through fracture simulation, sensitivity analysis of natural fracture related parameters, nonuniform fracture aperture, and unstructured gridding related parameters on well production performance are investigated, which are followed by well testing behaviors and CO2 EOR of complex fracture networks. This work presents an integrated workflow to model discrete fractures in unconventional shale reservoirs, together with detailed illustrations of each critical component using both synthetic and field application examples

Interval simplex splines for scientific databases

Thesis (Ph. D.)--Massachusetts Institute of Technology, Dept. of Ocean Engineering, 1995.Includes bibliographical references (p. 130-138).by Jingfang Zhou.Ph.D

Characterization and Simulation of Discrete Fracture Networks in Unconventional Shale Reservoirs

Fracture characterization and simulation of complex fracture networks are investigated with the emphasis on better and faster approaches to generate fractures by conforming to available data resources, and on accurate, robust, and efficient techniques to grid and discretize complex fracture networks. Three fracture characterization techniques such as fractal-based, microseismic-constrained, and outcrop-based are presented. Natural fractures are generated either stochastically from fractal-based theory, or constrained by microseismic information, or from outcrop maps. Hydraulic fractures are computed from a fast proxy model for fracture propagation that incooperates material balance and lab-measured conductivity data. Then, optimization-based unstructured gridding and discretization technique is developed to handle complex fracture networks with extensively fracture clustering, nonorthogonal and low-angle fracture intersections, and nonuniform fracture aperture distributions. Moreover, through fracture simulation, sensitivity analysis of natural fracture related parameters, nonuniform fracture aperture, and unstructured gridding related parameters on well production performance are investigated, which are followed by well testing behaviors and CO2 EOR of complex fracture networks. This work presents an integrated workflow to model discrete fractures in unconventional shale reservoirs, together with detailed illustrations of each critical component using both synthetic and field application examples

Robust convex optimisation techniques for autonomous vehicle vision-based navigation

This thesis investigates new convex optimisation techniques for motion and pose estimation. Numerous computer vision problems can be formulated as optimisation problems. These optimisation problems are generally solved via linear techniques using the singular value decomposition or iterative methods under an L2 norm minimisation. Linear techniques have the advantage of offering a closed-form solution that is simple to implement. The quantity being minimised is, however, not geometrically or statistically meaningful. Conversely, L2 algorithms rely on iterative estimation, where a cost function is minimised using algorithms such as Levenberg-Marquardt, Gauss-Newton, gradient descent or conjugate gradient. The cost functions involved are geometrically interpretable and can statistically be optimal under an assumption of Gaussian noise. However, in addition to their sensitivity to initial conditions, these algorithms are often slow and bear a high probability of getting trapped in a local minimum or producing infeasible solutions, even for small noise levels. In light of the above, in this thesis we focus on developing new techniques for finding solutions via a convex optimisation framework that are globally optimal. Presently convex optimisation techniques in motion estimation have revealed enormous advantages. Indeed, convex optimisation ensures getting a global minimum, and the cost function is geometrically meaningful. Moreover, robust optimisation is a recent approach for optimisation under uncertain data. In recent years the need to cope with uncertain data has become especially acute, particularly where real-world applications are concerned. In such circumstances, robust optimisation aims to recover an optimal solution whose feasibility must be guaranteed for any realisation of the uncertain data. Although many researchers avoid uncertainty due to the added complexity in constructing a robust optimisation model and to lack of knowledge as to the nature of these uncertainties, and especially their propagation, in this thesis robust convex optimisation, while estimating the uncertainties at every step is investigated for the motion estimation problem. First, a solution using convex optimisation coupled to the recursive least squares (RLS) algorithm and the robust H filter is developed for motion estimation. In another solution, uncertainties and their propagation are incorporated in a robust L convex optimisation framework for monocular visual motion estimation. In this solution, robust least squares is combined with a second order cone program (SOCP). A technique to improve the accuracy and the robustness of the fundamental matrix is also investigated in this thesis. This technique uses the covariance intersection approach to fuse feature location uncertainties, which leads to more consistent motion estimates. Loop-closure detection is crucial in improving the robustness of navigation algorithms. In practice, after long navigation in an unknown environment, detecting that a vehicle is in a location it has previously visited gives the opportunity to increase the accuracy and consistency of the estimate. In this context, we have developed an efficient appearance-based method for visual loop-closure detection based on the combination of a Gaussian mixture model with the KD-tree data structure. Deploying this technique for loop-closure detection, a robust L convex posegraph optimisation solution for unmanned aerial vehicle (UAVs) monocular motion estimation is introduced as well. In the literature, most proposed solutions formulate the pose-graph optimisation as a least-squares problem by minimising a cost function using iterative methods. In this work, robust convex optimisation under the L norm is adopted, which efficiently corrects the UAV’s pose after loop-closure detection. To round out the work in this thesis, a system for cooperative monocular visual motion estimation with multiple aerial vehicles is proposed. The cooperative motion estimation employs state-of-the-art approaches for optimisation, individual motion estimation and registration. Three-view geometry algorithms in a convex optimisation framework are deployed on board the monocular vision system for each vehicle. In addition, vehicle-to-vehicle relative pose estimation is performed with a novel robust registration solution in a global optimisation framework. In parallel, and as a complementary solution for the relative pose, a robust non-linear H solution is designed as well to fuse measurements from the UAVs’ on-board inertial sensors with the visual estimates. The suggested contributions have been exhaustively evaluated over a number of real-image data experiments in the laboratory using monocular vision systems and range imaging devices. In this thesis, we propose several solutions towards the goal of robust visual motion estimation using convex optimisation. We show that the convex optimisation framework may be extended to include uncertainty information, to achieve robust and optimal solutions. We observed that convex optimisation is a practical and very appealing alternative to linear techniques and iterative methods

Numerical solution of static and dynamic problems of imprecisely defined structural systems

Static and dynamic problems with deterministic structural parameters are well studied. In this regard, good number of investigations have been done by many authors. Usually, structural analysis depends upon the system parameters such as mass, geometry, material properties, external loads and boundary conditions which are defined exactly or considered as deterministic. But, rather than the deterministic or exact values we may have only the vague, imprecise and incomplete informations about the variables and parameters being a result of errors in measurements, observations, experiments, applying different operating conditions or it may be due to maintenance induced errors, etc. which are uncertain in nature. Hence, it is an important issue to model these types of uncertainties. Basically these may be modelled through a probabilistic, interval or fuzzy approach. Unfortunately, probabilistic methods may not be able to deliver reliable results at the required precision without sufficient experimental data. It may be due to the probability density functions involved in it. As such, in recent decades, interval analysis and fuzzy theory are becoming powerful tools. In these approaches, the uncertain variables and parameters are represented by interval and fuzzy numbers, vectors or matrices.In general, structural problems for uncertain static analysis with interval or fuzzy parameters simplify to interval or fuzzy system of linear equations whereas interval or fuzzy eigenvalue problem may be obtained for the dynamic analysis. Accordingly, this thesis develops new methods for finding the solution of fuzzy and interval system of linear equations and eigenvalue problems. Various methods based on fuzzy centre, radius, addition, subtraction, linear programming approach and double parametric form of fuzzy numbers have been proposed for the solution of system of linear equations with fuzzy parameters. An algorithm based on fuzzy centre has been proposed for solving the generalized fuzzy eigenvalue problem. Moreover, a fuzzy based iterative scheme with Taylor series expansion has been developed for the identification of structural parameters from uncertain dynamic data. Also, dynamic responses of fractionally damped discrete and continuous structural systems with crisp and fuzzy initial conditions have been obtained using homotopy perturbation method based on the proposed double parametric form of fuzzy numbers. Numerical examples and application problems are solved to demonstrate the efficiency and capabilities of the developed methods. In this regard, imprecisely defined structures such as bar, beam, truss, simplified bridge, rectangular sheet with fuzzy/interval material and geometric properties along with uncertain external forces have been considered for the static analysis. Fuzzy and interval finite element method have been applied to obtain the uncertain static responses. Structural problems viz. multistorey shear building, spring mass mechanical system and stepped beam structures with uncertain structural parameters have been considered for dynamic analysis. In the identification problem, column stiffnesses of a multistorey frame structure have been identified using uncertain dynamic data based on the proposed algorithm. In order to get the dynamic responses, a single degree of freedom fractionally damped spring-mass mechanical system and fractionally damped viscoelastic continuous beam with crisp and fuzzy initial conditions are also investigated.Obtained results are compared in special cases for the validation of proposed methods