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This paper presents an approach to modelling fracture networks in hot dry rock geothermal reservoirs. A detailed understanding of the fracture network within a geothermal reservoir is critically important for assessments of reservoir potential and optimal production design. One important step in fracture network modelling is to estimate the fracture density and the fracture geometries, particularly the size and orientation of fractures. As fracture networks in these reservoirs can never be directly observed there is significant uncertainty about their true nature and the only feasible approach to modelling is a stochastic one. We propose a global optimization approach using simulated annealing which is an extension of our previous work. The fracture model consists of a number of individual fractures represented by ellipses passing through the micro-seismic points detected during the fracture stimulation process, i.e. the fracture model is conditioned on the seismic points. The distances of the seismic points from fitted fracture planes (ellipses) are, therefore, important in assessing the goodness-of-fit of the model. Our aims in the proposed approach are to formulate an appropriate objective function for the optimal fitting of a set of fracture planes to the micro-seismic data and to derive an efficient modification scheme to update the model parameters. The proposed objective function consists of three components: orthogonal projection distances of the seismic points from the nearest fitted fractures, the amount of fracturing (fitted fracture areas) and the volumes of the convex hull of the associated points of fitted fractures. The functions used in the model update scheme allow the model to achieve an acceptable fit to the points and to converge to acceptable fitted fracture sizes. These functions include two groups of proposals: one for updating fracture parameters and the other for determining the size of the fracture network. To increase the efficiency of the optimization, a spatial clustering approach, the Distance-Directional Transform, was developed to generate parameters for newly proposed fractures. A simulated dataset was used as an example to evaluate our approach and we compared the results to those derived using our previously published algorithm on a real dataset from the Habanero geothermal field in the Cooper Basin, South Australia. In a real application, such as the Habanero dataset, it is difficult to determine definitively which algorithm performs better due to the many uncertainties but the number of association points, the number of final fractures and the error are three important factors that quantify the effectiveness of our algorithm. [ABSTRACT FROM AUTHOR]

Fracture network modelling plays an important role in many application areas in which the behaviour of a rock mass is of interest. These areas include mining, civil, petroleum, water and environmental engineering and geothermal systems modelling. The aim is to model the fractured rock to assess fluid flow or the stability of rock blocks. One important step in fracture network modelling is to estimate the number of fractures and the properties of individual fractures such as their size and orientation. Due to the lack of data and the complexity of the problem, there are significant uncertainties associated with fracture network modelling in practice. Our primary interest is the modelling of fracture networks in geothermal systems and, in this paper, we propose a general stochastic approach to fracture network modelling for this application. We focus on using the seismic point cloud detected during the fracture stimulation of a hot dry rock reservoir to create an enhanced geothermal system; these seismic points are the conditioning data in the modelling process. The seismic points can be used to estimate the geographical extent of the reservoir, the amount of fracturing and the detailed geometries of fractures within the reservoir. The objective is to determine a fracture model from the conditioning data by minimizing the sum of the distances of the points from the fitted fracture model. Fractures are represented as line segments connecting two points in two-dimensional applications or as ellipses in three-dimensional (3D) cases. The novelty of our model is twofold: (1) it comprises a comprehensive fracture modification scheme based on simulated annealing and (2) it introduces new spatial approaches, a goodness-of-fit measure for the fitted fracture model, a measure for fracture similarity and a clustering technique for proposing a locally optimal solution for fracture parameters. We use a simulated dataset to demonstrate the application of the proposed approach followed by a real 3D case study of the Habanero reservoir in the Cooper Basin, Australia. [ABSTRACT FROM AUTHOR]

Abstract: The purpose of this paper is to present a new method to solve the linear integro-differential equations using radial basis function (RBF) networks. The approximate solution is represented by means of RBFs, whose coefficients are computed by training a RBF network, and is written as a sum of two parts. The first part employs a growing RBF network, whose parameters are adjusted to minimize an appropriate error function, and are constructed so as not to effect the supplementary conditions of the equations. The second part only satisfies the supplementary conditions. Numerical examples are given to demonstrate the proposed idea and method. [Copyright &y& Elsevier]

Abstract: The purpose of this paper is to present a new method based on radial basis functions (RBFs) and iterative procedure for the solution of linear integral equations of Fredholm and Volterra types of the second kind. To obtain a primary approximate solution, the collocation method with a small number of nodes, based on the RBFs and their first-order derivatives, can be adapted. Moreover, we present an iterative procedure from the integral equation to improve the accuracy of solution. Numerical examples show that our approach has the potentiality to become an efficient method. [Copyright &y& Elsevier]

Abstract: In this paper, a new method using radial basis function (RBF) networks is presented for solving the linear second kind integral equations of Fredholm and Volterra types. This method employs a growing neural network as the approximate solution of the integral equations, whose the activation functions are RBFs. The parameters (weights, centers and widths) of the approximate solution are adjusted by using an unconstrained optimization problem. Numerical results show that our method has the potentiality to become an efficient approach for solving integral equations. [Copyright &y& Elsevier]

Abstract: In this paper, a novel learning strategy for radial basis function networks (RBFN) is proposed. By adjusting the parameters of the hidden layer, including the RBF centers and widths, the weights of the output layer are adapted by local optimization methods. A new local optimization algorithm based on a combination of the gradient and Newton methods is introduced. The efficiency of some local optimization methods to update the weights of RBFN is studied in solving systems of nonlinear integral equations. [Copyright &y& Elsevier]