Chaoshui Xu

A new computer code for discrete fracture network modelling

The authors describe a comprehensive software package for two- and three-dimensional stochastic rock fracture simulation using marked point processes. Fracture locations can be modelled by a Poisson, a non-homogeneous, a cluster or a Cox point process; fracture geometries and properties are modelled by their respective probability distributions. Virtual sampling tools such as plane, window and scanline sampling are included in the software together with a comprehensive set of statistical tools including histogram analysis, probability plots, rose diagrams and hemispherical projections. The paper describes in detail the theoretical basis of the implementation and provides a case study in rock fracture modelling to demonstrate the application of the software.

The cracked chevron notched Brazilian disc test- geometrical considerations for practical rock fracture toughness measurement

The two chevron notched rock fracture specimens, CB and SR, recommended by the ISRM to determine rock Mode I fracture toughness have several disadvantages, such as low loads required to initiate failure, relatively large amounts of intact rock core are required at the correct orientation, complicated loading fixtures and complex sample preparation for SR specimens. The Cracked Chevron Notched Brazilian Disc (CCNBD, Fig. 1.c) and the Cracked Straight Through Brazilian Disc (CSTBD, Fig.l.b) specimen geometries overcome these problems and are suitable for mixed fracture mode testing at the same time. The general case for the cracked Brazilian disc problem is when the sample is loaded diametrically with the crack inclined at an angle 0 to the loading direction (Fig. 1.a). Different combinations of mode I and mode II fracture intensities can be obtained simply by changing this angle.

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 flexible true plurigaussian code for spatial facies simulations

The current forms of plurigaussian simulation have serious limitations for applications to large numbers of geological facies, or units, which have complex contact relations. In this paper the authors present a true plurigaussian simulation (PGS) method, which can be applied in a simple way to any number of geological facies by using any number of Gaussians. A recursive technique is used for multi-dimensional integration of the Gaussian functions, which forms the major part of the PGS computation. A binary, dynamic contact matrix (DCM) is used to specify the contact relations among the facies; this method has proved to be simple, flexible and capable of dealing with general, complex contact relations. A method for incorporating into PGS multivariate correlations among any number of random variables is also included. A simulated example is used to demonstrate the application of the generalised PGS. This example shows that PGS is more robust to under-sampling than traditional direct indicator simulation.

Fluid Flow and Heat Transfer Within a Single Horizontal Fracture in an Enhanced Geothermal System

We present an analysis of fluid flow and heat transfer through a single horizontal channel with permeable walls which are at different temperatures. The problem is set in the context of hot dry rock geothermal energy extraction where water, introduced through an injection well, passes through a horizontal fracture by which transfer of heat is facilitated through advection of the fluid flowing toward the recovery well. We consider the walls of the fracture to have properties of a permeable medium and we study the effect of slip boundary conditions on velocity and temperature profiles for low Reynolds number (< 7) based on a similarity solution and perturbation expansion. We show that the velocity and heat transfer profiles are altered with the channel width, the permeability and a slip coefficient α, which is a dimensionless constant related to the inherent properties of the channel.

A Simplified Failure Criterion for Intact Rocks Based on Rock Type and Uniaxial Compressive Strength

The uniaxial compressive strength (UCS) of intact rock, which can be estimated using relatively straightforward and cost-effective techniques, is one of the most practical rock properties used in rock engineering. Thus, constitutive laws to represent the strength and behavior of (intact) rock frequently use it, along with additional intrinsic rock properties. Although triaxial tests can be employed to obtain best-fit failure criterion parameters that provide best strength predictions, they are more expensive and require time-consuming procedures; as a consequence, they are often not readily available at early stages of a project. Based on the analysis of an extensive triaxial test database for intact rocks, we propose a simplified empirical failure criterion in which rock strength at failure is expressed in terms of confining stress and UCS, with a new parameter which can be directly estimated from the UCS for a specified rock type in the absence of triaxial test data. Performance of the proposed failure criterion is then tested for validation against experimental data for eight rock types. The results show that strengths of intact rock estimated by the proposed failure criterion are in good agreement with experimental test data, with small discrepancies between estimated and measurements strengths. Therefore, the proposed criterion can be useful for preliminary (triaxial) strength estimation of intact rocks when triaxial tests data are not available.

Optimisation of a stochastic rock fracture model using Markov Chain Monte Carlo simulation

Abstract The characterisation of rock fracture networks is an important component of rock engineering applications involving stability assessment or fluid flow analysis. However, the derivation of a reliable rock fracture model remains a very challenging problem in practice. This paper describes a Bayesian framework, in the form of Markov Chain Monte Carlo (MCMC) simulation, for the construction of such a model. Model conditioning using different data sources is discussed including seismic events recorded during hydraulic fracture stimulation, rock face fracture mapping data and downhole geophysical survey data. The freeware FracSim3D is used for the simulations.

A Spatial Clustering Approach for Stochastic Fracture Network Modelling

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 assessxa0fluid 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 forxa0 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.

Stochastic Fracture Propagation Modelling for Enhanced Geothermal Systems

Fractures and fracture networks are the fundamental components of enhanced geothermal systems and determine their technical and economic viability. A realistic fracture model that can adequately describe a fracture-stimulated reservoir is critical for subsequent flow and heat transfer analyses of the system. Fractures in these systems are essentially the product of hydraulic stimulations of the reservoir that, together with ground conditions and the local stress regime, determine how fractures are formed and propagated. This paper describes three methods for generating realistic fracture models for enhanced geothermal systems; two of them incorporate the fracture propagation process in the modelling and hence provide a stochastic fracture propagation model. The methods are: a Bayesian framework in the form of Markov Chain Monte Carlo simulation, an extended Random Sampling Consensus model and a Point and Surface Association Consensus model. The conditioning data used in these methods are seismic events recorded during fracture stimulation. Geodynamics’ Habanero reservoir in the Cooper Basin of South Australia is used as a case study to test these methods.

The RANSAC Method for Generating Fracture Networks from Micro-seismic Event Data

Fracture network modeling is an essential part of the design, development and performance assessment of Enhanced Geothermal Systems. These systems are created from geothermal resources, usually located several kilometers below the surface of the Earth, by establishing a network of connected fractures through which fluid can flow. The depth of the reservoir makes it impossible to make direct measurements of fractures and data are collected from indirect measurements such as geophysical surveys. An important source of indirect data is the seismic event point cloud generated by the fracture stimulation process. Locations of these points are estimated from recorded micro-seismic signals generated by fracture initiation, propagation and slip. This point cloud can be expressed as a set of three-dimensional coordinates with attributes, for example Seijk={(x,y,z);u2009a|x,y,z∈R,u2009a∈I}. We describe two methods for reconstructing realistic fracture trace lines and planes given the point cloud of seismic events data: Enhanced Brute-Force Search and RANSAC. The methods have been tested on a synthetic data set and on the Habanero data set of Geodynamics’ geothermal project in the Cooper Basin of South Australia. Our results show that the RANSAC method is an efficient and suitable method for the conditional simulation of fracture networks.