C. F. Tsang

A variable aperture fracture network model for flow and transport in fractured rocks

A three-dimensional variable aperture fracture network model for flow and transport in fractured rocks was developed. The model generates both the network of fractures and the variable aperture distribution of individual fractures in the network. Before solving for the flow and transport of the whole network, a library of single-fracture permeabilities and particle transport residence time spectra is first established. The spatially varying aperture field within an individual fracture plane is constructed by geostatistical methods. Then the flow pattern, the fracture transmissivity, and the residence times for transport of particles through each fracture are calculated. The library of transmissivities and frequency distributions of residence times is used for all fractures in the network by a random selection procedure. The solution of flow through the fracture network and the particle-tracking calculation of solute transport for the whole network are derived from one side of the network to the other. The model thus developed can handle flow and transport from the single-fracture scale to the multiple-fracture scale. The single-fracture part of the model is consistent with earlier laboratory tests and field observations. The multiple-fracture aspect of the model was verified in the constant aperture fracture limit with an earlier code. The simulated breakthrough curves obtained from the model display dispersion on two different scales as has been reported from field experiments.

Theoretical and field studies of coupled hydromechanical behaviour of fractured rocks—1. Development and verification of a numerical simulator

Abstract Analyses of hydromechanical behaviour of fractured rocks requires the use of numerical methods, such as the ROCMAS code developed at LBL. We have developed a new version of this simulator which uses mixed Newton-Raphson linearization within an incremental configuration. This code, that is named ROCMAS II, was verified against: (1) a semi-analytic solution; and (2) against its predecessor ROCMAS which uses a direct iteration linearization scheme. This new coupled phenomenological model has been used successfully in a validation study of a field experiment which is reported in Part 2 [Int. J. Rock Mech. Min. Sci. & Geomech. Abstr.29, 411–419 (1992)]. The verified ROCMAS II with its new feature such as an incremental set-up, the strain-softening and dilating shear, and hyperbolic closure joint model and the new linearization scheme, allows more realistic simulations of a host of rock mechanical problems in saturated rocks. Furthermore, the ROCMAS II set-up provides a basis upon which procedures for general treatment of various kinds of material non-linearity can be built.

Multiple‐Peak Response to Tracer Injection Tests in Single Fractures: A Numerical Study

Under certain conditions, when pulse tracer injection tests are performed in a single fracture with a regional flow field, the breakthrough curves may display multiple peaks. Furthermore, the shape of these curves may change when the injection flow rate is varied. In this paper the conditions under which the breakthrough curve may present multiple peaks and analyzed numerically using stochastically generated fractures. The dispersivities of these peaks are also calculated. It is found that the dispersivity is small for each of the peaks and that the dispersivities of the different peaks in a breakthrough curve are quite similar. The results presented in this paper may be equally applied to tracer tests in a two-dimensional strongly heterogeneous medium.

A perspective on the numerical solution of convection‐dominated transport problems: A price to pay for the easy way out

In a brief but fundamental review of the evolution of the conventional numerical techniques used in the solution of convection-dominated transport problems, we explore the difficulties that have been remedied to various degrees by various workers. In the course of this review we obtain the performance characteristic of the Crank-Nicolson Galerkin finite element method in the form of a curve in Peclet number and Courant number space. We show that the performance can be altered through a new upwind parameter that can easily be incorporated into many of the existing numerical solution methods. By providing an insight into the limitations of some of these methods we demonstrate, by means of numerical experiments, that the proposed upwinding procedure ensures acceptable solutions throughout the Pe-Cr space at a reasonable cost of the smearing effect.

Theoretical and field studies of coupled hydromechanical behaviour of fractured rocks—2. Field experiment and modelling

Abstract A series of water injection experiments were performed on four horizontal fractures intercepted by a borehole at the University of Lulea Rock Mechanics Laboratory site in Sweden. The fractures are located in a borehole section 80–350m in depth. Three types of injection tests were carried out: (1) constant-pressure injection tests, with pressures ranging from below to above the overburden pressure; (2) constant-flowrate injection tests; and (3) step pressure tests (hydraulic jacking test). In the former two cases, the results clearly depict the coupled effect of mechanical fracture-aperture opening due to increased hydraulic pressure, even in the pre-hydrofracturing regime. A parallel numerical study was carried out to simulate these injection tests using the computer code ROCMAS II [see Part 1, Int. J. Rocl Mech. Min. Sci. & Geomech. Abstr. 29 , 401–409 (1992)]. We were able to simulate closely the pre-hydrofracturing coupled effect in the step pressure and constant pressure test. The success in this attempt validates the soundness of the conceptualized constitute relations governing the coupled hydromechanical behaviour of rock masses. The results also point out a potential methodology of using a joint field and theoretical study of fracture hydromechanical responses to extract key characterizing parameters of the rock and fractures.

Streamline upwind/full Galerkin method for solution of convection dominated solute transport problems

A new streamline method for the solution of convection-dominated transport problems is introduced. First, an analysis is made of the nature of classic streamline upwinding from the perspective of space and spacetime solution domains, as they pertain to the nature of the problems. From this analysis emerges a rigorous logic for upwinding, which can easily be implemented in the full (spacetime) Galerkin formulation of the transport equation. Comparative performance testing of this technique, in solving a number of examples, proves it to be robust and versatile. The advantage of this method resides in its applicability to a wider range of Courant numbers.