Unconfined Flow Through Jointed Rock1

Abstract

The two‐dimensional, steady‐state, unconfined flow of a homogeneous fluid through jointed rock is studied for both laminar and turbulent conditions by use of a method which is based on previously developed theoretical and experimental flow relationships. However, only the independent unknowns are selected in order to reduce the complexity of the problem and render it more readily tractable. The intact rock is assumed to be impermeable, and two intersecting systems of plane, parallel joints are used in the mathematical model, taking into account the surface roughness of the joints. The mathematical solution of the resulting nonlinear (due to turbulent flow in some joints) system of equations is obtained by use of a rapidly converging iterative procedure, wherein each iteration takes special advantage of the banded nature of the associated matrix. For the particular case where a free surface exists, the general flow equations are not satisfied, because some of the joints in the vicinity of the free surface do not flow full; therefore, new equations must be established to handle this condition. Once the development of the mathematical model is accomplished, several cases involving different geometric characteristics (width, orientation, and roughness of joints) are solved for a rectangular domain, and graphs are given to illustrate the influence of the various parameters on the manifested flow behavior.

Two‐phase flow in a variable aperture fracture

“…A much greater influence was felt from the implementation of trapping of nonwetting phase. Trapping conditions further reduced penetrating phase relative permeability and saturation for a given capillary pressure; however, with trapping conditions the relationships are plane is to characterize the fracture as a single pair of parallel plates [Castillo et al, 1972;Wollroth and Zielke, 1990] Capillary pressure at a fluid-fluid interface within a fracture may be expressed analytically. This is not feasible for interfaces in porous medium domains because of the complex nature of a fluid-fluid interface in a three-dimensional porous medium.…”

Stochastic Analysis of Groundwater Flow and Contaminant Transport in a fractured Rock System

“…The assumption that hydraulic conductivity is independent of stress is necessary to reduce the computational effort in the Monte Carlo simulations to a manageable level. Our method is very similar to that used by Castillo et al [1] except that a direct, rather than an iterative, technique is used to solve the resulting system of equations. Assigning values for hydraulic conductivity between nodes and using known values of the hydraulic head at the nodes, a seepage velocity is calculated for the fracture segment, using the Darcy equation.…”

“…The fracture networks we consider are much more general than those constructed by Castillo et al [1,2]. In addition, individual fractures are not continuous within their own plane.…”

“…The most important existing work is that of Castillo et al [1,2] and Krizek et al [3], who discuss the results of simulation and experimental studies designed to identify how features of the fracture geometry control the spread of contaminants. However, because their models involved an oversimplified geometry, with individual fractures that were either continuous through the region or unrealistically long, the applicability of these results is somewhat limited [4].…”

Geohydrological Properties of Tectonic Zones in Hard Rocks Obtained from Artificial Recharge Tests and Numerical Modeling

“…The next step towards a more accurate treatment of groundwater flow in fractured rock is to consider more than one set of fractures. Castillo, Karadi and Krizek (1972) have solved a problem involving a two-dimensional, unconfined flow in a medium with two crossing sets of joints. An even more sophisticated description of reality can be obtained when a porous medium with open fractures is considered.…”