Application of Mathematical Models to Mine Water Inflow

Williams, Roy E. ; Winter, Gerry V. ; Bloomsburg, George L. ; Ralston, Dale R.
Organization: Society for Mining, Metallurgy & Exploration
Pages: 12
Publication Date: Jan 1, 1986
The literature on four different topics is re¬viewed herein for purposes of mathematical mod¬eling of mine water inflow. The first of the topics reviewed is modeling of fissured or fractured ma¬terials; the second is general Darcy based flow models; the third is field methods for determining fracture flow properties; and the fourth is methods used presently for determining mine water inflows. The four topics are considered in the foregoing order. FRACTURE FLOW MODEL Two basic types of fracture flow models have been developed. The first type uses various tech¬niques for space averaging to obtain the equations. Systems are considered in which the porous media properties vary smoothly enough and the fracturing is sufficiently profuse and well distributed that the locally averaged properties are meaningful when viewed on the macroscopic scale. The final result is that a coefficient is used which is similar to saturated hydraulic conductivity and in many cases, simply is hydraulic conductivity. In other cases, the coefficient is apparent hydraulic conductivity be¬cause the response from flow in the fractures is more rapid than flow in the pore spaces. Faust and Mercer (1980) refers to this method as the contin¬uum approach. Some of the papers on this type of problem are by Duguid (1973), Verner et al. (1974), Owili-Eger (1975), Duguid and Abel (1974), duPrey and Weill (1974), and O'Neill (1978). Duguid and Lee (1977) also considered heat flow in the fluid and the porous medium. These papers all result in various types of computer programs. Some papers on this topic that do not result in computer programs are by Snow (1968, 1969) and Streltsova (1976). Some of the foregoing articles consider con¬solidation of the porous media and the resulting effect on hydraulic conductivity. Barenblatt et al. (1960) developed an analytical solution for fracture flow and discussed the time that is involved in the drainage process and the effect that fracture flow has on the drainage time. The second type of fracture flow model con¬siders the width of the fractures as a function of the pressure in the field. Faust and Mercer (1980) refers to this method as the discontinuum approach. This approach often requires two finite element programs that consider the stress in the material and the flow in the fractures separately. The pro¬grams are then linked to arrive at the final solution. Some of the articles that consider the interrela¬tionship between pressure and the size of the frac¬ture but do not use computer solutions are Gringarten et al. (1975), Narasimhan and Palen (1979), and Witherspoon et al. (1979). Papers that use a linked computer program between stress and flow are by Ayatollahi (1978), Gale et al. (1974), and Noorishad et al. (1971). Ayatollahi's program is primarily for the petroleum industry because it does not consider the effect of gravity. Ayatollahi assumes that pressure effects are very large in com¬parison to gravity effects. This assumption would apply only to very deep aquifers. Articles that consider fracture flow on a more applied basis are by Wittke et al. (1972), who con¬siders that the flow is entirely through fissures and negligible through the pores of the rock. Gringarten and Witherspoon (1972) developed type curves that may be used for analysis of fracture flow systems; the curves are based on the assumption that it is possible to distinguish between aquifers with hor¬izontal and vertical fractures and that it is possible to analyze the system as an equivalent anisotropic homogeneous porous medium with a single fracture with much higher permeability. DARCY FLOW MODELS The Darcy flow models of greatest interest to mine water inflow prediction are those which allow
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