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|The purpose of this section is to demonstrate the development of a method that we believe can be used for simulating and predicting mine water inflow. It will also show how important it is for personnel who model mine water inflow to have considerable experience with this subject, and with the conversion of hydrogeologic frameworks to conceptual models. Several of the models described previously are said to be three dimensional. However, closer examination reveals that there is considerable limitation in the variation possible in the third dimension. A true three-dimensional analysis would require a very large program. Therefore, it seems more reasonable to develop a procedure by which information from a two-dimensional model can be used for analysis of a three-dimensional problem. For a vertical mine shaft this is relatively easy because most two-dimensional models have an option for axisymmetric flow. If it can be assumed that axisymmetry exists about the centerline of the shaft it can be modeled easily as has been illustrated previously. For a horizontal drift or tunnel the analysis is not nearly as straightforward. However, the flow can be divided into two parts as indicated in Fig. 59. Part 1 considers the flow into the side of the drift while part 2 considers the flow into the end of the drift. To calculate the flow rate into the entire drift from the unsteady flow into a unit length the instantaneous flow per unit length may be integrated over the total length of the shaft. This procedure is shown in Fig. 60. The radial flow through any incremental length of the shaft is q. The total flow rate, Q, into the drift at any particular time is given by: The discharge q is a function of the time during which a particular segment has been draining that is dependent on the location x. In other words, a location at x = 0 has been draining during the entire time of expansion while a segment at x = L has only started to drain. Therefore, the time of draining at any point, x, is given by: [ ] where t' is the time over which the mine has been expanded. To determine the relationship between q and t it is necessary to refer to Polubarinova- Kochina (1962, pp. 566-569) and the equation given for the unsteady flow problem. This is: [ ] where q is the steady flow, q,, q, are the coefficients, and t is the time since drainage began. The expressions for q0, q1, and q2 are given as:|