During both transient stress periods the desired

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Unformatted text preview: be turned back on if the head in the well subsequently rises sufficiently. In this variation of the previous test, heads were simulated for two one-year (365-day) transient stress periods. During the first transient stress period, the three nearby wells were set at 31 discharge rates equal to -4,000 ft3/d each, and during the second transient stress period, these three wells were shut off so that heads would recover. During both transient stress periods, the desired discharge from the multi-node well was set equal to -7,800 ft3/d. Both transient stress periods were simulated using 15 time steps and a time-step multiplier of 1.2. The results (fig. 33) show that the simulated net discharge from the multi-node well was reduced relative to the desired discharge during every time step, until it was reduced to zero during the 12th time step when the head in the well dropped below the value yielding a lift greater than the maximum lift for this pump (in this case, a head in the well of -23.75 ft for a lift of 33.75 ft). During the first time step of the second transient stress period, when the three additional nearby wells were shut off, the heads recovered sufficiently quickly such that the pump in the multi-node well was reactivated. The computed net discharge continued to increase as the water levels rose in response to shutting off the three nearby wells. These two tests indicate that the pump-capacity relations work as expected. Additional tests indicated that, under some circumstances, oscillatory behavior or nonconvergence occurred, but these problems could be eliminated or minimized by adjusting numerical parameters or time-step size. Again, the use of pump-capacity relations is optional, and the user can deactivate it during any one or all stress periods. Horizontal and Slanted Wells Most of the methods and literature about computing water levels in wells represented in numerical models assume that the wells are vertical. Although this is usually the case, the construction and use of horizontal wells is becoming more common, and horizontal wells at depth require slanted (directional) drilling at shallower depths. Halford and Hanson Figure 32. Plot showing results of applying the pumpcapacity relations to the modified Reilly problem in which the desired discharge equals -7,800 cubic feet per day for a 300-day transient stress period. When the head in the well equals or exceeds -3.65 feet, the lift is equivalent to that for the maximum discharge of the pump. 32 Revised Multi-Node Well (MNW2) Package for MODFLOW Ground-Water Flow Model (2002, p. 9) state that for horizontal wells equation 15 “is not a good estimator of cell-to-well conductance (CWC). Suitable equations for estimating CWC of horizontal wells are not well defined.” This is also true for slanted wells or slanted sections of wells. Thus, Halford and Hanson (2002, p. 9) recommend that the user “experiment with defining CWC external to MODFLOW and directly specifying appropriate CWC values in the MNW Package input.” This approach, though still valid, may create additional work for the user without a clear and objective path to completion. Therefore, MNW2 offers the user an alternate approach for a nonvertical well, in which the model will calculate the appropriate value of CWC on the basis of user-defined well characteristics. These calculations are performed automatically by MNW2 whenever a nonvertical section of open interval is detected for which LOSSTYPE equals THIEM, SKIN, or GENERAL. As background to our approach, several aspects of hydraulic properties used in a numerical model such as MODFLOW are noted. First, certain hydraulic properties, such as hydraulic conductivity and transmissivity, have effective values that are directionally dependent. Mathematically, these parameters can be characterized as tensors. In three-dimensional space, a tensor is characterized by three orthogonal principal values. In MODFLOW, it is inherently assumed that the three principal directions of the hydraulic conductivity tensor are aligned with the three coordinate axes. The directional properties of a tensor quantity can be represented by an ellipsoid in which the lengths of the semiaxes are directly proportional to the square roots of the principal values of the tensor. Thus, the effective value of the parameter in any direction can be resolved in terms of the equation describing an ellipsoid. Voss and Provost (2002) provide a detailed example of these relations for the dispersion tensor. The cell-to-well conductance term (CWC) (L2/T) is analogous to the conductance of a streambed, which is proportional to the length of the streambed within a finite-difference cell, as defined in the Streamflow Routing Package (Prudic, 1989). Finite-difference discretization requires an assumption that a borehole is linear between sequential nodes in a multi-node well. The length of a borehole within a finite-difference cell is constrained by the dimensions of the cell, as determined by the local grid spacing, which can be represented as Δx, Δy, and Δz for the grid spacing in the row,...
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