Because lw y if the horizontal well passes through

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Unformatted text preview: appropriate parameters for b, bw, Kh, and Ky, yields (28) , and . As noted in figure 35, it is common that Δz will be much smaller than Δx or Δy. The linear well-loss coefficient (B), as described for a vertical well by equation 10, is examined next. Start by (29) (30) where By is the linear well-loss coefficient for the case of a horizontal well oriented in the y-direction, and Lw is the length of the horizontal well in the cell. Because Lw = Δy if the horizontal well passes through the entire length of the cell, equation 30 can be further reduced to . (31) 34 Revised Multi-Node Well (MNW2) Package for MODFLOW Ground-Water Flow Model Similarly, the linear well-loss coefficient for the case of a horizontal well oriented in the x-direction can be computed from . (32) The nonlinear well-loss coefficient (C) and related power term (P) do not explicitly depend on well or aquifer parameters, but are typically derived from certain types of well tests. Thus, given the estimates derived from field tests, no additional adjustments are needed to account for the well being horizontal. Equations 8, 10, 26, 28, 31, and 32 provide the means to compute CWC for each of three coordinate directions (recalling that no partial penetration corrections are made for nonvertical wells). The cell-to-well conductance per unit length in each principal direction can be represented by CLi, where i is the index for the x-, y-, and z- directions. CLi values for wells oriented in the three principal directions can be calculated from a modified version of equation 15: , (33) where i is the principal direction aligned with the well, j and k are the two orthogonal principal directions, Δxi represents Δx, Δy, or Δz depending on the orientation of i, and Lwi represents the length of a hypothetical fully-penetrating well aligned with the principal direction. The values of , , and constitute the semiaxes of the ellipsoid. Then, knowing the direction of the well’s orientation, the ellipsoid can be used to compute the correct value of CL in that direction. Finally, knowing the length of the well (or well segment) in that direction, multiply CLi by Lw (the length of the well in the cell) to compute the value of CWC for the well (or well segment) having that orientation and length. It is possible that a multi-node well passing through a particular grid cell to which it is connected might change direction at the node (fig. 36) (in fact, direction changes can only occur at nodes). In this case, the value of CWC is computed for each of the two segments in the cell separately because CWC can vary as a function of the well orientation; the total CWC for that cell is taken as the sum of the two components. The total length of the well within the cell is the sum of the lengths of the two segments. It is assumed that the alignment and orientation of a nonvertical well are adequately described by the line connecting successive active nodes of the multi-node well. The slant (or tilt angle), orientation (direction or angle of well axis relative to the x-direction of the MODFLOW grid), and length of that section of the well are determined by MNW2 on the basis of geometric considerations. The orientation and alignment of a nonvertical well or well segment can be given in terms of two angles, θ and ω, which respectively define the angle in the horizontal plane that the trace of the well makes with the x-direction of the model grid and the slant (or tilt angle) of the borehole alignment in the vertical plane containing the well, measured as a deviation from the vertically downward direction (fig. 37). By this convention, for example, a horizontal well oriented parallel to the x-direction would have values of θ = 0° and ω = 90°. If a well changes orientation or dip along its length, these same conventions apply to each individual linear segment of a well between two nodes. Because multinode wells are always defined in terms of connected nodes of the MODFLOW grid, well segments are assumed to be linear between nodes (fig. 36). MNW2 will automatically calculate θ and ω, when appropriate, and the user does not have to specify these values. If a nonvertical well, as defined by associated grid nodes to which it is connected, passes through a cell not associated with the multi-node well, it is assumed that the part of the well casing that passes through the unconnected cell of the grid is a blank (unperforated) section of casing (fig. 38). Thus, this part of the well does not contribute to the calculated cell-to-well conductance, although it is considered part of the total length of the well. Note that information describing open and closed intervals of a multi-node well are included in certain output files. By analogy to the development of Voss and Provost (2002), the effective value of cell-to-well conductance per unit length of well (CL) for a well oriented at angles θ and ω is calculated from (34) (A.M. Provost, USGS, written commun., 2008). The value of CL is...
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This document was uploaded on 01/20/2014.

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