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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 wellloss coefficient (B), as described for
a vertical well by equation 10, is examined next. Start by (29) (30) where By is the linear wellloss coefficient for the case of
a horizontal well oriented in the ydirection, 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 MultiNode Well (MNW2) Package for MODFLOW GroundWater Flow Model Similarly, the linear wellloss coefficient for the case of
a horizontal well oriented in the xdirection can be computed
from . (32) The nonlinear wellloss 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 celltowell 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 fullypenetrating 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 multinode 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 multinode well. The slant (or
tilt angle), orientation (direction or angle of well axis relative
to the xdirection 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
xdirection 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 xdirection 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 multinode 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 celltowell conductance, although it is considered part of the total length of the
well. Note that information describing open and closed intervals
of a multinode well are included in certain output files.
By analogy to the development of Voss and Provost
(2002), the effective value of celltowell 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.
 Winter '14

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