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Unformatted text preview: pecified in the MODFLOW discretization and internalflow
packages [BlockCentered Flow (BCF), LayerProperty Flow
(LPF), or HydrogeologicUnit Flow (HUF) Packages].
The linear wellloss coefficient (B) collectively defines
head loss from flow through formation damaged during well
drilling, the gravel pack (representing a possible increased
hydraulic conductivity relative to the aquifer), and the well
screen. The geometry of the problem and some of the relevant terminology are illustrated in figure 2. The coefficient B
can be used directly to define head loss or it can be recast in
terms of a dimensionless skin coefficient (Skin), as defined by
Earlougher (1977) and Halford and Hanson (2002). The skin
coefficient represents a zone of affected hydraulic properties
close to the wellbore or well screen. The value of Skin for a
model cell depends on the hydraulic conductivity of the skin,
the length of the borehole, and the thickness of the skin (which
equals rSKIN  rw), among other factors, as
, (9) where b is the saturated thickness of the cell (L), bw is the
saturated (or active) length of the borehole in the cell (bw = b where Δx is the grid spacing in the x (column) direction, and
Δy is the grid spacing in the y (row) direction. If the grid is
square, then this is simplified to
(6)
However, if the porous medium is anisotropic, then the
directional hydraulic conductivities must be considered, and
Peaceman (1983) indicates that, in this general case, ro is
given by , (7) where Kx and Ky are the values of hydraulic conductivity in
the x and ydirections. The definition of ro given in equation 7
is used in MNW2.
For general anisotropic conditions, transmissivity (T) can
be written
, where b is the saturated thickness of the
cell (L). The constant term
in equation 4
is the aquiferloss coefficient (A) for a vertical well, which can
be written for anisotropic conditions as Figure 2. Schematic horizontal cross section (plan view) through
a vertical well in a finitedifference cell showing some of the
factors affecting computed well loss. K is hydraulic conductivity
and r is radius. 6 Revised MultiNode Well (MNW2) Package for MODFLOW GroundWater Flow Model for a fully penetrating vertical well), and Kh is the effective
horizontal hydraulic conductivity of the cell (L/T) when horizontal anisotropy is present, wherein
.
The skin effect can be pictured as flow occurring across
a cylinder having a hydraulic conductance that differs from
(and is typically less than) the hydraulic conductance of the
media comprising the finitedifference cell in which the well is
located. The value of Skin would be negative if KSKIN is larger
than Kh. Halford and Hanson (2002) relate the coefficient B to
Skin as
. terms into the celltowell conductance term. The flow to the
nth node of the multinode well is thus defined by the head
difference between the cell and the well times a celltowell
hydraulic conductance as
(12)
where CWCn is the nth celltowell hydraulic conductance
(L2/T). After substituting the right side of equation 2 for the
term in parentheses, equation 12 can be rewritten to solve for
CWCn as (10) The user has the option of directly specifying a value of
B (by setting input parameter LOSSTYPE in dataset 2b equal
to “GENERAL”) or specifying the characteristics of the skin (if
LOSSTYPE is set equal to “SKIN”). In the latter case, MNW2
will automatically calculate a value of Skin and subsequently a
value of B using equations 9 and 10.
The nonlinear wellloss coefficient (C, with dimensions
TP/L(3P1)) defines head loss from any turbulent flow near
the well (Rorabaugh, 1953). The coefficient C and power
term (P, dimensionless) typically are estimated at specific wells through the application of stepdrawdown tests.
There remains some disagreement in the literature about the
nonlinear wellloss terms (see, for example, the review by
Ramey, 1982). Jacob (1947) states that “the loss of head that
accompanies the flow through the screen … is proportional
approximately to the square of the discharge.” Rorabaugh
(1953) argues that the power (P) is an empirical exponent
that “may be unity at very low rates of discharge or it may
be in excess of 2” where turbulent flow occurs in or near
the well; he provides examples from several field cases for
which P varied between 2.4 and 2.8. The higher the value of
P, the more likely that the numerical solution will have difficulty converging. If that happens, then the user can reduce
the value of P. Because this additional nonlinear term (
)
may cause numerical problems or may not be needed, the
user has the option of not including the nonlinear wellloss
term in any multinode well (for example, if LOSSTYPE =
GENERAL, then set C = 0.0 in dataset 2c).
Equation 2 can be rewritten in terms of the flow rate
to each node (Qn). For the simplest case in which only the
aquiferloss term AQn applies, the resulting equation is
. (11) The expression in brackets has dimensions of (L2/T) and can
be viewed as a hydraulic conductance term, which Halford
and Hanson (2002) refer to as the celltowell conductance
(CWCn).
A mor...
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