Specifying the location of the pump intake will not

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Unformatted text preview: , then the model will assume that it is located above the uppermost node associated with the well (that is, above the node located closest to the land surface or wellhead). Specifying the location of the pump intake will not affect the net discharge from the well, nor the inflows and outflows at any particular node. Instead, it will only affect the routing of flow and solute within the borehole. Head Loss Terms MODFLOW computes the head at a block-centered node of a finite-difference grid on the basis of a fluid mass balance for fluxes into and out of the volume of the cell of interest, including flow in or out of a well located within the surface area (and volume) of that cell. However, because of differences between the volume of a cell and the volume of a wellbore, as well as differences between the average hydraulic properties of a cell and those immediately adjacent to a well, it is not expected that the computed head for the node of a finitedifference cell will accurately reproduce or predict the actual head or water level in a well at that location. Furthermore, if the length of the open interval or screen of a vertical well is greater than the thickness of the cell, then the head in the well would be related to the head in the ground-water system at multiple levels (and at multiple locations for a nonvertical well). Thus, if the user needs to estimate the head or water level in a well, rather than just the head at the nearest node, then additional calculations are needed to correct for the several factors contributing to the difference between the two. Following the development and discussion of Jacob (1947), Rorabaugh (1953), Prickett (1967), and Bennett and others (1982), the difference between the head in the cell and the head in the well (the cell-to-well drawdown) can be calculated with a general well-loss equation as: , (2) where hWELL is the composite head (or water level) in the well (L), n is the index of nodes in a multi-node well, hn is the head in the nth cell associated with the well (L), Qn is the flow between the nth cell and the well (L3/T) (negative for flow out of the aquifer and into the well), A is a linear aquifer-loss coefficient (T/L2), B is a linear well-loss coefficient (T/L2), C is a nonlinear well-loss coefficient (TP/L(3P-1)), and P is the power (exponent) of the nonlinear discharge component of well loss. Equation 2 can alternatively be expressed in terms of the water level in the well as: . (3) Equation 3 states that the head in the well is equal to the head in the node in which the well is located (hn) plus several head-loss terms (noting again that for a pumping well, all of the Q terms would be negative in sign). The head at the node, hn, is calculated by the finite-difference solution to the partial differential equation of ground-water flow. The first head-loss term (AQn) accounts for head losses in the aquifer resulting from the well having a radius less than the horizontal dimensions of the cell in which the well is located (that is, cell-towell head losses); the second term (BQn) accounts for head losses that occur adjacent to and within the borehole and well screen (that is, skin effects); and the third term ( ) accounts for nonlinear head losses due to turbulent flow near the well. Most previous approaches for simulating head losses have included only the aquifer-loss term (AQn) (see, for example, Prickett, 1967; Trescott and others, 1976; Bennett and others, 1982; Anderson and Woessner, 1992; Planert, 1997; Neville and Tonkin, 2004). This common approach assumes that aquifer losses can be calculated on the basis of the Thiem (1906) steady-state flow equation and that head loss Conceptual Model and Numerical Implementation due to skin and local turbulence effects are negligible, such that equation 3 becomes: , 5 (8) (4) where T is transmissivity of the aquifer (L2/T), ro is the effective (or equivalent) radius of a finite-difference cell (L), and rw is the actual radius of the well (L). The effective radius of the cell is equivalent to the radius of a vertical pumping well that would have the same head as that calculated for the node of the cell. Because ro is typically much greater than rw, the head in a pumping (withdrawal) well will typically be lower than the model-computed head for the cell. Several assumptions underlie the use of the Thiem (1906) equation for estimating the aquifer loss, including that the aquifer is confined; the well is vertical and the screen fully penetrates a cell; the well causes radially symmetric drawdown; the well causes no vertical flow in the aquifer containing the well or from units above and below the aquifer; the transmissivity is homogeneous and isotropic in the cell containing the well and in the neighboring cells; and flow between the cell and well is at steady state for the time period used to solve the general ground-water flow equations in MODFLOW. Peaceman (1983) indicates that the effective external radius of a rectangular finite-difference cell for isotropic porous media is given by (5) where ro is calculated by MNW2 using equation 8 on the basis of a user-specified value of rw and values of Δx, Δy, Kx, and Ky s...
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This document was uploaded on 01/20/2014.

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