3.5. Pumping Wells

Users can define three pumping well types based on the pumping situation or desired outcome:

  1. Specified-Rate Wells - Users specify a pumping rate (constant or time-varying). MINEDW pumps at the specified rate until the node goes dry. Output files indicate when pumping nodes go dry. Specified-rate pumping wells help in groundwater flow model calibration to ensure that modeled pumping wells accurately simulate available pumping records.

  2. Specified-Head Wells - Users specify head values to maintain (constant or time-varying). MINEDW extracts water from the pumping well at a rate calculated to maintain the specified head.

  3. Lowest Pumping Elevation (LPE) Wells - Users specify a pumping rate (constant or time-varying) and a lowest pumping head for the well. MINEDW extracts water at the specified pumping rate until reaching the lowest head condition. Once reached, MINEDW decreases the pumping rate to maintain the lowest head condition. If the groundwater system recovers above the lowest head condition, the user-defined pumping rate resumes.

The pumping well boundary condition specifies values related to the source-sink term W in the equation, calculated in the general form below. The equation shows the calculation for sources or sinks occurring at user-specified nodes, as typically happens with pumping wells.

(3.10)\[q_{P}(t) = \sum_{i=1}^{n} Q_{Pi}(t)\]

Where:

  • \(q_P\) = functional representation of the internal source-sink fluxes [L³T⁻¹],

  • \(Q_{Pi}\) = pumping rate at node i [L³T⁻¹], and

  • n = number of nodes [L°].

The formulation for the pumping rate at node i (\(Q_{Pi}\)) differs for each pumping well type as discussed in the following sections.

3.5.1. Specified-Rate Pumping Wells

For specified-rate pumping wells, \(Q_{Pi}\) equals the user-defined value. If the phreatic surface falls below the pumping node, the pumping rate becomes zero, as shown below.

(3.11)\[\begin{split}Q_{Pi} = \begin{cases} Q_i, & \text{for } H_i > H_{Li},\\ 0, & \text{for } H_i \le H_{Li}. \end{cases}\end{split}\]

Where:

  • \(Q_i\) = user-specified pumping discharge rate at node i [L³T⁻¹],

  • \(H_i\) = calculated hydraulic head at node i [L], and

  • \(H_{Li}\) = elevation at node i [L].

3.5.2. Specified-Head Pumping Wells

For specified-head pumping wells, users specify the head at the pumping node. The pumping rate depends on the difference between the specified head and actual head, and the leakance factor. If the phreatic surface falls below the pumping node, the pumping rate becomes zero. The equation below shows the formulation for specified-head pumping wells.

(3.12)\[\begin{split}Q_{Pi} = \begin{cases} C_i\,\bigl(H_i - H_{iP}\bigr), & \text{for } H_i > H_{iP},\\ 0, & \text{for } H_i \le H_{iP}. \end{cases}\end{split}\]

Where:

  • \(C_i\) = leakance factor for node i [L²T⁻¹], and

  • \(H_{iP}\) = user-specified head at node i [L].

3.5.3. Lowest Pumping Elevation Pumping Wells

For LPE pumping wells, the pumping rate equals the user-specified rate when the head at the pumping node exceeds the user-specified LPE. If pumping at the user-specified rate would reduce the head at the next time step to or below the LPE, the pumping rate reduces to maintain the LPE. Thus, the head in the pumping well stays above the LPE, as shown mathematically below.

(3.13)\[\begin{split}Q_{Pi} = \begin{cases} C_i\,\bigl(H_i - LPE\bigr), & \text{for } H_i(Q_i) \le LPE,\\ Q_i, & \text{for } H_i(Q_i) > LPE. \end{cases}\end{split}\]

Where:

  • \(LPE\) = lowest pumping elevation [L],

  • \(H_i(Q_i)\) = head at node i that would result from pumping at rate \(Q_i\) [L], and

  • \(Q_i\) = user-specified pumping discharge rate at node i [L³T⁻¹].

LPE wells commonly appear in model simulations for prediction or testing dewatering well designs because they provide information about the maximum sustainable pumping rate in a given location.