Pumping Test Example Model Overview

Pumping tests are often analyzed with analytic solutions (e.g. Theis, Hantush-Jacob, Neuman) that assume radial symmetry, constant saturated thickness, and a single layer.  While these are appropriate in many situations, a more sophisticated analysis is better when partial penetration, layering, saturated thickness variations, and/or irregular boundary conditions are present.  This example shows how AnAqSim can be a used to analyze such situations.

This example model comes from a project where there was data from historical pumping of a partially-penetrating production well during three 12-hour pumping episodes.  The pumped well screen was short relative to the saturated thickness of the unconfined alluvial aquifer which was stratified with some layers much more conductive than others.  Drawdowns were measured at the pumping well and at three nearby observation wells that had partially-penetrating screens above the level of the pumped well screen (see profile at right).  The drawdown measurements were sparse hand measurements.  During one pumping episode, borehole flowmeter data was collected in the pumped well showing how the discharge to the well was distributed vertically along the screen.  There were no nearby boundaries that affected drawdowns here.

The available observations are:

• The aquifer was unconfined sand/gravel alluvium with a total of 1040 ft of saturated thickness.
• Boring and well logs indicated less permeable strata deeper than 300 ft below the water table compared to the strata at shallower depths.
• The pumped well was screened from 177 to 410 ft below the water table and had a radius (to the outside of the gravel pack) of 7 inches (0.583 ft).
• The pumped well pumped for a period of 12 hours at a rate of 850 gpm (114 ft³/minute).
• Observation well 1 was 268 ft radially from the pumped well and screened 0-70 feet below the water table. Observation well data is contained in files below.
• Observation well 2 was 167 ft radially from the pumped well and screened 30-65 feet below the water table.
• Observation well 3 was 167 ft radially from the pumped well and screened 65-112 feet below the water table.
• Drawdown at the pumped well stabilized between 38 and 42 ft during the latter portions of typical 12-hour pumping episodes at this discharge.
• Late in the 12-hour pumping period, the discharges coming into the well were distributed as shown in the table below, based on borehole flowmeter measurements. A large share of the discharge came into the uppermost part of the well screen.

The model consisted of 9 layers that correspond to the site geology and the elevations of the pumped and observation wells.  Levels 1 and 2 represent a recent alluvial formation and levels 3-9 represent an older alluvial formation.  Level 1 was modeled as an unconfined domain and levels 2-9 were modeled as a confined (fixed transmissivity) domains.  Domain inputs for the calibrated model are shown below.

The model covered a circular area of radius 6000 ft, which is significantly larger than the area impacted during a 12-hour episode of pumping.  The datum for elevations in the model is the initial water table and initial heads were set as constant and zero everywhere.  Heads at the outer boundary were maintained at zero through the simulation.   The outer boundary in all 9 layers was modeled with these lines of input shown at right.

The pumped well was simulated as a multi-level discharge-specified well screened across levels 5, 6, and 7 of the model with a discharge of 114 ft³/min.  Observation well MW-1 was simulated as a multi-level well screened across levels 1 and 2, with a discharge of zero.

Spatially-variable area sinks were used to simulate storage fluxes and vertical leakages between levels.  The input for the only domain SVAS is shown at right. and the input for special well basis point spacings at the pumping well (top row) and observation well 1 (second row) are also shown. The well basis point spacings around the pumping well determine the placement of most basis points except for some near observation well 1.  A plot showing basis points near the pumping well and observation well 1(to right of pumping well) is shown at right.

The model had 6 time steps and a time step multiplier of 2.0 (inputs at right).

The hydraulic properties of the layers were adjusted in a manual calibration that matched all the observations reasonably.  To constrain the parameters somewhat during this process, the following assumptions were made:

• A single anisotropy ratio Kh/Kv applies to all layers.
• The Ks in levels 1 and 2 were the same due to similarities in boring logs.
• The Ks in levels 3 and 4 were the same due to similarities in boring logs.
• The Ks in levels 7, 8, and 9 were the same due to similarities in boring logs.
• The specific storage in levels 3 through 9 were the same since they are the same geologic formation.

The calibrated model properties and the domain input table are shown at right.   The calibrated K, specific storage, and specific yield values are all within typical ranges for dense sand and gravel.

The simulation had negligible head changes at 12 hours of pumping outside a radius of 2000 ft, as shown at right.  Thus, the constant head boundary at a radius of 6000 ft had no significant impact on simulated drawdowns.  This plot was generated within AnAqSim using Analysis/Graph Conditions Along a Line.

The figure at right compares modeled drawdowns to observed drawdowns at observation wells.  The monitoring wells were measured three different days, each during a 12-hour episode of pumping at 850 gpm.  The simulation matches the shape and magnitude of the observed drawdown curves, and the simulation was sensitive to both hydraulic conductivities and storage parameters.  This plot was generated using Analysis/Graph Drawdown Hydrographs.

The simulated drawdown at the pumped well is shown at right, and it is in the same range as is typically observed during a pumping episode (38 to 42 ft).  This graph was created using Analysis/Discharge-Specified Well Heads/Graph Transient Heads.

The observed and simulated distribution of discharge to the pumped well screen is shown in the plot and table at right.  The simulation approximately matches this distribution, with much larger discharges in the upper portion of the well than in deeper portions.  The discharge breakdown for a multi-level well are available under Analysis/Multi-Domain Well Discharges by Domain.

The model was developed and calibrated manually in one day, and each run with 6 time steps took less than 10 seconds to solve on a standard laptop.

Here is a link to a zip file containing the AnAqSim model input file and the observation well drawdown data file, for those curious to experiment with this model.