11.3 Well Drawdown, Specific Capacity, and Interference

Drawdown and Well Performance

The April 2024 PE Civil WRE specification explicitly lists well and drawdown analysis. Items may demand a direct calculation or may ask what a pump-test result means for supply, dewatering, or site impacts. Begin every well problem by separating water levels, pumping rate, aquifer response, and well efficiency.

Core Terms

Static water level is the level before pumping or after full recovery. Pumping water level is the level during pumping. Drawdown s is static level minus pumping level at the same point. In a pumped well, measured drawdown includes aquifer drawdown plus extra head loss near and inside the well (well loss). In an observation well, drawdown better represents the true aquifer response because it excludes screen-entrance and wellbore losses.

Specific capacity is Q / s, often in gpm/ft. A larger value means more yield per foot of drawdown. It is not a fixed aquifer constant because it changes with pumping duration, rate, well condition, turbulent well loss, boundaries, and seasonal recharge. Theis-based theory shows specific capacity declines slowly with time as the cone of depression expands.

Radial Flow Equations

For steady confined radial flow to a fully penetrating well, the Thiem equation in flow form is Q = 2 pi T (h2 - h1) / ln(r2 / r1). The drawdown form is s = Q ln(R / r) / (2 pi T). Both reflect a cylindrical flow area that grows with radius. Do not substitute a rectangular Darcy area for a well unless the problem deliberately simplifies the geometry.

For an unconfined aquifer under Dupuit assumptions, steady radial flow is Q = pi K (h2^2 - h1^2) / ln(r2 / r1), where h1 and h2 are saturated thicknesses above the base. When drawdown is large relative to saturated thickness, a confined approximation can misstate the result; a corrected drawdown s' = s - s^2/(2b) is sometimes applied to convert observed unconfined drawdown to an equivalent confined value.

Pump-Test Workflow

1. Record static level, pumping rate, pumping level, time, and observation-well distances.
2. Compute drawdown at each measured point.
3. Compute specific capacity if well performance is requested.
4. Estimate transmissivity from observation-well data, since pumped-well data carry extra well losses.
5. Confirm assumptions match the formula: confined or unconfined, steady or transient, full or partial penetration, constant rate, valid boundaries.
6. Read late-time trends for recharge boundaries (flattening), impermeable boundaries (steepening), delayed yield, or nearby pumping.

Interference

When two wells pump near each other, their cones of depression overlap. In linear confined-aquifer problems the aquifer response is treated as linear, so drawdowns from separate wells add at a point by superposition. This supports wellfield spacing, dewatering layout, and judging whether a new production well will harm an existing one.

Interference is not always harmful. A dewatering system uses intentional interference among wellpoints or deep wells to depress groundwater across an excavation. For supply wells, excessive interference reduces available drawdown, raises pumping cost, and can trigger impacts at property lines or wetlands.

Well Loss and Step-Drawdown Tests

Total drawdown in a pumped well is often modeled as s = B Q + C Q^2, where B Q is the laminar aquifer (formation) loss that scales linearly with rate and C Q^2 is the turbulent well loss from flow through the screen and casing. Well efficiency is the ratio B Q / (B Q + C Q^2). A step-drawdown test runs the well at several increasing rates to separate B from C; a large C signals a clogged or undersized screen and a candidate for rehabilitation. Because specific capacity is Q / s = 1 / (B + C Q), it falls as Q rises even when the aquifer is unchanged, which is why specific capacity must always be quoted with its test rate.

Worked Example

A confined aquifer has T = 3,000 ft^2/day. A fully penetrating well pumps so that drawdown is 3.0 ft at r = 50 ft and 1.2 ft at r = 400 ft. Using the Thiem drawdown difference, s1 - s2 = Q ln(r2 / r1) / (2 pi T), so 3.0 - 1.2 = Q ln(400/50) / (2 pi x 3,000). Then 1.8 = Q (2.079) / 18,850, giving Q = 1.8 x 18,850 / 2.079 = 16,320 ft^3/day, about 85 gpm. Note the larger drawdown is at the smaller radius, closer to the well.

Practical Traps

• Specific capacity is Q divided by drawdown, never drawdown divided by Q; a deeper pumping level means a larger drawdown and a smaller specific capacity.
• Pumping and static levels given as elevations must be differenced as elevations, not as depths below grade.
• Radial-flow equations use natural log unless the supplied formula uses log base 10 with the 2.303 factor folded in.
• Use observation-well drawdown, not pumped-well drawdown, to estimate transmissivity, because the pumped well carries the C Q^2 well loss. Mixing these is a frequent distractor.