Hantush-Jacob Leaky Aquifer Formula: Leakage Factor B, Aquitard Resistance c & Steady Drawdown

Why real confined cones of depression stabilize once vertical aquitard leakage balances well pumping Q!

Theis’s classic non-leaky confined aquifer curve predicts drawdown growing forever as LN(t) unless a river recharge boundary intervenes! In reality, most "confined" sand-and-gravel aquifers are overlain by a semi-pervious silt/clay aquitard of thickness b_prime (m) and vertical hydraulic conductivity K_prime (m/day), defining Hydraulic Resistance c = b_prime / K_prime (days) and Mahdi S. Hantush & C. E. Jacob’s (1955, Trans. AGU) Characteristic Leakage Factor B = SQRT(T * c) = SQRT(T * b_prime / K_prime) (meters)!

Physically, B measures how far radial pumping spreads horizontally before vertical downward leakage through the aquitard supplies the well: large B (e.g., 2,500 m) indicates a tight aquitard, whereas small B (e.g., 250 m) indicates rapid vertical leakage! At steady state (De Glee, 1930 / Hantush, 1956), drawdown stabilizes at s_steady = (Q / (2 * PI() * T)) * K_0(r / B), which for observation wells inside r / B <= 0.05 simplifies accurately (< 0.2% error) to Hantush’s logarithmic law s_steady = (Q / (2 * PI() * T)) * LN(1.123 * B / r)!

Hantush-Jacob Characteristic Leakage Factor B (m) = SQRT(T * b_prime / K_prime)

Computes characteristic radial leakage length B (m) from aquifer transmissivity T (B2 m^2/day), aquitard thickness b_prime (B3 m), and aquitard vertical conductivity K_prime (B4 m/day).

=IF(OR(B2 <= 0, B3 <= 0, B4 <= 0), "Requires Transmissivity T > 0, b_prime > 0, and K_prime > 0", ROUND(SQRT(B2 * B3 / B4), 2))

Hantush Near-Well Steady-State Leaky Drawdown s_steady (m, Valid for r / B <= 0.10)

Evaluates (Q / (2 * PI() * T)) * LN(1.123 * SQRT(T * b_prime / K_prime) / r) for pumping rate Q (B5 m^3/day) and radial distance r (B6 m), guarding r / B > 0.10.

=IF(OR(B2 <= 0, B3 <= 0, B4 <= 0, B5 <= 0, B6 <= 0), "Invalid Leaky Aquifer Inputs", IF(B6 / SQRT(B2 * B3 / B4) > 0.1, "r / B > 0.10: Use Full Bessel K_0(r/B) Curve", ROUND((B5 / (2 * PI() * B2)) * LN(1.123 * SQRT(B2 * B3 / B4) / B6), 3)))

Further reading

• USGS Water-Supply Paper 2220 — Basic Ground-Water Hydrology (Leaky Confined Aquifers)