Hvorslev Slug Test Formula: Piezometer Hydraulic Conductivity & Basic Time Lag T_0

Why Hvorslev’s 37% unrecovered-head Basic Time Lag T_0 is the workhorse of hydrogeologic slug testing!

Published in U.S. Army Corps of Engineers Waterways Experiment Station Bulletin No. 36 by M. Juul Hvorslev (1951), the Hvorslev Slug Test method measures in-situ saturated hydraulic conductivity K (m/s) around a standpipe monitoring well without pumping contaminated groundwater to the surface! After displacing water level instantaneously by H_0, normalized unrecovered head H(t) / H_0 decays exponentially as EXP(-t / T_0)—meaning Basic Time Lag T_0 is the time at which H(T_0) / H_0 = 1/e ≈ 0.3679 (63.21% recovery), or computed from any observation (t, H_t) via T_0 = -t / LN(H_t / H_0)!

For a cylindrical screen/filter pack of effective length L_e and radius R with standpipe casing radius r_c (satisfying L_e / R > 8), Hvorslev’s shape factor yields K = (r_c^2 * LN(L_e / R)) / (2 * L_e * T_0)! With r_c = 0.025 m, R = 0.10 m, L_e = 1.50 m (L_e / R = 15 > 8), H_0 = 0.80 m, and H(t = 120 s) = 0.2943 m, T_0 = 120.0 s and K = 4.701e-6 m/s (0.406 m/day silty sand)!

Hvorslev Hydraulic Conductivity in Meters per Day (86,400 * K_m/s)

Computes T_0 = -t / LN(H_t / H_0) from slug recovery data (B5, B6, B7) and evaluates K in m/day when screen aspect ratio L_e / R >= 8.

=IF(OR(B2 <= 0, B3 <= 0, B4 / B3 < 8, B5 <= 0, B6 <= 0, B6 >= B5, B7 <= 0), "Invalid Slug Test Geometry (Requires Le/R >= 8 & 0 < Ht < H0)", ROUND(86400 * ((B2 ^ 2) * LN(B4 / B3)) / (2 * B4 * (-B7 / LN(B6 / B5))), 4))

Hvorslev Basic Time Lag T_0 (Seconds to 63.2% Recovery, H/H_0 = 0.3679)

Extracts Hvorslev’s exponential time constant T_0 (seconds) from head ratio H(t) / H_0 at elapsed time t.

=IF(OR(B5 <= 0, B6 <= 0, B6 >= B5, B7 <= 0), "Invalid Head Recovery Inputs", ROUND(-B7 / LN(B6 / B5), 2))

Further reading

• Microsoft Support — LN function