1. Slug Tests Under- versus Overestimation of Aquifer
Hydraulic Conductivity from Slug Tests
Hongbing Sun
Rider University, Lawrenceville, NJ
Manfred Koch
University of Kassel, Germany
Initial condition
t = 0
t = t1
t = t2
Slug Tests

2. Content 1. Introduction 2. Theory of slug tests
CBP-solution / Hvorslev-solution /Bouwer-Rice solution
3. Simulation of slug tests with MODFLOW
Set-up of FD-grid / Simulated drawdown curves
4. Effects of slug size and duration on estimated K
5. Over- and underestimation of K based on simulated data
CBP-solution / Hvorslev- and Bouwer-Rice solution/
Effects of gravel pack
6. Comparison of field slug- and pumping test estimations
7. Conclusions

3. 2. Slug test flow equation 𝜕 2 ℎ 𝜕 𝑟 2 + 1 𝑟 𝜕ℎ 𝜕𝑟 = 𝑆 𝑠 𝜕ℎ 𝐾𝜕𝑡
𝜕 2 ℎ 𝜕 𝑟 𝑟 𝜕ℎ 𝜕𝑟 = 𝑆 𝑠 𝜕ℎ 𝐾𝜕𝑡
(unconfined or confined) rc Ho
H(t) rw
Gravel/Sand Pack b
h(r,t)
2𝜋 𝑟 𝑤 𝐾 𝜕ℎ( 𝑟 𝑤 ,𝑡) 𝜕𝑟 = 𝜋 𝑟 𝑐 2 𝑏 𝑑𝐻(𝑡) 𝑑𝑡
Z=0 r
rw = radius of well casing
rc = radius of well screen
L= length of well screen d l rb
Z=-b

4. 2.1 Cooper – Bredehoeft – Papadopulos (CBP) method
Fully penetrating
confined aquifer
Match data to type curves
Read off t1 match point for Tt/rc2 = 1
Plot H/H0 (arithmetic) verses log(time)
T =
rc2 t1
S = (rc2u)/rw2

5. Inherent overestimation of K
2.2 Hvorslev method
𝜕 2 ℎ 𝜕 𝑟 𝑟 𝜕ℎ 𝜕𝑟 = 𝑆 𝑠 𝜕ℎ 𝐾𝜕𝑡
rc2ln(L/rw)
2Lt0
K =
K = hydraulic conductivity
rc = radius of well casing
rw = radius of well screen
L= length of well screen
t0= time when water level is
0.37 of initial one
Inherent overestimation of K

6. 2.3 Bouwer and Rice (BR) method 𝜕 2 ℎ 𝜕 𝑟 2 + 1 𝑟 𝜕ℎ 𝜕𝑟 = 𝑆 𝑠 𝜕ℎ 𝐾𝜕𝑡
𝜕 2 ℎ 𝜕 𝑟 𝑟 𝜕ℎ 𝜕𝑟 = 𝑆 𝑠 𝜕ℎ 𝐾𝜕𝑡
intended for unconfined aquifers
rc = radius of the well casing
R = radius of gravel pack
Re = effective radial distance
Le = length of screen
H0 = drawdown at time t = 0
Ht = drawdown at time t
t = time since test began
Tendency for overestimation of K

7. 3. Simulation of slug tests with MODFLOW 3.1 Set-up of FD-model
No gravel pack
Finite difference grid illustrating the 5-cm radius slug well
10000 cells within the inner 1m
78 cells for the well section
100m

8. 3.2 Simulated drawdown curves for confined aquifer
Semi-log plot of H/Ho vs. time of simulated slug tests with
K ranging from 0.01 to 100 m/day, Ss is 10-4.

9. 4. Effects of slug size and duration on estimated K
H/Ho vs. log(time) with varied slug sizes g (gallons) injected within 2 seconds
no effect !!

10. Duration of slug injections affects conductivity estimation
More for unconfined aquifer than for confined aquifer.
4. Effects of slug size and duration on estimated K

11. 5. Over- and underestimation of K based on simulated data
5.1 Estimated conductivites from the CBP method
Ratios of CPB-estimated K vs. actual K as function of Ss for confined aquifer
𝜕 2 ℎ 𝜕 𝑟 𝑟 𝜕ℎ 𝜕𝑟 = 𝑆 𝑠 𝜕ℎ 𝐾𝜕𝑡

12. 5.2 Estimated conductivites from Hvorslev- and BR-method
Ratios of Hvorslev-K vs. actual K as function of Sy for unconfined aquifer
Overestimation of K, due to omission of Sy

13. Low K =1 m/d 5.2 Estimated conductivites from Hvorslev- and BR-method
K varies significantly when different sections of straight line segment is taken.

14. 5.2 Estimated conductivites from Hvorslev- and BR-method
High K = 50m/day
every second counts

15. 5.3 Effects of gravel packs around well screen
Gravel pack K
Use late line segment (Bouwer, 1989)
Use 0.2 to 0.3 of H/Ho range (Butler, 1996)
Traditional textbook explanation of double straight line segments

16. Slug and PUMPING TEST SITES
6. Comparison of slug-test and pumping test data from field tests
Slug and PUMPING TEST SITES
Fort Worth, TEXas
(Houston and Braun, 2004).

17. 6. Comparison of slug-test and pumping test data from field tests
Histograms of slug and pumping test K-estimations from Fort Worth, TX
Slug test
K=10.17 m/d
N=154
Pumping test
K=71.03 m/d
N=40

18. 6. Comparison of slug-test and pumping test data from field tests
Which line segment should be used in a high conductivity aquifer?
“late line segment? 0.2 to 0.3 range of line segment?”
Texas well WHGLTA049
Is this the gravel
pack effect?

19. 6. Comparison of slug-test and pumping test data from field tests
Which line segment should be used in high conductivity aquifer?
6. Comparison of slug-test and pumping test data from field tests
“late line segment? 0.2 to 0.3 range of line segment?”
Texas well ST14-W23
Is this the gravel pack effect?

20. 7. Conclusions
In an unconfined aquifer, theoretically, both the Hvorselv- and the BR- method overestimate the aquifer conductivity, due to their omission of storativity.
2. Practically, Hvorslev- and BR-methods can either over- or underestimate
conductivity of an aquifer, when the “first” straight line segment is used.
3. For low conductivity aquifer, K is overestimated
=> use late line segment or 0.2 to 0.3 of normalized head of H/Ho vs
log (time). Or correct equation. Caution for gravel pack.
4. For high conductivity aquifer K> 5m/day, when using a later straight line
segment of H/Ho vs. log(time), K is less overestimated.
5. For K between 1 and 5 ms/day, choice of proper time segment depends on
gravel- pack and whether the water level is above or below the screen.
6. Field data slug test estimations appear to provide much smaller K-values
than those of pumping tests
=> better use the „early“ than the advocated „late-time“ segment.