1. An Assessment Tool For Aquifer Storage And Recovery In Coastal Aquifers Mark Bakker Delft University of Technology Kiwa Water Research mark.bakker@tudelft.com

2. Aquifer Storage and Recovery (ASR) systems in coastal aquifers ASR operation is influenced by a bunch of factors: Buoyancy effects Mixing (diffusion, dispersion)‏ Heterogeneity Geochemistry First order effect Objective: Create assessment tool for ASR systems based on buoyancy effects Recent extensive study: Two papers by James Ward et al., WRR

3. Dupuit interface flow Resistance to vertical flow neglected (but still 3D path lines!)‏ Transient, radial flow Hydrostatic conditions Homogeneous, confined aquifer Instantaneous steady-state flow + =

4. Dupuit interface flow is very accurate for a rotating interface Example of two rotating interfaces Bakker, Oude Essink, Langevin, 2004, JofH v.287 Lines: SWI (Dupuit) Grey transition zone: SEAWAT

5. Radial interface flow for an ASR system discharge Q fresh water salt water radial distance r interface elevation  (r,t)‏ top elevation z t bottom elevation z b dimensionless density difference:

6. The freshwater flow may be written as the average flow plus a term depending on the slope of the interface Comprehensive flow (flow integrated over the vertical)‏ Integrated flow in fresh water zone: Eliminate head gradient average flow Interface slope term flow to/from a well

7. Continuity of flow in the freshwater zone gives DEQ for interface position Continuity of flow in fresh water zone: Substitution of equation for gives:

8. Continuity of flow in the freshwater zone gives DEQ for interface position Continuity of flow in fresh water zone: Substitution of equation for gives:

9. Continuity of flow in the freshwater zone gives DEQ for interface position Continuity of flow in fresh water zone: Substitution gives:

10. Continuity of flow in the freshwater zone gives DEQ for interface position Continuity of flow in fresh water zone: Substitution gives: k s always together

11. Continuity of flow in the freshwater zone gives DEQ for interface position Continuity of flow in fresh water zone: Substitution gives: Or, writing in simpler form

12. Continuity of flow in the freshwater zone gives DEQ for interface position Continuity of flow in fresh water zone: Substitution gives: Or, writing in simpler form Doesn't that look like the advection-dispersion equation?

13. Continuity of flow in the freshwater zone gives DEQ for interface position Continuity of flow in fresh water zone: Substitution gives: Or, writing in simpler form advective term dispersive term

14. Solve the governing DEQ with a Lagrangian approach: Discretize interface in number of points. Every time step: 1. Move points with “advective velocity” 2. Do “dispersive” step Governing DEQ: Simpler form: Note that D = 0 at tip and toe of interface

15. Example of Aquifer Storage and Recovery discharge Q = 2000 m 3 /d injection for 15 days 2000 m 3 /d extraction for as long as possible  = 1000 kg/m 3 H = 20 m  = 1025 kg/m 3 k = 10 m/d n = 0.3 (porosity)

16. Example of Aquifer Storage and Recovery

26. Recovery rate surpasses 75% for this setup after 10 cycles

27. Example of Aquifer Storage and Recovery discharge Q = 2000 m 3 /d injection for 15 days 0 m 3 /d storage for 5 days 2000 m 3 /d extraction for as long as possible  = 1000 kg/m 3 H = 20 m  = 1025 kg/m 3 k = 10 m/d n = 0.3 (porosity)

28. Interface rotates during storage, which reduced recovery

29. After 10 cycles, recovery is up to 72%

30. Recovery rate reduces because of storage

31. Effect of partial penetration. Example: Well penetrates half the aquifer discharge Q fresh water salt water partially penetrating well screen only affects 1.5H of isotropic aquifer H

32. Partially penetrating well

34. Recovery ratio of partially penetrating well higher for this setup

35. Solution to assess feasibility of ASR systems based on buoyancy effects Includes injection, storage and recovery phases Accurate and quick May include partially penetrating well Solution for stratified aquifers is in the works Mark Bakker mark.bakkker@tudelft.nl