an assessment tool for aquifer storage and recovery in coastal aquifers mark bakker delft university...
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An Assessment Tool For Aquifer Storage And Recovery In Coastal Aquifers
Mark Bakker
Delft University of TechnologyKiwa Water [email protected]
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 ASRsystems based on buoyancy effects
Recent extensive study: Two papers by James Ward et al., WRR
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
+ =q1
q2
q1H f=q2H s
H f
H s
H
Dupuit interface flow is very accurate for a rotating interfaceExample of two rotating interfaces
Bakker, Oude Essink, Langevin, 2004, JofH v.287
Lines: SWI (Dupuit)Grey transition zone: SEAWAT
Radial interface flow for an ASR system
discharge Q
fresh water salt water
radial distance r
interface elevation (r,t)
top elevation zt
bottom elevation zb
dimensionless density difference:
The freshwater flow may be written as the average flowplus 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/froma well
Continuity of flow in the freshwater zone gives DEQfor interface position
Continuity of flow in fresh water zone:
Substitution of equation for gives:Q f , r
Continuity of flow in the freshwater zone gives DEQfor interface position
Continuity of flow in fresh water zone:
Substitution of equation for gives:Q f , r
Continuity of flow in the freshwater zone gives DEQfor interface position
Continuity of flow in fresh water zone:
Substitution gives:
Continuity of flow in the freshwater zone gives DEQfor interface position
Continuity of flow in fresh water zone:
Substitution gives:
ks always
together
Continuity of flow in the freshwater zone gives DEQfor interface position
Continuity of flow in fresh water zone:
Substitution gives:
Or, writing in simpler form
Continuity of flow in the freshwater zone gives DEQfor 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?
Continuity of flow in the freshwater zone gives DEQfor interface position
Continuity of flow in fresh water zone:
Substitution gives:
Or, writing in simpler form
advective term
dispersive term
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
Example of Aquifer Storage and Recovery
discharge Q = 2000 m3/d injection for 15 days 2000 m3/d extraction for as long as possible
= 1000 kg/m3 H = 20 m
= 1025 kg/m3
k = 10 m/dn = 0.3 (porosity)
Example of Aquifer Storage and Recovery
Example of Aquifer Storage and Recovery
Example of Aquifer Storage and Recovery
Example of Aquifer Storage and Recovery
Example of Aquifer Storage and Recovery
Example of Aquifer Storage and Recovery
Example of Aquifer Storage and Recovery
Example of Aquifer Storage and Recovery
Example of Aquifer Storage and Recovery
Example of Aquifer Storage and Recovery
Recovery rate surpasses 75% for this setup after 10 cycles
Example of Aquifer Storage and Recovery
discharge Q = 2000 m3/d injection for 15 days0 m3/d storage for 5 days
2000 m3/d extraction for as long as possible
= 1000 kg/m3 H = 20 m
= 1025 kg/m3
k = 10 m/dn = 0.3 (porosity)
Interface rotates during storage, which reduced recovery
After 10 cycles, recovery is up to 72%
Recovery rate reduces because of storage
Effect of partial penetration.Example: Well penetrates half the aquifer
discharge Q
fresh watersalt water
partially penetratingwell screen
only affects 1.5H of isotropic aquifer
H
Partially penetrating well
Partially penetrating well
Recovery ratio of partially penetrating well higherfor this setup
Solution to assess feasibility of ASR systems basedon buoyancy effects
Includes injection, storageand recovery phases
Accurate and quick May include partially penetrating well
Solution for stratified aquifersis in the works
Mark [email protected]