an assessment tool for aquifer storage and recovery in coastal aquifers mark bakker delft university...

An Assessment Tool For Aquifer Storage And Recovery In Coastal Aquifers

Mark Bakker

Delft University of TechnologyKiwa Water Researchmark.bakker@tudelft.com

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 Bakkermark.bakkker@tudelft.nl