Fully Three dimensional Poroelastic Model

Transcription

1 Fully Three dimensional Poroelastic Model SimulatingReverse GroundwaterFluctuations During Aquifer Pumping David J. Hart, Wisconsin Geological and Natural History Survey Madison, WI Joshua S. Roberts, Arcadis, Knoxville, TN; formerly University of Wisconsin Madison, WI Herbert F. Wang, University of Wisconsin Madison, WI

2 Fully Three dimensional Poroelastic Model SimulatingReverse GroundwaterFluctuations During Aquifer Pumping Data from pumping test in Wisconsin Water levels rise in an observation well during pumping? NOORDBERGUM EFFECT

3 Noordbergum Effect Conceptual Models Usually, only layered systems are considered. Hsieh (1996)

4 Water Level Rise During Aquifer Pumping Aquitard Confined Aquifer Aquitard Hih(1996) Hsieh Removing pore fluid increases effective stress and leads to aquifer compaction.

5 Water Level Rise During Aquifer Pumping Hsieh (1996) This raises water levels, especially in low K materials.

6 Conceptual Model Revisited

7 New Conceptual Model Without Layered Aquifer PW MW MW Sand Clay Didn t have layered aquifer in data shown

8 New Conceptual Model Without Layered Aquifer Q Sand Clay effective p pore Water level (head) drop in aquifer increases the effective stress and squeezes the low K unit. The heads in the low K unit go up as a result until the head drop diffuses into the low K unit.

9 Motivation Practical issues e.g. Reverse water levels during pump test Previousmodels are 2 D or rely on axisymmetry Two model objectives 1. Determine necessary K ratio for Noordbergum 2. Extend Noordbergum for non layered geologic g environment Rodrigues (1983)

10 Coupled Diffusion/Deformation Analysis in ABAQUS Governing oe Equations Darcy s Law K 2 h h ( u) gn t f fluid t Stress equilibrium equation Finite Element Mesh Finite element method solves these two equations simultaneously

11 Model Domain Radius = 100 m Depth = 10 m 12,000 elements Finer mesh near well Well located in center of mesh Screened over entire Screened over entire thickness of aquifer

12 Boundary Conditions Q No Flow/Free Surface No radi ial displace ment Sand Clay CH/ Free Surface No Flow/Pinned Surface Initial heads are set to 0 everywhere in the domain.

13 Aquifer and Aquitard Properties Physical Property Value in Aquifer Value in Clay Lens Hydraulic Conductivity (m/s) Young s Modulus (N/m 2 ) 7.5 x x 10 7 Poisson s s Ratio (dimensionless) Porosity (dimensionless) The aquifer was pumped at a constant rate of about 38,000 gallons per day (1.67 x m 3 /s or 26 gpm) for a total of eight days

14 Oxbow Cross sectionsection MW1 MW2,3,4 Clay Screen Sand MW2,3,4 MW1

15 Oxbow Map View

16 Pinched out Confining Unit Cross sectionsection MW1 MW2,3,4 Screen Sand MW2,3,4 MW1 Clay

17 Pinched out Confining Unit Map View

18 Verification of Theis Solution Aquitard Confined Aquifer Aquitard Lower model values reflect 3 D deformation rather than Lower model values reflect 3 D deformation rather than the vertical only deformation that is assumed by Theis, Ss

19 Oxbow Model Matrix Deformation

20 Pinched out Confining Unit Model Matrix Deformation

21 Hi K:Lo K ratio = 100 Before Above In Below Onset of Noordbergum Effect in Oxbow Model Hi K:Lo K ratio dependence Not seen at 100:1 Clearly seen at 1000:1 Maximum M i duration ~5 6 minutes Maximum water level rise at 1000:1 = 17cm 1.7 ~ 9% of total drawdown Hi K:Lo K ratio = 1000 Before Above In Below

22 Hi K:Lo K ratio = 100 Before Above In Below Onset of Noordbergum Effect in Pinched out Unit Model Hi K:Lo K ratio dependence Very slight at 100:1 Clearly seen at 1000:1 Maximum M i duration ~4 5 minutes Maximum water level rise at 1000:1 = 84mm 8.4 ~ 4% of total drawdown Hi K:Lo K ratio = 1000 Before Above In Below

23 Consider a wider range of K values (say, course sand to fine clay) Before Above In Below Ksand = 10 4 m/s Kl Kclay = m/s Hi K:Lo K ratio = 10 7 Before Above In Below Maximum water level rise in oxbow model dl(b (above) = 16 cm ~ 70% of total drawdown Maximum water level rise in pinched out confining unit model (left) = 12 cm ~ 60% of total drawdown What is the duration?

24 Water level rise persists in both oxbow (right) and pinched out confining unit (below) models for the entire model time (8 days) Recovery after 8 days Oxbow: ~56% Pinched out unit: ~66% Noordbergum effect will persist until fluid flow from high head to low head accounts for poroelastic compression.

25 Summary Groundwater pumping p => aquifer compression => Noordbergum effect Water level rise clearly seen when hi K:lo K = 1000:1 Lasted 4 6 minutes With very large K ratio, Noordbergum effect persisted 8+ days Noordbergum effect DOESNOT indicatebad data Water level rise indicates observation is in lower K unit. Acknowledgement: Thank you to Kurt Feigl and Shannon Graham in particular for assistance during this study. Also, thanks to Dan Peplinski of Layne Northwest for providing data.

26 Implications Noordbergum effect indicates heterogeneity Rethink conceptual model dlof underlying geology How extensive is the low K material? More geologic information is needed dd The measured Kis a lumped average of aquifer and aquitard. If looking for aquifer K, don t screen well in aquitard. Use drilling log to adjust screened interval. Acknowledgement: Thank you to Kurt Feigl and Shannon Graham in particular for assistance during this study. Also, thanks to Dan Peplinski of Layne Northwest for providing data.