A new Model for Karst Spring Hydrograph Analysis

Transcription

1 A new Model for Kars Spring Hydrograph Analysis Ming Ye Deparmen of Earh, Ocean, and Amospheric Science, FSU Bin Xu China Universiy of Mining and Technology, Beijing FSU 1 s Kars Symposium 11/3/2017

2 Characerizaion of Kars Hydrogeology Kars physical srucure scheme (Mangin, 1975) Kars environmen is very differen from oher environmens in erms of waer flow and sorage. Direc mehods for characerizaion: speleology, cave diving, camera recording, borehole logging, remoelyconrolled vehicles, racer experimens,

3 Kars Spring Hydrograph: An Indicaor of Kars Aquifers Naural experimens of rainfall and kars aquifer responses occur every day. kars spring hydrograph: he discharge hydrograph appearing a a spring in a kars region where surface flow is almos no possible due o well-developed surface and underground kars landforms (Bonacci, 1993). Differen hydrographs for differen kars ypes of kars springs.

4 Hydrograph Recession Curve Kars aquifers do no have a srong capabiliy of soring waer. Hydrograph recession curve: in a long-lasing period wih no precipiaion Q = Qe α 0 Maille (1905)

5 Florida Hydrograph Recession Curve Hydrograph of Madison Blue Spring More frequen rainfall evens More complicaed kars hydrogeology

6 Models of Hydrograph Recession Curve Mangin Model (1975) (a) Fiorillo Model (2011) (b) ψ() φ() i Torricelli reservoir (condui) Darcy reservoir (marix) Poiseuille reservoir (fracure) Q Q Condui reservoir: Unsauraed zone flow, Ψ() Marix reservoir: Sauraed zone flow: φ()

7 Our Concepual Model of Flow Dynamics Two reservoirs: Condui and marix (including fracure) Three sages: Condui-flow-dominaed, mixed-flow, and marix-flow-dominaed Explicily separaed condui and marix flows in he mixed-flow sage Condui-flow-dominaed Sage (a) h 1,m Sage I: 0 1 Marix Condui R 1,c h 0,c h 1,c Condui: head decreases from h 0,c o h 1,c Marix: head increases from h 0,m o h 1,m h 1,c = h 1,m h 0,m Q = Q γ I I 0 Rm

8 (b) Sage II: 1 2 Marix Mixed-flow Sage wih Muliple Condui Layers Condui Condui: head decreases from h 1,c o h 2,c Marix: head increases from h 1,m o h 2,m h 1,m h 2,m Rm R 2,c { Condui layer 1 i Condui layer n h 1,c =h L1s,c h L1e,c h 2,c Condi flow Marix flow h 2,c h 2,m Q = Q β ( ) II, Li, c Lis, c i Lis, c II 1( 1) m, = 1, m Q Q e α Marix-flow-dominaed Sage (c) Sage III: 2 h 2,m Marix Condui Condui: head remains a h 2,c Marix: head coninues decreasing Q = Q e α III 2, m ( ) 2 2 Rm h 2,c

9 Idealized Hydrograph Separaion Q = Q γ Spring discharge (Q) is linear wih ime (). I I 0 Condui-flow-dominaed sage (sage I) Discharge V II m V II L1,c : condui flow from layer 1 V II L2,c : condui flow from layer 2 V II m : marix flow Time } Mixed-flow sage (sage II) Marix-dominaed-flow sage (sage III) Q = Q e α III 2, m ( ) 2 2 Logarihm of spring discharge (logq) is linear wih ime ().

10 Real-World Applicaion and Model Comparison Madison Blue Spring locaed in SRWMD Two periods are seleced for model applicaion and evaluaion Recession period 1: small condui flow Recession period 2: large condui flow Recession period 1 Recession period 2

11 Our model Recession Period 1 When condui flow is small, he hree models fi he daa almos equally well. misfi n = i= 1 Our model: m 3 /s Mangin model: m 3 /s Fiorillo model: m 3 /s r i Mangin model (1975) Fiorillo model (2011)

12 Our model Recession Period 2 When condui flow is large, our model ouperforms he oher wo models. misfi n = i= 1 Our model: m 3 /s Mangin model: m 3 /s Fiorillo model: m 3 /s r i Mangin model (1975) Fiorillo model (2011)

13 Our model Why is our model beer? Mangin model: no considering hree sages of spring discharge. Fiorillo model: no separaing condui flow and marix flow in he mixed-flow sage. Mangin model (1975) Fiorillo model (2011)

14 Effecive Porosiy of Marix and Condui (b) Sage II: 1 2 A 1 h 1 h 2 Observaion well A 2 A c =259km 2 Marix Condui h 3 h 1,m h 2,m R 2,c { Condui layer 1 i h 1,c =h L1s,c h L1e,c h i-1 A i-1 h i Spring Rm Condui layer n h 2,c Marix n m = V II m ( ) h h A 1, m 2, m c 2 2 II II α1( 1) V Q d Q e d m m, 1,m 1 1 = = = Q1, m Q2, m α 1

15 Effecive Porosiy of Marix and Condui (b) Sage II: 1 2 Marix Condui A 1 h 1 h 2 Observaion well A 2 h 1,m h 2,m Rm R 2,c { Condui layer 1 i Condui layer n h 1,c =h L1s,c h L1e,c h 2,c h 3 h i-1 A i-1 h i Spring Condui Layer Li n Li, c = V II Li, c ( ) h h A Lis, c Lie, c c II Lie, c II VLi, c Q, Li, cd Lis, c = = Q Q 2 2 Lis, c Lie, c 2β i 2 II Q ( ), Li, c Lie, c = Lis, c 2, c + II 2, c Q, Li + 1, c h h h h

16 Saring Dae Head range (m) Resuls Released waer volume (m 3 ) Effecive porosiy (%) Marix Conduis Marix Condui Marix Condui Toal 2014/9/ , ,009, , /9/ ,306,007 2,103, ,

17 Saring Dae Head range (m) Resuls Released waer volume (m 3 ) Effecive porosiy (%) Marix Conduis Marix Condui Marix Condui Toal 2014/9/ , ,009, , /9/ ,306,007 2,103, , Two boreholes, W and W-15515, were compleed in W-15537: 5% ~ 16% W-15515: 1% ~ 26 % How do I know ha he esimaed condui porosiy is no wrong? Is i reasonable ha he marix flow is significanly larger han he condui flow during he mixed-flow sage?

18 Conclusions A new model is developed for simulaing he recession periods of kars spring hydrograph. The applicaion of he new model o he daa of he Madison Blue Spring indicaes ha he new model ouperforms he Mangin model and Fiorillo model. The new model enables he esimaion of effecive porosiy of marix and condui during he mixed-flow sage. Limiaions: The kars spring hydrograph mus have he marix-flow-dominaed sage so ha he condui flow and marix flow in he mixed-flow sage can be separaed. The model requires several parameers ha canno be direcly measured, such as he area of springshed and he hydraulic head of he condui reservoir a he beginning of he marix-flow-dominaed sage.