1 / 19

Ye Zhang 1 , Jianying Jiao 1 , Juraj Irsa 2 , Dongdong Wang 1 yzhang9@uwyo

MODFLOW and More, June 2-5, Golden, CO. Direct Method of Parameter Estimation for Steady-State Flow in Heterogeneous Aquifers with Unknown Boundary Conditions. Ye Zhang 1 , Jianying Jiao 1 , Juraj Irsa 2 , Dongdong Wang 1 yzhang9@uwyo.edu

grover
Télécharger la présentation

Ye Zhang 1 , Jianying Jiao 1 , Juraj Irsa 2 , Dongdong Wang 1 yzhang9@uwyo

An Image/Link below is provided (as is) to download presentation Download Policy: Content on the Website is provided to you AS IS for your information and personal use and may not be sold / licensed / shared on other websites without getting consent from its author. Content is provided to you AS IS for your information and personal use only. Download presentation by click this link. While downloading, if for some reason you are not able to download a presentation, the publisher may have deleted the file from their server. During download, if you can't get a presentation, the file might be deleted by the publisher.

E N D

Presentation Transcript

  1. MODFLOW and More, June 2-5, Golden, CO Direct Method of Parameter Estimation for Steady-State Flow in Heterogeneous Aquifers with Unknown Boundary Conditions Ye Zhang1, Jianying Jiao1, Juraj Irsa2, Dongdong Wang1 yzhang9@uwyo.edu 1Dept. of Geology & Geophysics, University of Wyoming, Laramie, WY 2 Optimum Engineering Solutions, Edwardsville, IL http://faculty.gg.uwyo.edu/yzhang/

  2. Aquifer Inversion: Non-Uniqueness Observations: 3 heads 1 flow rate Both solutions yield zero obj  both flow fields are perfectly calibrated to the observed data  Results are non-unique. obj=0 obj=0 Irsa, J., and Y. Zhang (2012) Water Resour. Res., 48, W09526, doi:10.1029/2011WR011756.

  3. New Inverse Method: Objective • Simultaneously estimate aquifer: • hydraulic conductivities (Ks), • source/sink strengths (Ns), • boundary conditions (BC), • while accounting for subsurface static & dynamic data uncertainty.

  4. New Inverse Method: Theory • Aquifer flow equation (below, unconfined) + a set of BC (not shown): • Global continuity of hydraulic head and Darcy flux at grid cell boundaries: Fundamental solution of the flow equation • Local Conditioning by measurement data: Depending on the goal of inversion, one or more data equations are needed. T • Parameter constraint equations (not used yet)

  5. Confined Aquifer: N=0 • No recharge, no wells • 40 hydraulic head measurements + 1 subsurface flow rate measurement • K varies over 2 orders of magnitude • only K1 is estimated: K2, K3, K4 obtained from prior info EQs Irsa & Zhang (2012) WRR True Field (FDM) Inversion (40+1) BC Recovery

  6. Confined Aquifer: Source/Sinks Inversion grid* Measurements: 62 fluid pressures + well rates (Q1, Q2) FDM (LGR at wells) * Inverse grid has 31 cells without LGR Jiao & Zhang, in prep.

  7. Unconfined Aquifer: Uniform N Jiao & Zhang, in review. True heads (<50x50x20) Inverted heads (31 cells + LGR)

  8. Inversion of Keq: Structured field Inversion for Keq: Random field Equivalent K True Keq • Given: • Random Gaussian ln(K) • 25 (5x5) observations on heads + 1 Qy (0%) • Inversion result: 30x30 grid, K=2.4 True: K(x,y) True Keq • Given: • Random Gaussian ln(K) • 15 (3x5) observations on heads +1 Qy (0%) • Inversion result: 30x30 grid, K=2.6 True equivalent K: 37.0 True equivalent K: K=2.7 • Given: • 18 (3x6) observed heads • 1 Qy along y=0.5 • error (3%, std=13) • Result: 2x2 grid K=39.6 • Given: • 18 (3x6) observed heads • 1 Qy along y=0.5 • error (3%, std=13) • Result: 10x10 grid K=1.6 • 30x30 grid K=1.8 True Keq Inverted: Keq • Given: • Random Gaussian ln(K) • 15 (3x5) observations on heads +1 Qy (0%) • Inversion result: 30x30 grid, K=2.2

  9. Reservoir Inversion: Effective Parameter Estimation

  10. Stochastic Inversion

  11. Stochastic Inversion hydrofacies Static Data Integration 12 wells sampled head & fluxes Dynamic Data Integration

  12. Stochastic Inversion Wang, Zhang, & Irsa, in prep.

  13. Fractured Aquifer Zhang, Zhang, & Wang, in prep.

  14. Summary • A new inverse theory for modeling steady-state single-phase flow in confined and unconfined aquifers; • Simultaneous estimation of heterogeneous parameters (multiple Ks, multiple Ns) and BC; • Given sufficient and adequate measurement data, solutions (parameters, BC, flow fields) are “unique”; • Stable outcomes with increasing measurement errors (not shown); • Computationally efficient; • Can account for subsurface static data uncertainty; • If underlying parameter (K, N) heterogeneity is unknown, yield equivalent or average parameter values; • Is not sensitive to high K contrast (Kmax/Kmin up to 106tested for 2D);

  15. Extra

  16. Inversion: Work Breakdown • Irsa & Zhang (2012): 2D confined aquifer inversion without source/sink: jointly estimate a single k & BC; • (2) Zhang (2013): 1D Unconfined aquifer inversion with source/sink: jointly estimate k1, k2, k3, N1, N2, N3, & BC, using pressure data and as few as flow rate from a single well; Estimate equivalent k* & average source/sink terms; • (3) Ongoing work: • 3D confined inversion without source/sink  parameter sensitivity; • 2D unconfined inversion with source/sink; estimate equivalent k* tensor & average source/sink; • 2D stochastic confined inversion (without source/sink): accounting for static data uncertainty; • 2D fractured aquifer inversion (without source/sink): strongly variable heterogeneity

  17. Confined Aquifer: Tensor Inversion (N=0) Inversion: 0% error (31 cells) True Model (<50x50 cells) Inversion: ±0.2% err (31 cells) FDM Solution: h(x,y) 31 heads + 10 q sampled Also successful: simultaneous inversion of diagonal K* (Kx/Ky=100) & nonzero N;

  18. 3D Inversion (Confined Aquifer)

  19. 3D Inversion (Confined Aquifer) Irsa & Zhang (2012) under review • Heterogeneous Aquifer: • 2 zones (Kmax/Kmin=1,000) • Linear flow • Homogeneous Aquifer • Non-linear flow Data: 12 heads & one qz (no flow rate measurement); FDM FDM One flow rate measurement One flow rate measurement inversion inversion FDM FDM

More Related