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GROUND WATER MANAGEMENT

GROUND WATER MANAGEMENT. PROBLEM DESCRIPTION. Aquifer of irregular geometry Pond - source of recharge Choose disposal sites to minimize the pollutant impact at various locations. MATHEMATICAL FORMULATION OF THE SIMULATION MODELS. Pollutant advection dispersion equation

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GROUND WATER MANAGEMENT

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  1. GROUND WATER MANAGEMENT

  2. PROBLEM DESCRIPTION • Aquifer of irregular geometry • Pond - source of recharge • Choose disposal sites to minimize the pollutant impact at various locations

  3. MATHEMATICAL FORMULATION OF THE SIMULATION MODELS • Pollutant advection dispersion equation • Steady state ground water flow equation

  4. ADVECTION PROCESSES • Seepage velocity • K hydraulic conductivity • n effective porosity • h hydraulic head • Advective flux h h1 h2 vx x1 x X2

  5. MATHEMATICAL FORMULATION OF THE MANAGEMENT MODEL • Maximize the objective function • subject to R(f){c*} {f}0 • where {u}=(1,1, …, 1) • f vector pollutant disposal rates • Steady state ground water flow equation

  6. SOLUTION OF THE MANAGEMENT MODEL • Transform the inequalities in equalities and modify the objective function • R(f)={c*}+dc • where p(dc) is a negative function if dc<0 and p(dc) = 0 if dc>0 • Use a constrained optimization procedure to solve the modified problem • Steady state ground water flow equation

  7. OPTIMIZATION TECHNIQUES • Steepest descent method • Example: F(x,y)=x2+2y2-4x-4y+6 y x

  8. OPTIMIZATION TECHNIQUES (ctd.) • Newton methods • Example: F(x,y)=x2+2y2-4x-4y+6

  9. EFFICIENT FORMULATION OF THE RESPONSE OPERATOR • Use the physical models to generate a large number of simulations corresponding to various combinations of {f} • Derive statistical relationships (universal functions) between {f} and {c} at the critical locations

  10. EFFICIENT FORMULATION OF THE RESPONSE OPERATOR (ctd) • Determine the set of parameters w that satisfies • F(w,fi)=R(fi)  fi in {f} • This is equivalent to • Once F(w,*) is determined, solve the initial management problem

  11. EXAMPLE x*w_11+w_12 y1 y1*h_1+y2*h_2 y3*h_3+h_4 x*w_21+w_22 y2 x x*w_21+w_12 y3

  12. WRAP-UP • A mathematically rigorous formulation for groundwater management may be derived • Mathematical tools for solving the groundwater management problems are available • Universal approximations can be effectively used to reduce the computational load

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