GROUND WATER MANAGEMENT

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GROUND WATER MANAGEMENT
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PROBLEM DESCRIPTION

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

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MATHEMATICAL FORMULATION OF THE SIMULATION MODELS

• Pollutant advection dispersion equation
• Steady state ground water flow equation

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ADVECTION PROCESSES

• Seepage velocity
• K hydraulic conductivity
• n effective porosity
• h hydraulic head
• Advective flux

h
h1
h2
vx
x1
x
X2
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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

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SOLUTION OF THE MANAGEMENT MODEL

• Transform the inequalities in equalities and
  modify the objective function
• R(f)cdc
• where p(dc) is a negative function if dclt0 and
  p(dc) 0 if dcgt0
• Use a constrained optimization procedure to solve
  the modified problem
• Steady state ground water flow equation

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OPTIMIZATION TECHNIQUES

• Steepest descent method
• Example F(x,y)x22y2-4x-4y6

y
x
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OPTIMIZATION TECHNIQUES (ctd.)

• Newton methods
• Example F(x,y)x22y2-4x-4y6

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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

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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

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EXAMPLE
xw_11w_12
y1
y1h_1y2h_2 y3h_3h_4
xw_21w_22
y2
x
xw_21w_12
y3
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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