Analytical Solutions of Intermittent Transient Groundwater Pumping Cost

Acknowledgments

Notation

A

constant coefficient;

C

pumping cost for steady state conditions;

D

matrix of the distances between wells;

D.S.

matrix of the values of different combinations;

E.V.

matrix of sums of D.S. matrix;

g_i

total pumping constraint for each time step;

H

Hessian matrix;

K

pumping cost for transient conditions;

L

objective function;

N

number of wells;

Q_j

flow rate of well j (m³/s);

$Q_T^i$

total pumping rate during period i (m³/s);

R

radius of influence (m);

r_mj

distance between wells m and j (m);

S

storativity of aquifer;

s_j

hydraulic head level drawdown at well j (m);

T

transmissivity of aquifer (m²/s);

W(u)

well function for infinite confined aquifer;

x

number of different combinations;

δ_j

distance between the initial horizontal level of the hydraulic head and the predefined reference level (m); and

λ_i

Lagrange multiplier for every constraint.

References