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Reliability-Based Pipe Size Computation of On-Demand Irrigation Systems

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Abstract

The variability of flow regimes in on demand pressurized irrigation systems leads to uncertainty in head at the nodes affecting the system performance, and thus it should be considered when designing and/or rehabilitating water distribution systems. Based on these considerations a new approach for the optimization of on demand pressurized irrigation systems is presented combining the minimization of cost with the maximization of reliability taking into account the stochastic variability of the flows into each section of the network. The new model, Clément and the cumulated random generated discharges model (FAO model) were applied to three pressurized irrigation networks of different dimensions (large, medium and small) operating on demand in Southern Italy. The optimization algorithm used in all the cases is the Labye iterative discontinuous method, a formulation of the dynamic programming. The results of the different models were compared showing that the cost of the optimal network calculated using the new model was reduced by more than 20%, without any significant decrease of the system reliability or reduction of the network capacity.

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Abbreviations

C :

total number of generated configurations

d :

hydrant nominal discharge, l s−1

dH :

variation of the pressure head, m

dP :

minimum cost variation, Euro

D s :

commercial pipe diameter, m

dY:

variation of the friction loss, m

EH :

minimum value of the excess head prevailing in all the nodes where the head changes, m

F :

set of all unsatisfactory states

H :

pressure head, m

Ih :

hydrant operation index

Ip :

pressure head index

J :

friction loss of the pipe diameter per unit length, m m−1

L :

generic length, m

M :

pathway starting form the network upstream end

m :

number of hydrants simultaneously operating

N :

total number of hydrants

P :

cost of the pipe diameter, Euro

Q :

discharge, l s−1 or m3 s−1

Re :

reliability

S :

set of all satisfactory states

SN :

sub-network

SN*:

elementary scheme

u :

dimensional coefficient of resistance, m−1 s2

v :

flow velocity, m s−1

Y :

head losses, m

Y*:

the value of the head loss corresponding to the largest diameter over its entire length if the section has two diameters, or the successive greater diameter if the section has only one diameter, m

Z 0 :

upstream piezometric elevation, m a.s.l

β:

coefficient

ΔYi :

the minimum value of (Yk,i - Y*)

ΔZ :

the difference between the upstream piezometric elevation for a particular flow regime, and the piezometric elevation, effectively available at the upstream end of the network.

γ :

roughness parameter of Bazin, m0.5

h :

hydrant

i :

iteration

in :

initial

j :

the most unfavorable hydrant

k :

section of the network

max :

maximum

min :

minimum

r :

configuration

sys :

system

t :

time

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Acknowledgement

The authors wish to acknowledge Dr. Alessandra Scardigno, researcher at the Mediterranean Agronomic Institute of Bari, who contributed in tuning up the modeling approach.

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Authors and Affiliations

  1. Land and Water Resources Management Department, CIHEAM – Mediterranean Agronomic Institute of Bari, Bari, Italy

    Nicola Lamaddalena, Roula Khadra & Youssef Tlili

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  1. Nicola Lamaddalena
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  2. Roula Khadra
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  3. Youssef Tlili
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Correspondence to Nicola Lamaddalena.

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Lamaddalena, N., Khadra, R. & Tlili, Y. Reliability-Based Pipe Size Computation of On-Demand Irrigation Systems. Water Resour Manage 26, 307–328 (2012). https://doi.org/10.1007/s11269-011-9919-6

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  • DOI: https://doi.org/10.1007/s11269-011-9919-6

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