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Pressurized Irrigation Network Modelling: A

Flow Driven Analysis Approach

M. J. Calejo a, N. Lamaddalena  b, and L. S. Pereira c 

a COBA, SA – Avenida 5 de Outubro, 323, 1600-011 Lisboa, Portugal, mjc@coba.pt 

b IAMB, 70010 Valenzano-Bari, Italy, lamaddalena@iamb.it 

c ISA-UTL,1349-017 Lisboa, Portugal, lspereira@isa.utl.pt 

Abstract

Pressurized irrigation systems operating on-demand are characterized by several flow regimes. Each flowregime is defined by the configuration of hydrants operating simultaneously. The ICARE and AKLAmodels perform the performance analysis of irrigation system taking into account such flow regimes. Theanalysis performed by ICARE model is at system level, while AKLA performs the hydraulic analysis atthe hydrant level. The hydraulics of the Lucefecit network was modelled with the steady flow ICARE andAKLA models. The relative pressure deficit and the reliability indicators were computed at the hydrantslevel. The results of both models show that the analysis with ICARE model should be complemented withone analysis at the hydrant level. Looking just for the analysis with ICARE, the performance of Lucefecitirrigation network is quite bad with all configurations falling at the unsatisfied status but results of AKLAshow an acceptable performance of the network with few hydrants operating below the minimum pressure required.

Key words: Flow driven analysis, irrigation system analysis, indexed characteristic curves, performanceindicators.

1 Introduction

The pressurized irrigation systems operating on demand were object of several research approaches suchas that leading to the development of the models XERXES (CEMAGREF, 1990) and ICARE (CTGREF,1979) for the design and analysis, respectively. Recently, Lamaddalena (1997) developed the modelAKLA and Lamaddalena et al. (1998) presented a new approach for the design and analysis of irrigationnetworks operating on-demand. In this approach it is considered that the network can only beconveniently characterized when several flow regimes are considered. The application of these models for analysis and design require a detailed characterization of the network operation conditions. In the case of 

existing networks, data concerning the discharges and piezometric elevations at the upstream end of thenetwork relative to the peak period are required.

ICARE and AKLA models consider that the flow rate delivered by each hydrant is known and constant(flow driven analysis). This is true when the hydrants of the irrigation system are equipped with flowlimiter and pressure regulator; and when the total discharge of the hydrants operating simultaneously issmaller than the upstream flow limiter discharge. These conditions are verified in the Lucefecit system,Southern Portugal, thus both models could be applied and compared, which is the objective of this study.

2 Methodology for Flow Driven Analysis of Irrigation Systems

Two models are considered: ICARE (CTGREF, 1979; Labye et al., 1988) and AKLA (Lamaddalena,

1997). The ICARE model aims the computation of the indexed characteristic curves for the network while the analyses performed by AKLA are at the hydrant level and the hydrants with pressure deficit are

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clearly identified. Both models consider that the flow rate delivered by each hydrant is known andconstant (flow driven analysis). This is approximately true when the irrigation system are equipped withflow limiters and the hydrants have pressure regulators, and when the total discharge of the hydrantsoperating simultaneously is smaller than the upstream limited discharge.

In ICARE the hydraulic performance of the irrigation system is considered satisfactory when, for all

hydrants in operation, the following relation is true:

minr , j HH ≥   (1)

where is the hydraulic head [m] of the hydrant j within the configuration r of simultaneous

operating hydrants, and Hmin is the minimum required head [m] for appropriate operation of the farm

irrigation systems. For any value of the discharge Qo at the upstream end of the network, within 0 to

Qmax, different values of the piezometric elevation Zo satisfy that condition (1), each one corresponding

to a different hydrants configuration. If for all possible configurations r the couples (Qo, Zo)r referred to

0 < Qo < Qmax are calculated, a cloud of points is obtained in the plane (Q, Z) and these points are

contained between an upper and a lower envelope. The upper envelope corresponds to 100 % of satisfactory configurations, while the lower one concerns a situation where any configuration is notsatisfied. Between these two curves, it is possible to define other curves, the indexed characteristic curves.

r , jH

The ICARE model was developed to the computation of the indexed characteristic curves. A discretenumber of flow regimes, C, is established. Assuming that the discharge delivered by each hydrant is equalto its nominal discharge, when the upstream discharge is Qo the hydrants in operation may be randomly

drawn until the relationship is not anymore satisfied:

to NO QQ δ≤−   (2)

where Q NO

is the discharge corresponding the NO hydrants in operation simultaneously; and δt is the

accepted tolerance. In general, δt is assumed as equal to the value of the smallest hydrant discharge.According to Bethery (1990), the number of configurations, C, to be investigated for each dischargeshould be close to the total number of hydrants, NR.

When testing an irrigation network under flow driven conditions, it is possible to associate a piezometricelevation at the upstream end of the network to each discharge configuration, such that it may satisfy therelationship (1). At the end of the computation, to each Qo tested there are C values of Zo. The indexed

characteristic curves can be drawn by plotting, in the plane (Q, Z), the discharge values chosen and thecorresponding vectors, and by joining the points having the same percentage of configurations satisfied.

The performance of the network can be evaluated by the percentage of satisfied configurationscorresponding to the to the design Qo and Zo, that correspond to the set-point of the network. Despite the

importance of the indexed characteristic curves (Lamaddalena and Piccini, 1993), this information doesnot allow to identify which are the hydrants unsatisfied or to evaluate the respective pressure deficits.

The AKLA model is an improvement of ICARE because it allows the hydraulic performance analysis atthe level of each hydrant. The model considers the flow driven model analysis and it is based on themultiple generation of a number of hydrants simultaneously operating using a random number generator having a uniform distribution. Within each generated configuration r, a hydrant (j) is considered satisfied

when the condition is true.minr , j HH ≥

The relative pressure deficit at each hydrant ∆H j,r  is computed by:

minminr , jr , j H/H-HH =∆  (3)

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where H j,r  is the hydraulic head at the hydrant j within the configuration r, and Hmin is the minimum

required head. The representation of ∆H j,r in a plane where abscises correspond to the hydrants number 

and the ordinates to ∆H j,r clearly identify the hydrants where the pressure head is insufficient.

The AKLA model allows also the computation of a reliability indicator. The reliability is a performance

indicator, which describes how often the system fails (Hashimoto et al., 1982). This criterion isformulated assuming that the performance of an irrigation system can be described by a stationarystochastic process. If Xt is the random variable denoting the state of the system at time t, the possible

values of Xt may be shared into two sets: S, relative to satisfied conditions, and F, relative to the failure

cases. At each instant t the system may fall in one of these sets. Therefore, the reliability of a system can be described by the probability α that the system is in a satisfactory state, i.e.:

[ ]SXobPr  t ∈=α   (4)

From the definition of reliability, the following relationship can be assumed:

∑

∑

=

==αC

1r r , j

r , j

C

1r r , j

 j

Ih

IpIh  (5)

where α j is the reliability of the hydrant j and

⎩⎨⎧=

=

⎩⎨⎧=

=

0

1Ip

0

1Ih

r , j

r , j

 

if the hydrant j is closed in the configuration r 

if the hydrant j is open in the configuration r 

if H j,r  ≥ Hmin 

if H j,r < Hmin 

3 Application

The ICARE and AKLA models have been applied to the pressurized irrigation network of Lucefecit,south of Portugal, serving 950 ha. The pumping station was designed for the discharge 1153 l s-1 and theupstream piezometric elevation is 260 m. The total number of hydrants is 107 and the number of outlets is204, with nominal discharge ranging from 10 to 280 m3 h-1, and are equipped with an upstream flowlimiter and pressure regulator valves at the hydrants. Real data collected during the irrigation season 2001have been used to validate the models.

For the hydraulic simulation, the head losses, hL [m], are computed with the Chézy formula, and the

roughness coefficient is given by the Bazin relationship (Mendonça, 1975). The roughness coefficient of Bazin were γ = 0,36 for cast iron pipes, γ = 0,16 for asbestos pipes, and γ = 0,10 PVC pipes.

According to the design data, the piezometric elevation at the upstream of the network should be of 260,00 m, which corresponds to a pressure of 944 kPa. Pressure records at the upstream of the network (Calejo, 2003) show that, in general, the pressure available is greater than the design value. This cancause a faster wear and tear of the tubes at the upstream sections, with the consequent reduction of their useful life and increase of the roughness.

In Figure 1 are shown the indexed characteristic curves computed with ICARE. It shows that for themaximum flow rates recorded at the upstream end (≈750 l s-1), the value Zo = 260 m set at design is not

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enough since, for at least one hydrant H j<Hmin, the indexed characteristic curves indicate a poor hydraulic performance of the Lucefecit irrigation network. Anyway the results in Fig. 1 do not allow analysing howmuch hydrants have pressure deficit, as well as the severity of those deficits.

   U  p  s   t  r  e  a  m   p

   i  e  z  o  m  e   t  r   i  c  e   l  e  v  a   t   i  o  n   (  m

   )

0 5 0 1 0 0 15 0 2 00 2 5 0 3 00 3 5 0 4 00 4 5 0 5 00 5 5 0 6 00 6 5 0 7 00 7 5 0 8 00 8 5 024 0

24 5

25 0

25 5

26 0

26 5

27 0

27 5

28 0

28 5

29 0

29 5

30 0

10%

90%

Discharge (l s-1) 

Fig. 1. Indexed characteristic curves of the Lucefecit irrigation network (simulations with ICARE for 2000 random configurations

to each discharge tested at the upstream end of the network).

Figure 2 shows the relative pressure deficits simulated with AKLA for 2 000 flow regimes, Qo = 750 l s-1

 

and Zo = 260,00. . The unsatisfied outlets can be easily identified. Important negative relative pressure

deficits are observed only for the outlets H223-3 (node 216); H236-1 (node 218), H340-1 (node 329);

H340-2 (node 330) and H318-1 (node 332). Values of ∆

Hj,r < - 0,5 are indicative of the need for rehabilitation. In this case, solutions at the local level should be enough to assure an appropriate operation

of the system, because values of ∆Hj,r < - 0,5 just occur at 5 outlets. When Zo = 265,00 the number of 

unsatisfied outlets decrease drastically.

Outlet number

Fig. 2. Relative pressure deficits at the hydrants of Lucefecit irrigation network simulated with AKLA for Zo=260 m and

Qo = 750 l s-1.

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The reliability of the system is illustrated in the Figure 3. For values of Zo = 260 m there are some outlets

that present very low reliability but it is significantly improved when the piezometric elevation isincreased to Zo = 265 m (Figure 4).

   R  e   l   i  a   b   i   l   i   t  y

 Outlet node number

Fig. 3. Reliability of Lucefecit irrigation network. Analysis with AKLA for 2000 configurations Zo=260 m and Qo = 750 l s-1.

   R  e   l   i  a   b   i   l   i   t  y

 Outlet node number

Fig. 4. Reliability of Lucefecit irrigation network. Analysis with AKLA for 2000 configurations Zo=265 m and Qo = 750 l s-1.

4 Conclusions

The pressurized irrigation system of Lucefecit was simulated with the models ICARE and AKLA, that proved to be capable to reproduce the respective operation. The AKLA results show to be precious toolsfor a clear analysis of the hydraulic performance. With the results of AKLA model it is possible toidentify the areas with special problems for which specific measures and special solutions may be

adopted. The analysis of Lucefecit systems show the occurrence of pressure deficit in several outlets,which indicate a near impossible operation of one of them, H236-1 for Zo = 260,0 m. The pressure

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deficits observed are usually < 20 % when the piezometric elevation at the upstream is greater then thedesign value, Zo = 260,0 m. The reliability is usually maximum (α = 1,0) in most of the outlets but thisvalue goes down for less than 0,5 in 9 outlets. The observed pressure deficits indicate that sub-pressuresmay occur in the network, with risk of rupture of the conduits.

5 References

Bethery, J., 1990. Réseaux collectifs ramifiés sous pression, calcul et fonctionnement, Études hydraulique agricole, nº6. Cemagref,Antony.

Calejo, M.J., 2003. Design and Performance analysis of pressurized irrigation systems. Demand Modelling. Two Case Studies:Lucefecit and Vigia. PhD thesis. Instituto Superior de Agronomia, Universidade Técnica de Lisboa. Portugal (in Portuguese).

CEMAGREF, 1990. Logiciel XERXES-RENFORS, Optimisation économique des réseaux ramifiés sous pression, CEMAGREF,Aix-en-Provence.

CTGREF, 1979. Programme ICARE – Calcul des caractéristiques indicées. CTGREF, Division Irrigation, Note Technique 6, Aix-en-Provence.

Hashimoto, T., Sredomger, J.R., Loucks, D.P., 1982. Reliability, resilience and vulnerability criteria for water resources system

 performance evaluation. Water Resources Research 18(1): 14-20.

Labye, Y., Olson, M.A., Galand, A., Tsiourtis, N., 1988. Design and optimization of irrigation distribution networks. Irrig. andDrain. Paper 44, FAO, Roma.

Lamaddalena, N., 1997. Integrated simulation model for design and performance analysis of on-demand pressurized irrigationsystems. PhD thesis, Instituto Superior de Agromonia, Universidade Técnica de Lisboa.

Lamaddalena, N., Piccinni, A.F., 1993. Sull’utilizzo delle curve caratteristiche indicizzate di una rete irrigua per il dimensionamentodegli impianti di sollevamento. AIGR – Rivista di Ingegneria Agraria 3, pp.: 129-135.

Lamaddalena, N., Pereira, L.S., Ait Kadi, M., 1998. Modeling approach for design and performance analysis of on-demand pressurized irrigation systems. In: Zazueta, F., Xin, J. (Eds), Computers in Agriculture 1998, ASAE, St. Joseph, MI, pp. 159-166.

Mendonça, P.V., 1975. Excertos das Lições de Hidráulica Geral e Agrícola (5ª Edição). Instituto Superior de Agronomia,Universidade Técnica de Lisboa, Lisboa.

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