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Water Utility Journal 16: 57-66, 2017. © 2017 E.W. Publications

Optimal design and on demand operational analysis using performance indicators in a pumped irrigation network

A-S. Petropoulou, D.K. Karpouzos* and P.E. Georgiou

Department of Hydraulics, Soil Science and Agricultural Engineering, School of Agriculture, Aristotle University of Thessaloniki, 54124, Thessaloniki, Greece * e-mail: [email protected]

Abstract: This study conducts an optimization and performance analysis of an on-demand pressurized irrigation network, which aims to combine least cost design and adequate hydraulic operation. For this purpose, the COPAM software was used as a modelling tool. First, the design of the irrigation network was optimized using Labye’s Iterative Discontinuous Method (LIMD) for three different values of operation quality. Next, the operational behavior of the network with the lowest annual total cost (lowest operation quality) is studied in conditions of normal and higher values of discharges. Performance analysis includes the design of characteristic curves at network level and the use of various indicators at hydrant level. Results were encouraging and highlighted the need for the design of a network with lower operation quality and of analysing its performance at higher demand conditions.

Key words: Pumped irrigation network, performance analysis, on demand operation

1. INTRODUCTION

Pressurized irrigation distribution networks are designed so that the pressure delivered at all hydrants is equal or higher than the established minimum pressure required to properly operate the on-farm irrigation systems. However, the actual operating conditions of these systems can be different from those assumed at the design stage (Fouial et al., 2017). Possible alterations may occur at a later stage due to modifications in the irrigation systems, changes in the practices and the behavior of users, or even in future trends related to the effective application of the irrigation water. Furthermore, economic resources are usually limited. Such alterations may cause higher demands of discharge in the upstream end of the network. Therefore, there is a need to design a network in an economical way while demand peaks are also taken into account. With this aim in view, several models have been developed in order to simulate demand flows in pressurized irrigation networks by incorporating the variability of the distribution of flows in each section of the network (e.g., Khadra and Lamaddalena, 2006; Diaz et al., 2007; Zaccaria et al., 2013a,b, 2014). Also, the replacement of open channel distribution systems with pressurized irrigation networks has significantly improved conveyance efficiency, but has resulted in high energy consumption (Diaz et al., 2011). The operational performance of irrigation networks is an additional important factor in the design procedure, and thus, various performance indicators have been proposed and applied in the relative international bibliography (e.g., Hashimoto et al., 1982; Molden and Gates, 1990; Lamaddalena and Pereira, 1998; Khadra and Lamaddalena, 2010; Lamaddalena et al., 2012).

The objective of this paper is the optimal design of a collective pressurized and on-demand irrigation network and the analysis of its operation during increased demand requirements which result to higher upstream discharges. The hydraulic performance assessment of the network is elaborated using characteristic curves and indicators through several flow regime modelling.

For this purpose, the COPAM software (Combined Optimization and Performance Analysis Model) (Lamaddalena, 1997; Lamaddalena and Sagardoy, 2000) was used for the optimal design and analysis of the network. More specifically, a type of Labye method based on dynamic programming was used for the pipeline design optimization and the ICARE (CTGREF, 1979) and

58 A-S. Petropoulou et al.

AKLA (Lamaddalena, 1997; Lamaddalena and Sagardoy, 2000) modules for the performance analysis. The ICARE model provides information for the general performance of an on-demand irrigation network through the calculated characteristic curves. In the AKLA model, the performance analysis is implemented at the hydrant level through the computation of two indicators: (i) the relative pressure deficit (RPD); and (ii) the reliability (α). In this paper, for a more detailed analysis at the hydrant level, two new complementary indicators are proposed: (i) the Hydraulic Pressure Surplus (HPS), and (ii) the Hydraulic Pressure Deficit (HPD), which represent the mean surplus or deficit of pressure at the hydrant level for all configurations, respectively.

The optimal design of the network is calculated for three operating quality values and the hydraulic response of the network, that was elaborated for P(U)=90% is investigated for normal (P(U)=90%) and increased demands (P(U)=95% and P(U)=99%). Results showed that the network, when higher discharges were applied at the upstream end, responded quite satisfactorily according to the obtained values of indexed characteristic curves and the ones computed by means of different performance indicators.

2. METHODOLOGY

2.1 Design of irrigation network

In an on-demand irrigation network, the determination of discharges is usually performed using Clément’s first model (Clement, 1966), which is based on a probabilistic approach, whereby within a population of R installed hydrants, the design discharge is calculated on the basis of the number of simultaneously operating hydrants N:

Q = N ⋅d = (R ⋅p+ U ⋅ R ⋅p 1− p( )) ⋅d, p= q ⋅s( ) r ⋅d( ) (1)

where Q [L/s] represents the discharge at the upstream end of the network, R the total number of installed hydrants, d [L/s] the nominal discharge of the hydrant, U is Clément’s use coefficient, r represents the coefficient of utilization of the network (quotient of operating hours per 24 hours), p the elementary probability of operation of each hydrant, q [L/s/ha] the specific continuous discharge, and s [ha] the irrigated area per hydrant.

The calculation of the head losses is elaborated based on Darcy’s equation using Bazin’s coefficient of roughness (Lamaddalena and Sagardoy, 2000):

( )20.5 2 5Y 0.000857 1 2γ D Q D L− −= + ⋅ (2)

where Y [m] denotes the head losses, Q [m3 s-1] is the discharge, γ [m0.5] defines the Bazin’s roughness parameter , L [m] represents the length of the section, and D [m] the diameter of the section.

The calculation of the minimum cost of the irrigation network is effected by the Labye’s Iterative Discontinuous Method (LIMD), which is a form of dynamic programming (Labye, 1981; Labye et al., 1988). The total cost of the irrigation network to be minimized is considered as the sum of the pipeline cost Cpipe and the pumping energy cost in an annual base Cenerpump according to the following simple equations (Karpouzos, 2012):

pipe enerpumpmin f C C= + (3)

( )( )

tNpman

pipe i i rf rf enerpumpti 1

r 1 r Α β g Q HC L CD C , C , Cn1 r 1=

+ ⋅ ⋅ ⋅ ⋅= ⋅ ⋅ = =+ −

∑ (4)

Water Utility Journal 16 (2017) 59

where r represents the annual interest rate equal to 0.05, t is the depreciation period of the network materials equal to 40 years, A is the irrigation period equal to 1000 h, β designates the electricity costs equal to 0.085 €/kWh, g defines the specific gravity of water equal to 9.81 kN/m3, Q represents [m3 s-1] the discharge at the upstream end of the network, Hman [m] the required pressure head, n the coefficient of efficiency of the pumping pair equal to 0.65, CDi [€ m-1] the cost of the nominal diameter of the section i, Li [m] the length of the pipe section i, and Np the total number of pipe sections of the network.

2.2 Performance analysis of irrigation network

After the calculation of the optimal diameters using Labye’s Iterative Discontinuous Method, the performance analysis of the network is conducted. The analysis was performed using the COPAM program (Lamaddalena and Sagardoy, 2000; Calejo et al., 2008; Kanakis et al., 2014), which incorporates the ICARE and AKLA models for the analysis at a network level and at a hydrant level, respectively.

The ICARE model (CTGREF, 1979) provides information for the general performance of an on-demand irrigation network through the calculated characteristic curves. For a range of discharge values and piezometric elevation values, different combinations of the above pairs are examined according to the hypothesis of successful minimum pressure delivery in order to form the characteristic curves of the network. Subsequently, the design piezometric elevation at the upstream end of the network is singled out and allocated to a specific characteristic curve. For example, a set point (discharge, piezometric elevation) allocated in a curve 80% means that 80% of the configurations with this combination were successful in terms of meeting the minimum pressure requirement of all the operating hydrants of the network.

The AKLA model (Lamaddalena and Sagardoy, 2000) allows analysis at the hydrant level through the computation of the relative pressure deficit and the reliability indicators. Analysis is also based on the generation of a set of configurations, i.e., the set of hydrants simultaneously open, corresponding to a specific discharge at the upstream end of the network. A configuration is satisfied when, for all the operating hydrants of the configuration, the following relationship is respected:

j,r minH H≥ (5)

where Hj,r [m] represents the hydraulic head of the hydrant j within the configuration r, and Hmin [m] represents the minimum required head of the hydrants for the appropriate operation of the irrigation system.

The relative pressure deficit (RPD) at each hydrant j and for each configuration r is defined as:

RPDj,r =

H j,r

Hmin

−1 (6)

where Hj,r and Hmin as described before. It should be noted that RPD takes positive values when a surplus occurs and a negative when a deficit occurs.

The reliability indicator describes the probability of a successful delivery of pressure requirement and it refers to the hydrant level. It is computed using the following equation:

C C

j j,r j,r j,rr 1 r 1

α Ih Ip Ih= =

= ⋅∑ ∑ (7)


where αj is the reliability of the hydrant j,Ih!,! Ihj,r =1 if the hydrant j is open in the configuration r, Ihj,r Ih!,!=0 if the hydrant j is closed in the configuration r,Ip!,! Ipj,r =1 if the pressure head at the hydrant j, which is open in the configuration r, is higher than the minimum pressure head,Ip!,! Ipj,r=0 if the pressure head at the hydrant j, which is open in the configuration r, is lower than the minimum pressure head, and C represents the total number of the generated configurations.

For a more detailed analysis at hydrant level, an indicator of Hydraulic Pressure Surplus (HPS) is proposed and incorporated in the present paper, as defined below:

Cj,r

j,rr 1 min

j C

j,rr 1

HI

HHPS 1

I

=

=

⎛ ⎞⎜ ⎟⎝ ⎠= −

∑

∑ (8)

where HPSj is the pressure surplus at hydrant j, Hj,r [m] is the pressure head of hydrant j in the configuration r, Hmin [m] represents the minimum required head of the hydrants for the appropriate operation of the irrigation system, Ij,r =1 if the hydrant j is open in the configuration r and its pressure head (Hj,r) is greater or equal than Hmin and Ij,r =0 otherwise, while C represents the total number of the generated configurations.

The complementary indicator Hydraulic Pressure Deficit (HPD) is defined in a similar way as HPS:

Cj,r

j,rr 1 min

j C

j,rr 1

HI

HHPD 1

I

=

=

⎛ ⎞⎜ ⎟⎝ ⎠= −

∑

∑ (9)

where HPDj is the pressure deficit at hydrant j, Hj,r [m] is the pressure head of hydrant j in the configuration r, Hmin [m] represents the minimum required head of the hydrants for the appropriate operation of the irrigation system, Ij,r =1 if the hydrant j is open in the configuration r and its pressure head (Hj,r) is less than Hmin and Ij,r =0 otherwise, while C represents the total number of the generated configurations.

3. IRRIGATION NETWORK DATA

The pressurized irrigation network under investigation and its pumping station (A) are presented in Figure 1. The distribution of the irrigation water is performed by an on-demand irrigation system using R=153 installed hydrants, with 6 L s-1 discharge per hydrant, each one serving 2.5 ha of irrigation land, with a minimum pressure head Hmin=35 m, while the elevation of the pumping station is equal to 61.4 m.

The specific continuous discharge for the peak month was considered equal to qο = 0.05 L s-1

acre-1. Clément’s coefficient of network use was considered equal to r=0.667 and the minimum number of terminal open hydrants was equal to 10. The roughness coefficient of the Darcy–Bazin equation is taken as equal to γ=0.06 m0.5 (Stefopoulou and Dercas, 2012). The optimal design is performed for operation quality P(U)=90% and the performance analysis is elaborated for three values of operation quality P(U)=90%, P(U)=95% and P(U)=99% in order to investigate the operational response of the network under different demand conditions. The performance analysis was based on ICARE and AKLA models using indicators and multiple configurations (C=300) of discharge distribution (Lamaddalena and Sagardoy, 2000).


Figure 1. Layout of the irrigation network

4. RESULTS AND DISCUSSION

The optimum design of the network with operation quality equal to P(U)=90% (Q=336 L s-1) resulted in an optimal pressure head at the upstream end of the network equal to 58.1 m while the annual total cost (energy and pipelines) is 54,488 €. If the network was designed using operation quality of P(U)=95% (Q=348 L s-1) and P(U)=99% (Q=366 L s-1), the annual total cost would be 55,921 € and 57,463 €, respectively. So, using higher values of operation quality, P(U)=95% and P(U)=99% in our case produces an increase of total annual cost in comparison to P(U)=90% by


2.63% and 5.46%, respectively. The aim of this paper is to analyze the operation behavior of a more economical network [P(U)=90%] with increasing demand conditions [P(U)=95% and P(U)=99%].

The performance analysis of the pressurized irrigation network designed with P(U)=90% is evaluated through 300 configurations of discharge values that correspond to the three operation qualities mentioned above. For the computed piezometric elevation at the upstream end of the network Zo==119.5 m (corresponds to P(U)=90%) and the minimum required head of the hydrants Hmin=35 m, the characteristic curves produced by the ICARE model for the discharges of 336 L s-1, 348 L s-1 and 366 L s-1 are presented in Figures 2a, b, c, respectively.

Figure 2. Characteristic curves for the discharges (a) 336 L s-1, (b) 348 L s-1 and (c) 366 L s-1

In Figure 2a, it can be seen that the total of the examined configurations is satisfied more than 90% as the set-point Po= (336 L s-1, 119.5 m) falls on the characteristic curve of 92%. The set-point Po= (348 L s-1, 119.5 m) (Figure 2b) corresponds to 90% while the more severely demanding state Po= (366 L s-1, 119.5 m) (Figure 2c) decreases to the 75% indexed characteristic curve. Results are encouraging, however; the characteristic curve analysis provides a general view of the performance and should be examined in combination with a more detailed analysis at the hydrant level.

Figure 3 shows the curves of the probabilities that a given percentage of unsatisfied hydrants (PUH) could be exceeded; they are computed using 300 random configurations with the upstream elevation 119.5 m. It can be noted that if a 10% probability curve is selected, the percentage of unsatisfied hydrants for the highest examined upstream discharge (366 L s-1) is only about 7 %, while if a 30% probability curve is selected, the percentage of unsatisfied hydrants for the highest examined upstream discharge (366 L s-1) decreases further and reaches 2 %.

Next, the AKLA model is used to calculate the indicators of reliability and relative pressure deficit at each hydrant. These indicators are presented in Figures 4, 5 and 6. For the upstream discharge of 336 L s-1, only 17 hydrants failed to obtain the minimum required pressure and the maximum failure did not exceed 4% (α=96%) of the total number of configurations (Figure 4a). The relative pressure deficit for these hydrants was very small and its maximum value did not exceed 15% (-0.15) while the rest of negative values were less than 10% (-0.1) (Figure 4b).

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Figure 3. Percentage unsatisfied hydrants (PUH, %) of the designed network P(U)=90% for various upstream discharges

Figure 4. (a) Reliability and (b) Relative pressure deficit of hydrants for upstream discharge of 336 L s-1

For the upstream discharge of 348 L s-1, 29 of the total number of 153 hydrants did not deliver

the minimum required pressure and the maximum failure did not exceed 8% (α=92%) of the total number of configurations (Figure 5a). The relative pressure deficit for these hydrants was quite limited and its maximum value did not exceed 18% (-0.18) while the majority of relative pressure deficits were also less than 10% (-0.1) (Figure 5b).

For the upstream discharge of 366 L s-1, 36 of the total number of 153 hydrants did not provide the minimum required pressure and the maximum failure was about 21% (α=79%) of the total number of configurations (Figure 6a). The relative pressure deficit for these hydrants was quite limited and its maximum value did not exceed 20% (-0.20) while the majority of relative pressure deficits were also less than 10% (-0.1) (Figure 6b).


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likely to fail are located near the downstream ends of the network. From the results of 300 configurations produced by the AKLA model, the HPS and HPD new

indicators were also computed. The HPS and HPD indicators aim to determine the surplus/deficit of pressure at the hydrant level for all the configurations where the hydrant was open and the pressure head was greater/less than the minimum required. They form an indicator of intensity rather than quantity, since they offer an overview of magnitude of pressure surplus/deficit. The estimation of these indicators is performed, in the same way as in our previous analysis, namely for the three upstream discharges.

Figure 7a concerns the upstream discharge of 336 L s-1 where the maximum HPS is 0.55, the median HPS is 0.38 and the minimum HPS is 0.18. Respectively, in Figure 7b, HPD ranges from 0.01 to 0.07 with a median of 0.04 and applies only for a very limited number of hydrants.

Figure 7. (a) Hydraulic Pressure Surplus (HPS) and (b) Hydraulic Pressure Deficit (HPD) of hydrants for an upstream discharge of 336 L s-1

Figure 8a concerns the upstream discharge of 348 L s-1 where the maximum HPS is 0.55, the median HPS is 0.35 and the minimum HPS is 0.16. Respectively, in Figure 8b, HPD ranges from 0.01 to 0.10 with a median of 0.04 and applies only to 29 hydrants.

Figure 9a concerns the upstream discharge of 366 L s-1 where the maximum HPS is 0.54, the median HPS is 0.32 and the minimum HPS is 0.12. Respectively, in Figure 9b, HPD ranges from 0.01 to 0.07 with a median of 0.04 and applies only to 36 hydrants.

It can been seen that the magnitude of surplus and deficit does not change significantly by the increase of the total water demand (from 336 L s-1 to 366 L s-1), which confirms, in conjunction with the above analysis, that the number of hydrants that failed to meet the minimum required pressure is the only main parameter that varies. However, even if this number of hydrants increases with the increase of the discharge, this indicator provides the information that the deficit is kept quite low since the median does not exceed 0.04 in all cases.

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Figure 8. (a) Hydraulic Pressure Surplus (HPS) and (b) Hydraulic Pressure Deficit (HPD) of hydrants for upstream discharge of 348 L s-1

Figure 9. (a) Hydraulic Pressure Surplus (HPS) and (b) Hydraulic Pressure Deficit (HPD) of hydrants for upstream discharge of 366 L s-1

5. CONCLUSIONS

The network was optimally designed by means of Labye’s Iterative Discontinuous Method (LIMD) using three operation qualities P(U)=90% (Q=336 L s-1), P(U)=95% (Q=348 L s-1) and P(U)=99% (Q=366 L s-1). The annual total cost of the network designed with the lowest P(U) was found to be equal to 54,488 € while for P(U)=95% and P(U)=99% the cost was 2.63% and 5.46% higher, respectively. Next, the network of P(U)=90% was selected as the base case and its performance was analyzed for the design discharge Q=336 L s-1 and also for higher discharges corresponding to P(U)=95% (Q=348 L s-1) and P(U)=99% (Q=366 L s-1). Results showed that the network of P(U)=90% responded very well, as expected, for the design discharge of 336 L s-1. Concerning the performance analysis of the base network (P(U)=90%), when higher discharges were applied at the upstream end, the network responded quite satisfactorily according to the obtained values of indexed characteristic curves and the ones computed by means of different performance indicators. The results of pressure delivery failure at the hydrant level highlight the need to investigate the design of an irrigation network with a lower operation quality and the analysis of the performance of the network at higher demand conditions (higher upstream discharge), in order to achieve the maximum economy with respect to the degree of pressure constraint violation.

ACKNOWLEDGEMENTS

An initial shorter version of the paper has been presented in Greek at the 3rd Joint Conference

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(13th of the Hellenic Hydrotechnical Association, 9th of the Hellenic Committee on Water Resources Management and 1st of the Hellenic Water Association) “Integrated Water Resources Management in the New Era”, Athens, Greece, December 10-12, 2015.

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