Optimal design of drip irrigation submains: presure-compensating emitters

154 Re is a de la Facul ad de Ciencias Ag a ias C. E. Schila di Sícoli e al. Op imal design o d ip i iga ion submains: p esu e-compensa ing emi e s Diseño óp imo de sec o es de iego po go eo: emiso es au ocompensados Ca los E. Schila di Sícoli 1 *, Rica do Aliod 2, Fe nando Zo illa 2, José An onio Mo ábi o 1, 3 O iginales: Recepción: 26/03/2018 - Acep ación: 18/05/2019 Abs ac Fo a d ip i iga ion sys em o be success ul, i mus be well designed, p ope ly ins alled, managed and main ained. In plo s wi h s eep slopes and i egula opog aphy ha ha e li le land le eling capaci y and/o ha equi e e y e icien ag icul u al machine y, d ip i iga ion designs gene ally use p essu e-compensa ing emi e s. This wo k de elops a me hodology and implemen s i in a compu e ool ha makes i possible o op imally de e mine in d ip-i iga ed plo s wi h p essu e-compensa ing emi e s: a) elescopic sizing o he submain mani old pipe, b) supply al e p essu e and c) subuni ’s in ake al e loca ion, when conside ing all hyd aulic-economic aspec s in he design phase. Techniques o op imal sizing o pipe ne wo ks and simula ion o hyd aulic ne wo ks unde p essu e a e linked o economic analyzes o o al annualized cos s. Finally, he p ac ical use ulness o he p oposed me hodology is shown wi h h ee examples o complex eal cases whe e pipe design cos s a e educed by 16-34% and ene gy cos s by 37-51%. Keywo ds d ip i iga ion • design • submain • p essu e-compensa ing emi e s 1 Uni e sidad Nacional de Cuyo. Facul ad de Ciencias Ag a ias. Almi an e B own 500. Luján. C. P. M5528AHB. Mendoza. A gen ina. * cschila di@ ca.uncu.edu.a 2 Uni e sidad de Za agoza. Escuela Poli écnica Supe io de Huesca (EPSH). Ca e e a de Cua e S/N. C. P. 22071. Huesca. España. 3 Cen o Regional Andino. Ins i u o Nacional del Agua. Belg ano 210 Oes e (M55500FIF). Mendoza. A gen ina. Re . FCA UNCUYO. 2019. 51(2): 154-166. ISSN (en línea) 1853-8665. 155 Tomo 51 • N° 2 • 2019 Op imal design o d ip i iga ion submains: P esu e-Compensa ing Emi e s Resumen Pa a que un sis ema de iego po go eo enga éxi o, debe es a bien diseñado, adecua- damen e ins alado, ap opiadamen e manejado y man enido. En pa celas con g andes pendien es, opog a ía i egula , con poca capacidad de ni elación y/o en si uaciones donde se p e ende ene una al a e iciencia de la maquina ia ag ícola, los diseños de iego po go eo gene almen e ecu en a la u ilización de emiso es au ocompensan es. El p esen e abajo desa olla una me odología y ealiza su implemen ación en una he amien a in o má ica que pe mi e en sec o es de iego po go eo con emiso es au ocompensan es de e mina de mane a óp ima: a) el dimensionado elescópico de la ube ía secunda ia (po a-la e ales), b) la p esión en ál ula de alimen ación del sec o y c) el pun o de alimen ación del sec o (ubicación de dicha ál ula); conside ando odos los aspec os hid áulicos-económicos in oluc ados en la ase de diseño. Pa a ello, se inculan écnicas de dimensionado óp imo de conducciones y simulación hid áulica de edes a p esión con análisis económicos de cos os o ales anualizados. Finalmen e, se demues a la u ilidad p ác ica de la me odología desa ollada median e ejemplos eales de aplicación, donde los cos os de diseño se educen en e 16-34% y los cos os de ene gía en e 37-51%. Palab as cla e iego po go eo • diseño • subunidades • emiso es au ocompensan es In oduc ion The success o a d ip i iga ion sys em depends essen ially on p ope design, selec ion and ins alla ion (25) and co ec managemen and main enance (12). In o de o ensu e i s inancial sus ainabili y, he bene i o he i iga ed c op mus co e he high capi al cos s which his me hod en ails (17). Op imal design o d ip i iga ion is impo an o inc ease he in es men s in and bene i s de i ed om i iga ion (16). Such design should aim a minimizing o al annualized piping and ene gy cos s (32, 33) and ensu ing wa e dis ibu ion uni o mi y (4, 6, 17, 19) In s eep slope plo s (20) wi h i egula opog aphy and li le land le eling capaci y and/o ha equi e highly e icien ag icul- u al machine y, d ip i iga ion sys ems gene ally use p essu e-compensa ing emi e s. They deli e a p ac ically cons an discha ge o e a wide ange o p essu es (20, 21, 35), called e ec i e p essu e compensa ion ange, be ween 5 and 35 m, and can lowe he limi s by ± 2 o aise hem by ± 5 m (3), depending on each manu ac- u e . P essu e egula ion is achie ed by means o an elas ic memb ane ha co e s he low pa h (36). A p essu e-compen- sa ing emi e can be desc ibed by he ollowing p essu e-discha ge unc ion (26): (1) whe e: q = low o he emi e [L] 3 [T] -1 K = cha ac e is ic discha ge coe icien o he emi e [L] 3-x [T] -1 h = emi e p essu e [L] x = emi e discha ge exponen q0 = cons an discha ge o he compen- sa ion ange [L] 3 [T] -1 0 0 0 max ,0 , x kh h h qq h h h  〈 ≤ 〈 〈  156 Re is a de la Facul ad de Ciencias Ag a ias C. E. Schila di Sícoli e al. h0 = minimum p essu e o he compen- sa ion ange [L]; his is de ined as: (2) Fo a good p essu e compensa ing emi e , mos designe s will y o keep he p essu es h oughou he ield in a ange be ween 7-24.5 m (5). Mon al o (2005) ecommends o sa e y easons a minimum p essu e alue o he emi e ha is a leas 2 m highe han he lowe limi o he compensa ion ange and a maximum p essu e o 25 m. I is necessa y o keep p essu es wi hin ha ange o a oid: a) disconnec ion o he d ip la e als o he mani old, b) b eakage o he d ip i iga ion la e al o exhaus ion o hei se ice li e, and c) high ene gy consump ion. Se e al au ho s add ess he hyd aulic- economic op imiza ion o design i iga ion subuni s. Saad and Ma iño (2002) de eloped a linea op imiza ion model o ec angula subuni s, wi h elescopic pipes placed in he di ec ion o he slope g adien which minimizes he annualized equi alen i iga ion and pumping cos s and maximizes dis ibu ion uni o mi y. Valian zas (2003) and Valian zas e al. (2007) de i ed a simple equa ion o calcula e he leng h and a ailable diame e s o pipes wi hin a subuni ha minimizes o al annualized pipe and ene gy cos s. De cas and Valian zas (2012) p esen ed wo simple analy ical me hods o calcula e he adequa e diame e s o he main pipes based on hyd aulic-economic analyzes. In I icad so wa e (2013), he pipe sizing is ca ied ou using a Linea P og amming op imiza ion (LP) in conjunc ion wi h hyd aulic g ade lines analysis me hod. Pipe sizes a e op imized based on he annualized cos o pipes and ene gy (18). In ake al e posi ion and p essu e a e de ined by he use wi hou op imiza ion c i e ia.   1/ 0 0 x q hK     Ca ión e al. (2013) and Ca ión e al. (2014) de ised a me hodology and compu e ool (PRESUD-P esu ized Submain Design) applied o u bulen d ippe s o he op imal design o submains. The c i e ion used o op imize he design was o educe he o al annualized cos s o wa e pe i iga ed uni a ea (CT). They adop ed a double i e a i e p ocess o he design o he submain mani old pipe and he in ake al e p essu e simila o he ones in oduced in he p esen a icle. Thei app oach is alid only o ec angula plo s, does no inco - po a e he elescopic design o submain mani old pipes and does no iden i y he op imum in ake al e loca ion. Mo eno e al. (2016) expands he PRESUD ool as PRESUD-IR o op imize he design o iangula o apezoidal plo s. I inco po a es an ex ension o he algo i hm abo e men ioned by Ca ión e al. (2013 and 2014); a a hi d i e a ion in ake al e loca ion is de e mined by conside ing he loca ion o each emi e as a possible eeding poin o he submain. The op imum in ake al e loca ion is he one ha maximizes dis ibu ion uni o mi y and minimizes he CT. This upda e does no inco po a e he elescopic design o submain mani old pipe and is no sui able o i egula ly shaped subuni s. Fo de e mining he op imum in ake al e loca ion in he submain, p e ious wo ks (20) s a ed ha he loca ion mus be aligned o he slope and p essu e loss in mani old pipes o a single diame e so as o balance he minimum p essu es on bo h sides o he al e. Fo elescopic mani old pipes, his depends on he selec ed diame e s and leng hs. Finally, in o de o op imize he eeding poin o an i iga ion subumain i is necessa y o imp o e i iga ion uni o mi y and conside ably educe he cos o pipes. 157 Tomo 51 • N° 2 • 2019 Op imal design o d ip i iga ion submains: P esu e-Compensa ing Emi e s Rod igo López e al. (1992) said ha when he a e age slope o he land in he di ec ion o mani old pipes is less han 3%, i is usually mo e economical o eed he subuni h ough an in e media e poin so as o ensu e ha p essu e a ia ion is almos he same in he mani old pipe o he ups eam and downs eam eeding poin . Al hough he e a e some gene al ecommenda ions and c i e ia o he op imal design o i iga ion submains wi h p essu e-compensa ing emi e s, he e is no me hodology o de ine, bo h in opog aphies and/o a bi a y geome- ies, he p essu e and he al e’s in ake poin and he elescopic sizing o he submain mani old pipe ha will lead o he bes possible hyd aulic-economic design. Objec i e To de elop a me hodology o subuni s wi h p essu e-compensa ing emi e s o op imize: a) elescopic sizing o he submain mani old pipe; b) he in ake al e's inpu p essu e o he subuni ; c) he in ake al e loca ion, by conside ing all hyd aulic-economic aspec s in ol ed in he design phase so as o minimize o al annualized cos s pe i iga ed uni a ea. The esul ing me hodology is applied wi hin he design module in d ip i iga ion plo s in he GESTAR compu e package (2), hus p o iding a new ad anced unc ionali y. Ma e ials and Me hods Fo i iga ion submains wi h p essu e- compensa ing emi e s, he me hodology uses as ini ial design condi ion an admis- sible ange o design p essu es based on he c i e ia p oposed by Bu and S yles (2007) and Mon al o (2005). Howe e , he use will be able o modi y he minimum and maximum al e's p essu e o he design (admissible ange o design p essu es) acco ding o he cha ac e is ics and knowledge o he submain. The Da cy-Weisbach o mula is used o calcula e p essu e losses in pipes and la e als whe e: 1) he ic ion ac o ( ) is de e mined by app oxima ion o he Basius equa ion (in he case o la e als) and o he Coleb ook's equa ion o mani old pipes; and 2) he Ch is iansen educ ion coe i- cien is used o calcula e p essu e losses in pipes o la e al acco ding o he numbe o ou le s as p essu e-compensa ing d ippe s con o m o his model. Fo op imal sizing o elescopic submain mani old pipe, he me hod de eloped by González and Aliod (2003), and González (2006) is applied. I is an op imiza ion algo i hm (LMM/KPH -LM) ha uses an imp o ed Lag ange Mul i- plie s Me hod (LMM) (27) in condi- ions o Know P essu e Head (KPH), in combina ion o a Labye- ype Me hod (LM) (22) o s anda diza ion o he con inous diame e s ob ained in LMM. A each connec ion poin o e e y la e al o he submain mani old pipe, he op imiza ion algo i hm mus supply a minimum equi ed p essu e so ha he mos un a o able p essu e-compensa ing d ippe o he espec i e la e al eaches i s minimum ope a ing p essu e. The Nodal Analysis me hod (1, 9, 10, 11) is used o hyd aulic simula ion o he i iga ion submain, once i is al eady designed, which includes a se o ma ix analysis echniques, ex ended o conside he speci i ies o p essu e i iga ion sys ems, ha inco po a es he in eg al-di e en ial hyd aulic modeling o d ip la e als whe e he emi e s discha ge low can depend on he local p essu e (10, 15, 34). I makes i possible o pe o m a de ailed quasi-s a iona y hyd aulic-ene gy simula ion ei he o u bulen o sel compensa ing d ippe s. 158 Re is a de la Facul ad de Ciencias Ag a ias C. E. Schila di Sícoli e al. The baseline da a o be selec ed includes: a) o he hyd aulic calcula ion o he subuni , he inne diame e (DI; mm), leng h (Ll; m), slope (So; m/m), sepa a ion (dis ance be ween ows; Sl; m) and la e als pe c op ow (N°la / ow); low (qo; L h-1) and emi e spacing (Se; m), maximum (PVmax; m) and minimum design p essu e (PVmin; m) o he subuni , as well as he design p essu e s ep ange (PV S ep; m); b) o he economic calcula ion o he subuni , g oss c op wa e equi emen s (Nb; m3 ha-1 yea -1) pe yea , pumping equipmen e iciency (Ep; %/100), ans- mission a io (T , his ep esen s he addi ional amoun o wa e ha mus be applied du ing he highes demand pe iod aking in o accoun he ine i able deep pe cola ion, wi h alues anging be ween 1.0 and 1.1 (20)), cos o ene gy (Ce; € kwh-1); wa e p ice (Cw; € m-3); in e es a e (i; %/100), se ice li e (N); main e- nance cos as a pe cen age o he i iga ion sys em pu chase cos (Cm; %/100). Figu e 1 (page 159), shows he low diag am o he design op imiza ion p ocess. The p oposed algo i hm i s de e - mines i he la e al should be ed om one end o h ough an in e media e poin by checking i Pmin = minimum design p essu e o he submain is highe han Pminobj = minimum a ge design p essu e. I also e alua es he in e me- dia e eeding poin o he la e al using he me hodology de ined by Kelle and Bliesne (1990) acco ding o he p oce- du es men ioned in Schila di e al. (2017). Figu e 1 (page 159), shows a nes ed i e a ion p ocess o op imally de e mine he al e p essu e (P op) and op imal in ake al e loca ion (Nop). The calcu- la ion sequence begins a he i s possible in ake poin (N1) wi h an ou e i e a i e p ocess (posi ion i e a ion), whe e op imal elescopic sizing o he submain mani old pipe is ca ied ou a di e en in akes p essu es which a e s ablished in a second inne i e a i e p ocess (p essu e i e a ion). Thus, o each possible in ake posi ion and o each possible al e p essu e head, om he minimum (P min) o he maximum design p essu e (P max) in an inc emen al ange de ined by he use (PV S ep - Ex: 1 m), he op imal sizing o he submain mani old pipe is ca ied ou wi h he abo e men ioned p ocess (LMM-LM/KPH). A a ian o he LMM me hod o unknown p essu e head (LMM /UPH) was no used o ind in a single sequence pipe sizing and op imal al e p essu e, a oiding he p essu e i e a ion cycle, since i depends on he a p io i iden i ica ion o he mos un a o able poin o he ne wo k, which is subjec o unce ain y. As addi ional condi ions o he design o he i iga ion submain, he speed in mani old pipes is es ic ed o a ange o maximum and minimum admissible alues, which a e de e mined by he use , usually be ween 2.5 and 0.5 m s-1. Fo each p essu e and posi ion i e a ion ( igu e 1, page 159) an op imal design o he submain mani old pipe is ob ained and i s annualized o al cos s pe uni o i iga ed a ea (CT; € ha-1 yea -1), li e-cycle, o al in es men cos (Ca, € ha-1 yea -1), main enance cos s (Cm - 5% o Ca; € ha-1 yea -1), ene gy cos s; i pumping is equi ed (Ce; € ha-1 yea -1) and wa e cos (Cw; € ha-1 yea -1) associa ed o he subuni a e calcu- la ed as shown in he ollowing equa ion (Ca ión e al. 2013) which s a es: (3) (4) 1.05 a e w CT C C C   CT P 9.81 (1 ) (1 ) 3600 (1 ) 1 (1 ) 1 1.05 N N OS O n c N N OS n w Q H R i i i i En Ep Q eA R T i i i i S S S EU   −−     159 Tomo 51 • N° 2 • 2019 Op imal design o d ip i iga ion submains: P esu e-Compensa ing Emi e s whe e: Ci = o al in es men cos (€) S = i iga ed a ea (ha) i = in e es a e N = se ice li e (yea s) Qos= design low (m3 s-1) Ho = subuni in ake p essu e (m) Ep = pumping e iciency (0.65 on a e age) Rn = annual ne c op wa e equi emen (m3 ha-1 yea -1) Enc = a e age cos o ene gy consumed, (€ kwh-1) Ea = gene al applica ion e iciency o he i iga ion sys em (%/100) T = ansmission a io o maximum demand pe iod (20) Pw = p ice o wa e , excluding ene gy cos s o p essu e supply (€ m-3). Figu e 1. Subuni op imiza ion p ocess wi h p essu e-compensa ing emi e s (GESTAR). Figu a 1. Diag ama de lujo del p oceso de op imización de sec o es con emiso es au ocompensan es (GESTAR). 160 Re is a de la Facul ad de Ciencias Ag a ias C. E. Schila di Sícoli e al. Though in he case o p essu e- compensa ing emi e s he alues o Cw and Cm a e cons an , hey a e inco - po a ed in o he calcula ion p ocess o be compa ed wi h designs made wi h o he so wa e and/o wi h designs ha include u bulen emi e s. The a o e- men ioned cos app oach does no conside explici elly he ex ended leng h o he main pipe necessa y o conec he op imum in ake poin o plo ne wo k. Ne e heless, his cos and all s o age and in as uc u e ine es men s equi ed o make he subuni ope a ional can be included in Cw and, i i is app op ia e, also he ene gy cos s asocia ed o head losses in he plo ne wo k and collec i e ne wo k ha d i e wa e o he subuni . Once he double nes ed i e a i e p ocess is comple ed, he op imal join design ( elescopic sizing o he submain mani old pipe, p essu e and al e in ake loca ion) is de e mined as he al e na i e ha minimizes he o al annualized cos pe uni o i iga ed a ea. A soon as he op imal design has been comple ed, i s hyd aulic simula ion can be pe o med o p edic he de ailed p essu e dis i- bu ion and e i y he p ope hyd aulic ope a ion o he submain. The desc ibed me hodology was implemen ed wi hin he d ip i iga ion design module, in he GESTAR so wa e package, using he Visual Basic 6.0 p og amming language, p o iding a new ad anced unc ionali y. Resul s The me hodology is applied o h ee examples o i iga ion submains wi h p essu e-compensa ing emi e s o hei op imal design, whe e he geome ical and opog aphic con igu a ion is he e oge- neous. The esul s ob ained a e compa ed wi h p e ious designs de eloped wi h ano he comme cial compu e ool (I icad P o) as a easibili y es . The submains i iga e ineya ds ha sha e he ollowing cha ac e is ics: a) dis ance be ween ows: 2 m, b) dis ance be ween plan s: 1 m, c) emi e low: 1.60 L h-1, d) emi e spacing: 0.60 m, e) emi e ange o compensa ion: 4-40 m, ) ex e nal diame e s o he la e al: 16 mm, g) in e nal diame e o he la e al: 15.5 mm, h) numbe o la e als pe ow: 1 la e al, i) emi e manu ac u ing a ia ion coe icien : 4%. Fo each example, he layou o he main pipe uns pa allel o e e y mani old pipe; his gi es he possibili y o connec ing he al e a any poin along he submain mani old pipes. Based on he ex e nal diame e s (mm), able 1 shows he cos s pe linea me e o he possible pipes ha a e used in he LMM/KPH-LM algo i hm o he submain mani old pipe op imiza ion. Fo he hyd aulic-economic op imiza ion o he submains, he ollowing a iables ha e been conside ed: a) ene gy p ice: 0.06 € kwh-1, b) wa e p ice: 0.10 € m-3, c) cos o he la e al: 0.33 € m-1, d) in e es a e: 7%, e) se ice li e: 25 yea s, ) pump e iciency: 65%, g) annual ne i iga ion equi emen s: 6,000 m3 ha-1, h) ansmission a io: 1.05, and i) main enance cos : 5% o annualized ma e ial acquisi ion cos (Ca). Table 1. Ex e nal diame e s o pipes and hei co esponding cos pe linea me e . Tabla 1. Diáme os ex e nos de ube ías y su co espondien e cos o po me o lineal. DE (mm) 50 63 75 90 110 125 140 160 200 €/m 1.33 1.39 2.62 2.71 3.12 3.89 4.97 3.36 10.4 161 Tomo 51 • N° 2 • 2019 Op imal design o d ip i iga ion submains: P esu e-Compensa ing Emi e s Figu e 2 and able 2 show he geome - ical and opog aphic cha ac e is ics and he esul s o he p e ious hyd aulic design o he h ee submains, whe e he al e’s p essu e (P ), submain low, leng h, diame e and o al cos o seconda y pipes a e shown. Figu e 3 (page 162), shows he new o m c ea ed wi h he GESTAR ool o in oduce he necessa y da a o he op imal hyd aulic-economic design o he submains. Table 3 (page 162), summa- izes he esul s o he hyd aulic design op imiza ion o he submains and shows: he numbe o hyd aulic designs (Designs No.), he op imized design al e p essu e (P ); he leng h, diame e and o al cos o he mani olds op imized pipes. While he cos o he la e al o each design al e na i e (ini ial and op imized) Table 2. Hyd aulic design cha ac e is ics o he i iga ion sec o acco ding o I icad P o. Tabla 2. Ca ac e ís icas hid áulicas de diseño de los sec o es de iego ejemplo según I icad P o. Ej. S Flow P Diame e (mm) and leng h (m) o pipes To al leng h To al Cos ha m3h-1 m 90 75 63 50 m € 1 2.30 30.67 28 66 56 78 200 354.5 2 1.94 25.87 24 49 70 38 157 369.8 3 2.09 27.87 24 50 65 118 232 376.6 is he same, signi ican cos sa ings a e achie ed by placing he al e a an in e - media e poin o he submain mani old pipe whe e he lows a e di ided and design is op imized using he p oposed algo ihm LMM/KPH-LM (13). Thus, in Example 1 a 22% mani old pipe cos educ ion is achie ed, while in Example 2 cos educ ion is in he o de o 34% (because he pipe h oughou i s en i e leng h is on an ascending slope) and in Example 3 i is 16%. Table 4 (page 162), summa izes he main esul s o he hyd aulic-economic op imi- za ion o he i iga ion submains and shows: he in ake poin o he subuni (X/Lp), whe e X is he dis ance downs eam o he submain mani old pipe wi h espec o he connec ion o he al e and Lp is he o al leng h o he submain mani old pipe (20). Figu e 2. Geome ic and opog aphic o m o submains (con ou lines e e y 1 m). Figu a 2. Fo ma geomé ica y opog á ica de sec o es de iego (cu as de ni el cada 1 m). 162 Re is a de la Facul ad de Ciencias Ag a ias C. E. Schila di Sícoli e al. Figu e 3. GESTAR o m o da a en y o economic hyd aulic op imiza ion o submains wi h p essu e-compensa ing emi e s. Figu a 3. Fo mula io GESTAR de ing eso de da os pa a la op imización hid áulica y económica de sec o es con emiso es au ocompensados. Table 3. Op imized hyd aulic design ea u es o he i iga ion submains (Ges a ). Tabla 3. Ca ac e ís icas de diseño hid áulicas op imizadas de los sec o es de iego (Ges a ). Table 4. Main hyd aulic ope a ion cha ac e is ics o he op imized Ges a design o he i iga ion submains (Ges a ). Tabla 4. P incipales ca ac e ís icas de uncionamien o hid áulico del diseño op imizado de los sec o es de iego (Ges a ). Ej. A ea Designs PVop Diame e (mm) and Leng h (m) o pipes To al To al Cos ha N° m 110 90 75 63 50 m € 1 2.30 1648 15 2 68 122 202 276.2 2 1.94 924 15 2 22.25 43.13 87.51 157 240.9 3 2.09 1648 15 2 72.31 157.59 232 315.4 Ej. X/Lp P (m) Pmax (m) Pmin (m) Vmax (m/s) Vmin (m/s) CeCeOp . 1 77 15 14.46 7.48 2.47 0.041 49.30 23.77 2 72 15 14.90 6.62 2.50 0.102 42.26 26.41 3 92 15 15.24 7.49 2.50 0.041 49.30 26.41