OPTIMISATION OF GAS FLOW USING NETWORK ANALYSIS (NEWTON LOOP-NODE METHOD)

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1 ICAST 2000 edited by Wn Rmli Wn Dud et. l 1001 Fculty of Engineering, Universiti Kebngsn Mlysi OPTIMISATION OF GAS FLOW USING NETWORK ANALYSIS (NEWTON LOOP-NODE METHOD) Zulkifli Abdul Mjid, Zulkefli Ycob nd Yng Kong Woh zulmjid@fkkks.utm.my, zuly@fkkks.utm.my, yngkw@tm.net.my Gs Technology Centre (GASTEG) Fculty of Chemicl nd Nturl Resources Engineering, Universiti Teknologi Mlysi Skudi, Johor Drul Tzim, Mlysi Keywords: gs flow optimiztion; network nlysis; softwre simultion. ABSTRACT Gs trnsport nd distribution networks round the world present lrge set of highly integrted pipe networks operting over wide rnge of pressures. Growing demnd for gs mkes it necessry to dpt nd expnd these systems while ensuring sfe delivery nd cost-effective engineering. Simultion nd nlysis ply mjor role in system plnning nd design, enbling the designer to optimize the network nd the pipelines themselves. Simultion llows us to predict the behvior of gs network systems under different conditions. Such predictions cn then be used to guide decisions regrding the design nd opertion of the rel system. A computer progrm ws developed to cter for the needs of computer ided design for gs distribution studies, which pply the Newton loop-node method to solve the gs networks problem. This computer softwre progrm lso incorporte drwing fetures, which describe the ccurte network configurtion with speed. This pckge is used for selecting pipe sizes, clculting pressures nd flows in gs distribution networks for stedy stte condition. The Newton loopnode method essentilly solves the set of loop equtions. The loop method hs the disdvntge of hving to define the loops in the networks. The dvntge of the loop method over the nodl method is its good convergence chrcteristics. The nodl method hving esy to solves the set of eqution but the min disdvntge of the nodl method is the poor convergence chrcteristics. The lgorithm used the Hrdy-Cross technique, which is widely used in distribution system. The Hrdy-Cross method solves the sme set of loop nd nodl equtions s do the Newton-loop nd Newton-nodl multi-dimensionl methods. However, the Hrdy- Cross method solves ech eqution of the set individully, wheres the Newton multi-dimensionl method solves the set of equtions s whole.

2 1002 INTRODUCTION The complex networks of pipes tht comprise gs distribution system present formidble flow nlysis problem. Gs my be fed into system from severl trnsmissions pipeline city-gte sttions, from one or more pek-lod gs production plnts or from storge fcilities scttered through the system. In ddition, mny distribution systems consist of severl superimposed networks of piping operted t different pressure levels. Networks of loops nd pipe section re very common. Mny networks contin over 1000 pipe sections nd some lrger cities hve interconnected piping networks contining tens of thousnds of pipe section. At one time the only method of solving network flow problem ws mnul tril-nd-error procedure. However, since 1951 nlog nd digitl computers hve been pplied to the solution of this problem, IGT, (1982). However, with the evolution of micro or personl computer, performing network nlysis on this desktop computer hs become very vible lterntive. A lot of commercil softwre hs been developed by the personl computer but the cost to purchse them is considerbly high. The most common softwre used loclly is GDNAP developed by CONGAS (Cnd Oil nd Gs Compny) nd NASS developed by Tokyo Gs. Both of the softwre uses the Hrdy Cross technique in solving network nlysis problem. FORMULAS AND METHODS The stedy stte gs flow rte cn be described by mny formuls, but none re universl. The effects of friction re difficult to quntify nd re the min reson for vritions in the flow formul. Most of the flow eqution is derived from Bernoulli s eqution. The following generl flow eqution is the expressions usully used for network nlysis in the gs industry. Q n = 2 π R 64 ir T x p n n [( p pvsgh 5 p2 ) ] D ZRirT fsltz (1) The network formultion ws solving by the Node-Loop method where bse on

3 1003 first nd second Kirchhoff s lws. The Node-Loop method is the combintion of Nodl nd Loop method, which is essentilly, solves the set of loop equtions. The Node-Loop method hs the dvntge of hving to define the loops esily nd good convergence chrcteristics in the networks, Osidz, A.j. (1987). The Newton loop-node method essentilly solves the set of loop equtions: F( q) = B[ φ( Q)] (2) The process of mking loop flow synonymous to chord flow in the network is quite complex. The following grph Figure 1 identicl the chord flow nd loop flow in gs network. Q t1 Q t2 Q AC Q t5 A B Q BC Q t4 Q t3 FIGURE 1 Grph of gs Q t1, Q t2.q t5 -- Brnch flow Q AC -- Chord flow identicl to flow in loop A -- Chord flow identicl to flow in loop B Q BC Severl orderly numericl methods of solving network flow problems hve been developing. These methods solve the simultneous equtions obtined by the ppliction of Kirchoff s lws to specific network problem; the eqution represents mthemticl description of network flow problem. In this reserch, the Newton Method ws selected to solving the roots of eqution in the network formuls. Newton method cn be derived from Tylor Series of expnsion for the function ƒ (x I+1 ), such tht; h f ( xi + 1 ) = f ( xi ) + hf '( xi ) + f ''( xi ) +... (3) 2! Where h = x I+1 -x i. In order to obtin x I+1 such tht ƒ (x I+1 ) = 0, the bove eqution cn be pproximtely reduce by, 0 i i f ( x ) + hf '( x )

4 1004 f ( xi ) + ( xi 1 xi ) f '( xi ) f ( xi ) xi+ 1 xi (4) f '( x ) + i The re mny numericl methods which cn be used for solving set of simultneous liner equtions. Numericl methods for solving systems of liner equtions fll into the direct methods. It led to n exct solution in finite number of steps if round off error is not involved. Most direct method re bse on Gussin elimintion which yields system of eqution with tringulr coefficient mtrix llowing their esy solution. The Gussin elimintion procedure is s follow; c1 c 2 c c1 c 2 c3 1 x 2 = ( x = ( c 1 x 3 ' c2 = 12 " " c3 / 33 ' 23x3 x 1 )/ 13 3 ' 22 x ) / 11 RESULT AND DISCUSSION The development of softwre to nlyse the gs network for stedy stte gs flow system is being done nmely GASNETT. In order to solve the network nlysis problem with this softwre, it requires simple drwing of network on the screen nd then inputs of vrious gs flow, nodes, nd pipe prmeters. It cn be grphiclly displyed nd results such s node pressures or pipe flow rtes cn be printed. After drwing network, simply click on ny node, pipe, or other object with the Edit tool to disply dt entry window. The following is summry of the informtion needed. Generl Informtion- Fluid Type (GAS); Friction Fctor Eqution; Node Informtion-Pressures, Elevtions, Flow Rtes; Gs Properties-Specific grvity, Temperture, Compressible fctor; Pipe Informtion-Lengths, Dimeters. The Newton Loop-Node method offered greter convergence nd speed. Additionl proprietry lgorithms developed by this reserch provide incresed efficiency, performnce, nd stbility. This softwre requires 486 or higher computer, 4 MB of RAM, VGA or better grphics (color), Windows 3.1/95/98 nd mouse. The following re the dilog box creted by this softwre nd the tbles for the comprison of ccurcy dt with the NASS softwre.

5 1005 Pipe Node Flow Upstre Pip Downstre m Node FIGURE 2 Dilog box for inserting the networks FIGURE 3 Dilog box for inserting dt input of nodes. FIGURE 4 Dilog box for inserting the dt input of brnch. FIGURE 5 Dilog box for properties.

6 1006 FIGURE 6 Dilog box of clcultion. FIGURE 7 Dilog box for viewing dt. TABLE 1 Dt input of brnch. No Brnch Brnch Dimeter Length (m) (mm) 1 1: : : : : : : : : : :

7 1007 TABLE 2 Dt input of node. No Node Sttus Lod 1 Source psi 2 Lod m 3 /hr 3 Lod m 3 /hr 4 Lod m 3 /hr 5 Lod m 3 /hr 6 Lod m 3 /hr 7 Lod m 3 /hr 8 Lod m 3 /hr 9 Lod m 3 /hr TABLE 3 Result of brnch between GASNETT nd NASS. No GASNETT NASS Accurcy Brnch Brnch Flow Rte Flow Rte (%) 1 1: : : : : : : : : : :

8 1008 TABLE 4 Result of node between GASNETT nd NASS. No GASNETT NASS Accurcy Node Pressure(psi Pressure(psi) (%) ) CONCLUSION Optimistion of gs flow network nlysis for stedy stte system will be esier by using this softwre. This user-friendly softwre hs been developed by the Newton Loop-Node method which is cpble to predict the flow rte nd the pressure drop. The time tken for the number of itertion required to converge within the desire tolernce is fst with the current computer model: Pentium 400 MMX nd 256 M RAM. This user-friendly softwre which runs on windows environment enbles the end-users to input dt nd view the gs network grphics more conveniently. Q Flow Rte m 3 /hr P Pressure kp D Dimeter mm L Length m T Temperture K NOTATIONS

9 1009 R S Z f Gs constnt Specific grvity Compressibility fctor Friction fctor ACKNOWLEDGEMENT The uthor is grteful nd wish to thnk Reserch Mngement Centre (RMC), Universiti Teknologi Mlysi for providing reserch fund through the Vot. Project no REFERENCES Abrmowitz, M, nd Stegun, J.A. 1965, Hndbook of Mthemticl Functions, Second Edition, New York.Dover: Publiction Inc, Christofides, N Grph Theory, New York: Acdemic Press inc. Cross, H Anlysis of Flow In Networks of Conduits or Conduits, Urbn: Bulletin, 12. Deo, N Grph Theory with Applictions to Engineering nd Computer Science, London: Prentice-Hll. Wilson.,G.G., Gs Distribution, First Edition, Chicgo: IGT GASTEG, 1999, Pressure nd Network Anlysis, Module 4, Johor Bhru, Mlysi: Universiti Technologi Mlysi, Hrry, F Grph Theory, London: Addison-Wesley. McCbe, W. L. nd Smith, J. C Unit Opertions of Chemicl Engineering, Third Edition, New York: McGrw-Hill, McCormick nd Bellmy, C. J. 1968, A Computer Progrm for the Anlysis of Pipes nd Pumps, The Journl of the Institution of Engineering Austrli, 38, (3):

10 1010 Orteg, J. M. nd Rheinbolt, W. C Itertive Solution of Nonliner Equtions in Severl Vribles, New York: Acdemic Press Inc. Osidcz, A.J Simultion nd Anlysis of Gs Network, First Edition, London: E nd F.N. Spon ltd Perry, R. H. nd Chilen, C. H Chemicl Engineers' Hndbook, Third Edition, New York: McGrw-Hill, Shhrul Azmn, Development Stges of Gs Network Anlysis Progrm, Mster Thesis, University Technology of Mlysi. SIRIM, Sizing nd Cpcity of Gs Piping, Tble 12, Equivlent Length of Fittings, Selngor, Mlysi: Stndrd nd industril Reserch Institute of Mlysi, Steven C. C. nd Rymond P. C Numericl Methods for Engineers, Third Edition, Singpore: McGrw-Hill