Numerical leak detection in a pipeline network of complex structure with unsteady flow

K. R. Aida-zade   ; Y. R. Ashrafova

Žurnal vyčislitelʹnoj matematiki i matematičeskoj fiziki, Tome 57 (2017) no. 12, pp. 1966-1982

Résumé

An inverse problem for a pipeline network of complex loopback structure is solved numerically. The problem is to determine the locations and amounts of leaks from unsteady flow characteristics measured at some pipeline points. The features of the problem include impulse functions involved in a system of hyperbolic differential equations, the absence of classical initial conditions, and boundary conditions specified as nonseparated relations between the states at the endpoints of adjacent pipeline segments. The problem is reduced to a parametric optimal control problem without initial conditions, but with nonseparated boundary conditions. The latter problem is solved by applying first-order optimization methods. Results of numerical experiments are presented.

Bibliographie

[1] Kutukov S. E., “Tekhnologicheskii i ekologicheskii monitoring sistem magistralnogo transporta i promyslovogo sbora nefti”, Bezopasnost zhiznedeyatelnosti, 2004, no. 8, Pril., 16 pp.

[2] Epifantsev B. P., “Obnaruzhenie lokalnykh izmenenii na trasse magistralnykh produktoprovodov na opticheskikh izobrazheniyakh: vvedenie v problemu”, Neftegazovoe delo, 2011, no. 3, 394–418

[3] Kutukov S. E., “Problema povysheniya chuvstvitelnosti, nadezhnosti i bystrodeistviya sistem obnaruzheniya utechek v truboprovodakh”, Neftegazovoe delo, 2 (2004), 29–45

[4] Aida-zade K. R., “Vychislitelnye zadachi na gidravlicheskikh setyakh”, Zh. vychisl. matem. i matem. fiz., 29:2 (1989), 184–193

[5] Aida-zade K. R., Asadova J. A., “Study of transients in oil pipelines”, Aut. and Remote Control, 72:12 (2011), 2563–2577 | DOI

[6] Aida-zade K. R., Ashrafova E. R., “Localization of the points of leakage in an oil main pipeline under non-stationary conditions”, J. of Eng. Phys. and Therm., 85:5 (2012), 1148–1156 | DOI

[7] Zhukov K. A., Popov A. V., “Issledovanie ekonomichnoi raznostnoi skhemy dlya nestatsionarnogo dvizheniya vyazkogo slaboszhimaemogo gaza”, Zh. vychisl. matem. i matem. fiz., 45:4 (2005), 701–717

[8] Konovalova D. S., Lukina E. V., “Optimalnoe startovoe upravlenie techeniyami vyazkogo gaza”, Zh. vychisl. matem. i matem. fiz., 40:3 (2000), 451–472

[9] Makhanov S. S., Semenov A. Yu., “Ustoichivyi neotritsatelnyi chislennyi metod dlya raschetov techeniya zhidkosti v otkrytom rusle”, Zh. vychisl. matem. i matem. fiz., 34:1 (1994), 104–116

[10] Rukavishnikov V. A., Tkachenko O. P., “Vliyanie izgiba profilya truboprovoda na rasprostranenie vnutrennikh gidrouprugikh voln”, Zh. vychisl. matem. i matem. fiz., 50:11 (2010), 1988–1997

[11] Smirnov M. E., Verigin A. N., Nezamaev N. A., “Computation of unsteady regimes of pipeline systems”, Russian J. of Applied Chemistry, 83:3 (2010), 572–578 | DOI

[12] Chis T., Pipeline Leak Detection Techniques, Annals. Comput. Sci. Series, 5, 1st Fasc., 2007

[13] Mashford J., Dhammika De S., Donavan M., Stewart B., “An approach to leak detection in pipe networks using analysis of monitored pressure values by support vector machine”, Third Internat. Conference on Network and System Security IEEE Xplore, 2009, 534–540

[14] Oyedeko K. F.K., Balogun H. A., “Modeling and simulation of a leak detection for oil and gas pipelines via transient model: a case study of the niger delta”, J. Energy Technol. and Policy, 5:1 (2015)

[15] Ming Liu, Shu Zang, Donghua Zhou, “Fast leak detection and location of gas pipelines based on an adaptive particle filter”, Internat. J. Appl. Math. Comp. Sci., 15:4 (2005), 541–550

[16] Zhou Zhi-Jie, Hu Chang-Hua, Xu Dong-Ling, Yang Jian-Bo, Zhou Dong-Hua, “Bayesian reasoning approach based recursive algorithm for online updating belief rule based expert system of pipeline leak detection”, J. Expert Systems with Applic., 2011, no. 38, 3937–3943 | DOI

[17] Butkovskii A. G., Pustylnikov L. M., Teoriya podvizhnogo upravleniya sistemami s raspredelennymi parametrami, Nauka, M., 1980, 384 pp.

[18] Ladyzhenskaya O. A., Kraevye zadachi matematicheskoi fiziki, Nauka, M., 1973, 408 pp.

[19] Evtushenko Yu. G., Metody resheniya ekstremalnykh zadach i ikh primenenie v sistemakh optimizatsii, Nauka, M., 1982

[20] Samarskii A. A., Vabischevich P. N., Chislennye metody resheniya obratnykh zadach matematicheskoi fiziki, LKI, M., 2009, 480 pp.

[21] Karchevskii A. L., “O povedenii funktsionala nevyazki dlya odnomernoi giperbolicheskoi obratnoi zadachi”, Sib. zhurnal vychislit. matem., 2:2 (1999), 137–160

[22] Karchevsky A. L., “Properties of the misfit functional for a nonlinear one-dimentioanal coefficient hyperbolic inverse problem”, J. Inverse and Ill-posed Problems, 5:2 (1997), 139–163 | DOI | MR

[23] Charnyi I. A., Neustanovivsheesya dvizhenie realnoi zhidkosti v trubakh, Nedra, M., 1975, 199 pp. | MR

[24] Chaudhry H. M., Applied hydraulic transients, Van Nostrand Reinhold, New York, 1988

[25] Wylie E. B., Streeter V. L., Fluid transients, McGraw-Hill International Book Co, New York, 1978

[26] Wichowski R., “Hydraulic transients analysis in pipe networks by the method of characteristics (MOC)”, Archives of Hydro-Engng and Environmental Mech., 53:3 (2006), 267–291

[27] Adamkowski A., “Analysis of transient flow in pipes with expanding or contracting sections”, J. Fluids Engng., 125:4 (2003), 716–722 | DOI

[28] Hyun Geun Lee, Junseok Kim, “Regularized Dirac delta functions for phase field models”, Internat. J. for Numerical Meth. Engng., 91:3 (2012), 269–288 | DOI

[29] Aida-zade K. R., Ashrafova E. R., “Raschet perekhodnykh rezhimov dvizheniya zhidkosti v truboprovodnykh setyakh”, Sib. zhurnal industrialnoi matem., 18:2(62) (2015), 12–23

[30] Aida-zade K. R., Ashrafova Y. R., “Solving systems of differential equations of block structure with nonseparated boundary conditions”, J. of Applied and Industrial Mathem., 9:1 (2015), 1–10 | DOI | MR

[31] Ayda-zade K. R., Abdullayev V. M., “On the solution of boundary value problems with nonseparated multipoint an integral conditions”, Different. Equations, 49:9 (2013), 1114–1125 | DOI | MR

[32] Denisov A. M., “Obratnaya zadacha dlya kvazilineinoi sistemy uravnenii v chastnykh proizvodnykh s nelokalnym kraevym usloviem”, Zh. vychisl. matem. i matem. fiz., 54:10 (2014), 1571–1579 | DOI

[33] Abdullaev V.-M., Aida-zade K. R., “Numerical method of solution to loaded nonlocal boundary value problems for ordinary differential equations”, Comput. Math. Math. Phys., 54:7 (2014), 1096–1109 | DOI | MR

[34] Tikhonov A. N., Samarskii A. A., Uravneniya matematicheskoi fiziki, Nauka, M., 1977, 736 pp.

[35] Ashrafova Y. R., “Numerical investigation of the duration of the effect exerted by initial regimes on the process of liquid motion in a pipeline”, J. of Engng. Physics and Therm., 88:5 (2015), 1–9 | MR

[36] Aida-zade K. R., Ashrafova Y. R., “Optimal control of sources on some classes of functions”, Optimizat.: A J. of Mathem. Prog. and Oper. Research, 63:7 (2014), 1135–1152 | MR

[37] Aida-zade K. R., Handzel A. V., “An approach to lumped control synthesis in distributed systems”, Applied and Comput. Math., 6:1 (2007), 69–79 | MR

[38] Samarskii A. A., Teoriya raznostnykh skhem, Nauka, M., 1989, 616 pp.

[39] Aida-zade K. R., Ashrafova E. R., “Raschet sostoyaniya sistemy diskretnykh lineinykh protsessov, svyazannykh nerazdelennymi kraevymi usloviyami”, Sib. zhurnal industrialnoi matem., 19:4 (2016), 3–14