The calculation methods of corrosion current in multielectrode system have been analysed. The algorithm of graph-analytical engineering method of corrosion current calculation in multielectrode system including the principles of graphic and analytical calculation methods is presented. As an illustrative example the case with three electrodes (copper, iron, and aldrey) is considered

Demin, Yu. V.

Ivanov, G. V.

Mozilov, А. I.

Safroshkina, L. D.

Electronic archive of Tomsk Polytechnic University

The main constructional elements of modern installations are concrete and steel structures. Hence, thesematerials should be in view of investigations on durability of network constructions.To provide life duration for network constructionsand, to greater extent, for designed constructions andground systems made from them it is necessary to calculate corrosion currents and potentials.There are analytical, numerical and graphical methods of corrosion current calculations.Graphical calculation method of corrosive currentsconsists in analysis of polarization curves (anode andcathode) in the conditions of corrosion and determination of general potential value in corrosive system (U0).However, given method does not allow for investigationof real construction in laboratory conditions.By analytical and numerical methods only one kindof corrosion is calculated, usually it is corrosion underthe influence of galvanocouple.Design of operation for each electrode of multielectrode system with any number of electrodes by the analytical method makes two assumptions:1. If multielectrode galvanic system is a short realclosed in external and internal circuits, the potential of its separate elements levels off at some generalpotential U0 due to polarization.2. If multielectrode system is in stationary condition, i.e. there is no charge accumulation in its separate point in time, the sum of all cathode currents in the system is exactly equal to the sum of all anode currents.Then, following algorithm of the given method, weset up a system of equations in the form of matrix:(1)where: Rij are the characteristic and cross values of crossresistances between i and j elements; Ij is the cross current,flowing from j element; U0 is the compromise potential ofthe system of the considered elements connected in «spider»; Ui is the specified (initial) electrode potentials ofelectric poles (before their connection into system).Characteristic (i=j) values of cross resistance are defined in the following way:(2)where RiiГ is the metalbase spread resistance; Riiu is thecross resistance of element insulating coating (in itspresence); RiiA,K is the polarization resistance (anode andcathode) of the element involved.In this case the metalbase spread resistance is calculated by the formula:(3)where ρ is the base specific resistance; Г is the main(largest) size of ground, m; l is the vertical groundlength, m; d is the vertical ground diameter, m.Difficulty in solution of the considered equation system and, hence, difficulty in calculation method consists in determination of polarization resistance type(anode or cathode) of the elements connected in system.Indeed, the sign of cross current Ij («plus» is forcathode, «minus» is for anode) defines the value of polarization resistance, since the values of RiiA and RiiK canbe sufficiently different from each other. Besides, thevalue RiiA,K is a prevailing one with regard to the resistance RiiГ, which is crucial in absence of element insulatingcoating (Riiu).To determine approximately the character of polarization for the considered elements preliminary analysisof equation system is to be carried out: matrix is to betransformed and some «р» equation is to be excludedfrom the system by subtracting it from other equations.Thus, we obtain the auxiliary equation system, by theright part the polarization character is judged: at positive potential difference cathode resistance is used RiiK, atnegative one – that of anode RiiA. In such a way all elements of the system involved are analyzed except theelements with maximum and minimal values (the sign istaken into account) of electrode potential, as the first isalways anode, and the second one is cathode.Having determined the approximate character of allelement polarization in construction and according tothis having included the required polarization resistance RiiA,K, we solve the initial equation system relative tocarrion currents and compromise potential. Comparingthe signs of the corrosion currents obtained with the results of preliminary determination of polarization type,we see their agreement. In case of sign disagreement for1 4ln ,2ÃiilRÃ dρπ=, ,Ã è À Êii ii ii iiR R R R= + +1 111 1 1110... ... 1... ...... ... ... ... ... ...... ... 1,... ...... ... ... ... ... ...... ... 101 1 1 1 1 0p np pp pp pnn nn np nnI UR R RI UR R RI UR R RU× =Mathematics and mechanics. Physics77UDC 621.316.9GRAPHANALYTIC ENGINEERING METHOD OF CORROSION CURRENT CALCULATION IN MULTIELECTRODE SYSTEMА.I. Mozilov, G.V. Ivanov, L.D. Safroshkina, Yu.V. DeminNovosibirsk State Academy of Water Transport, NovosibirskEmail: gennadivanov@yandex.ruThe calculation methods of corrosion current in multielectrode system have been analysed. The algorithm of graphanalytical engineeringmethod of corrosion current calculation in multielectrode system including the principles of graphic and analytical calculation methods ispresented. As an illustrative example the case with three electrodes (copper, iron, and aldrey) is considered.separate elements their type of polarization is changedaccording to the result of the last calculation, this calculation being repeated to complete agreement in signs ofcorrosion currents of the last and previous calculationdata, i. e. iteration process is started.Application of iteration solution often results in iteration disagreement due to manyvaluedness of the problem solved.The disadvantages of the given method can be avoided, if one develops some general method including positive features of graphical and analytical methods, thesocalled graphanalytical engineering method.Let us give the algorithm of method.1. Construct «current value – potential» polarizationdiagram. On one diagram plot anode and cathodepolarization curves for the conditions interesting forus (anode and cathode polarization curves are usually obtained in independent experiments on polarization from external power supply), reconstructingthem in such a way that not current density i is plotted on abscissa axis as it was in polarization curvedesign, but current value I is. In Fig. 1 such diagramis schematically presented for fiveelectrode system.Here U1, U2, U3, U4, U5 are stationary electrode potentials of separate system constituents in the corrosion conditions (for electrodes 1, 2, 3, 4, 5 respectively) without current flow. There are the curves ofanode polarization (U1A1–U5A5), the curves ofcathode polarization (U1K1–U5K5).Fig. 1. Graphic calculation of multielectrode system on the basis of real multielectrode curves2. Plot the summary curves of anode and cathode polarization on the diagram. The summary curves ofanode (stqu) and cathode (mnqr) polarisations areproduced by simple addition of current values of allanode processes for each potential between U1 andU5, and hence, current values of all cathode processes for the same potential path. This diagram characterizes the current values for each system electrode depending on general potential in the system.This general potential of multielectrode system(U0) equals to potential, at which the sum of all system cathode currents equals to the sum of all anode currents.3. Determine the conditions (anode or cathode) ofevery electrode operation in multielectrode system.Abscissa values of cross points of anode and cathodepolarization curves with the line U0q parallel to abscissa axis give the current direction and value in eachsystem electrode. In the given example the cathodepolarization curves of electrode 4 and 5 cross the line U0q, hence, these electrode operate by the cathode, in this case the value of cathode current on themis consequently proportional to segments ас and аf.For electrodes 1, 2, and 3 the U0–q line is crossed byanode polarization curve. Consequently, electrodes 1, 2and 3 operate by anodes in the given system, in so doinganode current values are correspondingly determined bythe values of the segments ае, ad and ab. It is seen fromthe diagram that anode polarization curve for the mostpositive electrode and cathode polarization curve for themost negative electrode are redundant for this diagram,as they cannot be summed up with anode and cathodepolarization curves correspondingly in the U1 and U0 potential path.4. Set up the equation system in the form of matrix (1).To generate the equation system it is necessary todefine self and mutual electrode resistances. Propervalues of cross resistance are calculated by the formula 2. Since proper values Rii of cross resistancesexceed essentially their mutual values Rij, we take thelatter as equal to zero to simplify the calculation.5. Solve the equation system (1) relative to unknowncorrosion currents and system compromise potential.Let us consider the method behaviour for corrosioncurrent calculation by the example of three electrodes:copper (Cu), iron (Fe), and aldrey (Pl). Radius of electrode cross section is rel=0,3 sm, length of the first twoelectrodes Lel=4,0 sm and the third is Lel=3,5 sm. Allelectrodes were placed in a box and partly exposed today surface, being at the distance of d=7 sm from eachother, i. е. on the vertexes of equilateral triangle. Propervalues of spread resistance for these electrodes amounted Relг=120 Om for the first two electrodes, but for thethird one is Relг=131 Om. Specific resistance (of box filler) amounted approximately ρr≈10 Om.m.In Fig. 2 polarization curves of the electrodes involved (the Evance diagram) are presented. Their electrode potentials were: UCu=–0,112 V, UFe=–0,525 V andUPl=–0,970 V. Anode (CuA, FеА, Р1А) and cathode(CuK, FeК, PlК) polarization curves of the electrodes inBulletin of the Томsк Pоlytеchnic University. 2007. V. 310. № 278volved are shown in Fig. 2 by dashed line. Accumulationcurve of polarization and spread resistance for considered electrodes are depicted in Fig. 2 in the form of fullline. From the presented diagram we determine theconditions of electrode operation: Pl electrodes playedthe part of anode, only anode accumulation curve isplotted for it, but Сu electrode appeared to be cathode,only cathode curve is shown for it, Fe electrode is ananode with respect to the other electrodes.Fig. 2. The Evance diagramThus, from the diagram we find anode resistance forPl and Fe electrodes, as well as cathode resistance forCu electrode.According to the algorithm, the next step is determinations of proper value of electrode cross resistance bythe formula (2), we obtain: Om, Om, Om.Then we set up the equation set and present it in theform of matrixes:The solution for the set of equations is the followingmatrix:Now let us try to trace the influence of four time increase in cathode square on corrosion process, i. e.LCu=16,0 sm. Then RГCu=108 Om. The set of equationshas the following view:The solution for the given system is the matrix:The results of calculation show that increase insquare of, for example, cathode by a factor of four, leadsto 2 times increase in anode current of iron. This conclusion is of practical value. For example, extension ofoperating substation results in changing corrosive conditions in grounding system which is necessary to takeinto account in designing substation reconstruction. Insimilar way we can trace the changes in corrosion currents and compromise potential of the system at changes of specific medium resistance, i. е. at changes incorrosion conditions.Conclusion: Universal method of corrosion currentcalculation permitting for sufficiently exact determination of operation conditions for each of electrodes inmultielectrode system as well as tracing the way of influencing the change in electrode sizes and conditions ofthe system on corrosion processes has been obtained.CuFePl02,11ìÀ0,31ìÀ.1,80 ìÀ0,408 ÂIIIU== −= −= −CuFePl0108 0 0 1 0,2110 215 0 1 0,525.0 0 239 1 0,9701 1 1 0 0IIIU−−× = −CuFePl02,12 ìÀ0,16 ìÀ.1,96 ìÀ0,511 ÂIIIU== −= −= −CuFePl0181 0 0 1 0,2110 215 0 1 0,525.0 0 239 1 0,9701 1 1 0 0IIIU−−× = −Mathematics and mechanics. Physics79REFERENCES1. Demin Yu.V., Demina R.Yu., Gorelov V.P. Provision of duration fornetwork materials and constructions in corrosive medium: in 2 parts.Part 1. Theoretical bases / Yu.V. Demin, R.Yu. Demina, V.P. Gorelov; Edited by V.P. Gorelov. – Novosibirsk: Novosibirsk State Academy of Water Transport, 1998. – 209 p.2. Karyakin R.N. Ground grids of electric installation: reference book/ R.N. Karyakin. – Moscow: Energoservice, 1998. – 376 p.3. Tomashov N.D. Theory of corrosion and metal protection /N.D. Tomashov. – Moscow: AS of USSR, 1959. – 600 p.Received on 03.11.2006

Graph-analytic engineering method of corrosion current calculation in multielectrode system

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