_20201019_010851论文igu2009docswgcfinal00105VIP

1、AC CORROSION COMPUTER SIMULATIONAS AN ELEMENT OF PIPELINE SYSTEM INTEGRITY PROCESSKRZYSZTOF BUDNIK, WOJCIECH MACHCZYSKIPOZNAN UNIVERSITY OF TECHNOLOGY, POLANDAbstract. Overhead power lines are often placed in the same right of way as earth return circuits (ERC), e.g. pipelines. Long term AC interfer

2、ence on an ERC may cause corrosion due to an exchange of AC-induced current between the exposed bare metal at unavoidable coating defects in the structure and the surrounding soil.The paper presents calculations of the AC corrosion on the metallic pipelines under the inductive influence of power lin

3、es. An electrical equivalent diagram is presented and the corrosion current, the pipeline potential to the adjacent earth and corrosion rate are calculated. The use of a platform for multidomain simulation and model-based-design of dynamic systems Matlab Simulink permits the complex analysis of the

4、electromagnetic interference (EMI) on ERC, whereas the electrochemical phenomena on the interface metal soil are taken into account. The EMI on the circuit is treated as a process constructed by Simulink as a block diagram - a graphical representation of the process, which is composed of an input, t

5、he system, and an output. The block connected with the AC corrosion in which the electrochemical phenomena are represented by the non-linear Butler-Volmer equations has been implemented in the simulation package. The system is described by state equations, which can be iteratively solved by tools pr

6、ovided by Matlab.Keywords: transmission line, inductive interference, pipeline, AC induced corrosion, calculation model, Simulink .INTRODUCTIONAssessing risk on a pipeline system can be determined by assessing the likelihood or probability of a failure event occurring, and the consequences resulting

7、 from that failure event. AC corrosion on pipelines under the inductive influence of power lines can be critical to the pipeline operator for ensuring pipeline safety 1.Overhead power lines are often placed in the same right of way as buried pipelines. Electromagnetic interference (EMI) on pipelines

8、 occurs when there is extended and close parallel routing with three-phase HVAC overhead transmission lines. The inductive interference is the result of the magnetic field generated by currents in a power line, which induces voltages in adjacent pipelines. The voltages are due to any phase imbalance

9、 in the lines, Fig. 1. The likelihood of interference increases with rising operating currents in the overhead lines, with increasing quality of the coating on the pipeline, and with the length of line parallel to and close to the HVAC transmission lines. Voltages induced in the pipeline by magnetic

10、 coupling result in currents flowing along the pipeline. These currents result in a voltage difference between the pipeline and the surrounding soil.Fig.1. AC interference on a pipelineThe EMI is present both during normal operating conditions ( long-term interference) and faults (short-term interfe

11、rence). When an induced AC voltage exists on a pipeline, it can be dangerous and potentially life-threatening for operations personnel to touch the pipeline or appurtenances. Especially during fault conditions, high voltages can be induced to nearby pipelines, even when the fault occurs far away fro

12、m the approach section of a pipeline. In addition, there is a high risk of damaging the pipeline coating, insulating flanges or cathodic protection systems. The other important aspect of the EMI, especially during the long-term interference on pipelines is the AC corrosion as a result of the AC disc

13、harge from the pipeline.The AC voltage on a pipeline interfered by AC systems is to be considered as the most important parameter to be taken into account to evaluate the corrosion likelihood on buried pipelines. The AC voltage on the pipeline affected by AC systems can either be calculated (in case

14、 of construction of a new pipeline within the area of possible AC influence) or directly measured on the existing structure itself. Many computer programs (e.g. 2) can be used to calculate the pipeline AC voltage by taking into account the worst case under normal operating conditions of the interfer

15、ing systems.Corrosion caused by the discharge of 50 (16 2/3) Hz AC current from a pipeline in a high voltage AC corridor has been discussed and studied over the past 20 or more years. Long term AC interference on a buried pipeline may cause corrosion due to an exchange of AC current between the expo

16、sed bare metal at unavoidable coating defects in the structure and the surrounding electrolyte (soil). The exchange of current depends on the AC voltage whose amplitude is related to various parameters. Multiple publications described cases of apparent AC corrosion damage and several articles sugges

17、ted explanations for mechanism of the attack. However, the mechanism of the AC corrosion is not very well understood, particularly as it applies to corrosion in soils 3 - 10.When an AC voltage is present on an underground pipeline, current will flow through the metal surface at defects in the coatin

18、g. This current depends on the impedance of the system. During the positive half wave of the AC voltage, the current will leave the metal surface if the AC voltage is sufficiently large. The current leaving the metal surface can cause the charging of the double layer capacitance, oxidation of hydrog

19、en and reduced corrosion products and oxidation of the pipeline. Since the current leaving the metal surface is consumed by several non-corrosive processes, generally higher voltages than between 4 and 10 V are required to result in a significant corrosion attack on the pipeline. Various parameters

20、are additionally influencing this process, such as leakage resistance of the defect, soil composition, cathodic protection level, etc. 9.The objective of the paper is to develop a simulation model of the metallic pipeline under the inductive influence of power lines, in which the AC corrosion is tak

21、en into account. An electrical equivalent diagram is presented and the corrosion current, the pipeline potential to the adjacent earth and corrosion rate are calculated. The use of a platform for multidomain simulation and model-based- design of dynamic systems Matlab Simulink permits the complex an

22、alysis of the electromagnetic interference (EMI) on earth-return circuits (ERC), whereas the electrochemical phenomena on the interface metal soil are taken into account. In the approach presented, the ERC with excitation by AC signal is modelled as a chain of basic circuits, which are equivalents o

23、f homogenous sections of the ERC with uniform exposure to interfering electric field. The EMI on the circuit is treated as a process constructed by Simulink as a block diagram - a graphical representation of the process, which is composed of an input, the system, and an output. The block connected w

24、ith the AC corrosion in which the electrochemical phenomena are represented by the non-linear Butler-Volmer equations has been implemented in the simulation package. The system is described by state equations, which can be solved iteratively by tools provided by Matlab.EQUIVALENT CIRCUIT OF A CONDUC

25、TOR WITH EARTH RETURNEquivalent model of an earth-return circuit is essential to the computer simulation of effects of external electromagnetic excitation on the ERC. The basic model subjected to the external (primary) electric field is shown in Fig. 2.In Fig. 2 a single circuit of the differential

26、length dx, consists of a unit-length electrical parameters R0, L0, G0 and C0. The driving voltage source Edx represents the external excitation, producing a current i(t,x) and a potential v(t,x) along the circuit.EdxL0 dxi(t,x)R0 dxi(t,x+dx)v(t,x+dx) Go dxv(t,x)C0 dxdxFig. 2. Equivalent model of an

27、elementary section of earth-return circuit with external excitationGenerally E, the primary electric field intensity impressed at every point of the circuit, is the sum of an induced and a static componentrrrE =Ei +Es(1)The induced electric field is associated with the inductive, whereas the static

28、electric field with the conductive influence on the earth-return circuit.In the case of the inductive interferencerE i =- jwA(2)rwhere A is the vector potential along the earth-return circuit due to the current in an externalinfluencing source, w - angular frequency, j =- 1 .It should be noted that

29、the primary electric field is considered in the absence of the earth-return circuits.ELECTROCHEMISTRY AND ELECTROCHEMICAL CIRCUIT FOR THE CORROSION PROCESSTo develop a simulation model of a pipeline under AC inductive influence, with electrochemical effects taken into account, the following phenomen

30、a should be considered: double layer capacitance, charge transfer kinetic and diffusion of reactants 11.Double Layer CapacitanceAn electrical double layerelectrolyte. This double layer is formed as ions from the solution stick on the electrode surface. Charges in the electrode are separated from the

31、 charges of these ions. The separation is very small, on the order of angstroms. Charges separated by an insulator form a capacitor. On a bare metal immersed in an electrolyte, one can estimate that there will be approximately 30 F of capacitance for every cm2 of electrode area.The value of the doub

32、le layer capacitance depends on many variables including electrode potential, temperature, ionic concentrations, types of ions, oxide layers, electrode roughness, impurity adsorption, etc.Charge Transfer Resistance / Polarization ResistanceWhenever the potential of an electrode is forced away from i

33、ts value at open circuit that is referred to as polarizing the electrode. When an electrode is polarized, it can cause current to flow via electrochemical reactions that occur at the electrode surface. The amount of current is controlled by the kinetics of the reactions and the diffusion of reactant

34、s both towards and away from the electrode.In cells where an electrode undergoes uniform corrosion at open circuit, the open circuit potential is controlled by the equilibrium between two different electrochemical reactions. One of the reactions generates cathodic current and the other anodic curren

35、t. The open circuit potential ends up at the potential where the cathodic and anodic currents are equal. It is referred to as a mixed potential. The value of the current for either of the reactions is known as the corrosion current.A resistance is formed by a single kinetically controlled electroche

36、mical reaction. In this case we do not have a mixed potential, but rather a single reaction at equilibrium.Consider a metal substrate in contact with an electrolyte. The metal molecules can electrolytically dissolve into the electrolyte, according to:Me Men+ + ne -(3)or more generally:Re d Ox + ne -

37、(4)In the forward reaction in the first equation, electrons enter the metal and metal ions diffuse into the electrolyte. Charge is being transferred. This charge transfer reaction has a certain speed. The speed depends on the kind of reaction, the temperature, the concentration of the reaction produ

38、cts and the potential.When the concentration in the bulk is the same as at the electrode surface, the general relation between the potential and the current is:-(1-a )h nFa nF hi = icorr eRT RT- e(5)with,icorr - exchange current densityF - Faradays constant,T - temperature, R - gas constant, - react

39、ion order,n - number of electrons involved, - overpotential ( E Ecorr ).This equation is called the Butler-Volmer equation. It is applicable when the polarization depends only on the charge transfer kinetics.When the overpotential, , is very small and the electrochemical system is at equilibrium, th

40、e expression for the charge transfer resistance is:RT=Rct(6)nFicorrThe Butler-Volmer equation can be written also as a combination of the Tafel equations in the form:2.303(E-Ecorr )ba-2.303(E-Ecorr )bci = ie- e(7)corrwhere:i- the measured cell current in ampsicorr- the corrosion current in ampsE- th

41、e electrode potentialEcorrbabc- the corrosion potential in volts- the anodic Beta Tafel Constant in volts/decade- the cathodic Beta Tafel Constant in volts/decade.DiffusionDiffusion can create an impedance known as the Warburg impedance (W). This impedance depends on the frequency of the potential p

42、erturbation. At high frequencies the Warburg impedance is small since diffusing reactants dont have to move very far. At low frequencies the reactants have to diffuse farther, thereby increasing the Warburg impedance.The equation for the infinite Warburg impedance is:- 1W = sw 2 (1 - j )(8)In Equati

43、on (9), is the Warburg coefficient defined as:11RT +o =(9)2 2*CRDRn F A 2 CDOOin which: -radial frequency,DO - diffusion coefficient of the oxidant, DR - diffusion coefficient of the reductant, A - surface area of the electrode,n - number of electrons transferred,C* - bulk concentration of the diffu

44、sing species (moles/cm3).Equivalent electrical circuitIn the simplified electrical circuit of the pipeline with coating fault, the total pipe to soil impedance can be regarded as a sum of the spread resistance Rs and the polarisation impedance related to the electrochemistry of the pipe-soil interfa

45、ce.As a first approximation the spread impedance steel pipe remote earth can be treated as the sum of the leakage resistance and the pore resistance:rpore -In the case of a circular coating fault (diameter d, coating thickness t, rsoil - soil resistivity, resistivity of medium in the pore) the leaka

46、ge resistance:= rsoilR(10)leakage2dand the pore resistance: 4t pd 2Rpore = r pore(11)When the electrochemical charge transfer processes of the system should be taken into account, the equivalent circuit, Fig. 3a, with Rs=Rleakage+Rpore has to be applied.The Randles cell, Fig.3a, is one of the simple

47、st and most common cell models. It includes a solution resistance, a double layer capacitor and a charge transfer or polarization resistance. In addition to being a useful model in its own right, the Randles cell model is often the starting point for other more complex models.a)CdliCiRsERct or RpiFb

48、)CdliCRsiERctiFWFig. 3. Equivalent circuits; a) Randles cell schematic diagram, b) equivalent circuit with chargetransfer control and diffusionThe circuit shown in Fig. 3b models a cell where polarization is due to a combination of kinetic and diffusion processes.The model for the AC corrosion proce

49、ss has been proposed in 7.APPLICATION OF THE SIMULINKSimulinkSimulink is a software package for modelling, simulating, and analyzing dynamical systems. It supports linear and nonlinear systems, modelled in continuous time, sampled time, or a hybrid of the two. Systems can also be multirate, i.e., ha

50、ve different parts that are sampled or updated at different rates.Simulink is an extension to Matlab, which uses an icon-driven interface for the construction of a block diagram representation of a process. A block diagram is simply a graphical representation of a process, which is composed of an in

51、put, the system, and an output. For modelling, Simulink provides a graphical user interface (GUI) for building models as block diagrams, using click-and-drag mouse operations. Assorted sections of the block diagram are represented by icons, which are available via various windows that the user opens

52、. The block diagram is composed of icons representing different sections of the process and connections between the icons. Simulink includes a comprehensive block library of sinks, sources, linear and nonlinear components, and connectors. Users blocks can be also customized and created. Once the blo

53、ck diagram is built, one has to specify the parameters in the various blocks. After defining a model, one can simulate it, using a choice of integration methods, either from the Simulink menus or by entering commands in Matlabs command window. Model analysis tools include linearization and trimming

54、tools, which can be accessed from the Matlab command line, plus the many tools in Matlab and its application toolboxes. The simulation results can be put in the Matlab workspace for postprocessing and visualization 12.The application of the Simulink to the simulation of the ERC under inductive effec

55、ts of a nearby power line has been first presented in 13.Simulink basic circuitsThe use of a platform for multidomain simulation and model-based-design of dynamic systems Matlab Simulink permits the complex analysis of the DC/AC interference on the ERC, whereas the electrochemical phenomena on the i

56、nterface metal soil are taken into account. Simulink circuit of homogeneous line with external steady-state excitation (chain of n basic circuits) is shown in Fig. 4.R0DLR0DLL0DL R0DLin-1R0DLL0DLL0DLL0DLe1e2en-1eni3ini1i2i03in+1i01i02inG0DL/2G0DL/2C DLC DL/2C0DLG0DLG0DLC0DLG0DL00un+1uuu1u23nFig. 4. Simulink circuit of a single earth-return circuit with inductive influenceThe voltage source in the case of inductive interference due to e.g. current I in a power line overhead conductor is:E = IZmDL(12)where Zm - unit-length mutual impedance between