JP3801328B2

JP3801328B2 - Method and apparatus for simulation analysis of cathodic protection field

Info

Publication number: JP3801328B2
Application number: JP32311097A
Authority: JP
Inventors: 明伸西川; 英正野中; 繁青木; 賢治天谷
Original assignee: Osaka Gas Co Ltd
Current assignee: Osaka Gas Co Ltd
Priority date: 1997-11-25
Filing date: 1997-11-25
Publication date: 2006-07-26
Anticipated expiration: 2017-11-25
Also published as: JPH11160271A

Description

【０００１】
【発明の属する技術分野】
本発明は、水溶液環境中あるいは土壌環境中において電気防食（カソード防食）を施す際に、被防食対象物の近くに他の金属構造物が存在する場合に問題となる干渉現象をコンピュータを使用して数値解析的に解く技術に関する。
【０００２】
【従来の技術】
従来、この種の干渉問題を取り扱ったシミュレーション解析は行われておらず、対極と被防食対象物とからなる系に対して、所謂、ラプラス場を解く解析が行われているに過ぎない。
このようなシミュレーション解析の例について説明すると、火力原子力発電Ｖｏｌ４４，Ｎｏ．４，１９９２の６１〜７１頁の「海水系電気防食への電位分布解析技術の応用」では、数値解析手法の一種である有限要素法を使用して電気防食場の解析が行われている。
この技術にあっては、環境中に於ける電位分布がラプラス場となることを利用して、非常に強い非線形を有する熱伝達係数を有する熱伝導問題を解析可能な有限要素法を用いた解析ソフトを、電気防食場に対応して生成される数値解析モデルに適応して、解析（電位分布の導出）をおこなっている。
この先行技術では、対極に於ける境界条件を定電流条件とし、被防食対象物である管体表面における境界条件を、被防食対象物を構成する管体材料の電気化学的な反応抵抗である電位−電流曲線（分極曲線）を満足するものとしている。そして、このような対極及び被防食対象物の境界条件を満足する解析解で、対極から場内に流入する電流の全てが、被防食対象物に流入する条件を満足する解析解（定常解）を求めて、電気防食場（特に管体表面）に於ける電位分布としている。
【０００３】
【発明が解決しようとする課題】
上記従来技術を、そのまま干渉問題に適応しようとすると、対極を定電流源とみなし、被防食対象物及び被干渉対象物に於ける境界条件をこられが共に所定の分極曲線を満たすような条件の下に解析を進めることとなる。結果、実質上、両者が電気的につながった状態となる。この解にあっては、干渉問題を解いたこととはならない。このような条件の下に、本願が例示的に対象とする電気防食場（図２に示す場で、シルト８内に、１個の試験片からなる対極９と、８個の試験片からなる被干渉対象物１０と、５個の試験片からなる被防食対象物１１とから構成される）を解析した結果（各試験片から流出する電流のシミュレーション結果）を、図１０に示した。この結果からも判明するように、対極９から被防食対象物１０及び被干渉対象物１１に共に電流が流れ込む状態となっており、干渉問題を合理的に解析しているとは、いいにくい。
従って、本発明の目的は、対極、被干渉対象物及び被防食対象物とを含む電気防食系を、合理的に数値解析することができる解析手法を得ることにある。
【０００４】
【課題を解決するための手段】
この目的を達成するための本発明による、解析対象の電気防食場の電位分布を、ラプラス方程式に従うラプラス場と見なし、前記電気防食場に対応した数値解析モデルを構築するとともに、線形及び非線形な境界条件下でラプラス場を解くことが可能な数値解析手段を前記数値解析モデルに適用して、前記電気防食場のシミュレーション解析をおこなう解析方法の特徴手段は、以下のとおりである。
即ち、被干渉対象物があり、対極より被防食対象物に防食電流を流して前記被防食対象物の電気防食をおこなう電気防食場を解析対象とする場合に、
前記対極、被干渉対象物及び被防食対象物を加味した干渉問題数値解析モデルを構築し、少なくとも前記対極、被干渉対象物及び被防食対象物に於ける電気化学的条件を、それぞれ対応するモデル部位に於ける境界条件とする演算条件の下に、前記ラプラス場を解いて定常解を得るに、
前記被干渉対象物が前記被防食対象物に対して所定の電位状態にある境界条件を加味した干渉問題演算条件の下で、前記数値解析手段を適用して前記定常解を得、
得られる前記定常解の中から、前記対極から場内に流入する電流の全てが前記被防食対象物内に流入するとともに、前記被干渉対象物に流入する電流の総量がこの被干渉対象物から流出する電流条件を満足する最適定常解を求め、
求められた前記最適定常解を、前記被干渉対象物がある電気防食場の解とするものとするのである。
【０００５】
この手法を採用する場合にあっては、先ず、被干渉対象物が被防食対象物に対して、所定様々な電位状態にある場合に対応する定常解が得られ、得られる解で、被干渉対象物が満たすべき電流条件を満足する定常解を最適定常解をして抽出する。従って、被干渉対象物は、本来、これが満たすべき電流条件が満足された状態の防食場の解が得られることとなるため、合理的な解を得ることができる。
【０００６】
さらに、このような手法は、以下のような構成を取ることとなる。
即ち、対極より被防食対象物に防食電流を流して被防食対象物の電気防食をおこなう電気防食場を解析対象とし、
前記電気防食場における電位分布を、ラプラス方程式に従うラプラス場と見なして、前記電気防食場に対応する数値解析モデルを構築し、
少なくとも前記対極及び前記被防食対象物に於ける電気化学的条件を、それぞれ対応するモデル部位に於ける境界条件とする演算条件の下に、前記ラプラス場を解いて定常解を得て、前記電気防食場の解析をおこなうシミュレーション解析方法の構造を有する場合にあって、
前記電気防食場内に被干渉対象物が存在する場合に、
前記被干渉対象物を加味した干渉問題数値解析モデルを構築し、
前記構築された干渉問題数値解析モデルを使用して、前記被干渉対象物が前記被防食対象物に対して所定の電位状態にある境界条件を加味した干渉問題演算条件の下に定常解を得、得られる定常解であって、前記対極から場内に流入する電流の全てが前記被防食対象物内に流入するとともに、前記被干渉対象物に流入する電流の総量がこの被干渉対象物から流出する電流条件を満たす最適定常解を求め、
求められる前記最適定常解を、前記被干渉対象物がある電気防食場の解とする構造をとる。
【０００７】
即ち、この構造は、先に説明した従来技術が採用していた手法において、被干渉対象物が電気防食場内にある場合に、これに対応したモデル部を作成し、この被干渉対象物に流れ込む電流と、流出する電流の関係を満足することにより、適切な最適解を求めるようにすることに対応する。
従って、この場合も、合理的な解を求めることができる。
【０００８】
上記したような解析方法を採る場合にあって、前記構築された干渉問題数値解析モデルを使用して、前記最適定常解を求めるに、
予め求められている被干渉対象物の干渉物分極特性に対して、所定電位量だけ電気的にシフトしたシフト済分極特性を求め、前記被干渉対象物に対応するモデル部位に於ける境界条件として前記シフト済分極特性を加味した演算条件の下に定常解を求める演算操作を、前記所定電位量をパラメータとしながら繰り返し、
得られた前記定常解の中から、前記電流条件を満たす前記最適定常解を求めることが好ましい。
分極特性は、その部材における電流と電圧の関係として求められるができるが、本願のように、被干渉対象物があり、この被干渉対象物が被防食対象物に対して、ある電位を保った状態で、初めて現実の状態を代表できる場合は、この被干渉対象物に於ける境界条件の設定にあたって、シフト済分極特性を採用する。このようにすると、被干渉対象物が被防食対象物に対して電位がシフトした状態での解析が可能となり、実情に適した解析をおこなうことができる。
【０００９】
さらに、上記の場合にあって、前記干渉物分極特性が、前記被干渉対象物の電位と電流密度との関係である被干渉対象物分極曲線として与えられ、前記シフト済分極特性が、前記被干渉対象物分極曲線に対して、前記所定の電位量だけ電気的に貴側もしくは卑側にシフトされたシフト済分極曲線として与えられることが好ましい。
被干渉対象物の分極曲線は、現場等の状況に対応して容易にこれを求めることができ、この分極曲線を利用して、解析対象場内の被干渉対象物の境界条件をシフトした状態で設定する。この様にすると、結果的に、被干渉対象物がある場を適切に解くことができる。
【００１０】
さらに、被防食対象物に対応するモデル部位に於ける境界条件としては、これが、被防食対象物の電位と電流密度との関係である被防食対象物分極曲線を満たす条件として与えられ、
さらに、対極に対応するモデル部位に於ける境界条件としては、定電位条件、定電流条件もしくは対極の電位と電流密度との関係である対極分極曲線を満たす条件として与えられるように構成されることが好ましい。
この様な境界条件の設定手法により、対極が定電位にある状態、定電流にある状態、定電圧にある状態に対応した解析をおこなうことができる。さらに、被防食対象物に関しては、所謂、被防食対象物分極曲線を満たす状態を満足することにより、実情に適した解析となる。
【００１１】
上記の方法を使用する干渉問題を取り扱うことができるシミューレーション解析装置としては、以下のような構造を取ることとなる。
即ち、この装置は、従来型のものと同様に、解析対象の電気防食場の電位分布を、ラプラス方程式に従うラプラス場と見なした電気防食場の数値解析モデルと、線形及び非線形な境界条件下でラプラス場を解くことが可能な数値解析手段とを備え、この数値解析手段を数値解析モデルに適用して、場内の状況に応じてラプラスの方程式を満たす電位分布を得る手段を備えて構成されるのであるが、被干渉対象物があり、対極より被防食対象物に防食電流を流して被防食対象物の電気防食をおこなう電気防食場を解析対象とするものにおいては、これに以下の構成が置き代わることとなる。
即ち、数値解析モデルとしては、対極、被干渉対象物及び被防食対象物に対応するモデル部を有する干渉問題数値解析モデルが備えられることとなる。数値解析手段は、これまでのものと同様のものが使用される。そして、前記被干渉対象物が前記被防食対象物に対して所定の電位状態にある境界条件を加味した干渉問題演算条件の下で数値解析手段を適用して定常解を得、前記所定の電位をパラメータとして得られる定常解の中から、対極から場内に流入する電流の全てが被防食対象物内に流入するとともに、被干渉対象物に流入する電流の総量がこの被干渉対象物から流出する電流条件を満足する最適定常解を求める最適定常解抽出手段を備えて構成されることとなる。
ここで、最適定常解抽出手段は、数値解析手段を干渉問題数値解析モデルに適応する場合に、被干渉対象物が被防食対象物に対して所定の電位状態にある境界条件を加味した演算条件の下に定常解を得る機能を有し、さらに、この所定の電位状態をパラメータ的に変化させる機能を有している。従って、電位値の異なった境界条件の下での定常解が複数得られることとなるが、このような定常解の中から、上記条件を満たす最適定常解を抽出する機能をも有し、これを実行するのである。従って、結果的に最適定常解抽出手段の働きで、これまで説明してきた本願の方法で、被干渉対象物が場内にある電気防食場を合理的に解き、解を得ることができる。
この場合も、少なくとも被干渉対象物に於ける境界条件の設定にあたっては、その干渉物分極特性（例えば被干渉対象物の分極曲線）を使用し、これが、被防食対象物に対して所定の電位だけシフトした状態にある境界条件を設定して解析をおこなうことが好ましいことは当然である。
【００１２】
【発明の実施の形態】
本願の実施の形態に関して、以下図面を参照しながら説明する。
本願のように、被干渉対象物１０がある防食防食場を取り扱う場合にあっても、電気防食場の数値解析的な取扱は、基本的には、従来のものと同一であり、解析対象の電気防食場の電位分布を、ラプラス方程式に従うラプラス場と見なし、この電気防食場に対応した数値解析モデルを構築するとともに、線形及び非線形な境界条件下でラプラス場を解くことが可能な数値解析手段３を、構築される数値解析モデル４に適用して、シミュレーション解析をおこなう。
本願に於ける解析対象の干渉問題の電気防食場は、水または土壌といった電位分布が発生する媒体内に、防食対象の被防食対象物１１（カソードとなる）と、前記被防食対象物１１に対する給電極としての対極９（アノードとなる）とを備え、さらに、前述の被干渉対象物１０が存在する構成となる。
【００１３】
シミュレーション解析にあたっては、図１に示すように、コンピュータ１が使用される。このコンピュータ１の記憶装置２には、図示するように、数値解析手段３、解析対象の物理条件に適合して構築される干渉問題数値解析モデル４が格納されるとともに、解を求める場合に必要となる演算条件である特定モデル部に於ける境界条件が格納される境界条件格納部５、さらに、解析演算の初期設定である初期条件が格納される初期条件格納部６が設けられている。従って、数値解析にあたっては、数値解析手段３は、境界条件格納部５、初期条件格納部６に格納される条件を、対応する数値解析モデルのモデル部に適応しながら解析演算を実行する。
さらに、本願にあっては、後に説明するように、最適定常解を求める必要があるため、この抽出操作を実行する最適定常解抽出手段７が設けられている。
【００１４】
以下、個々に説明していく。
【００１５】
前記数値解析モデル４は、解析対象の電気防食場に対応して、場内に存在するものの物理的形状条件を満足し、且つ、モデル内にある各要素間の物理量（電位）が、ラプラス方程式を満たすように接続されて構築される。
ここで、解法として、以下に示すように境界要素法を採用する場合は、各境界上に、各要素が構築される。一方、数値解析手法として、有限要素法、差分法等を採用する場合は、電気防食場領域全体が、演算対象の各要素に分割される。
【００１６】
前記数値解析手段３としては、所謂、ソルバーがこれにあたり、解析手法として境界要素法を採用することができる。さらに、有限要素法を採用する場合は、ＡＢＡＱＵＳ（Ｈｉｂｂｉｔｔ，Ｋａｒｌｓｓｏｎ＆Ｓｏｒｅｎｓｅｎ，Ｉｎｃ．製）等の公知のソルバーを採用する。
このようなソルバーに関する要件として、干渉問題を取扱う必要がある場合は、少なくとも、被干渉対象物１０、被防食対象物１１に於ける境界条件として、これらのものの分極特性（材料の電位と電流密度との関係と示す特性）もしくは、このような分極特性に相当する特性（後にシフト済分極特性として使用する特性）を取扱う必要があるため、所謂、非常に強い非線形な境界条件を取扱ことができる数値解析手段を使用する。先に有限要素法のおりに説明したソルバーＡＢＡＱＵＳは、このような非常に強い非線形な境界条件を取扱ことができる。
この境界条件が分極曲線として与えられる場合は、対応するモデル部位において、この分極曲線を満足する状態で電流と電位との関係が決定される。
さらに、所謂、非常に強い非線形な特性の熱伝達係数を有する熱伝導問題を解析可能な数値解析手段（数値解析ソフトであり、ＭＡＲＣ（マークアナリシスリサーチコーポレーション社製）等）を、本願の用途に使用することができる。このような熱伝導問題を解析可能な数値解析手段を使用する場合は、先に先行技術の項で挙げた例に示されるように、電位と電流密度との関係として与えられる境界条件を、数値解析手段内で熱伝達係数が満たすべき境界条件に書き換えて適用することにより、使用することができる。
【００１７】
以下、干渉問題を取扱う場合について、その解析手法として、境界要素法（ＢＥＭ法）を適応する場合に具体例を取って説明する。
この境界要素法を電気防食場に適応する場合の基本的な構成に関して、以下付言しておく。ここでは、被干渉対象物はないものとする。
電気防食場の電位（φ）は数１のラプラス方程式に支配される。
【００１８】
【数１】
▽²φ＝０
【００１９】
場が境界Γ₁，Γ₂，Γ_aおよびΓ_cに囲まれているとする。ここで、Γ₁は電位φの値がφ₀に指定された境界（電位一定の境界）、Γ₂は電流密度ｑの値がｑ₀に指定された境界（電流密度一定の境界）、Γ_aおよびΓ_cは、それぞれ対極９および被防食対象物１１の表面となる。各境界における境界条件は次式で与えられる。
【００２０】
【数２】
Γ₁上：φ＝φ₀
Γ₂上：ｑ｛≡−κ∂φ／∂ｎ｝＝ｑ₀
Γ_a上：φ＝ｆ_a（ｑ）
Γ_c上：φ＝ｆ_c（ｑ）
【００２１】
ここで、κは場の電気伝導率、∂／∂ｎは外向き法線方向の微分であり、ｆ_a（ｑ）およびｆ_c（ｑ）は対極９および被防食対象物１１の分極特性を表す非線形の関数（分極曲線）で、実験によって求められる。数１を境界条件（数２）のもとで解けば、表面近傍の電位および電流密度分布を求めることができる。
【００２２】
２−３境界要素法による解法
境界要素法の通常の定式化に従い、数１より境界積分方程式が導かれる。
【００２３】
【数３】

【００２４】
ここでφ^*はラプラス方程式の基本解であり、ｑ^*＝−κ∂φ^*／∂ｎである。また、ｃは形状係数で、滑らかな境界ではｃ＝１／２、角度ωの角点ではｃ＝ω／２πである。
この境界積分方程式を数値的に解くためには離散化を行う必要があり、境界を多くの要素に分割し、φとｑをそれぞれの節点における離散的な値と内挿関数により近似すると次の連立代方程式が導かれる。
【００２５】
【数４】

【００２６】
ここで、ｂ_i（ｉ＝１，２，……，ｐ）はΓ₁＋Γ₂上のφまたはｑの既知の成分の値、ｘ_i（ｉ＝１，２，……，ｐ）はｂ_iに対応する未知量である。ｆ_i（ｑｉ）（ｉ＝１，２，……，ｓ）は分極特性を表す非線形の関数である。ｐおよびｓは境界Γ₁＋Γ₂およびΓ_a＋Γ_c上の要素数を示している。また、 [Ａ] および [Ｂ] は境界Γの幾何学的形状によって決まるマトリックスである。この式は非線形であるため、これを解くためには繰り返し計算を必要とする。この計算は、例えばニュートン・ラフソン法を採用することにより、解くことができる。
【００２７】
以上が、一般的な意味で電気防食場を境界要素法（ＢＥＭ解析）を適応して解く場合の構成であり、このようにして、対極、被干渉対象物及び被防食対象物を加味した干渉問題数値解析モデルを構築し、少なくとも前記対極、被干渉対象物及び被防食対象物に於ける電気化学的条件を、それぞれ対応するモデル部位に於ける境界条件として与えることにより、境界条件を満たす定常解を得ることができる。
しかしながら、本願のように、干渉問題を取扱おうとすると、さらなる手続きが必要となる。即ち、前記対極から場内に流入する電流の全てが被防食対象物内に流入するとともに、被干渉対象物に流入する電流の総量がこの被干渉対象物から流出する電流条件を満足する必要がある。従って、この条件を満足する最適定常解を求め、求められた最適定常解を、解析対象となっている被干渉対象物がある電気防食場の解として出力する構成とする。この最適定常解を求める操作をおこなうのが、先に示した最適定常解抽出手段７の働きであるが、この手段７は、被干渉対象部に対応するモデル部位における境界条件を、被防食対象物に対して所定の電位状態にある境界条件として解析をおこないながら、最終的に先に示した電流条件を満たす最適定常解を求めるものである。この最適定常解抽出手段７の働きは、図６、ステップ４に示す部位の演算を繰り返し、適切な解を求める働きであり、以下のフローの説明において詳細に説明する。
【００２８】
以上が、本願の電気防食場のシミュレーション解析方法の主要構成の説明であるが、図２に示す電気防食場を対象とする場合について、実際の適用状況を説明していく。
この電気防食場は、縦４０ｃｍ、横１００ｃｍ、深さ７ｃｍのシルト８（比抵抗１６６７Ｓ^-1ｃｍ）から構成されており、その表面の所定位置に、対極９（試験片１個）、被干渉対象物１０（試験片９個で構成され、各片は電気的に接続され、等電位に保たれる）、被防食対象物１１（試験片５個で構成され、各片は電気的に接続され等電位に保たれる）が備えられている。この試験片はＳＳ４００の厚み２ｍｍのものであり、その寸法は６０ｍｍ×８０ｍｍ（金属露出面は４０ｍｍ×４０ｍｍ）とし、その周部（下面を除く）を絶縁コーティングした。また、金属露出面の中央に電位測定用の孔（５ｍｍ×５ｍｍ）をあけ、その端面も絶縁コーティングを施した。従って、この試験片は、シルト８と、その裏面で電気的に接続される。さらに、対極９と被防食対象物１１との間には、１ｍＡの電流が流れるものとした。従って、この例では、対極９の条件は定電流条件である。
以下、図６に示す解析作業フローに従って説明する。
１モデル化
上記の電気防食場の物理的な関係を満足するように、干渉問題数値解析モデル４が構築される。上記の防食対象に対して構築される数値解析モデル４の物理的形状を図３に示した。これは、解析場を平面視したものと相似であり、この例にあっては、数値解析手段３として境界要素法を採用するため、解析対象の境界に沿って、境界要素が分割形成される。さらに、図４に対極９、被干渉対象物１０、被防食対象物１１に対応する各試験片モデル部に於ける境界要素の分割構造を示した。この工程が、図６に示すステップ１である。このモデル化操作は、電気防食場の物理的形状等を入力装置から入力することで、これに対応した領域がコンピュータ内で確保され、境界要素法を適応する境界が設定されるとともに、境界の要素分割が自動的に行われる。さらに、各境界要素間の電位は、先に示した数２の式に対応して、ラプラス場の条件に対応した状態で接続される。
２場内の電気電導率の入力
電気防食場は、一般に、水、土壌等の媒質に満たされており、これらの媒質に従って、その電気電導率が異なる。従って、解析対象によって決定される電気電導率を入力する。この例の場合は、シルト８から形成されるため、電気電導率は、０．０００５９９８８Ｓ／ｃｍである。場内全領域で、電気電導率は一定とする。この工程が、図６に示すステップ２である。
３境界条件入力
解析対象とする電気防食場によって、対極９、被干渉対象物１０、被防食対象物１１、それぞれに設定されるべき境界条件は異なるが、これを、適宜、設定する。
解析対象の条件から、対極９に対しては、定電流条件（１ｍＡ）とする。
被干渉対象物１１に関しては、これを構成する材質の検討対象条件（環境）下での、電位と電流密度の関係である被干渉対象物分極曲線を与える。この曲線の一例を、図５に実線で示した。ただし、以下の解析にあたっては、この被干渉対象物分極曲線を被干渉対象物に於ける境界条件とするのみならず、この被干渉対象物分極曲線が所定の電位量だけシフトされたシフト済分極曲線（破線）が、被干渉対象物に於ける境界条件として与えられる。
被防食対象物１１に関しては、これを構成する材質の検討対象条件（環境）下での、電位と電流密度の関係である被防食対象物分極曲線を与える。この曲線は、図５に示すものと、材質が同じであるため、同一である。この曲線（実線）が、そのまま、被防食対象物に対応するモデル部位に於ける境界条件とされる。
この工程が、図６に示すステップ３−１、２、３である。
さらに、電位分布の初期値としては、最終的に収束解を得るのに、解析演算時間をできるだけ短縮することができる初期値を与えておく。例えば、対極を一定電位に設定した状態で、対極と被防食対象物との間で、電位が線形に被防食対象物の電位まで減少していくような分布を与えておく。
【００２９】
以上のような作業を完了することにより、数値解析モデル４は、その境界条件にしたがった解を与えることができる状態となる。しかしながら、このようにして与えられる解は、先に説明した電流条件を必ずしも満たす最適定常解となっているわけではない。むしろ、上記の外部入力境界条件だけを使用すると、従来と同様な不合理な結果しか得られない。
４最適定常解の導出
従って、図６ステップ４に示すように、予め求められている被干渉対象物１０の干渉物分極特性に対して、所定電位量Ｖだけ電気的にシフトしたシフト済分極特性を求め、被干渉対象物１１に対応するモデル部位に於ける境界条件として、このシフト済分極特性を適応し、この条件が加味された演算条件の下に定常解を求める演算操作を、所定電位量Ｖをパラメータとしながら繰り返す。さらに、具体的には、先に説明した、干渉物分極特性として与えられている被干渉対象物の電位と電流密度との関係である被干渉対象物分極曲線から、この被干渉対象物分極曲線に対して、所定電位量Ｖだけ電気的に貴側にシフト（このシフト量は正負値を共に含みシフト量が負の場合は結果的に卑側にシフトする）されたシフト済分極曲線（図５破線）を求め、これを被干渉対象物１０に対応するモデル部位に於ける境界条件とする。そして、この境界条件を加味した演算条件の下に、逐次、定常解を求めるのである。このようにして得られる定常解の中から、先に説明した電流条件（対極９から場内に流入する電流の全てが被防食対象物１１内に流入する（ｉａ＝Σｉｃ）とともに、被干渉対象物１０に流入する電流の総量がこの被干渉対象物１０から流出する条件（Σｉｋ＝０））を満足する解を最適定常解として求める。上記した図２の系の場合、被防食対象物１１に対する被干渉対象物１０の電位は、解析上、４９１．８ｍＶとなった。一方、実測された電位差は４９２ｍＶであった。
【００３０】
上記のようにして求められた解析解（最適定常解）に於ける、対極９、被干渉対象物１０、被防食対象物１１に於ける電流分布を図１０に対応して、図７に示した。
さらに、解析値と実測値との比較を、図８、９に示した。図８は、被干渉対象物１０に於ける電位分布と電流密度との結果を示している。一方、図９は、被防食対象物１１に於ける電位分布と電流密度との結果を示している。両者ともに、個々の試験片が元来有する自然電位のばらつきを考慮しても、解析値が実測値とよく一致していることが判る。
従って、本願手法を採用することにより、ラプラス場を解析対象領域とし、その境界条件が非線形境界条件を扱える汎用の数値解析ソフトによって、電気防食時に於ける干渉現象を数値解析により把握できることが判る。
本願を適応することにより、実際に干渉問題が発生しているかどうか、また、その影響度合い等を定量的に判断することが可能であり、その状況を可視化することが可能である。また、干渉の対策案の評価・選定にも使用可能となる。
【図面の簡単な説明】
【図１】本願で使用する電気防食場の解析装置のシステム構成を示す図
【図２】解析対象の電気防食場の一例を示す図
【図３】モデルの物理的対応関係を示す図
【図４】対極、被干渉対象物及び被防食対象物に対応するモデル部の境界要素構造を示す図
【図５】被干渉対象物の分極曲線（初期入力値）を示す図
【図６】解析手順のフローチャートを示す図
【図７】本願の解析手法を適応した解析結果に於ける試験片番号と電流の関係を示す図
【図８】被干渉対象物に於ける実測値と解析計算結果の関係を示す図
【図９】被防食対象物に於ける実測値と解析計算結果の関係を示す図
【図１０】従来手法を適応した場合に於ける図７に対応する解析結果を示す図
【符号の説明】
３数値解析手段
４干渉問題数値解析モデル
５境界条件格納部
７最適定常開抽出手段
９対極
１０被干渉対象物
１１被防食対象物[0001]
BACKGROUND OF THE INVENTION
The present invention uses a computer for the interference phenomenon that becomes a problem when other metal structures are present near an object to be protected when performing anticorrosion (cathodic protection) in an aqueous solution environment or a soil environment. And technology for numerical analysis.
[0002]
[Prior art]
Conventionally, simulation analysis dealing with this kind of interference problem has not been performed, and so-called Laplace field analysis is merely performed on a system composed of a counter electrode and an object to be protected.
An example of such simulation analysis will be described. 4, 1992, pages 61 to 71, “Application of potential distribution analysis technique to seawater system anticorrosion”, analysis of the cathodic protection field is performed using a finite element method which is a kind of numerical analysis method.
In this technology, using the fact that the potential distribution in the environment becomes a Laplace field, analysis using a finite element method that can analyze a heat conduction problem with a heat transfer coefficient having a very strong nonlinearity The software is applied to the numerical analysis model generated corresponding to the cathodic protection field, and analysis (derivation of potential distribution) is performed.
In this prior art, the boundary condition at the counter electrode is a constant current condition, and the boundary condition on the surface of the tube that is the object to be protected is the electrochemical reaction resistance of the tube material constituting the object to be protected. The potential-current curve (polarization curve) is satisfied. An analytical solution that satisfies the boundary conditions between the counter electrode and the object to be protected, such that all of the current flowing from the counter electrode into the field satisfies the condition of flowing into the object to be protected (steady solution). The electric potential distribution in the cathodic protection field (especially the tube surface) is obtained.
[0003]
[Problems to be solved by the invention]
If the above prior art is applied to the interference problem as it is, the counter electrode is regarded as a constant current source, and the boundary conditions in the corrosion-protected object and the interfered object both satisfy the predetermined polarization curve. The analysis will proceed below. As a result, the two are substantially electrically connected. This solution does not solve the interference problem. Under such conditions, the cathodic protection field to which the present application is exemplarily illustrated (in the field shown in FIG. 2, the silt 8 is composed of a counter electrode 9 consisting of one test piece and eight test pieces. FIG. 10 shows the result of analyzing the object to be interfered 10 and the object to be protected 11 consisting of five test pieces (a simulation result of the current flowing out from each test piece). As can be seen from this result, it is difficult to reasonably analyze the interference problem because both current flows from the counter electrode 9 to the protected object 10 and the interfered object 11.
Therefore, an object of the present invention is to obtain an analysis method capable of rationally analyzing an anticorrosion system including a counter electrode, an object to be interfered with, and an object to be protected.
[0004]
[Means for Solving the Problems]
According to the present invention for achieving this object, the electric potential distribution of the cathodic protection field to be analyzed is regarded as a Laplace field according to the Laplace equation, and a numerical analysis model corresponding to the cathodic protection field is constructed, and linear and non-linear boundaries are formed. The characteristic means of the analysis method for performing the simulation analysis of the cathodic protection field by applying the numerical analysis means capable of solving the Laplace field under the conditions to the numerical analysis model is as follows.
That is, when there is an object to be interfered, and an electric corrosion protection field that conducts electric corrosion protection of the object to be protected by flowing an anticorrosion current from the counter electrode to the object to be protected is an analysis target,
An interference problem numerical analysis model including the counter electrode, the object to be interfered, and the object to be protected is constructed, and at least the electrochemical conditions in the counter electrode, the object to be interfered, and the object to be protected are corresponding to each other. In order to obtain the steady solution by solving the Laplace field under the calculation condition as the boundary condition in the region,
Under an interference problem calculation condition that takes into account a boundary condition in which the object to be interfered is in a predetermined potential state with respect to the object to be protected, the numerical analysis means is applied to obtain the steady solution,
From the obtained steady solution, all of the current flowing into the field from the counter electrode flows into the protected object, and the total amount of current flowing into the interfered object flows out of the interfered object. Find the optimal steady-state solution that satisfies the current conditions
The obtained optimum steady solution is assumed to be a solution of the cathodic protection field where the interfered object is located.
[0005]
In the case of adopting this method, first, a steady solution corresponding to a case where the interfered object is in various predetermined potential states with respect to the protected object is obtained. A stationary solution that satisfies the current condition to be satisfied by the object is extracted as an optimum stationary solution. Therefore, the object to be interfered with can obtain a reasonable solution since the solution of the corrosion prevention field in a state where the current condition to be satisfied is originally satisfied.
[0006]
Further, such a method has the following configuration.
That is, the analysis target is an anticorrosion field that conducts an anticorrosion of the object to be protected by passing an anticorrosion current from the counter electrode to the object to be protected.
Considering the potential distribution in the cathodic protection field as a Laplace field according to the Laplace equation, constructing a numerical analysis model corresponding to the cathodic protection field,
At least the electrochemical conditions in the counter electrode and the object to be protected are set as boundary conditions in the corresponding model parts, respectively, and the Laplace field is solved to obtain a steady solution, and the electric condition is obtained. In the case of having a structure of a simulation analysis method for analyzing a corrosion prevention field,
When there is an object to be interfered in the cathodic protection field,
Build an interference problem numerical analysis model that takes into account the interfered object,
Using the constructed interference problem numerical analysis model, a steady solution is obtained under an interference problem calculation condition including a boundary condition in which the interfered object is in a predetermined potential state with respect to the protected object. The obtained steady solution is that all of the current flowing into the field from the counter electrode flows into the object to be protected, and the total amount of current flowing into the object to be interfered flows out of the object to be interfered. Find the optimal steady-state solution that satisfies the current conditions
The optimum steady solution to be obtained is configured to be a solution of the cathodic protection field where the object to be interfered is.
[0007]
In other words, in this method, when the object to be interfered is in the cathodic protection field in the method adopted by the prior art described above, a model portion corresponding to this is created and flows into the object to be interfered. This corresponds to finding an appropriate optimal solution by satisfying the relationship between the current and the flowing current.
Therefore, in this case as well, a reasonable solution can be obtained.
[0008]
In the case of adopting the analysis method as described above, using the constructed interference problem numerical analysis model, to obtain the optimum steady solution,
As a boundary condition in the model part corresponding to the interfered object, a shifted polarization characteristic that is electrically shifted by a predetermined potential amount is obtained with respect to the interferer polarization characteristic of the interfered object that is obtained in advance. The calculation operation for obtaining a steady solution under the calculation conditions taking the shifted polarization characteristics into account is repeated while using the predetermined potential amount as a parameter,
It is preferable to obtain the optimum steady solution that satisfies the current condition from the obtained steady solutions.
Although the polarization characteristics can be obtained as a relationship between the current and voltage in the member, there is an object to be interfered as in the present application, and the object to be interfered maintains a certain potential with respect to the object to be protected. When the actual state can be represented for the first time in the state, the shifted polarization characteristic is adopted in setting the boundary condition in the interfered object. If it does in this way, the analysis in the state where the potential of the object to be interfered is shifted with respect to the object to be protected becomes possible, and the analysis suitable for the actual situation can be performed.
[0009]
Further, in the above case, the interference object polarization characteristic is given as an interfered object polarization curve which is a relationship between the potential of the interfered object and a current density, and the shifted polarization characteristic is The interference object polarization curve is preferably given as a shifted polarization curve that is electrically shifted to the noble side or the base side by the predetermined potential amount.
The polarization curve of the object to be interfered can be easily obtained according to the situation at the site, etc., and this polarization curve is used in a state where the boundary condition of the object to be interfered in the analysis object field is shifted. Set. If it does in this way, as a result, the field with an interference target object can be solved appropriately.
[0010]
Furthermore, as a boundary condition in the model part corresponding to the object to be protected, this is given as a condition satisfying the object to be protected object polarization curve, which is the relationship between the potential of the object to be protected and the current density,
Furthermore, the boundary conditions in the model part corresponding to the counter electrode may be configured so as to satisfy a constant potential condition, a constant current condition, or a condition that satisfies a counter electrode polarization curve that is the relationship between the potential of the counter electrode and the current density. Is preferred.
By using such a boundary condition setting method, it is possible to perform analysis corresponding to a state where the counter electrode is at a constant potential, a state where the counter electrode is constant current, and a state where the counter electrode is constant voltage. Furthermore, with respect to the object to be protected, an analysis suitable for the actual situation is achieved by satisfying a state satisfying a so-called corrosion curve of the object to be protected.
[0011]
A simulation analysis apparatus capable of handling the interference problem using the above method has the following structure.
That is, this device, like the conventional type, has a numerical analysis model of an electric corrosion prevention field in which the electric potential distribution of the electric corrosion prevention field to be analyzed is regarded as a Laplace field according to the Laplace equation, and linear and nonlinear boundary conditions. And a numerical analysis means capable of solving the Laplace field, and applying this numerical analysis means to a numerical analysis model to obtain a potential distribution satisfying the Laplace equation according to the situation in the field. However, if there is an object to be interfered, and the object to be analyzed is an anticorrosion field that conducts the anticorrosion of the object to be protected by passing an anticorrosion current from the counter electrode to the object to be protected, the following configuration is included. Will be replaced.
That is, as the numerical analysis model, an interference problem numerical analysis model having a model portion corresponding to the counter electrode, the object to be interfered, and the object to be protected is provided. The numerical analysis means is the same as that used so far. Then, a stationary solution is obtained by applying numerical analysis means under an interference problem calculation condition in consideration of a boundary condition in which the object to be interfered is in a predetermined potential state with respect to the object to be protected, and the predetermined potential is obtained. From the steady-state solution obtained using as a parameter, all of the current flowing into the field from the counter electrode flows into the protected object, and the total amount of current flowing into the interfered object flows out of the interfered object An optimum stationary solution extraction means for obtaining an optimum stationary solution that satisfies the current condition is provided.
Here, the optimum steady solution extraction means is a calculation condition that takes into account the boundary condition that the interfered object is in a predetermined potential state with respect to the protected object when the numerical analysis means is applied to the interference problem numerical analysis model. Has a function of obtaining a steady solution below, and further has a function of changing the predetermined potential state parameterically. Therefore, a plurality of stationary solutions under boundary conditions having different potential values can be obtained. From such stationary solutions, there is also a function of extracting an optimal stationary solution that satisfies the above conditions. Is executed. Therefore, as a result, the optimum steady solution extracting means can reasonably solve the electric corrosion prevention field where the interfered object is in the field and obtain a solution by the method of the present application described so far.
In this case as well, at least in setting the boundary conditions for the object to be interfered, the interference object polarization characteristics (for example, the polarization curve of the object to be interfered) are used, and this is a predetermined potential with respect to the object to be protected. Naturally, it is preferable to perform the analysis by setting the boundary condition that is shifted by only the boundary condition.
[0012]
DETAILED DESCRIPTION OF THE INVENTION
Embodiments of the present application will be described below with reference to the drawings.
Even in the case of handling an anticorrosion field with an object 10 to be interfered with as in the present application, the numerical analysis of the electric corrosion field is basically the same as the conventional one, Numerical analysis means capable of solving Laplace field under linear and non-linear boundary conditions, considering potential distribution of cathodic field as Laplace field according to Laplace equation, constructing numerical analysis model corresponding to this cathodic field 3 is applied to the constructed numerical analysis model 4 to perform simulation analysis.
The electrocorrosion field of the interference problem of the analysis object in the present application is the anticorrosion object 11 (to be a cathode) and the anticorrosion object 11 in a medium in which a potential distribution such as water or soil occurs. A counter electrode 9 (which serves as an anode) as a supply electrode is provided, and the above-described interfered object 10 is present.
[0013]
In the simulation analysis, a computer 1 is used as shown in FIG. As shown in the figure, the storage device 2 of the computer 1 stores numerical analysis means 3 and an interference problem numerical analysis model 4 constructed in conformity with the physical condition to be analyzed, and is necessary for obtaining a solution. A boundary condition storage unit 5 that stores boundary conditions in a specific model unit, which is a calculation condition to be, and an initial condition storage unit 6 that stores an initial condition that is an initial setting of an analytical calculation are provided. Therefore, in the numerical analysis, the numerical analysis means 3 executes an analysis operation while adapting the conditions stored in the boundary condition storage unit 5 and the initial condition storage unit 6 to the model part of the corresponding numerical analysis model.
Further, in the present application, as described later, since it is necessary to obtain an optimum steady solution, an optimum steady solution extracting means 7 for executing this extraction operation is provided.
[0014]
Each will be described below.
[0015]
The numerical analysis model 4 satisfies the physical shape condition of what exists in the field, corresponding to the cathodic protection field to be analyzed, and the physical quantity (potential) between each element in the model is the Laplace equation. Connected and built to meet.
Here, when the boundary element method is adopted as a solution as described below, each element is constructed on each boundary. On the other hand, when a finite element method, a difference method, or the like is adopted as a numerical analysis method, the entire cathodic protection field is divided into elements to be calculated.
[0016]
The numerical analysis means 3 is a so-called solver, and a boundary element method can be adopted as an analysis method. Furthermore, when the finite element method is employed, a known solver such as ABAQUS (manufactured by Hibbitt, Karlsson & Sorensen, Inc.) is employed.
When it is necessary to deal with the interference problem as a requirement regarding such a solver, at least as a boundary condition in the object 10 to be interfered and the object 11 to be protected, the polarization characteristics (material potential and current density of these materials). Or the characteristics corresponding to such polarization characteristics (characteristics used later as shifted polarization characteristics), so-called very strong non-linear boundary conditions can be handled. Use numerical analysis means. The solver ABAQUS described above in the finite element method can handle such a very strong nonlinear boundary condition.
When this boundary condition is given as a polarization curve, the relationship between the current and the potential is determined in a state satisfying this polarization curve in the corresponding model part.
Furthermore, numerical analysis means (numerical analysis software, such as MARC (manufactured by Mark Analysis Research Corporation), etc.) capable of analyzing a heat conduction problem having a heat transfer coefficient with a very strong non-linear characteristic is used for the present application. Can be used. When using numerical analysis means that can analyze such heat conduction problems, as shown in the example given in the section of the prior art, the boundary condition given as the relationship between the potential and the current density is expressed numerically. It can be used by rewriting and applying the boundary conditions that the heat transfer coefficient should satisfy in the analysis means.
[0017]
Hereinafter, a case where the interference problem is handled will be described by taking a specific example when the boundary element method (BEM method) is applied as the analysis method.
The basic configuration when this boundary element method is applied to the cathodic protection field is described below. Here, it is assumed that there is no object to be interfered with.
The potential (φ) of the cathodic protection field is governed by the Laplace equation of Equation 1.
[0018]
[Expression 1]
▽²φ = 0
[0019]
Field is boundary Γ₁, Γ₂, Γ_aAnd Γ_cSuppose you are surrounded by Where Γ₁Is the value of potential φ₀Boundary (constant potential boundary), Γ₂The value of the current density q is q₀Boundary (constant current density boundary), Γ_aAnd Γ_cAre the surfaces of the counter electrode 9 and the object 11 to be protected. The boundary condition at each boundary is given by the following equation.
[0020]
[Expression 2]
Γ₁Top: φ = φ₀
Γ₂Top: q {≡-κ∂φ / ∂n} = q₀
Γ_aTop: φ = f_a(Q)
Γ_cTop: φ = f_c(Q)
[0021]
Where κ is the field electrical conductivity, ∂ / ∂n is the outward normal differential, f_a(Q) and f_c(Q) is a non-linear function (polarization curve) representing the polarization characteristics of the counter electrode 9 and the object 11 to be protected, and is obtained by experiment. If Equation 1 is solved under the boundary condition (Equation 2), the potential and current density distribution in the vicinity of the surface can be obtained.
[0022]
2-3 Solution by boundary element method
In accordance with the usual formulation of the boundary element method, a boundary integral equation is derived from Equation 1.
[0023]
[Equation 3]

[0024]
Where φ^*Is the basic solution of the Laplace equation, q^*= -Κ∂φ^*/ ∂n. Further, c is a shape factor, and c = ½ at a smooth boundary and c = ω / 2π at a corner point of an angle ω.
In order to solve this boundary integral equation numerically, it is necessary to discretize it. When the boundary is divided into many elements and φ and q are approximated by discrete values and interpolation functions at each node, Simultaneous algebraic equations are derived.
[0025]
[Expression 4]

[0026]
Where b_i(I = 1, 2,..., P) is Γ₁+ Γ₂The value of the known component of φ or q above, x_i(I = 1, 2,..., P) is b_iIt is an unknown quantity corresponding to. f_i(Qi) (i = 1, 2,..., S) is a non-linear function representing polarization characteristics. p and s are boundaries Γ₁+ Γ₂And Γ_a+ Γ_cThe number of elements above is shown. [A] and [B] are matrices determined by the geometric shape of the boundary Γ. Since this equation is non-linear, iterative calculations are required to solve it. This calculation can be solved by adopting the Newton-Raphson method, for example.
[0027]
The above is a configuration in the case where the electric corrosion prevention field is solved by applying the boundary element method (BEM analysis) in a general sense. In this way, the interference including the counter electrode, the interference target object, and the corrosion protection object is included. By constructing a problem numerical analysis model and providing at least the electrochemical conditions in the counter electrode, the object to be interfered with, and the object to be protected as the boundary conditions in the corresponding model parts, A solution can be obtained.
However, as in the present application, further procedures are required to deal with interference problems. That is, all of the current flowing into the field from the counter electrode flows into the object to be protected, and the total amount of current flowing into the object to be interfered needs to satisfy the current condition for flowing out from the object to be interfered. . Accordingly, an optimum steady solution that satisfies this condition is obtained, and the obtained optimum steady solution is output as a solution for an electro-corrosion field where an object to be analyzed is an interference target. The operation for obtaining the optimum steady solution is the function of the optimum steady solution extraction means 7 described above. This means 7 determines the boundary condition in the model part corresponding to the interference target part as the target to be protected. While analyzing the object as a boundary condition in a predetermined potential state, an optimum steady solution that finally satisfies the current condition described above is obtained. The function of the optimum steady solution extraction means 7 is a function of repeatedly calculating the part shown in FIG. 6 and step 4 to obtain an appropriate solution, and will be described in detail in the following description of the flow.
[0028]
The above is the description of the main configuration of the simulation analysis method of the cathodic protection field of the present application, but the actual application situation will be described for the case of targeting the cathodic protection field shown in FIG.
This cathodic protection field has a silt 8 (specific resistance 1667S) 40 cm long, 100 cm wide and 7 cm deep.^-1cm), and at a predetermined position on the surface, the counter electrode 9 (one test piece) and the object 10 to be interfered with (9 test pieces), each piece being electrically connected and equipotentially To be protected) is provided with an object 11 to be protected (consisting of five test pieces, each piece being electrically connected and kept at an equal potential). This test piece was SS400 having a thickness of 2 mm, and its dimensions were 60 mm × 80 mm (metal exposed surface was 40 mm × 40 mm), and its peripheral portion (excluding the lower surface) was insulation coated. In addition, a hole for potential measurement (5 mm × 5 mm) was formed in the center of the exposed metal surface, and the end surface was also provided with an insulating coating. Therefore, this test piece is electrically connected to the silt 8 on the back surface thereof. Furthermore, a current of 1 mA is assumed to flow between the counter electrode 9 and the object 11 to be protected. Therefore, in this example, the condition of the counter electrode 9 is a constant current condition.
Hereinafter, description will be given according to the analysis work flow shown in FIG.
1 Modeling
The interference problem numerical analysis model 4 is constructed so as to satisfy the physical relationship of the above-described cathodic protection field. FIG. 3 shows the physical shape of the numerical analysis model 4 constructed for the above anticorrosion object. This is similar to a plan view of the analysis field. In this example, since the boundary element method is adopted as the numerical analysis means 3, boundary elements are divided and formed along the boundary to be analyzed. . Furthermore, FIG. 4 shows the division structure of boundary elements in each test piece model portion corresponding to the counter electrode 9, the object 10 to be interfered with, and the object 11 to be protected. This process is step 1 shown in FIG. In this modeling operation, by inputting the physical shape of the cathodic protection field from the input device, an area corresponding to this is secured in the computer, and a boundary to which the boundary element method is applied is set. Element splitting is performed automatically. Further, the potentials between the boundary elements are connected in a state corresponding to the Laplace field condition, corresponding to the equation (2).
2 Input of electric conductivity in the field
The cathodic protection field is generally filled with media such as water and soil, and the electric conductivity varies depending on these media. Therefore, the electric conductivity determined by the analysis target is input. In this example, since it is formed from the silt 8, the electric conductivity is 0.00059988 S / cm. The electric conductivity is constant throughout the field. This process is step 2 shown in FIG.
3 Boundary condition input
Although the boundary conditions to be set for the counter electrode 9, the object 10 to be interfered, and the object 11 to be protected are different depending on the cathodic protection field to be analyzed, these are set as appropriate.
The constant current condition (1 mA) is set for the counter electrode 9 from the analysis target condition.
As for the object 11 to be interfered with, a polarization curve of the object to be interfered, which is the relationship between the potential and the current density, is given under the examination object condition (environment) of the material constituting the object 11. An example of this curve is shown by a solid line in FIG. However, in the following analysis, not only the interference target polarization curve is used as a boundary condition in the interference target, but also the polarized polarization in which the interference target polarization curve is shifted by a predetermined potential amount. A curved line (broken line) is given as a boundary condition in the interfered object.
With respect to the protection target object 11, a protection target object polarization curve, which is a relationship between the potential and the current density, is given under the examination target condition (environment) of the material constituting the protection target object 11. This curve is the same as that shown in FIG. 5 because the material is the same. This curve (solid line) is directly used as a boundary condition in the model portion corresponding to the object to be protected.
This process is steps 3-1, 2 and 3 shown in FIG.
Furthermore, as an initial value of the potential distribution, an initial value that can shorten the analysis calculation time as much as possible is obtained in order to finally obtain a converged solution. For example, in a state where the counter electrode is set to a constant potential, a distribution is provided so that the potential decreases linearly to the potential of the object to be protected between the counter electrode and the object to be protected.
[0029]
By completing the above operations, the numerical analysis model 4 is in a state in which a solution according to the boundary condition can be given. However, the solution given in this way is not necessarily an optimal steady solution that satisfies the current condition described above. Rather, if only the above external input boundary condition is used, only an unreasonable result similar to the conventional one can be obtained.
4 Derivation of optimal steady-state solution
Therefore, as shown in Step 4 of FIG. 6, a shifted polarization characteristic that is electrically shifted by a predetermined potential amount V is obtained with respect to the interference object polarization characteristic of the interference object 10 that is obtained in advance, and the interference object As a boundary condition in the model part corresponding to the object 11, this shifted polarization characteristic is applied, and an arithmetic operation for obtaining a steady solution under an arithmetic condition in which this condition is taken into account is performed with the predetermined potential V as a parameter. repeat. Further, more specifically, from the interfered object polarization curve, which is the relationship between the potential of the interfered object given as the interferent polarization characteristic and the current density described above, this interfered object polarization curve is obtained. In contrast, a shifted polarization curve that is electrically shifted to the noble side by a predetermined potential amount V (this shift amount includes both positive and negative values and consequently shifts to the base side when the shift amount is negative) (see FIG. (5 broken lines) is obtained, and this is set as a boundary condition in the model portion corresponding to the object 10 to be interfered with. Then, a steady solution is obtained sequentially under the calculation conditions taking this boundary condition into account. From the steady solution obtained in this way, the current condition described above (all of the current flowing into the field from the counter electrode 9 flows into the corrosion-protected object 11 (ia = Σic) and the object to be interfered with. A solution that satisfies the condition (Σik = 0) that the total amount of current flowing into the object 10 flows out from the interfered object 10 is obtained as an optimum steady solution. In the case of the system in FIG. 2 described above, the potential of the object 10 to be interfered with the object 11 to be protected is 491.8 mV in the analysis. On the other hand, the measured potential difference was 492 mV.
[0030]
FIG. 7 shows the current distribution in the counter electrode 9, the object 10 to be interfered with, and the object 11 to be protected in the analytical solution (optimal steady solution) obtained as described above, corresponding to FIG. It was.
Further, comparison between the analysis value and the actual measurement value is shown in FIGS. FIG. 8 shows the result of potential distribution and current density in the object 10 to be interfered with. On the other hand, FIG. 9 shows the results of the potential distribution and current density in the object 11 to be protected. In both cases, it can be seen that the analysis values are in good agreement with the actual measurement values even when the variation of the natural potential inherent in each specimen is taken into account.
Therefore, by adopting the method of the present application, it is understood that the interference phenomenon at the time of cathodic protection can be grasped by numerical analysis by using general-purpose numerical analysis software in which the Laplace field is an analysis target region and the boundary condition can handle the nonlinear boundary condition.
By adapting the present application, it is possible to quantitatively determine whether or not an interference problem has actually occurred, the degree of influence, etc., and to visualize the situation. It can also be used to evaluate and select interference countermeasures.
[Brief description of the drawings]
FIG. 1 is a diagram showing a system configuration of an analysis apparatus for an electric corrosion prevention field used in the present application.
FIG. 2 is a diagram showing an example of a cathodic protection field to be analyzed
FIG. 3 is a diagram showing a physical correspondence between models.
FIG. 4 is a diagram showing a boundary element structure of a model unit corresponding to a counter electrode, an object to be interfered, and an object to be protected
FIG. 5 is a diagram showing a polarization curve (initial input value) of an object to be interfered with
FIG. 6 is a flowchart showing an analysis procedure.
FIG. 7 is a graph showing the relationship between the test piece number and the current in the analysis result to which the analysis method of the present application is applied.
FIG. 8 is a diagram showing the relationship between actual measurement values and analysis calculation results for an object to be interfered with
FIG. 9 is a diagram showing the relationship between actual measurement values and analysis calculation results for an object to be protected
FIG. 10 is a diagram showing an analysis result corresponding to FIG. 7 when the conventional method is applied;
[Explanation of symbols]
3 Numerical analysis means
4 Interference problem numerical analysis model
5 Boundary condition storage
7 Optimal steady-open extraction means
9 Counter electrode
10 Object to be interfered with
11 Protected objects

Claims

The potential distribution of the cathodic field to be analyzed is regarded as a Laplace field according to the Laplace equation, and a numerical analysis model corresponding to the cathodic field can be constructed and the Laplace field can be solved under linear and nonlinear boundary conditions. Applying numerical analysis means to the numerical analysis model, an analysis method for performing simulation analysis of the cathodic protection field,
When there is an object to be interfered, and an electric corrosion prevention field that conducts electric corrosion prevention of the object to be protected by flowing an anticorrosion current from the counter electrode to the object to be protected is to be analyzed,
An interference problem numerical analysis model including the counter electrode, the object to be interfered, and the object to be protected is constructed, and at least the electrochemical conditions in the counter electrode, the object to be interfered, and the object to be protected are corresponding to each other. In order to obtain the steady solution by solving the Laplace field under the calculation condition as the boundary condition in the region,
Under an interference problem calculation condition that takes into account a boundary condition in which the object to be interfered is in a predetermined potential state with respect to the object to be protected, the numerical analysis means is applied to obtain the steady solution,
From the obtained steady solution, all of the current flowing into the field from the counter electrode flows into the protected object, and the total amount of current flowing into the interfered object flows out of the interfered object. Find the optimal steady-state solution that satisfies the current conditions
A simulation analysis method for an anticorrosion field, wherein the obtained optimum steady solution is a solution of the anticorrosion field with the interfered object.

The analysis target is an anti-corrosion field that conducts an anti-corrosion of the object to be protected by applying an anti-corrosion current to the object to be protected from the opposite electrode
Considering the potential distribution in the cathodic protection field as a Laplace field according to the Laplace equation, constructing a numerical analysis model corresponding to the cathodic protection field,
At least the electrochemical conditions in the counter electrode and the object to be protected are set as boundary conditions in the corresponding model parts, respectively, and the Laplace field is solved to obtain a steady solution, and the electric condition is obtained. A simulation analysis method for analyzing a corrosion prevention field,
When there is an object to be interfered in the cathodic protection field,
Build an interference problem numerical analysis model that takes into account the interfered object,
Using the constructed interference problem numerical analysis model, a steady solution is obtained under an interference problem calculation condition including a boundary condition in which the interfered object is in a predetermined potential state with respect to the protected object. The obtained steady solution is that all of the current flowing into the field from the counter electrode flows into the object to be protected, and the total amount of current flowing into the object to be interfered flows out of the object to be interfered. Find the optimal steady-state solution that satisfies the current conditions
A simulation analysis method of an anticorrosion field, wherein the optimum steady solution obtained is a solution of the anticorrosion field where the interfered object is present.

Using the constructed interference problem numerical analysis model to find the optimal stationary solution,
As a boundary condition in the model part corresponding to the interfered object, a shifted polarization characteristic that is electrically shifted by a predetermined potential amount is obtained with respect to the interferer polarization characteristic of the interfered object that is obtained in advance. The calculation operation for obtaining a steady solution under the calculation conditions taking the shifted polarization characteristics into account is repeated while using the predetermined potential amount as a parameter,
The simulation analysis method of the cathodic protection field according to claim 1 or 2, wherein the optimum steady solution satisfying the current condition is obtained from the obtained steady solutions.

The interference object polarization characteristic is given as an interfered object polarization curve that is a relationship between the potential of the interfered object and a current density, and the shifted polarization characteristic is obtained with respect to the interfered object polarization curve. The simulation analysis method of the cathodic protection field according to claim 3, which is given as a shifted polarization curve electrically shifted to the noble side or the base side by the predetermined potential amount.

The boundary condition at the model site corresponding to the corrosion-protected object is given as a condition that satisfies a corrosion-protected object polarization curve that is a relationship between the potential and current density of the corrosion-protected object,
The boundary condition in the model part corresponding to the counter electrode is given as a condition satisfying a constant potential condition, a constant current condition, or a counter polarization curve that is a relationship between the potential of the counter electrode and current density. The simulation analysis method of the cathodic protection field of any one of Claims 1.

A numerical analysis model of the above-described cathodic protection field in which the potential distribution of the cathodic protection field to be analyzed is regarded as a Laplace field according to the Laplace equation; and a numerical analysis means capable of solving the Laplace field under linear and nonlinear boundary conditions; And applying the numerical analysis means to the numerical analysis model to perform a simulation analysis of the cathodic protection field,
There is an object to be interfered with, and the object to be analyzed is subjected to an anticorrosion field in which an anticorrosion current is applied to the object to be protected from the counter electrode and the object to be protected is electrically protected.
An interference problem numerical analysis model having a model portion corresponding to the counter electrode, the object to be interfered, and the object to be protected;
Applying the numerical analysis means under an interference problem calculation condition that takes into account a boundary condition that the object to be interfered is in a predetermined potential state with respect to the object to be protected, obtains a steady solution, Of the steady solution obtained as a parameter, all of the current flowing from the counter electrode into the field flows into the protected object, and the total amount of current flowing into the interfered object is the interfered object. A simulation analysis device of an anticorrosion field provided with an optimum steady solution extraction means for obtaining an optimum steady solution that satisfies the current condition flowing out from the vessel.