Petrol sızıntısının durgun su yüzeyindeki yayılımının sonlu elemanlar yöntemiyle modellenmesi

Öz

Bu çalışmada, durgun su üzerinde petrol yayılımının zaman içindeki evrimini simüle etmek için, yerçekimi, yüzey gerilimi ve viskoz kuvvetleri dikkate alan ve rüzgâr ile akıntılar gibi dıştan dayatılmış adveksiyonu ihmal eden bir sonlu elemanlar modeli (FEM) geliştirilmiştir. Nihoul’un kütle ve momentum korunumu denklemlerine dayanan yaklaşımı, hem ani hem de sürekli sızıntı senaryolarına uygulanmıştır. Petrol özelliklerinin, sızıntı koşullarının ve yüzey gerilimi kuvvetlerinin yayılma dinamikleri üzerindeki etkisi ayrıntılı parametrik analiz yöntemi yapılarak incelemiştir. Euler tabanlı Sonlu Elemanlar modellerinin aksine, standart Lagrange yöntemler uygulama kolaylığı ve daha düşük hesaplama gücü gereksinimleri nedeniyle petrol sızıntı modellerinde yaygın olarak kullanılmaktadır. Ancak standart Lagrangian rastgele-yürüyüş yöntemlerinde parçacıklar birbirleriyle etkileşime girmez ve uzayda stokastik olarak hareket eder. Buna karşılık, Euler yaklaşımlarında süreklilik gösteren bir kalınlık dağılımını doğası gereği kendiliğinden hesaplanır. Bulgular, çözümün sonlu elemanların büyüklüğüne duyarlı olduğunu göstermiştir; büyük elemanlar sayısal difüzyon olarak adlandırılan yapay etkilere yol açarlar. Model deneysel sonuçlarla kıyaslandığında, petrolün yayılmasını başarıyla modelleyebilmiştir. Farklı hacimlerdeki (12, 120, or 1200 m³) sürekli sızıntı durumunda petrol tabakasının kalınlığı sızıntı süresince (2, 4, or 8 dk.) nispeten sabit kalmış; yayılma davranışı ve şekli sızıntı bittikten sonra ani sızıntılara oldukça benzerlik göstermiştir. Bu sonuçlar, yayılma parametrelerinin ve ara yüzey kuvvetlerinin yayılma davranışını belirlemedeki kritik rolünü ortaya koymaktadır. Sonlu elemanlar yöntemi, karmaşık sızıntı senaryoları için etkili olsa da, daha küçük ve fazla eleman gereksinimi sebebiyle hesaplama maliyetini artırmaktadır.

Anahtar Kelimeler

• Petrol sızıntı yayılımı
• petrol-su ara yüzü
• sonlu elemanlar metodu
• yerçekimi-viskoz- yüzey gerilimi kuvvetleri
• ani/sürekli sızıntılar

Modeling the fate of oil spill on quiescent water surface using the finite element method

Öz

In this study, a finite‑element model (FEM) was developed to simulate the evolution of oil spreading on calm water considering gravitational, surface‑tension, and viscous forces while ignoring externally imposed advection (wind and currents). The model solves Nihoul’s spreading equation based on mass and momentum conservation laws both for instantaneous and continuous spills considering gravity, viscous and surface tension forces. In contrast to Eulerian based Finite Element models, Lagrangian methods are widely used for oil spill models because of their ease of implementation and less computational power requirements. However, in standard Lagrangian random-walk methods particles don’t interact with each other and stochastically move in space. By contrast, Eulerian formulations evolve into a continuous thickness field and thus inherently compute the thickness distribution. The results revealed that the accuracy of the Finite Element Model is sensitive to the grid refinement, where coarse grids result in artificial numerical diffusion in the solution of slick spreading. Observed spreading patterns in experiments were successfully reproduced: uniform thickness was maintained during continuous releases, and, once the release ceased, the geometries closely resembled those from instantaneous spills, regardless of release duration (2, 4, or 8 min) or volume (12, 120, or 1200 m³). The numerical model was verified against an analytical solution for instantaneous releases and calibrated against laboratory experiment, by comparing slick radius and slick thickness as functions of time. The dominant roles of release parameters and interfacial forces were thus confirmed. While the finite element method was proven suitable for complex scenarios, computational expense was shown to increase considerably with mesh refinement.

Anahtar Kelimeler

• Oil slicks spreading
• Oil-water interface
• Finite Element Method
• Gravity-viscous-surface tension forces
• Instantaneous vs. continuous releases

Kaynakça

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