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摘要
This paper presents a Robin boundary condition on truncated boundary (instead of infinity), and establishes an equivalued surface boundary value problem model of array lateral logging in the axisymmetric formation composing of borehole, invaded zone, surrounding rock and target zone. Robin boundary condition is more accurate than the Dirichlet boundary condition, thus the computational domain can be greatly reduced without affecting the simulation accuracy. Taking into account the linearities of differential equations and boundary conditions, we use the principle of superposition to simplify the calculation of the original boundary value problem, and overcome the difficulty of the prior uncertainty of the current on shielded electrode. Sparse storage mode based on the address matrix is proposed, which significantly reduces the memory requirements. At the same time, the physical meaning of the address matrix is clear, so it is convenient to solve finite element (FE) equation by using iteration methods. A preconditioned conjugate gradient (PCG) method is introduced to solve large sparse systems of linear equations derived from FE modeling, which greatly increases the computing speed of the logging responses. The effects of various factors on array lateral logging response, including bed thickness, bore-hole diameter, invasion zone and so on, are quantitatively investigated by the proposed method, which lays the foundation for later inversion of array lateral logging and provides some guiding significance for practical logging engineering.
- 出版日期2013-9
- 单位复旦大学
