General Three-Dimensional Electromagnetic Model for Nondipolar Transmitters in Layered Anisotropic Media with Dip.
Wilson C.Chin.Ph.D.(strataMagnetic Software,LLC,Houston,Texas)
The general, three dimensional, electromagnetic problem in layered anisotropic media with dip is solved using a full finite difference, frequency domain solution of Maxwell's equations that does not bear the inherent limitations behind Born, geometric factor, hybrid, and linearized integral equation approaches. Several important physical capabilities are introduced. First, transmitter coils, no longer represented by point dipoles, are modeled using eight azimuthally equidistant nodes where complex currents are prescribed. The coil may reside across multiple beds, a feature useful in modeling responses from thinly laminated zones; the transmitter operates in wireline “coil alone” or Measurement While Drilling “steel collar” modes, with or without conductive mud or anisotropic invasion, and with or without borehole eccentricity. Because coil size and nearfield details are explicitly considered, accurate simulation of charge radiation from bed interfaces and Nuclear Magnetic Resonance “sensitive volume” size and orientation in layered media are both assured. Second, dipping interfaces are importantly oriented along coordinate planes, eliminating well known “numerical noise” effects associated with “staircase grids.” Transmitter and layer conforming variable meshes, which expand in the farfield to reduce computational overhead, are automatically generated by the simulator. Third, costly performance penalties incurred by anisotropic “staggered grid” formulations are avoided in the vector and scalar potential method, where all complex Helmholtz equations are solved by modern inversion algorithms that “intelligently” seek high gradient fields, “relaxing” and suppressing their numerical residuals. Fourth, rapid computing speeds, e.g., twenty seconds to two minutes on typical PCs, make the approach invaluable for array deconvolution, NMR applications,and rigsite log and geosteering analysis. The availability of a single, self consistent model, eliminates the uncertainties associated with different formulations solved by different methodologies. Benchmark studies show excellent agreement with analytical dipole solutions in uniform and layered media and with classical Biot Savart responses for finite loop coils. Suites of results are described, for responses in complicated media, with or without steel mandrels, invasion and borehole eccentricity, for a range of dip angles. Depth of penetration simulations, for electric and magnetic fields, are offered, with a view towards integrated resistivity and NMR formation evaluation. The new algorithm, which is extremely stable and robust, is highly automated and does not require user mathematical expertise or intervention. It is hosted by user friendly Windows interfaces that support approximately twenty complete simulations every hour. Fully integrated three dimensional, color graphics algorithms display electromagnetic field solutions on convergence. Receiver voltage responses are given along tool axes, together with circumferential contributions in separate plots; detailed tabulated field results are reported in both rectangular and tool oriented cylindrical coordinates. Features useful to modern logging instrument design and interpretation are available. For example, users may “reconfigure” transmitter coils to noncircular geometries; results for an elliptical cross section potentially useful in resistivity and NMR tool design are given. In addition, users may “rewire” nodal outputs in order to experiment with novel receiver and formation evaluation concepts.
【CateGory Index】： P631.81