| Electromagnetic methods in well are defined as two kinds of measured systems:the first one is the sources and the receivers are located in either well or ground surface; the other one is both of sources and receivers are located inside well. This kind of electromagnetic measured systems in well includes electromagnetic logging technique, cross hole, borehole to surface and surface to borehole technique. In those four measured systems, the first three measured systems are widely used in reservoir detection, metallic mineral exploration, hydrology and engineering exploration and so on, while the last measured system is new in China and no research reports are published in practical applications yet. With the presented measured systems, a good intensity of illumination to target objects would be obtained when the transmitter or the receiver are located inside well. Thus this electromagnetic measured systems in well is available for reservoir boundary monitoring, evaluating the potential of oiliness in the adjacent favorable area, monitoring the dynamic transformation of oil-water, detecting the rent oil in blind area and so on. This paper develops the fast inversion algorithms under the 3D cross hole, borehole to surface electromagnetic measured systems and 2D vertical electromagnetic profiling data via using integral equation method. The effectiveness of those fast inversion algorithms is demonstrated in some representative examples.First, a detailed analysis of the electromagnetic propagation in 3D cross hole measured systems is implemented using integral equation method. Then this 3D integral equation method is incorporated in parametric inversion using the least square inversion algorithm for reservoir monitoring. This kind of parametric inversion improves the ill-pose problem because of only the geometrical parameters and a constant conductivity of target object are considered. We also show that a high accuracy of this inversion algorithm is obtained by considering multiple components in multiple receiver wells. A logarithmic operation to measured data and predicted data is used to improve the stable convergence of this inversion algorithm. The multiplication is applied to model update, then the negative value is removed from the inverse resistivity model. It is realistic that the unknown resistivity of the background media is considered to be inverted. The analysis of forward and inversion in cross hole electromagnetic method shows the tolerance of its potential applications.Based on the least square inversion, a fast inversion algorithm for 3D complicated reservoir model with borehole to surface electromagnetic measurement is developed and formulated in detail. This fast inversion algorithm is a two sequential optimization approach:the first step is parametric inversion to determine the approximate target area for reservoir, in which the needed area for discretization in computation is small. Once the favorable target area is obtained, the computation for Green’s function related to background media is only needed to calculate one time and kept unchanged during the inversion process. With this presented inversion algorithm, the computation time and CPU requirement is reduced significantly in inversion process. Whereas the cost of the computation time and CPU requirement is expensive in conventional inversion process because of a large fix discretized area or the repeat computation of Green’s function for background media in changed discretized area is needed.The stable Bi-conjugate gradient-fast Fourier transform algorithm is applied to 2D vertical electromagnetic profiling of surface to borehole electromagnetic method modeling. This paper also formulates the dyad Green’s function in detail, which incorporates the fast Fourier transform algorithm to accelerate the computation significantly. The efficiency of this fast solver is validated with analytic solution in a representative case. Then the analysis of some multiple sources vertical electromagnetic profiling for three cases embedded in half homogeneous and layered background media is presented in this paper, which pays a good foundation for developing a fast inversion algorithm for 2D vertical electromagnetic profiling.Then this kind of Bi-conjugate gradient-fast Fourier transform algorithm is incorporated into contrast source inversion algorithm for 2D vertical electromagnetic profiling. The FFT accelerates the computation in the forward process to calculate the electromagnetic field from 2D scatter object and the matrix multiplication in the iteration process. The efficiency of the forward solver and the effectiveness of the contrast source inversion are demonstrated in some representative examples considering the half homogeneous and layered background media. Compared to those inverse results with measurement on the ground surface, the inverse results for vertical electromagnetic profiling provide more information in depth direction.The numerical case studies on the practicability of the parametric inversion algorithm for 3D cross well electromagnetic, the fast inversion algorithm for 3D borehole to surface electromagnetic and the contrast source inversion algorithm for 2D vertical electromagnetic profiling. It is observed that the different resistivities for reservoir objects in dynamic process is detected efficiently using the parametric inversion in 3D cross well electromagnetic. The parametric inversion also is capable to reconstruct the thin layered reservoir which embedded in layered media. The complex reservoir with low resistivity, which embedded in a half homogeneous medium and a layered medium, is reconstructed well using the fast inversion algorithm in 3D borehole to surface electromagnetic. The reconstructed results in VEP using CSI show the detail distribution of the true reservoir objects, especially in terms of the shape, location and conductivity for the true reservoir objects. Based on the calculated data with different noise levels, some examples are shown and demonstrated the effectiveness of the inversion algorithms in well. |
PDF Full Text Request