In this paper, we advance an efficient algorithm to compute the responses of multicomponent induction logging (MCIL) tool in deviated and layered anisotropic formations through a numerical mode matching method (NMM). First, the three mutually orthogonal magnetic dipoles located at the borehole axis are represented as the sum of three harmonic components about the dipole angle θ so that the electromagnetic (EM) fields produced by the dipoles can be transformed into three axisymmetric problems. And new boundary conditions satisfied by every EM harmonic component at borehole axis are given to assure the EM field near the borehole axis can still be calculated. Then NMM is used to solve the three axisymmetric problems and obtain a semianalytic expression of a dyadic Green function by magnetic current source in the formation. Furthermore, the formula to compute the MCIL response is given. The numerical tests are carried out to validate the algorithm and investigate the characteristics of MCIL response in several different cases.

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S U M M A R YPermeability is a key parameter associated with the subsurface production and injection. This paper introduces a new method which uses the complex resistivity of rock to estimate permeability in petroleum reservoirs.Complex resistivity measurements were carried out on 53 shaly sand samples from Daqing Oil Filed with a wide variation in permeability and porosity in the frequency range from 100 Hz to 20 MHz using a four-electrode technique. This paper investigates the relationship between the complex resistivity measurements and the permeabilities of the samples. The imaginary part of the complex impedance shows a power-law relation to the frequency ranges from 100 Hz to 1.5 kHz. The results show that permeability can be estimated well with expressions of the form of A · φ B · β C , where β is the slope of the bilogarthmic plot of the imaginary part versus frequency, φ is the porosity, A, B and C are constants. The salinity of NaCl has little influence of the slope in the range of 1-10 g l −1 .The isovalue maps of the error factor δ, which show substantial regions of near-minimum values of δ, are used to analyse the behaviour of δ with the change of the exponents B and C. The permeability estimation is more sensitive to the changes of the slopes than the porosity. The slope and the porosity are not completely independent. The slope is the decisive parameter for the estimation of the permeability. The additional use of the porosity improves the formula fit to the data significantly.

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In this paper, we advance a fast approximative iterative inversion technique (FAIIT) of dual induction tool (DIT) logs. First, we establish the fast algorithm of Fréchet derivatives of DIT logs with respect to bed interfaces and formation resistivities simultaneously, and give the process of the iterative inversion by use of normalization and singular value decomposition (SVD). The initial model parameters including interface and resistivities per bed must be extracted by comprehensively blocking of DIT logs for realization of the inversion of both synthetic and field logs. After the initial model is obtained, the bed resistivity and interface per bed are iteratively revised through the inversion of the medium induction log (IM) only. Then, deep induction log (ID) is only used to reconstruct other bed resistivities. Due to the difference of ID and IM at exploring depth, the former can obviously give shallower resistivities at exploring depth than the later. The inversion results of both synthetic and field logs clearly prove that the inversion results from ID and IM respectively can demonstrate the exact characteristics of formation invasion. Besides, because of ID with deeper exploring depth, inversion results of ID are largely closer to formation virgin resistivities than apparent resistivity of ID in beds of either deep or shallow invasion, so the better estimation of formation virgin resistivity is also obtained.