Numerical Modeling And Inversion Of Dual Induction Well Logging Data And Their Application In Daqing Oil Field

Dual induction logging tool (DIT) has been used in oil industry as one important logging means for several decades. The tool consists of several transmitter and receiver coils with different spacing, measures two apparent resistivities with different investigation depth simultaneously. Using the measurement, we can recognize the invasion characteristics of formation and find positions of oil and gas bed. However, the measurements become to impossibly reflect the real invasion of natural formation and the true value of formation resistivity in thin bed because of influence of shoulder beds and invasion zone invasion depth in thin reservoir or deeper invasion formation, so it will causes more difficultly to process and explain logging datum. How to deal with dual induction logging datum, eliminate the effect of shoulder bed and invasion zone on measurement result, and recover true invasion character and formation resistivity, by modern numerical process and inversion method, is an important research task in geophysical logging.Putaohua formation in eastern of Daqing is a key exploring part for a long time, where the geological conditions are complicated, transverse connectivity of reservoirs is somewhat bad, and the distribution of oil and water are irregular. Due to the thin reservoir, the excessive mud and deep invasion, the logging data is often far from the true values of formation so it leads to the evaluation of oil and water more difficult. Presently, the second process and interpretation of well logging in Daqing oil field is executed so that we can find new oil beds. Prof. Wang Hongnian, my supervisor finished the project titled as identification of oil and water layer through inversion of DIT supported by Daqing logging company. In the project, a fast inversion of software for DIT has been developed to solve the previous problems, and greatly improve evaluation of well logging data.For finishing my candidate thesis, I attended the project and finished some of the research. In this paper, I systematically summarize the main work and achievement in the project, including the fast forward algorithm, the picking out raw apparent resistivity, and new iterative inversion algorithm. The main contents are following as:In Chapter 1, I summarize and point out the present status, signification of the inversion of DIT, the main contents in this paper.In Chapter 2, we study fast forward algorithm of DIT by the mode matching method (NMM), and investigate the response character in several different environments. Simulation results indicate the resolution of DIT is usually very low in the high resistance, its apparent resistivities are still largely different from the true value of formation even in bed thicker than 8.m. Furthermore, the influence of change in mud resistivity on the response is small. In addition, the invasion zone affects the response. In the case of shallow invasion (invasion radius less than 0.7 m), the effect of the change in invasion radius on middle induction logging response is larger than that of deep induction response. However, when invasion zone becomes deeper, e.g. larger than 1m, the effects of change in invasion radius on responses of both deep and middle induction loggings are almost same.In Chapter 3, I give an approach to eliminate the skin effect correction and three-point deconvolution entirely. Apparent resistivities of DIT have been processed by skin effect correction and shoulder bed correction so the raw apparent resistivities must be recovered before inversion. An iterative method is advanced to eliminate skin effect. Compared with previous method, the new method can greatly enhance the precision of algorithm of elimination of skin effect. The numerical tests show that after 5 iterations, correction of skin effect can be completely removed. After removing of the skin effect, the inverse filter of three-point deconvolution is accurately obtained by Z-transformation theory, so that we can entirely eliminate the influence of three-point deconvolution on the deep induction logging through the 7 or 9 points of inverse numerical filter.In Chapter 4, it is first given that the relation of spatial distribution of formation conductivity to the model vector consisting of the virgin formation resistivity, flushed zone resistivity, invasion radius and horizontal boundary depth of each bed. And through differential formula, the equation of perturbation in formation conductivity with the change in model vector is derived. In addition, the fast algorithm of Fréchet derivative matrix of DIT is established on base of Born approximation and the semi-analytic expression of electromagnetic (EM) field. Then, normalization is introduced to transform the model vector and logging data into dimensionless variables. Model parameters are iteratively updated to realize best fit of field logging data with synthetic logs through singular value decomposition (SVD).Theoretically, the inversion algorithm can simultaneously reconstruct all model parameters. However, due to two logs being available only during inversion, an approximative algorithm is used to reconstruct virgin resistivity for improvement of stability of inversion results. First, resistivity in a investigation depth can be gotten through the inversion of the medium induction log (IM) only, then fixing the interface positions. Then, deep induction log (ID) is only used to reconstruct other different bed resistivities. Since IM and ID have different investigation depth, the inversion results from ID will be closer to virgin. So we can know the invasion character (high invasion or low invasion) around borehole by their relative sizes,and help to identify oil or water formation. Besides, because of ID with deep exploring depth, errors of inversion resistivity of ID from formation virgin resistivity are largely less than that of apparent resistivity of ID in either deep or shallow invasion bed, so the better estimation of formation virgin resistivity is also obtained.