The radial basis function （RBF） interpolation approach proposed by Freedman is used to solve inverse problems encountered in well-logging and other petrophysical issues. The approach is to predict petrophysical prop...The radial basis function （RBF） interpolation approach proposed by Freedman is used to solve inverse problems encountered in well-logging and other petrophysical issues. The approach is to predict petrophysical properties in the laboratory on the basis of physical rock datasets, which include the formation factor, viscosity, permeability, and molecular composition. However, this approach does not consider the effect of spatial distribution of the calibration data on the interpolation result. This study proposes a new RBF interpolation approach based on the Freedman＇s RBF interpolation approach, by which the unit basis functions are uniformly populated in the space domain. The inverse results of the two approaches are comparatively analyzed by using our datasets. We determine that although the interpolation effects of the two approaches are equivalent, the new approach is more flexible and beneficial for reducing the number of basis functions when the database is large, resulting in simplification of the interpolation function expression. However, the predicted results of the central data are not sufficiently satisfied when the data clusters are far apart.展开更多
One-dimensional nuclear magnetic resonance （1D NMR） logging technology is limited for fluid typing, while two-dimensional nuclear magnetic resonance （2D NMR） logging can provide more parameters including longitudi...One-dimensional nuclear magnetic resonance （1D NMR） logging technology is limited for fluid typing, while two-dimensional nuclear magnetic resonance （2D NMR） logging can provide more parameters including longitudinal relaxation time （71） and transverse relaxation time （T2） relative to fluid types in porous media. Based on the 2D NMR relaxation mechanism in a gradient magnetic field, echo train simulation and 2D NMR inversion are discussed in detail. For 2D NMR inversion, a hybrid inversion method is proposed based on the damping least squares method （LSQR） and an improved truncated singular value decomposition （TSVD） algorithm. A series of spin echoes are first simulated with multiple waiting times （Tws） in a gradient magnetic field for given fluid models and these synthesized echo trains are inverted by the hybrid method. The inversion results are consistent with given models. Moreover, the numerical simulation of various fluid models such as the gas-water, light oil-water, and vicious oil-water models were carried out with different echo spacings （TEs） and Tws by this hybrid method. Finally, the influences of different signal-to-noise ratios （SNRs） on inversion results in various fluid models are studied. The numerical simulations show that the hybrid method and optimized observation parameters are applicable to fluid typing of gas-water and oil-water models.展开更多
The microscopic response characteristics of nuclear magnetic resonance(NMR) are widely used for characterizing complex pore structures of rocks. Due to the prohibitive NMR experiment cost, numerical simulation was emp...The microscopic response characteristics of nuclear magnetic resonance(NMR) are widely used for characterizing complex pore structures of rocks. Due to the prohibitive NMR experiment cost, numerical simulation was employed as an alternative approach to verify some theoretical aspects of NMR responses. Firstly, the basic principles of pore-scale NMR simulation based on random-walk method(RWM) were introduced. The RWM-simulated results were benchmarked with the analytical results for an ideal spherical pore model. Then, the effects of two numerical parameters, namely diffusion radius and walk numbers, were studied on the simulation accuracy. The simulation method is then applied to various pore models with different pore sizes and pore shapes filled with different fluids to study the microscopic NMR response characteristics. The numerical experiments are useful for understanding and interpreting NMR measurements and the simulation code provides a numerical tool to perform pixel-based digital rock analysis.展开更多
基金supported by the National Science and Technology Major Projects(No.2011ZX05020-008)Well Logging Advanced Technique and Application Basis Research Project of Petrochina Company(No.2011A-3901)
文摘The radial basis function （RBF） interpolation approach proposed by Freedman is used to solve inverse problems encountered in well-logging and other petrophysical issues. The approach is to predict petrophysical properties in the laboratory on the basis of physical rock datasets, which include the formation factor, viscosity, permeability, and molecular composition. However, this approach does not consider the effect of spatial distribution of the calibration data on the interpolation result. This study proposes a new RBF interpolation approach based on the Freedman＇s RBF interpolation approach, by which the unit basis functions are uniformly populated in the space domain. The inverse results of the two approaches are comparatively analyzed by using our datasets. We determine that although the interpolation effects of the two approaches are equivalent, the new approach is more flexible and beneficial for reducing the number of basis functions when the database is large, resulting in simplification of the interpolation function expression. However, the predicted results of the central data are not sufficiently satisfied when the data clusters are far apart.
基金sponsored by the National Natural Science Foundation of China(41172130)the Fundamental Research Funds for the Central Universities(2-9-2012-48)+1 种基金the National Major Projects(No.2011ZX05014-001)CNPC Innovation Foundation(No.2011D-5006-0305)
文摘One-dimensional nuclear magnetic resonance （1D NMR） logging technology is limited for fluid typing, while two-dimensional nuclear magnetic resonance （2D NMR） logging can provide more parameters including longitudinal relaxation time （71） and transverse relaxation time （T2） relative to fluid types in porous media. Based on the 2D NMR relaxation mechanism in a gradient magnetic field, echo train simulation and 2D NMR inversion are discussed in detail. For 2D NMR inversion, a hybrid inversion method is proposed based on the damping least squares method （LSQR） and an improved truncated singular value decomposition （TSVD） algorithm. A series of spin echoes are first simulated with multiple waiting times （Tws） in a gradient magnetic field for given fluid models and these synthesized echo trains are inverted by the hybrid method. The inversion results are consistent with given models. Moreover, the numerical simulation of various fluid models such as the gas-water, light oil-water, and vicious oil-water models were carried out with different echo spacings （TEs） and Tws by this hybrid method. Finally, the influences of different signal-to-noise ratios （SNRs） on inversion results in various fluid models are studied. The numerical simulations show that the hybrid method and optimized observation parameters are applicable to fluid typing of gas-water and oil-water models.
基金Project(265201248) supported by the Fundamental Research Funds for the Central Universities,ChinaProject(41172130) supported by the National Natural Science Foundation of China+2 种基金Project(2011ZX05014-001) supported by the Major State S&T Special Fund,ChinaProject(201205002) supported by the China Scholarship CouncilProject(2011D-5006-0305) supported by the China National Petroleum Co.Innovation Foundation,China
文摘The microscopic response characteristics of nuclear magnetic resonance(NMR) are widely used for characterizing complex pore structures of rocks. Due to the prohibitive NMR experiment cost, numerical simulation was employed as an alternative approach to verify some theoretical aspects of NMR responses. Firstly, the basic principles of pore-scale NMR simulation based on random-walk method(RWM) were introduced. The RWM-simulated results were benchmarked with the analytical results for an ideal spherical pore model. Then, the effects of two numerical parameters, namely diffusion radius and walk numbers, were studied on the simulation accuracy. The simulation method is then applied to various pore models with different pore sizes and pore shapes filled with different fluids to study the microscopic NMR response characteristics. The numerical experiments are useful for understanding and interpreting NMR measurements and the simulation code provides a numerical tool to perform pixel-based digital rock analysis.
