Study On The Inversion Method Of NMR Logging Data And The Uncertainty Of T₂ Spectrum

Nuclear magnetic resonance?NMR?logging has been widely used in reservoir evaluation.The inversion of NMR data is the foundation of NMR logging interpretation application,the raw echo data gathered from NMR logging need to be inversed to obtain the NMR spectrum,which can be used to further estimate pore size distribution and identify fluid type of reservoir,as well as to provide a variety of petrophysical parameters.The inversion of NMR data is a seroius ill-posed problem,hence it is of great importance to study a stable NMR inversion method of high precision and analyze the uncertainty of NMR T₂ spectrum for reservoir evaluation.One problem confronted by NMR inversion is the huge amount of NMR logging echo data.In order to realize rapid NMR data inversion and content the demand of NMR logging data real-time processing,fast NMR data compression methods with high compression ratio are required to be developed.In this thesis,the pros and cons of traditional truncated singular value decomposition?TSVD?and window compression methods were first analyzed by path of numerical simulation thoroughly: TSVD compression method can implement high compression ratio but cost too much time,while window method avoids the time consuming problem but the compression of it is too low.Combining with the advantages of those two methods,a modified compression method called joint method was proposed: window method was preliminarily used to deduce the data redundancy,TSVD method was then implemented to realize the final compression.This method not only maintains high compression ratio but is also less time-consuming,its effectiveness was verified through compressing one-,two-and three-dimensional NMR data,the results display that this new method has great advantages especially in multi-dimensional NMR data compression.A regularization parameter selection method based on the slop of L-curve was put forward,and was compared with the deviation principle,the generalized cross validation,S-curve,and L-curve methods.The inversion result got from the deviation principle greatly depends on the noise level which is hard to be estimated accurately,in contrast,the inversion results from the other three methods are more satisfactory.Generalized cross validation and L-curve method need to compute a wide range of regularization parameters,which calls for a large amount of calculation,S-curve and L-curve slope method can rapidly search for the optimal regularization parameter through iteration,actually L-curve slope method gives a comparative inversion result but needs less computation.An innovative maximum entropy inversion method was put forward using a modified Shannon entropy function as the regularization item to suppress the highly tilted tail in the short relaxation part caused by the noise.Applied constant value and priori value respectively to the weighting coefficient p of the modified Shannon entropy function,analyzed and compared the results with different noise levels and the final results show that the inversion quality of the latter with weighting coefficient p applied priori value performs better than that of the former with weighting coefficient p applied constant value.The residual as well as the regularization item of the objective function are analyzed by attempting to realize the NMR inversion with different residual and regularization items.To be specific,l2 norm and hybrid l1/l2 norm,Tikhonov regularization and maximum entropy regularization are respectively applied to the residual item and regularization item.TSVD,Tikhonov regularization and maximum entropy methods were compared,the results show that maximum entropy method avoids the low resolution of TSVD method when the signal to noise ratio is low and improves the T₂ spectrum short relaxation peak expending to the short relaxation direction of Tikhonov regularization method.Inversion result with hybrid l1/l2 norm serving as residual item is better than that with l2 norm,hybrid l1/l2 norm is less sensitive to abnormal data points,while the inversion spectral peak of it is more focused.Adopted double parameters regularization methods to inverse NMR data with the regularization item applied Tikhonov regularization and maximum entropy regularization simultaneously.Two regularization parameters selection methods were given and by which the weights between regularization and maximum entropy regularization were adjusted,the result show that the inversion quality is between Tikhonov regularization and maximum entropy regularization method.Bayesian inference and frequentist method were used respectively to analyze the uncertainty of T₂ spectrum.Hamiltonian Monte Carlo method was adopted based on the Bayesian inference to sample the truncated multivariate normal distribution and a large amount of T₂ spectrums were obtained,then the mean and variance of T₂ spectrum,porosity and logarithmic mean of T₂ spectrum were calculated.Use prior information of T₂ spectrum as the constraint condition based on the theory of frequentist method,the upper and lower boundary of the T₂ spectrum deviation was calculated,and the deviation was further corrected accordingly,then the confidence interval was constructed using the standard deviation of the T₂ spectrum.