Numerical Simulation Of NMR Responses And Study Of Data Inversion Method In Tight Sandstone

Nuclear magnetic resonance(NMR)logging is an important geophysical logging method for evaluating oil and gas resources,and it has been used for conventional reservoir evaluation.However,unconventional tight sandstone reservoirs have characteristics of a lot of micro-pores and complex fluid occurrence state,resulting in that the existing NMR logging theory has some problems in application of tight sandstone reservoirs,which are manifested that: restricted diffusion of pore fluid in tight sandstone reservoirs is obvious,conventional fluid identification method based on NMR map is limited;porosity of tight sandstone is low,the echo data acquired by NMR logging have a low signal to noise ratio(SNR),the inversion accuracy of the existing inversion method for the low SNR data is low.Because of difficulty NMR experiment for tight sandstone saturated two-phase fluids,this paper starts from numerical simlation of NMR responses based on tight sandstone digital core model,and explores NMR response law of tight sandstone,and studies the fluid identification methods based on NMR diffusion-relaxation maps with restricted diffusion,and develops NMR data inversion method with a high accuracy for low SNR data.Firstly,three-dimensional(3D)digital core model of the tight sandstone is constructed by the X-ray CT method and Markov Chain-Monte Carlo(MCMC)method.Because of the strong heterogeneity of tight sandstone reservoirs,we divide tight sandstone digital core into multiple sub-cores,and then choose two-dimensional(2D)image of each sub-core,and next reconstruct 3D dightal core of each sub-core based on chosen 2D image.Tight sandstone 3D digital core is obtained from superimposing reconstructed digital core of sub-cores.The comparison of tight sandstone digital core reconstructed by the X-ray CT method and by the MCMC method validates the effectiveness of the proposed reconstruction method.Subsequently,the random walk method is modified accordingly,and is used to simulate the mesurements of diffusion-editing,saturation-recovery CPMG,and diffusion-editing saturation-recovery CPMG pulse sequences based on the reconstructed 3D digital core of tight sandstone with the X-ray CT method.We study the characteristics of 2D and 3D NMR responses of tight sandstone,and explore the fluid identification based on NMR diffusion-relaxation maps with restricted diffusion.The simulation results show that restricted diffusion phenomena of the wetting fluid exists in the tight sandstone pore sapce,and the restricted diffusion coefficient line can be used for identifying wetting fluid.To improve the inversion speed of NMR data,fast sigular value decomposition(SVD)method is proposed for compressing NMR data before NMR data inversion.The proposed method reduces the dimension of the kernel matrix and then does SVD for the matrix,and it has a fast compression speed and high compression ratio,and the compression speed and accuracy are not affected by different Hadamard matrice.To develop effective and accurate NMR inversion method for a low SNR data,we constructed the different types of inversion objective function,including the objective function without regularization parameter,the objective function with L1 regularization,and the objective function with L2 regularization and maximum entropy regularization.Then we proposed a normalized iterative hard thresholding method to solve the objective function without regualrization parameter,a two-step iterative shrinkage/thresholding method to solve the L1 regularization problem,and a chosen method of the optimal regularization parameter for double-parameter regularization problem.The effectiveness of the inversion methods is validated by numerical simulation examples.