Study On The Algorithm Of Singular Value Decomposition For The Spectrum Of Nuclear Magnetic Resonance Logging

Nuclear Magnetic Resonance Logging (NMR) has been the most excitedtechnique in logging areas since the nineties of the twentieth century. It detectnuclear magnetic elements in formation, hydrogen as one of nuclear magneticelements with the characteristic of rich and great magnetic moment, can havethe greatest nuclear magnetic resonance signals, thereby becoming a nuclearmagnetic resonance logging observation of the object. The signal from noimpact of solid matrix, can give Parameters of porosity that has nothing to dowith the lithology, irreducible water saturation, free fluid saturation andPermeability etc. So it can overcome the limitations from traditional logs, suchas influence of borehole, lithology, as well as salinity of brine, and solved someissues from benefit reservoirs which are complex lithologies or low-resistivityreservoirs.The application of nuclear magnetic resonance logging technology is basedon the principle of nuclear magnetic resonance, it mainly through research thefluid in the rock pores of the NMR relaxation process to understanding of thereservoir rock characteristics, using the initial Amplitude of logging spin echostring to research the content of free fluid in the rock; using the relaxation timeto study the properties and location state of fluids, so it requires the transformation of NMR logging data into a spectrum Domain.Since NMR logging had begun, the research of the transformation of thespectrum has also begun. For practical project, the longitudinal relaxation timeis too long to measure, so, usually NMR only acquires the signal of 1TTtransverse relaxation time . Through the research found that the 2 Tmagnetization intensity signals of a single pore relaxation accord with thesingle index of decay. When the pore is a complex system, the total number ofrelaxation process is the summation of the single index of decay.Corresponding develop arithmetices of a simple single index fitting, doubleindex fitting, Multi-index fitting for the singular value decomposition(SVD)and non-negative least square method Etc. usually, the signal of NMR is thesummation of several single index of decay. Arithmetic of a simple single,double index of fitting can not meet the fine handling of the issue, and have noapplicability. The SVD is a multi-index fitting process, however, due to theconditions of matrix is too large, the small singular value is thrown, reducingthe original rank of matrix, with the bad continuity of the spectrum. 2 TThrough throw the optimal solution which less than zero and re-calculatedSVD of the entire process, making a very large amount of computation, verytime-consuming and less efficient; the SVD is also a multi-index fitting process,In joining the penalty item when there is a constant to the noise ratio ? andthe experience, according to experience increase uncertainty of solution.Based on NMR logging basic theory and the original algorithm of thespectrum, analyze the non-negative constraints from Vector space. Based on theSVD, use the algorithm of iteration to solve, using of a process for leastsquaresinstead of a complex matrix decomposition process, greatly improvingefficiency; cut-off the singular value with a constant signal to noise ratio andthe constant to meet that in a different signal to noise ratio condition can get astable spectrum; As the iterative process not lost weight, so it can get a better continuity of the spectrum.As a valuable tool of oil and gas evaluation in borehole, NMR still needsdeveloping and improving. It also has more potential capability waiting fordigging in its data interpretation and application area. The differences betweenthe vertical and horizontal relaxation time and Characteristics affected themeasured signal, also the density of hydrogen and the viscosity of the oil. NMRis the technique taking account well of the contrasts between the NMRcharacteristics of formation fluids and accordingly building a series ofinterpretation models for evaluation work of oil-gas reservoir under predictedcondition. Basing the contrast between formation fluids(oil, gas, and 1TTwater), the differential distribution form measure signals can indicate 2 Tpresence of oil and gas. So DSM interpretation models is built for recognizingthe presence of oil and gas, specially for the oil-gas reservoir containing lighthydrocarbon, this kind of model is very robust. Basing the diffusion contrast,when oil-filled reservoir contains varies of viscosity of oils, differentdiffusivities are showing in their signals. So SSM interpretation model is builtrely on this principle to separate viscosity oils.Using new algorithms to prepare the corresponding procedures for dealingwith the actual data, get the corresponding echo-fitting curve and thespectrum, According the formula related to NMR log interpretation calculate 2 Tporosity, bound fluid porosity, free fluid porosity and permeability of rock, andinterpret the data, compared the conclusions with the comprehensiveexplanation, the conclusion is consistent.The completion of this paper, first of all affirmed advantage of the nuclearmagnetic resonance logging in the reservoir evaluation followed by that theimportance of the whole spectrum in the course of nuclear magnetic resonancelogging; this paper also presented the general development of NMR loggingand process from the data collection, treating to explain. Finally, the data process program compiled can be used to process and interpret NMR data frompractical measurement, and for more studied work will done in the future it is avery good contribution.