LINEAR VS. NONLINEAR POROSITY ESTIMATION OF NMR OIL RESERVOIR DATA

Nuclear Magnetic Resonance (NMR) is widely used to assess oil reservoir properties especially those that can not be evaluated using conventional techniques. In this regard, porosity determination and the related estimation of the oil present play a very important role in assessing the economic value of the oil wells. Nuclear magnetic resonance data is usually fit to the sum of decaying exponentials. The resulting distribution; i.e. T2 distribution; is directly related to porosity determination. In this work, three reservoir core samples (Tight Sandstone and two Carbonate samples) were analyzed. Linear Least Square method (LLS); using reguiarization parameter (or) to smoothen the solution; and non-linear iterative least square fitting; using Levcnberg- Marquardt method; were applied to calculate the Tt distribution and the resulting incremental porosity. The linear solution was used as the initial guess for the iterative nonlinear solution.Linear modeling is usually used to extract T2 information from NMR logging data in real time. In experimental NMR logging, the goal is how to get the best inversion of the data into T2 distribution regardless of the time of analysis. In terms of porosity, linear modeling assumes that the pore sizes are pre-selected while nonlinear modeling, starting from a properly chosen initial value, predicts pore sizes in an iterative way to properly predict real pore size values. Thus, it is more favorable to use nonlinear models over linear models. However, the order of magnitude of time needed for the linear solution is in the range of few minutes while it is in the range of few hours for the nonlinear solution.Abou Mandour et al.Parametric analysis for the linear vs. nonlinear methods was performed to evaluate the impact of number of exponentials, and effect of the reguiarization parameter on the smoothing of the linear solution. Effect of the type of solution on porosity determination was carried out. Twelve exponentials were used for both the linear and nonlinear solutions. It was shown that the linear solution begins to be smooth at a = 0.5 which corresponds to the commonly used industry value. Regardless of the fact that small differences exist between the linear and nonlinear solutions for the three samples, these small values make an appreciable difference in porosity. The nonlinear solution predicts 12% less porosity for the tight sandstone sample and 4.5 % and 13 % more porosity in the two carbonate samples respectively.