NMR INVERSE PROBLEM SOLUTION

Abstract

Nuclear Magnetic Resonance (NMR) tool provides information about the porosity, permeability, free fluid index (FF1), bulk volume irreducible (By!), pore-size, fluid type and amount of fluid present in a formation. Nuclear Magnetic Resonance data represent sums or distributions of decaying exponential function. Multi-exponential response mechanism of NMR spin echo trains of dual- TW activation in reservoir filled with oil water and gas. In the inversion of multiexponential relaxation data, it is necessary to apply some form of smoothing or regularization to the computed distributions of relaxation times to get stable solutions. A common procedure is opted to minimize the sum of the squared errors of fit to which a penalty function has been added. The penalty function is often a smoothing coefficient, C, times the sum of the squares of the computed amplitudes, slops or curvatures. If the distribution has both a sharp peak and either a broad peak or a long tail, then most of the penalty is incurred by the sharp peak. For avoiding this problem we implemented variable smoothing. The same iterative procedure is used to apply the usual non-negative constraint. Our inversion algorithm is based on Tikhonov's Regularization Method and Simplex Method (linear programming).