The identification and description of lithological parameters of a formation are essential in the evaluation of complex formations. Based on this, the combination of the nuclear tool response in uncased wells has been used systematically. The resultant logs can be considered as the interaction between two distinct phases: • The radiation transport phase from a source to one or more detectors through the formation. • The detection phase that consists of the collection of radiation, its transformation into current pulses, and the spectral distribuition of these pulses. As the presence of the detector does not strongly affect the radiation transport result, each phase can be simulated independent of the other, which allows us to introduce a new type of model in which the transport phase and the detection phase are uncoupled. In this work, the final response is simulated combining transport numerical solutions with a library of the detector responses to different incident energies and for each specific source - detector array. The radiation is calculated by the Finite Elements Method (FEM), as a 2½-D scalar flux derived from the numerical solution of the multigroup diffusion approximation of the Boltzmann transport equation in phase space. This is known as P1 approximation, where the variable direction is expanded in terms of the Legendre orthogonal polymonials, leading to the dimensionality reduction of the problem in such a way as to let it be more consistent with the FEM, where the flux depends only on the spatial variable and the physical properties of the formation. The NaI(Tl) response function is obtained separately by the Monte Carlo method (MC) where the life of a particle within the scintillator crystal is reconstructed simulating interaction by interaction the position, direction and energy of the different particles using a random number technique with associated appropriate probabilities laws. Each type of interaction (e.g., Rayleigh, Photo-electric, Compton and Pair production) is determined similarly and the simulation is concluded when the detector response functions are convolved with the scalar flux. The final response is the pulse-height spectrum of the simulated system. From this spectrum, a set of channels called detection windows are then selected. The count rates in each window show different dependencies on density and lithology. This fact allows one to use a combination of these windows in determining the density and photoelectric absorption factor of the formation. According to the method developed in this work, the logs in both thin and thick layers can be simulated. The performance of the method has been tested in complex formations, mainly where the presence of clay minerals, feldspars and micas have produced considerable effects sufficient to perturb the final response of the sonde. The results show that it is possible to identify physical and lithological parameters in formations having densities between 1.8 and 4.0 g/cm3 and photoelectric absorption factors in the interval of 1.5 to 5.0 barns/e-. The concentrations of Potassium, Uranium and Thorium can be obtained through the introduction of a new system of calibration which corrects the effects due to high variances and negative correlations observed on the mass concentration of Uranium and Potassium. In the simulation of the CNL response using the Tittle polynomial regression algorithm, it is verified that due to the limited vertical resolution of this sonde, the porosity value is poorly measured for most layers of thickness less than the source - far detector spacing, thus it has application only in thick layers. A new method was developed to solve this problem; the contribution of the relative area of each layer within the maximum information zone is determined. Thus, this neutron porosity makes possible an in-depth evaluation of expected CNL porosity-lithology response, convolving that area factor with the local formation porosity index, considering only thick layers. The presence of perturbating minerals is solved by considering the formation as formed by a predominant base matrix mineral, totally saturated by fresh water; the rest of the components are then considered as a perturbation of this base case. These results enable the calculation of synthetic well logs that can be used in inversion schemes in order to get a more detailed quantitative evaluation of complex formations.
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