Well Log Analysis by Global Optimization-based Interval Inversion Method

Artificial intelligence methods play an important role in solving an optimization problem in well log analysis. Global optimization procedures such as genetic algorithms and simulated annealing methods offer robust and highly accurate solution to several problems in petroleum geosciences. According to experience, these methods can be used effectively in the solution of well-logging inverse problems. Traditional inversion methods are used to process the borehole geophysical data collected at a given depth point. As having barely more types of probes than unknowns in a given depth, a set of marginally over-determined inverse problems has to be solved along a borehole. This single inversion scheme represents a relatively noise-sensitive interpretation procedure. For the reduction of noise, the degree of over-determination of the inverse problem must be increased. To fulfill this requirement, the so-called interval inversion method is developed, which inverts all data from a greater depth interval jointly to estimate petrophysical parameters of hydrocarbon reservoirs to the same interval. The chapter gives a detailed description of the interval inversion problem, which is solved by a series expansion-based discretization technique. Different types of basis functions can be used in series expansion depending on the geological structure to treat much more data against unknowns. The high degree of over-determination significantly increases the accuracy of parameter estimation. The quality improvement in the accuracy of estimated model parameters often leads to a more reliable calculation of hydrocarbon reserves. The knowledge of formation boundaries is also required for reserve calculation. Well logs do contain information about layer thicknesses, which cannot be extracted by the traditional local inversion approach. The interval inversion method is applicable to derive the layer boundary coordinates and certain zone parameters involved in the interpretation problem automatically. In this chapter, it is analyzed how to apply a fully automated procedure for the determination of rock interfaces and petrophysical parameters of hydrocarbon formations. Cluster analysis of well-logging data is performed as a preliminary data processing step before inversion. The analysis of cluster number log allows the separation of formations and gives an initial estimate for layer thicknesses. In the global inversion phase, the model including petrophysical parameters and layer boundary coordinates is progressively refined to achieve an optimal solution. The very fast simulated re-annealing method ensures the best fit between the measured data and theoretical data calculated on the model. The inversion methodology is demonstrated by a hydrocarbon field example, which shows an application for shaly sand reservoirs. The theoretical part of the chapter gives a detailed mathematical formulation of the inverse problem, while the case study focuses on the practical details of its solution by using artificial intelligence tools.