Proportional integral derivative controller used to simulate the mineral concentration and fluid saturations from geological data and well logs in the Namorado reservoir, Southeastern Brazil

Abstract

This study aimed to simulate the influence of lithology on geophysical well logs, using, as a starting point, the mineralogical composition of the geological formations. The mineral content and fluid saturation were, inversely, estimated from the logs. The equations, to calculate the responses of the gamma ray, resistivity, density, neutron, and sonic logs, were consulted in the bibliography and analyzed, as well as the porosity ones. A code was developed, hereafter, which implemented these equations in a forward modelling approach. The properties of each mineral, i.e., density, radioactivity, and delay time, were considered, which are part of each sedimentary layer. To check the proper functioning of this code, these theoretical results were compared with published models and then considered as true or target model. To infer the mineralogy from logs, the Proportional Integral Derivative Controller algorithm was used as an inverse approach. In this method, gamma ray, density, neutron, and delay time logs of the Namorado Oilfield in Campos Basin - Southeastern Brazil were used to construct a model considered as an initial attempt in the inverse modelling. The performance of the approach was verified in some layers, noting that the volume of formation water increased, as well as the concentrations of quartz, calcite, and biotite. The volumes of dolomite, anhydrite, gypsum, illite, chlorite and others, on the other hand, decreased significantly, from the initial attempt to the target data. Thus, the inverse approach was useful at this stage with simple models, showing good prospects for more complex log models in the future.