Modelagem e simulação da sedimentação de sólidos adensantes em fluidos de perfuração

Abstract

This work has aimed to evaluate the predictive ability of simplified mathematical models to describe the dynamics of the thickening of solids in drilling fluids. In the early stages, settling experiments of barite and calcite in water-based fluids at graduated cylinders were done at initial volumetric concentrations of 6.7%, 12% and 20%, while the change of interface height was measured on the time steps. The first data modelling approach has used conservation laws, considering the relative velocity between the solid and the liquid phase as function of volumetric concentration of solids. This way, the conservation laws used to simulate these systems were based in mass conservation law and in the flux density functions. For the accuracy evaluation in the numerical data provided by conservation laws, this work has used the interface height variation through a period of time, which was determined by experiments as an auxiliary variable, to imply the prediction quality provided by the proposed model, because there was not any equipment available to determine the spatial profiles of solids concentration. Through this procedure, it was found that conservation laws was capable of predict the interface variation through a period of time with relative errors below 10%, except in regions of rapid increase of local concentration. In the second approach of modelling was used a simplified model consisting of the continuity equation and the momentum equation, considering the interaction forces between the solid and liquid phases. The simplified model describe the variation of the interface height through a period of time in several sedimentations, and the displayed results were quite satisfactory and with relative errors lower than the results showed by the conservation laws. In the final stage of this work, the simplified model was used in the simulation of time and spatial concentration profile of the barite suspended in the BR-Mul fluid, which is a real drilling fluid often used by Petrobras. The concentration profiles obtained by simulation were compared with the experimental data reported by authors from Faculty of Chemical Engineering in Federal University of Uberlandia (FEQ/UFU). In this case study, it was possible to directly compare the model output with the experimental data, and the results has showed that the relative error of the model was lower to the fluid with the highest concentration suspensions of barite, specially in the points near to the compacted zone. However, the experimental methodology used in FEQ/UFU has exhibit much imprecision in the regions of high solids concentration, because of the experimental error in the gamma ray emitter.