Estudo teórico-experimental da sedimentação em batelada: monitoramento e modelagem de perfis de concentração de sólidos e análise de equações constitutivas

Abstract

In order to ensure the control of pressures inside an oil well, high-density minerals such as barite are commonly added to drilling fluids, increasing some of their physical properties, especially density. Nonetheless, a great number of problems has been related to gravitational settling of weighting agents. Among the aforementioned problems, this study focused on obtaining information pertinent to a mitigation strategy of the phenomenon known as APB (Annular Pressure Build-up). This strategy consists of communicating the drilling fluid contained in the annular with the rock formation, but it might be compromised if the weighting particles of the fluid settle to the point of obstructing the fluid-rock communication window. Thus, the present work aimed to investigate the sedimentation process of weighting agents, specifically barite, through theoretical and experimental techniques. The experimental investigation of this phenomenon was based on the use of electrical conductivity as a technique for monitoring the concentration of solids over time and in different positions of the experimental apparatus designed for the study of sedimentation. Since barite particles are nonconducting materials, as the separation between the continuous and the dispersed phases occurs, the conductivity of the medium undergoes changes. This is the basic principle of the technique. In the experimental tests, aqueous suspensions of barite were used in three different concentrations for the purpose of evaluating the initial solids content on the settling behavior of particulate materials. Furthermore, to assist in the physical description of the process, analyses of particle size distribution along the sediment were performed. In terms of modeling, experimental data of dynamic profiles of solids concentration in a synthetic drilling fluid served as the basis for the mathematical representation of settling of weighting agents. Following the standard approach of continuum mechanics, the proposed model was obtained by the conservation laws of mass and linear momentum for the solid phase. Moreover, the material properties of the solid and liquid constituents of the mixture were considered by specific assumptions, which were introduced into the model by constitutive equations. It is also worth noting that the batch sedimentation model proposed herein takes into account the compressibility of solids due to the accumulated weight of particles, as well as the permeability of the sediment. Since there is no analytical solution for the model, numerical techniques had to be employed. The spatial variable of the equations was discretized by the finite volume method. The resulting set of ordinary differential equations was then numerically integrated in the dimensionless temporal variable. Finally, the parameters of the constitutive equations for pressure on solids and permeability of the porous matrix were determined from a rigorous estimation procedure, and statistically analyzed. In particular, the results obtained in this work indicated a good agreement between model predictions and experimental data