Mathematical model of dissolution of particles of NaCl in well drilling: Determination of mass transfer convective coefficient

Abstract

The drilling of salt formations generates particulate material composed of salt mixtures. In water-based muds (WBM) along the annular section, these salt mixtures tend to dissolve. The dissolution can cause changes to the drilling fluids. Its can lead to the well enlarging, to salt gravels accumulating at the bottom of the borehole, and other operational problems. The objective of this work is to study the dissolution of salt particles in brine and evaluate the mass transfer coefficient. The experimental data of the salt dissolved in brine along a flow system was obtained through an experimental apparatus consisting essentially of a mixer tank and a flow line. This study proposes a model based on the mass conservation equations for brine and solid salt particles. Samples of brine were taken along the flow system with the aim of evaluating the profiles of brine concentration versus position. The experiments were conducted for different operational conditions of brine flow and solid particles fed into the system. The experimental data were used as input for evaluating the overall coefficient of mass transfer. The system of partial differential equations (PDE׳s) was discretized in space by finite differences. The discretized model becomes a system of ordinary differential equation (ODE׳s) that can be solved using a subroutine LSODE in FORTRAN language. The hypothesis of steady state simplifies the model, allowing it to be solved analytically. The mathematical model is able to simulate the experimental data under different conditions, showing that the proposed model is capable of predicting experimental outputs under the studied range. The average deviation between the experimental values and the simulated values was less than 2.3%.