Development of a Mathematical Model to Predict Sedimentation Rates for at least 24h

Abstract

In this project it was developed a mathematical model to predict sedimentation rates of suspended soil for a period of 24h. The final goal is the development of a mathematical model considering different polymers and concentrations (between 0 and 1 g.L-1) in aqueous medium with a pH between 5 and 12,5, using different soil types (clay, sand and a mixture of clay and sand) at concentration ranging from 25 to 200 g.L-1. The first step consisted in performing a series of laboratorial experiments gradually combining the goal variables. In these experiments, values of initial and final density were measured, as well as Brookfield and Marsh viscosity, electrical conductivity and pH. After collecting these data, it was organised in a data base to be introduced in the R software. With the R software a set of equations, combining the study variables, were built in function of initial and final density. Sedimentation rate was later calculated through the difference between initial and final density. The model obtained was validated once it achieved an average sedimentation rate error ≤15%. Once a set of equations (for initial and for final density) considering certain goal variables were validated, another variable was introduced into the model until it considers all the conditions set in the goal. At the end, it was achieved a mathematical model composed of two equations, one in function of initial density and the other in function of final density. Through these equations it is possible to predict sedimentation rates for a 24h period, considering polymer concentration (between 0 and 1 g.L-1), pH (between 5 and 12,5), clay concentration (between 25 and 200 g.L-1), and polymers with different anionic percentages (between 0 and 100%) and molecular weight (between 5 and 40 MDa). To achieve this, the fixed variables were soil type (clay), volume of deionized water (4L), bucket diameter (280 mm) and mixing time (150 min). The final model presented an average error for sedimentation rate of 18%, with a standard deviation of 15%.