Modelagem matemática de fenômenos transitórios em fluidos não newtonianos

Abstract

In the current work a mathematical model is presented in order to predict pressure propagation in transient compressible non-Newtonian flow problems. The physical problems dealt are: i) fluid hammer problem; ii) pressure transmission in well drilling fluids and; iii) flow start-up of waxy crude oils in pipelines. The flow is considered one-dimensional, weakly compressible and isothermal. The model is based on the mass balance and momentum balance equations that are solved iteratively by the method of characteristics. The fluid compressibility is considered by employing a equation of state that correlates fluid density and pressure. Two constitutive models were used to represent the fluid behavior: viscoplastic and thixotropic. The shear stress distribution across the pipeline section is considered linear in the radial direction so that the friction factor approach is used for the viscoplastic fluid and the velocity profile is integrated across the pipeline section for the thixotropic fluid. These models were presented into three publications: “Mathematical model for viscoplastic fluid hammer”; “Modeling and validation of pressure propagation in drilling fluids pumped into a closed well” and; “The effect of compressibility on flow start-up of waxy crude oils”. The main conclusions are: i) pressure is not fully transmitted in viscoplastic fluids; ii) pressure propagation depends on pipeline boundary condition and; gel breaking of thixotropic fluids depends on the ratio of the pressure wave propagation time and the breaking characteristic time.