| Περίληψη: | In this study, we investigate the rheology of waxy crude oil in a porous media tube. We simplify the oil rheology, neglecting thixotropic effects, and we use Carbopol gels as prototype material since they display similar rheological behavior. The Saramito-Herschel-Bulkley (SHB) constitutive equation is used to predict the elasto-visco-plastic effects. Τhe rheology of the Carbopol solutions recent is based on recent studies of Lopez and Pourzahedi. The problem is considered in cartesian coordinates assuming axial symmetry. The governing equations are solved numerically using the open-source toolbox based on OpenFOAM, namely RheoTool is used to simulate the flows, and it’s based on finite-volume element solvers. The purpose of this study is to examine the pressure drop, that needs to set the material in motion (one phase problem) and its displacement from gas-CO2 in an undulating tube (two-phase problem).
Firsty, we examine the one-phase problem by setting a steady inlet U_x velocity and we analyze the rheology of Carbopol. We implement three different fixed inlet velocities and we investigate the elasto-viscoplastic phenomena. Then, in the two phase problem we use a two-phase simulation, using pressurized carbon dioxide (CO2) to set in motion the initially static carbopol in the tube. We implement a steady pressure in the CO2, at the inlet of the tube. We start with 300 Pa and we escalate to 450 Pa and 600 Pa in an attempt to investigate the total time that needs the air phase to displace the Carbopol solutions out of the pipe and it’s remaining percentage in the pipe. Also the rheology of the fluids and the normal and shear stresses are analyzed in the tube and around the gas/fluid interface.
In all cases, we decrease the Rmin/R¬max from 0.7 to 0.5 and finally to 0.3. Also, we plot the normal and shear stresses to investigate the visco-elastic effects and the yielded/unyielded regions to display the visco-plasticity.
With increasing velocity fields, we observe more intense visco-elastic phenomena since, the resulting pressure gradient and normal stresses are increased, while a slight deviation between the velocity streamlines takes place. Also, the decreasing Rmin/R¬max ratio leads to more intense viscoelastic effects since the actual channel geometry determines the ratio of shearing and extensional contribution.
As regards the materials, the 0.1% Carbopol solution from Pourzahedi study, is defined with higher consistency index k than the respective carbopol with 0.1% Carbopol solution from Lopez study. A higher consistency index leads to higher visco-elastic stresses and a higher pressure drop to sustain the steady inlet flow. In the gas-displaced experiment, Pourzahedi’s Carbopol is deformed much more difficult since it needs the longest time to be displaced from the CO2 gas phase.
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