Non-Newtonian flow in porous media

Abstract

The thesis investigates the flow of non-Newtonian fluids in porous media using network modeling. Non-Newtonian fluids occur in diverse natural and synthetic forms and have many important applications including in the oil industry. They show very complex time and strain dependent behavior and may have initial yield stress. Their common feature is that they do not obey the simple Newtonian relation of proportionality between stress and rate of deformation. They are generally classified into three main categories: time-independent in which strain rate solely depends on the instantaneous stress, time-dependent in which strain rate is a function of both magnitude and duration of the applied stress and viscoelastic which shows partial elastic recovery on removal of the deforming stress and usually demonstrates both time and strain dependency.The methodology followed in this investigation is pore-scale network modeling. Two three-dimensional topologically-disordered networks representing a sand pack and Berea sandstone were used. The networks are built from topologicallyequivalent three-dimensional voxel images of the pore space with the pore sizes, shapes and connectivity reflecting the real medium. Pores and throats are modeled as having triangular, square or circular cross-section by assigning a shape factor, which is the ratio of the area to the perimeter squared and is obtained from the pore space description. An iterative numerical technique is used to solve the pressure field and obtain the total volumetric flow rate and apparent viscosity. In some cases, analytical expressions for the volumetric flow rate in a single tube are derived and implemented in each throat to simulate the flow in the pore space. The time-independent category of the non-Newtonian fluids is investigated using two time-independent fluid models: Ellis and Herschel-Bulkley. Thorough comparison between the two random networks and the uniform bundle-of-tubes model i is presented. The analysis confirmed the reliability of the non-Newtonian network model used in this study. Good results are obtained, especially for the Ellis model, when comparing the network model results to experimental data sets found in the literature. The yield-stress phenomenon is also investigated and several numerical algorithms were developed and implemented to predict threshold yield pressure of the network. An extensive literature survey and investigation were carried out to understand the phenomenon of viscoelasticity and clearly identify its characteristic features, with special attention paid to flow in porous media. The extensional flow and viscosity and converging-diverging geometry were thoroughly examined as the basis of the peculiar viscoelastic behavior in porous media. The modified Bautista-Manero model, which successfully describes shear-thinning, elasticity and thixotropic timedependency, was identified as a promising candidate for modeling the flow of viscoelastic materials which also show thixotropic attributes. An algorithm that employs this model to simu...

Effective rheology of Bingham fluids in a rough channel

“…Equation (26) is the approximation used e.g., by Roux and Herrmann [17] in their study of Bingham fluids in disordered networks. Since the effective pressure threshold, Equation (27) is proportional to the real threshold, it is still given by Equation (14). This justifies the approach of Roux and Herrmann [17].…”

“…There have been a number of experimental [2,9], numerical [10][11][12][13][14][15][16] and theoretical [17,18] studies of the flow of yield stress fluids in porous media. One of the main objective is to derive an generalized Darcy equation for yield stress fluids relating mean flow rate, the pressure gradient and a critical pressure gradient.…”

Flow of non‐newtonian fluids in porous media

“…We therefore present a general background on this subject followed by a rather detailed account of one of the network models as an example. This is the model developed by Blunt and co-workers [66,67,68]. One reason for choosing this example is because it is a well developed model that incorporates the main features of network modeling in its current state.…”

Microfluidic systems for the analysis of viscoelastic fluid flow phenomena in porous media

“…The general strategy in network modeling is to use the rheology of the fluid and the void space description of the porous medium as an input to the model. The flow simulation in a network starts by modeling the flow in a single capillary and is subsequently extended to the network of capillaries, represented by a set of equations and satisfying mass conservation and momentum balance, which are solved simultaneously to find the pressure field and other relevant physical quantities (Sochi 2007). 4.…”