non-Newtonian Fluids In Porous Media Research Articles

A numerical method for simulating non-Newtonian fluid flow and displacement in porous media

Flow and displacement of non-Newtonian fluids in porous media occurs in many subsurface systems, related to underground natural resource recovery and storage projects, as well as environmental remediation schemes. A thorough understanding of non-Newtonian fluid flow through porous media is of fundamental importance in these engineering applications. Considerable progress has been made in our understanding of single-phase porous flow behavior of non-Newtonian fluids through many quantitative and experimental studies over the past few decades. However, very little research can be found in the literature regarding multi-phase non-Newtonian fluid flow or numerical modeling approaches for such analyses. For non-Newtonian fluid flow through porous media, the governing equations become nonlinear, even under single-phase flow conditions, because effective viscosity for the non-Newtonian fluid is a highly nonlinear function of the shear rate, or the pore velocity. The solution for such problems can in general only be obtained by numerical methods. We have developed a three-dimensional, fully implicit, integral finite difference simulator for single- and multi-phase flow of non-Newtonian fluids in porous/fractured media. The methodology, architecture and numerical scheme of the model are based on a general multi-phase, multi-component fluid and heat flow simulator — TOUGH2. Several rheological models for power-law and Bingham non-Newtonian fluids have been incorporated into the model. In addition, the model predictions on single- and multi-phase flow of the power-law and Bingham fluids have been verified against the analytical solutions available for these problems, and in all the cases the numerical simulations are in good agreement with the analytical solutions. In this presentation, we will discuss the numerical scheme used in the treatment of non-Newtonian properties, and several benchmark problems for model verification. In an effort to demonstrate the three-dimensional modeling capability of the model, a three-dimensional, two-phase flow example is also presented to examine the model results using laboratory and simulation results existing for the three-dimensional problem with Newtonian fluid flow.

Linear and nonlinear, scalar and vector transport processes in heterogeneous media: Fractals, percolation, and scaling laws

We discuss recent developments in the application of fractal concepts and percolation theory to transport processes in heterogeneous media. The phenomena that we discuss include several types of nonlinear transport processes in disordered systems, which are relevant to the flow of non-Newtonian fluids in porous media, to electrical current in composites and doped polycrystalline semiconductors, to fracture and breakdown in disordered materials and natural rock, to elastic and viscoelastic properties of solids, polymers and gels, to flow in geological formations, and to several other problems. We emphasize the universal aspects of such phenomena, i.e., those that are independent of the microscopic or small-scale features of the systems in which they occur.

Flow and displacement of Bingham Non-Newtonian fluids in porous media : Wu, Y S; Pruess, K; Witherspoon, P A SPE Reservoir EngngV7, N3, Aug 1992, P369–376

This work presents a theoretical study of the flow and displacement of a Bingham fluid in porous media. An integral method of analyzing the single-phase flow of this type of fluid is developed. The accuracy of a newly developed approximate analytical solution for transient-flow problems is confirmed by comparison with numerical solutions. The flow behavior of a slightly compressible Bingham fluid is discussed, and a new well-test-analysis method is developed by use of the integral solution. To obtain some understanding of the physics of immiscible displacement with Bingham fluids, a Buckley-Leverett analytical solution with a practical graphic evaluation method was developed and applied to the problem of displacing a Bingham fluid with water

Flow and Displacement of Bingham Non-Newtonian Fluids in Porous Media

Summary This work presents a theoretical study of the flow and displacement of a Bingham fluid in porous media. An integral method of analyzing the single-phase flow of this type of fluid is developed. The accuracy of a newly developed approximate analytical solution for transient-flow problems is confirmed by comparison with numerical solutions. The flow behavior of a slightly compressible Bingham fluid is discussed, and a new well-test-analysis method is developed by use of the integral solution. To obtain some understanding of the physics of immiscible displacement with Bingham fluids, a Buckley-Leverett analytical solution with a practical graphic evaluation method was developed and applied to the problem of displacing a Bingham fluid with water. Results revealed that the saturation profile and displacement efficiency are controlled not only by the relative permeabilities, as in the case of Newtonian fluids, but also by the inherent complexities of Bingham non-Newtonian behavior. In particular, we found that in the displacement process with a Bingham fluid, a limiting maximum saturation exists beyond which no further displacement can be achieved.

Displacement of a Newtonian fluid by a non-Newtonian fluid in a porous medium

This paper presents an analytical Buckley-Leverett-type solution for one-dimensibnal immiscible displacement of a Newtonian fluid by a non-Newtonian fluid in porous media. The non-Newtonian fluid viscosity is assumed to be a function of the flow potential gradient and the non-Newtonian phase saturation. To apply this method to field problems a practical procedure has been developed which is based on the analytical solution and is similar to the graphic technique of Welge. Our solution can be regarded as an extension of the Buckley-Leverett method to Non-Newtonian fluids. The analytical result reveals how the saturation profile and the displacement efficiency are controlled not only by the relative permeabilities, as in the Buckley-Leverett solution, but also by the inherent complexities of the non-Newtonian fluid. Two examples of the application of the solution are given. One application is the verification of a numerical model, which has been developed for simulation of flow of immiscible non-Newtonian and Newtonian fluids in porous media. Excellent agreement between the numerical and analytical results has been obtained using a power-law non-Newtonian fluid. Another application is to examine the effects of non-Newtonian behavior on immiscible displacement of a Newtonian fluid by a power-law non-Newtonian fluid.

The rheology of pseudoplastic fluids in porous media using network modeling

This paper considers the rheology of pseudoplastic (shear thinning) fluids in porous media. The central problem studied is the relationship between the viscometric behavior of the polymer solution and its observed behavior in the porous matrix. In the past, a number of macroscopic approaches have been applied, usually based on capillary bundle models of the porous medium. These simplified models have been used along with constitutive equations describing the fluid behavior (usually of power law type) to establish semiempirical macroscopic equations describing the flow of non-Newtonian fluids in porous media. This procedure has been reasonably successful in correlating experimental results on the flow of polymer solutions through both consolidated and unconsolidated porous materials. However, it does not allow an interpretation of polymer flow in porous media in terms of the flows on a microscopic scale; nor does it allow us to predict changes in macroscopic behavior resulting from variations at a microscopic level in the characteristics of the porous medium such as pore size distribution. In this work, we use a network approach to the modeling of non-Newtonian rheology, in order to understand some of the more detailed features of polymjer flow in porous media. This approach provides a mathematical bridge between the behavior of the non-Newtonian fluid in a single capillary and the macroscopic behavior as deduced from the pressure drop-flow rate relation across the whole network model. It demonstrates the importance of flow redistribution within the elements of the capillary network as the overall pressure gradient varies. As an example of a pseudoplastic fluid in a porous medium, we consider the flow of xanthan biopolymer. This polymer is important as a displacing fluid viscosifier in enhanced oil recovery applications and, for that reason, a considerable amount of experimental data has been published on the flow of xanthan solutions in various porous media.

Boundary-layer flow and heat transfer of non-Newtonian fluids in porous media

Boundary-layer flow and heat transfer of non-Newtonian fluids in porous media are explored analytically. The local Nusselt number for forced and natural convection of non-Newtonian fluids in porous media on an isothermal semi-infinite plate is obtained as a function of the rheological parameters n and Ω. The results show that these parameters have a significant effect on the heat transfer rate and flow behavior.

Well Test Analysis for Enhanced Oil Recovery Projects

Recent studies on the transient flow of non-Newtonian fluid in porous media have proposed new well test analysis techniques for non-Newtonian injection wells. This paper extends these new techniques to non-Newtonian injection well falloff testing. The practical use of this well test analysis method is demonstrated. The limitations of the techniques are also addressed. Exmaples of field data are used to demonstrate how this analysis can aid in well test interpretation and provide data and insight for the design and operation of enhanced oil recovery projects.

Transient Flow of Non-Newtonian Power-Law Fluids in Porous Media

Abstract The transient flow behavior of non-Newtonian fluids in petroleum reservoirs is studied. A new partial differential equation is derived. The diffusivity equation is a special case of the new equation. The new equation describes the flow of a slightly compressible, non-Newtonian, power-law fluid in a homogeneous porous medium. This equation should govern the flow of most non-Newtonian oil-displacement agents used in secondary and tertiary oil-recovery projects, such as polymer solutions, micellar projects, such as polymer solutions, micellar solutions, and surfactant solutions. Analytical solutions of the new partial differential equation are obtained that introduce new methods of well-test analysis for non-Newtonian fluids. An example is presented for using the new techniques to analyze injection well-test data in a polymer injection project. project. Graphs of the dimensionless pressure function also are presented. These may be used to investigate the error when using Newtonian fluid-flow equations to model the flow of non-Newtonian fluids in porous media. Introduction Non-Newtonian fluids, especially polymer solutions, microemulsions, and macroemulsions, often are injected into the reservoir in various enhanced oil-recovery processes. In addition, foams sometimes are circulated during drilling. Thermal recovery of oil by steam and air injection may lead to the flow of natural emulsions and foams through porous media. Some enhanced oil-recovery projects involving the injection of non-Newtonian fluids have been successful, but most of these projects either failed or performed below expectation. These results suggest the need for a thorough study of the stability of non-Newtonian fluids at reservoir conditions, and also a new look at the flow of non-Newtonian fluids in porous media. porous media. Many studies of the rheology of non-Newtonian fluids in porous media exist in the chemical engineering, rheology, and petroleum engineering literature. In 1969, Savins presented an important survey on the flow of non-Newtonian fluids through porous media. In some cases, he interpreted porous media. In some cases, he interpreted published data further and compared results of published data further and compared results of different investigators. van Poollen and Jargon presented a numerical study of the flow of presented a numerical study of the flow of non-Newtonian fluids in homogeneous porous media using finite-difference techniques. They considered steady-state and unsteady-state flows and used the Newtonian fluid-flow equation. They considered non-Newtonian behavior by using a viscosity that varied with position. No general method was developed for analyzing flow data. Bondor et al. presented a numerical simulation of polymer presented a numerical simulation of polymer flooding. Much useful information on polymer flow was presented, but transient flow was not considered.At present, there is no standard method in the petroleum engineering literature for analyzing petroleum engineering literature for analyzing welltest data obtained during injection of non-Newtonian fluids into petroleum reservoirs. However, injection of several non-Newtonian oil-displacement agents is an important oilfield operation. Interpretation of well-test data for these operations should also be important. Obviously, procedures developed for Newtonian fluid flow are not appropriate. SPEJ P. 164

Rheological Properties of Pseudoplastic Fluids in Porous Media

Abstract With flow of non-Newtonian fluids in porous media, effective viscosities are needed for use in the Darcy equation. These viscosities depend on the rock parameters and flowing conditions. In this investigation, rheological and flow results were correlated to develop an expression for calculating effective viscosities. Surfactant-stabilized dispersions of water in hydrocarbon were used with consolidated sandstone cores of different permeabilities. The average shear rate in a core was related to the permeability and porosity of the core and the frontal velocity through the core. By using the correlation obtained for determining effective viscosity, experimental and theoretical values were compared for each fluid system by determining average and maximum errors. For the fluid system showing the largest average error, the correlation fit 38 experimental points with an average and maximum percentage error of 4.3 and 14.8, respectively. For the fluid system showing the least error, average and maximum percentage errors of 1.8 and 4.3, respectively, were calculated using 29 experimental points. Introduction Use of non-Newtonian fluids in the petroleum industry is not new. Fluids of this type have been used for many years as fracturing agents and drilling muds. Recently, attention has focused on the use of high molecular weight polymer solutions for secondary recovery. Results have been reported on studies relating to the flow behavior of polymer solutions in porous media. Each study gives the viscosity in the Darcy equation as a function of the rheological properties of the fluid, the characteristics of the porous medium and the pressure gradient. The functional forms of the reported expressions differ somewhat in each study.