Rheological Properties of Pseudoplastic Fluids in Porous Media

1967 ◽  
Vol 7 (02) ◽  
pp. 149-160 ◽  
Author(s):  
W.B. Gogarty
Keyword(s):  
Porous Media ◽  
Rheological Properties ◽  
Polymer Solutions ◽  
Newtonian Fluids ◽  
Fluid System ◽  
High Molecular Weight Polymer ◽  
Molecular Weight Polymer ◽  
Maximum Percentage ◽  
The Core ◽  
Darcy Equation

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.

Polymer Solution Flow in Porous Media

1970 ◽  
Vol 10 (02) ◽  
pp. 111-118 ◽  
Author(s):  
A. Herbert Harvey ◽  
D.E. Menzie
Keyword(s):  
Porous Media ◽  
Polymer Solution ◽  
Oil Recovery ◽  
Polymer Solutions ◽  
Flow In Porous Media ◽  
High Molecular Weight Polymer ◽  
Molecular Weight Polymer ◽  
Rate Dependent ◽  
Polymer Flood ◽  
Prediction Techniques

Abstract A method is described for the analysis of rate-dependent effects in the flow of polymer solutions through unconsolidated porous media. Experimental data are presented for solutions of polyacrylamide, polyethylene oxide, and polyacrylamide, polyethylene oxide, and polysaccharide. polysaccharide Introduction A major obstacle to wider use of polymer flooding seems to be the lack of a satisfactory method for predicting the performance of this oil recovery predicting the performance of this oil recovery process. Although it is frequently possible to process. Although it is frequently possible to predict that a polymer flood would recover more oil predict that a polymer flood would recover more oil from a reservoir than could be produced with a waterflood, it is difficult to make a realistic economic comparison of the two processes. Waterflood prediction techniques which consider areal sweep and reservoir stratification have been used to evaluate the effect of improved mobility ratio on oil recovery. If accurate relative permeability data are available and if stratigraphic permeability data are available and if stratigraphic variations in the reservoir are known, then these prediction techniques may lead to a rough prediction techniques may lead to a rough approximation of the performance of a polymer flood. However, such prediction techniques fail to consider that the apparent flow resistance to a polymer solution depends on flow velocity as well polymer solution depends on flow velocity as well as permeability. These rate-dependent effects may be significant in a pattern flood, since fluid velocity is not constant. They may also be significant in a heterogeneous reservoir. Under favorable conditions some rate-dependent fluids will tend to even out the flood front in a stratified reservoir and thereby increase oil recovery. This effect cannot be anticipated with conventional waterflood prediction techniques. The basis for much of the difficulty in predicting the performance of a polymer flood is a lack of understanding of the behavior of high molecular weight polymer solutions flowing through porous materials. Until we are able to predict how these solutions will flow through a simple system such as a glass bead pack, it seems unlikely that we will be able to develop a realistic mathematical model to describe the much more complex problem of flow in an oil reservoir. It is the purpose of this study to develop a method for investigating the flow of these high molecular weight polymer solutions through unconsolidated porous media and to study the rheologic properties of solutions of certain polymers which, are of interest from the standpoint of possible application to polymer flooding. EQUATIONS DESCRIBING NON-NEWTONIAN FLOW IN POROUS MEDIA In analogy to the Blake-Kozeny equation for Newtonian fluids, equations have been developed to describe the flow of certain non-Newtonian fluids through porous media. These relationships are based on the assumptions that the fluid behavior may be approximated by the "power law" (Ostwaldde Waele flow model) and that the hydraulic radius concept is applicable to the porous media. If we write the power (1) lawmr  =  m y , and let N = Reynolds number for porous mediaRe f* = friction factor for porous media W = mass velocity dp = particle diameter of porous media 0 = porosity p = fluid density, the relationships may be written (2)L 2 1-0W d 3* pd pf  = (3)NRE * 1f  =  ----- , SPEJ P. 111

Inaccessible Pore Volume in Polymer Flooding

1972 ◽  
Vol 12 (05) ◽  
pp. 448-452 ◽  
Author(s):  
Rapier Dawson ◽  
Ronald B. Lantz
Keyword(s):  
Porous Media ◽  
Mathematical Models ◽  
Pore Volume ◽  
Polymer Solutions ◽  
Polymer Flooding ◽  
Reservoir Rock ◽  
Front Edge ◽  
Polymer Molecules ◽  
The Core ◽  
Inaccessible Pore Volume

Abstract We have found that solutions of typical waterflooding polymers do not occupy all of the connected pore volume in porous media. The remainder of the pore volume is inaccessible to polymer. This inaccessible pore volume is occupied polymer. This inaccessible pore volume is occupied by water that contains no polymer, but is otherwise in equilibrium with the polymer solution. This allows changes in polymer concentration to be propagated through porous media more rapidly than propagated through porous media more rapidly than similar changes in salt concentration. At the front edge of a polymer bank the effect of inaccessible pore volume opposes the effect of adsorption and pore volume opposes the effect of adsorption and may completely remove it in some cases. This paper presents three experimental polymer floods showing the effect of inaccessible pore volume in the presence of varying amounts of adsorption. Results of these floods clearly show that about 30 percent of the connected pore volume in the rock samples used was not accessible to The polymer solutions. The changes required to include polymer solutions. The changes required to include inaccessible pore volume in mathematical models of polymer flow and in held prediction methods are discussed. Introduction One way o improving the mobility ratio during waterflooding operations is by addition of a water-soluble polymer to the flood water. Several different polymers have been proposed and a number of investigators have presented results on the behavior of these polymer solutions in porous media. In addition, mathematical models have been developed for predicting the field behavior of polymer flooding. In all these studies movement polymer flooding. In all these studies movement of the polymer bank through the reservoir rock is of great importance. One phenomenon that has been repeatedly observed in polymer flooding is the removal of polymer from solution by adsorption on the reservoir rock. As a polymer bank propagates through porous media, the polymer bank propagates through porous media, the front edge is gradually denuded of polymer. The amount of polymer lost from a bank may be large or small, depending on the nature of the polymer and rock surface. This loss of polymer must be measured and included in any realistic mathematical model of polymer behavior. It has been widely assumed that polymer behavior. It has been widely assumed that adsorption is the most significant factor causing polymer to propagate through porous media at a polymer to propagate through porous media at a velocity different from that of water. In this paper we present data that demonstrate that all of the pores may not be accessible to polymer molecules and that this "inaccessible polymer molecules and that this "inaccessible pore volume" can affect polymer propagation pore volume" can affect polymer propagation significantly. In addition to the experimental results, we discuss the changes in interpretation and in mathematical models that are required to include this phenomenon. EXPERIMENTAL The experiments described in this paper were single-phase displacement of polymer solutions through consolidated sandstone. All the cores were prepared by evacuating and saturating with brine; prepared by evacuating and saturating with brine; the pore volumes of the cores were measured at this time. The experimental floods reported here were then done in three steps.An "initial solution" was injected until the core was at complete equilibrium with that solution.A bank of a different solution was injected into the core.Injection of the initial solution was resumed and continued until the end of the experiment. During each experiment the effluent from the core was collected in small samples; the analyses of these samples for polymer and salt content gave the basic data which is presented here. In plotting the results we used a "concentration fraction" defined as (Ce -Ci)/(Cb -Ci), where C is concentration and the subscripts e, i and b refer to the effluent, initial inlet and bank inlet values, respectively. All the solutions used were mixed in distilled water; concentrations are given in weight percent or in ppm by weight. Two polymers were used; one was a polyacrylamide (Pusher 700, The Dow Chemical Co.); the other a polysaccharide (XC biopolymer, Xanco, Div. of Kelco Co.). SPEJ P. 448

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

1979 ◽  
Vol 19 (03) ◽  
pp. 164-174 ◽  
Author(s):  
Chi U. Ikoku ◽  
Henry J. Ramey
Keyword(s):  
Porous Media ◽  
Fluid Flow ◽  
Newtonian Fluid ◽  
Oil Recovery ◽  
Transient Flow ◽  
Polymer Solutions ◽  
Newtonian Fluids ◽  
Petroleum Engineering ◽  
Published Data ◽  
Well Test

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

Experimental Study on Flow-Front Fingering Instabilities in Injection Molding of Polymer Solutions and Melts

2004 ◽  
Author(s):  
Kalonji K. Kabanemi ◽  
Jean-Franc¸ois He´tu ◽  
Samira H. Sammoun
Keyword(s):  
Molecular Weight ◽  
High Molecular Weight ◽  
Polymer Solutions ◽  
Low Molecular Weight ◽  
Flow Front ◽  
High Molecular Weight Polymer ◽  
Molecular Weight Polymer ◽  
Polymer Molecules ◽  
Molecular Weights ◽  
Solvent Molecules

An experimental investigation of the flow behavior of dilute, semi-dilute and concentrated polymer solutions has been carried out to gain a better understanding of the underlying mechanisms leading to the occurrence of instabilities at the advancing flow front during the filling of a mold cavity. Experiments were performed using various mass concentrations of low and high molecular weight polyacrylamide polymers in corn syrup and water. This paper reports a new type of elastic fingering instabilities at the advancing flow front that has been observed only in semi-dilute polymer solutions of high molecular weight polymers. These flow front elastic instabilities seem to arise as a result of a mixture of widely separated high molecular weight polymer molecules and low molecular weight solvent molecules, which gives rise to a largely non-uniform polydisperse solution, with respect to all the kinds of molecules in the resulting mixture (solvent molecules and polymer molecules). The occurrence of these instabilities appears to be independent of the injection flow rate and the cavity thickness. Moreover, these instabilities do not manifest themselves in dilute or concentrated regimes, where respectively, polymer molecules and solvent molecules are minor perturbation of the resulting solution. In those regimes, smooth flow fronts are confirmed from our experiments. Based on these findings, the experimental investigations have been extended to polymer melts. Different mixtures of polycarbonate melts of widely separated molecular weights (low and high molecular weights) were first prepared. The effect of the large polydispersity of the resulting mixtures on the flow front behavior was subsequently studied. The same instabilities at the flow front were observed only in the experiments where a very small amount of high molecular weight polycarbonate polymer has been mixed to a low molecular weight polycarbonate melt (oligomers).

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