Viscoelastic Effects in Polymer Flow Through Porous Media

Abstract

This paper was prepared for presentation at the 47th Annual Fall Meeting of the Society of Petroleum Engineers held in San Antonio, Tex., Oct. 8–11, 1972. Permission to copy is restricted to an abstract of not more than 300 words. Illustrations may not be copied. The abstract should contain conspicuous acknowledgment of where and by who the paper is presented. Publication elsewhere after publication in the JOURNAL paper is presented. Publication elsewhere after publication in the JOURNAL OF PETROLEUM TECHNOLOGY or the SOCIETY OF PETROLEUM ENGINEERS JOURNAL is usually granted upon request to the Editor of the appropriate journal provided agreement to give proper credit is made. provided agreement to give proper credit is made. Discussion of this paper is invited. Three copies of any discussion should be sent to the Society of Petroleum Engineers office. Such discussion may be presented at the above meeting and, with the paper, may be considered for publication in one of the two SPE magazines. Introduction The oil industry has shown a great deal of interest in polymer solutions for use in recovery operations. A small amount of polymer in the injected water of flooding polymer in the injected water of flooding operations reduces the mobility of the driving phase. With the use of polymer solutions for phase. With the use of polymer solutions for recovery operations, the need has developed to understand and describe the mechanisms of non-Newtonian flow through porous media. Many investigators have studied the flow of fluids through porous media. Early investigators, such as Darcy and Kozeny, formulated equations for predicting pressure drop versus flow rate relationships for Newtonian fluids. In recent years, investigators have modified Darcy's equation to account for flow of purely viscous, non-Newtonian fluids. Some purely viscous, non-Newtonian fluids. Some workers have mentioned the effects of elasticity on flow through porous media. One rheological model has been reported where an empirical term is used to describe the effect of elasticity during flow through porous media. porous media. The present investigation shows how viscoelastic fluids behave while flowing through unconsolidated porous media. Details are given on the performance of various polymer solutions in a capillary flow device. polymer solutions in a capillary flow device. This instrument was used to determine if selected polymer solutions exhibited elastic properties. Rheological results are presented properties. Rheological results are presented for different polymer solutions. Flow results in porous media are given for these same polymer solutions. Rheological and flow results polymer solutions. Rheological and flow results are compared as a means of considering the effect of viscoelasticity on polymer solution flow through porous media. A modified form of Darcy's law is presented for use with viscoelastic liquids. SOLUTION CHARACTERIZATION Polymer solutions for this investigation were prepared as specified in Table 1. All polymers were mixed in distilled water. polymers were mixed in distilled water. Polymer was added slowly and the solution stirred Polymer was added slowly and the solution stirred gently by hand to avoid shear degradation. For the more concentrated solutions, the polymer addition period took up to one day. After polymer addition period took up to one day. After standing for a few days, solutions were filtered through a cotton cloth to remove any gelled material.

Flow of non‐newtonian fluids in porous media

“…A relaxation time term was also introduced as a correction to account for viscoelastic effects in the case of polymer solutions of high molecular weight. Gogarty et al [45] developed a modified form of the non-Newtonian Darcy equation to predict the viscous and elastic pressure drop versus flow rate relationships for the flow of elastic carboxymethylcellulose (CMC) solutions in beds of different geometry. Park et al [46,47] used the Ergun equation to correlate the pressure drop to the flow rate for a Herschel-Bulkley fluid flowing through packed beds by using an effective viscosity calculated from the Herschel-Bulkley model.…”

“…A second argument is that any geometry that involves a diameter change will generate a flow field with elongational characteristics, and hence the flow field in porous media involves both shear and elongational components with elastic responses. A third argument suggests that elastic effects are expected in the flow through porous media because of the acceleration and deceleration of the fluid in the interstices of the bed upon entering and leaving individual pores [45,46,59].…”

“…However, both explanations have a place as long as the flow regime is considered. Furthermore, the geometry of the porous media must be taken into account when considering elastic responses [38,45].…”

“…Although experimental evidence for viscoelastic effects is convincing, an equally convincing theoretical analysis is not available. One general argument is that when the fluid suffers a significant deformation in a time comparable to the relaxation time of the fluid, elastic effects become important [8,38,45,101].…”

“…The particular response in a given process depends on the time scale of the process in relation to a natural time of the material. With regard to this time scale dependency of viscoelastic flow process at pore level, the fluid relaxation time and the rate of elongation or contraction that occurs as the fluid flows through a channel or pore with varying cross sectional area should be used to characterize and quantify viscoelastic behavior [6,45,102,113]. Sadowski and Bird [9] analyzed the viscometric flow problem in a long straight circular tube and argued that in such a flow no time-dependent elastic effects are expected.…”