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The flow of solutions of poly(ethylene oxide) (PEO), hydrolyzed polyacrylamide (HPAA), and their blends through opposed jets is investigated. Measurements of pressure drop across the jets as a function of strain rate were used to characterize the elongational flow behavior. In deionized water, solutions of PEO/HPAA mixtures exhibit a synergistic increase in flow resistance with respect to the parent polymer solutions. The addition of amounts of HPAA as low as 2 ppm to a 500 ppm PEO solution cause sizeable increases in pressure drops. Such increases have been interpreted as arising from the formation of interpolymer transient entanglement networks that become mechanically active at time scales equivalent to the lowest strain rates available. In the case of excess salt environment, the flow resistance of the mixtures seems to be dominated by the PEO in the concentration range explored.
The flow of solutions of poly(ethylene oxide) (PEO), hydrolyzed polyacrylamide (HPAA), and their blends through opposed jets is investigated. Measurements of pressure drop across the jets as a function of strain rate were used to characterize the elongational flow behavior. In deionized water, solutions of PEO/HPAA mixtures exhibit a synergistic increase in flow resistance with respect to the parent polymer solutions. The addition of amounts of HPAA as low as 2 ppm to a 500 ppm PEO solution cause sizeable increases in pressure drops. Such increases have been interpreted as arising from the formation of interpolymer transient entanglement networks that become mechanically active at time scales equivalent to the lowest strain rates available. In the case of excess salt environment, the flow resistance of the mixtures seems to be dominated by the PEO in the concentration range explored.
Understanding non‐Darcian flow of shear‐thinning fluids through rough‐walled rock fractures is of vital importance in a number of industrial applications such as hydrogeology or petroleum engineering. Different laws are available to express the deviations from linear Darcy law due to inertial pressure losses. In particular, Darcy's law is often extended through addition of quadratic and cubic terms weighted by two inertial coefficients depending on the strength of the inertia regime. The relations between the effective shear viscosity of the fluid and the apparent viscosity in porous media when inertial deviations are negligible were extensively studied in the past. However, only recent numerical works have investigated the superposition of both inertial and shear‐thinning effects, finding that the same inertial coefficients obtained for non‐Darcian Newtonian flow applied in the case of shear‐thinning fluids. The objective of this work is to experimentally validate these results, extending their applicability to the case of rough‐walled rock fractures. To do so, flow experiments with aqueous polymer solutions have been conducted using replicas of natural fractures, and the effects of polymer concentration, which determine the shear rheology of the injected fluid, have been evaluated. Our findings show that the experimental pressure loss‐flow rate data for inertial flow of shear‐thinning fluids can be successfully predicted from the empirical parameters obtained during non‐Darcian Newtonian flow and Darcian shear‐thinning flow in a given porous medium.
Many natural phenomena in geophysics and hydrogeology involve the flow of non‐Newtonian fluids through natural rough‐walled fractures. Therefore, there is considerable interest in predicting the pressure drop generated by complex flow in these media under a given set of boundary conditions. However, this task is markedly more challenging than the Newtonian case given the coupling of geometrical and rheological parameters in the flow law. The main contribution of this paper is to propose a simple method to predict the flow of commonly used Carreau and yield stress fluids through fractures. To do so, an expression relating the “in situ” shear viscosity of the fluid to the bulk shear‐viscosity parameters is obtained. Then, this “in situ” viscosity is entered in the macroscopic laws to predict the flow rate‐pressure gradient relations. Experiments with yield stress and Carreau fluids in two replicas of natural fractures covering a wide range of injection flow rates are presented and compared to the predictions of the proposed method. Our results show that the use of a constant shift parameter to relate “in situ” and bulk shear viscosity is no longer valid in the presence of a yield stress or a plateau viscosity. Consequently, properly representing the dependence of the shift parameter on the flow rate is crucial to obtain accurate predictions. The proposed method predicts the pressure drop in a rough‐walled fracture at a given injection flow rate by only using the shear rheology of the fluid, the hydraulic aperture of the fracture, and the inertial coefficients as inputs.
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