Abstract
In this paper we describe the use of a novel technique, laser Doppler anemometry (LDA), to obtain information on fracturing fluid behavior. This technique permits measurement of fluid velocity at any point in a flow system. By scanning across the flow geometry, it is possible to obtain the velocity profile, which is related, possible to obtain the velocity profile, which is related, in turn, to the rheology of the fluid.
At low shear rates, velocity profiles obtained for aqueous solutions of hydroxypropyl guar showed significant deviations from those calculated using known power law parameters. The investigation was extended by power law parameters. The investigation was extended by conducting a series of rheological experiments using rotational and capillary viscometers over a wide shear-rate range (10(–2) to 2 × 10(3) seconds (–1)) The data have been fitted to a three-parameter Ellis model, and the velocity profiles calculated from these data agree well with profiles calculated from these data agree well with experimental ones.
The immediate results of this work are of interest in proppant transport modeling and correlate well with proppant transport modeling and correlate well with published data that show that apparent viscosities obtained published data that show that apparent viscosities obtained from proppant settling velocities are lower than those obtained from power law parameters.
Introduction
The role played by the rheology of fracturing fluids in the design of stimulation treatments does not need to be stressed. Friction pressure through pipes and/or annuli, fracture geometry, and proppant placement depend primarily on the rheological properties of treating fluids. primarily on the rheological properties of treating fluids. Fracturing fluids usually exhibit a non-Newtonian behavior. Under isothermal conditions, their rheological properties may be shear-dependent only, as in linear gels, properties may be shear-dependent only, as in linear gels, or much more complex (i.e., time/shear-dependent), as in the case of crosslinked gels. Several types of rheometers have been used to characterize the behavior of fracturing fluids: coaxial cylinder viscometers, cone and plate rheometers, and capillary viscometers. These traditional means of evaluating non-Newtonian rheology are subject to several drawbacks inherent in the measuring technique itself or in the type of fluid under study.
For instance, coaxial cylinder and capillary viscometers do not allow for the direct computation of the shear rate that is applied to measured fluids. For a time-independent non-Newtonian fluid, a proper interpretation of the measurements must involve the determination of the first, or even higher order, derivative of the experimental curve Copyright 1985 Society of Petroleum Engineers (rotational speed/torque or flow-rate/pressure-drop curves). The time-dependent nature of some fluids complicates the problem, since, in these viscometers, fluid particles experience different shear rates and, therefore, particles experience different shear rates and, therefore, different shear histories.
On the experimental side, difficulties may arise from the three-dimensional structure and from the correlative elasticity of crosslinked fluids-e.g., the Weissenberg effect in coaxial cylinder viscometers or the ejection of the fluid from cone and plate rheometers in steady rotation even at low speeds.
Some of the limitations encountered in the rheological characterization of time-dependent fracturing fluids may be overcome with an improved experimental techniqueLDA. LDA is a direct and nondestructive technique for measuring particle velocities in a moving fluid. Therefore, it allows characterization of the flow kinematics. The technique was tested first on the simplest case of a time-independent fluid to evaluate its validity for fracturing rheological studies.
In the following sections, after a description of the LDA technique and of the equipment, we illustrate the use of the LDA by the study of a noncrosslinked fluid that has been characterized using classical rheometrical methods. We stress the importance of the frequently forgotten Newtonian behavior of these linear gels at low shear rates. Implication of the results on the design of fracturing treatments also is discussed.
The LDA Technique
Principle
LDA uses the Doppler shift of light scattered Principle. LDA uses the Doppler shift of light scattered by moving particles in a flow system to determine particle velocity and thus measure the fluid velocity at a given point. In dual-beam mode, the most common technique, two point. In dual-beam mode, the most common technique, two coherent laser beams of equal intensity intersect, and light scattered in any one direction is picked up by a photodetector (Fig. 1). The difference, fD, between the photodetector (Fig. 1). The difference, fD, between the two scattering frequencies, fsi and fs2 is independent of the scattering direction, es, and proportional to a velocity component, Vx, of the particles flowing through the beam intersection (Fig. 2).
LDA has the great advantage of being a direct and nonperturbative velocimetry technique in that only light beams enter the flow through a transparent window. No flow calibration is required, and no probe (hot wire, turbine) is necessary inside the flow, thereby eliminating any disturbances.
SPEJ
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