Enhancement of Liquid Flow Through a Porous Medium by Ultrasonic Radiation

Abstract

Summary A new method to enhance the oil production rate is irradiation of the near-wellbore region by an ultrasonic source. The limited success for the application of ultrasound in well stimulation to date, however, is due to the lack of understanding of the physical mechanisms between an acoustic wave field and a porous medium. In this paper the mechanism in which ultrasonic radiation deforms the walls of the pores in the shape of traveling transversal waves is studied. A quantitative description of the mechanism indicates that these waves induce a net flow of the liquid inside the pores, identical to peristaltic transport. Numerical calculations show a damping effect of liquid compressibility and a strong influence of pore wall hardness and power output on the net flow rate induced. The occurrence of a flow induced by ultrasound has been confirmed by laboratory experiments. In these experiments a water velocity of almost 1 cm/s through a rubber capillary of 0.15 mm radius could be induced by an ultrasonic source of frequency of 20 kHz. By a comparison between the trends observed in the experiments and the theoretically predicted trends, the role of the peristaltic transport mechanism in acoustic well stimulation is discussed. Introduction Declining oil production is of major concern in the oil producing industry. Acidizing the near-wellbore region has been a commonly applied technique to increase the production rate of oil from the wells. The corrosion caused by the acid as well as the environmental impact, however, has led to the search for new methods of stimulation. One promising new method in well stimulation is the use of ultrasound. Laboratory experiments have shown that ultrasonic radiation can considerably increase the rate of liquid flow through a porous medium. For instance, Chen1 investigated the influence of ultrasonic radiation on the flow of oil through porous sandstone samples, and observed that ultrasonic radiation increased the oil flow rate by a factor of 3. Although the ultrasonic energy heated the oil, and hence, decreased its viscosity, he showed that only a part of the increase of the flow rate could be caused by the viscosity decrease. Also, in field trials an acoustic source lowered in a well has been reported to increase the oil production. However, the effects of acoustic irradiation of the near-wellbore region have been found to strongly vary, and in some cases even a lasting decrease of oil production has been observed. Beresnev and Johnson2 have presented various tests and results of acoustic stimulation in a review article. What is missing in the present state of investigation is a quantitative description of the major mechanisms and a theory or numerical model that could predict the result. One theoretical explanation for the increase of the rate of liquid flow through a porous medium by ultrasonic radiation has been given by Ganiev et al.3 They propose that ultrasonic radiation deforms the pore walls in a porous medium in the shape of traveling transversal waves. After having carried out a perturbation analysis, in which the ratio of the wave amplitude to the pore radius is the small parameter, they found in the second-order approximation a net flow of the liquid. Ganiev et al.,3 however, do not analyze the influence of the acoustic power output and the material properties of the porous medium and the liquid. Furthermore, they do not refer to a validation of the mechanism by experiments. The mechanism proposed by Ganiev et al.3 is identical to peristaltic pumping which is often used in medical instruments and frequently occurs in the organs in the living body. Various papers have been written about peristaltic transport in medical applications, see, for instance, Yin and Fung.4 However, usually the liquids considered are assumed to be incompressible, so that the effects of liquid compressibility are left out of consideration. In this paper, we elaborate the peristaltic transport mechanism in order to analyze the enhancement of liquid flow through a porous medium by ultrasonic radiation. Although natural porous media are a random network of interacting capillaries of variable cross section, we depart from an idealistic representation in which the porous medium consists of a set of noninteracting, straight, and circular capillaries in an elastic medium. We consider a flexible axisymmetric cylindrical pore of radius rp with its wall deformed in the shape of a traveling transversal wave of constant amplitude a and speed u. The pore is saturated with a compressible viscous liquid, which is taken to be in rest when the acoustic source is switched off. We relate the wave amplitude and wave speed to the power output W generated at the acoustic source, to the shear modulus G of the porous medium and to the compressibility ? of the liquid. A perturbation analysis, valid for small values of ϵ•a/rp, reveals in the second-order approximation a net flow of the liquid. Details about the derivation of the equations governing the net flow can be found in Ref. 5. Numerical calculations show the influence of the compressibility of the liquid, the shear modulus of the porous medium, and of the frequency and power output of the acoustic wave field on the net flow rate induced. In addition to the theoretical model, laboratory experiments are carried out to demonstrate the potential of acoustics and to validate the peristaltic transport mechanism. In the experimental setup, the porous medium is represented as a rubber stopper with a single capillary through it, which is saturated with water. Radiation by an ultrasonic source, which is submerged in the water and placed above the rubber, induces a flow of the water through the capillary. By changing the power output settings as well as the hardness of the rubber, we derive various trends for the ultrasonically induced flow velocity. Finally, the role of the peristaltic transport mechanism in well stimulation is discussed. To that end, we compare the net flow rate of the peristaltic transport to the rate of a Poiseuille flow due to a pressure gradient. It appears that although the ultrasonically induced net flow is an effect of O(ϵ2), it might have the same order of magnitude of rate as a Poiseuille flow due to the pressure gradient in the near-wellbore region. Next, the trends observed in the experiments are compared to the numerically calculated trends of the peristaltic transport flow. Finally, the application of ultrasound in well stimulation is discussed, by considering its ability to remove or destruct thin films of solids adhered to pore walls.

Comparison of Acidizing and Ultrasonic Waves, and Their Synergetic Effect for the Mitigation of Inorganic Plugs

“…The damaged permeability recoveries caused by the application of #4 and #5 transducers were 10.9% and 9.9%, respectively. Despite the same power in irradiation of the first three core samples, the #2 transducer frequency (20 kHz) worked well, because of fluid flow enhancement in core samples due to peristaltic transport . Peristaltic transport can simply be understood as clasping and compressing of the fluid contained conduit which is thought to occur under the action of wave propagation in the direction of the liquid contained distensible pipe .…”

Hydromechanical vibrator-pulsator for restoring the injectivity of injection wells

“…This leads to a decrease in the intake capacity of the well formation, changes the hydrodynamic conditions of injection in the reservoir pressure maintenance system and reduces the production rate of hydrocarbon raw materials, increases the pressure in the oil collection system [3][4]. Periodically, such wells and pipelines are treated with injection of oil, acid, aqueous solutions of surfactants, gas-liquid mixtures, energy-releasing binary mixtures [5][6][7][8].…”

Processes of vibroimpact treatment of wells

“…Injection wells are an important element in the overall chain of the reservoir pressure maintenance system. Failure to comply with the quality requirements of the injected liquid, which contains residual oil, mechanical impurities in the form of inert particles and corrosion products, clogs the bottom-hole zone of wells [5][6][7]. The problem of reducing the intake capacity of injection wells, which is observed everywhere, changes the hydrodynamic mode of operation of oil reservoirs, which leads to a decrease in hydrocarbon production [8][9][10].…”