SPE Journal
Volume 13, Number 4, December 2008, pp. 465-473

Summary

The organic fluids entrapped in pore constrictions by capillary forces can be mobilized by the application of elastic-wave vibrations because of the nudging effect, which allows quantitative description. The model used for such calculations is a single-pore channel with converging/diverging geometry, in which the organic phase is entrapped as a continuous blob occupying several adjacent pores. The ganglion is released from the constriction when the wave-acceleration amplitude exceeds a threshold value that scales with the frequency as A/f = a constant. This means that the wave intensity is the only required criterion for the release. In an ensemble of ganglia, the percentage of them mobilized and, therefore, the flow rate increases with the amplitude and decreases with frequency. The vibrations are inefficient for mobilization if the frequency is sufficiently high. The typical vibratory amplitudes required to produce noticeable increases in the average flow rates are on the order of 10 m/s² and much higher at the frequencies in excess of approximately 10 Hz. These estimates provide guidelines for the possible applications of elastic-wave stimulation of organic-fluid flow in porous environments.

Introduction

A great deal of attention in recent years has been devoted to the possibility of enhanced petroleum recovery using elastic waves and vibrations (Beresnev and Johnson 1994, Hilpert et al. 2000, Roberts et al. 2001 and 2003, Dobronravov 2002, Poesio et al. 2002). Nonetheless, the difficulty of the method has been insufficient understanding of the physical mechanism by which the low-frequency vibrations could mobilize the entrapped organic fluids. Hilpert et al. (2000) calculated the frequencies of pulsing pressure in an axisymmetric channel with a sinusoidal profile that maximized the volume of the displaced nonwetting phase; however, no explicit mobilization criteria were established. Several studies recently have proposed a specific oil-release mechanism showing how vibrations overcome capillary entrapment that holds the fluids in place (Graham and Higdon 2000, Iassonov and Beresnev 2003, Beresnev et al. 2005), which allowed explanation of miscellaneous observations of the enhancement in organic-phase flow by vibrations under field and laboratory conditions. This mobilization mechanism, as summarized by Beresnev et al. (2005), can be represented as follows.

The conditions for the capillary entrapment of nonwetting fluids in pores of variable diameter (the so-called Jamin effect) of course have been understood since the 1930s (Taber 1969). The residual fluids are immobilized in the form of isolated blobs (ganglia) because of an excess capillary pressure (P_c⁺) building up on the inner side of the downstream meniscus as it enters a narrow pore constriction, relative to the upstream meniscus (P_c^– ) (water-wet porous media will be assumed) (Payatakes 1982). Referring to Fig. 1, the oil ganglion can move if the absolute pressure in the oil at the left meniscus (P_w⁺ + ΔP_w + P_c^-)is greater than that at the right meniscus (P_w⁺ + P_c⁺), where P_w is the pressure in the water phase and P_c^± is the capillary pressure determined from the Laplace equation. Equating the two leads to ΔP_0w = P_c⁺ – P_c^- as the threshold external pressure drop in the water above which the ganglion is mobile (Taber 1969). It follows that the external gradient in the surrounding water needs to exceed a certain unplugging threshold ∇P_0w to carry the ganglion through (Taber 1969, Melrose and Brandner 1974).

This process is represented schematically on a flow-force diagram in Fig. 2. The solid line depicts the oil-phase flow for various values of the external static forcing. Under an external gradient ∇P_sw < ∇P_0w , the system resides in static equilibrium. The flow can commence only when ∇P_sw exceeds the unplugging threshold ∇P_0w .

Suppose that the flow is plugged (∇P_sw < ∇P_0w ). In a cylindrical channel, the application of longitudinal vibrations of the wall (without a loss of generality, we consider the motion parallel to the pore axis) is equivalent to the addition of an external (inertial) oscillatory body force P_osc to the constant gradient,
P_osc = ρ_pa,............................................(1)
where ρ_p is the density of the oil (petroleum) and a is an instantaneous amplitude of the acceleration of the wall (Biot 1956). One period of the oscillatory forcing adding to the gradient is shown in Fig. 2. When this forcing acts along the gradient and the total ∇P_sw + P_osc exceeds ∇P_0w , instant unplugging occurs (total forcing in the flow zone in Fig. 2). During the unplugged period, if a ganglion’s leading meniscus moves beyond the narrowest point in the constriction, the magnitude of the restraining capillary force starts to decrease progressively. As a result, the blob accelerates upon exiting the constriction (Beresnev et al. 2005). This explains why the application of the reversed polarity of vibrations, opposing the gradient, cannot return the blob to its original position. The minimum amplitude for the vibrations needed to mobilize the blob is set by the condition ∇P_sw + P_osc > ∇P_0w .

Because the leading meniscus must reach the throat of the constriction to become mobilized, the period of vibrations should be long enough (for a given amplitude) to allow sufficient time for this movement. Frequencies above a certain threshold value will fail to mobilize the blob. We infer that, in addition to the existence of the minimum-amplitude threshold for the onset of mobilization, there will also be a maximum-frequency threshold.

This mechanism of residual-organic-phase mobilization by elastic waves and vibrations allows quantitative description of the flow-enhancement effect produced by seismic waves of particular amplitudes and frequencies, which would be of direct practical interest and has so far been lacking. Performing such calculations is the goal of this paper.

© 2008. Society of Petroleum Engineers

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History

• Original manuscript received: 30 March 2006
• Revised manuscript received: 13 March 2008
• Manuscript approved: 30 May 2008
• Version of record: 15 December 2008