Microscopic Aspects of Capillary Imbibition

Abstract

Abstract As a general rule, the action of capillary forces cannot be ignored in treating capillary imbibition (where one fluid is displaced by another replacing fluid). This circumstance requires that the capillary driving force term be identified and cast in a form which will serve the needs of analysis and throw some light on the details of the displacement process. Given a saturation gradient defining the flood-front profile at a particular instant, the corresponding capillary pressure gradient is found to have only qualitative meaning as a measure of the capillary driving force acting to project flood-front forward. This viewpoint is contrary to common opinion; hence, it is necessary to re-examine the microscopic aspects of capillary imbibition so that a quantitatively meaningful capillary driving force term can be derived which has a macroscopic importance. The microscopic analysis leads to some interesting conclusions. Of major importance is the idea that a Darcy Law analog cannot be written as the macroscopic law of force descriptive of the unsteady states of multiphase-flow systems. This means, for example, that published solutions of the Buckley-Leverett problem are in error, as are other analyses which depend on use of the conventional relative permeability concept. A second conclusion which can be drawn is that the capillary forces are the major factor determining microscopic displacement efficiency, even for cases when the injection rates are high (e.g., there is a large imposed gradient in pressure energy). It is found, moreover, that the capillary driving force and, hence, the displacement efficiency are rate-dependent in ways usually overlooked. In this paper, the Buckley-Leverett problem is discussed at length as a device to show the importance of taking the microscopic viewpoint before attempting to deduce how capillary imbibition and displacement can be characterized in the macroscopic sense. Attention is thus focused on the need to derive a valid law of force for the unsteady states of multiphase flow, if valid equations of motion are to be written. Although this paper does not suggest a law of force to replace the rejected Darcy Law analog, at least the capillary driving force term is given in unambigious form. It is concluded that, for a while at least, capillary imbibition of a wetting fluid into and through porous media cannot be cast in an analytically or numerically integrable form; hence, experimental procedures (scaled-model experiments) are proposed as an appropriate way to investigate fluid-fluid displacement. To be noted is the fact that these experimental procedures are no more difficult to undertake than the relative permeability and capillary pressure experiments required to give the basic data needed for conventional Buckley-Leverett calculations.