ABSTRACT
In this chapter we consider one of the possible scenarios according to which the stationary regimes of two-phase multicomponent reservoir flow may lose their stability and, as a consequence, according to which autowaves may appear. Pulsatory reservoir flow regimes are constantly encountered by engineers when they study the exploitation of oil-gas-condensate deposits. The observed pulsations may be caused by the action of nonmonotonic or periodic external forces (the moon, earthquakes, microseismic action, etc.). Such effects will not be considered here. We shall be interested in a situation where there is a time-monotonic (e.g., constant) inflow of energy into an open system, which, owing to its own nonlinearity, transforms the incoming energy into oscillations. We shall also be interested in the conditions (bifurcational values of the parameters) under which branching of the solution occurs and the stationary regime is replaced by the autowave. Such effects are studied by synergetics.1 This approach is rather general: the specific aim of our present study is to find the relationship between the observed instabilities and typical features of phase diagrams for multicomponent mixtures. In our scenario the autowaves are associated with the cyclic changing of the following processes: the increase of the volume occupied by the liquid phase (condensation), the flow of the liquid as it becomes sufficiently mobile in the porous medium, and the diminishing of the volume occupied by the liquid phase (evaporation). Correspondingly, the conditions of instability are equivalent to the conditions of the system being in the region of retrograde condensation. We shall discuss in detail the relationship between retrograde phenomena and the so-called effect of negative volume of heavy components. It will be shown that there is a direct connection between these phenomena and the negative compressibility of an individual volume of the two-phase continuum moving in a porous medium, and that this is what leads to instability. It is shown that, mathematically, the loss of stability occurs via Hopf bifurcation and that the autowaves are the relaxation oscillations in a distributed system. Finally, we discuss the results of recent experiments to check the predictions of the considered theory. These experiments have confirmed the correctness of our theoretical concepts.2-5
