Abstract
The pressure-driven growth model that describes the two-dimensional (2-D) propagation of a foam through an oil reservoir is considered as a model for surfactant-alternating-gas improved oil recovery. The model assumes a region of low mobility, finely textured foam at the foam front where injected gas meets liquid. The net pressure driving the foam is assumed to reduce suddenly at a specific time. Parts of the foam front, deep down near the bottom of the front, must then backtrack, reversing their flow direction. Equations for one-dimensional fractional flow, underlying 2-D pressure-driven growth, are solved via the method of characteristics. In a diagram of position versus time, the backtracking front has a complex double fan structure, with two distinct characteristic fans interacting. One of these characteristic fans is a reflection of a fan already present in forward flow mode. The second fan however only appears upon flow reversal. Both fans contribute to the flow's Darcy pressure drop, the balance of the pressure drop shifting over time from the first fan to the second. The implications for 2-D pressure-driven growth are that the foam front has even lower mobility in reverse flow mode than it had in the original forward flow case.
Highlights
During oil and gas production, typically only a fraction of the oil available in a reservoir can be extracted under the reservoir’s own pressure
The implications for 2-D pressure-driven growth are that the foam front has even lower mobility in reverse flow mode than it had in the original forward flow case
Equations (4.24)–(4.26) taken together constitute a model for what happens in 2-D pressure-driven growth in situations in which a flow reversal occurs due to a reduction in driving pressure
Summary
During oil and gas production, typically only a fraction of the oil available in a reservoir can be extracted under the reservoir’s own pressure. We need to understand such flow direction changes, and flow reversal in particular, in order to know how the totality of fluids distribute in this system, even though admittedly in oil recovery applications, the flow-reversed part of the front at depth should contain rather less oil than the forward flowing part that we continue to recover higher up This follows because (as mentioned earlier) it is advantageous to inject at as high a pressure as possible [52], meaning that, by design, foam already penetrates rather deeper than the majority of oil is likely to be present. Sl decreasing characteristics with upstream low liquid saturation (coarsely−textured t high mobility foam) liquid & gas filled region
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