Simulation of Dynamic Foam-Acid Diversion Processes
- L. Cheng (U. of Texas) | S.I. Kam (U. of Texas) | M. Delshad (U. of Texas) | W.R. Rossen (U. of Texas)
- Document ID
- Society of Petroleum Engineers
- SPE Journal
- Publication Date
- September 2002
- Document Type
- Journal Paper
- 316 - 324
- 2002. Society of Petroleum Engineers
- 1.10 Drilling Equipment, 5.2.1 Phase Behavior and PVT Measurements, 2.5.2 Fracturing Materials (Fluids, Proppant), 4.1.2 Separation and Treating, 5.6.5 Tracers, 5.3.2 Multiphase Flow, 3.2.4 Acidising, 4.1.4 Gas Processing, 4.3.4 Scale, 1.6.9 Coring, Fishing, 5.3.1 Flow in Porous Media, 4.1.5 Processing Equipment, 5.4.2 Gas Injection Methods, 1.8 Formation Damage, 3 Production and Well Operations
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A new simulator for foam-acid diversion is described. The simulator explicitly accounts for the first time for the effects of gas trapping on gas mobility in foam and in liquid injected after foam and for the effects of pressure gradient on gas trapping. The foam model fits steady-state foam behavior in both high- and low-quality flow regimes and steady-state liquid mobility after foam. Previous laboratory experiments suggested that a relatively slow transition between steady states during foam and acid injection may control the diversion process in the field. The simulator fits this transition period in laboratory corefloods qualitatively with no additional adjustable parameters.
Simulations and new data agree that the transition is faster at higher pressure (with lower gas compressibility) and that response to a shut-in period depends on how much gas escapes during the shut-in (i.e., on how long the shut-in lasts). Simulations and data suggest that a dead volume present upstream of the core in previous studies strongly affects the transition period seen in those experiments.
In foam/acid well stimulation, foam can help divert acid to reservoir layers most in need of stimulation.1-7 Foam acts by partially blocking undamaged or higher-permeability layers and allowing acid to enter other layers in greater need of stimulation. Foam may be injected along with acid or in alternating slugs with acid. This paper focuses on foam injected in alternating slugs with acid, although the simulator described could be applied to either process. Numerous studies report that foam does not directly alter the relative-permeability function krw(Sw) or viscosity of the aqueous phase.8-11 Foam does enormously reduce the mobility of gas, in part by trapping a large fraction of gas in place.11,12 Foam reduces the mobility of acid by reducing the mobility of gas in flowing foam, which drives up the gas saturation, and then trapping this gas in place during subsequent injection of acid.3,13,14 The success of foam then depends on both the mobility of flowing foam and the trapped-gas saturation during acid injection.
One cannot hope to match all aspects of field application in a laboratory experiment; even if one matches rock type and damage and presence of residual oil, backpressure (which controls gas compressibility) is usually higher in the field than in the laboratory, and linear flow into a finite core is essentially different from radial flow into a porous medium much larger than the treatment volume.14 Therefore, the goal of laboratory work is to understand and match the dynamics observed in the laboratory and then apply the models tuned to laboratory experiments to the field process. One studies foam dynamics separately from acid reactions in the rock on the assumption that, in sandstones at least, the two processes are separable. For acid injection into carbonates, the foam may alter the acid-dissolution pattern significantly, coupling the two processes in a complex way not accounted for here.15,16
A typical laboratory coreflood apparatus for study of foam-acid diversion is shown in Fig. 1, and a typical result is shown in Fig. 2.13 In this experiment, foam is injected for 8 pore volumes (PV), at which point gas injection ceases and injection of surfactant continues, to represent injection of acid with surfactant after foam. The low pressure gradient ?p in Section 1 could represent a rock anomaly there or slow foam generation within the core.5,13,17 At the end of foam injection, ?p falls over a period of injection of about 1 PV of liquid injection (about 75 minutes) to a second, steady value lower than that with foam. It is hard to quantify the length of this period unambiguously; ?p declines at first very steeply, but does not fully stabilize until after about 13 PV injection, beyond the range of Fig. 2. Rather than choose a rigid definition for the duration of this period, throughout this paper we characterize it informally by the time it takes ?p to fall to the vicinity of its stabilized value during liquid injection. A transition period of one hour, as in Fig. 2, could be significant in field application, in which acid and foam injection could alternate on a time scale of 1/2 hour. It is remarkable that this decline in ?p occurs nearly simultaneously throughout the core, because most displacement processes occur sequentially from core inlet to outlet. During this period, pressure falls, gas expands, some gas escapes, and gas saturation falls a few percent.14 In the laboratory, most escaping gas represents the increase in gas volume from expansion, not the decrease in gas saturation. Thus one expects that gas compressibility plays an important role in the transition period.
Later on, ?p falls a second time, this time to nearly zero, starting with the first section of the core and ending with the last. (This second decline has just begun in Section 1 in Fig. 2.) This latter decline, because of gas dissolution into injected unsaturated liquid, would be very harmful to diversion,14 but fortunately it can be avoided by presaturating the acid with gas (or including a small amount of gas with the injected acid).5,14
The steady-state pressure gradient during liquid injection after foam (but before the second decline because of gas dissolution) is not a fixed constant but depends weakly on uw, as illustrated in Fig. 3. Each (uw,?p) datum in Fig. 3 represents a final steady state, wherein only liquid flows and all gas is trapped at the given ?p. The slow increase of ?p with uw suggests that the extent of gas trapping depends on pressure gradient: as ?p increases, less gas is trapped, and Sw and krw increase. During the approach to this steady state (Fig. 2), pressure gradient falls, gas expands because of decompression, some escapes, and the fraction of remaining gas that is trapped increases. While the fall in ?p causes more remaining gas to be trapped, this increase of trapped-gas saturation Sgr in turn slows down the further decrease in ?p until a final steady state is reached. In other words, as pressure gradient falls, gas continues to expand and escape until no more gas can be liberated at the given pressure gradient. At this time, all remaining gas is trapped.18
There are few direct data on Sgr during foam flow or liquid injection following foam. Using gas tracers, Friedmann et al.11 found large trapped-gas saturations with foam that showed a gentle decrease with increasing ?p. (They considered the experimental scatter too great and the data too few to infer a decrease, and treated Sgr as a constant.) Radke and Gillis12 report substantial trapped-gas saturations as well, but no trend with ?p. Robert and Mack5 found that ?p does not vary at all as liquid injection rate varies in post-foam liquid injection, which implies that Sgr is very sensitive to ?p.
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