Enhanced Visualization of Acid Carbonate Rock Interaction
- M.J. Economides (Texas A&M U.) | T.P. Frick (Mining U. Leoben) | J. Nittman (Digital)
- Document ID
- Society of Petroleum Engineers
- Journal of Petroleum Technology
- Publication Date
- April 1994
- Document Type
- Journal Paper
- 82 - 82
- 1994. Society of Petroleum Engineers
- 3.2.4 Acidising, 5.3.4 Integration of geomechanics in models, 1.6 Drilling Operations
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Visualization of the reaction patterns between acid and carbonate rocks isthe subject of this note.
Carbonate rocks (chalks, limestones, and dolomites) account for a sizableportion of all petroleum reservoirs. Wells drilled in these reservoirs usuallyneed stimulation, as all types of wells do. The acid/rock reaction patternshave often been referred to as wormholes, a term that reflects their actualshape.
The reaction of acid with reservoir rocks is controlled primarily by thediffusive flux, which depends on the concentration gradient from the live acidto the rock surface and, once the acid is in contact, by the reaction rate atthe rock surface.
Clearly, the slower mechanism would control the reaction kinetics. Inlimestones at any temperature and dolomites above 50 C, the activation energyis low; every acid/rock collision results in a reaction, and the reaction ratedepends on how fast the acid can be brought in contact with the rock. Thesesystems are controlled by mass-transfer (or diffusion)-limited kinetics.
For sandstones and very low-temperature dolomites, the activation energy ishigh, and only a small number of acid/rock collisions result in a reaction.These systems are controlled by surface-reaction-limited kinetics.
The phenomenological behavior of the two extreme cases of acid/rockinteractions is well understood and is described in a number of publications.Thus, we do not address that topic. Our work focuses on the diffusion-limitedcase-i.e., acid/carbonate rock interactions.
Several attempts have been made to quantify and thus to predict reactionpatterns. Hoefner and Fogler considered simultaneous momentum, mass transfer,and reaction kinetics. They used network models to simulate and predictwormhole patterns.
Wormhole growth is an unstable process, with a number of possible phaseswhose durations (or even their presence) depend on several variables and rangesof their values. For example, the magnitude of the injection rate in a givenformation may cause compact dissolution, wormholes with multiple branches(dendritic shape), or a single dominant wormhole. Thus, appropriatelyconditioned stochastic modeling can be used to visualize reaction patterns, todiscern differences, to reproduce laboratory results, and ultimately toreproduce and predict field results.
One of the first models to simulate the process is Witten and Sander'sdiffusion-limited aggregation (DLA) model. The DLA model is a random simulator,requiring (and implying) field isotropy and a constant-pressure surface at thecluster. In this environment, it would be difficult to bias the randomness.
To circumvent the problem, the dielectric breakdown model (DBM) wasintroduced. In the DBM, the cluster propagates with a probability to grow at asite conditioned (or weighted) by the local pressure gradient. This featuremakes the DBM particularly attractive in describing viscous fingering andwormholes resulting from acidizing because the pressure gradient and flowcharacteristics of the already-created patterns greatly influence subsequentgrowth.
Pichler et al. presented a modification to the DBM, the permeability-drivenfingering (PDF) model, where the growing cluster is treated as an interfacebetween two regions of distinctly different properties: mobility in viscousfingering and permeability in acidizing. The PDF model lends itself to a numberof interesting studies and visualizations.
We have simulated the reaction patterns in linear cores, and showed that onedominant wormhole is created (Fig. 1). Other 2D results demonstrate thescreening effect; some branches grow preferentially while others stop. Thelongest fingers control the flow distribution, and the shape of the clusterdepends on the shape of the previous stage. This suggests that experimentalresults from linear cores may be of questionable value when extrapolated in aradial environment unless appropriate dimensional analysis is undertaken.
For 3D simulation, Zirngast constructed an extension of the 2D dynamic grid.A grid cube was positioned within a sphere of zero potential, representing theouter boundary. A cylindrical outer boundary can be used for a closerapproximation to field stimula tion patterns that may emanate for a well.
Stochastic models (2D PDF, 3D PDF, and their derivatives) can simulate thegrowth of reaction patterns (wormholes) between acids and carbonate rocks,allowing their visualization and study. The impact of variables on the wormholecharacter can readily assessed. The models can and must be conditioned byexperimentally determined quantities such as diffusion constants, therelationship between injection rate and the type of stimulation, and therelative impact of the individual mechanisms.
1. Daccord, G., Lenormand, R., and Touboul, E.: "Carbonate Acidizing:Toward a Quantitive Study of the Wormholing Phenomenon," SPEPE (Feb. 1989)63; Trans., AIME, 287.
2. Levich, V.G.: Physicochemical Hydrodynamics, Prentice-Hall Inc.,Englewood Cliffs, NJ (1962).
3. Hoefner, M.L. and Fogler, H.S.: "Fluid-Velocity and Reaction-RateEffects During Carbonate Acidizing: Application of Network Model," SPEPE(Feb. 1989) 56.
4. Witten, T.A. and Sander, L.M.: "Diffusion-Limited Aggregation. AKinetic Critical Phenomenon," Phys. Rev. Let. (1981) 47/19, 1400.
5. Niemyer, L., Pietronero, L., and Weismann, H.J.: "Fractal Dimensionof Dielectric Breakdown," Phys. Rev. Let. (1984) 52/12, 1033.
6. Pichler, T. et al.: "Stochastic Modeling of Wormhole Growth inCarbonate Acidizing With Biased Randomness," paper SPE 25004 presented atthe 1992 SPE European Offshore Petroleum Conference, Cannes, Nov. 9-11.
7. Zirngast, E.: "Stochastic Modeling of Wormhole Growth in ThreeDimensions," diploma thesis, Mining U. Leoben, Leoben, Austria (1993).
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