Summary Acid jetting occurs as a result of pumping acid through limited-entry liner completions, causing high-velocity streams to impinge against the wellbore wall. The dissolution effect of jetting differs significantly from conventional matrix acidizing. Acid jetting causes cavities to be formed at the points of contact of the jet with the rock, with wormholes forming beyond the cavity. Jetting has been shown to be an effective technique for placing acid along extended-reach laterals, removing filter cake, and enhancing wormhole propagation. The velocity of the impinging jet and its standoff distance from the rock cause some of the acid to penetrate the formation and some to flow back in the annular space of the liner. Two types of dissolution mechanisms occur: surface dissolution forming the cavity and matrix dissolution forming the wormholes. These dissolution mechanisms are highly dependent on the acid-injection rate, velocity of the jet, temperature, and permeability of the formation. The differences between the matrix dissolution mechanism of acid jetting and that of conventional matrix acidizing are most obvious at low acid-injection rates. Experiments were performed with the intention of quantifying the difference in pore volume (PV) to breakthrough between acid jetting and matrix acidizing, as well as determining the effect of increased temperature, rock permeability, and acid concentration on this value with respect to the acid-injection rate. The baseline parameters of room temperature, 15% hydrochloric (HCl) acid, and 2- to 4-md Indiana limestone were individually compared with experiments run at 180°F, 28% HCl, and Indiana limestone cores of 30, 60, and 140 md. The effect of jetting velocity was also investigated. A direct comparison with conventional matrix acidizing was made by eliminating the jetting effect of the stream through mechanical dispersion. Acid jetting creates a point of heightened interstitial velocity at the contact of the acid and the rock, causing wormhole propagation to occur at a faster rate than it would in conventional matrix acidizing at that injection rate. This effect is especially pronounced as the jetting velocity is increased above that of matrix acidizing, and it tapers off at progressively higher jetting velocities.
SPE Members Abstract "Wormholes", which are characteristic shapes resulting from the acidizing of carbonate formations have been considered in the past as fractals. In previous publications, analytical relationships of the area penetrated by wormholes, the wormhole porosity and the fractal dimension have been presented. Local mineral compositional heterogeneities and structures result in uneven reaction profiles when acid reacts with carbonate rocks. This, coupled with permeability heterogeneities, leads to microscopic flow instabilities which may evolve into macroscopic wormhole patterns. The understanding of the physics of acidizing is becoming a serious issue with the emergence of horizontal wells, where massive volumes of acid may be needed for effective stimulation. The stochastic nature of the wormholing process has been a limiting factor for a physical interpretation. The simulation of this unstable growth process is the purpose of this paper. The impacts of permeability anisotropy, heterogeneous distribution of the properties of the formation, such as microfractures and zones of different permeabilities, are investigated. A simulation model, the permeability driven fingering model (PDF) is presented. This technique is a new approach to diffusion limited growth, which traditionally has been simulated with diffusion limited aggregation models (DLA). The randomness of fractal growth is changed by introducing a bias representing the permeability anisotropy and the preferential reaction kinetics of lithologic heterogeneities. Introduction The formation of wormholes in carbonate acidizing is driven by a dynamic fluid instability which is conceptually similar to what is known as viscous finger instability. The physical difference of wormhole growth is that the instability is caused by a discontinuous jump in the permeability between the untreated matrix and the highly conductive paths of the wormhole network. In viscous fingering it is the difference between the viscosity of the displacing and displaced fluids which causes the growth of small perturbations to the two-fluid interface. In the case of the wormhole instability (later referred to as permeability fingering, in contrast to viscous fingering) the viscosity ratio between injection fluid and the reservoir fluids is close to one, especially if an acid pre-flush is considered. Therefore, viscosity will not be the primary driving force for the instability in the injection front which leads to wormhole growth. The striking similarity between how a viscosity ratio and permeability ratio cause a fingering pattern to develop has encouraged us to apply a similar model based on stochastic growth. In this paper we will describe the permeability driven fingering model (PDF) which is an extension of the dielectric breakdown model with tunable noise. P. 413^
Research Note Visualization of the reaction patterns between acid and carbonate rocks is the subject of this note. Carbonate rocks (chalks, limestones, and dolomites) account for a sizableportion of all petroleum reservoirs. Wells drilled in these reservoirs usually need stimulation, as all types of wells do. The acid/rock reaction pattern shave often been referred to as wormholes, a term that reflects their actual shape. The reaction of acid with reservoir rocks is controlled primarily by the diffusive flux, which depends on the concentration gradient from the live acid to the rock surface and, once the acid is in contact, by the reaction rate at the rock surface. Clearly, the slower mechanism would control the reaction kinetics. In limestones at any temperature and dolomites above 50 C, the activation energy is low; every acid/rock collision results in a reaction, and the reaction rate depends on how fast the acid can be brought in contact with the rock. These systems are controlled by mass-transfer (or diffusion)-limited kinetics. For sandstones and very low-temperature dolomites, the activation energy is high, 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/rock interactions is well understood and is described in a number of publications. Thus, we do not address that topic. Our work focuses on the diffusion-limited case-i.e., acid/carbonate rock interactions. Several attempts have been made to quantify and thus to predict reaction patterns. Hoefner and Fogler considered simultaneous momentum, mass transfer, and reaction kinetics. They used network models to simulate and predict wormhole patterns. Wormhole growth is an unstable process, with a number of possible phases whose durations (or even their presence) depend on several variables and ranges of their values. For example, the magnitude of the injection rate in a given formation may cause compact dissolution, wormholes with multiple branches(dendritic shape), or a single dominant wormhole. Thus, appropriately conditioned stochastic modeling can be used to visualize reaction patterns, to discern differences, to reproduce laboratory results, and ultimately to reproduce 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 the cluster. In this environment, it would be difficult to bias the randomness. To circumvent the problem, the dielectric breakdown model (DBM) was introduced. In the DBM, the cluster propagates with a probability to grow at a site conditioned (or weighted) by the local pressure gradient. This feature makes the DBM particularly attractive in describing viscous fingering and wormholes resulting from acidizing because the pressure gradient and flow characteristics of the already-created patterns greatly influence subsequent growth. Pichler et al. presented a modification to the DBM, the permeability-driven fingering (PDF) model, where the growing cluster is treated as an interface between two regions of distinctly different properties: mobility in viscous fingering and permeability in acidizing. The PDF model lends itself to a number of interesting studies and visualizations. We have simulated the reaction patterns in linear cores, and showed that one dominant wormhole is created (Fig. 1). Other 2D results demonstrate the screening effect; some branches grow preferentially while others stop. The longest fingers control the flow distribution, and the shape of the cluster depends on the shape of the previous stage. This suggests that experimental results from linear cores may be of questionable value when extrapolated in a radial 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 the outer boundary. A cylindrical outer boundary can be used for a closer approximation to field stimulation patterns that may emanate for a well. Stochastic models (2D PDF, 3D PDF, and their derivatives) can simulate the growth of reaction patterns (wormholes) between acids and carbonate rocks, allowing their visualization and study. The impact of variables on the wormhole character can readily assessed. The models can and must be conditioned by experimentally determined quantities such as diffusion constants, the relationship between injection rate and the type of stimulation, and the relative impact of the individual mechanisms. References Daccord, G., Lenormand, R., and Touboul, E.: "Carbonate Acidizing: Toward a Quantitive Study of the Wormholing Phenomenon," SPEPE (Feb. 1989)63; Trans., AIME, 287. Levich, V.G.: Physicochemical Hydrodynamics, Prentice-Hall Inc., Englewood Cliffs, NJ (1962). Hoefner, M.L. and Fogler, H.S.: "Fluid-Velocity and Reaction-Rate Effects During Carbonate Acidizing: Application of Network Model," SPEPE(Feb. 1989) 56. Witten, T.A. and Sander, L.M.: "Diffusion-Limited Aggregation. A Kinetic Critical Phenomenon," Phys. Rev. Let. (1981) 47/19, 1400. Niemyer, L., Pietronero, L., and Weismann, H.J.: "Fractal Dimension of Dielectric Breakdown," Phys. Rev. Let. (1984) 52/12, 1033. Pichler, T. et al.: "Stochastic Modeling of Wormhole Growth in Carbonate Acidizing With Biased Randomness," paper SPE 25004 presented at the 1992 SPE European Offshore Petroleum Conference, Cannes, Nov. 9–11. Zirngast, E.: "Stochastic Modeling of Wormhole Growth in Three Dimensions," diploma thesis, Mining U. Leoben, Leoben, Austria (1993). P. 282^
Acid jetting occurs as a result of pumping acid through limited entry liner completions, causing high velocity streams to impinge against the wellbore wall. The dissolution effect of jetting differs significantly from conventional matrix acidizing. Acid jetting causes cavities to be formed at the points of contact of the jet with the rock, with wormholes forming beyond the cavity. Jetting has been shown to be an effective technique for placing acid along extended reach laterals, removing filter cake, and enhancing wormhole propagation. The velocity of the impinging jet and its standoff distance from the rock causes some of the acid to penetrate the formation and some to flow back in the annular space of the liner. Two types of dissolution mechanisms occur: surface dissolution forming the cavity, and matrix dissolution forming the wormholes. These dissolution mechanisms are highly dependent on acid injection rate, velocity of the jet, temperature, and permeability of the formation. The differences between the matrix dissolution mechanism of acid jetting and that of conventional matrix acidizing are most obvious at low acid injection rates. Experiments were performed with the intention of quantifying the difference in pore volume to breakthrough between acid jetting and matrix acidizing, as well as determining the effect of increased temperature, rock permeability and acid concentration on this value with respect to acid injection rate. Baseline parameters of room temperature, 15% HCl and 2-4 mD Indiana limestone were individually compared with experiments run at 180°F, 28% HCl, and Indiana limestone cores of 30, 60 mD, and 140 mD. The effect of jetting velocity was also investigated by changing the diameter of the orifice from which the stream exits. Direct comparison with conventional matrix acidizing was made by eliminating the jetting effect of the stream through mechanical dispersion. Acid jetting creates a point of heightened interstitial velocity at the contact of the acid and the rock, causing wormhole propagation to happen at a faster rate than it would in conventional matrix acidizing at that injection rate. This effect is especially pronounced as jetting velocity is raised above that of matrix acidizing, and tapers off at progressively higher jetting velocities.
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