Wormholing

FIG. 12 The behavior of the internal energy U (per site), heat capacity Cy (per site), the average Euler characteristic (x) and its variance (x") — (x) close to the transition line and at the transition to the lamellar phase for/o = 0. The changes are small at the transition and the transition is very weakly first-order. The weakness of the transition is related to the proliferation of the wormhole passages, which make the lamellar phase locally very similar to the microemulsion phase (Fig. 13). Note also that the values of the energy and heat capacity are not very much different from their values (i.e., 0.5 per site) in the Gaussian approximation of the model [47]. (After Ref. 49.)... 

In general, chelating agents possess some unique chemical characteristics. The most significant attribute of these chemicals is the high solubility of the free acids in aqueous solutions. Linear core flood tests were used to study the formation of wormholes. Both hydroxyethylethylene diaminetriacetic acid and hydroxyethyliminodiacetic acid produced wormholes in limestone cores when tested at 150° F. However, the efficiency and capacities differ. Because these chemicals have high solubility in the acidic pH range, it was possible to test acidic (pH less than 3.5) formulations [644]. 

So-called "wormholes" can be formed when the injected acid primarily enters the largest diameter flow channels in carbonate rock further widening them (107). Acid only invades the small flow channels a short distance greatly reducing treatment effectiveness. High fluid loss rates, low injection rates, and reduced rates of acid-rock reactions decrease the wormhole length. 

Actual responses of tuo carbonate petroleum reservoirs to matrix injection of hydrochloric acid are compared with a recently proposed experimental model for wormholing. This model is shown to be applicable in undamaged primary porosity reservoirs, and should be useable in damaged double porosity ones. Formations of no primary porosity are shown to respond very differently. 

The dissolution channels (wormholes), obtained under certain conditions of attack of carbonate rocks by hydrochloric acid, have been recently proven to have a fractal geometry. An equation was proposed, relating the increase of the equivalent wellbore radius (i.e. the decrease of the skin) to the amount of acid injected, in wellbore geometry and in undamaged primary porosity rocks. This equation is herein extended to damaged double porosity formations through minor modifications. 

LIETARD AND DACCORD Acid Wormholing in Carbonate Reservoirs... 

When submitting a carbonate rock to the flov of an acidic solution, the attack, most of the time, leads to the preferential grovth of large pores. The dissolution of the rock is not uniform, and the final pore size distribution is much broader than the original one. This fact has been recognized and described in detail more than fifteen years ago (4j 5). Macroscopic pores, which are the end result of such an unstable attack, have received the name of wormholes. 

It has been shown that the development of wormholes in carbonate rocks is a consequence of diffusion-limited (mass-transfer-limited) kinetics of attack (6). Such kinetics prevail in most of these rocks, i.e. limestones and dolomites, providing that, for the latter, the temperature is larger than about 200°F (90°C) (7-8). 

Another approach of the problem has been proposed recently (9). Based on a comprehensive experimental study, it considers that wormholes have an almost infinite conductivity in comparison with the original pores of the rock. Consequently, a fair approximation of the permeability profile of an acidized piece of rock of length L is a step function. From its inlet up to almost the tip of the wormholes, the permeability is infinite. In the rest of the rock, it is equal to the original one, i.e. ko, and the overall permeability of this core becomes ... 

Similarly, in 3D-radial geometries of interest for petroleum engineers, an equivalent wellbore radius re is defined. The near-wellbore region, including radially distributed wormholes from rw up to re, is infinitely permeable and therefore becomes a mere radial extension of the wellbore itself. Equation 2 can be used to calculate the pseudodecrease of the skin when an undamaged primary porosity formation of permeability k0 includes wormholes as described hereabove ... 

This wormholing model was shown to agree with previously published experimental data (14). 

Injecting acid in such an interval produces wormholes in the nearwellbore region, which is damaged, so that the acid flow only takes place in the clean primary porosity of the rock. This superposes to the original step function of the permeability profile a second, similar function, stating that the acidized profile now includes in the vicinity of the wellbore, from rw up to re, a zone of infinite conductivity... 

Figure 1 Permeability profile in a damaged double porosity reservoir during acidizing. rw wellbore radius, re wormholes penetration, damage radius, kptp undamaged reservoir permeability (total contribution of both primary and secondary porosities), kPP damaged permeability (primary porosity contribution only).

The rest of the 15 /, HC1 injection (5 - 9.7 m3) shows a much more rapid skin decrease this is interpreted as being the sign of the establishment of communication between the wellbore and some adjacent fissures by propagating wormholes. 

Figure 6 Comparison of actual and model skin curves during wormholing of 15 / HC1 (first acid stage of Well B treatment).

Again, according to Equations 6 and 13, the theoretical response during the acid stage, if wormholing were to take place, would be ... 

Because of the highly unstable nature of the acid attack in most of the carbonate reservoirs (propagation of wormholes), the development of a descriptive model of the skin evolution was not possible until the recent advent of the theory of fractals. In addition, the characteristics of the damaged zone greatly affect the behavior of the skin during acid injection in any type of reservoir, but particularly in carbonate ones. 

Acid attack, propagation of wormholes, 619 Acid corrosion inhibition, time dependence, 644... 

Acid fracturing, friction reducers, 15 Acid hydrolysis, lignin, 173 Acid injection into carbonate reservoir, 610-611 Acid-rock reactions, rate, 15,16 Add wormholing in carbonate reservoirs, 608-620 in carbonate rocks, 610-611 Acidity-controlled redox reactions, 141-142 Addization... 

Wang Y, Tang X, Lin L, Huang W, Haochen Y, Gedanken A (2000) Sonochemical synthesis of mesoporous titanium oxide with wormhole-like framework structures. Adv Mater 12 1183-1186... 

Wormhole mesoporous carbon X-ray photoelectron spectroscopy X-ray diffraction... 

As noted in Sect. 10.1, heterogeneities play a dominant role in the migration of contaminants in the subsurface. Nonuniform, preferential patterns of flow and transport are ubiquitous. It is important to recognize that, at the field scale, contaminant movement generally is very difficult to anticipate. In natural soils and aquifer materials, macropores, soil cracks and aggregates, fissures, solution channels, root paths, and wormholes, as well as variable mineral composition (e.g., clay aggregates... 

Houdayer, J. The wormhole move a new algorithm for polymer simulations. J. Chem. Phys. 2002, 116,1783-7. 

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