Wormholes models

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

About a year after Morris and Thorne delved into wormholes. Matt Visser of Washington University developed a wormhole model that looked more like a rectangular spool of thread than the hourglass shape of Morris and Thorne. A rectangular... 

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.)... 

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. 

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

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. 

The exterior of the Visser wormhole acts like a giant mirror. Light shining on it would bounce off as if it hit a reflecting material. Visser also proposed another mathematical model for a wormhole that resembles two coreless apples. The inner walls of the fruit are connected along the fourth dimension. You can read more about this structure in Halpern s Cosmic Wormhole book or in Visser s original scientific paper. 

Figure 18.1 Models for different modes of peptide-lipid interaction of membrane-active peptides. The peptide remains unstructured in solution and acquires an amphipathic structure in the presence of a membrane. The hydrophobic face of the amphipathic peptide binds to the membrane, as represented by the grayscale. At low concentration, the peptide lies on the surface. At higher peptide concentrations the membrane becomes disrupted, either by the formation of transmembrane pores or by destabilization via the "carpet mechanism." In the "barrel-stave pore" the pore consists of peptides alone, whereas in the "toroidal wormhole pore" negatively charged lipids also line the pore, counteracting the electrostatic repulsion between the positively charged peptides. The peptide may also act as a detergent and break up the membrane to form small aggregates. Peptides can also induce inverted micelle structures in the membrane.

Both in the laboratory and theoretically, the optimum combination of treatment injection rate and stimulation fluid reactivity (fluid type) can be determined for a given set of conditions. These conditions include formation type and characteristics. In the field, though, it is very difficult (if not impossible) to make this determination. This is because leak-off of reactive fluid from the dissolution path, or wormhole, to the surrounding formation cannot be accurately determined. The difficulty in achieving accurate leak-off measurement persists despite the use of models and laboratory leak-off data. 

A semiempirical model to calculate wormhole growth in carbonate acidizing. Paper SPE 96892, presented at the Society of Petroleum Engineers Annual Technical Conference and Exhibition, Dallas. 

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