Effective fracture length

Two key factors that determine the success of add fracturing are the resulting length of the etched fracture and conductivity. The effective fracture length is influenced by the following ... 

Foamed acid can be useful in increasing effective fracture length, as well as in improving contact in longer treatment intervals. Foamed acid is essentially a gas-in-add emulsion stabilized with a foaming agent. The amount of gas in the foam on a volume basis is called the quality for example, a foam composed of 70% gas and 30% liquid is a 70-quality foam. The gas phase is usually nitrogen, but CO can also be used. Most foamed acids are 60-75 quality. 

In deep formations with high closure pressure, proppant may create a more conductive fracture than can be retained after closure of an add-etched fracture. This is also true in shallow, soft carbonates. A propped fracturing treatment may create a longer effective fracture length because fluid properties, especially leak-off, are not compromised by reactivity. 

Consequently the upper part of the crack zone (Fig. 8.11) is free to relax (contract) in response to the compression applied by the liquid, but the gel network ahead of the crack (zone II, Fig. 8.11) is constrained. Large (tensile) stresses occur especially in the zone around the crack tip (zone W). Fracture occurs as soon as the value of surpasses the strength of the gel and this occurs sooner the larger the (effective) crack length is and the larger are the drying stresses (and thus drying rates). 

In this case, the crack size is much larger than the plane strain crack-tip plastic zone size. As such the effective crack length 2a = 2ao + 2rjy would be effectively equal to the initial (or physical) size of the crack 2ao. The load-displacement trace would be essentially hnear up to the point at which the specimen fractures abruptly (see Fig. 4.5a). The plane strain fracture toughness Kic can be computed directly from the maximum load Pmax or stress a ax i e., the load or stress at fracture) and the initial crack size ao using Eqn. (4.7). 

The question now is how much nonlinearity is considered to be not excessive. Formally, the nonlinearity should not exceed that which would correspond to an increase in the initial (or physical) crack diameter (2ao) by the plane strain plastic zone correction factor i.e., by Iriy (see Eqn. (3.49)). Physically, it is acceptance of the fact that a plastically deformed zone would develop at the crack tip, and its presence is equivalent to a change in the effective crack length at the onset of fracture from Itto to Itto -I- 2riy i.e.,... 

Finally, the sensitivity of fracture aperture to block size and fracture length was analysed. Fracture networks with domain sizes of 5 m x 5 m and 10 mx 10 m revealed differences in median hydraulic apertures of less than 0.5 pm. Even with a block size of 15mxl5m and effectively infinitely long fractures, the change in median hydraulic aperture remained less than I pm. It can be concluded that the size of the REV determined for flow only is also suitable for mechanical calculations, and that, for the assumed spatial distribution and orientation of fracturing, fracture length has only a minor impact on the hydraulic aperture distribution. 

Tijki has also been determined at 2 m scale considering the real length of the joint. Differences with the previous simulation remain below 10 %. This could lead us to think that this factor is not very important for the equivalent mechanical behaviour. This result is consistent with the fact that no significant fracture length threshold effect has been shown on Tijn. 

A Cr specimen machined from PMMA plate has thickness B 6 mm, effective width W= 50 mm and effective crack length a = 25 mm. The force F at the loading pins increases linear with deflection until fracture occurs at F = 225 N. (1) Find Kjq] (2) find G c given E 3.2 GPa and 0.42 and (3) estimate the critical length of cradc for a wide plate... 

Furthermore, by considering differing initial defect sizes, Oq, it can be seen that the effective fracture toughness at failure will increase with the length of the initial defect, although the failure stress will decrease. 

A number of systems investigated as possible carbon fiber sizes are given in Table 9.8. Dauksys [24] attempted to apply a size to form a microductile region adjacent to the interface, which could act as a stress relief medium, a crack inhibitor/arrestor and also attempt to increase the effective transfer length of the fractured fibers. Dauksys, at best, applied a 0.9 /w solution of polyhydroxyether in Cellusolve to Thornel 50 carbon fiber (with the PVA size removed) and from composites prepared from Union Carbide ERL2256 resin,... 

Baghbanan, A. Jing, L. 2008. Stress effects on permeability in a fractured rock mass with correlated fracture length and aperture. International Journal of Rock Mechanics and Mining Sciences 45(08) 1320-1334. 

T. Lin, D. Jia, P. He, M. Wang, D. Liang, Effects offiber length on mechanical properties and fracture behavior of short carbon fiber reinforced geopolymer matrix composites, Mater. Sci. Eng. A 497 (2008) 181-185. 

A sufficiently small value of EF o/a. h indicates that the adherends exhibit only elastic deformation during the fracture. However, this does not mean that LEFM results can be used without any modifications. Instead, one needs to examine further the effects of loading the adherends in shear, and the influence of large deformations in the adhesive layer. While numerical approaches are required for a rigorous analysis of these effects, approximate approaches based on the concept of replacing the actual crack length, Oq, with an effective crack length, effeciive. are possible (Eqs. 2.12-2.15). 

Overflush. The purpose of the overflush is to displace add from the wellbore and push the acid volume forward, thereby increasing the penetration distance. When viscous acid is used, a large overflush can effectively increase the etched fracture length. The overflush is a critical step in the treatment design. A high rate is beneficial. 

Computation of the depth of a crack taking into consideration its length effect end the product thickness allowing to reduce the complementary error while measuring short cracks and fractures with their depth more then half the thickness from 20 - 100% to 2 - 5%,... 

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