Change, rate threshold

Based on a limiting component constraint, an exchange probability kernel is developed for multi-component systems. The LDF-type model with the kernel is continuous with time and axial direction. Two tuning parameters such as concentration layer thickness and function change rate at the threshold point are needed for the probability kernels, which are not sensitive to problems considered. 

In this study, the generalized adsorption rate model involving two exchange possibility kernels (i.e., sum and product kernels) is extended to multi-components systems. For the possibility kernels, two tuning parameters, (i.e., the concentration thickness and function change rate at the threshold point) are required. These tuning parameters are found to be insensitive to the problems considered. 

A number of investigations concerning the effect of added electrolytes and change in the solvent polarity have been reported (see ref. 25 pp. 17-19 for a more detailed account). The addition of neutral salts causes a large increase in the rate of reaction in both the one and two-proton mechanisms. In addition, the effect of increasing the water content in a dioxan-water solvent, provided that the concentration of water is above a certain threshold value, also produces a large increase in... 

The purpose of the various Ingredients Is to provide desirable fluid properties at different times 1n the treatment. For example, the crosslinker system may be designed to have a low reaction rate while the fluid 1s at low temperatures (such as those found 1n the mixing tanks and before the fluid has traveled very far Into the fracture). Then as the fluid temperature Increases above a threshold value, the crosslinking rate accelerates and changes the rheology of the fluid to one more desirable 1n the low-shear, but high-temperature, environment of the fracture. 

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