The Determination of Radon Diffusion Coefficient and Radon Speed Advection in the Conditions of Instantaneous Source with Diffusion-Advective Transfer in Rocks

Experimental determination of diffusion parameters in the upper part of geological section (presented by clayey weathering crust) was made by a point instantaneous source method in a diffusion mode and a linear instantaneous source diffusion-advective mode. The results obtained by these methods showed a fairly good coincidence of the obtained diffusion characteristics of the medium. The time to determine the diffusion characteristics of the medium is significantly reduced by more than an order of magnitude when using the advective method. This is a prerequisite for the widespread use of methods for determining radon hazard based on measurements of the vertical distribution of radon volume activity in the upper part of the geological section.

On the regularization problem with functions generalized

In physics and mathematics, there are idealized concepts exist, such as the density of a material point, the point density, the intensity of an instantaneous source, etc., These are necessary for real engineering and physical problems. Treating this type of concepts correctly is done with the theory of generalized functions, it´s properties are outside the framework of the properties of conventional functions. The concept of generalized function is a generalization of the conventional concept of function and encompasses functions that contain singular points. In order to mathematically treat this type of functions or functions, it is necessary to introduce regularization processes. In this article we analyze the process of regularization of singular functions with generalized functions and compare the integrity of the function before and after the regularization. Keywords: Generalized functions, distributions, regularization, information

Finite Horizontal Well in a Uniform-Thickness Reservoir Crossing a Natural Fracture Normally

Summary The instantaneous source solutions of Prats and Raghavan (2012) and the method of images are used to develop analytic expressions for the pressure distribution in a three-region composite reservoir of finite thickness produced by a finite-length horizontal well that is oriented perpindicular to the interfaces. The composite reservoir is assumed to be infinite in its lateral extents; the outer regions represent the reservoir, and the central region represents a thin natural fracture of relatively high permeability. In most of the cases considered, the well is completed in all three zones. The computational scheme is shown to be both viable and robust. The Shanks (1955) transformation is used to accelerate convergence. Pressure traces are logarithmic in time at early and late times for any well configuration examined here. Early-time pressure characteristics are similar to those discussed in Prats and Raghavan (2012). The duration of the early semilogarithmic responses is mediated not only by the presence of the higher-permeability natural fracture, as before, but also now by the interaction of the upper and lower boundaries with the well. Late-time semilogarithmic responses, however, are distinctly different. Their slope is inversely proportional to the product of the formation thickness and the arithmetic average permeability of the two regions that sandwich the fracture. This result holds even when the well does not cross the natural fracture. We expect this conclusion to apply to a composite system consisting of more than three regions. Observations concerning the late-time slope represent the central finding of this study. A relationship is given for the late-time performance of any horizontal well in terms of that of a vertical well with a constant pseudoskin. Pseudoskin equivalents are reported for all cases discussed.