11/5/2023 0 Comments XnConvert 1.70 Final![]() ![]() ( 1) and ( 2) are another way to predict permeability from structural properties than the Kozeny–Carman equation. Since the flow rate is proportional to the cube of the fracture aperture, this relationship between flow and aperture is well-known as the “cubic law” 4– 7.Įquations ( 1) and ( 2) are only ways to obtain a simplified analytic solution to describe the relationship between the flow and structures. Using Darcy’s law, a representative permeability, K HP, for the capillary can be calculated depending only on the radius: This is an exact solution for the flow, can be derived from the (Navier–) Stokes equations, and is another way of expressing the relationship between structure and flow. The Hagen–Poiseuille equation is a physical law that describe a steady laminar flow of a viscous, incompressible, and Newtonian fluid through a circular tube of constant radius, r. ![]() Let us also consider flow in a channel from an inlet to an outlet. These additional parameters can only be determined by fitting, which is not the best way to go about flow prediction based on structural information. The correlation has been modified to represent real phenomena by adding parameters such as fractal dimension, and tortuosity 2. Therefore, the Kozeny–Carman equation does not always work. However, no matter how many voids there are, if they are not connected, water cannot flow. This Kozeny–Carman equation provides a relationship between structure and flow. The porosity–permeability correlation has been studied extensively in the literature to estimate permeability using porosity (so-called Kozeny–Carman equation) 2, 3. In contrast, porosity is a parameter that is often used to characterize the structures. Permeability cannot be determined only from structure data, and needs to be obtained from laboratory experiments or numerical fluid flow simulations. Permeability is a key parameter for examining flow phenomena in porous media 1. It has been a long-term scientific challenge to predict flow behavior of porous media from structural properties. It is also attracting attention to understand flow behaviors in complex fracture networks in developments of natural resources, as in the case of shale gas and geothermal developments. In particular, recent miniaturization of artificial devices has led to the need for understanding and controlling flow in finer structures. ![]() This method can easily derive the flow phenomena based on the information of the structure.įluid flow processes are ubiquitous in the world, and most are governed by the geometry and nature of the surrounding structures. The results suggest that the persistent homology can estimate fluid flow in fracture network based on the image data. Synthetic 3D fracture network patterns and their direct flow simulations are used for the validation. We propose a method to estimate permeability in fracture networks from parameters of persistent homology. In this study, we focus on connectivity and apertures of flow channels detected from persistent homology analysis. Although persistent homology is useful for revealing the topological and geometric information, it is difficult to interpret the parameters of persistent homology themselves and difficult to directly relate the parameters to physical properties. A state-of-the-art tool in topological data analysis is persistent homology, which is expected to summarize quantified topological and geometric features. Note that PDF files opened in XnView software are rasterised by Ghostscript at the resolution set in the XnView application: the resolution of your file read in another software is 300 DPI.Topological data analysis is an emerging concept of data analysis for characterizing shapes. I was going to extract the four pages and attach them for you in the expectation that you would be able to use those, but encountered the problem that even compressing the output PDF file using JPEG compression with a low quality setting, the individual page file sizes are much larger than the file size of the four-page PDF that you provided.Ĭould you please tell me how you compressed the file to which you linked, and whether you still need a solution to the original problem? For some reason the file properties shown in my screenshot above indicate that the file is not compressed, whereas the uncompressed size of the first page alone is >1.0 GB. I have opened your file on another laptop with much more free memory, and although operations are very slow due to the large pixel dimensions, I have not encountered any other obvious issue. ![]()
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