Publication D: Network model of porous media – Review of old ideas with new methods (Paper_D)
The paper takes up the old ideas of describing porous media with several tube and network models. The wellknown models received from literature gave a good concept of dewatering equilibria resulting in capillary pressure curves and pore size distributions (PoSD). However, numerical methods and measurement techniques were not sophisticated allowing to evaluate the models appropriately. In this work, a numerical method based on statistics is introduced to validate the network model of FATT from 1956: The porous filter cake structure is implemented as a matrix, which elements represent the pore size correlating with the capillary entrance pressure for each pore. The input for the calculations can be any mathematical approximation of a PoSD, which can be derived from capillary pressure tests or micro computer tomography (μCT) analysis of the filter cake. A procedure based on the concept of FATT is presented to generate dewatering equilibria for different applied pressures. Therefore, the elements of the matrix are checked to be ‘dewatered’ regarding to their size, position, the applied pressure level and the progress of dewatering. The network model known from literature is improved by implementing additional conditions for the description of physical phenomena, such as the formation of residual bridge liquid or hydrodynamic isolated areas. X-ray microscopy, mercury intrusion tests and laboratory desaturation experiments by using semipermeable membranes for capillary pressure tests are used to validate the pore size distribution. The different results are integrated into the matrix model as starting parameters. For the laboratory experiments, the PoSD is calculated from the measured capillary pressure curve, using the distributed tube model and the YOUNG-LAPLACE-equation on an equal basis to the established mercury intrusion analysis. However, with the tomography measurements, it is possible to determine PoSD using different defined geometry elements fitting inside the pore space. The force balance is evaluated at the pore entrance by using the wetting line of the pore throat. The direct measurement of the void geometry allows the calculation of the pressure distribution without the LAPLACIAN assumptions. In this way, the difference between experimental, measured and modelled PoSDs is emphasised to validate the old (and improved) ideas of network models describing porous media
This collection is open access and publicly accessible.