چكيده به لاتين
Flow simulation in porous medium has various applications in the analysis of geological phenomena and oil reservoirs. One of the major challenges in this field is to determine the macroscopic properties of porous media such as permeability. In the past, determining these properties was only possible through laboratory methods. However, with the advances made in the field of imaging, it became possible to reconstruct the geometry of the porous medium with high accuracy at the pore scale, which became the starting point for the numerical simulation of the flow at the pore scale. Various computational fluid dynamics methods can be used to simulate the fluid behavior on the generated images in the pore-scale. In the present study, Lattice Boltzmann method is used. This method has many advantages such as easy coding, simple dealing with complex boundaries, high ability to simulate multiphase flows and high adaptability to parallel processing algorithms.
The achievements of the present study can be divided into two areas, analytical analysis and numerical simulation. In the field of analytical analysis, first, due to the importance of the no-slip boundary condition in simulating the pore-scale, the error of this boundary condition was reduced as much as possible in the Boltzmann method. In this regard, based on an interpolation, it was found that the magic parameter 0.21 in the Lattice Boltzmann method creates the least error in geometries with complex boundaries. Also, a very simple model was presented to analyze and estimate the imaging error and its effect on the simulation results, and then the amplitude of the numerical simulation error was compared with the amplitude of the imaging error. It was found that the simulation error amplitude is often a subset of the imaging error amplitude, and by changing and adjusting the magic parameter in the LBM, in addition to reducing the simulation error, a suitable estimation of the effect of imaging error at different resolutions on simulation results, could be obtained. Then, the results of LBM and Navier-Stokes methods in basic geometries were compared and the reasons for the differences in the results of simulations were investigated.
In the numerical simulation aspect, a C ++ code was first developed under the PALABOS library based on the LBM, which is capable of processing micro-tomographic images and determining the properties of porous media such as permeability, non-Darcy coefficient and porosity of porous media. Similar calculations were performed in the OpenFoam open source program to compare the results of the Boltzmann network method with the Navier-Stokes method. Also, for accurate comparison of results in horizontal and diagonal channels, a set of scripts was developed to move information between PALABOS and OpenFoam and to form a comprehensive and integrated program for flow simulation in pore-scale.
Then, two samples of micro-tomography images in different qualities were simulated using two different methods. In the laboratory sample, permeability was equal to 1952D with LBM with the magic parameter of 0.21, while the Navier-Stokes result was equal to 1795D and according to the experimental process permeability was equal to 2279D. It can be seen that the results of the LBM under these conditions are closer to the experimental results of the sample. Also, the interval of permeability changes due to imaging error with the help of changing magic parameter was [2461-1645], which the experimental results are exactly in this interval and confirm the achievements of the analytical part. It was also found that the reason for the difference in the results of the LBM and NSE methods, which can be up to 35%, is only related to the type of no-slip boundary condition and by selecting the magic parameter in the interval [0.01-3/16], NSE results can be reconstructed. However as mentioned, Navier-Stokes results are not necessarily better answers. Also, by magnifying the Beadpack image, the amount of permeability was calculated in different resolutions. The results revealed that the least change was made in the magic parameter 0.21, so that up to three times the magnitude of the sample's image permeability is exactly equal to 5.90D and it reached 6.25D when the image was enlarged for the fourth time.
