Lattice Boltzmann Modelling For Fluid Flow Based On Micro-structure Characterization With Multi-energy CT Reconstruction

Multiple macroscopic permeability characteristics of porous media depend on themicro-structure and compositions to a large extent. Therefore, it is highly important to applysuch an approach to investigate the fluid flow through porous media for unveiling the flowmechanism and exploring unknown flow patterns at micro-structure scale. Currently thistopic is highly novel and resulting in a flurry of activity among the international academic andresearch community.The Lattice Boltzmann method has recently attracted considerable attention in fluid flowsimulations in porous media with the advantages of simple calculation, intrinsic parallelismand easy implementation for boundary conditions, which can describe the microscopic fluidparticles movement in an extremely simplified way and at the macroscopic level which alsocan give a correct average description of the motion. The micro-structural details of theporous media are the foundation for the fluid flow modeling, and the CT reconstructed imagesof the porous media are the foundation for the micro-structure characterization. Consequentlyin order to determine these properties, the CT reconstruction of the porous media samplesmust be carried out first, followed by the extraction and determination of the micro-structuredetails based on the CT reconstructed images. Finally the novel Lattice Boltzmann methodwill be used to simulate and analyze the fluid flow in the porous media samples.For the CT reconstruction, the traditional X-ray absorption CT imaging technologycannot be used to distinguish the sample details for weakly absorbing materials which aremainly composed by light elements such as soft tissue and low Z materials, because thecontract and resolution of these kinds of materials is too low to be distinguished. However, the X-ray phase retrieval CT imaging technology has overcome the deficiency of thetraditional absorption CT technology from the mechanism, which is capable of imaging theweak absorption and low Z materials successfully. Therefore, the X-ray phase retrieval CTimaging technology will be used to reconstruct the porous media, which can providesufficient details for the subsequent micro-structure characterization.For the micro-structure characterization, the traditional image segmentation methodbased on the CT reconstructed images under single energy will lose the small scale structureinformation below CT resolutions. In addition, for a sample which was composed of severalmaterials, when the X-ray absorption and refractive index of two compositions are quiteclosed, they could not be separated by the image segmentation method. In view of this, aDCM (Data Constraint Model) micro-structure characterization method based on multi X-rayenergies has been developed to predict the micro-structure distributions. This method cangenerate volume fractions of the compositions in each voxel, and the small scale structurebelow CT resolutions will be included into these volume fractions. Therefore, this methodwill be used to characterize the micro-structure of porous media to provide more reliableinformation for the following fluid flow modelling.Traditional Lattice Boltzmann methods for simulating fluid flow are based on the0/1style voxels, which are obtained by image segmentation method. The0/1style refers to thefact that each voxel was used to represent either full void or no void. When the voxel ispartially void, the traditional Lattice Boltzmann method will not be applicable. In order toimprove the traditional Lattice Boltzmann method, a new parameter was proposed, which iseffective percolating fraction. This fraction is the total reflection of the permeabilitycharacteristics for each voxel and varies with different voxels. Finally, a partially percolatingLattice Boltzmann model has been proposed based on the effective percolating fractions.In order to demonstrate the correctness and stability of the new partially percolatingLattice Boltzmann model, the parallel walls flow and rectangle duct flow have been simulated.The simulated results have been used to compare with the analytical solutions, and they are instrong agreement with each other. When simulating the fluid flow in real world porous media by the partially percolatingLattice Boltzmann model, one of the most important things is to convert the LatticeBoltzmann model units to the physical units. Therefore the Reynolds number was used toconnect the model units and physical units and the relationship between them also has beenobtained.Finally, the partially percolating Lattice Boltzmann model was used to simulate the fluidflow in two real word samples which are tight sandstone and sandstone, and the velocitydistributions of these samples have been obtained. Based on the velocity distributions, thebulk permeability of the samples was calculated. As anticipated, the bulk permeabilityincreases with the effective percolating fractions of calcite. The bulk permeability of thetight-sandstone is more sensitive to the effective percolating fraction of calcite than forsandstone. That is, fine flow paths in calcite have a greater influence on tight-sandstone thanon sandstone. Flow in calcite phase in sandstone makes an insignificant contribution to thebulk permeability. The sandstone has a permeability value up to two orders of magnitudegreater than that of the tight sandstone. In relation to bulk permeability, flow in the calcitephase is essential for tight-sandstone, whereas it could be neglected for sandstone.