The Application Of The Shortest Path Algorithm In Pore Network Model

It is of great significance to study the morphology and topology of pore space in porous media at the pore-scale for predicting macroscopic flow properties of porous media.Alongside many researches on microscopic flow simulation carried out world-widely,the pore network modelling?PNM?based on SEM or CT images is one of the most popular and efficient approaches for simulating phase fluid flow at pore-scale.It is evident so far that within any pore network model,no matter which approach is utilized to generate,there exists a lot of redundant network elements?i.e.pore-bodies or pore-throats?.In the prediction of single-phase flow based on PNM,if the size of the digital rock is large in volume,these redundant network elements could deteriorate the simulation efficiency massively due to the big cost on the massive computation and storage capability,and further causes it impossible to model fluid flow through complicated samples that should be sufficiently large to have representative elementary volume.Therefore,on the basis of pore-level network model proposed by Jiang^[1]et al.,this work proposes an effective method for identifying dominating flow paths in single-phase flow from pore network models,analyzing characterization of the essential geometry that has impacts on fluid flow notably,and removing redundant network elements.Firstly,in this thesis,based on the shortest path algorithm in graph theory,I regard PNM model as a graph,in which nodes in PNM are thought of as vertices of the graph,while bonds as the edges of the graph.In particular,five controlling parameters are selected as the possible"length"?or weight factors?of the graph edges.A heuristic algorithm is used to apply the identified shortest path to any PNM to obtain the shortest path pore network model?SPNM?with significantly reduced network elements but retaining the main flow channels of single-phase flow.And the numerical simulation of fluid flow based on SPNM model is carried out to predict absolute permeability.With the coupling between a PNM and a graph,from the perspective of permeability,in order to match the original PNM and SPNM,namely the two network models are equivalent or approximate,how to quantify the appropriate"length"of the corresponding edge is crucial.To validate this method and to show its effectiveness,a set of rock samples with different porosity ranges have been selected and studied in this work,and five parameters related to the micro-geometry and pore topology of porous media are chosen as the"length"of the edge of the graph,separately.The numerical results show that the absolute permeability of the four SPNMs for most samples can reach to around 40%of their absolute permeability calculated based on PNM,and the corresponding SPNM gives the best performance when the selected"length"is closely related to the distance between two pore bodies,and the approximation can reach to approximately 70%in some cases.Besides,for most samples,when the combination of two controlling parameters are used as the"length"of the edge,the absolute permeability of the SPNM extracted can reach to about 75%of their absolute permeability calculated based on PNM.Secondly,the differences in permeability,porosity and pore size distribution between the PNM and the SPNM are compared and analyzed,and the effects of selected parameters on macro-permeability are investigated as well.A phenomenon of imbibition in a sandstone 4D rock images is also briefly discussed.Finally,with the idea of principal component analysis,the relationship between permeability and these geometric and topological parameters of pore space which have important influence on fluid flow is established through principal component regression.It provides a reliable and accurate empirical formula for calculating permeability.