Application Of Reduced-order Model In Numerical Of Simulation Of Low Permeability Reservoir

With the development of the oil field,reservoir simulation has become one of the indispensable tools to assist the development of reservoir.The physical process in reservoir simulation like other disciplines is usually described by systems of deferential equations.And equations are usually solved by numerical solution considering the complexity of the problem.With the increasing dimension of equations,it becomes a great challenge for the optimization and history-match in the development of reservoir.Reduced-order model as a method which reserves the coherent properties of the system and reduces the scale of the problem,has been widely used in cutting-edge industries,so it might be meaningful to introduce the ideas of the reduced order model into reservoir simulation.This paper based on widespread investigation,taking low permeability reservoir simulation as a starting point,introduces the reduced order modeling methods in reservoir simulation.Fluid flow in low permeability reservoir does not abide by Darcy's law because the existence of the threshold gradient pressure.First,mathematical model in two dimension of oil and water is built in accordance with the practical situation.And the model is solved with finite difference method in full-implicit scheme.Based on that,the dimension of the equation system is reduced by projecting the original model on the reduced space spanned by the basis function with proper orthogonal decomposition.Through theoretical analysis and comparing the original model and reduced order model,it is displayed including the basic procedure of constructing the reduced order model and the advantages of reduced order model.Based on the above research,a method to deal with the snapshots based on centroidal Voronoi tessellation and its corresponding disadvantages are discussed.In the practical example,different cluster number is set for the clustering analysis in the snapshots for the purpose of obtaining the reduced order model and the corresponding influence on the accuracy for the reduced-order model is also discussed.The results indicate that reduced order model based on proper orthogonal decomposition could approximate the original model with enough accuracy and reduce the scale;Considering that the quality of reduced order model created from snapshots is not linearly dependent on the quantity of snapshots gathered,cluster analysis based on centroidal Voronoi tessellation could properly eliminate the redundancy of snapshots and improve the accuracy of the reduced order model.