The Study On Bound-preserving Algorithm For Solving Large-Scale Wormhole Propagation In Carbonate Reservoir Acidification

The in-depth research of complicated oil reservoirs makes challenges of reservoir simulation arise,such as multiple models,high resolution,complex grid structures,and long time spans.In the reservoir simulation,for most producing wells,matrix acidification will be carried out before production,during which the acidetched wormholes,i.e.wormholes,are formed.The formulation and expansion of the wormholes are generally simulated by mathematical models.As numerous uncertain factors exist and mathematical models vary,it is crucial to build and study appropriate wormhole models in realistic simulations.In addition,by adding acidic catalysts to the carbonate rock matrix layer which is rich in calcium carbonate material,chemical reactions lead to intense and rapid changes in the porosity of the matrix layer.Therefore,physical quantities such as pressure,concentration,and porosity may exceed their practical physical meaning.To constrain the physical quantities,a bound-preserving algorithm,namely the active-set reduced-space algorithm,is designed in this work.The new algorithm ensures the boundedness requirement of the solutions and also guarantees nonlinear consistency after fully implicit discretization.Finally,for two types of carbonate rock,robust and scalable solvers are designed in numerical simulation of reservoir matrix acidizing.The main contents are demonstrated as follows:1.A parallel,highly scalable active-set reduced-space algorithm is proposed for the single-phase flow compressible acidified wormhole propagation in porous media,and the algorithm is compared with the traditional inexact Newton method.Numerical results verify the active-set reduced-space algorithm guarantee the good properties of Newton method and can guarantee the actual meaning of physical quantities.In addition,this thesis is based on a family of mixed finite element methods for the spatial discretization and the implicit Backward Euler scheme for the temporal integration,to handle the combination of complicated flow physics and high resolution grids in their full complexity.Numerical experiments are presented to demonstrate the effectiveness and efficiency of the proposed algorithm,and the algorithm developed is scalable on the supercomputer for this nonlinear systems with more than several hundreds of millions of unknowns.2.For the coupled mathematical model of the propagation of carbonated hydrochloric acid wormhole in porous media,a constrained pressure residual preconditioner is introduced,combined with a nonlinear complementary solver that ensures physical implications and a highly parallel domain decomposition method.All subsystems in the constrained pressure residual method are calculated using the restricted additive Schwarz preconditioner,and the corresponding subdomain solvers are constructed by LU decomposition.In the first stage of the constrained pressure residual preconditioner,accurately identifying update elements has a significant impact on the efficiency of the overall algorithm.The numerical experiments in this thesis show that a class of constrained pressure-velocity residual methods is effective and robust for wormhole propagation problems in two-or three-dimensions.By using tens of thousands of processors on a supercomputer,the simulation of nonlinear complementary solvers with this preconditioner is parallel and scalable.