Research On Efficient Solver In Numerical Simulation Of Fine Reservoirs

With complex reservoirs(low permeability,high water content,complex stone lithology,etc.)are being further explored and enhancing oil recovery technologies are widely used,mathematical models for describing reservoir,become more and more complex;additionally,reservoir geological models tend to use fine cells,unstructure meshes,more wells to meed demand for accuracy,these factors cause Jacobian linear equations of porous medium model are large and with bad condition.In fully implicit reservoir simulation,solving linear algebraic equations is a major bottleneck,which accounts for 70%?80%of total simulation time.Moreover,as the problem size increases,the proportion will become larger.Designing efficient algorithms to improve the speed of solving linear algebraic equations is one of efficient ways to reduce the simulation time.As hardware architecture of computer tends to be heterogenous,the solution that many-core processors are used to accelerate CPU cores to handle with computing task plays an important role in scientific computing,and sets off a new wave of high performance heterogeneous parallel computing.This thesis focuses on the standard black-oil model and designs efficient serial and parallel algorithms for solving Jacobian linear algebraic equations arising from fully implicit discretizations of the black-oil model.Firstly,we analyze several commonly used decoupling methods,including ABF method,Quasi-IMPES method,True-IMPES method,for the strongly coupled dis-crete black-oil models,compare decoupling effect of these methods,and observe the elliptic nature of pressure equation.We find that the ABF method can weaken the coupling among physical variables(pressure and saturations),also help to cluster eigenvalues of Jacobian matrices and speedup the convergence rate of the outer iter-ative method in return,but it destroies elliptic nature of pressure equations,making solving pressure equations more difficult;Quasi-IMPES and True-IMPES methods mimic the ideas of IMPES method,and to obtain an approximate elliptical pressure equations via some algebraic operations to Jacobian linear systems,but they do not reduce the coupling among the variables.For pressure equations obtained by different decouple methods,we solve them with the classic AMG,VMB aggregation AMG,and pairwise aggregation AMG methods,respectively,and compare performance of differ-ent AMG methods.Based on above analysis,we combine the True-IMPES method with the classic CPR preconditioner to form a splitting preconditioners,and use the pairwise aggregation AMG method to replace the classic AMG method to solve the pressure equation,the new preconditioner has a 50%performance improvement over the combination of ABF method and classic CPR preconditioners.Secondly,since cell-size of reservoir simulation tends to be small,the finer the model,the worse condition number of Jacobian matrices,which bring great difficulties to solve linear algebraic systems,thus it is necessary to develop efficient linear solver for larger scale Jacobian linear systems.Motivated by the ABF method,which can help to cluster Jacobian matrix eigenvalues and partially weaken the decoupling among physical variables,and idea of auxiliary space correction method,we propose a robust,efficient,memory saving splitting preconditioners.The splitting preconditioner uses the ABF method as the left preconditioner,and uses a multi-stage subspace correction method as the right preconditioner BASP.The right preconditioner is specifically designed with the nature of Jacobian matrices decoupled by the ABF method,and its first stage is to approximately solve the saturation equation by the block Gauss-Seidel method to eliminate high-frequency part of the error.For solving elliptic pressure equations with strong discontinuous coefficients in the second stage,we use the AMG preconditioned Krylov methods to solve it to certain accuracy,and eliminate low-frequency errors controlled by pressure equation;finally,we solve Jacobian linear system in the whole space by block Gauss-Seidel method.A large number of field examples,including a ten-million-cell reservoir problem,were simulated on a desktop computer,the splitting preconditioner acclerated by VFGMRES method is about 2?3 times faster than commercial simulator,and numerical results prove robustness and effectiveness of the proposed method,and show the benefits of fine-scale petroleum reservoir simulation in oil recovery.Finally,this thesis's another goal is to design an efficient parallel linear solver for Jacobian linear algebraic equations on CPU-GPU heterogeneous systems.Archi-tecture of supercomputers are becoming increasingly complex,most supercomputers are designed with multi-core,many-core,large cache,high bandwidth communication structure,and high-speed I/O hardwares,which make computer more powerful.How to build a modern high-performance applications to take advantage of fea-tures and resources of heterogeneous computer systems are well worth studying.First-ly we design a BHYB sparse storage format to meet GPU memory access character-istics,the speedup of SpMV based on BHYB format reaches 19x,and 30%faster than Nvidia's state-of-the-art HYB format;Secondly,with proposed parallel algo-rithms based on graph coloring and dual intensive parallel strategy,we design a high parallelism and good scalability BILU(l)method,the average speedup of triangular decomposition and solution phases of BILU(O)are 6.27x,9.46x,respectively;Thirdly,combined heterogeneous computer and parallelism of each part of AMG algorithm,we design a heterogeneous parallel UA AMG method.Based on the above parallel modules,we designed a parallel CPU-GPU heterogeneous BCPRP preconditioner.Nu-merical experiments show that:the parallel preconditioner is very robust,when com-pared with the serial improved BCPRP preconditioner,the parallel BCPRP preconditioner has a 3.Ox speedup in solution phase,and the whole simulation time is 50%of the serial BCPR preconditioner.Additionally,we develop a distributed parallel reservoir simulator on the "Tianhe-2" supercomputer,the simulator is capable of simulating hundred million cells,and greatly improve the efficiency of large scale simulation.The distributed parallel reservoir simulator has a good scalability when using less than one thousand cores.However,the scalability is not ideal when 10,008 CPU or more cores are used,the linear solver need a further optimization.