Applied Research Of Proper Orthogonal Decomposition Method

Reservoir numerical simulation is one of the important means of modern reservoir engineering research,which can be used to understand the reservoir development process,evaluate the sensitivity and uncertainty,predict the reservoir performance under different production systems,and formulate the optimal development plan.However,some reservoir models established by actual oilfields may include tens of millions of grids,resulting in a large number of equations to be solved,which need to repeatedly call the reservoir simulator to calculate,and it is time-consuming.Therefore,in order to apply to the actual reservoir model,reduce the amount of calculation of the simulator,improve the speed of calculation is very critical.In this paper,model reduction technology is applied to reservoir numerical simulation to reduce the simulation time of reservoir simulator.The model reduction method can project the high-dimensional space into the low dimensional space while maintaining the input-output characteristics of the system.This technology first appeared in the field of automatic control and circuit system,and has been widely used in the fields of data simulation,classification,visualization and high-dimensional data compression.Proper orthogonal decomposition(POD)is a widely used method in nonlinear system model reduction.This method needs low computational cost,has good stability,and can maintain some basic properties of the original system.However,this method relies too much on the input parameters of the model,which reduces the simulation accuracy.Therefore,this paper extends the standard POD method program,adopts two-step POD algorithm to reduce the dependence on the input parameters,executes POD method to obtain the base matrix for each input sample,and then executes POD algorithm again for all the obtained base matrices to obtain the final reduced order base matrix.The dimension of the system is significantly reduced,the computing time is reduced,and the computing speed is improved.The simulation example shows that the two-step POD method can carry out accurate numerical simulation within a reasonable experimental range,and is superior to the POD method in terms of calculation accuracy and simulation time,which verifies the effectiveness and practicability of the method.