Improvements Of Pattern-based Multiple-point Geostatistics Modeling Algorithm

There are two methods for early reservoir geological modeling: two-point geostatistics and object-based methods.Two-point geostatistics,which is easy to satisfy well data,belong to pixel-based simulation methods.However,this method is limited to two-point statistics,and it is difficult to reproduce the connectivity of complex geological structures.Object-based method is used to simulate complex geometric reservoir structural units,such as curved channels.This method directly determines geometric shape parameters according to river geological characteristics,and simulates a complete geological object(such as river course)at a time.This method is difficult to satisfy the condition data.For a small amount of discrete condition data,it can also make the model conform to the constraints of the condition data by post-processing correction,but it is very difficult to cope with the dense condition data of well.Combining the advantages of two-point geostatistics and object-based modeling methods,multipoint geostatistics can not only satisfy well data,but also can simulate complex geometry.After 30 years of development,multipoint geostatistics have achieved fruitful results.ENESIM algorithm firstly combines the advantages of two-point geostatistics and object-based methods.Taking training image as prototype model,ENESIM algorithm can not only reproduce the complex geological structures,but also easily satisfy well data.It provides an important idea for the development of multipoint geostatistics.Snesim uses data templates to scan training image,then extract and store probabilities of all data events in a search tree.So the modeling efficiency is greatly improved.However,the search tree occupies a lot of computer memory.To solve the problems of MPS computing efficiency and memory,scholars and experts improve multipoint geostatistics from the following ideas.The first improvement is applying pattern-based modeling method,which simulates many grid cells in one step.This method has two advantages.Firstly,it can store multiple points in a data pattern for reducing memory overhead.Secondly,simulating a pattern is more efficient than simulating a cell one-step.Simpat is the first pattern-based modeling algorithm.This method queries the mostly similar data pattern from the pattern database,then predicts and covers the unknown part and finally freezes all nodes of the data event.The improved algorithm Filtersim uses filter to cluster patterns,and further improves the modeling efficiency.DisPat algorithm uses MDS to reduce dimension and uses kmeans to cluster the patterns of database,which improves the modeling efficiency.The second idea is to use a single grid node as the basic modeling unit,and use more advanced data structure to store the probability of training image.Taking IMPALA as an example,the advantage of combining list structure with index tree structure is that it can improve modeling efficiency by parallel computation and avoid occupying too much computer memory.The third improvement idea is to simulate one cell by one step with constraining the data template.Taking the Direct Sampling as example,this method scans training image to get the most similar pattern with the data event,and then assign the center node value of the pattern to the grid node as the target estimation value.The efficiency of DS is high,but the disadvantage is that the parameters of the algorithm are difficult to adjust.The fourth idea is to introduce other technologies(such as image processing and analysis),take image quilting as an example.This algorithm uses GPU parallel computing,which has high efficiency.The disadvantage is that this algorithm lacks the support of statistical theory and it is difficult to fuse conditional data.With the development software and hardware of computer,in addition to the optimization of the algorithm,domestic and foreign scholars regard the parallelization of CPU and GPU as the research orientation of optimizing and improving the multipoint geostatistics modeling algorithm.In this paper,three algorithms,including PSCSIM,LSHSIM and ASNMI,are proposed to solve the three main problems of efficiency,memory and non-stationarity.PSCSIM uses adjacent equidistant resampling to reduce dimension of patterns and to cluster them,which speeds up the modeling efficiency.LSHSIM introduces local sensitive hash retrieval technology to hash data pattern,which greatly improves the modeling efficiency.ASNSIM integrates MDS and kmeans,divides non-stationary training images into several parts objectively,and then completes non-stationary modeling.PSCSIM analyzes the basic principle of multipoint geostatistics modeling Simpat,and finds out the efficiency bottleneck of process of calculating the similarity between data events and pattern.Based on above concept,an idea of reduced-dimension pattern is put forward.The method of adjacent equal interval resampling is used to reduce the dimension of pattern,which not only retain multipoint statistical information,while reducing the dimension of pattern effectively.Finally,a large number of pattern databases are clustered to build pattern cluster.Comparing PSCSIM with Simpat,Snesim and Filtersim,the test results show that PSCSIM can greatly improve the calculation efficiency and effectively balance the calculation efficiency and memory occupation on the basis of guaranteeing the modeling quality.Based on the understanding of the inherent relationship between local anisotropy and spatial non-stationarity,an ASNSIM algorithm is proposed to quantitatively characterize spatial non-stationarity based on local anisotropy.Combining MDS analysis and kmeans clustering,ASNSIM reduce dimension of all sub-regions of training image by its rose.And then the non-stationary training images are automatically partitioned.The results of the partitioning are objective and true.The sub-regions are stationary internally,and the sub-regions are independent of each other.Finally,the non-stationary modeling experiment of fracture network is carried out by using ASNSIM algorithm.ASNSIM can reproduce the spatial non-stationarity of the training image well,for non-stationary modeling have a very good reference!Based on p-stable local sensitive hashing technology,a multipoint geostatistics modeling algorithm LSHSIM is proposed.Algorithm LSHSIM uses a locally sensitive hash to compute the feature vectors of the data pattern and maps them into a hash table.When searching for the most similar pattern of data event,the pattern with the same hash value of data event is found from the hash table firstly,and then the most similar data pattern is found from the target hash value data patterns to cover the data event in the area to be evaluated.Procedure mentioned above is one step simulation.By comparing Simpat,Filtersim,DisPat and LSHSIM,LSHSIM not only saves computer memory expenditure,but also has the highest computational efficiency.Through parameter sensitivity analysis,it provides basis for obtaining optimal modeling parameters.