Patent Application: US-201615204249-A

Abstract:
the present disclosure describes a method that improves the long - range geobody continuity in multiple point statistical methods , wherein the coarsest multi - grid level cells are simulated in a regular path , and the subsequent level cells are simulated in a random path as usual . the method is general and is applicable to different cases : such as hard data conditioning , soft data conditioning , non - stationarity modeling , 2 or more than 2 types of facies modeling , and 2d and 3d modeling . the method is particularly useful in reservoir modeling , especially for the channelized systems , but can be generally applied to other geological environments .

Description:
the mps facies modeling method proposed by strebelle is increasingly gaining attention in the petroleum geological modeling community . mps models reproduce the geological patterns and also are flexible in data conditioning since they are based on a pixel - based algorithm . one issue of the current mps algorithm , however , is that the long range or larger scale sinuous geobody ( e . g . fluvial channel ) continuity cannot be accurately reproduced . discontinued channels are generated in mps models even though they do not exist in the training image . the resulting blind end channels will negatively impact predictions of reservoir connectivity and reservoir flow performance . to reproduce the large scale pattern continuity , daly and hu proposed to use a unilateral path on all grid cells . this method improved channel continuity , but reduced uncertainty ranges resulting from deterministic path and also it could not accurately condition model realizations to hard data . as another possible solution , strebelle and remy proposed a re - simulating method . they identified the nodes simulated with a limited conditioning data and re - simulated them . this method required several iterations of re - simulation to complete a realization . thus , it consumed more cpu time . we propose a novel approach herein to address the long geobody continuity reproduction problem in mps . this disclosure addresses the geobody continuity and hard data conditioning issues from one or more of the following aspects : 1 . the regular path is used on the cells at the coarsest level of the multiple grid system and the random path is used on the rest of cells . this method significantly improves geobody continuity in mps facies simulation . a unilateral or bilateral regular simulation path can be used , or the path can be regular in one axis and random in others , but this may be less preferred . 2 . in the lateral direction , the regular unilateral path can follow i or j direction , and it has been proven that they produce equally much improved geobody continuity for unconditional simulations . 3 . in the vertical direction , an improved vertical continuity can be achieved by reducing multiple grid level in the vertical axis ; hence it increases the number of cells ( along that axis ) using the regular path since the regular path is only applied to the cells at the coarsest level of multiple grids and in the vertical direction there are now more cells . 4 . using the regular path following the minor geobody continuity direction resolves the hard data conditioning issue related to the regular simulation path . 5 . we demonstrated the claimed method works for modeling 2d and 3d cases , modeling non - stationarity and modeling the geobodies with various major continuity directions . the disclosure thus helps to build more geologically realistic facies model , which can provide better guidance in drilling new wells and production optimization . in geostatistical simulation algorithms , the random simulation path is typically used . see fig1 illustrating a random path ( right ) and a unilateral regular path ( left ). fully regular path is not used because 1 ) it will reduce the uncertainty variations ; 2 ) an error introduced at the early stage of the simulation path will be propagated to the subsequent cells in the model . in geostatistical simulation algorithms , multiple grid schemes are usually used , as shown in fig2 . red cells are at the coarsest multiple grid level ( multiple grid level 3 ), yellow cells are at the intermediate multiple grid level ( multiple grid level 2 ) and grey ones are at the finest multiple grid level ( multiple grid level 1 ). normally , the stochastic simulation is performed first at the coarsest level and then move to the cells at the next level of the multiple grids . at each grid level , the cells are simulated one by one in a random sequence . instead of the random simulation sequence , in this disclosure we used a regular unilateral path on the coarsest multi - grid and used a random path for the rest of multi - grid levels . this is referred to as a “ regular - random - hybrid path ” or just “ hybrid path ” herein . the intention is to capture the large scale continuity at the highest level of the multiple grids , in the meantime to maintain the uncertainty assessment capability on the lower level multi - grid cells . although the work presented herein used a regular unilateral path , such as in fig4 . 2 or 4 . 3 , there are many different ways of defining a regular lateral path for the coarsest grid . see e . g ., fig4 showing a random path , along with a variety of regular paths , including unilateral regular row - by - row , column - by - column , and partially regular patterns including random rows , random columns , and random row within a random column . although not shown in fig4 , one can also travel back and forth across the grid , rather than traversing to the left side each time a row is initiated . one could also travel up and down , rather than proceeding to the top for each column . further , one can also travel in a diagonal line across the grid , and the diagonal lines can also go back and forth rather than in a single direction . fig5 shows regular simulation paths along the three available axes — i , j and k , wherein the i and j axes are along the lateral directions and the k axis follows the vertical direction . in fig6 , we can see the channel continuity in the training image is very well reproduced in the regular - random - hybrid path case comparing to the typical random path case that has previously been used . fig7 shows 5 different realizations using a hybrid path and the average map ( lower left ) of 30 realizations , which gives the probability map of the channel facies . the facies probability map indicates the channel spatial distribution is relatively uniform or stationary , as expected for unconditional simulation without hard or soft data constraint . this map should be uniform with a large number of realizations . fig8 shows that using the path following i or j direction gives equally improved channel continuity in the unconditional simulation cases . the reason is that the regular path , either along i or j , results in more conditioning data available in the search template , which makes it easier to find pattern replicates from the training image search tree . one issue of regular path is that it creates problems in conditioning the hard data ( see the green ellipses in fig9 ). two factors can cause these problems : 1 ) the unilateral path moves along a row of cells from one side to the other . it can potentially create conflicts between training image pattern and hard data ; 2 ) the major channel continuity is along axis i ( in this example ), which increases the chance of conflicts to model the long features if the unilateral regular path follows the i direction . we proposed that the regular path should therefore be along the minor continuity direction , which is along axis j in this case . we achieved perfect well data conditioning by following the minor continuity direction ( perpendicular to channel direction ) as well as much better channel continuity . examples demonstrating this are shown in fig1 . if the channel orientation is not along i or j , but is instead at a 45 degree angle , both i and j regular paths give equally improved channel continuity . see e . g ., fig1 . however , by employing a diagonal grid pathway , we would still be able to have a pathway perpendicular to the major continuity direction . although these simulations have not yet been run , we predict it would improve the results in a manner similar to that shown in fig1 . fig1 shows a three facies example , wherein the use of a fully random simulation path gives a realization with far poorer continuity than the use of hybrid simulation path does described herein . fig1 shows the applicability of the proposed method to model non - stationary cases . the non - stationarity of a mps model can be characterized through spatially varying channel sand proportions , orientations and widths . they are integrated with stationary training image to generate facies model realizations ( the bottom 2 figures ). the hybrid path approach improves the model quality when non - stationary regions exist . for 3d cases , our studies indicated that we needed to include more cells in the regular path in order to improve the vertical geobody continuity . we proposed to reduce the number of multiple grid levels in the vertical direction , say from 3 to 2 or 1 . reducing the multi - grid level to 2 or 1 increases the numbers of cells in the vertical axis , thus improving continuity . in fig1 the colored cells are at the coarsest level of the multiple grids , hence those cells will follow the regular path . the left figure has 3 multiple grid levels along k direction ( i . e ., there is one cell at the coarsest grid level every 4 cells along k ); the middle figure has 2 multiple grid levels along k direction ( i . e ., there is one cell at the coarsest grid level every 2 cells along k ); the right figure has 1 multiple grid level along k direction ( every cell along k is at the coarsest grid level ). the modeled channel continuity is improved using the proposed method , see fig1 and 16 . the following references are incorporated by reference in their entirety for all purposes : caers , j ., zhang , t ., multiple geostatistics : a quantitative vehicle for integrating geologic analogs into multiple reservoir models , in grammer , g . m . al , eds , aapg memoir “ integration of outcrop and modern analogs in reservoir modeling ”, ( 2004 ). daly , c ., higher order models using entropy , markov random fields and sequential simulation , in leuanthong , o . and deutsch , c . v ., eds ., geostatistics banff 2004 , springer ( 2005 ). hu l . y ., chugunova t ., multiple - point geostatistics for modeling subsurface heterogeneity : a comprehensive review . water resource research 44 : wi1413n ( 2008 ). strebelle s ., conditional simulation of complex geological structures using multiple - points statistics . math geol . 34 ( 1 ): 1 - 21 ( 2002 ). strebelle s ., remy n ., post - processing of multiple - point geostatistical models to improve reproduction of training patterns , in leuanthong , o . and deutsch , c . v ., eds ., geostatistics banff 2004 , springer ( 2005 ). strebelle s ., multiple - point statistics ( mps ) simulation with enhanced computational efficiency . 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