a multi-scale, pattern-based approach to sequential simulation annual scrf meeting, may 2003 stanford university burc arpat ( coaching provided by jef caers )

let’s talk business… - geostatistics :: business of generating reservoir models using available data from many scales ( data integration ) - reservoirs might contain complex geological shapes such as channels that effect the flow behavior of the reservoir - thus, accurate modeling of reservoirs is needed for flow performance and prediction studies

two schools of geostatistics – part 1 of 2 an object-based reservoir model - generate objects, drop them on to the reservoir and move them around until they match all data - crisp shape reproduction due to operating directly with objects - poor data conditioning, especially to dense well data and 3D seismic object-based modeling ::

two schools of geostatistics – part 2 of 2 a pixel-based reservoir model - infer or model the statistics and build the reservoir model one pixel at a time accounting for data - only sufficient shape reproduction due to the pixel-based nature - good data conditioning to any type of data including 3D seismic pixel-based modeling ::

two schools of geostatistics – part 2 of 2 a pixel-based SNESIM realization - infer or model the statistics and build the reservoir model one pixel at a time accounting for data - only sufficient shape reproduction due to the pixel-based nature - good data conditioning to any type of data including 3D seismic pixel-based modeling ::

two schools of geostatistics – part 2 of 2 a pixel-based SNESIM realization - infer or model the statistics and build the reservoir model one pixel at a time accounting for data - only sufficient shape reproduction due to the pixel-based nature - good data conditioning to any type of data including 3D seismic pixel-based modeling ::

a popular methodology :: sequential simulation step 1 :: obtain the statistics of the reservoir using a mathematical model such as a variogram or infer it step 2 :: decide on a random path to visit all your uninformed node on your simulation grid step 3 :: during simulation, at every node, using the obtained statistics and the available neighborhood data, construct a ccdf and draw from it sequential simulation is the dominating methodology in pixel-based methods. the basic idea is straightforward ::

examples of sequential simulation algorithms - SGSIM uses a variogram-based continuous variable model in gaussian space - SNESIM infers the statistics from a training image by constructing a smart catalog of training image events sequential gaussian simulation ( SGSIM ), sequential indicator simulation ( SISIM ) and single normal equation simulation ( SNESIM ) are all typical examples :: - SISIM uses indicator variables and a divided model with multiple variograms to handle multiple categories

a powerful idea :: training images – part 1 of 2 a training image - the original idea is due to srivastava ( 1992 ), later published in guardino and srivastava ( 1993 ) - training images are non-conditional and purely conceptual depictions of how the reservoir should look like - the authors proposed a sequential simulation algorithm which is also used by SNESIM ( strebelle, 2000 )

a powerful idea :: training images – part 2 of 2 training image step 1 :: during simulation, extract the neighborhood of the visited node using a template ( a data event ) step 2 :: scan the training image to look for matches to this data event the basic algorithm :: step 3 :: once all matches are found, construct the ccdf using the central values of matched events and draw simulation grid

a powerful idea :: training images – part 2 of 2 training image step 1 :: during simulation, extract the neighborhood of the visited node using a template ( a data event ) step 2 :: scan the training image to look for matches to this data event the basic algorithm :: step 3 :: once all matches are found, construct the ccdf using the central values of matched events and draw simulation grid data event replicates in the training image ( 2/3 sand ratio) 123

problem :: reproduction of large scale continuity a training image - to capture the details of the very continuous and complex channels, a large template is required - yet, a large template means many template nodes to process and that is not feasible for real-life problems - reproduction of large scale continuity is not a challenge only associated with training images

solution :: multiple-grids to the rescue – part 1 of 2 in 1994, tran suggested use of multi-grids as a solution :: instead of using one large and dense template, utilize a series of cascading multi-grids and sparse templates empty full coarse template fine template

solution :: multiple-grids to the rescue – part 2 of 2 coarse grid 15 fine grid sandnon-sandunknown

standard multi-grid approach is not problem-free coarse grid - the multi-grid approach might introduce artificial discontinuities to the reservoir model - in the coarse grid, once a value is simulated, it is frozen and cannot be changed in finer grids - this is a dangerous practice! we are making consequential decisions without having enough information

standard multi-grid approach is not problem-free coarse grid - the multi-grid approach might introduce artificial discontinuities to the reservoir model - in the coarse grid, once a value is simulated, it is frozen and cannot be changed in finer grids - this is a dangerous practice! we are making consequential decisions without having enough information demonstration ::

standard multi-grid approach is not problem-free fine grid - the multi-grid approach might introduce artificial discontinuities to the reservoir model - in the coarse grid, once a value is simulated, it is frozen and cannot be changed in finer grids - this is a dangerous practice! we are making consequential decisions without having enough information demonstration ::

an improved multi-grid approach – a proposal coarse grid - instead of drawing at coarser grids, we propose to retain the ccdf and propagate this ccdf to finer grids - in finer grids, we allow previously calculated ccdfs to be modified, i.e. coarse nodes are never frozen - we only draw/simulate at the finest grid; before this step, it’s only progression of ccdfs

an improved multi-grid approach – a proposal coarse grid demonstration :: - instead of drawing at coarser grids, we propose to retain the ccdf and propagate this ccdf to finer grids - in finer grids, we allow previously calculated ccdfs to be modified, i.e. coarse nodes are never frozen - we only draw/simulate at the finest grid; before this step, it’s only progression of ccdfs

an improved multi-grid approach – a proposal fine grid demonstration :: - instead of drawing at coarser grids, we propose to retain the ccdf and propagate this ccdf to finer grids - in finer grids, we allow previously calculated ccdfs to be modified, i.e. coarse nodes are never frozen - we only draw/simulate at the finest grid; before this step, it’s only progression of ccdfs

a strong requirement of the improved multi-grid approach - this eliminates SNESIM as the candidate method; it only works with indicators. SGSIM and SISIM fit the bill but we would like to get past variogram-based methods already! - a new approach to sequential simulation is needed. the approach should (1) account for more than 2-point statistics for shape reproduction, (2) handle continuous variables to be used with the new multi-grid approach - the improved multi-grid approach assumes that the sequential simulation implementation of your choice is capable of dealing with continuous variables

- a new approach to sequential simulation is needed. the approach should (1) account for more than 2-point statistics for shape reproduction, (2) handle continuous variables to be used with the new multi-grid approach a strong requirement of the improved multi-grid approach - this eliminates SNESIM as the candidate method; it only works with indicators. SGSIM and SISIM fit the bill but we would like to get past variogram-based methods already! - the improved multi-grid approach assumes that the sequential simulation implementation of your choice is capable of dealing with continuous variables

- a new approach to sequential simulation is needed. the approach should (1) account for more than 2-point statistics for shape reproduction, (2) handle continuous variables to be used with the new multi-grid approach a strong requirement of the improved multi-grid approach - this eliminates SNESIM as the candidate method; it only works with indicators. SGSIM and SISIM fit the bill but we would like to get past variogram-based methods already! - the improved multi-grid approach assumes that the sequential simulation implementation of your choice is capable of dealing with continuous variables

coming soon to a computer near you :: the SIMPAT algorithm step 1 :: scan the training image using a template to extract all available, unique patterns ( a.k.a. data events ) step 2 :: using a clustering algorithm, group all patterns into classes based on ’similarity’ ( construct prototypes ) step 3 :: during simulation, at each unknown node, (a) extract the data event, (b) find the ‘most similar’ prototype to the dev and (c) draw from its central value training image

coming soon to a computer near you :: the SIMPAT algorithm step 1 :: scan the training image using a template to extract all available, unique patterns ( a.k.a. data events ) step 2 :: using a clustering algorithm, group all patterns into classes based on ’similarity’ ( construct prototypes ) step 3 :: during simulation, at each unknown node, (a) extract the data event, (b) find the ‘most similar’ prototype to the dev and (c) draw from its central value patterns

coming soon to a computer near you :: the SIMPAT algorithm step 1 :: scan the training image using a template to extract all available, unique patterns ( a.k.a. data events ) step 2 :: using a clustering algorithm, group all patterns into classes based on ’similarity’ ( construct prototypes ) step 3 :: during simulation, at each unknown node, (a) extract the data event, (b) find the ‘most similar’ prototype to the dev and (c) draw from its central value patterns similar patterns prototype

coming soon to a computer near you :: the SIMPAT algorithm step 1 :: scan the training image using a template to extract all available, unique patterns ( a.k.a. data events ) step 2 :: using a clustering algorithm, group all patterns into classes based on ’similarity’ ( construct prototypes ) step 3 :: during simulation, at each unknown node, (a) extract the data event, (b) find the ‘most similar’ prototype to the dev and (c) draw from its central value patterns

coming soon to a computer near you :: the SIMPAT algorithm step 1 :: scan the training image using a template to extract all available, unique patterns ( a.k.a. data events ) step 2 :: using a clustering algorithm, group all patterns into classes based on ’similarity’ ( construct prototypes ) step 3 :: during simulation, at each unknown node, (a) extract the data event, (b) find the ‘most similar’ prototype to the dev and (c) draw from its central value prototypes

coming soon to a computer near you :: the SIMPAT algorithm step 1 :: scan the training image using a template to extract all available, unique patterns ( a.k.a. data events ) step 2 :: using a clustering algorithm, group all patterns into classes based on ’similarity’ ( construct prototypes ) step 3 :: during simulation, at each unknown node, (a) extract the data event, (b) find the ‘most similar’ prototype to the dev and (c) draw from its central value prototypes

step 3 :: during simulation, at each unknown node, (a) extract the data event, (b) find the ‘most similar’ prototype to the dev and (c) draw from its central value coming soon to a computer near you :: the SIMPAT algorithm step 1 :: scan the training image using a template to extract all available, unique patterns ( a.k.a. data events ) step 2 :: using a clustering algorithm, group all patterns into classes based on ’similarity’ ( construct prototypes ) prototypes

step 3 :: during simulation, at each unknown node, (a) extract the data event, (b) find the ‘most similar’ prototype to the dev and (c) draw from its central value coming soon to a computer near you :: the SIMPAT algorithm step 1 :: scan the training image using a template to extract all available, unique patterns ( a.k.a. data events ) step 2 :: using a clustering algorithm, group all patterns into classes based on ’similarity’ ( construct prototypes ) prototypes

step 3 :: during simulation, at each unknown node, (a) extract the data event, (b) find the ‘most similar’ prototype to the dev and (c) draw from its central value coming soon to a computer near you :: the SIMPAT algorithm step 1 :: scan the training image using a template to extract all available, unique patterns ( a.k.a. data events ) step 2 :: using a clustering algorithm, group all patterns into classes based on ’similarity’ ( construct prototypes ) prototypes

step 3 :: during simulation, at each unknown node, (a) extract the data event, (b) find the ‘most similar’ prototype to the dev and (c) draw from its central value coming soon to a computer near you :: the SIMPAT algorithm step 1 :: scan the training image using a template to extract all available, unique patterns ( a.k.a. data events ) step 2 :: using a clustering algorithm, group all patterns into classes based on ’similarity’ ( construct prototypes ) prototypes the modeling of the current node ccdf occurs when the ‘most similar’ prototype to the data event is found using the similarity criterion. the data event is fit to a previously determined prototype; hence, explicit modeling of the ccdf, instead of mere sampling, is achieved

( what is similarity? ) pattern apattern b

a SIMPAT tutorial – the training image tutorial training image ( channel ratio = 0.5 ) 2 multi-grid templates ( 5x5 and 3x3 )

a SIMPAT tutorial – coarse grid patterns coarse grid patterns

a SIMPAT tutorial – coarse grid prototypes coarse grid prototypes

a SIMPAT tutorial – fine grid patterns fine grid patterns

a SIMPAT tutorial – fine grid prototypes fine grid prototypes

a SIMPAT tutorial – the final realization end of the coarse gridduring the fine grid…

a SIMPAT tutorial – the final realization end of the coarse gridduring the fine grid…

a SIMPAT tutorial – the final realization end of the coarse gridduring the fine grid…

a SIMPAT tutorial – the final realization end of the coarse gridduring the fine grid…

a SIMPAT tutorial – the final realization end of the coarse gridduring the fine grid…

a SIMPAT tutorial – the final realization end of the coarse gridfinal realization

let’s see some results :: boxes 150 SIMPAT realizationtraining image

let’s see some results :: the ‘standard’ training image training image 250 SIMPAT realization

let’s see some results :: the ‘standard’ training image SIMPAT realization 250 SIMPAT realization ( no multiple-grid communication )

let’s see some results :: hard data conditioning 100 SIMPAT realization ( 50 data points ) reference image

let’s see some results :: hard data conditioning 100 SIMPAT realization ( 150 data points ) reference image

let’s see some results :: hard data conditioning 100 SIMPAT e-type ( average of 20 realizations ) 50 data points

let’s see some results :: hard data conditioning data points SIMPAT e-type ( average of 20 realizations )

let’s see some results :: channel mesh training image 250 SIMPAT realization

let’s see some results :: thin channels in 3D training image 100 SIMPAT realization 25

let’s see some results :: meandering channels training image 300 SIMPAT realization

let’s see some results :: simpat mimicking sgsim continuous training image from SGSIM 200 continuous SIMPAT realization

let’s see some results :: simpat mimicking sgsim comparison of 0 , 45  and 90  variograms

conclusions and future work - we just saw the power of patterns! not only they provide better shape reproduction but have some unique advantages such as modeling of ccdfs and ability to work with continuous variables - still tons of things to do :: true multi-category, secondary data experiments, continuous value experiments, better data relocation, angle and affinity support, etc. - the implementation is very generic ( different clustering methods, distance functions, search structures can easily be used ), less memory demanding and potentially faster

a multi-scale, pattern-based approach to sequential simulation annual scrf meeting, may 2003 stanford university burc arpat ( coaching provided by jef caers ) acknowledgements :: Dr. Sebastien Strebelle from ChevronTexaco for sharing his experience on the subject matter and Dr. Renjun Wen from Geomodeling Technology Corp. for providing us with the SBED software