a multi-scale, pattern-based approach to sequential simulation
DESCRIPTION
a multi-scale, pattern-based approach to sequential simulation. burc arpat ( coaching provided by jef caers ). annual scrf meeting, may 2003 stanford university. let’s talk business…. - PowerPoint PPT PresentationTRANSCRIPT
a multi-scale, pattern-based approach tosequential simulation
annual scrf meeting, may 2003stanford 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-basedreservoir 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-basedreservoir 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 drawsimulation 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 drawsimulation grid
dataevent
replicates in the training image ( 2/3 sand ratio)
1 2 3
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, utilizea series of cascading multi-grids and sparse templates
empty
full
coarsetemplate
finetemplate
solution :: multiple-grids to the rescue – part 2 of 2
coarse grid
1515
fine grid
sand non-sand unknown
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 valuetraining 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 valuepatterns
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 valuepatterns
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 valuepatterns
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 valueprototypes
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 valueprototypes
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
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 a pattern b
n
iii ba
1
distancemanhattan
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 grid during the fine grid…
a SIMPAT tutorial – the final realization
end of the coarse grid during the fine grid…
a SIMPAT tutorial – the final realization
end of the coarse grid during the fine grid…
a SIMPAT tutorial – the final realization
end of the coarse grid during the fine grid…
a SIMPAT tutorial – the final realization
end of the coarse grid during the fine grid…
a SIMPAT tutorial – the final realization
end of the coarse grid final realization
let’s see some results :: boxes
150
150
SIMPAT realizationtraining image
let’s see some results :: the ‘standard’ training image
training image
250
250
SIMPAT realization
let’s see some results :: the ‘standard’ training image
SIMPAT realization
250
250
SIMPAT realization( no multiple-gridcommunication )
let’s see some results :: hard data conditioning
100
100
SIMPAT realization( 50 data points )
reference image
let’s see some results :: hard data conditioning
100
100
SIMPAT realization( 150 data points )
reference image
let’s see some results :: hard data conditioning
100
100
SIMPAT e-type( average of
20 realizations )
50 data points
let’s see some results :: hard data conditioning
100
100
150 data points SIMPAT e-type( average of
20 realizations )
let’s see some results :: channel mesh
training image
250
250
SIMPAT realization
let’s see some results :: thin channels in 3D
training image
100
100
SIMPAT realization
25
let’s see some results :: meandering channels
training image
300
300
SIMPAT realization
let’s see some results :: simpat mimicking sgsim
continuous trainingimage from SGSIM
200
200
continuousSIMPAT
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 tosequential simulation
annual scrf meeting, may 2003stanford 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
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