A multi-scale, pattern-based approach to sequential simulation annual scrf meeting, may 2003...

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 ::


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 ::


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 )


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


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


coarse grid




demonstration ::


fine grid




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


coarse grid

demonstration ::- instead of drawing at coarser grids, we propose to retain the ccdf and propagate this ccdf to finer grids




fine grid

demonstration ::- instead of drawing at coarser grids, we propose to retain the ccdf and propagate this ccdf to finer grids



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

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




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




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




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

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 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


100

100

SIMPAT realization( 150 data points )

reference image


100

100

SIMPAT e-type( average of

20 realizations )

50 data points


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

A multi-scale, pattern-based approach to sequential simulation annual scrf meeting, may 2003...

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