WO2010057505A1 - Version déterministe du procédé de simulation/reconstruction de géostatistique à points multiples avec laquelle les valeurs simulées/reconstruites sont directement issues des images d'entraînement sans estimation antérieure de la condition - Google Patents

Version déterministe du procédé de simulation/reconstruction de géostatistique à points multiples avec laquelle les valeurs simulées/reconstruites sont directement issues des images d'entraînement sans estimation antérieure de la condition Download PDF

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WO2010057505A1
WO2010057505A1 PCT/EP2008/009819 EP2008009819W WO2010057505A1 WO 2010057505 A1 WO2010057505 A1 WO 2010057505A1 EP 2008009819 W EP2008009819 W EP 2008009819W WO 2010057505 A1 WO2010057505 A1 WO 2010057505A1
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simulation
data
previous
grid
node
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PCT/EP2008/009819
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WO2010057505A8 (fr
Inventor
Gregoire Mariethoz
Philippe Renard
Julien Straubhaar
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Université De Neuchâtel
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Priority to GB1110088.0A priority Critical patent/GB2478244B/en
Priority to PCT/EP2008/009819 priority patent/WO2010057505A1/fr
Publication of WO2010057505A1 publication Critical patent/WO2010057505A1/fr
Priority to US13/108,393 priority patent/US8682624B2/en
Publication of WO2010057505A8 publication Critical patent/WO2010057505A8/fr

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    • G—PHYSICS
    • G01—MEASURING; TESTING
    • G01V—GEOPHYSICS; GRAVITATIONAL MEASUREMENTS; DETECTING MASSES OR OBJECTS; TAGS
    • G01V99/00—Subject matter not provided for in other groups of this subclass
    • G—PHYSICS
    • G01—MEASURING; TESTING
    • G01V—GEOPHYSICS; GRAVITATIONAL MEASUREMENTS; DETECTING MASSES OR OBJECTS; TAGS
    • G01V11/00—Prospecting or detecting by methods combining techniques covered by two or more of main groups G01V1/00 - G01V9/00
    • G—PHYSICS
    • G06—COMPUTING; CALCULATING OR COUNTING
    • G06F—ELECTRIC DIGITAL DATA PROCESSING
    • G06F30/00—Computer-aided design [CAD]
    • G—PHYSICS
    • G01—MEASURING; TESTING
    • G01V—GEOPHYSICS; GRAVITATIONAL MEASUREMENTS; DETECTING MASSES OR OBJECTS; TAGS
    • G01V2210/00—Details of seismic processing or analysis
    • G01V2210/60—Analysis
    • G01V2210/66—Subsurface modeling
    • G01V2210/665—Subsurface modeling using geostatistical modeling

Definitions

  • the present invention concerns generally methods for completing or reconstructing an incomplete data sample, and to their uses and applications.
  • the present invention relates to the use of the 5 method in building statistical models of geological reservoirs, but also to the generation and scaling of synthetic images, to the reconstruction of defective images, as well as to the prediction of time series.
  • Such simulations typically use 2D or 3D models of the reservoir that includes a grid of a large number, often in excess of a million, of individual cells.
  • Oil reservoirs present several different morphologies, possess a large amount of heterogeneity, and typically span a large extension, both in surface and in volume.
  • Conditioning data derived from wells are almost always quite sparse and other data, like seismic data, have, in general, a relatively coarse resolution. It is therefore necessary to find methods to deal with non-exhaustive and coarse sampling, in order to make the most of available data.
  • Several probabilistic, or geostatistical methods have been devised to this purpose and are applied to oil reservoir or aquifer simulations but also in other fields of earth science.
  • Multiple-point statistics is a known technique allowing the simulation of heterogeneous geological facies images.
  • the simulated images (either in 2D or in 3D) respect the structures and morphology of a given reference training image and adhere to the conditioning data. This technique has been described, among others in the following documents, which are incorporated hereby by reference:
  • the training image is scanned with a search template and all pixel configurations contained in the template are stored, most often, in a dynamically allocated tree structure. Further on, the statistics so gathered are used to compute the conditional probability at each simulated node and to fill a simulated model.
  • WO2006/023602 teaches a method for creating a reservoir facies model based on multiple-point statistics.
  • FR2905181 also describes a similar method that further includes steps to take non-stationary models into account.
  • the search template is not large enough to capture large scale structures such as channels. Multi-grid techniques have been devised to attempt to overcome this limitation.
  • the size of the search template, the number of facies and the degree of entropy of the training image determine the memory load. These parameters are quickly limited by the available memory, especially for large 3D grids. Particularly for 3D images, the need to keep the size of the tree within manageable limits imposes the use of a small search template, with the result that complex structures are much worse represented in 3D than in 2D.
  • known multiple- point simulation techniques comprise a step of determining the probability distribution for the variable of interest Z at location u s/m , conditioned to the ensemble ⁇ /(u s/m ) of the values of the n neighboring nodes of u s/m :
  • the conditional distribution is derived from a training image (Tl) given as a prior model and representing the desired spatial structure of the field.
  • Tl training image
  • the Tl is scanned and all pixel configurations up to a certain size (the template size) are stored in a catalogue of data events, most often a tree structure.
  • the size of the data events catalogue grows very rapidly with the size of the template, and the accuracy of the simulation is quickly limited, for practical cases, by the available memory. Because of this limitation, this approach is limited to categorical variables (facies).
  • Another aim of the invention is to propose a method to create a 3D reservoir model that allows a better representation of complex structures.
  • Another aim of the present invention is the provision of a modeling method that can deal effectively with continuous variables.
  • Another aim of the present invention is to propose a method of creating simulated images derived from a model image.
  • Another object of the present invention is a method of completing a partial data set, like for example replacing missing or defective parts into a digital image, or extrapolating or interpolating data series.
  • a further object of the present invention is a method of increasing the resolution of a sampled data set or a sampled image.
  • Figures 1a-1e shows a very simplified example of the direct sampling method of the invention
  • Figures 2a-2c illustrate the results obtainable with the method of the present invention.
  • Figures 3a-3e illustrate an example of joint simulation of two variables that are spatially correlated by some unknown function with the simulation method of the invention.
  • Figures 4a-4f show a simulation with a secondary variable used to reduce the uncertainty on a primary variable.
  • Figures 5a-5d show a simulation with a secondary variable used to describe non-stationarity of the training data.
  • Figures 6a-6d exemplify a reconstruction of a partial image according to an aspect of the invention.
  • Figures 7 and 8 show a downscaling method according to another aspect of the invention.
  • the simulation method of the present invention skips the step of creating a catalogue of data events that will be sampled, but rather samples directly the Training Image (also designated Tl in the following) for a given data event.
  • Events distributed according to function (1) are generated without extracting and storing all conditional distributions, as in the known methods. This is no limitation because, in the context of a stochastic simulation, the complete probability distribution of an event to occur is not relevant, but only one representative event issued from the probability distribution (1) is needed.
  • Figures 1a-1e shows a very simplified example of the direct sampling method of the invention.
  • Figure 1a illustrates a simulation grid 110 in which most of the nodes are unknown, and that must be filled with a dual-valued categorical variable, illustrated by black and white squares.
  • Figure 1b represents the training image 130, which is filled with a dual-valued categorical variable.
  • the simulation of a point of interest 112 comprises the step of defining a neighborhood ⁇ / ⁇ (u s/m ) comprising three discontinuous neighboring points 117.
  • the method of the invention includes a step of defining a search window 135, represented in figure 1c, in the training image.
  • the search window is obtained by the offsets a, b, c, d in the neighborhood ⁇ / T (u 5 TM).
  • the points in the search window 135 can be the centers of neighborhood N ⁇ (v ⁇ ) without going beyond image borders. Other strategies are possible, however.
  • the method of the invention searches the training image for a ⁇ / r (v") satisfactorily matching ⁇ / ⁇ (u s/m ) .
  • this sampling is done by scanning randomly the training image 130 until a neighborhood ⁇ / r (v f/ ) satisfactorily matching ⁇ / T (u 5 ' m ) is found.
  • Figure 1d shows an example of unsuccessful matching.
  • the node 141 is chosen randomly in the scanning window.
  • the values at nodes 147 of /V x (V'') do not correspond to the values of nodes 117 of ⁇ / r (u s/m ) .
  • Figure 1e shows an example of successful matching.
  • the node 145 is chosen randomly in the scanning window of the training image.
  • the neighborhood ⁇ / T (v f/ ) consists of nodes 148 that have the same values as the nodes 117 of N ⁇ (u s ⁇ m ) .
  • the value of the central node 145 of ⁇ / r (v t( ) becomes the value of the point of interest 112 in the simulation grid 110.
  • the first ⁇ / T (v") satisfactorily matching ⁇ / r (u 5 ' m ) is retained.
  • the invention could however include further validation steps on N ⁇ (v ⁇ ) .
  • the vectors defining the position of the nodes in the neighborhood can be different. In fact, even if we use the term central to define the point of interest 112, this point needs not necessarily be in the centre of the data event.
  • the dimensions and size of the data event are only limited by the size of the Tl and the simulation grid.
  • the dynamic event definition illustrated above has the advantage that multiple scales in the training image are automatically taken into account, as the algorithm will initially select large neighborhoods, when the determined points in the simulated image are relatively sparse, and later naturally reduce the neighborhood size, exploring finer structures in the training image.
  • the decrease in the size of the data event proceeds continuously and smoothly during the simulation, so all the structure scales in the Tl are taken into account.
  • this approach is self-adapting and needs not be "steered" by external parameters, as it is the case in known multi-grid algorithms in which the correct number of grids and template size must be set externally.
  • the changing shape of the data events has also the advantage of exploring the space of different pixel configurations.
  • the method can traverse the simulation grid according to a random path, or according to any other path, for example a unilateral path.
  • the algorithm searches the Tl for a matching data event, it is not always necessary to exhaust the whole training image but, in typical cases, the search will succeed after having scanned only a small fraction of the available search space. In the best case, a match will be found at the first tried node of the Tl. In the worst case, the number of tries will equal the number of nodes in the search space: that is the whole Tl or a search window in the Tl.
  • the algorithm of the invention stops the scanning when a predefined fraction of the search space has been explored, in order to speed up execution.
  • the distance c/ ⁇ / ⁇ (u 5/m ), ⁇ / r (v t ')j between the data events can be defined in several ways, and can be adapted to the simulation of both continuous and categorical variables.
  • the distance used for categorical variables is the fraction of matching versus non-matching nodes in the data event, given by the indicator variable a that equals zero if two nodes have identical value and one otherwise:
  • the simulation method of the invention could use the mean absolute difference, or any other suitable norm function.
  • FIGS. 2a-2c illustrate the results obtainable with the method of the present invention.
  • the image in 2a is a training image with a continuous variable, represented by different levels of gray in a 200x200 grid.
  • the conditioning data are 100 initial random values marked by the circles 125 in the simulation grid of figure 2b.
  • the algorithm of the invention produces the simulated image of fig. 2b that is consistent with the Tl and respects the conditioning data.
  • the histograms of fig. 2c finally, represent the distribution of the variable's value in both the Tl and the simulated data.
  • each simulated variable is defined in the training image.
  • the conditioned distribution function for the simulated variable v is
  • the distance between data events is defined, for example, as the weighted average of all distances specific for each variable v , with suitable weights w .
  • the user is in general capable of choosing the weights w according to the relative importance of the variables in the Tl. The distance thus becomes:
  • Figures 3a-3e illustrate an example of joint simulation of two variables that are spatially correlated by some unknown function.
  • the variable 1 (fig. 3a) is a binary categorical image
  • the Tl for the variable 2 (Fig. 3b) is obtained by smoothing variable 1 and adding an uncorrelated noise component.
  • the result is that the Tl for variables 1 and 2 are related by a non-linear, nonparametric transfer function.
  • Figures 3c and 3d show the result of an unconditioned simulation on both variables 1 and 2 using a neighborhood composed of the thirty closest nodes for each variable.
  • the distance (3) was used for variable 1
  • the distance (4) for the continuous variable 2.
  • the correlation is well maintained in the simulation, both visually and in term of the cross-variogram (Fig. 3e).
  • the method of the invention is used to simulate joint variables distributions in which one of the variables is known.
  • the known variable becomes conditioning data guiding the simulation of other variables.
  • This embodiment can be regarded as a simulation using a secondary variable.
  • the knowledge of the secondary variable can be used to reduce the uncertainty on the primary variable, as it is shown in figures 4a-4f .
  • the Tl (figures 4a and 4b) is the same as in the previous embodiment, and the reference field (Fig. 4c) is the result of an unconditional simulation.
  • the secondary variable of the reference field (Fig. 4d) is fully known and is used as conditioning data for the simulation (Fig. 4e).
  • Fig. 4f shows the mean of 100 simulations, reproducing the features of the reference map.
  • a secondary variable is used to describe the non-stationarity of the Tl.
  • the Tl for the variable 1 is a set of hand-drawn channels (fig. 5a), in which the angle of the channel is a function of the x coordinate.
  • the non-stationarity is thus described by a secondary variable that is simply a mapping of the X coordinate of the Tl grid (fig 5b).
  • the resulting simulation is conditional to variable 2, which is known, but is this time the coordinate Y of the simulation grid (fig. 5d)
  • the algorithm of the present invention can be used to reconstruct partial images.
  • the known elements of the image are used as Tl for simulating the missing part, that is they are both conditioning data and training data for the simulation.
  • Figures 6a-6d exemplify such reconstruction.
  • Figure 6a is an image comprising a two- valued categorical variable showing, for example, a network of sand channels in an impermeable clay matrix.
  • the central square 610 is considered unknown and it is reconstructed by scanning the edges of the image.
  • Figures 6b-6d illustrate three instances of simulated images obtained by the algorithm of the invention using the distance defined in. (3). It can be appreciated that simulated regions integrate seamlessly at all scales with the known region.
  • this example is relative to a categorical variable, it is possible to apply the invention to completion of images with a continuous variable as well.
  • the method of the invention can be applied to the task of increasing the resolution of an image, thus obtaining from a coarse grid a fine grid having a larger number of grid points, or pixels, and representing an image with a higher resolution.
  • this variant of the invention relates to a downscaling method comprising a step of dividing each node 701 of the coarse image into a number of children nodes 704, (typically four children nodes for a 2D case, corresponding to a factor two scaling in both directions, but other scaling ratios are possible), and attributing the value of the coarse node 701 into one children node (arrow 710), for example a randomly chosen children node.
  • the remaining three children nodes are then simulated by the direct sampling algorithm presented above (arrow 720), choosing a suitable distance function, and using the coarse grid as training image.
  • the process can be iterated as many times as required (arrows 730, 740, 750).
  • Figure 8 represents two steps of downscaling of an image including a continuous variable using the above-illustrated method.
  • the scaling method based on the direct sampling simulation algorithm of the invention provides a fine-scale image having small-scale structure that are inferred from the large-scale structures present in the coarse input image.
  • the method of the invention generates realistic details at all scales, based on the assumption that the formation of interest has a fractal structure with scale invariance.
  • a valuable feature of this scaling algorithm is the absence of adjustable downscaling parameters and of steps of prior estimation of the fractal dimension, required in other known methods.
  • the algorithm of the present invention is suitable for an efficient parallel implementation in a multi-processor computer, or in a network of distributed computers or processing units. Parallelization is straightforward on shared memory machines: each processing unit performs the search in a limited portion of the Tl only.
  • the parallelization of the algorithm of the invention includes a master agent, which could be a processor, for example, or a specific software or hardware resource.
  • the master agent is responsible for distributing sub-tasks to slave agents, each sub-task consisting, for example in scanning the training image with a given neighborhood and returning a simulated value.
  • the master sends sequentially to each slave a pattern to find, and then waits for a resulting simulated value coming from any slave processor. Once this result is obtained, the master includes it in the simulation grid, finds the pattern associated to the next node and sends it to the same slave processor from which the result just came from. Then it waits again for a result coming from any slave processor.
  • the method of the invention includes simulations in three-dimensional grids, for example in the field of geostatistics, and simulation, interpolation and extrapolation of one- dimensional data, for example data representing the sampled time evolution of one variable, or of several coupled variables.
  • the invention can be applied to the interpolation or extrapolation of scientific data or to the forecast of financial indexes.

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Abstract

L'invention porte sur un procédé géostatistique à multiples points, consistant à simuler, reconstruire et mettre à l'échelle des ensembles de données numériques, en particulier, mais non exclusivement, des images. Le procédé selon l'invention est fondé sur une image d'entraînement qui est directement échantillonnée à chaque fois qu'un point dans l'image de simulation doit être rempli, et qui ne nécessite pas la création préliminaire d'une structure de données stockant des probabilités conditionnelles, comme c’est souvent le cas dans les procédés connus de simulation à multiples points. Par conséquent, le procédé selon l'invention, qui est moins exigeant en termes de mémoire que les procédés classiques, est davantage approprié pour des simulations comprenant des variables continues. Des modes de réalisation concernant l'application à la reconstruction d'images partielles et à la réduction de la résolution sont également décrits.
PCT/EP2008/009819 2008-11-20 2008-11-20 Version déterministe du procédé de simulation/reconstruction de géostatistique à points multiples avec laquelle les valeurs simulées/reconstruites sont directement issues des images d'entraînement sans estimation antérieure de la condition WO2010057505A1 (fr)

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GB1110088.0A GB2478244B (en) 2008-11-20 2008-11-20 Multiple point statistics method for optimizing the recovery of oil or gas from geological reservoirs
PCT/EP2008/009819 WO2010057505A1 (fr) 2008-11-20 2008-11-20 Version déterministe du procédé de simulation/reconstruction de géostatistique à points multiples avec laquelle les valeurs simulées/reconstruites sont directement issues des images d'entraînement sans estimation antérieure de la condition
US13/108,393 US8682624B2 (en) 2008-11-20 2011-05-16 Deterministic version of the multiple point geostatistics simulation/reconstruction method with the simulated/reconstructed values are directly taken from the training images without prior estimation of the conditional

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