WO2009138290A2 - Modélisation de gisement multipoint - Google Patents

Modélisation de gisement multipoint Download PDF

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Publication number
WO2009138290A2
WO2009138290A2 PCT/EP2009/053614 EP2009053614W WO2009138290A2 WO 2009138290 A2 WO2009138290 A2 WO 2009138290A2 EP 2009053614 W EP2009053614 W EP 2009053614W WO 2009138290 A2 WO2009138290 A2 WO 2009138290A2
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Prior art keywords
list
facies
nodes
simulation
training image
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PCT/EP2009/053614
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English (en)
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WO2009138290A3 (fr
Inventor
Julien Alexis Straubhaar
Grégroire MARIETHOZ
Philippe Renard
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Ephesia Consult Sa
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Publication of WO2009138290A2 publication Critical patent/WO2009138290A2/fr
Publication of WO2009138290A3 publication Critical patent/WO2009138290A3/fr

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    • 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
    • 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

  • Embodiments of the present invention relate generally to methods for building statistic models of geological reservoirs, to an improved method for storing and building such models.
  • Reservoir simulation is a technique used by major oil and gas companies to predict oil and gas flow through the porous media of the reservoir.
  • 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. These models typically represent the values of one physical property, often the underlying geological facies expressed as a discrete- valued category variable.
  • the goal of modelling is to obtain an image of the underground reservoir that reflect the knowledge of the general geological structures presents on the site, restrained by conditioning values measured at certain points, for example corresponding to exploration and production wells, and by other auxiliary information, like seismic data.
  • 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 assay wells are almost always quite sparse and other data, like seismic data, have, in general, a relatively coarse resolution.
  • reservoir modelling must necessary use probabilistic, or geostatistical methods.
  • 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: "Sequential Simulation Drawing Structures from Training Images"
  • the training image is scanned with a search template and the multiple-point statistics are stored in a dynamically allocated tree structure. Further on, the statistics so gathered are used to fill a simulated model.
  • Another aim of the invention is to propose a method to create a 3D reservoir model that allows a better representation of complex structures.
  • Figure 1 and 2 show an example of a training image and of a search template.
  • Figure 3 is a graphical representation of a tree structure issued from the training image and the template of figures 1 and 2.
  • Figure 4 is a graphical comparison of the memory usage in the method of the invention and in a known method.
  • FIG. 5 illustrates an aspect of the method of the invention.
  • Figure 6 shows possible weight distribution for selection and penalization in presence of an auxiliary variable representing non- stationarity
  • a search template is defined as a set of relative nodes locations h v ...h N .
  • the multigrid approach as proposed in the above- identified art is used to capture structures within the training image that are defined at different scales. Let us introduce some terminology. A 2D or
  • 3D grid is a box-shaped set of pixels
  • N x , ⁇ / y , ( ⁇ / z ) are the dimensions in the x-axis, y-axis (and z-axis) directions respectively.
  • the subgrid with a step of 2' between neighbouring nodes is defined as
  • m levels of multigrid G 0 ,...,G m _ ⁇ are defined as
  • the simulation proceeds successively with the simulation of all the nodes in the multigrid level G m _ ⁇ .
  • the lag vectors in the search template are then scaled such that their value is 2 m ⁇ 1 -/i, instead of /i, .
  • the process continues with the nodes in the multigrid level G m _ 2 and repeats for all the multigrid levels (in decreasing order) similarly.
  • the simulation starts with the coarsest multigrid level and finishes with the finest one.
  • the multiple- point statistics inferred from the training image and provided by a search template are stored in a dynamically allocated list.
  • the training image is scanned moving the search template such that:
  • C ⁇ 1 Q .
  • a given value C mm represents the minimal number of replicates that must be found in the training image for validating the corresponding pdf, i.e. the pdf above is validated only if C ⁇ C mm .
  • the positions of the known components (corresponding to the nodes that has been already simulated) in d(u) are /., ⁇ ... ⁇ / tripod (with O ⁇ n ⁇ N).
  • Figure 1 shows a training image, in this case a 2D 6x 6 grid containing values of a binary variable, assuming the values 0 or 1, represented as white and black squares.
  • a possible corresponding search template is shown in figure 2, containing four cells in the neighbourhood of the considered cell u.
  • a tree structure is used instead of a list for storing the multiple-points statistics inferred from the training image.
  • the levels of the tree are numbered from 1 to N+1 and the subcells in a cell from 0 to M-1. Each subcell holds a counter and can have a child cell (in the next level of the tree): the tree is an M-ary tree.
  • the counter in a subcell is defined as follows. Let /(1), /(2), ., i ⁇ k + 1) a path in the tree where i(j ) is the identification number of a subcell in a cell of level j. The counter in the last subcell of the path is the number of data events found in the training image with facies i(j ) at node v + h j of the search template ⁇ (v) for
  • the multiple-point statistics inferred from the training image is stored in a list structure as explained above. Only the data events corresponding to the last level in the search tree of figure 3 are stored in the list of table 1. The statistics stored in the list and the search tree are identical. The knowledge of the list allows reconstructing exactly the search tree.
  • L 6 (1,0,0,1), (0,2) (0, ⁇ (4,1),(4,4) ⁇
  • Lio (1,1,1,0), (1,1) ⁇ (1,1) ⁇ , ⁇ (2,1) ⁇
  • Table 1 list for training image and template of figures 1 and 2
  • the size of the search tree and the list depends on the size ⁇ / of the search template, the number M of facies and the entropy of the training image. Moreover, the size of the search tree can also depend on the order of the nodes numbering in the search template.
  • a node location (n ⁇ l n y (,n z )) in the simulation grid is the pixel [n ⁇ l n x + 1[x[n y ,n y + 1[(x[n z ,n z + 1[) (the notation [...[ indicates a inferiorly closed and superiorly open real interval) and corresponds to the region
  • a conditioning data is a point (x,y(,z)) with an attributed facies.
  • the coordinates x,y(,z) are real and must be in the area defined by (7).
  • each conditioning node u c in G obtained by the step above is spread in the subgrid SG ⁇ as follows: a. We select all the closest nodes in the subgrid SG ⁇ to u c , i.e. the realize the minimum where d is the dimension (2 or 3) and u(j) (resp. u c (j) are the integer coordinates in G of the node u (resp. u c ). b.
  • O 1 (4.4,6.4)
  • Q 2 (8.5,8.8)
  • O 3 (9.2,4.7)
  • O 4 (11.4,7.3) .
  • the nodes selected in step 2)a) above are marked as white circles 141 in figure 5 for the subgrid SG ⁇ ( (4,6) for u c 1 , (8,8) for u c 2 , (8,4) and (10,4) for u c 3 , and (10,6), (10,8), (12,6) and (12,8) for u cA ) and marked as crosses 142 in figure 5 for the subgrid SG 2 ((4,4) and (4,8) for u c l , (8,8) for u c 2 , (8,4) for u c 3 , and (12,8) for u c ⁇ ).
  • step 2)b) above one of the two nodes (8,4), (10,4) and one of the four nodes (10,6), (10,8), (12,6), (12,8) will be simulated for the subgrid SG ⁇ .
  • the subgrid SG 2 one of the two nodes (4,4), (4,8) will be simulated, and the nodes (8,4) and (12,8) will be also simulated if they are not chosen during the spreading of the data in SG ⁇ .
  • a path covering all the un-simulated nodes should be chosen. A possible strategy is to build, in a given multigrid level, a path from the simulated nodes in this multigrid level (provided by conditioning data and the steps described above).
  • a layer of nodes is simply made up of nodes in the border (edges of faces) of a box.
  • the proposed path visits all the nodes in the first layers, then all of them in the second layers, and so on. Thus, such a path moves away from the conditioning data.
  • a vector m is appended to each element of the list described above.
  • the auxiliary variable t is normalized in the interval [0,1], via the linear transformation [a,b] -> [0,1], t ⁇ (t - a) l (b - a), where a and b are respectively the minimum and the maximum of the auxiliary variable t(v), v in 77 aux u G aux .
  • a and b are respectively the minimum and the maximum of the auxiliary variable t(v), v in 77 aux u G aux .
  • a tolerance error ⁇ ue [0,1] is fixed. For each facies k, we retain the set E of the elements in the list that are compatible with the data event d(u) and that satisfy
  • M-1 yjmarg) N _
  • a nd y(marg) £ ⁇ TM ⁇ > (1 2 )
  • M k J) ⁇ marg) is the mean of the y-th auxiliary variable at the nodes in the training image with the facies k.
  • the multiple-point statistics provide a pdf used for attributing a facies at a given node u.
  • the elements of the list matching with the data event d(u) are retained, as previously explained, for simulation, eventually also considering auxiliary variables expressing non-stationarity.
  • the sum C of all the occurrence counters of these elements is the number of replicates found in the training image that are compatible with the node u to be simulated.
  • this number of replicates should be large enough, i.e. C > C m ⁇ n . If it is not the case, the data event is reduced (dropping its last simulated nodes) as much as needed for obtaining this condition, i.e.
  • the method of the invention comprises steps for eliminating or reducing such incompatibilities.
  • a method called synchronized post-processing is adopted. It is a real-time process, for avoiding the propagation of inconsistencies during the simulation.
  • the synchronized postprocessing algorithm consists in the following steps at each node u of the simulation grid:
  • the simulation of the facies at the node N ⁇ D (u) u is postponed, and one of the simulated nodes in d(N ⁇ D (u)) , N ⁇ D ⁇ ⁇ u), is un-simulated and re-simulated; b. if the multiple-point pdf is acceptable for N ⁇ D (u) , the facies at this node is simulated, and a new attempt at the node N ⁇ D+ ⁇ u) is done.
  • D is the number of currently un-simulated (removed) nodes from the initial node u , called depth.
  • a maximum total number of un-simulations for each initial node is preferably fixed.
  • a maximal depth can also be fixed. If one of these maximal values are reached, the simulation continues using the current ((un)acceptable) multiple-point pdf for the current step.
  • the nodes u + h, , J ⁇ j ⁇ n were dropped for computed the multiple-point pdf, i.e. the condition C ⁇ C m ⁇ n is satisfied considering the data event with the first 7 - 1 simulated nodes (d ⁇ ⁇ (u)) but not satisfied if the next simulated node (u + h : ) is taken in account in the data event.
  • the node u + h h is un-simulated and re- simulated.
  • the method of the invention contains steps to ensure that some particular nodes not be un-simulated. It is the case, for example, of the conditioning nodes or the nodes that are not included in the multigrid currently simulated. To this end, before the simulation of a multigrid, these nodes might be marked as "fixed nodes" (for instance with a Boolean flag). Then in the case above, we re-simulate the node u + h lk where k is the greatest index in ⁇ 1,...,7 ⁇ such that u + is not flagged as "fixed node” instead of the node u + h ⁇ r If no such index exists, the simulation might continue using the current (unacceptable) multiple- point pdf for the current step.
  • the synchronized post-processing can sometimes un-simulate and re-simulate the same nodes in a cyclic manner. Such a situation is a waste of time because the simulation is not improved. Moreover, these cycles generate biases: a facies could be simulated many times at a node with the same multiple-point pdf.
  • the method of the present invention includes steps to avoid useless re-simulation cycles. For avoiding these cycles, for example, all the un-simulations (location, facies and depth) from the initial node are recorded in a log.
  • the log is scanned to determine if the simulation grid is found in the same state as in the past and if the node that would be un-simulated is the same one in the both situations. If it is the case, no un-simulation is done and the simulation continues using the current (unacceptable) multiple-point pdf for the current step (or another simulated node in the data event could be un-simulated, for breaking the cycle).
  • the following embodiment of the invention presents a possible parallel implementation of the multiple-point simulation algorithm of the present invention that, advantageously, can reduce the simulation time. Other manner of parallelising the method of the invention are however possible.
  • the simulation is carried out by a number p of parallel processes, numbered from 0 to p-7, that may, or may not, be executed by several physically distinct hardware processors.
  • the list containing the multiple-point statistics is then divided in p parts of balanced size. Each part is called a partial list. Every process contains one different partial list.

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Abstract

La présente invention porte sur une amélioration dans les procédés utilisés pour modéliser des structures souterraines, en particulier des gisements souterrains, avec modélisation statistique multipoint. L'amélioration implique le stockage des statistiques dans une image d'apprentissage dans une structure de liste, plutôt que dans une structure d'arbre. De cette façon, une économie de mémoire considérable est obtenue. Le système de l'invention est ensuite apte à gérer des modèles bien plus grands et des patrons de recherche étendus, pour ainsi décrire des modèles 3D complexes.
PCT/EP2009/053614 2008-05-16 2009-03-26 Modélisation de gisement multipoint WO2009138290A2 (fr)

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Cited By (29)

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FR2954557A1 (fr) * 2009-12-23 2011-06-24 Inst Francais Du Petrole Methode d'exploitation d'un gisement petrolier a partir d'une construction d'une carte de facies
US20120101786A1 (en) * 2010-10-20 2012-04-26 Conocophillips Company Method for parameterizing and morphing stochastic reservoir models
US8612195B2 (en) 2009-03-11 2013-12-17 Exxonmobil Upstream Research Company Gradient-based workflows for conditioning of process-based geologic models
WO2013188008A1 (fr) * 2012-06-11 2013-12-19 Chevron U.S.A. Inc. Système et procédé d'optimisation du nombre de données de conditionnement dans une simulation de statistique à points multiples
US8666149B2 (en) 2012-08-01 2014-03-04 Chevron U.S.A. Inc. Method for editing a multi-point facies simulation
CN103886216A (zh) * 2014-04-04 2014-06-25 中国石油大学(北京) 一种基于地质矢量信息的多点地质统计方法
US8818780B2 (en) 2008-11-14 2014-08-26 Exxonmobil Upstream Research Company Forming a model of a subsurface region
US8825461B2 (en) 2008-12-18 2014-09-02 Exxonmobil Upstream Research Company Overlapped multiple layer depth averaged flow model of a turbidity current
US8855987B2 (en) 2009-10-23 2014-10-07 Exxonmobil Upstream Research Company Method for optimization with gradient information
US8892412B2 (en) 2009-03-11 2014-11-18 Exxonmobil Upstream Research Company Adjoint-based conditioning of process-based geologic models
US9058446B2 (en) 2010-09-20 2015-06-16 Exxonmobil Upstream Research Company Flexible and adaptive formulations for complex reservoir simulations
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US9121971B2 (en) 2012-08-01 2015-09-01 Chevron U.S.A. Inc. Hybrid method of combining multipoint statistic and object-based methods for creating reservoir property models
US9128212B2 (en) 2009-04-20 2015-09-08 Exxonmobil Upstream Research Company Method for predicting fluid flow
US9134454B2 (en) 2010-04-30 2015-09-15 Exxonmobil Upstream Research Company Method and system for finite volume simulation of flow
US9187984B2 (en) 2010-07-29 2015-11-17 Exxonmobil Upstream Research Company Methods and systems for machine-learning based simulation of flow
US9260947B2 (en) 2009-11-30 2016-02-16 Exxonmobil Upstream Research Company Adaptive Newton's method for reservoir simulation
US9489176B2 (en) 2011-09-15 2016-11-08 Exxonmobil Upstream Research Company Optimized matrix and vector operations in instruction limited algorithms that perform EOS calculations
US9626466B2 (en) 2010-11-23 2017-04-18 Exxonmobil Upstream Research Company Variable discretization method for flow simulation on complex geological models
US9891344B2 (en) 2011-03-09 2018-02-13 Total Sa Computer estimation method, and method for oil exploration and development using such a method
US10036829B2 (en) 2012-09-28 2018-07-31 Exxonmobil Upstream Research Company Fault removal in geological models
US10087721B2 (en) 2010-07-29 2018-10-02 Exxonmobil Upstream Research Company Methods and systems for machine—learning based simulation of flow
US10319143B2 (en) 2014-07-30 2019-06-11 Exxonmobil Upstream Research Company Volumetric grid generation in a domain with heterogeneous material properties
US20190243024A1 (en) * 2016-07-07 2019-08-08 Total Sa Method of characterising a subsurface region using multiple point statistics
US10519766B2 (en) 2011-10-26 2019-12-31 Conocophillips Company Reservoir modelling with multiple point statistics from a non-stationary training image
US10578767B2 (en) 2012-09-26 2020-03-03 Exxonmobil Upstream Research Company Conditional process-aided multiple-points statistics modeling
US10803534B2 (en) 2014-10-31 2020-10-13 Exxonmobil Upstream Research Company Handling domain discontinuity with the help of grid optimization techniques
US10839114B2 (en) 2016-12-23 2020-11-17 Exxonmobil Upstream Research Company Method and system for stable and efficient reservoir simulation using stability proxies
US11409023B2 (en) 2014-10-31 2022-08-09 Exxonmobil Upstream Research Company Methods to handle discontinuity in constructing design space using moving least squares

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US8818780B2 (en) 2008-11-14 2014-08-26 Exxonmobil Upstream Research Company Forming a model of a subsurface region
US8825461B2 (en) 2008-12-18 2014-09-02 Exxonmobil Upstream Research Company Overlapped multiple layer depth averaged flow model of a turbidity current
US8892412B2 (en) 2009-03-11 2014-11-18 Exxonmobil Upstream Research Company Adjoint-based conditioning of process-based geologic models
US8612195B2 (en) 2009-03-11 2013-12-17 Exxonmobil Upstream Research Company Gradient-based workflows for conditioning of process-based geologic models
US9128212B2 (en) 2009-04-20 2015-09-08 Exxonmobil Upstream Research Company Method for predicting fluid flow
US10162080B2 (en) 2009-04-20 2018-12-25 Exxonmobil Upstream Research Company Method for predicting fluid flow
US8855987B2 (en) 2009-10-23 2014-10-07 Exxonmobil Upstream Research Company Method for optimization with gradient information
US9260947B2 (en) 2009-11-30 2016-02-16 Exxonmobil Upstream Research Company Adaptive Newton's method for reservoir simulation
FR2954557A1 (fr) * 2009-12-23 2011-06-24 Inst Francais Du Petrole Methode d'exploitation d'un gisement petrolier a partir d'une construction d'une carte de facies
US8874419B2 (en) 2009-12-23 2014-10-28 IFP Energies Nouvelles Method of developing a petroleum reservoir from a facies map construction
EP2343576A1 (fr) * 2009-12-23 2011-07-13 IFP Energies nouvelles Méthode d'exploitation d'un gisement pétrolier à partir d'une construction d'une carte de faciès représentative du gisement
US9134454B2 (en) 2010-04-30 2015-09-15 Exxonmobil Upstream Research Company Method and system for finite volume simulation of flow
US9187984B2 (en) 2010-07-29 2015-11-17 Exxonmobil Upstream Research Company Methods and systems for machine-learning based simulation of flow
US9058445B2 (en) 2010-07-29 2015-06-16 Exxonmobil Upstream Research Company Method and system for reservoir modeling
US10087721B2 (en) 2010-07-29 2018-10-02 Exxonmobil Upstream Research Company Methods and systems for machine—learning based simulation of flow
US9058446B2 (en) 2010-09-20 2015-06-16 Exxonmobil Upstream Research Company Flexible and adaptive formulations for complex reservoir simulations
US8942966B2 (en) 2010-10-20 2015-01-27 Conocophillips Company Method for parameterizing and morphing stochastic reservoir models
US20120101786A1 (en) * 2010-10-20 2012-04-26 Conocophillips Company Method for parameterizing and morphing stochastic reservoir models
US9626466B2 (en) 2010-11-23 2017-04-18 Exxonmobil Upstream Research Company Variable discretization method for flow simulation on complex geological models
US9891344B2 (en) 2011-03-09 2018-02-13 Total Sa Computer estimation method, and method for oil exploration and development using such a method
US9489176B2 (en) 2011-09-15 2016-11-08 Exxonmobil Upstream Research Company Optimized matrix and vector operations in instruction limited algorithms that perform EOS calculations
US10519766B2 (en) 2011-10-26 2019-12-31 Conocophillips Company Reservoir modelling with multiple point statistics from a non-stationary training image
US9164193B2 (en) 2012-06-11 2015-10-20 Chevron U.S.A. Inc. System and method for optimizing the number of conditioning data in multiple point statistics simulation
WO2013188008A1 (fr) * 2012-06-11 2013-12-19 Chevron U.S.A. Inc. Système et procédé d'optimisation du nombre de données de conditionnement dans une simulation de statistique à points multiples
US8666149B2 (en) 2012-08-01 2014-03-04 Chevron U.S.A. Inc. Method for editing a multi-point facies simulation
US9121971B2 (en) 2012-08-01 2015-09-01 Chevron U.S.A. Inc. Hybrid method of combining multipoint statistic and object-based methods for creating reservoir property models
US10578767B2 (en) 2012-09-26 2020-03-03 Exxonmobil Upstream Research Company Conditional process-aided multiple-points statistics modeling
US10036829B2 (en) 2012-09-28 2018-07-31 Exxonmobil Upstream Research Company Fault removal in geological models
CN103886216A (zh) * 2014-04-04 2014-06-25 中国石油大学(北京) 一种基于地质矢量信息的多点地质统计方法
US10319143B2 (en) 2014-07-30 2019-06-11 Exxonmobil Upstream Research Company Volumetric grid generation in a domain with heterogeneous material properties
US10803534B2 (en) 2014-10-31 2020-10-13 Exxonmobil Upstream Research Company Handling domain discontinuity with the help of grid optimization techniques
US11409023B2 (en) 2014-10-31 2022-08-09 Exxonmobil Upstream Research Company Methods to handle discontinuity in constructing design space using moving least squares
US20190243024A1 (en) * 2016-07-07 2019-08-08 Total Sa Method of characterising a subsurface region using multiple point statistics
US11960045B2 (en) * 2016-07-07 2024-04-16 Total Se Method of characterising a subsurface region using multiple point statistics
US10839114B2 (en) 2016-12-23 2020-11-17 Exxonmobil Upstream Research Company Method and system for stable and efficient reservoir simulation using stability proxies

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