WO2014142976A1 - Systèmes et procédés pour améliorer la simulation numérique directe de propriétés de matériau à partir d'échantillons de roche et déterminer l'incertitude dans les propriétés de matériau - Google Patents

Systèmes et procédés pour améliorer la simulation numérique directe de propriétés de matériau à partir d'échantillons de roche et déterminer l'incertitude dans les propriétés de matériau Download PDF

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WO2014142976A1
WO2014142976A1 PCT/US2013/032141 US2013032141W WO2014142976A1 WO 2014142976 A1 WO2014142976 A1 WO 2014142976A1 US 2013032141 W US2013032141 W US 2013032141W WO 2014142976 A1 WO2014142976 A1 WO 2014142976A1
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volume
material property
additional
test volumes
difference value
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PCT/US2013/032141
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English (en)
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Laurent LOUIS
Joanne FREDRICH
Elizabeth LIU
Dianne NI
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Bp Corporation North America Inc.
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Priority to PCT/US2013/032141 priority Critical patent/WO2014142976A1/fr
Publication of WO2014142976A1 publication Critical patent/WO2014142976A1/fr

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    • G—PHYSICS
    • G06—COMPUTING; CALCULATING OR COUNTING
    • G06T—IMAGE DATA PROCESSING OR GENERATION, IN GENERAL
    • G06T7/00—Image analysis
    • G06T7/0002—Inspection of images, e.g. flaw detection
    • G06T7/0004—Industrial image inspection
    • G—PHYSICS
    • G01—MEASURING; TESTING
    • G01N—INVESTIGATING OR ANALYSING MATERIALS BY DETERMINING THEIR CHEMICAL OR PHYSICAL PROPERTIES
    • G01N33/00—Investigating or analysing materials by specific methods not covered by groups G01N1/00 - G01N31/00
    • G01N33/24—Earth materials
    • G—PHYSICS
    • G06—COMPUTING; CALCULATING OR COUNTING
    • G06T—IMAGE DATA PROCESSING OR GENERATION, IN GENERAL
    • G06T2200/00—Indexing scheme for image data processing or generation, in general
    • G06T2200/04—Indexing scheme for image data processing or generation, in general involving 3D image data
    • G—PHYSICS
    • G06—COMPUTING; CALCULATING OR COUNTING
    • G06T—IMAGE DATA PROCESSING OR GENERATION, IN GENERAL
    • G06T2207/00—Indexing scheme for image analysis or image enhancement
    • G06T2207/10—Image acquisition modality
    • G06T2207/10056—Microscopic image
    • G06T2207/10061—Microscopic image from scanning electron microscope
    • G—PHYSICS
    • G06—COMPUTING; CALCULATING OR COUNTING
    • G06T—IMAGE DATA PROCESSING OR GENERATION, IN GENERAL
    • G06T2207/00—Indexing scheme for image analysis or image enhancement
    • G06T2207/10—Image acquisition modality
    • G06T2207/10072—Tomographic images
    • G—PHYSICS
    • G06—COMPUTING; CALCULATING OR COUNTING
    • G06T—IMAGE DATA PROCESSING OR GENERATION, IN GENERAL
    • G06T2207/00—Indexing scheme for image analysis or image enhancement
    • G06T2207/20—Special algorithmic details
    • G06T2207/20016—Hierarchical, coarse-to-fine, multiscale or multiresolution image processing; Pyramid transform
    • G—PHYSICS
    • G06—COMPUTING; CALCULATING OR COUNTING
    • G06T—IMAGE DATA PROCESSING OR GENERATION, IN GENERAL
    • G06T2207/00—Indexing scheme for image analysis or image enhancement
    • G06T2207/20—Special algorithmic details
    • G06T2207/20021—Dividing image into blocks, subimages or windows

Definitions

  • This disclosure relates generally to methods and systems for analyzing three dimensional digital volumes of material samples to determine petrophysical properties.
  • REV Representative Elementary Volume
  • FIG. 1 illustrates the traditional definition of the REV for porosity for a porous medium.
  • the sampling volume is denoted by AV
  • the REV volume is denoted byAV 0
  • ⁇ is the void space volume divided by the sampling volume.
  • Figure 2 left pane: sampling volume AV i smaller than REV AV 0 volume
  • porosity calculation for volume reflects local pore scale variability and not the porosity of the porous medium.
  • This means that porosity of the volume is not strictly defined as there isn't a sufficient number of pores and grains to permit a physically meaningful statistical average to be determined.
  • the calculated ratio of void space to total volume will approach one or zero depending on whether the centroid P of the sampling volume is situated within a pore or grain.
  • n t is dominated by local micro scale variability of the pore space.
  • both the presence and size of the classical REV can be quantified for a specific pore system.
  • the REV can be quantified for porosity, permeability and specific surface area for x-ray tomographic images of sandstone.
  • REV can be determined by two different approaches. The first approach consists of selecting a fixed location within the digital volume. Around that location point, an averaging volume is specified of certain scale. Over the averaging volume the porosity, permeability and specific surface is calculated. The size of the averaging volume is then incrementally increased and the properties recalculated.
  • the second approach relates to determining a statistical representative elementary volume, for this case the average statistical properties of the quantity of interest are considered. That is, the SREV is defined as the volume size below which the average of the property begins to fluctuate. The statistical average is determined by choosing volumes of the specified size at a number of different locations throughout the volume and computing the petrophysical property at that point.
  • Implementations of the present teachings relate to a method for analyzing material samples to determine physical properties.
  • the method can include receiving a three- dimensional (3D) digital volume of a material sample. Further, the method can include defining a plurality of test volumes, wherein each of the plurality of test volumes comprises a number of voxels, and wherein the number of voxels for each of the plurality of test volumes is different. Additionally, the method can include determining, for each of the plurality of test volumes, a difference value between a petrophysical property for two adjacent test volumes from the 3D digital volume, each adjacent test volume comprising the number of voxels associated with the test volume. The method can also include plotting the difference value for each of the plurality of test volumes and determining, from the plot of the difference values, a representative elementary volume for testing the material sample.
  • determining the difference value for each of the plurality of test volumes can include selecting a first portion of the 3D digital volume containing the number of voxels and selecting a second portion of the 3D digital volume that is adjacent to the first portion and contains the number of voxels. Then, the method can include calculating a first petrophysical property value for the first portion and calculating a second petrophysical property value for the second portion. Further, the method can include calculating a difference value based on the first petrophysical property value and the second petrophysical property value.
  • Figure 2 is a diagram that illustrates examples of sampling volumes.
  • Figure 5 is a diagram that illustrates an example of a constructed volume generated by a cubic packing of spheres, according to various implementations.
  • Figure 6 is flow diagram that illustrates an example of a process utilized to analyze 3D digital volumes, according to various implementations.
  • Figure 7 is a diagram that illustrates an example of sampling strategy, according to various implementations.
  • Figure 8 is a diagram that illustrates one example in which the test volume sizes can be chosen to sample a 3D digital volume, according to various implementations.
  • Figure 9 is a diagram that illustrates an example of a rock sample and an example of a plot of the difference values, according to various implementations.
  • Figure 10 is a diagram that illustrates an example of a study of REV% for porosity uncertainty for four different digital volumes, according to various implementations.
  • Figure 11 is a diagram that illustrates an example of an x-ray tomographic image and an example of a plot to assess anisotropy, according to various implementations.
  • Figure 12 is a generic block diagram that illustrates components of a computing device, according to various implementations. DETAILED DESCRIPTION
  • Constructed volumes refer to data volumes generated using numerical processes, they may be statistically driven, geologically modeled or a result of data mining or machine learning.
  • Each digital volume can be partitioned into 3D regular elements called voxels. Generally, each voxel is cubic in dimension having a side length equal in x, y, and z directions. The digital volume can contain a different number of voxels in x, y and z directions. Each voxel within a digital volume has an assigned numeric value also known as amplitude. The nature of the numeric value depends on the type of digital volume.
  • image volumes often have a range of numeric values from a lower limit to an upper limit, these limits depend on the acquisition system, in particular whether the data is stored as 8 bit or 16 bit, etc. This range is commonly known as the grayscale range of an image.
  • a typical x-ray tomographic image volume acquired utilizing 16 bit data can have voxels with amplitudes ranging from 0 to 63535. The amplitude of a particular voxel depends on the relative material properties of the imaged sample at that location.
  • relative material properties mean the material properties of the sample at a specific location relative to the material properties of the sample at another location.
  • the relative material properties can be a measure of the relative density at a specific location.
  • Figure 3 illustrates one example of an input type for the process described below, according to various implementations.
  • Figure 3 illustrates an x-ray tomographic image acquired from a sandstone rock sample under ambient pressure and dry fluid saturation.
  • the image volume shows a range of grayscale values, which represent the intensity of the x-ray absorption within the sample. Variation in grayscale data resulting from different amounts of x-ray absorption can be correlated to changes in material density throughout the rock sample.
  • Thresholding can commonly be utilized to separate pore space from grain space within an image volume.
  • a threshold value is chosen within the voxel amplitude range. Voxels having amplitudes below the threshold value are assigned a specific numeric value to denote pore space, while voxels having values above the threshold are assigned another numeric value to denote grain space.
  • the Thresholding process converts a grayscale image volume to a derivative volume consisting of two numeric values, commonly 0 and 1. Thresholding can be applied any number of times to denote various features within a grayscale image.
  • Otsu's method Another example of a segmentation process is called Otsu's method.
  • the Otsu's method includes a histogram-based thresholding technique, where the threshold is chosen so that the variance between a bimodal distribution of grayscale values is minimized.
  • This method can be automated and can also be extended for thresholding a number of times.
  • automated segmentation algorithms of varying complexity which can be utilized to distinguish different features of an image volume, such as Indicator Kriging, Converging Active Contours, Watersheding, etc.
  • Figure 4 illustrates an example of an application of a simple segmentation algorithm to the x-ray tomographic image of Figure 3, according to various implementations.
  • the segmentation algorithm has been utilized to convert a grayscale micro-tomographic image into a derivative volume.
  • the black colored portions of the volume are labeled as pore space.
  • the gray portions of the volume are labeled as grain space.
  • Constructed volumes refer to digital volumes which are usually algorithmically generated.
  • the numerical algorithms can vary in complexity, from replicating granular and porous material by producing cubic packing of spheres, randomly inserting spheres into a cubic volume, or mimicking depositional and compaction processes.
  • geostatistical routines can be utilized to generate random binary media, based on correlation functions and the like.
  • the constructed volumes do not require subsequent segmentation to identify different features of the digital volume, as usually there is sufficient algorithmic labeling. However, in some circumstances it may be necessary to perform subsequent segmentation to identify additional features within the constructed digital volume.
  • Figure 5 illustrates an example of a constructed volume generated by a cubic packing of spheres, according to various implementations. As illustrated in Figure 5, the cubic packing of spheres has been generated numerically by inserting spheres of uniform radius into a three dimensional cubic lattice.
  • a testing tool can be utilized to analyze 3D digital volumes including 3D digital image volumes, derivative volumes, and constructed volumes.
  • the 3D digital volumes can be based on 3D digital image volumes of rock samples.
  • the rock samples can be obtained from whole core, side wall cores, outcrops, drill cuttings and laboratory generated synthetic rock samples, such as sand packs and cemented packs.
  • the 3D image volumes of rock samples can be acquired under ambient pressure conditions, under confining stress, having fluid saturation and under an assortment of other experimental conditions.
  • the testing tool can be utilized to perform the processes described herein on 3D digital volumes of other porous materials, such as paper, bone, etc.
  • the testing tool can be implemented as software, hardware, or a combination of both software and hardware.
  • the testing tool can include the necessary logic, instructions, routines, and algorithms to perform the functionality and processes described herein.
  • the testing tool can be a standalone application program or can be a program module that is part of another application or program.
  • Figure 6 illustrates an example of a process 600 for analyzing a 3D digital volume, according to various implementations.
  • the illustrated stages are examples and any of the illustrated stages can be removed, additional stages can be added, and the order of the illustrated stages can be changed.
  • the process can begin.
  • the testing tool can define one or more test volumes containing a different number of voxels. For each test volume, the testing tool can acquire two adjacent portions of 3D digital volume that are the size of the test volume currently being analyzed. In particular, in 606, the testing tool can acquire first volume of the 3D digital volume that is equal to a test volume. In 608, the testing tool can acquire a second volume of the 3D digital volume that is adjacent to the first volume and equal to the test volume.
  • the testing tool can calculate the petrophysical properties for each of the acquired volumes.
  • the testing tool can calculate, using direct numerical simulation or other methods, material properties.
  • the petrophysical properties can include physical properties, such as porosity, absolute permeability, relative permeability, electrical properties, elastic properties, NMR, etc.
  • the material properties can also include geometrical properties, such as correlation lengths, surface to volume ratio, chord lengths, pore throat radii, grain size and grain shape, etc. for the two adjacent portions of the 3D volume. That is, for a segmented derivative volume, porosity can be obtained by dividing the total number of pore space voxels by the total number of voxels contained within the test volume.
  • absolute permeability can be computed by using a variety of numerical methods such as finite element, finite difference or lattice Boltzmann (LB) methods. These numerical approaches can simulate the physics of single phase fluid flow to compute permeability by either directly solving/approximating the Navier-Stokes equations or recovering the Navier-Stokes equation from a discretization of the Boltzmann equation.
  • Geometrical properties such as correlation lengths, chord lengths, etc. can be obtained using Monte Carlo-like methods, where certain characteristics are randomly sampled throughout each adjacent test volume. For instance, the correlation length can be estimated by randomly sampling two points displaced at a given distance.
  • the testing tool can then calculate the difference value between the two petrophysical properties extracted from adjacent test volumes of the 3D volume.
  • the difference value can represent the percentage difference in the physical or geometrical property values between the two adjacent portions.
  • the testing tool can calculate either the mean of the difference value for the set of adjacent test volumes or can calculate the cumulative mean of the difference values of all previously selected adjacent test volumes and use convergence of the cumulative mean to a value as stopping criterion for selection of further adjacent test volumes.
  • the mean of the difference value for the set of adjacent test volumes or the cumulative mean can be used to determine a difference value that is representative of the specific test volume size. As described herein, the mean of the difference value can also be understood as including the cumulative mean of the difference value.
  • the testing tool can repeat for additional sample of the first volumes and second volumes of the 3D digital volume.
  • the testing tool can use a sampling strategy to select a number of adjacent test volumes.
  • the total number of adjacent test volumes selected can be fixed to a certain number or can vary according to a convergence criterion.
  • the location of the two adjacent test volumes can be selected randomly, systematically, or according to a stratified strategy providing both adjacent test volumes lie within the entire 3D digital volume.
  • the choice of sampling strategy depends on the heterogeneity or homogeneity of the pore structure. For instance, if the pore structure appears homogeneous on a scale much less than the initial test volume size, then a systematic sampling strategy can provide a more efficient method to sample the 3D digital volume than straight random sampling.
  • FIG. 7 illustrates an example of sampling strategy, according to various implementations.
  • the testing tool can utilize random sampling.
  • three different adjacent test volumes have been selected to sample the 3D volume.
  • the testing tool can calculate and plot mean difference values for test volume data and analyze the plot of the mean difference value.
  • the testing tool can analyze the plot to determine a representative elementary volume (REV) that meets a predefined difference value.
  • the plot of the mean difference values can be utilized to determine the uncertainty in petrophysical properties that are calculated or numerically simulated using portions of the 3D volume having different sizes.
  • the testing tool can repeat the process for additional sample volumes.
  • the additional sample volumes can include the same test volume size.
  • the additional sample volumes can include different test volume sizes in order to determine the mean difference value for different sized portions of the 3D digital volume.
  • the different test volume sizes can be selected incrementally to include greater voxels or fewer voxels.
  • Figure 8 illustrates one example in which the test volume sizes can be chosen to sample a 3D digital volume, according to various implementations. As illustrated in Figure 8, the test volume size changes using increments of 25 voxels. That is, the first test volume size is 25 voxels, the second test volume size is 50 voxels, the third test volume size is 75 voxels, and so on.
  • size refers to the length in voxels of one side of the cubic volume.
  • the process can end, return to any point, or repeat.
  • the testing system can improve the efficiency by determining an ideal size of a digital volume to analyze that minimizes the uncertainty in the physical properties simulated due to heterogeneity within the input volume. As such, the testing system can determine a testing size that minimizes the uncertainty in the physical property values without unduly increasing the size of a portion of the digital volume to analyze. Accordingly, the testing tool and system can improve both computational accuracy and computational efficiency.
  • the testing tool can utilize the process described above to determine the representative elementary volume (REV) for a rock sample.
  • REV is defined as being a volume size for which a mean difference value (/?) or /?% of calculated petrophysical property values between two adjacent portions of a digital volume of that size differ by predetermined percentage difference value REV%.
  • Figure 9 illustrates an example of a rock sample and an example of a plot of the difference values, according to various implementations.
  • Figure 9 (right pane) shows the plot of the mean difference values for porosity, here labeled as REV% volumes. The plot shows the porosity uncertainty curve by a power law fit and REV% volumes. The arrows point to REV 10% volume and REV 5% volume sizes.
  • Figure 9 illustrates an x-ray tomographic image of rock having domain size of approximately 5000 microns. REV volumes for 5% (-1200 microns) and 10% (-800 microns) porosity uncertainty are shown. This illustrates the REV volume sizes for both 5% and 10% porosity uncertainty.
  • the testing tool can define the pre-determined percentage as any percentage difference value REV%> that provides a desired percentage difference value between two adjacent test volumes while reducing the size of the test volume. As such, the testing tool can determine a REV that balances the REV% with the size of the test volume.
  • Figure 10 illustrates one study of REV%> for porosity uncertainty for four different digital volumes, according to various implementations.
  • the image domain size is given by the black bar, the mid gray bar shows the 5% uncertainty in porosity domain size, and the light gray bar shows the 10% porosity uncertainty domain size.
  • the greater the difference in domain sizes between the digital volume and the specified REV% domain size the greater the computational savings by using the REV volume.
  • the computation proceeds on the full domain, there is more certainty that the computation of the petrophysical property is not affected by local heterogeneity within the digital volume.
  • the testing tool can calculate the difference value p and difference value percentage p% using
  • V A , V B are either physical or geometrical property values calculated or simulated for the adjacent volumes.
  • the testing tool computes the difference value p a number of times for each test volume size. From the set of difference values for each test volume size, the mean difference value or mean difference value as a percentage (/>%) may be calculated using
  • the testing tool utilizes a cumulative mean difference value p or percentage p% , after the difference value p (or difference value percentage p% ) is computed for two adjacent volumes, the mean difference value p (or mean difference value percentage p% ) is calculated using that value and any previous values calculated for that test volume size.
  • the testing tool can be configured to analyze anisotropy within the digital volume by conducting the REV analysis in orthogonal directions. For example, the testing tool can be configured to conduct REV analysis by selecting adjacent test volumes, so as that they are aligned in the x-direction. The testing tool can then be configured to conduct REV analysis by selecting adjacent test volumes, so as that they are aligned in the z-direction. The testing tool can then compare the plots of the mean difference value percentage or the cumulative mean difference value percentage for each direction. If anisotropy is present within the volume, there is a difference in the shape of the mean (or cumulative mean) difference curves for each direction.
  • the testing tool can be configured to assess the REV% volume when larger scale heterogeneity is present in the digital volume. That is, in some circumstances the desired uncertainty in terms of REV% for a certain petrophysical property can have a domain size which is greater than that of the digital volume.
  • the testing tool can compute the REV% by fitting a power law to the mean difference data plot and extrapolating to larger domain sizes. In Figure 9, right pane, the power law fit to the REV data is shown by a dotted line. This projects uncertainty to domain sizes past 5000 microns.
  • Figure 12 illustrates an example of a hardware configuration for a computing device 1200 that can implement the testing tool for performing one or more of the processes described above. While Figure 12 illustrates various components contained in the computing device 1200, it will be appreciated that additional components can be added and existing components can be removed.
  • the computing device 1200 can also include one or more network interfaces 1208 for communicating via one or more networks, such as Ethernet adapters, wireless transceivers, or serial network components, for communicating over wired or wireless media using protocols.
  • the computing device 1200 can also include one or more storage devices 1210 of varying physical dimensions and storage capacities, such as flash drives, hard drives, random access memory, etc., for storing data, such as images, files, and program instructions for execution by the one or more processors 1202.
  • the computing device 1200 can include one or more software programs 1212, such as the testing tool.
  • the one or more software programs 1212 can include instructions that cause the one or more processors 1202 to perform the processes described herein. Copies of the one or more software programs 1212 can be stored in the one or more memory devices 1204 and/or in the one or more storage devices 1210. Likewise, the data utilized by one or more software programs 1212 can be stored in the one or more memory devices 1204 and/or in the one or more storage devices 1210.
  • the components of the computing device 1200 as described above need not be enclosed within a single enclosure or even located in close proximity to one another.
  • the above-described componentry are examples only, as the computing device 1200 can include any type of hardware componentry, including any necessary accompanying firmware or software, for performing the disclosed implementations.
  • the computing device 1200 can also be implemented in part or in whole by electronic circuit components or processors, such as application-specific integrated circuits (ASICs) or field-programmable gate arrays (FPGAs).
  • ASICs application-specific integrated circuits
  • FPGAs field-programmable gate arrays

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Abstract

L'invention concerne un système de mise à l'essai pouvant analyser un volume numérique en 3D d'un échantillon de matériau. Le système de mise à l'essai peut définir plusieurs volumes d'essai, chaque volume d'essai incluant des nombres différents de voxels. Les volumes d'essai peuvent définir la taille de parties du volume numérique en 3D à analyser. Pour chaque volume d'essai, le système de mise à l'essai peut acquérir deux parties adjacentes d'un volume numérique en 3D qui sont la taille du volume d'essai actuellement en analyse. Le système de mise à l'essai peut calculer une valeur de propriété pétrophysique pour les deux parties adjacentes du volume numérique en 3D et peut calculer la valeur de différence entre les deux parties adjacentes du volume numérique en 3D. Le système de mise à l'essai peut répéter le procédé pour les différents volumes d'essai. Le système de mise à l'essai peut tracer les valeurs de différence moyennes pour les différents volumes d'essai. Le système de mise à l'essai peut analyser le tracé pour déterminer un volume élémentaire représentatif qui satisfait une valeur de différence prédéfinie.
PCT/US2013/032141 2013-03-15 2013-03-15 Systèmes et procédés pour améliorer la simulation numérique directe de propriétés de matériau à partir d'échantillons de roche et déterminer l'incertitude dans les propriétés de matériau WO2014142976A1 (fr)

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