METHOD FOR IDENTIFYING A REPRESENTATIVE DIGITAL VOLUME OF SUB-SAMPLE, METHOD OF OBTAINING AN ESTIMAT

专利摘要:
efficient method for selection of representative elemental volume in digital representations of porous media. The present invention relates to a method for estimating representative elemental volume (rev) in a porous medium sample, in which the selected subvolume is a better approximation of the elemental volume than existing methods. rev in a sample of porous media such as rock can be defined where rev is selected with respect to the expected direction of fluid flow through the porous media. the method can quantify how good the digital representation of a rock is and how accurate the description of a fluid flow through darcy's law will be, and allows the evaluation of different length scales in different directions for the rev and an evaluation of the anisotropy of pore structures when the method is applied in different directions. the method can also determine a robust criterion to understand when a porosity-permeability trend breaks due to insufficient subsample size.
公开号:BR112014024357B1
申请号:R112014024357-3
申请日:2013-02-04
公开日:2021-06-22
发明作者:Giuseppe DE PRISCO；Jonas Toelke
申请人:Ingrain, Inc；
IPC主号:

专利说明:

BACKGROUND OF THE INVENTION
[001] The present invention relates to methods and systems for predicting the properties of fluid flow through a porous medium such as porous rock and, in particular, refers to such methods and systems to select from a digital representation of a heterogeneous porous medium forms the most representative subsample to be used to predict properties such as porosity, permeability, and/or related characteristics.
[002] Digital representations of porous media such as rock, bone, soil and other materials can be produced using x-ray computerized tomographic image scans, scanning electron microscopy, confocal microscopy, and other techniques. Such digital representations are useful for characterization of porous media using computer simulations (Knackstedt, MA, et al, "Digital Core Laboratory: 3D Imaging Derived Reservoir Core Properties", Society of Petroleum Engineers, 2004 and Vermeulen, JP , "New Developments in FESEM Technology", Carl Zeiss nano-Technology Systems Division, http://www.zeiss.com/C1256E4600307C70/EmbedTitelIntern/NewDevelo pmentinFESEMTechnology/$FileNew_Development_FESEM_Technolog y.pdf.).
[003] An important issue in the digital simulation of porous media characteristics is the sample size. Many of the samples of practical interest, such as porous rock, are heterogeneous and average properties for large volumes of porous media would require large samples to be digitized. Many of the rock features, such as absolute permeability, require significant computational resources to simulate and as a result sample sizes are generally much smaller than the volume of interest for representative characterization. Subsamples can be visually selected by a trained geologist, but this approach is subjective and highly variable. In addition, technical and business decisions, such as investment in wells, well drilling plans, estimates of recoverable reserves and other such decisions, made based on digital simulation of rock characteristics often involve large expenses. As a result, there is a need to remove subjectivity, error and variation in the characterization of such porous media.
[004] One approach to identifying suitable subsamples is to identify a representative elementary volume (REV). The REV is the smallest volume over which a specific measurement can be taken that will yield a value representative of the whole. Volumes below the REV, exhibit variation in the specific measurement by making samples smaller than the REV unsuitable for simulations. A method for calculating REV using volumetric porosity as the measurement is described in the literature by Bear (Bear, J., Fluid Dynamics in Porous Media; General Publishing Company Ltd., Canada, 1972, pp 19-21.). Many methods that are labeled REV are not truly "elementary" in the result. That is, many of the methods in use can find subvolumes of a larger volume that are representative of the larger volume, but the method may not produce the smallest possible or elementary volume.
[005] Razavi et al. describes a common approach to REV (Razavi, et al., "Representative Elementary Volume Analysis of Sands Using X-Ray Computed Tomography", Geotechnical Testing Journal, 30 vol., No. 3, Article ID GTJ100164, 2006). The flowchart for the method described by Razavi et al. is shown in Figure 1 thereof. In the method shown by Razavi et al., a point at the approximate center of a sample is selected and then a spherical subsample volume is examined around this central point. Sample properties are calculated for the spherical subsample. The subsample radius is increased and the properties recalculated. The subsample volume is increased step by step until REV is reached. This method has a number of shortcomings. It may not produce an adequate result in certain heterogeneous samples. While it may result in an acceptable RV, it may not produce a REV. As mentioned above, calculations on digital representations of rock samples can require significant computer time to complete, so determining the lowest REV within a sample is of great value.
[006] US Patent No. 6,516,080 (Nur) discloses a method for selecting a REV from a representative area. Figure 2 shows the same way as a square area centered on a face of a sample is increased in size until a representative area is found. The side length of the representative area square is then chosen as the length of sides of a cube centered on the three-dimensional sample. This method depends on the sample being homogeneous and isotropic. This is not typical of many real-world samples such as well cores.
[007] Patent Application Publication No. US 2011/0004447 (Hurley et al.) refers to a method for characterizing a three-dimensional sample of porous media using at least one measurement tool that retrieves two or more sets of data measured transmitted at two or more depths of the sample. In this method, the Porosity Representative Element Volume (REV) is estimated by (1) randomly selecting multiple non-overlapping blocks of uniform size from a measured or modeled sample, (2) plotting individual block porosity against corresponding block volume , and (3) determine the variation between the porosity measured for each sample for a given block volume. Porosity is the average of porosity within the selected sample. When the measured porosity variation falls below a chosen threshold, the corresponding volume is the porosity REV of the rock under study. This method by Hurley et al. it does not grow a volume from a point and as such will cover possible additional subvolumes that would effectively reduce the sample size. The method has shortcomings in that it is designed to use many sub-samples such that a statistically relevant variance can be obtained and may need to use a large sample in order to achieve the desired convergence, which are two needs that are not always possible and can give the entire original sample as RV. The present investigators recognized that this is the case for a sample submitted to Confocal Laser Scanning Microscopy (LSCM). The method by Hurley et al. it may also not identify the lowest possible REV within a sample.
[008] An interesting and powerful approach to characterize the microstructures of a porous medium is the stochastic analysis of the local porosity theory of Hilfer (1992). This method is formulated in a scale dependent fashion and gives a good estimate of the full length scale for a REV. However, the local porosity method does not give results regarding pore space anisotropy. An improvement of this method was made by Liu et al (2009 and 2010) where a local anisotropy distribution, evaluated in a scale-dependent fashion, was evaluated. This improvement required the application of the method by Ketcham (2005), where anisotropy is a function of the variation in the direction of the nature of the pore structures.
[009] Many estimates of the properties of porous media, such as rock, are made using Darcy's Law. Darcy's law is a phenomenologically derived equation that approximates the flow of a fluid through a porous medium. The law was formulated by Henry Darcy based on the results of experiments carried out on the flow of water through sand beds. Darcy's Law is essentially an expression of the conservation of the moment. Darcy's Law, as it is often applied to flow through porous media such as rock samples, can be used to estimate volumetric flow with the following Equation 1, which has Darcy flow parameters such as illustrated in Figure 24:
where Q = volumetric flow rate within a phase in the sample per unit of time, k = is the absolute permeability of the porous medium A = cross-sectional area for flow μ = the dynamic viscosity Pb, Pa = pressure at the inlet and outlet of the volume. L = sample length.
[0010] Formally, to derive Darcy's law, in order to define a permeability, for example, from the first principle some hypotheses must be verified. In particular, as shown by Whitaker, S., Transport in Porous Media 1, 1986, pp. 3-25, one way to derive Darcy's law from Navier Stokes equations (ie, the equation for the moment) is to apply the Gary decomposition:
which is fundamentally a scale decomposition: it is an average quantity (in this case pressure) that is supposed to be "well behaved" over the average integral scale (which can be the sample length scale as well as the transverse or longitudinal dimension ). In other words, these average functions must sufficiently describe the quantities they represent. For example, a pressure signal that changes rapidly over a length scale comparable to the average length scale cannot represent pressure over that length. The quantity is the fluctuating part of the pressure, where it represents the variation of the function. The hypothesis is that the average quantities do not change on small scales where the floating part is allowed to have little variation. To derive Darcy's law, together with Gary decomposition, an averaging operation must be applied to the Navier-Stokes equations (eg, the volume averaging method). However, in this case, one obtains the average of the field gradients while it is the gradient of the average quantities that is desired (as shown in Darcy's law). One can easily prove that the two operators (gradient and averaging) switch when applied to functions that do not change quickly on the averaging length scales. In particular, if the porosity is uniform. Darcy's law can then be written in a more general notation like the following equation 2:
where = average volume flow at an x position. k = is the absolute permeability of the porous medium at position x μ = dynamic viscosity = mean intrinsic pressure gradient (within pores) at position x. Using this equation, on a scale where the average quantities change with position are searched for and the floating part is no longer seen. This equation can be used to simulate the flow in a reservoir.
[0011] When a REV is selected by any of the means described above, the possibility exists that porosity variation within the REV may exist which makes assumptions about Darcy Flow invalid or error prone. Furthermore, the pressure gradient can change rapidly along the flow direction which makes it impossible to define a permeability associated with a particular subsample. This is especially true for highly heterogeneous samples, such as those that can be found in real-world rock formations.
[0012] The present investigators recognized that there is a need for a more efficient method to estimate a representative elemental volume (REV) in a porous medium sample, including for heterogeneous samples. Furthermore, the analysis must represent directional variation of the pore structure in order to take into account the anisotropy of the porous medium and, in the case where a directional property such as flow is considered, the flow direction. SUMMARY OF THE INVENTION
[0013] An important feature of the present invention is to provide an efficient method for estimating a representative elemental volume (REV) in a sample of porous media such as rock, in which the selected subvolume is a better approximation of the elemental volume than existing methods .
[0014] Another feature of the present invention is to provide an efficient method for setting a REV in a sample of porous media such as rock in which the REV is selected in relation to the expected direction of fluid flow through the porous media.
[0015] Another feature of the present invention is to provide an efficient method to quantify how good (or bad) the digital representation of a rock is and how accurate a description of a fluid flow through Darcy's law will be.
[0016] Another feature of the present invention is to provide a method to determine a robust criterion for understanding when a porosity-permeability trend breaks due to an insufficient subsample size.
[0017] Another feature of the present invention is to provide a method to analyze the porous structure in a scale-dependent manner including directional information of the variation of heterogeneities.
[0018] To achieve these and other advantages, and in accordance with the purposes of the present invention, as embodied and broadly described herein, the present invention relates, in part, to a method for identifying a representative subsample digital volume corresponding to a sample of a porous medium, comprising the steps of a) obtaining a segmented volume featuring pore space and at least one solid phase; b) derive an average property value <P1> from a first target function P1 for the entire segmented volume; c) calculate an Ovoi standard deviation from the mean property value <P1> for the entire segmented volume; d) defining a plurality of subvolumes within the volume; e) calculate a standard deviation Oi of the property value P of the first target function P1 relative to the average property value <P1> for each of said subvolumes; f) find all candidate representative subvolumes for which the Oi standard deviation is a satisfactory match for Ovol; g) select and store a representative subvolume among candidates; and h) using the representative subvolume to derive at least one property value of interest.
[0019] The present invention also relates to a method for identifying a digital volume representative of a subsample corresponding to a sample of a porous medium, comprising the steps of: a) obtaining a segmented volume characterizing pore space and at least one phase solid; b) orient a selected axis of the Cartesian grid of the segmented volume to a defined flow direction; c) deriving values as one or more functions of at least a first target function P1 for the entire segmented volume by means of digital slice analysis orthogonal to the defined flow direction; d) defining a plurality of subvolumes within the volume; e) calculate values for the one or more functions of at least a first target function P1 for each of said subvolumes respecting the defined flow direction; f) find all representative subvolume candidates for which the function(s) identifies a correspondence between volume and subvolume values; g) select a representative volume form among the candidates; h) store the representative subvolume; and i) use the representative subvolume for simulation or to obtain at least one property value of interest.
[0020] The present invention also relates to a method to obtain an efficient estimate of a representative elementary volume from a larger 3D digital image of a porous sample, comprising the steps of: a) obtaining a segmented volume characterizing space of pore and at least one solid phase; b) deriving values as at least a function of at least a first target function P1 for the entire segmented volume; c) defining a plurality of subvolumes within the volume, comprising defining an initial size for a subvolume, populating the entire volume with subvolumes of the defined initial size, iterating the sized for additional subvolumes, and populating the entire volume with subvolumes of that size and repeating this step until a stop criterion is met; d) calculating values as at least one function for at least the first target function for each of said subvolumes; e) find all representative candidate subvolumes for the volume values and the satisfactory subvolume match; f) select and store a representative subvolume from among the candidates; and g) use the representative subvolume to conduct a simulation or derive at least one property value of interest.
[0021] The present invention also relates to a method for obtaining an efficient estimate of a representative elementary volume from a larger 3D digital image of a porous sample, comprising the steps of a) obtaining a segmented volume characterizing pore space and at least one solid phase; b) orient a selected axis of the Cartesian grid of the segmented volume to a defined flow direction; c) deriving an average property value <P1> of a first target function P1 for the entire segmented volume using a digital multiple-slice analysis of the sample volume taken orthogonal to the defined flow direction; d) calculate a standard deviation from the mean property value <P1> for the entire segmented volume; e) defining a plurality of subvolumes within the volume, comprising defining an initial size for a subvolume, populating the entire volume with subvolumes of the defined initial size, iterating the sizes for additional subvolumes from small to large, and populating the entire volume with subvolumes of such size and repeat this step until a stopping criterion is reached; f) calculate a standard deviation Oi of property P in relation to the average property value <P1> for each of the referred subvolumes, respecting the defined flow direction; g) find all candidate representative subvolumes for which Oi is a satisfactory match for OWI; h) select the smallest candidate and store it as a representative elementary volume; and i) use the representative elementary volume to obtain at least one property value of interest.
[0022] The present invention also relates to a method for identifying a subsample representative digital volume corresponding to a sample of a porous medium, comprising the steps of 1) loading a three-dimensional segmented image of a porous medium to a computer system , wherein the segmented three-dimensional image comprises voxels each of which is assigned a gray scale value; 2) select a flow direction which is defined as the Z direction; 3) define interrogation volume sizes where i) an interrogation volume is a subsample of the original segmented three-dimensional image with dimensions Xi, Yi and Zi, where the dimensions of the entire sample are Xs, Ys, Zs, ii) a maximum number of interrogation volumes, imax, is defined, iii) dimensions in voxels for each interrogation volume (Xi, Yi, Zi) are defined, where Xi, Yi and Zi are defined for values of i from 1 to imax , and iv) the initial value of i is set to 1; 4) calculate selected properties Ps(0,0,0) to Ps(0,0,Zs) for each slice of the interrogation volume; 5) calculate os(0,0,0); 6) define the maximum coordinates that the interrogation volume of size Xi, Yi, Zi occupies within the entire sample of size Xs, Ys, Zs, where amax = Xs- Xi + 1, bmax = Ys- Yi + 1, cmax = Zs-Zi + 1; 7) set current interrogation volume location coordinates to a = b = c = 0; 8) calculate selected properties Pi(a,b,c) to Pi(a,b,c + Zi) for slices of current interrogation volume, where selected properties include porosity, surface area to volume ratio, similar properties , or any combination thereof, 9) calculate oi(a,b,c) wherein, optionally, the values of Pi that are used to calculate the value of oi are filtered, wherein, optionally, an average value for Pi is defined; 10) move the interrogation volume location by 1 voxel in the X direction, a = a + 1; 11) repeat steps 8) to 10) and store all values of Pi and oi up to the X coordinate value of the current interrogation volume, a, equals the maximum value the current interrogation volume can occupy, amax; 12) set the X coordinate of the current interrogation volume to zero, a = 0, and increment the Y coordinate of the current location volume by 1 voxel, b = b + 1; 13) repeat steps 8) to 12) and store all values of Pi and oi up to the Y coordinate value of the current interrogation volume, b, equals the maximum value the current interrogation volume can occupy, bmax; 14) set the X coordinate of the current interrogation volume to zero, a = 0, setting the Y coordinate of the current interrogation volume to zero, b = 0, and increment the Z coordinate of the current location volume by 1 voxel, c = c+1; 15) repeat steps 8) to 14) and store all values of Pi and oi up to the Z coordinate value of the current interrogation volume, c, equals the maximum value the current interrogation volume can occupy, cmax; 16) increasing the size of the current interrogation volume, comprising: i) selecting the next set of interrogation volumes by increasing the pointer to the next interrogation volume, i = i + 1, and ii) setting the current interrogation size to Xi, Yi, Zi; 17) repeat steps 6) to 16) until all interrogation volumes have been selected and all Pi and Oi values have been calculated and stored; 18) choose one or more selected properties to match; 19) calculate Xi for each interrogation volume; 20) select the interrogation volume with the smallest value of Xi, where the selected interrogation volume is the size and location of the REV; and 21) calculate properties of the porous medium.
[0023] Computer systems, computer readable media, and programs for performing the methods are also provided.
[0024] It is to be understood that the above general description as well as the following detailed description are exemplary and explanatory only and are intended only to provide a further explanation of the present invention.
[0025] The accompanying drawings, which are incorporated in and constitute a part of this application, illustrate some of the embodiments of the present invention and together with the description, serve to explain the principles of the present invention. Drawings are not necessarily to scale. Like numbers in the drawings refer to like elements in the various views. BRIEF DESCRIPTION OF THE DRAWINGS
[0026] Figure 1 is a flowchart illustrating a prior practice for identifying a REV using an M-REV program.
[0027] Figure 2 illustrates another previous sampling scheme to identify a REV with selecting REV from a representative area.
[0028] Figure 3 illustrates another previous sampling scheme to identify a REV using a porosity REV method.
[0029] Figure 4 is a plot of measured property versus sample volume illustrating a previous definition of REV.
[0030] Figures 5A and 5B illustrate subsample selection in pore space connectivity modeled having a tube fluid flow system having large ducts connected through small restrictive ducts according to an example of the present application.
[0031] Figure 6 illustrates a flowchart of a method to estimate a REV based on statistically qualifying subvolumes according to an example of the present application.
[0032] Figure 7 illustrates a sample volume and an interrogation volume, which includes a definition of terms related to the sample and interrogation volume, according to an example of the present application.
[0033] Figures 8A and 8B illustrate subvolume selection in a fluid flow system modeled having a steering fluid flow characteristics markedly according to an example of the present application, where Figure 8A is an aerial view of ducts of fluid flow and Figure 8B is a cross-sectional view of the fluid flow ducts along line 8B-8B of Figure 8A.
[0034] Figure 9 illustrates a digital slice of an interrogation volume according to an example of the present application.
[0035] Figure 10 is a flowchart illustrating a method for estimating a REV including further orienting the grid to flow, testing subvolume suitability with various properties, and methodically moving through the subvolumes according to an example of the present application.
[0036] Figures 11A and 11B illustrate subvolume selection in a more complex fluid flow system modeled according to an example of the present application, in which the Cartesian grid is realigned in Figure 11A and Figure 11B is a cross-sectional view made at line 11B-11B in Figure 11A.
[0037] Figure 12 illustrates a segmented volume that represents a sample of natural rock having substantially heterogeneous characteristics according to an example of the present application.
[0038] Figure 13 illustrates a segmented volume that represents a sample of natural rock having a less heterogeneous structure than that illustrated in Figure 12 according to an example of the present application.
[0039] Figure 14 is a detailed flowchart describing a modality according to an example of the present application.
[0040] Figures 15A and 15B illustrate standard deviation distributions for surface / volume ratio and porosity, respectively, for the fluid flow system modeled in Figures 11A and 11B in which the size of the interrogation volume corresponds to the corresponding elementary cell to periodicity within the entire sample according to an example of the present application.
[0041] Figures 16A-16E illustrate the standard deviation of porosity in the fluid flow system for different interrogation volume sizes in the fluid flow system modeled in Figure 11A-11B according to an example of the present application.
[0042] Figures 17A-17E illustrate the standard deviation of surface to pore space volume ratio in the fluid flow system for different interrogation volume sizes in the fluid flow system modeled in Figure 11A-11B according to an example of this application.
[0043] Figures 18A-18B illustrate the standard deviation for the target porosity functions (Figure 18A) and the surface to volume ratio (Figure 18B) for the rock sample in Figure 13 for a 450X450X450 interrogation volume according to an example of this application.
[0044] Figures 19A-19B illustrate the standard deviation for the target porosity functions (Figure 19A) and the surface to volume ratio (Figure 19B) for the rock sample in Figure 13 for an interrogation volume 300X300X300 according to an example of this application.
[0045] Figures 20A-20B illustrate the standard deviation for the target porosity functions (Figure 20A) and the surface to volume ratio (Figure 20B) for the rock sample in Figure 13 for an interrogation volume 200X200X200 according to an example of this application.
[0046] Figures 21A-21B illustrate the standard deviation for the target porosity functions (Figure 21A) and the surface to volume ratio (Figure 21B) for the rock sample of Figure 12 for a 450X450X450 interrogation volume according to an example of this application.
[0047] Figures 22A-22B illustrate the standard deviation for the target porosity functions (Figure 22A) and the surface to volume ratio (Figure 22B) for the rock sample of Figure 12 for an interrogation volume 300X300X300 according to an example of this application.
[0048] Figures 23A-23B illustrate the standard deviation for the target porosity functions (Figure 23A) and the surface to volume ratio (Figure 23B) for the rock sample of Figure 12 for an interrogation volume 200X200X200 according to an example of this application.
[0049] Figure 24 is a schematic illustration of the Darcy flow.
[0050] Figure 25 illustrates three pore-permeability trends in a plot of absolute permeability (MD) versus porosity (as a fractional value between 0-1.0) for a rock sample from Fountainebleau for subsample dimensions of 95x95x95 ( gray triangles) 190x190x190 (grey circles) and 285x285x285 (grey crosses) and that includes a pore-permeability value for an original sample size of 500x500x500 for a trendline (the solid gray "UL" line that includes the data point of hollow diamond symbol) and black symbols are the optimal choices made by targeting both the surface/volume and porosity function, according to an example of the present application. The two lines are the lower and upper limits, respectively, which are from experiments done on these rocks.
[0051] Figure 26 illustrates correlation of porosity / permeability (poro-permeability) trends in plots of absolute permeability (MD) versus porosity for an unconsolidated sandstone sample for subsample dimensions of 300x300x300 (grey crosses) 200x200x200 (grey circles) and 100x100x100 (grey triangles) according to an example of the present application. The two data sets, namely "1_100" and "1_200" and also "2_100" and "2_200," are for two different samples (Samples 1 and 2). The two samples are very similar.
[0052] Figure 27 illustrates pore-permeability trend curves in absolute permeability (MD) plots versus porosity for a Fontainebleau sample of lower porosity than the sample in Figure 25, which includes pore-permeability trends for dimensions of subsample of 190x190x190 (grey triangles), 285x285x285 (grey circles) and 380x380x380 (grey crosses) and which includes a pore-permeability value for an original sample size of 500x500x500 for a UL trendline (solid gray line intersecting the symbol diamond) and black symbols are the best choices made by targeting both the surface/volume and porosity function, according to an example of the present application. The "Lower Lab" curve is a lower limit of experiments done on these rocks.
[0053] Figures 28A-28H illustrate the mean ratio value (A) of the standard deviation distribution for porosity (Figure 28A), the surface to volume ratio (Figure 28B), the variance (V) of the same distribution for porosity (Figure 28C), the variance of the surface to volume ratio (Figure 28D), the asymmetry to porosity (Figure 28E), the asymmetry variance (Figure 28F), the kurtosis to porosity (Figure 28G), and the kurtosis variance (Figure 28H), all in relation to the subvolume sample dimension (size), for the two different Fontainebleau rocks addressed in Figure 25 and Figure 27, respectively, according to an example of the present application. The Fontainebleau rock discussed in Figure 25 is represented by the curves in Figure 28A-28H, which are defined by black circles, and the rock discussed in Figure 27 is represented by the curves defined in Figures 28A-28H by gray circles. In Figures 28A-28H, plots are numbered in correspondence with the numbers given in their embedded legends and in Figures 25 and 27.
[0054] Figures 29A-29H illustrate the mean ratio value (A) of the standard deviation distribution for porosity (Figure 29A), the surface to volume ratio (Figure 29B), the variance (V) of the same distribution for porosity (Figure 29C), the variance of the surface to volume ratio (Figure 29D), the asymmetry to porosity (Figure 29E), the asymmetry variance (Figure 29F), the kurtosis to porosity (Figure 29G), and the kurtosis variance (Figure 29H), all in relation to the subvolume sample dimension (size), for two different carbonate rocks, respectively, with one of the samples indicated by gray circles and the other by black circles in the plots, according to an example of this application. In Figures 29A-29H, plots are numbered in correspondence with the numbers indicated in their embedded legends and in Figures 29I and 29J.
[0055] Figures 29I-29J illustrate pore-permeability trends for the two different carbonate rocks discussed in Figures 29A-29H according to an example of the present application. Figure 29I includes pore-permeability trends for the sample identified by gray circles in Figures 29A-29H for subsample dimensions of 95x95x95, 190x190x190, and 285x285x285, and which includes a pore-permeability value for an original sample dimension size of 500x500x500 for a D1 trendline (solid gray line, hollow diamond symbol) and black symbols are the best choices made for targeting both surface/volume function and porosity. Figure 29J includes pore-permeability trends for the sample identified by black circles in Figures 29A-29H for subsample dimensions of 190x190x190, 285x285x285 and 380x380x380, and which includes a pore-permeability value for an original sample size of 500x500x500 for a D2 trendline (solid gray line, hollow diamond symbol) and black symbols are the best choices made for targeting both surface/volume function and porosity.
[0056] Figures 30A-30H illustrate the mean ratio value (A) of the standard deviation distribution for porosity (Figure 30A), the surface to volume ratio (Figure 30B), the variance (V) of the same distribution for porosity (Figure 30C), the variance of the surface to volume ratio (Figure 30D), the asymmetry to porosity (Figure 30E), the asymmetry variance (Figure 30F), the kurtosis to porosity (Figure 30G), and the kurtosis variance (Figure 3 OH) all versus subvolume sample dimension (size) for two different relatively homogeneous rocks, respectively, with one sample indicated by gray circles and the other by black circles in these plots, according to an example of the present application. In Figures 30A-30H, plots are numbered in correspondence with the numbers shown in the legends embedded in them. As with the previous numbers, these Figures show plots for two different homogeneous rock samples.
[0057] Figures 31A-31H illustrate the mean ratio value (A) of the standard deviation distribution for porosity (Figure 31A), the surface to volume ratio (Figure 31B), the variance (V) of the same distribution for porosity (Figure 31C), the variance of the surface to volume ratio (Figure 31D), the asymmetry to porosity (Figure 31E), the asymmetry variance (Figure 31F), the kurtosis to porosity (Figure 31G) and the kurtosis variance ( Figure 31H) all versus subvolume sample dimension (size) for two additional rocks, respectively, with one sample indicated by gray circles and the other by black circles in these plots, according to an example of the present application. In Figures 31A-31H, plots are numbered in correspondence with the numbers indicated in their embedded legends and in Figures 31I and 31J. The rocks used as samples were sandstones (Fontainbleau).
[0058] Figures 31I-31J illustrate pore-permeability trends for the two different rocks addressed in Figures 31A-31H according to an example of the present application. Figure 31I includes pore-permeability trends for the sample identified by gray circles in Figures 31A-31H for subsample dimensions of 190x190x190, 285x285x285 and 380x380x380, and which includes a pore-permeability value for an original sample dimension size of 500x500x500 for a D3 trendline (solid gray line, hollow diamond symbol) and black symbols are the best choices made for targeting both surface/volume function and porosity. Figure 31J includes pore-permeability trends for the sample identified by black circles in Figures 31A-31H for subsample dimensions of 95x95x95, 190x190x190 and 285x285x285, and which includes a pore-permeability value for an original sample size of 500x500x500 for a D4 trendline (solid gray line, hollow diamond symbol) and black symbols are the best choices made for targeting both surface/volume function and porosity.
[0059] Figures 32A-32B, 33A-33B, and 34A-34B illustrate the standard deviation DISTRIBUTION for the target functions of porosity (Figure 32A, 33A, 34A) and surface to volume ratio (Figure 32B, 33B, 34B ) for an analyzed sandstone rock sample with original dimension of 550x550x550, where the standard deviation distribution was obtained with a subsample of 200x200x200, and where the segmentation resolution was 10X for Figures 32A-32B, 20X for Figures 33A- 33B, and 40X to Figures 34A-34B, respectively, according to an example of the present application.
[0060] Figures 35A-35B and 36A-36B illustrate the standard deviation for the target functions of porosity (Figure 35A, 36A) and surface to volume ratio (Figure 35B, 36B) for an analyzed sandstone rock sample with dimension original of 550x550x550, where the standard deviation distribution was obtained with a subsample of 200x200x200, and where the segmentation resolution was 4X for Figures 35A-35B and 10X for Figures 36A-36B, respectively, according to an example of the present application.
[0061] Figure 37 shows a system that integrates three-dimensional (3D) scanning images analysis of a porous medium with a method applied to a 3D digital representation of the porous medium, according to an example of the present application. DETAILED DESCRIPTION OF THE PRESENT INVENTION
[0062] The present invention relates, in part, to an efficient method for estimating a representative elementary volume (REV) in a sample of a porous medium, such as rock, in which the selected subvolume is a better approximation of the elementary volume than provided by existing methods.
[0063] The present invention also relates, in part, to a method for characterizing a porous sample such as a reservoir rock by using a smaller subsample that has the same or very similar selected characteristics and selected characteristics variation in the direction of expected fluid flow through the sample. If the samples are too large, they can compromise computer memory and excessive computer time may be required to complete calculations. Therefore, the present invention relates, in part, to a method of collecting REV for subsampling that is representative of the entire sample so computation time can be decreased and computer memory is not compromised. The REV has a sample size and a specific location within the original sample. The REV can be, for example, the physical size and location of the sub-sample in the original sample or the REV can be the digital size and location of the sub-sample in the representation of the original sample. This method produces a subsample at the location within the sample that best matches the porous media characteristics of interest such as porosity and absolute permeability of the larger sample.
[0064] The method of the present invention can be performed on a digital representation of a sample of a porous medium. The digital representation of the porous medium sample can be produced by first generating a CT scan X-ray image of the sample and then segmenting the digital representation to identify each voxel as a grain or pore. Then, the sample main flow direction can be selected by choosing the inlet face where pressure is applied for subsequent Core Analysis (RCAL) and Special Core Analysis (SCAL) measurements. Properties such as porosity, the surface to pore volume ratio (which is also identified as surface / volume and here is calculated as the ratio between the length (2d) or area (3d) of the boundary between pore and solid space and the area (2d) or the volume (3d) of the pore space), other sample properties or combinations thereof are calculated for each subsample slice, orthogonal to the flow direction, so that a property that depends only on the direction coordinate of flow is obtained by the subsample. For such a property function f(z), the standard deviation (a number), with respect to the mean value fv of the entire sample, can be calculated by the equation:

[0065] If o in the previous equation is a small number, the sample function f deviates by a small amount with respect to the same function evaluated in the original large domain (fv), so that is a good representation of that function to the along the main flow direction (since its variations are small in that direction). In the ideal case (that is, for an infinitely large shape), the value for o goes to zero. Initial subsample dimensions are selected close to the original sample size. The standard deviation from the mean fv value of the entire sample is calculated for a subsample location i. Note that in this procedure the "information" contained in the function f is used exhaustively: for each subsample statistic information is extracted along the flow direction. In some previous patents, only an average volume was used for each subsample. The subsample is then moved into the initial sample at all possible locations x_i and the standard deviation is calculated for each location. This gives a T distribution of the standard deviations S_i of the selected property described by f. The frequency among all subsamples defines the distribution of occurrences. The variance of the distribution (its standard deviation) is defined as V, the mean as A, and the mode as M in the descriptions below.
[0066] Subsample dimensions are decreased, for example, by 1 voxel or more on each side, or only in one direction, and selected properties are calculated for all possible subsample locations. This process is repeated until all possible subsample sizes are evaluated or until a stopping criterion is satisfied.
[0067] The REV is selected by using the M mode, or the mean A and variance V of the T distribution of standard deviations. The mode or mean and variance of T are good indicators of the characteristics of the larger sample. If the mode of the T distribution is close to the standard deviation of the larger sample volume, and the variance of the T distribution is small, then a large number of subsamples have the same selected property variation as the original large volume (eg, heterogeneity in the case where the selected property is porosity) so that the subvolume length scale is large enough to represent the entire original volume. In the case that the standard deviation of the selected property of the large original volume is small, and the variance V of the distribution is small also two instructions can be made: 1) the original size of the entire volume is large enough with respect to the variation (eg, heterogeneity) in the direction of flow described by the function f. This scale is an integral scale with respect to the property selected for the original volume, and 2) heterogeneity in the flow direction is small for most subvolumes as well, so these samples are good candidates to represent the larger volume. If the selected properties are, for example, porosity and surface over volume, the subsample corresponding to the same variation as the original volume is expected to have an absolute permeability close to that of the original volume. In the extreme case that the standard deviation of the selected property of the original volume is equal to zero and the variance of the T distribution is also zero, this means that the original large volume is formed by replicating the subvolume in a periodic way in the flow direction: in this case the subvolume represents the elementary volume of the specific quantity described by f. The best subsample location, the REV, is the location where the standard deviation of one, two, or more selected properties matches as close as possible to the standard deviation of the entire original sample. If the standard deviation of the selected sub-sample properties is less than that of the original sample, the sub-sample has less variation than the original sample, meaning it is absent from some of the heterogeneities that the original sample contains and is artificially better. If the standard deviation is greater than that of the original sample, the subsample has stronger heterogeneities than the original sample, and the subsample must be rejected. As a result, the method of the present invention can identify the most representative subsample of near elementary size and can also determine if the initial sample heterogeneity is too large to allow a representative subsample to be used because Darcy's law cannot be applied.
[0068] As discussed in the background above, Figures 1-3 illustrate previous efforts to identify REVs for application in representing porous materials such as rock samples in digital simulations and analysis. Figure 1 illustrates flowchart 300 for investigating concentric spherical subsample volumes of increasing diameter. Figure 2 illustrates concentric squares 302a, 302b, and 302c, range-increasing and converted to three-dimensional cubes in an effort to select a suitable REV. Figure 3 illustrates a modeled volume 310 with several uniformly sized sets of subvolumes, here 312a, 312b and 312c, randomly (but not overlapping) arranged within volume 310. The subvolumes are shown having cubic or cuboid geometries. Volume 310 and subvolumes 312a, 312b, and 312c have the respective dimensions shown in Figure 3. For example, volume 310 has dimensions of 600 x 600 x 150 and subvolume 312a has dimensions of 150 x 150 x 150. Parameters such as porosity and/or permeability are selected and calculated for each subsample and the variance or variability is calculated. Variance limits are chosen and adequacy of a REV is determined by compliance to that limit, eg plus or minus (±) 5% for the mean value of the mean.
[0069] Previous attempts have not yielded an efficient method to approximate the lowest REV and have not addressed the heterogeneous nature of natural rocks or other porous samples either. Furthermore, previous attempts have not provided guidance on the adequacy of the REV for applying Darcy's law.
[0070] Figure 6 is a flowchart of a process of the present invention to further address one aspect of the heterogeneity of actual samples. A 3D digital image of the sample is obtained as a segmented volume 110 from which one or more "P" property values are derived and averaged over the entire volume to generate an average property value for the entire volume, per example, designated <Pvol> or <P> as indicated in the Figure, as shown in step 112. As will be discussed further here below, porosity and surface area/volume are convenient target functions or properties to apply when qualifying REVs, although the invention is not limited thereto. The standard deviation Ovol for the selected properties is also calculated for the entire volume in step 114 ("o"). A set of subvolumes is defined in step 116, and in step 118 moved through the total volume, with the standard deviation oi calculated for each target function in each subvolume. The output of step 118 is compared with stop criteria 120, and if the stop criteria is not met, the size of the subvolumes is set at step 122, and step 116 of defining subvolumes, step 118 for moving through subvolumes and calculating the hi standard deviation for each target function, and step 120 of comparing against stopping criteria are iteratively repeated until stopping criteria 120 is met. The stopping criteria can be, for example, a certain size for the subvolume where adjusting the size of the subvolume comprises successively and progressively decreasing or increasing the subvolume. A specific appropriate stopping criterion is described later in this document within an illustration of an actual application. When stop criterion 120 is met, the process advances to step 124 of finding the smallest suitable REV subvolume. Adequacy is tested, for example, by comparing the standard deviation of the sub-sample oi against that of the total ovol volume for agreement. The REV is stored and used in step 126 to derive property values of interest that are issued in step 128. Practice of this aspect of the present invention provides for selecting a more representative REV, that is, one that corresponds to the heterogeneous nature of the overall sample volume as well as the average property values for one or more selection criteria properties.
[0071] Figure 4 is a graph schematically illustrating an earlier general definition of representative elementary volume or REV. A measured property is represented as a function of the sample volume size. Fluctuations in the measured property tracked by curve 320 reduce with the size of the sample volume until it reduces to a point where the property value in the sub-sample can be taken as representative of the entire volume. In this illustration, this is true for the region beyond sample volume size 322. The REV is the smallest sample sized for this to be observed.
[0072] Although the definition of REV illustrated in Figure 4 is a useful idealized model to start with, it is best suited when the sample is homogeneous and isotropic. This is often not the case. Consider, for example, the situation modeled in Figures 5A and 5B. In this example, a volume 130, which is described in the figures as a cubic volume, has a tube 131 through it. The tube is the pore space, and has a range of diameters, from large tube 134 to small duct constraints 132. An elementary cell containing a representative structure with respect to surface/volume (not with respect to porosity) In this case, it is a segment of tube 131 that includes a transition from large duct 134 to small duct 132. The surface / volume of the total sample volume 130 has, in this case, the same value as the surface / volume of the elementary cell, subvolume 136 In fact, the entire volume is made up of an integer number of repetitions of the elementary cell repeated in the flow direction. If, as in Figure 5A, the interrogation volume 136 used in the REV analysis is exactly the base cell volume, and the target function is surface/volume, the optimal choice is provided. Thus, the hi standard deviation for subvolume 136, which exactly corresponds to the surface/volume ovol standard deviation for the total volume 130 along the flow direction is the same as the elementary cell volume.
[0073] If the elementary volume is smaller than the elementary cell, see subvolume 138 in Figure 5B, the end result will be a volume that cuts a portion of tube 131 to match the surface/volume standard deviation of the entire volume as close as possible.
[0074] Prior art efforts to find a REV constrained to probe randomly or concentrically around a selected point are not well placed to find or identify such an elementary cell. Thus, another feature in some practices of the present invention is a methodical subsampling that sequentially and incrementally moves across the entire sample volume with incrementally varying size subvolumes. This aspect is introduced in the discussion of Figure 10, below, and is facilitated by using a Cartesian grid 140 to define sample volume 142 with coordinates a, b, c and scaled to (Xs, Ys, Zs) and move an interrogation volume scaled iteratively (Xi, Yi, Zi) 144 through it, as shown in Figure 7.
[0075] Returning to Figure 5B, at best, subvolume 138 minimizes the difference between the standard deviation O, of its own surface/volume with the standard deviation of the surface/volume of the entire ovol volume. Note that for this example it makes no sense to define a subvolume 138 that corresponds to the standard deviation for porosity of one for every sample. Another feature benefiting some practices of the present invention is the use of multiple target functions or properties to identify a much more robust REV useful in the wide range of simulations and property derivations. For example, constraints to satisfy both porosity and surface/volume with a match or an optimized combination will produce a more useful REV. This issue is addressed in the following additional discussion here of Figure 10.
[0076] Figures 5A and 5B introduce another problem, the importance of the flow direction and the definition of a REV in relation to a fixed flow direction. This is illustrated more particularly in Figures 8A and 8B. As shown in Figure 8A, arrays of parallel ducts 152 traverse sample volume 150. Figure 8B is a cross-section of Figure 8A taken at line 8B-8B in Figure 8A. Sub-sample 154 is the identified REV having as target functions both porosity and surface/volume standard deviation. It is not uncommon for important properties, including fluid transport properties, to be anisotropic in porous materials such as natural rock samples. That is, properties have directionality. Aligning the Cartesian grid to take this into account makes it easy to settle for the true REV. Returning to Figure 7, aligning the flow direction with, for example, the Z axis will make the solution easier. Visual inspection of the segmented volume may be sufficient to align the grid by discerning a pattern between cracks or ducts providing pore space connectivity, or it may be suggested by pore asymmetry. Alternatively, the anisotropic nature of properties can be determined by preliminarily deriving value estimates from the sample or subsamples. Furthermore, the flow direction can be fixed as a constraint with respect to the position of the core in the reservoir. The illustrated examples are with a fixed flow direction, but it will be appreciated that it may be useful to implement the invention for a combination of different flow directions.
[0077] Figure 9 illustrates the application of a Cartesian grid 160 aligned with the flow direction (arrow 162) and advancing through digital slices 164 of the interrogation volume 166 made orthogonal to the flow direction. Interrogation volume 166 and digital slice 164 are composed of individual voxels 168. Sequentially processing digital slices taken orthogonal to the flow direction facilitates the calculation not only of the standard deviation for the interrogation volume oi, but is also applicable for the calculation of the value mean for target function(s) or property(s) <P1>, <Pn> and standard deviation(s) o1, on for the entire sample, as related to the discussion of steps 112 and 114 in Figure 6.
[0078] Preparation of selection of REV in alignment with the flow direction is another feature benefiting from some practices of the present invention and illustrated in the adopted Figure 10, below.
[0079] Figure 10 presents the flowchart 170 functionally illustrating an embodiment of the present invention incorporating features presented above and will be discussed with a further level of detail. The step of obtaining a segmented volume 172 starts with a 3D grayscale image of the sample of natural rock or other porous material taken by X-ray computed tomography, focused ion beam scanning electron microscope, magnetic resonance imaging, image synchrotron, or other microtomography or microradiology procedures or the like. Examples of CT scanners suitable for imaging usable with methods in accordance with the present invention include, for example, 3D tomographic X-ray transmission microscopes such as MicroXCT-200 and Ultra XRM-L200 CT, which are made by Xradia, Inc. (Pleasanton, California, USA). The grayscale image may, for example, be filtered or otherwise pre-processed prior to segmentation into several phases representing pore spaces and one or more solid phases such as grains and eventually one or more matrix phases. And the initial segmentation can, for example, have post-processing steps to present a better representation of the material sample originally image-formed.
[0080] However, as discussed above, many of the simulations and derivations through which the properties and behavior of the sample can be better understood are computationally extensive and memory extensive and are neither efficient nor feasible to conduct for the entire sample. Thus, the estimation of the lowest REV is very useful.
[0081] As shown in Figure 10, the segmented volume obtained at 172 is oriented in a Cartesian grid aligned with the flow direction, step 174. It is convenient to align the Z axis with the flow direction evident from a visual inspection of the pore space connectivity in the segmented volume representing the sample.
[0082] Successive vertical slices taken orthogonal to the flow direction can be used to develop the means <Pi>, <Pn> in step 176 and standard deviations o1, on in step 178 for multiple target functions or properties, Pi to Pn. The discussion of Figure 9 above is referenced in this regard. Preferably, the target functions are not computationally difficult and are also selected to provide a diversity of inputs that lead to a robust REV estimate useful for a wide range of simulations and property derivations among more computationally and memory demanding applications. Porosity (Φ) and the surface to volume ratio of the pore space are good candidates. As used here, porosity (Φ) is simply calculated as the number of voxels allocated for pore space in the digital slice divided by the total number of voxels in the slice, and this provides a basic target function. Calculating the surface area of the interface between the pore space and solid and matrix phase(s) and dividing this by the total area in the pore spaces of the digital slice provides a second useful digital function. For many applications, these two properties are also the desired criteria for suitable target functions, although it should be understood by those having the benefit of this description and those skilled in the art that other properties may be substituted and/or added. For each property, values for digital slices are averaged to establish a target property function that only depends on the flow direction, and to evaluate the values for the overall sample volume. Another option is to apply a filter to the target function in order to modify it at a specific location along the fixed flow direction. For example, a porosity greater than that of an original rock could be desired by the subsample at the inlet or outlet.
[0083] A size of subsamples or subvolumes is defined in step 180. Subvolumes of the defined size are then propagated throughout the volume, completing the step of defining the subvolume. This could start at a very small size and increase step by step, reference being made to the basic definition of REV illustrated in Figure 4, or it could start with a large size and work towards smaller sub-samples. Having defined a continuous grid of subvolumes, step 182 methodically moves through the subsamples and calculates and stores the standard deviation 01, On for each of the selected target functions. Step 184 searches whether the stopping criteria is met and determines whether to qualify and select the REV from available subsamples or otherwise increases the number of candidates. Stopping criteria can be as simple as reaching a pre-selected size, or they can, for example, be based on the analysis of one or more of the variance (V) and mean (A) calculated for the last set of subsamples against the set previous subsamples. If the stopping criteria is not met, the subsample candidate set is augmented by proceeding with an iterative execution loop and incrementally adjusting the size of the subvolumes in step 186 before returning to step 180 and defining a continuous grid of subvolumes like this scaled across the entire sample. Standard deviations are recalculated and stored and stop criterion 184 is re-searched. When the stop criterion is met, REV selection proceeds by first identifying all subvolumes so that the standard deviation(s) of the subvolume satisfactorily matches that of the sample volume, as indicated in step 186. In the case of multiple target functions, for example , porosity and surface to pore space volume ratio, it may be that no sample provides an appropriate match. In this case, it may be desired to combine the two functions and apply a minimization procedure to select subsamples that correspond to all functions as closely as possible. The smallest subsample from this set of corresponding subsamples is located by step 188 and used for simulations or to derive property values of interest, eg those that require greater memory and/or computational demands, in step 190.
[0084] Figures 11A and 11B illustrate a more complex fluid flow model for sample volume 192. Here, the volume to analyze is made by periodic replication in all directions of an emmental cell 194. Reference is made to the Figures 5A and 5B. The emmental cell is made by a large 196 to small 198 transition that is staggered in the transverse direction of flow. Here, Cartesian grid 200 is realigned to orient with the flow direction and each XY plane within the elementary cell orthogonal to the flow direction has the same porosity value and surface to pore space volume ratio, so the standard deviation of these quantities in the flow direction is zero (no variation). The entire sample has the same value of porosity and surface / volume of the elementary cell because it is formed by an integer number of replication of the elementary cell.
[0085] As in the example of Figures 5A and 5B, if the interrogation volume has the same dimension as the elementary cell, because of the periodicity all the possible volume of that dimension in the entire sample will have the same porosity and surface value / volume with zero standard deviation. In this case modeled in Figures 11A and 11B (actually different views of the same system illustrated with Figures 8A and 8B, discussed above), a surface/volume or porosity standard deviation distribution will be zero with a variation that is also zero . See Figure 15A and 15B, for example, to illustrate the same standard deviation curves for both porosity and surface to pore space volume ratio respectively.
[0086] When the interrogation volume dimension starts to change relative to the elementary cell, the standard deviation distribution shows that the specific dimension is no longer periodic within the entire region: the distribution with the greatest variance is the one in which the volume The question mark is smaller than the elementary cell. In this case, a large variation is expected because the flow direction of the porosity or surface/volume variation will be greater. Figures 16A-16E illustrate the porosity standard deviation distribution for different interrogation volume sizes. The elementary cell illustrated in Figure 11B has a dimension of 80x80x40. Figure 16A covers an interrogation volume of 20x20x10. Figure 16B covers an interrogation volume of 40x40x20 and Figures 16C-E covers interrogation sizes of 79x79x39, 81x81x41, and 120x120x60, respectively. Figures 17A-E discuss the surface/volume distribution for interrogation volume sizes corresponding to Figures 16A-16E, respectively.
[0087] From the examples above, it should be clear that when the distribution mode is close to zero and its variance is also small, the interrogation volume is an almost periodic structure within the entire sample, with respect to the target function specific (either porosity or surface / volume).
[0088] In addition, it is useful to apply the same analysis to a real rock, see Figures 12 and 13. In Figure 12, the sample shows small heterogeneities in contrast to Figure 13, illustrating an example with greater heterogeneities. The sample dimension for both rocks is 500x500x500. For each of these rocks, three distributions are derived for two different target functions, porosity and surface/pore space volume ratio, based on the variable size interrogation volumes. The distributions for the least heterogeneous rock, see Figure 12, are defined in Figures 18A-18B, 19A-19B and 20A-20B, which represent target function pairs for volumes of size 450x450x450, 300x300x300 and 200x200x200, respectively. In the graphs in Figures 18A-18B, 19A-19B, and 20A-20B showing the target function pairs, porosity is shown in Figures 18A, 19A, and 20A and surface/pore space volume is shown in Figures 18B, 19B, and 20B . The same size samples and presentation are applied to the most heterogeneous rock illustrated in Figure 12 in Figures 21A-2 IB, 22A-22B, and 23A and 23B. Each graph presents the standard deviation of the specific property of the whole sample <Pvol> as a point and the standard deviation oi distribution of the interrogation subsample.
[0089] Therefore, it is clear that as the size of the subvolume decreases, the variance of the distribution increases and its mode starts to move in a range of greater value. This means that variations of the target function within a smaller dimensional subsample along the flow direction are expected to be statistically greater than the original volume. In both rocks, the distribution has a very close mode relative to the initial rock standard deviation value whether the subrock dimension is very close to the original rock dimension, or the target function heterogeneities in the flow direction are small for the selected dimension of the subrock. The latter case is for the least heterogeneous rock (eg Figure 12). In the case of rock in Figure 13, it can be seen that the distribution has a large variance and the mode is very far from the value of the entire original rock already for size 300x300x300.
[0090] Figure 14 is a flowchart illustrating an embodiment of the present invention. The following definitions are used in connection with this detailed description of this embodiment of the invention. 1) Flow direction is perpendicular to XY plane 2) Xs = sample width in voxels 3) Ys = sample height in voxels 4) Zs = sample depth in voxels 5) Selected properties can be Φ, Sv, ect 6) i = pointer to the ith interrogation volume 7) imax = number of interrogation volumes 8) Xi = width of interrogation volume i in voxels 9) Yi = height of interrogation volume i in voxels 10) Zi = depth of interrogation volume i in voxels 11) Xmin, Ymin, Zmin = minimum interrogation volume dimension 12) Xmax, Ymax, Zmax = maximum interrogation volume dimension 13) a, b, c = coordinates of the interrogation volume. The a, b, c coordinates are the X, Y, and Z coordinates, respectively, of the upper left corner of the interrogation volume as represented in Figure 6. 14) Ps(a, b, c) = selected property of whole slice sample at location a, b, c 15) Os = standard deviation of the set of selected properties Ps(a, b, c) a Ps(a, b, c + Zi) 16) Pi(a, b, c) = property selected from the slice of the interrogation volume i at location a, b, c 17) Oi = standard deviation of the set of selected properties Pi(a, b, c) a Pi(a, b, c + Zi) relative to all of a sample.
where μ = the mean of all Os, which is the mean of the distribution (A); Os is either the standard deviation of the entire sample or is the minimum value of the distribution in the case that this minimum value is greater than the value of the original sample. The index i of X is a specific target function, eg porosity. If multiple target functions are present, an overlap (or combination) of Xi can be considered where I is the index of the target function.
[0091] This illustrative example of the present invention can use many of the features mentioned above in combination, as comprising the following steps, wherein numbers placed in parentheses are references to related process flowchart boxes identified in Figure 14: 1) An image Three-dimensional segmentation of a porous medium such as a reservoir rock can be loaded into a computer system for image processing and computing of rock properties (10). i. The segmented three-dimensional image can be segmented using any segmentation technique that is used by those skilled in the art. One or more of the segmentation techniques mentioned in Patent Nos. US 8,170,799.; 8,155377; 8,085,974; 8,081,802, and 8,081,796 may be used herein, and these patents are incorporated in their entirety by reference. The segmented three-dimensional images can comprise voxels each of which can be assigned a gray scale value, where each value represents the relative density of the voxel. ii. The three-dimensional segmented image can be produced by a raw image from a computerized tomographic x-ray scanner, which is then segmented by an appropriate software program to classify the voxels as grain, pore or other. 2) The three-dimensional segmented image will be later used in a simulation to estimate the fluid flow through the porous medium. The flow direction is selected and this is defined as the Z direction (11). 3) Sizes of interrogation volumes are defined. Details of this nomenclature are shown in Figure 6. i. An interrogation volume is a subsample of the original three-dimensional segmented image with dimensions Xi, Yi, and Zi. The dimensions of the entire sample are Xs, Ys, Zs (12). ii. A maximum number of interrogation volumes, imax, is defined. iii. Voxel dimensions for each interrogation volume (Xi, Yi, Zi) are defined. Xi, Yi and Zi are defined for values of i from 1 to imax (12). iv. The initial value of i is set to 1 (12). 4) Calculate selected properties Ps(0,0,0) to Ps(0,0, Zs) for each slice of the interrogation volume (13). In Figure 7, the shaded area represents a slice of a 5x5x5 interrogation volume. The coordinates of the slice corners are (0,0,0)(0,5,0)(5,5,0) and (5,0,0). There are 5 slices in this example moving from Z = 0 to Z = 5. The coordinates of the corners of the last slice are (0.0.5) (0.5.0) (5,0.5) and (5.5, 5). 5) Calculate the (0.0.0) (14). 6) Define the maximum coordinates that the interrogation volume of size Xi, Yi, Zi can occupy within the entire sample of size Xs, Ys, Zs (15). i. amax = Xs-Xi + 1 ii. bmax = Ys-Yi + 1 iii. cmax = Zs- Zi +1 7) Set current interrogation volume location coordinates to a = b = c = 0 (16). 8) Calculate selected properties Pi(a,b,c) to Pi(a,b,c + Zi) for slices of the current interrogation volume (17). 1. Selected properties include porosity, surface area to volume ratio, similar properties, or any combination thereof. 9) Calculate oi(a,b,c)(18). i. Optionally mean values of Ps that are used to calculate the value of Oi can be filtered out (19). ii. Optionally, an average value for Pi can be set (20). 10) Move the interrogation volume location by 1 voxel in the X direction, a = a + 1 (21). 11) Repeat steps 8) to 10) of this method storing all values of Pi and oi up to the X coordinate value of the current interrogation volume, a, equal the maximum value that the current interrogation volume can occupy, amax (22) . 12) The X coordinate of the current interrogation volume is set to zero, a = 0, and the Y coordinate of the current location volume is incremented by a voxel, b = b + 1 (23). 13) Repeat steps 8) to 12) of this method storing all values of Pi and oi up to the Y coordinate value of the current interrogation volume, b, equal the maximum value the current interrogation volume can occupy, bmax (24 ). 14) The X coordinate of the current interrogation volume is set to zero, a = 0, the Y coordinate of the current interrogation volume is set to zero, b = 0, and the Z coordinate of the current locating volume is incremented by 1 voxel , c = c + 1 (25). 15) Repeat steps 8 to 14)) of this method storing all values of Pi and oi up to the Z coordinate value of the current interrogation volume, c, equal the maximum value that the current interrogation volume can occupy, cmax (26 ). 16) Increase (or decrease) the size of the current interrogation volume (27). i. Select the next set of interrogation volumes by raising the pointer to the next interrogation volume, i = i + 1. ii. The current question size is set to Xi, Yi, Zi. 17) Repeat steps 6 a) to 16) until all interrogation volumes have been selected and all Pi and oi values have been calculated and stored (28). 18) Choose one or more selected properties to match (29). 19) Calculate Xi for each interrogation volume (30). 20) Select the interrogation volume with the lowest value of Xi. This is the size and location of the REV (31). 21) Calculate desired properties of the porous medium. (1) Desired properties may comprise Routine Core Analysis (RCAL) and Special Core Analysis (SCAL). RCAL analysis includes but is not limited to porosity (connected, isolated, total) kerogen content, absolute permeability on multiple axes (x, y, z). SCAL analysis includes, but is not limited to, relative permeability (relative permeability of two phases: oil-water, oil-gas, or water-gas displacement), capillary pressure (capillary pressure values at each saturation for primary drainage, cycles of secondary drainage and soaks), particle size distribution, electrical properties (formation factor, resistivity index, a, m, n), elastic properties (Vp.Vs, E, K, G, Poisson ratio) and similar analyses.
[0092] Referring to Figure 24, another feature of the present invention is an analysis of the adequacy of the REV for applying Darcy's Law. As noted above, Darcy's Law as it is often applied to flow through porous media such as rock samples is shown in Equation 1. Permeability is often obtained by applying Darcy's Law through Navier Stokes equations (equation for the moment ) using Gary decomposition (see Equation 2). However, as discussed above, this method relies on an average quantity (in this case pressure) that is supposed to be "well behaved" on the average integral scale. Unfortunately, a pressure signal that changes rapidly over a length scale comparable to the average length scale cannot represent the pressure over that length for these applications to provide reliable results. When a REV is selected in accordance with the above, there remains a possibility that porosity variations within the subsample may exist making assumptions about Darcy Flow invalid or error-prone. Furthermore, the pressure gradient can change rapidly along the flow direction making it impossible to define a permeability associated with a particular subsample. This is especially true for highly heterogeneous samples, such as those found in rock formations in the real world.
[0093] Thus, a further aspect of the present invention is an efficient method to quantify how good (or how poor) the digital representation of a rock is and how accurate a description of a fluid flow through Darcy's law will be, i.e. , to robustly and efficiently predict the breaking of the porosity/permeability trend correlation ("pore-permeability") because the digital subsample has become too small. Figure 25 addresses this issue by illustrating pore-permeability trends in a cross-sectional plot of log permeability versus porosity.
[0094] Here, the original rock is an example of a well-documented Fontainebleau rock and the original digital sample has a dimension of 500 x 500 x 500. The pore-permeability value derived from the entire digital sample is the large hollow diamond and it is exactly in the "upper lab" experimental trend shown for Fontainebleau rocks (solid gray line "UL"). "LL" represents the lower limit. This proves that the original size is large enough to have a correct pore-permeability ratio, confirming that it is a RV (Representative Volume). It may be useful to know whether a pore-permeability trend by subdividing the starting whole rock into smaller samples can be traced. Smaller samples will correctly conform to the pore-permeability trend shown with the hollow diamond if they are large enough to be considered an RV. The issue is the point at which the single subsample becomes smaller than the REV, in other words, when the subsample is no longer a representative volume. The gray cross and gray circle symbols are pore-permeability trends derived from subsamples of dimensions 285x285x285 and 190x190x190, respectively. Through these dimensions, the experimental trend of "superior lab" is satisfied. However, the trend breaks down to dimensions of ~100x100x100, illustrated by the trend (grey triangles) for a dimension of 95x95x95. Note that the optimal value (black triangle), limited by this subsample size, is substantially separate from the experimental "upper lab" trend. Compare optimal pore-permeability values shown for subsamples of size 190x190x190 and 285x285x285, respectively, which are indicated by the black circle and cross symbols, respectively.
[0095] Figure 26 is an example of another rock type, which is an unconsolidated sandstone, showing a study of data points indicated by gray crosses, gray circles, and gray triangles, for subsample dimensions of 300x300x300, 200x200x200, and 100x100x100 , respectively, demonstrates that the elemental volume for this rock is evidently equal to or less than 100x100x100.
[0096] Results from a Fontainebleau sample with lower porosity than the sample in Figure 25 are illustrated in Figure 27. The pore-permeability value (the hollow diamond) for the original sample size of 500x500x500 is at the top of the experimental curve of "Upper Lab" (the upper solid gray line "UL"), so size is a representative size. "LL" represents the lower limit. In this case, the pore-permeability correlation breaks down in size to almost 300x300x300, with reference made in this respect to the values shown by the gray circles for sample sizes of 285x285x285, and compared to the trends shown by the gray triangles and gray crosses for sample sizes. sample of 190x190x190 and 380x380x380, respectively.
[0097] Thus, the porosity-permeability cross plots of Figures 25-27 illustrate very different behavior. Clearly, it would be useful to be able to accurately and efficiently predict this behavior.
[0098] Figures 28A-28H illustrate the mean value (UM) of the standard deviation distribution for porosity (Figure 28A) and for surface/volume ratio (Figure 28B), the variance (V) of the same distribution for porosity (Figure 28C ), and the variance of the surface/volume ratio (Figure 28D)) versus subsample dimension (size) for the two Fontainebleau rocks discussed in Figures 25 and 27, respectively. Asymmetry and kurtosis are also assessed, with the results shown in Figures 28E-28H. In Figures 25, 26 and 27, the black diamond, circle and cross symbols are the ideal choices made by the tool aiming at both surface / volume and porosity function. In Figures 28A through 28H, the lines defined by the black circle are for the most porous sample in Figure 25, and the lines defined by the gray circle are the least porous sample in Figure 27. The following is evident from these trends. of data: both distribution means are decreasing with increasing subrock dimension. For a given size, the rate of change of the mean with the subrock dimension becomes small. This happens for a size of 190 (for high porosity rock, black line) and a size of 380 (for low porosity rock, gray line). The variance of the distribution is decreasing and thus reaches a very small value for the same subrock dimension. Higher order moments provide an indication of distribution symmetry when the subsample size is large enough that the distribution becomes Gaussian type.
[0099] Retrieve the meaning of mean and standard deviation (or variance) of the distribution, where the mean, which is the same as the mode of distribution when the distribution is a Gaussian, gives the "position" of the distribution with respect to " zero", and the variance is responsible for its dispersion in relation to the mean value. Figures 11A-11B and 15A-15B show, for example, that a zero-centered distribution with zero variance means perfect periodicity of the chosen subvolumes. Thus, mean and variance are a measure of the "periodicity" for the target function (porosity or surface/volume) of the subvolume across the rock.
[00100] When the dimension of the subrock is decreasing by slowing down from the original size (at the limit, decreasing by one voxel per time), different things happen to the distribution: firstly, the variance starts to increase; second, when the size is reduced by more than a specific threshold, the mean of the distribution starts to change and the distribution becomes non-symmetric (it increases, which means more variation of the target function in the direction of flow) with respect to the value of the target function evaluated in the entire initial rock. Basically, the distribution is moving to the right of the original position (see previous plots referenced here for two different rocks).
[00101] It is evident that for the sub-rock dimension that gives a displacement of the mean, the pore-permeability correlation is broken. This makes sense because when the mean is large and the variance is also large, there is a high probability of choosing a subsample with a large variation in porosity and surface/volume with respect to the original value of this variation. Note that when the mean has the same value as in the entire initial sample, there is a high probability of choosing a subsample with the same porosity and surface / volume variation, but this does not imply the same porosity or surface / volume value (thus permeability ). In other words, there may still be a tendency towards pore-permeability. To further demonstrate these features, other cases for carbonates and sandstones are provided below.
[00102] As other embodiments, for example, Figures 29A-29H illustrate application of methods of the present invention to two different carbonate samples. For both carbonates, the results are seen to be similar to the previous rock. That is, when the mean porosity and standard deviation stop decreasing (or decreasing at a slow rate) for a specific size, the variance is also small and a good pore-permeability trend can be expected. In Figures 29A-29H, the lines defined by the black circle are for the most porous carbonate sample, and the lines defined by the gray circle are for the lowest porosity carbonate sample. The two carbonate samples differ in porosity and especially permeability. The one with the lowest porosity has a permeability of less than 100 MD, and the one with the highest porosity has a permeability of several hundred mD. In Figure 29I, the gray triangle, gray circle, and gray cross symbols relate to the pore-permeability trends for subsample dimensions of 95x95x95, 190x190x190, and 285x285x285, respectively, relative to the pore-permeability trends for the sample identified by gray circles in Figures 29A-29H. In Figure 29J, the gray triangle, gray circle, and gray cross symbols relate to the pore-permeability trends provided for subsample dimensions of 190x190x190, 285x285x285, and 380x380x380, respectively, relative to the pore-permeability trends for the sample identified by black circles in Figures 29A-29H. Note that in each plot of Figures 29I and 29J, the black triangle, circle and cross symbols are the ideal choice made by the tool aiming at both the surface/volume and porosity function.
[00103] Figures 30A-30H illustrate other applications of the present invention, here cases where the rock is relatively homogeneous and can offer good pore-permeability trends from a sub-sample size of 100x100x100. Two different relatively homogeneous rocks were used for this study. In Figures 30A-30H, the line defined by the black circle is for the sample with the greatest porosity, and the line defined by the gray circle is the sample with the least porosity. The pore-permeability of Figures 30A-30H is shown in Figure 26.
[00104] Figures 31A-31H provide still further examples, here two rocks are investigated where the pore-permeability rupture is in dimensions 100x100x100 and almost 200x200x200. In Figures 31A-31H, the line defined by the black circle is for the sample with the highest porosity, and the line defined by the gray circle is the sample with the least porosity. The samples were sandstone. In Figure 31I, the gray triangle (corresponding to the outer surrounding plot), the gray circle (corresponding to the inner surrounding plot), and the gray cross symbols relate to the pore-permeability trends for subsample dimensions of 190x190x190, 285x285x285, and 380x380x380, respectively, related to the pore-permeability trends for the sample identified by gray circles in Figures 31A-31H. In Figure 31J, the gray triangle symbols (corresponding to the largest surrounding plot), the gray circle symbols (corresponding to the intermediate sized surrounding plot), and the gray cross symbols (corresponding to the smallest surrounding plot) refer to pore trends. permeability of subsample dimensions of 95x95x95, 190x190x190, and 285x285x285, respectively, relative to pore-permeability trends for the sample identified by black circles in Figures 31A-31H. In each plot of Figures 31I and 31J, the black triangle, circle and cross symbols are the ideal choice made by the tool aiming at both the surface/volume and porosity function.
[00105] A different way to use this invention is to estimate which resolution and field of view is best suited for a rock. In fact, the dimension of the sub-sample can be fixed, for example up to 400x400x400, and what is changed is the resolution and field of view of the scan. Typically, the number of stitches used is fixed by the scanner and stitches can be allocated in different size volume. This gives different resolution for rock sweep: for a smaller field of view, the resolution will be larger than a large field of view. One of the problems is understanding that the field of view (thus resolution) is adequate for the rock. The standard deviation distribution of the target functions can be used to solve this issue, where the subsample size will be fixed for all fields of view. For example, in Figures 32A-32B, 33A-33B, and 34A-34B, a sandstone is analyzed with an original dimension of 550x550x550. The standard deviation distribution (right surface porosity / left volume) is obtained with a subsample of 200x200x200. What's changing from Figures 32A-32B to Figure 33A-33B to Figures 34A-34B is the segmentation resolution, where the segmented sample has a resolution of 10X, 20X, 40X, and respectively, which can mean that a voxel is 2, 1 and 0.5 microns respectively. It is evident from Figures 33A-33B that a 20X resolution has a distribution with a very large variance and a mean that is much larger than the mean at a 10X resolution as shown in Figure 32A-32B. In order to work with a resolution of 20X, a larger field of view must be used in the segmentation. 10X resolution is acceptable for this example.
[00106] In the following example, which is illustrated in Figures 35A-35B and 36A-36B, another sandstone is analyzed and the standard deviation distribution (right porosity, left surface / volume) is obtained with a subsample of 200x200x200 as before. In this case, the 4X resolution, which is shown in Figures 35A-35B, is more suitable than the 10X resolution, which is shown in Figures 36A-36B, with respect to one in the previous example, where the 10X resolution has a very large mean and variance.
[00107] Referring to Fig. 37, a system 100 is shown, which can be adapted to perform the present methods. As shown in this example, three-dimensional (3D) images of the porous media samples obtained from the source 101 are generated by the scanner 102. The scanner's 3D image output 103 can be transferred to a computer 104 with program instructions for performing of the 3D image analysis, and the indicated simulation data and analysis, to generate modeling sample output / results that can be transmitted to one or more devices 105, such as a screen, a printer, a data storage medium, or combinations thereof. Computer programs used for 3D image analysis and CFD calculations and simulation models can be stored, as a program product, on at least one computer-usable storage medium 104B (e.g., a hard disk, a device of flash memory, a compact disk, a tape/magnetic disk, or other medium) associated with at least one 104A processor (eg a CPU) that is adapted to run the programs, or may be stored on a usable storage medium by external computer (not shown) that is accessible by the computer processor. Computer 104 may include at least one memory unit 104C for storing programs, input data and output data, and other program results, or combinations thereof. For output display, device 105 may be, for example, a display monitor, CRT, or other visual display means (not shown). Computer 104 may include one or more system computers, which may be implemented as a single personal computer or as a computer network. However, those skilled in the art will appreciate that various implementations of techniques described herein can be practiced in a variety of computer system configurations, including hypertext transfer protocol (HTTP) servers, handheld devices, multiprocessor systems, programmable electronics by consumer or microprocessor-based, network computers, minicomputers, mainframe computers, and the like. System units 100 including scanner 102, computer 104, and output display, a printer and/or data storage device/medium 105, may be connected to each other for communication (e.g., data transfer, etc.) via of any cabling, radio frequency communications, telecommunications, Internet connection, or other means of communication.
[00108] The present invention includes the following aspects / modalities / functions in any order and / or in any combination: 1. The present invention relates to a method for identifying a representative subsample digital volume corresponding to a sample of a medium porous, comprising: a) obtaining a segmented volume featuring a pore space and at least one solid phase; b) derive an average property value <P1> from a first target function P1 for the entire segmented volume; c) calculate an Ovoi standard deviation from the mean property value <P1> for the entire segmented volume; d) defining a plurality of subvolumes within the volume; e) calculate a standard deviation oi of property value P of the first target function P1 relative to the average property value <P1> for each of said subvolumes; f) find all candidate representative subvolumes for which the Oi standard deviation is a satisfactory match for OVOI; g) select and store a representative subvolume among candidates; and h) using the representative subvolume to derive at least one property value of interest. 2. The method of any previous or next modality/resource/aspect, wherein defining a plurality of subvolumes within the volume further comprises: defining an initial size for a subvolume; populate the entire volume with subvolumes of the defined initial size; and iterate the sizes for additional subvolumes and populate the entire volume with subvolumes of that size and repeat this step until a stop criterion is satisfied. 3. The method of any previous or next modality / feature / aspect, where iterating the sizes proceeds from large to small in small increments. 4. The method of any previous or next modality / resource / aspect, in which selecting and storing a representative volume further comprises finding the smallest representative digital volume. 5. The method of any previous or next modality / feature / aspect, where the stopping criteria comprises a certain size for the subvolume. 6. The method of any previous or next modality / resource / aspect, which further comprises: orienting a selected axis of the segmented volume Cartesian grid to a defined flow direction; and wherein: deriving an average property value <P1> of a first target function P1 for the entire segmented volume comprises analyzing multiple digital slices of the sample volume taken orthogonal to the defined flow direction; and calculating a standard deviation oi of property of P of the first target function P1 with respect to the average property value <P1> for each of said subvolumes takes place with respect to the flow direction. 7. The method of any previous or next modality / resource / aspect, further comprising: deriving an average property value <P2> from a second target function P2 for the entire segmented volume; calculate an ovol standard deviation from the mean property value <P2> for the entire segmented volume; define a plurality of subvolumes within the volume; calculating a standard deviation oi of the property value P of the second target function P2 relative to the average property value <P2> for each of said subvolumes; find all representative subvolumes for which standard deviation hi is a satisfactory match for ovol by a combination of first target function P1 and second target function P2. 8. The previous or next any modality / feature / aspect method, where the first target function P1 is porosity and the second target function P2 is the ratio of surface area to volume of porous spaces. 9. The method of any previous or next modality / resource / aspect, further comprising a step of qualifying a candidate subvolume prior to selection, comprising determining its suitability for use in deriving fluid transport properties by means of Darcy's Law, said step comprising: constructing a standard deviation distribution of target functions; assess the mean, or optionally any other first-order characterization for the standard deviation distribution of the target function, and the variance, kurtosis, or skewness of the distribution; assess the first-order and higher-order momentum trend in relation to the subvolume dimension; and stop decreasing the subvolume dimension when the first-order moment has changed by at least 0.1 from its value for distribution built into larger subvolume and/or when higher moments are greater than a specific threshold of 0, 1 for variance. 10. The present invention also relates to a method for identifying a sub-sample representative digital volume corresponding to a sample of a porous medium, comprising: a) obtaining a segmented volume characterizing pore space and at least one solid phase; b) orient a selected axis of the Cartesian grid of the segmented volume to a defined flow direction; c) deriving values as one or more functions of at least a first target function P1 for the entire segmented volume by means of digital slice analysis orthogonal to the defined flow direction; d) defining a plurality of subvolumes within the volume; e) calculate values for the one or more functions of at least a first target function P1 for each of said subvolumes respecting the defined flow direction; f) find all representative subvolume candidates for which the function(s) identifies a correspondence between volume and subvolume values; g) select a representative volume form among the candidates; h) store the representative subvolume; and i) use the representative subvolume for simulation or derive at least one property value of interest. 11. The present invention also relates to a method for obtaining an efficient estimate of a representative elementary volume from a larger 3D digital image of a porous sample, said method comprising: a) obtaining a segmented volume characterizing pore space and hair minus one solid phase; b) deriving values as at least a function of at least a first target function P1 for the entire segmented volume; c) defining a plurality of subvolumes within the volume, comprising: defining an initial size for a subvolume, populating the entire volume with subvolumes of the defined initial size, iterating the size for additional subvolumes, and populating the entire volume with subvolumes of that size and repeat this step until a stop criterion is met; d) calculating values as at least one function for at least the first target function for each of said subvolumes; e) find all representative candidate subvolumes for the volume values and the satisfactory subvolume match; f) select and store a representative subvolume from among the candidates; and g) use the representative subvolume to conduct a simulation or derive at least one property value of interest. 12. The method of any previous or next modality / resource / aspect, further comprising a step of qualifying a candidate subvolume prior to selection, comprising determining its suitability for use in deriving fluid transport properties by means of Darcy's Law, said step comprising: constructing a standard deviation distribution of target functions; assess the mean, or optionally any other first-order characterization for the standard deviation distribution of the target function, and the variance, kurtosis, or skewness of the distribution; assess the trend of the first-order and higher-order moment with respect to the size of the subvolume; and stop decreasing the subvolume dimension when the first-order moment has changed by at least 0.1 relative to its value for distribution built into larger subvolume and/or when superior moments are higher than a specific threshold of 0, 1 for variance. 13. The present invention also relates to a method for obtaining an efficient estimate of a representative elementary volume from a larger 3D digital image of a porous sample, comprising: a) obtaining a segmented volume featuring pore space and at least one solid phase; b) orient a selected axis of the Cartesian grid of the segmented volume to a defined flow direction; c) deriving an average property value <P1> of a first target function P1 for the entire segmented volume using a digital multiple-slice analysis of the sample volume taken orthogonal to the defined flow direction; d) calculate a standard deviation from the mean property value <P1> for the entire segmented volume; e) defining a plurality of subvolumes within the volume, comprising: defining an initial size for a subvolume, populating the entire volume with subvolumes of the defined initial size, iterating the sizes for additional subvolumes from large to small, and populating the entire volume with subvolumes of such size and repeat this step until a stop criterion is met; f) calculate a standard deviation oi of property P in relation to the average property value <P1> for each of the referred subvolumes, respecting the defined flow direction; g) find all candidate representative subvolumes that hi is a satisfactory match for ovol; h) select the smallest candidate and store it as a representative elementary volume; and i) use the representative elementary volume to obtain at least one property value of interest. 14. The method of any previous or next modality / resource / aspect, further comprising: deriving an average property value <P2> from a second target function P2 for the entire segmented volume; calculate a standard deviation from the mean property value <P2> for the entire segmented volume; define a plurality of subvolumes within the volume; calculating a standard deviation oi of the second target function P2 relative to the mean property value <P2> for each of said subvolumes; finding all representative subvolumes for which the i is a satisfactory match for Ovol for a combination of first target function P1 and second target function P2. 15. The previous or next any modality / feature / aspect method, where the first target function P1 is porosity and the second target function P2 is the ratio of surface area to volume of porous spaces. 16. The method of any previous or next modality / resource / aspect, further comprising a step of qualifying a candidate subvolume prior to selection, comprising determining its suitability for use in deriving fluid transport properties by means of Darcy's Law, said step comprising: constructing a standard deviation distribution of target functions; assess the mean, or optionally any other first-order characterization for the standard deviation distribution of the target function, and the variance, kurtosis, or skewness of the distribution; assess the trend of the first-order and higher-order moment with respect to the size of the subvolume; and stop decreasing the subvolume dimension when the first-order moment has a change of at least 0.1 (or at least 0.5, 1, 2, 5, or any value) in relation to its value for distribution built in subvolume higher and/or when higher moments are greater than a specific threshold of 0.1 (or other value) for the variance. 17. A method for identifying a sub-sample representative digital volume corresponding to a sample of a porous medium, comprising: 1) uploading a segmented image of a porous medium to a three-dimensional computer system; wherein the segmented three-dimensional image comprises voxels each of which is assigned a gray scale value, 2) select a flow direction which is defined as the Z direction; 3) define interrogation volume sizes, where i) an interrogation volume is a subsample of the original segmented three-dimensional image with dimensions Xi, Yi and Zi, where the dimensions of the entire sample are Xs, Ys, Zs, ii) a maximum number of interrogation volumes, imax, is defined, iii) dimensions in voxels for each interrogation volume (Xi, Yi, Zi) are defined, where Xi, Yi and Zi are defined for i values from 1 to imax, iv) the initial value of i is set to 1; 4) calculate selected properties Ps(0,0,0) to Ps(0,0, Zs) for each slice of the interrogation volume; 5) calculate os(0,0,0); 6) define the maximum coordinates that the interrogation volume of size Xi, Yi, Zi occupies within the entire sample of size Xs, Ys, Zs, where i) amax = Xs- Xi + 1, ii) bmax = Ys- Yi + 1, iii) cmax = Zs-Zi + 1; 7) set current interrogation volume location coordinates to a = b = c = 0; 8) calculate selected properties Pi(a,b,c) to Pi(a,b,c + Zi) for slices of current interrogation volume, where selected properties include porosity, surface area to volume ratio, similar properties , or any combination thereof; 9) calculate oi(a,b,c) i) wherein optionally values of Pi that are used to calculate the value of oi are filtered out, ii) wherein optionally an average value for Pi is defined; 10) move the interrogation volume location by 1 voxel in the X direction, a = a + 1; 11) repeat steps 8) to 10) and store all values of Pi and oi up to the X coordinate value of the current interrogation volume, a, equals the maximum value the current interrogation volume can occupy, amax; 12) set the X coordinate of the current interrogation volume to zero, a = 0, and increment the Y coordinate of the current location volume by 1 voxel, b = b + 1; 13) repeat steps 8) to 12) and store all values of Pi and oi up to the Y coordinate value of the current interrogation volume, b, equals the maximum value that the current interrogation volume can occupy, bmax; 14) set the X coordinate of the current interrogation volume to zero, a = 0, setting the Y coordinate of the current interrogation volume to zero, b = 0, and increment the Z coordinate of the current location volume by 1 voxel, c = c+1; 15) repeat steps 8) to 14) and store all values of Pi and oi up to the Z coordinate value of the current interrogation volume, c, equals the maximum value the current interrogation volume can occupy, cmax; 16) increasing the size of the current interrogation volume, comprising: i) selecting the next set of interrogation volumes by increasing the pointer to the next interrogation volume, i = i + 1, and ii) setting the current interrogation size to Xi , Yi, Zi; 17) repeat steps 6) to 16) until all interrogation volumes have been selected and all Pi and oi values have been calculated and stored; 18) choose one or more selected properties to match; 19) calculate Xi for each interrogation volume; 20) select the interrogation volume with the smallest value of Xi, where the selected interrogation volume is the size and location of the REV; and 21) calculate properties of the porous medium. 18. The previous or next method of any modality / feature / aspect, in which the segmented three-dimensional image is produced as an image of the sample obtained by scanning the sample with a computerized tomographic x-ray scanner, and segmenting the image by a scanning program software to classify voxels as grain, pore and optionally other phases. 19. The method of any previous or next modality / feature / aspect, where the properties comprise Routine Core Analysis (RCAL) properties, Special Core Analysis (SCAL) properties, or both. 20. The method of any modality / feature / aspect above or below, where the RCAL analysis properties are porosity, kerogen content, absolute permeability in several axes, and the SCAL properties are relative permeability, capillary pressure, size distribution of grain, electrical properties, elastic properties, and any combinations thereof. 21. A system for identifying a sub-sample digital volume corresponding to a sample of a porous medium, comprising: a) a scanner capable of producing a three-dimensional digital image of a porous medium, b) a computer comprising at least one operable processor for executing a computer program capable of obtaining a segmented volume featuring pore space and at least one solid phase, c) a computer (the same or different from b)) comprising at least one operable processor for executing a program computer capable of performing calculations, said calculations comprising i) deriving an average property value <P1> from a first target function P1 for the entire segmented volume, ii) calculating an ovol standard deviation from the average property value <P1> for the entire segmented volume, iii) define a plurality of subvolumes within the volume, iv) calculate an Oi standard deviation of the property value ade P of first target function P1 relative to the mean property value <P1> for each of said subvolumes, v) find all candidate representative subvolumes so that standard deviation hi is a satisfactory match for ovol, vi) select and store a subvolume representative from among the candidates, and vii) using the representative subvolume to derive at least one property value of interest, and d) at least one device for displaying, printing or storing the results of the calculations. 22. A computer program product on a computer-readable medium (eg, non-transient) which, when run on a processor in a computerized device, provides a method for performing calculations of one or more or all of the indicated method steps and previous system.
[00109] The present invention may include any combination of these various features or embodiments above and/or below, as set out in sentences and/or paragraphs. Any combination of features described herein is considered to be part of the present invention and no limitation is intended with respect to the combinable features.
[00110] Other features, aspects and advantages will be evident from the foregoing description and the appended claims. Furthermore, not all features, aspects and advantages need to be present in each embodiment of the invention and may appear individually, in various combinations, or in combination with other features, aspects and advantages, without departing from the scope of the claimed invention.

权利要求:
Claims (21)
[0001]
1. Method to identify a representative subsample digital volume corresponding to a sample of a porous medium, characterized by the fact that it comprises: a) obtaining a segmented volume characterizing pore space and at least one solid phase through the steps of: 1 ) upload a three-dimensional segmented image from a porous medium to a computer system; wherein the three-dimensional segmented image comprises voxels each of which is assigned a gray scale value; 2) select a flow direction which is defined as the Z direction; 3) define interrogation volume sizes, where i. an interrogation volume is a subsample of the original three-dimensional segmented image with dimensions Xi, Yi, and Zi, where the dimensions of the entire sample are Xs, Ys, Zs, ii. a maximum number of interrogation volumes, imax, is defined, iii. Voxel dimensions for each interrogation volume (Xi, Yi, Zi) are defined, where Xi, Yi and Zi are defined for values of i from 1 to imax, iv. the initial value of i is set to 1; 4) calculate selected properties Ps(0,0,0) to Ps(0,0, Zs) for each slice of the interrogation volume; 5) calculate os(0,0,0); 6) define the maximum coordinates that the interrogation volume of size Xi, Yi, Zi occupies within the entire sample of size Xs, Ys, Zs, where i. amax = Xs-Xi + 1, ii. bmax = Ys-Yi + 1, iii. cmax = Zs-Zi + 1; 7) set current interrogation volume location coordinates to a = b = c = 0; 8) calculate selected properties Pi(a, b, c) to Pi(a, b, c + Zi) for slices of current interrogation volume, 1. where selected properties include porosity, surface area to volume ratio , similar properties, or any combination thereof; 9) calculate the i (a, b, c) i. where the optionally values of Pi that are used to calculate the value of oi are filtered out, ii. wherein, optionally an average value for Pi is defined; 10) move the interrogation volume location by 1 voxel in the X direction, a = a + 1; 11) repeating steps 8) to 10) and storing all values of Pi and oi up to the X coordinate value of the current interrogation volume, a, equals the maximum value that the current interrogation volume can occupy, amax; 12) set the X coordinate of the current interrogation volume to zero, a = 0, and increment the Y coordinate of the current location volume by 1 voxel, b = b + 1; 13) repeat steps 8) to 12) and store all values of Pi and oi up to the Y coordinate value of the current interrogation volume, b, equaled the maximum value that the current interrogation volume can occupy, bmax; 14) set the X coordinate of the current interrogation volume to zero, a = 0, setting the Y coordinate of the current interrogation volume to zero, b = 0, and increment the Z coordinate of the current location volume by 1 voxel, c = c+1; 15) repeat steps 8) to 14) and store all values of Pi and oi up to the Z coordinate value of the current interrogation volume, c, equals the maximum value the current interrogation volume can occupy, cmax; 16) increase the size of the current interrogation volume, comprising: i. select the next set of interrogation volumes by raising the pointer to the next interrogation volume, i = i + 1, and ii. set the current question size to Xi, Yi, Zi; 17) repeat steps 6) to 16) until all interrogation volumes have been selected and all Pi and oi values have been calculated and stored; 18) choose one or more selected properties to match; 19) calculate Xi for each interrogation volume, where Xi = |(oj) - (os)|/|(μs - os)| where μ = the mean of all Oj's, that is, the mean of the distribution (A), where (A) is the mean ratio value of the standard deviation distribution to porosity, os is the standard deviation of the entire sample or the minimum value of the distribution where this minimum is greater than the original sample value and the index i of X is for a specific target function; 20) select the interrogation volume with the smallest value of Xi, where the selected interrogation volume is the size and location of the REV; and 21) calculate properties of the porous medium; b) derive an average property value <P1> from a first target function P1 for the entire segmented volume; c) calculate an ovol standard deviation from the mean property value <P1> for the entire segmented volume; d) defining a plurality of subvolumes within the volume; e) calculate a standard deviation oi of the property value P of the first target function P1 relative to the average property value <P1> for each of the subvolumes; f) find all candidate representative subvolumes for which the standard deviation oi is a satisfactory match with ovol; g) select and store a representative subvolume among candidates; and h) using the representative subvolume to derive at least one property value of interest.
[0002]
2. Method according to claim 1, characterized in that defining a plurality of subvolumes within the volume further comprises: defining an initial size for a subvolume; populate the entire volume with subvolumes of the defined initial size; and iterate the sizes for additional subvolumes and populate the entire volume with subvolumes of that size and repeat this step until a stop criterion is satisfied.
[0003]
3. Method according to claim 2, characterized in that iterating the sizes proceeds from large to small in small increments.
[0004]
4. Method according to claim 3, characterized in that selecting and storing a representative volume further comprises finding the smallest representative digital volume.
[0005]
5. Method according to claim 4, characterized in that the stopping criteria comprise a certain size for the subvolume.
[0006]
6. Method according to claim 2, characterized in that it further comprises: orienting a selected axis of the Cartesian grid of the segmented volume to a defined flow direction; and wherein: deriving an average property value <P1> of a first target function P1 for the entire segmented volume comprises analyzing multiple digital slices of the sample volume taken orthogonal to the defined flow direction; and calculating a standard deviation Oi of property P of the first target function P1 with respect to the mean property value <P1> for each of the subvolumes takes place with respect to the flow direction.
[0007]
7. Method according to claim 6, characterized in that it further comprises: deriving an average property value <P2> from a second target function P2 for the entire segmented volume; calculate an Ovol standard deviation from the mean property value <P2> for the entire segmented volume; define a plurality of subvolumes within the volume; calculate a standard deviation Oi of the property value P of the second target function P2 relative to the mean property value <P2> for each of the subvolumes; find all representative subvolumes for which the standard deviation Oi is a satisfactory match with Ovol for a combination of first target function P1 and second target function P2.
[0008]
8. Method according to claim 7, characterized in that the first target function P1 is porosity and the second target function P2 is the ratio of surface area to volume of porous spaces.
[0009]
9. Method according to claim 8, characterized in that it further comprises a step of qualifying a candidate subvolume before selection, comprising determining its suitability for use in deriving fluid transport properties through Darcy's Law, the step comprising: constructing a standard deviation distribution of target functions; assess the mean, or optionally any other first-order characterization for the standard deviation distribution of the target function, and the variance, kurtosis, or skewness of the distribution; assess the trend of the first-order and higher-order moment with respect to the size of the subvolume; and stop decreasing the subvolume dimension when the first-order moment has changed by at least 0.1 relative to its value for distribution built into larger subvolume and/or when superior moments are higher than a specific threshold of 0, 1 for variance.
[0010]
10. Method to identify a representative subsample digital volume corresponding to a sample of a porous medium, characterized in that it comprises: a) obtaining a segmented volume characterizing pore space and at least one solid phase through the steps of: 1 ) upload a three-dimensional segmented image from a porous medium to a computer system; wherein the three-dimensional segmented image comprises voxels each of which is assigned a gray scale value; 2) select a flow direction which is defined as the Z direction; 3) define interrogation volume sizes, where i. an interrogation volume is a subsample of the original three-dimensional segmented image with dimensions Xi, Yi, and Zi, where the dimensions of the entire sample are Xs, Ys, Zs, ii. a maximum number of interrogation volumes, imax, is defined, iii. Voxel dimensions for each interrogation volume (Xi, Yi, Zi) are defined, where Xi, Yi and Zi are defined for values of i from 1 to imax, iv. the initial value of i is set to 1; 4) calculate selected properties Ps(0,0,0) to Ps(0,0, Zs) for each slice of the interrogation volume; 5) calculate os(0,0,0); 6) define the maximum coordinates that the interrogation volume of size Xi, Yi, Zi occupies within the entire sample of size Xs, Ys, Zs, where i. amax = Xs-Xi + 1, ii. bmax = Ys-Yi + 1, iii. cmax = Zs-Zi + 1; 7) set current interrogation volume location coordinates to a = b = c = 0; 8) calculate selected properties Pi(a, b, c) to Pi(a, b, c + Zi) for slices of current interrogation volume, 1. where selected properties include porosity, surface area to volume ratio , similar properties, or any combination thereof; 9) calculate Hi (a, b, c) i. where the optionally values of Pi that are used to calculate the value of Oi are filtered out, ii. wherein, optionally an average value for Pi is defined; 10) move the interrogation volume location by 1 voxel in the X direction, a = a + 1; 11) repeating steps 8) to 10) and storing all values of Pi and Oi up to the X coordinate value of the current interrogation volume, a, equals the maximum value that the current interrogation volume can occupy, amax; 12) set the X coordinate of the current interrogation volume to zero, a = 0, and increment the Y coordinate of the current location volume by 1 voxel, b = b + 1; 13) repeat steps 8) to 12) and store all Pi and Oi values up to the Y coordinate value of the current interrogation volume, b, equaled the maximum value that the current interrogation volume can occupy, bmax; 14) set the X coordinate of the current interrogation volume to zero, a = 0, setting the Y coordinate of the current interrogation volume to zero, b = 0, and increment the Z coordinate of the current location volume by 1 voxel, c = c+1; 15) repeat steps 8) to 14) and store all values of Pi and oi up to the Z coordinate value of the current interrogation volume, c, equals the maximum value the current interrogation volume can occupy, cmax; 16) increase the size of the current interrogation volume, comprising: i. select the next set of interrogation volumes by raising the pointer to the next interrogation volume, i = i + 1, and ii. set the current question size to Xi, Yi, Zi; 17) repeat steps 6) to 16) until all interrogation volumes have been selected and all Pi and oi values have been calculated and stored; 18) choose one or more selected properties to match; 19) calculate Xi for each interrogation volume, where Xi = |(θj) - (os)|/|(μs - os)| where μ = the mean of all the j's, that is, the mean of the distribution (A), where (A) is the mean ratio value of the standard deviation distribution to porosity, os is the standard deviation of the entire sample or the minimum value of the distribution where this minimum is greater than the original sample value and the index i of X is for a specific target function; 20) select the interrogation volume with the smallest value of Xi, where the selected interrogation volume is the size and location of the REV; and 21) calculate properties of the porous medium; b) orient a selected axis of the Cartesian grid of the segmented volume to a defined flow direction; c) deriving values as one or more functions of at least a first target function P1 for the entire segmented volume by means of digital slice analysis orthogonal to the defined flow direction; d) defining a plurality of subvolumes within the volume; e) calculate values for one or more functions of at least a first target function P1 for each of the subvolumes respecting the defined flow direction; f) find all representative subvolume candidates for which the function(s) identifies a correspondence between volume and subvolume values; g) select a representative volume form among the candidates; h) store the representative subvolume; and i) use the representative subvolume for simulation or derive at least one property value of interest.
[0011]
11. Method to obtain an estimate of a representative elementary volume from a larger 3D digital image of a porous sample, characterized by the fact that it comprises: a) obtaining a segmented volume characterizing pore space and at least one solid phase by means of of the steps of: 1) uploading a three-dimensional segmented image from a porous medium to a computer system; wherein the three-dimensional segmented image comprises voxels each of which is assigned a gray scale value; 2) select a flow direction which is defined as the Z direction; 3) define interrogation volume sizes, where i. an interrogation volume is a subsample of the original three-dimensional segmented image with dimensions Xi, Yi, and Zi, where the dimensions of the entire sample are Xs, Ys, Zs, ii. a maximum number of interrogation volumes, imax, is defined, iii. Voxel dimensions for each interrogation volume (Xi, Yi, Zi) are defined, where Xi, Yi and Zi are defined for values of i from 1 to imax, iv. the initial value of i is set to 1; 4) calculate selected properties Ps(0,0,0) to Ps(0,0, Zs) for each slice of the interrogation volume; 5) calculate Os(0,0,0); 6) define the maximum coordinates that the interrogation volume of size Xi, Yi, Zi occupies within the entire sample of size Xs, Ys, Zs, where i. amax = Xs-Xi + 1, ii. bmax = Ys-Yi + 1, iii. cmax = Zs-Zi + 1; 7) set current interrogation volume location coordinates to a = b = c = 0; 8) calculate selected properties Pi(a, b, c) to Pi(a, b, c + Zi) for slices of current interrogation volume, 1. where selected properties include porosity, surface area to volume ratio , similar properties, or any combination thereof; 9) calculate Hi (a, b, c) i. where the optionally values of Pi that are used to calculate the value of Oi are filtered out, ii. wherein, optionally an average value for Pi is defined; 10) move the interrogation volume location by 1 voxel in the X direction, a = a + 1; 11) repeating steps 8) to 10) and storing all values of Pi and oi up to the X coordinate value of the current interrogation volume, a, equals the maximum value that the current interrogation volume can occupy, amax; 12) set the X coordinate of the current interrogation volume to zero, a = 0, and increment the Y coordinate of the current location volume by 1 voxel, b = b + 1; 13) repeat steps 8) to 12) and store all values of Pi and oi up to the Y coordinate value of the current interrogation volume, b, equaled the maximum value that the current interrogation volume can occupy, bmax; 14) set the X coordinate of the current interrogation volume to zero, a = 0, setting the Y coordinate of the current interrogation volume to zero, b = 0, and increment the Z coordinate of the current location volume by 1 voxel, c = c+1; 15) repeat steps 8) to 14) and store all values of Pi and oi up to the Z coordinate value of the current interrogation volume, c, equals the maximum value the current interrogation volume can occupy, cmax; 16) increase the size of the current interrogation volume, comprising: i. select the next set of interrogation volumes by raising the pointer to the next interrogation volume, i = i + 1, and ii. set the current question size to Xi, Yi, Zi; 17) repeat steps 6) to 16) until all interrogation volumes have been selected and all Pi and oi values have been calculated and stored; 18) choose one or more selected properties to match; 19) calculate Xi for each interrogation volume, where Xi = |(oj) - (os)|/|(μs - os)| where μ = the mean of all the j's, that is, the mean of the distribution (A), where (A) is the mean ratio value of the standard deviation distribution to porosity, os is the standard deviation of the entire sample or the minimum value of the distribution where this minimum is greater than the original sample value and the index i of X is for a specific target function; 20) select the interrogation volume with the smallest value of Xi, where the selected interrogation volume is the size and location of the REV; and 21) calculate properties of the porous medium; b) deriving values as at least a function of at least a first target function P1 for the entire segmented volume; c) defining a plurality of subvolumes within the volume, comprising: defining an initial size for a subvolume, populating the entire volume with subvolumes of the defined initial size, iterating the sized for additional subvolumes, and populating the entire volume with subvolumes of that size and repeating this step until a stopping criterion is satisfied; d) calculating values as at least one function for at least the first target function for each of the subvolumes; e) find all representative candidate subvolumes for the volume values and the satisfactory subvolume match; f) select and store a representative subvolume from among the candidates; and g) use the representative subvolume to conduct a simulation or derive at least one property value of interest.
[0012]
12. Method according to claim 11, characterized in that it further comprises a step of qualifying a candidate subvolume before selection, comprising determining its suitability for use in deriving fluid transport properties through Darcy's Law, the step comprising: constructing a standard deviation distribution of target functions; assess the mean, or optionally any other first-order characterization for the standard deviation distribution of the target function, and the variance, kurtosis, or skewness of the distribution; assess the trend of the first-order and higher-order moment in relation to the subvolume dimension; and stop decreasing the subvolume dimension when the first-order moment has changed by at least 0.1 relative to its value for distribution built into larger subvolume and/or when superior moments are higher than a specific threshold of 0, 1 for variance.
[0013]
13. Method for obtaining an estimate of a representative elementary volume from a larger 3D digital image of a porous sample, characterized by the fact that it comprises: a) obtaining a segmented volume characterizing pore space and at least one solid phase by means of of the steps of: 1) uploading a three-dimensional segmented image from a porous medium to a computer system; wherein the three-dimensional segmented image comprises voxels each of which is assigned a gray scale value; 2) select a flow direction which is defined as the Z direction; 3) define interrogation volume sizes, where i. an interrogation volume is a subsample of the original three-dimensional segmented image with dimensions Xi, Yi, and Zi, where the dimensions of the entire sample are Xs, Ys, Zs, ii. a maximum number of interrogation volumes, imax, is defined, iii. Voxel dimensions for each interrogation volume (Xi, Yi, Zi) are defined, where Xi, Yi and Zi are defined for values of i from 1 to imax, iv. the initial value of i is set to 1; 4) calculate selected properties Ps(0,0,0) to Ps(0,0, Zs) for each slice of the interrogation volume; 5) calculate Os(0,0,0); 6) define the maximum coordinates that the interrogation volume of size Xi, Yi, Zi occupies within the entire sample of size Xs, Ys, Zs, where i. amax = Xs-Xi + 1, ii. bmax = Ys-Yi + 1, iii. cmax = Zs-Zi + 1; 7) set current interrogation volume location coordinates to a = b = c = 0; 8) calculate selected properties Pi(a, b, c) to Pi(a, b, c + Zi) for slices of current interrogation volume, 1. where selected properties include porosity, surface area to volume ratio , similar properties, or any combination thereof; 9) calculate the i (a, b, c) i. where the optionally values of Pi that are used to calculate the value of oi are filtered out, ii. wherein, optionally an average value for Pi is defined; 10) move the interrogation volume location by 1 voxel in the X direction, a = a + 1; 11) repeating steps 8) to 10) and storing all values of Pi and oi up to the X coordinate value of the current interrogation volume, a, equals the maximum value that the current interrogation volume can occupy, amax; 12) set the X coordinate of the current interrogation volume to zero, a = 0, and increment the Y coordinate of the current location volume by 1 voxel, b = b + 1; 13) repeat steps 8) to 12) and store all Pi and Oi values up to the Y coordinate value of the current interrogation volume, b, equaled the maximum value that the current interrogation volume can occupy, bmax; 14) set the X coordinate of the current interrogation volume to zero, a = 0, setting the Y coordinate of the current interrogation volume to zero, b = 0, and increment the Z coordinate of the current location volume by 1 voxel, c = c+1; 15) repeat steps 8) to 14) and store all Pi and Oi values up to the Z coordinate value of the current interrogation volume, c, equals the maximum value the current interrogation volume can occupy, cmax; 16) increase the size of the current interrogation volume, comprising: i. select the next set of interrogation volumes by raising the pointer to the next interrogation volume, i = i + 1, and ii. set the current question size to Xi, Yi, Zi; 17) repeat steps 6) to 16) until all interrogation volumes have been selected and all Pi and Oi values have been calculated and stored; 18) choose one or more selected properties to match; 19) calculate Xi for each interrogation volume, where Xi = l(θj) - (os)l/l(μs - os)l where μ = the mean of all Oj's, that is, the mean of the distribution (A ), where (A) is the mean ratio value of the standard deviation distribution to porosity, Os is the standard deviation of the entire sample or the minimum value of the distribution where this minimum is greater than the value of the original sample and the index i of X is for a specific target function; 20) select the interrogation volume with the smallest value of Xi, where the selected interrogation volume is the size and location of the REV; and 21) calculate properties of the porous medium; b) orient a selected axis of the Cartesian grid of the segmented volume to a defined flow direction; c) deriving an average property value <P1> of a first target function P1 for the entire segmented volume using a digital multiple-slice analysis of the sample volume taken orthogonal to the defined flow direction; d) calculate a standard deviation from the mean property value <P1> for the entire segmented volume; e) defining a plurality of subvolumes within the volume, comprising: defining an initial size for a subvolume, populating the entire volume with subvolumes of the defined initial size, iterating the sizes for additional subvolumes from large to small, and populating the entire volume with subvolumes of such size and repeat this step until a stop criterion is met; f) calculate a standard deviation oi of property P in relation to the average property value <P1> for each of the subvolumes respecting the defined flow direction; g) find all candidate representative subvolumes for which Oi is a satisfactory match for OWI; h) select the smallest candidate and store it as a representative elementary volume; and i) use the representative elementary volume to obtain at least one property value of interest.
[0014]
14. Method according to claim 13, characterized in that it further comprises: deriving an average property value <P2> from a second target function P2 for the entire segmented volume; calculate a standard deviation from the mean property value <P2> for the entire segmented volume; define a plurality of subvolumes within the volume; calculate a standard deviation σi of the second target function P2 in relation to the mean property value <P2> for each of the subvolumes; find all representative subvolumes for which σi is a satisfactory match for σνοl for a combination of first target function P1 and second target function P2.
[0015]
15. Method according to claim 14, characterized in that the first target function P1 is porosity and the second target function P2 is the ratio of surface area to volume of porous spaces.
[0016]
16. Method according to claim 15, characterized in that it further comprises a step of qualifying a candidate subvolume before selection, comprising determining its suitability for use in deriving fluid transport properties through Darcy's Law, the step comprising: constructing a standard deviation distribution of target functions; assess the mean, or optionally any other first-order characterization for the standard deviation distribution of the target function, and the variance, kurtosis, or skewness of the distribution; assess the trend of the first-order and higher-order moment with respect to the size of the subvolume; and stop decreasing the subvolume dimension when the first-order moment has changed by at least 0.1 relative to its value for distribution built into larger subvolume and/or when superior moments are higher than a specific threshold of 0, 1 for variance.
[0017]
17. Method for identifying a sub-sample representative digital volume corresponding to a sample of a porous medium, characterized in that it comprises: 1) uploading a three-dimensional segmented image of a porous medium to a computer system; wherein the three-dimensional segmented image comprises voxels each of which is assigned a gray scale value; 2) select a flow direction which is defined as the Z direction; 3) define interrogation volume sizes, where i. an interrogation volume is a subsample of the original three-dimensional segmented image with dimensions Xi, Yi, and Zi, where the dimensions of the entire sample are Xs, Ys, Zs, ii. a maximum number of interrogation volumes, imax, is defined, iii. Voxel dimensions for each interrogation volume (Xi, Yi, Zi) are defined, where Xi, Yi and Zi are defined for values of i from 1 to imax, iv. the initial value of i is set to 1; 4) calculate selected properties Ps(0,0,0) to Ps(0,0, Zs) for each slice of the interrogation volume; 5) calculate σs(0,0,0); 6) define the maximum coordinates that the interrogation volume of size Xi, Yi, Zi occupies within the entire sample of size Xs, Ys, Zs, where i. amax = Xs-Xi + 1, ii. bmax = Ys-Yi + 1, iii. cmax = Zs-Zi + 1; 7) set current interrogation volume location coordinates to a = b = c = 0; 8) calculate the selected properties Pi(a,b,c) to Pi(a,b,c + Zi) for slices of the current interrogation volume, i. wherein selected properties include porosity, surface area to volume ratio, similar properties, or any combination thereof; 9) calculate σi (a, b, c) i. where the optionally values of Pi that are used to calculate the value of σi are filtered out, ii. wherein, optionally an average value for Pi is defined; 10) move the interrogation volume location by 1 voxel in the X direction, a = a + 1; 11) repeating steps 8) to 10) and storing all values of Pi and σi up to the X coordinate value of the current interrogation volume, a, equals the maximum value that the current interrogation volume can occupy, amax; 12) set the X coordinate of the current interrogation volume to zero, a = 0, and increment the Y coordinate of the current location volume by 1 voxel, b = b + 1; 13) repeat steps 8) to 12) and store all values of Pi and σi up to the Y coordinate value of the current interrogation volume, b, equaled the maximum value that the current interrogation volume can occupy, bmax; 14) set the X coordinate of the current interrogation volume to zero, a = 0, setting the Y coordinate of the current interrogation volume to zero, b = 0, and increment the Z coordinate of the current location volume by 1 voxel, c = c+1; 15) repeat steps 8) to 14) and store all values of Pi and σi up to the Z coordinate value of the current interrogation volume, c, equals the maximum value the current interrogation volume can occupy, cmax; 16) increase the size of the current interrogation volume, comprising: i. select the next set of interrogation volumes by raising the pointer to the next interrogation volume, i = i + 1, and ii. set the current question size to Xi, Yi, Zi; 17) repeat steps 6) to 16) until all interrogation volumes have been selected and all values of Pi and σi have been calculated and stored; 18) choose one or more selected properties to match; 19) calculate λi for each interrogation volume, where λi = |(σj) - (σs)|/|(µs - σs)| where µ = the mean of all σj's, ie the mean of the distribution (A), where (A) is the mean ratio value of the standard deviation distribution to porosity, σs is the standard deviation of the entire sample or the minimum value of the distribution where this minimum is greater than the value of the original sample and the index i of λ is for a specific target function; 20) select the interrogation volume with the smallest value of λi, where the selected interrogation volume is the size and location of the REV; and 21) calculate properties of the porous medium.
[0018]
18. Method according to claim 17, characterized in that the segmented three-dimensional image is produced as an image of the sample obtained by scanning the sample with a computerized tomographic x-ray scanner, and segmenting the image by a software program to classify voxels as grain, pore and optionally other phases.
[0019]
19. Method according to claim 17, characterized in that the properties comprise Routine Core Analysis (RCAL) properties, Special Core Analysis (SCAL) properties or both properties.
[0020]
20. Method according to claim 19, characterized in that the RCAL analysis properties are porosity, kerogen content, absolute permeability in several axes, and the SCAL properties are relative permeability, capillary pressure, grain size distribution, electrical properties, elastic properties, and any combinations thereof.
[0021]
21. A computer-readable medium characterized by containing instructions that, when executed, cause the computer to perform the method calculations as defined in any one of claims 1 to 20.

类似技术:

---

公开号 | 公开日 | 专利标题

---

BR112014024357B1|2021-06-22|METHOD FOR IDENTIFYING A REPRESENTATIVE DIGITAL VOLUME OF SUB-SAMPLE, METHOD OF OBTAINING AN ESTIMATE OF A REPRESENTATIVE ELEMENTARY VOLUME FROM A LARGER 3D DIGITAL IMAGE OF A POROUS SAMPLE, AND MEDIUM-READABLE COMPUTER

---

US9396547B2|2016-07-19|Output display for segmented digital volume representing porous media

---

AlRatrout et al.2017|Automatic measurement of contact angle in pore-space images

---

Jing et al.2016|Coal cleat reconstruction using micro-computed tomography imaging

---

CN107449707B|2020-01-07|Three-dimensional characterization determination method and device for quantification of pores with different scales in shale reservoir

---

ES2701906T3|2019-02-26|Procedure to determine the permeability of a rock formation using computed tomographic images of it

---

US9927554B2|2018-03-27|Digital core model construction

---

AU2017239499B2|2018-09-27|Digital rock analysis systems and methods that reliably predict a porosity-permeability trend

---

RU2656256C2|2018-06-04|Determination of trends using digital physics wastes and their application for scaling

---

Wu et al.2019|Imaged based fractal characterization of micro-fracture structure in coal

---

Ji et al.2018|An improved method for reconstructing the digital core model of heterogeneous porous media

---

Adeleye et al.2018|Pore-scale analyses of heterogeneity and representative elementary volume for unconventional shale rocks using statistical tools

---

Callow et al.2020|Optimal X-ray micro-CT image based methods for porosity and permeability quantification in heterogeneous sandstones

---

BR112016002538B1|2020-10-13|method for generating forming properties of a pressurized downhole environment and system for generating forming properties of a pressurized downhole environment

---

Mohammadmoradi et al.2017|Pore network and morphological characterization of pore-Level structures

---

Xu et al.2020|Identifying the comprehensive pore structure characteristics of a rock from 3D images

---

Song2019|An improved simulated annealing algorithm for reconstructing 3D large-scale porous media

---

Hou et al.2011|Prediction of microscopic remaining oil distribution using fuzzy comprehensive evaluation

---

Hu et al.2015|Correlating recovery efficiency to pore throat characteristics using digital rock analysis

---

Ju et al.2017|Topological representation of the porous structure and its evolution of reservoir sandstone under excavation-induced loads

---

Deglint2018|Use of Imaging Techniques to Quantify Fluid-Rock Interaction and Petrophysical Properties in Low Permeability Hydrocarbon Reservoirs

---

Guo et al.2021|A New Method of Central Axis Extracting for Pore Network Modeling in Rock Engineering

---

Cao2018|Digital image-based computational approaches for three-dimensional microstructure characterization

---

Zhang2019|Comparative Study of Pore Structure Characterization for Different Rock Samples Using Digital Images

---

Wang et al.2018|Improved skeleton extraction method considering surface feature of natural micro fractures in unconventional shale/tight reservoirs

同族专利:

---

公开号 | 公开日

---

EP2831578A1|2015-02-04|

---

MX2014011709A|2014-12-08|

---

AU2013240570B2|2015-05-14|

---

CN104335042A|2015-02-04|

---

CA2868872C|2017-05-16|

---

US20130262028A1|2013-10-03|

---

CN104335042B|2016-08-24|

---

MX336642B|2016-01-26|

---

WO2013147995A1|2013-10-03|

---

RU2586397C2|2016-06-10|

---

CA2868872A1|2013-10-03|

---

RU2014143802A|2016-05-27|

---

AU2013240570A1|2014-10-16|

---

CO7081149A2|2014-10-10|

引用文献:

---

公开号 | 申请日 | 公开日 | 申请人 | 专利标题

---

---

US4903207A|1986-05-15|1990-02-20|Restech, Inc.|Method for determining reservoir bulk volume of hydrocarbons from reservoir porosity and distance to oil-water contact level|

---

US5430291A|1992-05-01|1995-07-04|Texaco Inc.|X-ray CT measurement of fracture widths and fracture porosity in reservoir core material|

---

US6516080B1|2000-04-05|2003-02-04|The Board Of Trustees Of The Leland Stanford Junior University|Numerical method of estimating physical properties of three-dimensional porous media|

---

GB2414072B|2004-05-12|2006-07-26|Schlumberger Holdings|Classification method for sedimentary rocks|

---

US7516055B2|2004-08-20|2009-04-07|Chevron U.S.A. Inc|Multiple-point statistics simulation with enhanced computational efficiency|

---

US7630517B2|2005-07-13|2009-12-08|Schlumberger Technology Corporation|Computer-based generation and validation of training images for multipoint geostatistical analysis|

---

EP2198121A1|2007-08-31|2010-06-23|Saudi Arabian Oil Company|Artificial neural network models for determining relative permeability of hydrocarbon reservoirs|

---

US8068579B1|2008-04-09|2011-11-29|Xradia, Inc.|Process for examining mineral samples with X-ray microscope and projection systems|

---

WO2009126881A2|2008-04-10|2009-10-15|Services Petroliers Schlumberger|Method to generate numerical pseudocores using borehole images, digital rock samples, and multi-point statistics|

---

US8081796B2|2008-11-24|2011-12-20|Ingrain, Inc.|Method for determining properties of fractured rock formations using computer tomograpic images thereof|

---

US8085974B2|2008-11-24|2011-12-27|Ingrain, Inc.|Method for determining elastic-wave attenuation of rock formations using computer tomograpic images thereof|

---

US8170799B2|2008-11-24|2012-05-01|Ingrain, Inc.|Method for determining in-situ relationships between physical properties of a porous medium from a sample thereof|

---

US8155377B2|2008-11-24|2012-04-10|Ingrain, Inc.|Method for determining rock physics relationships using computer tomographic images thereof|

---

US8081802B2|2008-11-29|2011-12-20|Ingrain, Inc.|Method for determining permeability of rock formation using computer tomograpic images thereof|

---

US20110004447A1|2009-07-01|2011-01-06|Schlumberger Technology Corporation|Method to build 3D digital models of porous media using transmitted laser scanning confocal mircoscopy and multi-point statistics|

---

US8805616B2|2010-12-21|2014-08-12|Schlumberger Technology Corporation|Method to characterize underground formation|RU2015104162A|2012-08-10|2016-09-27|Ингрейн, Инк.|METHOD FOR INCREASING THE ACCURACY OF VALUES OF ROCK PROPERTIES OBTAINED FROM DIGITAL IMAGES|

---

US20140052420A1|2012-08-20|2014-02-20|Ingrain Inc.|Digital Rock Analysis Systems and Methods that Estimate a Maturity Level|

---

US20140270393A1|2013-03-15|2014-09-18|Bp Corporation North America Inc.|Systems and methods for improving direct numerical simulation of material properties from rock samples and determining uncertainty in the material properties|

---

US9070049B2|2013-03-15|2015-06-30|Bp Corporation North America Inc.|Systems and methods for improving direct numerical simulation of material properties from rock samples and determining uncertainty in the material properties|

---

WO2015084447A1|2013-12-05|2015-06-11|Schlumberger Canada Limited|Method and system of showing heterogeneity of a porous sample|

---

RU2642556C1|2014-03-31|2018-01-25|Ингрейн, Инк.|Definition of standard volume element for statistical data of cluster analysis|

---

EP3251097A4|2015-01-30|2018-09-26|Hewlett-Packard Development Company, L.P.|Variable density modeling|

---

WO2016122634A1|2015-01-30|2016-08-04|Hewlett-Packard Development Company, L.P.|Generating slice data from a voxel representation|

---

US9892321B2|2015-06-27|2018-02-13|New England Research, Inc.|Using maximal inscribed spheres for image-based rock property estimation|

---

US9841387B2|2015-07-22|2017-12-12|Test Research, Inc.|Inspection method and device|

---

US10394974B2|2015-10-01|2019-08-27|Arizona Board Of Regents On Behalf Of Arizona State University|Geometry based method for simulating fluid flow through heterogeneous porous media|

---

CA2999220A1|2015-10-02|2017-04-06|Repsol, S.A.|Method for providing a numerical model of a sample of rock|

---

CN105651964B|2015-12-29|2017-11-03|河海大学|A kind of method for determining Investigation of Representative Elementary Volume For Fractured Rock Mass product|

---

US10431419B2|2016-07-19|2019-10-01|Battelle Memorial Institute|Sparse sampling methods and probe systems for analytical instruments|

---

CN107290358B|2017-06-20|2019-11-08|大连理工大学|CO in a kind of application CT measurement porous media2The method of saline interface area change|

---

US10256072B2|2017-08-01|2019-04-09|Battelle Memorial Institute|Optimized sub-sampling in an electron microscope|

---

CN107680131B|2017-09-08|2020-09-11|北京理工大学|Method for rapidly determining volume size of porous medium characterization unit|

---

CN107784169B|2017-10-11|2020-10-13|上海电力学院|Porous medium characterization unit body determination method based on variation function and porosity|

---

CN110029989B|2018-01-11|2021-11-02|中国石油化工股份有限公司|Unconventional oil and gas extraction degree calculation method and system|

---

CN108320307B|2018-01-19|2020-09-08|中国石油天然气股份有限公司|Method and device for determining effective unit volume of reservoir rock sample|

---

US10969323B2|2018-05-30|2021-04-06|Saudi Arabian Oil Company|Systems and methods for special core analysis sample selection and assessment|

---

US11009497B2|2018-06-22|2021-05-18|Bp Corporation North America Inc.|Systems and methods for estimating mechanical properties of rocks using grain contact models|

---

CN109191423B|2018-07-18|2019-07-02|中国矿业大学|A kind of porous media Permeability Prediction method based on machine image intelligence learning|

---

CN109145407B|2018-08-01|2020-08-04|浙江大学|Implicit curved surface porous entity structure performance analysis method based on slice section|

法律状态:
2018-03-27| B06F| Objections, documents and/or translations needed after an examination request according [chapter 6.6 patent gazette]|

---

2019-09-10| B06U| Preliminary requirement: requests with searches performed by other patent offices: procedure suspended [chapter 6.21 patent gazette]|

---

2020-09-01| B07A| Technical examination (opinion): publication of technical examination (opinion) [chapter 7.1 patent gazette]|

---

2021-02-02| B07A| Technical examination (opinion): publication of technical examination (opinion) [chapter 7.1 patent gazette]|

---

2021-05-25| B09A| Decision: intention to grant [chapter 9.1 patent gazette]|

---

2021-06-22| B16A| Patent or certificate of addition of invention granted|Free format text: PRAZO DE VALIDADE: 20 (VINTE) ANOS CONTADOS A PARTIR DE 04/02/2013, OBSERVADAS AS CONDICOES LEGAIS. |

优先权:

---

申请号 | 申请日 | 专利标题

---

US201261618265P| true| 2012-03-30|2012-03-30|

---

US61/618,265|2012-03-30|

---

US13/546,053|2012-07-11|

---

US13/546,053|US20130262028A1|2012-03-30|2012-07-11|Efficient Method For Selecting Representative Elementary Volume In Digital Representations Of Porous Media|

---

PCT/US2013/024593|WO2013147995A1|2012-03-30|2013-02-04|An efficient method for selecting representative elementary volume in digital representations of porous media|

---