阅读说明：本技术 用于确定多孔介质的渗透率的方法和系统 (Method and system for determining permeability of porous media ) 是由 哈桑·阿·马尔祖奇 桑德拉·韦加 孙华峰 于 2017-11-06 设计创作，主要内容包括：描述了一种用于确定多孔介质的渗透率的方法,该方法包括以下步骤：a)通过成像系统获得多孔介质的三维图片；b)将三维图片划分为n个二维平行切片,其中,n为2或更大的整数；c)使用限定图像像素的网格来识别第一最外层切片(n<Sub>1</Sub>)中的一个或多个孔；d)使用与用于第一最外层切片(n<Sub>1</Sub>)的限定图像像素的相同的网格来识别直接邻近第一最外层切片(n<Sub>1</Sub>)的第二切片(n<Sub>2</Sub>)中的一个或多个孔；以及e)如果在第一最外层切片(n<Sub>1</Sub>)中第二切片(n<Sub>2</Sub>)的相邻者中的至少一个是孔,则将该第二切片(n<Sub>2</Sub>)中的一个或多个孔标记为连通的,以给出连通孔的数量作为连通性结果。还描述了一种系统,该系统包括用于执行这种方法的装置。(A method for determining the permeability of a porous medium is described, the method comprising the steps of: a) obtaining a three-dimensional picture of the porous medium through an imaging system; b) dividing the three-dimensional picture into n two-dimensional parallel slices, wherein n is an integer of 2 or more; c) identifying a first outermost slice (n) using a grid defining image pixels 1 ) One or more holes therein; d) using and for the first outermost slice (n) 1 ) Define the same grid of image pixels to identify the immediate vicinity of the first outermost slice (n) 1 ) Second slice (n) 2 ) One or more holes therein; and e) if the slice (n) is at the first outermost layer 1 ) Middle second slice (n) 2 ) Is a hole, the second slice (n) is sliced 2 ) One or more of the apertures are marked as communicating, toThe number of communication holes is given as a result of the connectivity. A system is also described, which comprises means for performing such a method.)

1. A method for determining the permeability of a porous medium, the method comprising the steps of:

a) obtaining a three-dimensional picture of the porous medium by an imaging system;

b) dividing the three-dimensional picture into n two-dimensional parallel slices, wherein n is an integer of 2 or more;

c) identifying a first outermost slice (n) using a grid defining image pixels₁) One or more holes therein;

d) using and using for the first outermost slice (n)₁) Defining the same grid of image pixels to identify the first outermost slice (n)₁) Directly adjacent second slice (n)₂) One or more holes therein;

e) if slicing (n) at the first outermost layer₁) Is a hole, the second slice (n) is sliced₂) One or more of the holes are marked as communicating to give the number of communicating holes as a result of the connectivity.

2. Method according to claim 1, wherein steps c) to e) are a first iteration, and wherein these steps are iterated to subsequent slices (n)₃，n₄…) until the last slice (n) is reached_last) Wherein, in each iteration, the connectivity result in a previous iteration is treated as a first slice to give the number of connected holes as a final connectivity result.

3. Method according to claim 1 or 2, wherein in the opposite direction with respect to said steps c) to e), i.e. from said last slice (n)₂Or n_last) Beginning to repeat the method, wherein after the repeating, an average number of the communicating holes is calculated as an average connectivity result.

4. The method of claim 3, wherein a Permeability Connectivity Index (PCI) is calculated, the permeability connectivity index being defined as the average number of interconnected pores divided by the total number of image pixels.

5. The method of any of claims 1 to 4, wherein the grid defines square image pixels.

6. The method of claim 5, wherein each image pixel has nine neighboring image pixels in a previous slice and/or a subsequent slice.

7. The method of any one of claims 1 to 6, wherein the porous medium is rock.

8. A system comprising means for performing the method of any one of claims 1-7.

9. The system of claim 8, wherein the device comprises an imaging system and a computer.

10. The system of claim 8 or 9, wherein the apparatus comprises an imaging system, the imaging system being a computed tomography scanner.

Technical Field

The present invention relates to a method for determining the permeability of a porous medium, in particular a method using a combination of image translation and logical operations. The invention also relates to a system for determining the permeability of a porous medium, i.e. a system capable of performing the method of determining the permeability of a porous medium.

Background

Digital Rock Physics (DRP) has evolved and commercialized rapidly over the past few years. Digital rock physics is a relatively new technology that can compute rock properties from digital rock images. Some relevant publications are listed below:

-Arns,C.M.,Knackstedt,M.,Pinczewski,M.and Garboczi,E.2002.Computationof linear elastic properties from microtomographic images:methodology andagreement between theory and experiment.Geophysics.67:1396-1405.

-Garboczi,E.and Day,A.1995.Algorithm for computing the effectivelinear elastic properties of heterogeneous materials:Three dimensionalresults for composites with equal phase poisson ratios.Journal of theMechanics and Physics of Solids.43:1349-1362.

-Jouini,M.S.and Vega,S.2010.Elastic properties computation and fluidsubstitution simulation from X-ray CT scan images in Middle East carbonatessample.Eos Trans.AGU.91(49).American Geophysical Union,December2010,SanFrancisco,California,USA.

-Jouini,M.S.and Vega S.2011a.Numericalsimulations of linear elasticproperties of carbonates rock samples using 3D computed tomography images.inEAGE GeoInformatic.Theoretical and Applied Aspects Conference,Kyiv,Ukraine,2011.

-Jouini,M.S.and Vega S.2011b.Simulation of elastic properties incarbonates.The Leading Edge Journal,30(12):838-842,2011.

-Jouini,M.S.and Vega,S.2012.Simulation of carbonate rocks elasticproperties using 3D X-Ray computed tomography images based on DiscreteElement Method and Finite Element Method.in the 46th American Rock MechanicsAssociation conference,Chicago,USA,2012.

-Nur A.M.2003.Numerical method of estimating physical properties ofthree dimensional porous media.US 6,516,080B1.

the digital petrophysical technology has the following advantages: it is non-destructive and enables computational experiments to be performed in a shorter time than in a laboratory. However, this technique is not perfect; it counts under some constraints and needs to be better developed. Because of the cleanliness and relatively rapid results of this technology, more and more petroleum companies around the world use this technology as an alternative. Its main use is for calculating porosity and permeability, and more recently for elastic properties and capillary pressure curves.

The internal code may facilitate counting with an open algorithm adapted to e.g. local rocks. However, absolute permeability codes can often be computationally expensive and time consuming compared to experiments in the laboratory. Therefore, finding optimized code that reduces computer and time requirements is highly desirable. The invention specifically addresses the optimization of permeability codes in DRP, thereby reducing computation time and memory.

The lattice-boltzmann (LBM) method is one of the methods often used to estimate permeability from CT scans of rock samples. LBM models fluid Flow based on principles of molecular dynamics and statistical mechanics (see, e.g., Ju, Y., Wang, J., and Gao, F.2014.Lattice-Boltzmann Simulation of Microcale CH4 Flow in porous sub Subject to Force-induced development. China Science Bull,59(26): 3292. f., and Kang Q, Lichner PC, Zhang D.2006.LattBoltzmann hole-scale model for multiple reactive transport in porous media. J Geophy Res 111: B05203).

The Finite Difference Method (FDM) isAnother method for fluid simulation, which can be used for permeability estimation (see, e.g.,PE,Bakke S.2002.Process based reconstruction of sandstonesprediction of transport properties.Transp Porous Media46:311-343andMostaghimi,P.,Blunt,M.J.,and Bijeljic,B.2012.Computations of absolutepermeability on micro-CT images:Mathematical Geosciences,vol.45,no.1,pp.103-125)。

these methods are computationally intensive. For example, when a digital rock model with image sizes of 200 × 200 × 200 is simulated using LBM with a modern PC, it takes about five hours to obtain results. In addition, these algorithms require high memory requirements and images with large sizes will not run on a typical PC.

Disclosure of Invention

It is an object of the present invention to provide a method and system for determining the permeability of a porous medium, in particular rock, which gives a reliable estimate of the permeability and significantly reduces the calculation time.

It is another object of the present invention to provide a method and system for determining the permeability of a porous medium, in particular rock, which requires only limited memory, can process images of small size and run on a typical PC.

To achieve one or more of the mentioned objects, the present invention provides a method for determining the permeability of a porous medium, comprising the steps of:

a) obtaining a three-dimensional picture of the porous medium through an imaging system;

b) dividing the three-dimensional picture into n two-dimensional parallel slices, wherein n is an integer of 2 or more;

c) identifying a first outermost slice (n) using a grid defining image pixels₁) One or more holes therein;

d) by using the same as for the first outermost slice (n)₁) Is defined byThe same grid of image pixels to identify the slice (n) as the first outermost slice₁) Directly adjacent second slice (n)₂) One or more holes therein;

e) if slicing at the first outermost layer (n)₁) Second slice (n) of (1)₂) Is a hole, the second slice (n) is sliced₂) One or more of the holes are marked as communicating to give the number of communicating holes as a result of the connectivity.

Preferably, in the method of the invention, steps c) to e) are a first iteration and these steps are iterated to subsequent slices (n)₃，n₄…) until the last slice (n) is reached_last) Wherein, in each iteration, the connectivity result in the previous iteration is regarded as a first slice to give the number of communicating holes as a final connectivity result.

It is also preferred in the present invention that it is in the opposite direction (i.e. from the last slice (n)) with respect to steps c) to e)₂Or n_last) Start) the method of the invention is repeated, wherein after the repetition the average number of interconnected pores is calculated as the average connectivity result. More preferably, a Permeability Connectivity Index (PCI) is thereafter calculated, which is defined as the average number of interconnected pores divided by the total number of image pixels.

It is further preferred that in the method of the invention the grid defines square image pixels, wherein each image pixel has a particularly preferred nine neighbouring image pixels in the previous slice and/or the subsequent slice.

In a particularly preferred embodiment according to the invention, the porous medium is rock.

To achieve one or more of the mentioned objects, the present invention also provides a system comprising means for performing the method of the invention as described herein. Preferably, the apparatus comprises an imaging system and a computer. It is also preferred that the apparatus comprises an imaging system which is a computed tomography scanner, particularly preferably in combination with a further computer.

Each limitation of the invention may include various embodiments of the invention. It is therefore contemplated that each limitation of the invention relating to any one element or combination of elements may be included in each aspect of the invention. The invention is not limited in its application to the details of construction and the arrangement of components set forth in the following description or illustrated in the drawings. The invention is capable of other embodiments and of being practiced or of being carried out in various ways. Also, the phraseology and terminology used herein is for the purpose of description and should not be regarded as limiting. The use of "including," "comprising," or "having," "including," "involving," and variations thereof herein, is meant to encompass the items listed thereafter and equivalents thereof as well as additional items.

Drawings

The invention will be described with reference to the accompanying drawings, in which:

FIG. 1 is an example of operations for illustrating a developed hole connectivity index; (a) first cuts, e.g. n₁(b) a second slice, e.g. n₂. The wells are marked by index 1.

FIG. 2 is another example of operations for illustrating a developed hole connectivity index; (a) first cuts, e.g. n₁(b) a second slice, e.g. n₂. The wells are marked by index 1.

Detailed Description

According to the present invention there is provided a method for determining the permeability of a porous medium, the method comprising the steps of:

a) obtaining a three-dimensional picture of the porous medium through an imaging system;

b) dividing the three-dimensional picture into n two-dimensional parallel slices, wherein n is an integer of 2 or more;

c) identifying a first outermost slice (n) using a grid defining image pixels₁) One or more holes therein;

d) in use and for the first outermost slice (n)₁) When defining the same grid of image pixels, the first outermost slice (n) is identified₁) Directly adjacent second slice (n)₂) One or more holes in；

e) If slicing at the first outermost layer (n)₁) Second slice (n) of (1)₂) Is a hole, the second slice (n) is sliced₂) One or more of the holes are marked as communicating to give the number of communicating holes as a result of the connectivity.

In the method of the invention, the image is preferably an electronic image, so that it can be easily processed by, for example, a computer. Furthermore, for the first two slices, the two-dimensional parallel slice of the generated image is indexed by n₁And n₂. In case three slices are obtained in step b), the slice is indexed by n₁、n₂And n₃. The same logic applies to the case where n is an integer of 4 or more. The final or last slice in the set of slices as generated in step b) is indexed by n_last. Thus, in the case of creating, for example, 100 slices in total, n_lastWill be equal to n₁₀₀. The stack of whole slices forms the three-dimensional picture obtained in step a), and the outermost layer thereof is a slice n₁And n_last. In addition, in the sense of the present invention, slice n₁With one direct neighbor, i.e. slice n₂And slicing n₂Usually with two direct neighbors of itself, i.e. slice n₁And n₃-assuming the presence of n₃(ii) a Otherwise n₂Is equal to n_lastAnd therefore also only one direct neighbor, i.e. n₁. Slice n₁And n_lastIs the outermost slice of the stack of n slices generated in step b).

According to the invention, preferably, in the method of the invention, steps c) to e) are considered as a first iteration. This iteration gives a connectivity result, via step e). In a subsequent step, and assuming that n is greater than 2, the first connectivity result is used for the first slice, and steps c) to e) are repeated using the newly generated first and subsequent slices. For example, in the case where an image is decomposed into three slices, and after steps a) to e) are performed for the first time, slice n₁And n₂The result of (A) is used as a new first cut piece, which canTo be marked as e.g. n_1'. The new first slice n is then used in the repeated steps c) and e)_1'And using the slice n in repeated steps d) and e)₃. Thus, after the inventive method has been performed once, steps c) to e) are preferably iterated to subsequent slices (n) depending on the number of slices₃，n₄…) until the last slice (n) is reached_last). This means that in each iteration, the connectivity result of the previous iteration is treated as the first slice to give the number of communicating holes as the final connectivity result.

Following the above scheme, pores through the imaged porous medium that are substantially perpendicular to the plane of the generated parallel and two-dimensional images can be identified. To improve the accuracy of the measurement, the entire exercise is preferably redone, this time reversing the order of the slices, i.e. using n_lastAs the first slice, and use n₁As the final slice. Thereafter, the resulting connectivity may be averaged. Therefore, it is particularly preferred in the present invention to reverse direction (i.e., from the last slice (n)) with respect to steps c) to e)₂Or n_last) Start) the method is repeated, wherein after the repetition the average number of interconnected pores is calculated as the average connectivity result.

Further, according to the present invention, the Permeability Connectivity Index (PCI) is preferably calculated to obtain a measure of the permeability of the porous media being analyzed. Preferably, therefore, in the method of the invention, a Permeability Connectivity Index (PCI) is calculated, which is defined as the average number of interconnected pores divided by the total number of image pixels.

In a simple, analytically complete and therefore particularly preferred method according to the invention, the grid defines square image pixels, i.e. two-dimensional rectangular pixels of equal length and width are defined by the grid. Although other shapes (such as hexagonal) may also be considered, calculations done with image pixels having a square shape are more efficient in reducing calculation time and memory. In this case, the image pixels are preferably arranged such that each image pixel has nine neighboring image pixels in a previous and/or subsequent slice.

The method is particularly suitable for use in the oil and gas industry when the porous medium being analyzed by the method of the invention is actually rock.

To achieve one or more of the mentioned objects, the present invention also provides a system comprising means for performing the method of the invention as described herein. Preferably, the apparatus comprises an imaging system and a computer. It is also preferred that the apparatus comprises an imaging system which is a computed tomography scanner, particularly preferably in combination with a further computer.

Particularly preferred embodiments of the present invention will now be described. According to this particularly preferred embodiment of the invention, the inventive method is a method for determining the permeability of rock using a combination of image translation and logical operations. In this particular embodiment, the method developed depends on tracking the connectivity of the pores within the rock sample. The method first assumes that the holes in the first slice are filled with fluid. Next, a hole filled with fluid is found in the second slice. If a hole in the second slice is connected to a hole in the first slice, the hole in the second slice is marked as filled with fluid. If one of the nine neighbors in the previous slice is a hole, the hole is marked as connected. Fig. 1 and 2 show examples of connectivity between two slices. These figures show two slices of the image of size 3 by 3.

In fig. 1, only the center pixel in the first slice is the hole. In the second slice, all pixels indicate the presence of a hole. According to the connectivity definition as used in the present invention, all the holes in the second image are connected to the first slice and will allow fluid to pass through them. If the first image does not include holes, no holes in the second slice will be marked as connected.

In the second example shown in fig. 2, only the top left corner element of the first slice is labeled as a hole. The output of the corresponding method step will indicate that there are 4 communicating holes in the upper left corner of the image. The remaining pores are not connected.

The foregoing connectivity calculations are iterated to subsequent slices. In each iteration, the connectivity result in the previous iteration is considered the first slice. Once the final slice is reached, the number of interconnected pores is used as a measure of the permeability of the rock sample. To get a more reliable estimate, the previous operation is repeated in the opposite direction (i.e. starting from the last slice).

Finally, the Permeability Connectivity Index (PCI) is calculated, which is defined as the average number of connected pores found in both calculation directions divided by the total number of image pixels.

The basic experiment of the invention establishes a linear relation between the PCI value and the rock permeability index. Calculating the PCI values of rock samples with different permeability values is preferably used as a pre-processing step to obtain a parameter that calibrates the relationship between PCI and rock permeability index. This calibration procedure allows accounting for variations between different scanners and the use of different imaging resolutions. The invention therefore preferably comprises a calibration step to be performed on, for example, a Computed Tomography (CT) scanner from which data is acquired.

The calculation of hole connectivity between slices may be performed using binary logic operations. The simplicity of the proposed method and the use of binary logic operations make the developed permeability index an attractive alternative to other methods often used in practice.

The invention provides a reliable estimate of rock permeability calculations and significantly reduces the calculation time.

Although illustrative embodiments of the invention have been shown and described, it should be understood that various modifications and substitutions may be made by those skilled in the art without departing from the novel spirit and scope of the invention.

Further references:

periodical

·Sun H F,Vega S,Tao G.Analysis of Heterogeneity and PermeabilityAnisotropy in Carbonate Rock Samples Using Digital Rock Physics.Journal ofPetroleum Science and Engineering,2017,156:419-429.(IF 1.873)

·Sun H F,Tao G,Vega S,Al-Suwaidi A.Simulation of Gas Flow inOrganic-Rich Mudrocks Using Digital Rock Physics.Journal of Natural GasScience and Engineering,2017,41:17-29.(IF 2.718)

Conference

·Sun H F,Tao G,Vega S,Wang B,Liu H,Li,K S.Multi-Scale CT ImageAnalysis of Digital Carbonate Rock.Paper presented at the 79^thEAGE Conference&Exhibition,Paris,France,12June-15June 2017.

·Li K S,Gao J,Wu C,Zhao X,Chen F G,Liu S,andSun H.The New ToolDesign of Ultra-deep Azimuthal Electromagnetic Resistivity Logging-While-Drilling based on Gray Relational Analysis Method.Paper presented at the 79^thEAGE Conference&Exhibition,Paris,France,12June-15June 2017.

·Sun H F,Vega S,Tao G,Yong H,Li B.Estimation of PetrophysicalParameters of a Heterogeneous Carbonate Rock Sample with Multi-scale CTImages.E-Poster in 2016 PIRC R&D Conference and Exhibition,November 21,2016.

·Sun H F,Vega S,Tao G,Yong H,Li B.Estimation of PetrophysicalParameters of Heterogeneous Carbonate Rock Sample with Multi-Scale CTImages.SPE-183114-MS.Paper presented at Abu Dhabi International PetroleumExhibition and Conference,7-10 November,Abu Dhabi,UAE,2016.

·Sun H F,Vega S,Tao G.Determination of Transport Properties inCarbonate Rock Sample Using Multi-scale CT Images.Paper presented at the 78thEAGE Conference&Exhibition,Reed Messe Wien,Vienna,Austria,30 May-2 June 2016.

·Li K S,Gao J,Li H,Sun H F.Porosity Calculation of Horizontal Wellswhen Acoustic Slowness Is Abnormal-A Case Study in Northern Ordos Basin,China.Paper presented at the 78th EAGE Conference&Exhibition,Reed Messe Wien,Vienna,Austria,30 May-2 June 2016.

·Sun H F,Tao G,Vega S.Study on Permeability Anisotropy in CarbonateReservoir Samples Using Digital Rock Physics.SPE-177540-MS.Paper Presented atAbu Dhabi International Petroleum Exhibition and Conference,9-12 November,AbuDhabi,UAE,2015.

·Sun H F,Vega,S,Tao G.Study of Heterogeneity in Carbonate RockSamples Using Digital Rock Physics.Paper Presented at the 3rd EAGE Workshopon Rock Physics,Istanbul,Turkey,15-18 August 2015.

·Sun H F,Vega S,Tao G.Simulation of Shale Gas Flow in Nano Poreswith Parallel Lattice Boltzmann Method.Paper presented at the 77th EAGEConference&Exhibition,IFEMA Madrid,Spain,1-4June2015.

Chen P, Tao G, Dong M J, Sun H F The Effects of The Water-Oil Flow in Rock Reservoirs in progress in Geophysics,2013,28(2):0824-

Li Y, Xiao L Z, Sun H F. analytes of sizing Factors of Hydrocarbon Identification Using NMR Time Domain analysis. Chinese Journal of magnetic Resonance,2012,29(1):21-31 (Chinese)

Di D J, Tao G, Sun H F, Yue W Z, analysis and correlation of formatting Technology, well Logging Technology,2012,36(3):294-

Sun H F, Tao G, Zhou Y M, etc., the evaluation Roles of WFT in formatting and Reservoir evaluation, well Logging Technology,2010,34(4):314-

Others

Saenger,E.H.,Vialle S.,Lebedev,M.,Uribe,D.,Osorno,M.,Duda,M.,andSteeb,H.2016.Digital carbonate rock physics.Solid Earth Discuss,7(4):1185-1197.

Saenger,E.H.,Enzmann,F.,Keehm,Y.,and Steeb,H.2011.Digital rockphysics:Effect of fluid viscosity on effective elastic properties.Journal ofApplied Geophysics,74,236-241.

Bultreys,T.,Boever,W.D.,Hoorebeke,L.V.,Cnudde,V.2015.A multi-scale,image-based pore network modeling approach to simulate two-phase flow inheterogeneous rock.Paper presented at the International Symposium of theSociety of Core Analysist held in St.John's Newfoundland and Labrador,Canada,16-21 August 2015.

Teles,A.P.,Machado,A.C.,Pepin,A.,Bize-Forest,N.,Lopes,R.T.,Lima,I.2016.Analysis of subterranean Pre-salt carbonate reservoir by X-raycomputed microtomography.Journal of Petroleum Science and Engineering,144:113-120。