CN115081210A - Method for calculating flow tortuosity in porous medium through limited walk simulation - Google Patents
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Abstract
The invention discloses a method for calculating the flow tortuosity in a porous medium by restricted wandering simulation, which comprises the steps of simplifying and correcting a sample digital core based on a watershed algorithm; the method comprises the steps of combining the collision probability of micro-scale continuous phase particles represented by a digital core gray value in different migration directions in different areas; the method comprises the steps of calculating continuous phase operator migration directions aiming at different digital core resolutions and a digital core mirror face expansion mapping method; the tortuosity in different states is quantified by simulating a stable diffusion coefficient under infinite mirror mapping and combining the operator migration mode under the real condition in the above. Compared with the existing methods of koponen, sousa, barrande and other ideal mathematical models, the tortuosity data obtained by the method introduces complex pore structures and stress influence in migration, and the tortuosity obtained by the new method is subjected to analog calculation, so that the result conformance rate is improved by 11% compared with the tortuosity obtained by the traditional method.
Description
Technical Field
The invention relates to the technical field of gas reservoir development, in particular to the field of unconventional oil and gas development, and specifically relates to a method for calculating the flow tortuosity in a porous medium through restricted walk simulation.
Background
As an important parameter for the description of the percolation channels, the tortuosity of a channel is defined as the ratio of the actual length of a given migration during percolation to the macroscopic length of the percolation channel. With the development of unconventional oil and gas reservoirs in recent years, the oil and gas seepage process is increasingly complicated, and the tortuosity obtained by a conventional tortuosity method obtained by simple calculation through a pore structure is used for explaining the seepage process with large errors.
In recent years, experts and scholars tend to use high-precision CT inversion to make digital cores to simulate migration in complex unconventional oil and gas reservoirs, but the explanation on tortuosity only stays in quantification of different average particle sizes of pore medium minerals, and the inter-particle acting force in a real seepage process and the anisotropic influence of reservoir rocks are ignored.
Disclosure of Invention
In view of the above problems, the present invention aims to provide a technique for accurately characterizing the tortuosity of a complex porous medium so that the result is closer to the true seepage situation.
The technical scheme of the invention is as follows:
a method of constrained migration simulation to calculate flow tortuosity in a porous medium, comprising the steps of:
step 1: scanning the rock sample by 360 degrees, and performing three-dimensional correction processing based on the multi-angle image of the rock sample;
step 2: and separating rock sample pores and a rock sample framework from the processed three-dimensional gray data of the rock sample through image threshold segmentation. Comparing matrix statistics pore and actual test porosity adjustment threshold data to obtain data representing a real rock sample skeleton and pores;
step 3: and (3) combining a field experiment, segmenting a space phase Euclidean distance matrix by using a watershed algorithm, converting the complex matrix into a simpler corresponding sample space connection point set, and setting the matrix area as a random walk non-collision area.
Step 4: by continuously removing rock gap phase boundary voxels, the collision and rebound probability of a single voxel of a corresponding rock sample under the corresponding scanning resolution is correspondingly obtained by combining a field experiment.
Step 5: selecting any point in a pore in a sample digital core matrix, carrying out random walk simulation, recording a corresponding walk distance corresponding to the corresponding step number in the walk process, and carrying out mirror image mapping on a matrix boundary in the walk process. And (4) adopting different measures to limit the step number or the migration distance when the random migration simulation coordinate contacts the digital core skeleton.
Step 6: and characterizing the reservoir tortuosity of the sample through the relation between the random walk step number and the distance.
Further, the Step1 specifically comprises the following steps:
and traversing the reconstructed three-dimensional digital core matrix by using a computer, dividing the gray data into two frequency bands by taking the gray data amount as a standard, and converting the gray value into density data on the part which is difficult to distinguish based on a reconstruction algorithm of the corresponding gray value and the density for the data after the frequency bands are divided, and replacing the gray value data.
Further, the Step2 specifically comprises the following steps:
step 201: and measuring the porosity of the sample by a rock sample porosity experimental measurement method such as a liquid saturation drainage method or a helium method.
Step 202: based on the corrected three-dimensional digital core data, a framework and pores are divided by setting a gray level or density threshold value, the divided binary pores are traversed, the independence of the coordinates marked as the pores in the matrix is calculated by a bwleabel algorithm, and the volume occupied by the disconnected pores after the threshold value is marked and calculated is adjusted. Comparison of the porosity φ obtained in the experiment in Step201 1 After adjusting the threshold, the porosity phi is counted 2 And a disconnected pore phi u . By continuously adjusting the threshold value phi 1 ＝φ 2 -φ u And determining data capable of reflecting the pore and skeleton structure of the real core.
Further, the Step3 specifically comprises the following steps:
and performing Gaussian smoothing operation on gray values in the region divided into pores in the digital core according to Step2, adjusting a pore gray threshold in a watershed algorithm after erasing a minimum value, dividing the region into a plurality of similar cells according to the gray values in the digital core, and numbering according to the gray values, wherein the voxel radius R and the corresponding threshold Th are stored in a corresponding [ x, y, z ] position matrix of the corresponding digital core.
Based on the impact of continuous phase velocity on collision phase in the Boltzmann equation:
wherein: f is dimensionless external force, X α Is corresponding to the position, xi α To a dimensionless particle diffusion velocity
Considering the influence of the external force neglected by the tortuosity calculation in the porous medium, and combining the equation of the boltzmann equation for the velocity field in the collision phase, the diffusion distribution probability of a certain pore point in the digital core can be equivalent to:
considering that the pore network in the digital core can be equivalent to a long circular tube, and therefore, in combination with the poisson equation in the flow process and the independent pores separated by the watershed algorithm in the Step3 process, the distribution probability of each voxel in the rock sample flow process can be expressed by the following equation:
simplifying, the probability of each direction of a single voxel in the core pore in the microscopic scale during free diffusion flow is as follows:
further, the Step5 specifically comprises the following steps:
step501, randomly generating an operator in a pore network based on the pore network model obtained in the Step2, reading a data matrix obtained in the Step3 process, calculating the migration probability of N surrounding voxels of the operator in the next iteration time Step by combining the Step4 process, and if the resolution of the digital core is low, namely the size of a single voxel is large and limited to the precision limit, the model cannot finely express the pore structure, so that a pore structure lower than the precision possibly exists, and the 27 surrounding voxels are considered as the migration direction; if the digital core resolution is high and the fine pore structure can be characterized, the 14 or 6 directions of the periphery of a single voxel are taken. The corresponding voxel migration probability is:
when the operator is transported to the skeleton position in the digital core matrix in the random migration process, the operator position is kept still, and the current migration position probability is ignored in the next iteration migration process.
Step 502: acquiring the probabilities in different directions acquired in the digital core matrix through the Step501 process, and calling a random number library in programming software to enable operators to randomly walk in the positions of the corresponding holes of the digital core matrix with the probabilities in the corresponding directions; performing transverse and longitudinal mirror mapping on the digital core matrix to expand the boundary, wherein the process corresponding to the mirror mapping of the boundary is as follows:
wherein: x is the number of i+1 ，y i+1 Representing coordinates in a matrix where an operator before mapping is located; REF (x, y) represents the matrix coordinates of the mapped digital core; b is the matrix boundary size.
Step 503: the iterative Step501-Step502 process is repeated using programmed software. Simultaneously, running migration simulation in an unlimited space once, namely, all the matrixes are pores; and designing and recording the positions of operators under different time step lengths according to different requirements.
Further, the Step503 process of selecting different Step lengths according to different requirements to obtain specific positions of different operators can be interpreted as follows: if the research process is planar two-dimensional migration, recording the distance r under the corresponding two-dimensional coordinates under different iteration steps according to the records of the iteration process; and if the integral tortuosity is considered, recording the distance r under the corresponding three-dimensional coordinates under different iteration steps according to the iteration process record. And if the tortuosity under different migration scales is considered, recording the corresponding step number of the operator reaching the specified migration distance by combining the resolution of the corresponding digital core.
On the basis of ensuring easy implementation, compared with the prior art, the method is more practical in screening the main control factors influencing the yield of the dense gas, and has a profound meaning on the subsequent prediction and research of the yield of the dense gas.
Drawings
In order to more clearly illustrate the embodiments of the present invention or the technical solutions in the prior art, the drawings used in the description of the embodiments or the prior art will be briefly described below, and it is obvious that the drawings in the following description are only some embodiments of the present invention, and for those skilled in the art, other drawings can be obtained according to these drawings without creative efforts.
FIG. 1 is a schematic flow chart of a method for calculating the flow tortuosity in a porous medium by a restricted migration simulation according to the present invention;
FIG. 2 is a digital core matrix after Avizo visualization calculated in example 1;
FIG. 3 is matrix data (Avizo visualization) calculated and processed based on the watershed algorithm in example 1;
FIG. 4 is the diffusion coefficient calculated in example 1 for different time step lengths;
Detailed Description
The invention is further illustrated with reference to the following figures and examples. It should be noted that, in the present application, the embodiments and the technical features of the embodiments may be combined with each other without conflict. It is noted that, unless otherwise indicated, all technical and scientific terms used herein have the same meaning as commonly understood by one of ordinary skill in the art to which this application belongs. The use of the terms "comprising" or "including" and the like in the present disclosure is intended to mean that the elements or items listed before that term include the elements or items listed after that term and their equivalents, without excluding other elements or items.
Example 1
As shown in the attached figure 1, the method for accurately determining the seepage dynamic tortuosity in the porous medium based on the random walk comprises the following steps:
step 1: scanning the rock sample by 360 degrees, and performing three-dimensional correction processing based on the multi-angle image of the rock sample; the transformed three-dimensional digital core matrix is shown in table 1, and the data read by Avizo visualization is shown in the attached fig. 2 of the specification.
TABLE 1 converted three-dimensional digital core data matrix
Step 2: and separating rock sample pores and a rock sample framework from the processed three-dimensional gray data of the rock sample through image threshold segmentation. Comparing matrix statistics pore and actual test porosity adjustment threshold data to obtain data representing a real rock sample skeleton and pores;
after adjusting the threshold, the porosity 0.143 obtained by setting 4817 to the threshold is closest to the experimental result, and the porosity is divided by the threshold, and fig. 2 is the result of Avizo visualization of the matrix data after processing.
Step 3: and (3) combining a field experiment, segmenting a space phase Euclidean distance matrix by using a watershed algorithm, converting the complex matrix into a simpler corresponding sample space connection point set, and setting the matrix area as a random walk non-collision area.
The random walk collision-free areas after watershed algorithm and correction are shown in three blue positions in fig. 3.
Step 4: by continuously removing rock gap phase boundary voxels, the collision and rebound probability of a single voxel of a corresponding rock sample under the corresponding scanning resolution is correspondingly obtained by combining a field experiment.
Taking the digital core matrix coordinates [77,77 and 77] as an example, the migration probability in 9 directions is calculated to be 163/814,5/906,16/103,49/370,5/56,25/222,24/299,50/841 and 35/213 based on the gray value of the digital core matrix coordinates.
Step 5: selecting any point in a pore in a sample digital core matrix, carrying out random walk simulation, recording a corresponding walk distance corresponding to the corresponding step number in the walk process, and carrying out mirror image mapping on a matrix boundary in the walk process. And (4) adopting different measures to limit the step number or the migration distance when the random migration simulation coordinate contacts the digital core skeleton.
The digital core samples have different particle sizes, the digital core samples are divided into large particle sizes, small particle size aggregates and 10000 times of 100000 steps of wandering are respectively carried out according to unconstrained spaces, and the migration distances under different conditions are recorded.
Step 6: and characterizing the reservoir tortuosity of the sample through the relation between the random walk step number and the distance.
As shown in FIG. 4, when the number of walk steps is higher than 70000 times, the diffusion coefficients in four different cases tend to be constant, so that the area of large particle diameter, the area of small particle diameter and the overall tortuosity in the sample are respectively 1.7, 2.1 and 1.9, the values are substituted into the Poisea equation to carry out flow simulation, the simulation result is different from the real result by 8%, and compared with the tortuosity value calculated by porosity, the simulation error is reduced by 11%.
Although the present invention has been described with reference to a preferred embodiment, it should be understood that various changes, substitutions and alterations can be made herein without departing from the spirit and scope of the invention as defined by the appended claims.
Claims (8)
1. A method of constrained migration simulation to calculate flow tortuosity in a porous medium, comprising the steps of:
step 1: scanning the rock sample by 360 degrees, and performing three-dimensional correction processing based on the multi-angle image of the rock sample;
step 2: separating rock sample pores and rock sample frameworks from the processed three-dimensional gray data of the rock sample through image threshold segmentation, and comparing matrix statistics on the pores and actual test porosity adjustment threshold data to obtain data representing real rock sample frameworks and pores;
step 3: in combination with a field experiment, a watershed algorithm is used for segmenting a space phase Euclidean distance matrix, a complex matrix is converted into a simpler corresponding sample space connection point set, and the matrix area is set as a random walk non-collision area;
step 4: continuously removing rock gap phase boundary voxels, and correspondingly acquiring the collision and rebound probability of a single voxel of a corresponding rock sample under the corresponding scanning resolution by combining a field experiment;
step 5: selecting any point in a pore in a sample digital core matrix, performing random walk simulation, recording a corresponding step number and a corresponding walk distance in the walk process, performing mirror image mapping on a matrix boundary in the walk process, and taking different measures to limit the step number or the walk distance when a random walk simulation coordinate is in contact with a digital core framework;
step 6: and characterizing the reservoir tortuosity of the sample through the relation between the random walk step number and the distance.
2. A method for calculating the flow tortuosity in a porous medium by using a limited walk simulation is characterized in that Step1 is specifically processed by the following steps: and traversing the reconstructed three-dimensional digital core matrix by using a computer, dividing the gray data into two frequency bands by taking the gray data amount as a standard, and converting the gray value into density data on the part which is difficult to distinguish based on a reconstruction algorithm of the corresponding gray value and the density for the data after the frequency bands are divided, and replacing the gray value data.
3. A method for calculating the flow tortuosity in a porous medium by using a limited walk simulation is characterized in that Step2 is specifically processed by the following steps:
step 201: measuring the porosity of the sample by a rock sample porosity experimental measurement method such as a liquid saturation drainage method or a helium method;
step 202: based on the corrected three-dimensional digital core data, a framework and pores are divided by setting a gray level or density threshold value, divided binary pores are traversed, coordinates marked as pores in a matrix are subjected to a bwlabel algorithm to calculate the independence of the coordinates, the volumes of the unconnected pores are marked and calculated after the threshold value is adjusted, and the porosity phi obtained in the experiment in Step201 is compared 1 After adjusting the threshold, the porosity phi is counted 2 And a disconnected pore phi u By continuously adjusting the threshold value to phi 1 ＝φ 2 -φ u And determining data capable of reflecting the pore and skeleton structure of the real core.
4. A method for calculating the flow tortuosity in a porous medium by using a limited walk simulation is characterized in that Step3 is specifically processed by the following steps: and performing Gaussian smoothing operation on gray values in the region divided into pores in the digital core according to Step2, adjusting a pore gray threshold in a watershed algorithm after erasing a minimum value, dividing the region into a plurality of similar cells according to the gray values in the digital core, and numbering according to the gray values, wherein the voxel radius R and the corresponding threshold Th are stored in a corresponding [ x, y, z ] position matrix of the corresponding digital core.
5. A method for calculating the flow tortuosity in a porous medium by using a limited walk simulation is characterized in that Step4 is specifically processed by the following steps: based on the effect of continuous phase velocity on the collision phase in the Boltzmann equation:
wherein: f is a dimensionless external force, X α Is corresponding to the position, xi α To a dimensionless particle diffusion velocity
Considering the influence of the external force neglected by the tortuosity calculation in the porous medium, and combining the equation of the boltzmann equation for the velocity field in the collision phase, the diffusion distribution probability of a certain pore point in the digital core can be equivalent to:
considering that the pore network in the digital core can be equivalent to a long circular tube, and therefore, in combination with the poisson equation in the flow process and the independent pores separated by the watershed algorithm in the Step3 process, the distribution probability of each voxel in the rock sample flow process can be expressed by the following equation:
simplifying, the probability of each direction of a single voxel in the core pore in the microscopic scale during free diffusion flow is as follows:
wherein: th N The value is the grey value in the digital rock core; r i Calculating an equivalent radius for the watershed algorithm; theta.theta. * Is the contact angle; μ is the fluid viscosity.
6. A method for calculating the flow tortuosity in a porous medium by using a limited walk simulation, which is characterized in that the Step5 comprises the following specific processes:
step501, randomly generating an operator in a pore network based on the pore network model obtained in the Step2, reading a data matrix obtained in the Step3 process, calculating the migration probability of N surrounding voxels of the random voxel in the next iteration time Step by combining the Step4 process, and if the resolution of the digital core is low, namely the size of a single voxel is large and is limited to the precision limit, the model cannot finely express the pore structure, so that a pore structure lower than the precision possibly exists, and the 27 surrounding voxels are considered as the migration direction; if the resolution of the digital core is high and the fine pore structure can be represented, taking 14 or 6 directions around a single voxel, wherein the corresponding voxel migration probability is as follows:
when the operator is transported to the skeleton position in the digital core matrix in the random migration process, the operator position is kept still, and the current migration position probability is ignored in the next iterative migration process;
step 502: acquiring the probabilities in different directions acquired in the digital core matrix through the Step501 process, and calling a random number library in programming software to enable operators to randomly walk in the positions of the corresponding holes of the digital core matrix with the probabilities in the corresponding directions; performing transverse and longitudinal mirror mapping on the digital core matrix to expand the boundary, wherein the process corresponding to the mirror mapping of the boundary is as follows:
wherein: x is the number of i+1 ，y i+1 Representing coordinates in a matrix where an operator before mapping is located; REF (x, y) represents the matrix coordinates of the mapped digital core; b is the matrix boundary size;
step 503: repeatedly iterating the Step501-Step502 process by using programming software, and simultaneously running migration simulation in an unlimited space, namely all pores are in the matrix; and designing and recording the positions of operators under different time step lengths according to different requirements.
7. A method for calculating the flow tortuosity in a porous medium by using a limited walk simulation is characterized in that the specific positions of different operators obtained by selecting different Step lengths according to different requirements in the Step503 process can be interpreted as follows: if the research process is planar two-dimensional migration, recording the distance r under the corresponding two-dimensional coordinates under different iteration steps according to the records of the iteration process; and if the integral tortuosity is considered, recording the distance r under the corresponding three-dimensional coordinates under different iteration steps according to the iteration process, and if the tortuosity under different migration scales is considered, combining the corresponding digital core resolution recording operator to reach the corresponding step number of the specified migration distance.
8. A method for calculating the flow tortuosity in a porous medium by using a limited walk simulation is characterized in that Step6 is specifically processed by the following steps: counting the operator average moving distance variance under the corresponding Step length acquired in the Step5 process, calculating the diffusion coefficient in the digital core matrix and the unlimited space, judging the tortuosity through the slope of the image of the average moving distance variance and the Step number, and judging the corresponding tortuosity as follows:
wherein: d diff Diffusion parameter for free migration, d lmtd In order to limit the diffusion coefficient of the migration,
corresponding to the image slope.
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| CN115078438A (en) * | 2022-06-19 | 2022-09-20 | 西南石油大学 | Method for establishing pore network model based on nuclear magnetic resonance test digital core |
| CN117451582A (en) * | 2023-10-26 | 2024-01-26 | 中国科学院武汉岩土力学研究所 | Core hydrogen diffusion coefficient simulation calculation method and related equipment |
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| CN115078438A (en) * | 2022-06-19 | 2022-09-20 | 西南石油大学 | Method for establishing pore network model based on nuclear magnetic resonance test digital core |
| CN115078438B (en) * | 2022-06-19 | 2024-09-24 | 西南石油大学 | Method for establishing pore network model based on nuclear magnetic resonance test digital rock core |
| CN117451582A (en) * | 2023-10-26 | 2024-01-26 | 中国科学院武汉岩土力学研究所 | Core hydrogen diffusion coefficient simulation calculation method and related equipment |
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