CN115479992A - Method for determining longitudinal and transverse wave speeds of three-dimensional digital core - Google Patents
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Abstract
The invention discloses a method for determining longitudinal and transverse wave speeds of a three-dimensional digital core. The method comprises the following steps: imparting compressional and shear wave velocities to each mineral component and fluid in the three-dimensional digital core; setting the bottom surface of the three-dimensional digital core as a sound wave propagation starting point; setting a voxel adjacent to the acoustic wave propagation starting point voxel in the digital rock core as a central voxel from the acoustic wave propagation starting point voxel, and finding out the voxel adjacent to the central voxel; determining a shortest time for a sound wave to propagate from the neighboring voxels to the central voxel; determining a first arrival time of the central voxel; then determining the first arrival time of the next voxel adjacent to the central voxel until all voxels are traversed; and taking the minimum value of the first arrival time in the top surface of the three-dimensional digital core as the first arrival time of the propagation of the longitudinal wave or the transverse wave, and further determining the velocity of the longitudinal wave or the transverse wave of the three-dimensional digital core.
Description
Technical Field
The invention relates to the field of digital rock physics research in rock physics research, in particular to a method for determining longitudinal and transverse wave speeds of a three-dimensional digital core.
Background
Digital core technology has developed rapidly in the field of oil and gas exploration and development in the last two decades with continuous efforts of numerous petrophysical researchers. From the research content of the digital core technology, the method mainly comprises two aspects of digital core modeling and rock physical property numerical calculation. In the aspect of calculating rock physical property values based on digital cores, simulation and calculation of rock acoustic properties, electrical properties, seepage properties and nuclear magnetic resonance have been carried out at present. In the aspect of rock acoustic property calculation, two main categories of a sound lattice method, a finite element method and a rotary staggered grid finite difference method are mainly used at present.
The acoustic lattice model introduces variable speed particles on the basis of a lattice gas model to simulate the fluctuation phenomenon in a complex medium. The model reveals an intrinsic connection between particle motion and fluctuations. Compared with a finite difference method and different models, the comparison calculation result shows that the acoustic lattice model can effectively overcome the problem that the conventional calculation method is smooth to the model in the operation process, and is more suitable for the calculation of a complex medium model. However, the method is large in calculation amount, and is only applied to two-dimensional numerical simulation research at present.
At present, a finite element method is mainly adopted for calculating the longitudinal wave speed and the transverse wave speed based on the three-dimensional digital core. Makarynska et al studied the elastic properties of partially saturated rocks using a finite element method and compared the calculated results with a low frequency Gassmann-Wood equation and a high frequency Gassmann-Hill equation, and found that the calculated results were consistent with the calculated results of the low frequency Gassmann-Wood equation under uniform saturation of the rocks. The rotation staggered grid finite difference simulation can avoid the problem that the staggered grid is easy to be unstable due to common dispersion on a highly heterogeneous medium. The elastic wave propagation characteristics of the medium containing cracks and pores and without definite boundary conditions can be simulated by using the modified grid.
From the current method for calculating the longitudinal and transverse wave speeds of the three-dimensional digital core, two problems mainly exist. Firstly, the calculation amount and the storage amount of the existing method are very large, the time consumption is long, and only the longitudinal and transverse wave speeds of the digital core with a small scale can be calculated under the condition of specific calculation resources; secondly, the calculation result only reflects the longitudinal and transverse wave speeds under the specific frequency condition, and the research on the change of the longitudinal and transverse wave speeds across the frequency band cannot be met.
Disclosure of Invention
The invention aims to provide a method for determining the longitudinal and transverse wave speeds of a three-dimensional digital core, which is used for solving the difficulty in calculation of the longitudinal and transverse wave speeds of the three-dimensional digital core in the prior art.
In order to achieve the purpose, the invention adopts the following technical scheme:
a method for determining longitudinal and transverse wave speeds of a three-dimensional digital core comprises the following steps:
imparting compressional and shear wave velocities to each mineral component and fluid in the three-dimensional digital core;
setting the bottom surface of the three-dimensional digital core as a sound wave propagation starting point;
setting a voxel adjacent to the acoustic wave propagation starting point voxel in the digital rock core as a central voxel from the acoustic wave propagation starting point voxel, and finding out the voxel adjacent to the central voxel;
determining a shortest time for a sound wave to propagate from the neighboring voxels to the central voxel;
determining whether a straight-line path in the same phase exists between the central voxel and the acoustic wave propagation starting point;
if a straight line path in the same phase exists, determining the shorter time of the time corresponding to the straight line path and the shortest time of the sound wave from the adjacent voxel to the central voxel as the first arrival time of the central voxel; if no straight-line path in the same phase exists, determining the shortest time of the sound wave from the adjacent voxels to the central voxel as the first arrival time of the central voxel;
then determining the first arrival time of the next voxel adjacent to the central voxel until all voxels are traversed;
and taking the minimum value of the first arrival time in the top surface of the three-dimensional digital core as the first arrival time of the propagation of the longitudinal wave or the transverse wave, and further determining the velocity of the longitudinal wave or the transverse wave of the three-dimensional digital core.
According to the determination method of the present invention, preferably, in the step of assigning a longitudinal wave velocity and a transverse wave velocity to each mineral component and fluid in the three-dimensional digital core, the longitudinal wave velocity and the transverse wave velocity are assigned to each mineral component and fluid respectively according to the mineral component and the pore fluid type of the framework of the three-dimensional digital core.
According to the determination method of the invention, preferably, in the step of setting the bottom surface of the three-dimensional digital core as the sound wave propagation starting point, the sound wave propagation starting point is set as a point source, a line source or a plane source according to actual needs.
According to the determination method of the invention, preferably, when the starting point of the sound wave propagation is a point source, setting the first arrival time of a voxel where the point source is located on the bottom surface of the three-dimensional digital core to be 0;
when the initial point of the acoustic wave propagation is a line source, setting the first arrival time of all voxels on the line source on the bottom surface of the three-dimensional digital core to be 0;
and when the acoustic wave propagation starting point is a surface source, setting the first arrival time of all voxels on the surface source on the bottom surface of the three-dimensional digital core to be 0.
According to the determination method of the present invention, preferably, the voxels adjacent to the center voxel include: all voxels adjacent to the central body voxel face, adjacent to the edge, and adjacent to the point.
According to the determination method of the present invention, preferably, the step of finding the voxels neighboring to the center voxel comprises:
setting Cartesian coordinates of the center voxel to (x) 0 ，y 0 ，z 0 )；
Finding 6 voxels adjacent to the central body element plane with cartesian coordinates: (x) 0 +1，y 0 ，z 0 )、(x 0 -1，y 0 ，z 0 )、(x 0 ，y 0 +1，z 0 )、(x 0 ，y 0 -1，z 0 )、(x 0 ，y 0 ，z 0 +1)、(x 0 ，y 0 ，z 0 -1)；
Finding 12 voxels adjacent to the central voxel edge, whose cartesian coordinates are: (x) 0 +1，y 0 +1，z 0 )、(x 0 +1，y 0 -1，z 0 )、(x 0 -1，y 0 +1，z 0 )、(x 0 -1，y 0 -1，z 0 )、(x 0 +1，y 0 ，z 0 +1)、(x 0 +1，y 0 ，z 0 -1)、(x 0 -1，y 0 ，z 0 +1)、(x 0 -1，y 0 ，z 0 -1)、(x 0 ，y 0 +1，z 0 +1)、(x 0 ，y 0 +1，z 0 -1)、(x 0 ，y 0 -1，z 0 +1)、(x 0 ，y 0 -1，z 0 -1)；
Finding 8 voxels adjacent to the centrosome voxel points, whose cartesian coordinates are: (x) 0 +1，y 0 +1，z 0 +1)、(x 0 +1，y 0 +1，z 0 -1)、(x 0 +1，y 0 -1，z 0 +1)、(x 0 +1，y 0 -1，z 0 -1)、(x 0 -1，y 0 +1，z 0 +1)、(x 0 -1，y 0 +1，z 0 -1)、(x 0 -1，y 0 -1，z 0 +1)、(x 0 -1，y 0 -1，z 0 -1)。
According to the determination method of the present invention, preferably, the step of determining the shortest time for the acoustic wave to propagate from the neighboring voxel to the central voxel is performed according to the fermat principle.
According to the determination method of the present invention, preferably, the step of determining the shortest time for the acoustic wave to propagate from the neighboring voxels to the central voxel comprises:
setting the first arrival time of the longitudinal wave of the voxels adjacent to one surface as t for the voxels adjacent to the centrosome voxel surface pf The time t at which the longitudinal wave propagates from the voxel to the central voxel pf0 Comprises the following steps:
in the formula, a is the resolution ratio of the three-dimensional digital core; v. of p0 The longitudinal wave velocity of the central voxel; v. of pf The longitudinal wave velocity of the adjacent voxel of the surface;
setting the longitudinal wave first arrival time of one edge adjacent voxel as t for the voxels adjacent to the edge of the central voxel pl The time t at which the longitudinal wave propagates from the voxel to the central voxel pl0 Comprises the following steps:
in the formula, v pl The longitudinal wave velocity of the adjacent voxel of the edge;
setting the longitudinal wave first arrival time of the voxels adjacent to one point as t for the voxels adjacent to the central body pixel point pp The time t at which the longitudinal wave propagates from the voxel to the central voxel pp0 Comprises the following steps:
in the formula, v pp The longitudinal wave velocity of the adjacent voxel of the point;
according to the Fermat principle, taking the shortest time of the longitudinal wave from all 26 surface-adjacent voxels, edge-adjacent voxels and point-adjacent voxels to propagate to the central voxel as the shortest time of the longitudinal wave to propagate to the central voxel;
and changing the longitudinal wave velocity into the transverse wave velocity to obtain the shortest time for the transverse wave to propagate the central voxel.
According to the principle that the straight-line propagation time of sound waves in the same phase is the shortest, the method firstly determines whether a straight-line path exists between a central voxel and a source in the same phase, and if the straight-line path exists, the length of the straight-line path is divided by the speed of the phase, namely the first arrival time.
According to the determination method of the present invention, preferably, the step of determining whether or not a straight-line path in the same phase exists between the central voxel and the acoustic wave propagation starting point includes:
for voxels in the same base plane as the acoustic wave propagation starting point, the determination method is as follows:
let the central voxel Cartesian coordinate be (x) 0 ，y 0 0), the acoustic propagation starting point voxel has cartesian coordinates of (x) i ，y i ，0)；
Calculating the slope k and the intercept b of the straight line by taking the central voxel and the acoustic wave propagation starting point voxel as two points on the straight line, wherein the slope k and the intercept b are respectively as follows:
k＝(y 0 -y i )/(x 0 -x i )x 0 ≠x i
b＝y i -k·x i
determining Cartesian coordinates corresponding to all voxels through which a straight line between the central voxel and the voxel at the acoustic propagation starting point passes according to the slope and the intercept; these voxels together with the central voxel and the acoustic propagation start point voxel form a set;
determining whether all voxels in the set are of the same mineral composition or fluid type, i.e. are of the same phase; if the two phases are the same, a straight line path in the same phase exists between the central voxel and the sound wave propagation starting point;
aiming at the fact that the sound wave propagation starting point is a surface source or a line source, replacing the voxel of the sound wave propagation starting point, repeating the steps, and finding out straight-line paths in other same phases between the central voxel and the sound wave propagation starting point; selecting the shortest straight line path from all straight line paths in the same phase as the straight line path in the same phase between the central voxel and the sound wave propagation starting point;
for voxels that are not in the same base plane as the acoustic wave propagation starting point, the method of determination is as follows:
let the central voxel cartesian coordinate be (x) 0 ，y 0 ，z 0 ) The acoustic wave propagation starting point voxel has a Cartesian coordinate of (x) i ，y i ，0)；
Determining a linear equation of a three-dimensional space by taking the central voxel and the acoustic wave propagation starting point voxel as two points on a straight line:
(x-x i )/(x 0 -x i )＝(y-y i )/(y 0 -y i )＝z/z 0 ；
according to the linear equation, determining Cartesian coordinates corresponding to all voxels through which a straight line between the central voxel and the acoustic wave propagation starting point voxel passes; these voxels together with the central voxel and the acoustic propagation start point voxel form a set;
determining whether all voxels in the set are of the same mineral composition or fluid type, i.e. are of the same phase; if the two phases are the same, a straight line path in the same phase exists between the central voxel and the sound wave propagation starting point;
aiming at the fact that the sound wave propagation starting point is a surface source or a line source, replacing the voxel of the sound wave propagation starting point, repeating the steps, and finding out straight-line paths in other same phases between the central voxel and the sound wave propagation starting point; and selecting the shortest straight-line path from all the straight-line paths in the same phase as the straight-line path in the same phase between the central voxel and the sound wave propagation starting point.
According to the determination method of the invention, preferably, the step of further determining the longitudinal wave or transverse wave velocity of the three-dimensional digital core comprises:
and dividing the length of the three-dimensional digital core in the z direction by the first arrival time of the propagation of the longitudinal wave or the transverse wave to obtain the velocity of the longitudinal wave or the transverse wave of the three-dimensional digital core in the z direction.
The method for determining the longitudinal and transverse wave speeds of the three-dimensional digital core, provided by the invention, has the advantages of small calculated amount, small occupied memory and calculation speed block, can be used for calculating the longitudinal and transverse wave speeds of the large-scale three-dimensional digital core and calculating the longitudinal and transverse wave speeds under different frequency conditions, and provides a calculation means for carrying out frequency dispersion research and rock acoustic response mechanism research based on the three-dimensional digital core. The method can also be popularized to the calculation of the longitudinal and transverse wave speeds of the digital core of the standard plunger rock sample and the digital cores of other scales.
Drawings
Fig. 1 is a flowchart of a method for determining a longitudinal wave velocity and a transverse wave velocity of a three-dimensional digital core according to an embodiment of the present disclosure.
Fig. 2 a-2 c are schematic diagrams of different types of sources arranged on the bottom surface of a three-dimensional digital core according to an embodiment of the invention.
Fig. 3 a-3 c show 26 voxels adjacent to a central voxel in accordance with an embodiment of the present invention.
FIG. 4 is a schematic diagram of a linear path between a central voxel and an acoustic emission source in accordance with one embodiment of the present invention.
FIG. 5 is a three-dimensional digital core longitudinal wave first arrival time field in accordance with an embodiment of the present disclosure.
FIG. 6 is a three-dimensional digital core shear wave first arrival time field according to an embodiment of the present invention.
Fig. 7 a-7 b are cross-sectional views of test results of longitudinal and transverse wave velocity experiments on three-dimensional printed core samples according to an embodiment of the invention. FIG. 7a is a graph showing the relationship between the calculated longitudinal wave velocity and the experimentally measured longitudinal wave velocity according to the embodiment of the present invention; FIG. 7b is a graph of the calculated shear wave velocity versus the experimentally measured shear wave velocity according to an embodiment of the present invention.
Detailed Description
In order to more clearly illustrate the invention, the invention is further described below in connection with preferred embodiments. It is to be understood by persons skilled in the art that the following detailed description is illustrative and not restrictive, and is not to be taken as limiting the scope of the invention.
As shown in fig. 1, the present invention provides a preferred embodiment, wherein the determination of the longitudinal and transverse wave velocities of the three-dimensional digital core specifically includes the following steps:
and S100, respectively endowing each mineral component and each fluid with a longitudinal wave velocity and a transverse wave velocity according to the mineral components of the three-dimensional digital core skeleton and the types of pore fluids.
S200, setting the bottom surface of the three-dimensional digital core as a sound wave propagation starting point, and setting the bottom surface as a point source, a line source or a surface source according to actual needs.
In order to calculate the longitudinal and transverse wave speeds of the three-dimensional digital core by adopting the Fermat principle, the starting point of sound wave propagation needs to be set. According to actual needs, different parts of the three-dimensional digital core can be set as the starting points of sound wave propagation, and the bottom surface of the three-dimensional digital core is preferably used as the starting point of sound wave propagation. The starting point setting method comprises the following steps:
s201, if the starting point of sound wave propagation is set to be a point source, setting the first arrival time of a voxel where the point is located on the bottom surface of the three-dimensional digital rock core to be 0.
S202, if the initial point of sound wave propagation is set as a line source, setting the first arrival time to be 0 for all voxels on the line on the bottom surface of the three-dimensional digital core.
And S203, if the acoustic wave propagation starting point is set as a surface source, setting the first arrival time of all voxels on the surface on the bottom surface of the three-dimensional digital rock core to be 0.
S300, starting from the acoustic wave propagation starting point voxel, setting a voxel adjacent to the acoustic wave starting point voxel in the digital rock core as a central voxel, and finding out the voxel adjacent to the central voxel.
In order to find out the voxels adjacent to the central voxel, the adjacent voxels need to be classified, and one class is the voxels in surface contact with the central voxel, and is called as surface adjacent voxels; one class is voxels that are edge neighbors to the central voxel, called edge neighbors; one class is voxels that are point-contacted with a central voxel, called point-neighbors. The steps for finding the three types of adjacent voxels are as follows:
s301, setting the Cartesian coordinate of the central voxel as (x) 0 ，y 0 ，z 0 ) First, 6 voxels adjacent to the central body element plane are found, whose cartesian coordinates are: (x) 0 +1，y 0 ，z 0 )、(x 0 -1，y 0 ，z 0 )、(x 0 ，y 0 +1，z 0 )、(x 0 ，y 0 -1，z 0 )、(x 0 ，y 0 ，z 0 +1)、(x 0 ，y 0 ，z 0 -1)。
S302, finding 12 voxels adjacent to the central voxel edge, wherein the Cartesian coordinates of the voxels are respectively as follows: (x) 0 +1，y 0 +1，z 0 )、(x 0 +1，y 0 -1，z 0 )、(x 0 -1，y 0 +1，z 0 )、(x 0 -1，y 0 -1，z 0 )、(x 0 +1，y 0 ，z 0 +1)，(x 0 +1，y 0 ，z 0 -1)、(x 0 -1，y 0 ，z 0 +1)、(x 0 -1，y 0 ，z 0 -1)、(x 0 ，y 0 +1，z 0 +1)、(x 0 ，y 0 +1，z 0 -1)、(x 0 ，y 0 -1，z 0 +1)、(x 0 ，y 0 -1，z 0 -1)。
S303, finally finding out 8 voxels adjacent to the centrosome element point, wherein the Cartesian coordinates are respectively as follows: (x) 0 +1，y 0 +1，z 0 +1)、(x 0 +1，y 0 +1，z 0 -1)、(x 0 +1，y 0 -1，z 0 +1)、(x 0 +1，y 0 -1，z 0 -1)、(x 0 -1，y 0 +1，z 0 +1)、(x 0 -1，y 0 +1，z 0 -1)、(x 0 -1，y 0 -1，z 0 +1)、(x 0 -1，y 0 -1，z 0 -1)。
S400, according to the Fermat principle, the shortest time for the sound waves to propagate from the adjacent voxels to the central voxel is determined, and the time is set to be t0.
The time of propagation from neighboring voxels to the central voxel of a longitudinal wave or a transverse wave in a straight-line propagation manner needs to be calculated, and then the shortest propagation time is selected from the time set of propagation from all 26 neighboring voxels to the central voxel, and the steps are as follows:
s401, setting the longitudinal wave first arrival time of voxels adjacent to a central body voxel surface as t pf The time t for the propagation of the longitudinal wave from this voxel to the central voxel pf0 Comprises the following steps:
in the above formula, a is the resolution of the three-dimensional digital core; v. of p0 The longitudinal wave velocity of the central voxel; v. of pf The longitudinal wave velocity of the adjacent voxel of one surface. The calculation method of the propagation time of other face-adjacent voxels to the central voxel is the same as the above equation.
S402, setting the longitudinal wave first arrival time of one edge adjacent voxel as t for the voxels adjacent to the edge of the central voxel pl The time t at which the longitudinal wave propagates from the voxel to the central voxel pl0 Comprises the following steps:
in the above formula v pl The physical meaning of other parameters is the same as the longitudinal wave velocity of one edge adjacent voxel. The calculation method of the propagation time of other edge-neighboring voxels to the central voxel is the same as the above equation.
S403, for voxels adjacent to the centrosome voxel point, setting the longitudinal wave first arrival time of the voxels adjacent to one point as t pp The time t at which the longitudinal wave propagates from the voxel to the central voxel pp0 Comprises the following steps:
in the above formula v pp The physical meaning of other parameters is the same as the longitudinal wave velocity of the adjacent voxel of one point. The calculation method of the propagation time of the neighboring voxels to the central voxel at other points is the same as the above equation.
S404, according to the Fermat principle, the shortest time of all 26 surface-adjacent voxels, edge-adjacent voxels and point-adjacent voxels to propagate to the central voxel is taken as the time of the longitudinal wave to propagate to the central voxel and is calculated as t0.
S405, the calculation method of the shortest time for the transverse wave to propagate to the central voxel is similar to that of the longitudinal wave, and the longitudinal wave speeds of all voxels only need to be changed into the transverse wave speed.
S500, according to the principle that the straight line propagation time of the sound wave in the same phase is shortest, whether a straight line path in the same phase exists between the central voxel and the source is determined firstly.
In order to find out whether a straight line path exists between the central voxel and the source in the same phase, the processing needs to be carried out in two cases, and the steps are as follows:
s501, for voxels in the same bottom plane as the source, the determination method is as follows:
(1) let the center voxel have cartesian coordinates of (x) 0 ，y 0 0), surface source (or line source, point source) voxel cartesian coordinates of (x) i ，y i ，0)；
(2) Taking the central body voxel and the surface source voxel as two points on a straight line, calculating the slope k and the intercept b of the straight line, which are respectively
k＝(y 0 -y i )/(x 0 -x i )x 0 ≠x i
b＝y i -k·x i
(3) And determining the corresponding Cartesian coordinates of all voxels through which the straight line between the central body voxel and the surface source voxel passes according to the slope and the intercept. These voxels together with the centrosome voxels and the area source voxels form a set;
(4) it is determined whether all voxels in the set are of the same mineral composition or fluid type, that is, the same phase. If the central voxel is the same phase, a straight line path in the same phase exists between the central voxel and the source;
(5) replacing a surface source voxel, repeating the steps (1) to (4), and finding out other straight-line paths in the same phase between the central voxel and the source;
(6) from all the in-phase straight-line paths, the shortest path is selected as the in-phase straight-line path between the central voxel and the source.
S502, for the voxels which are not in the same bottom surface as the source, the determination method is as follows:
(1) let the center voxel have cartesian coordinates of (x) 0 ，y 0 ，z 0 ) The Cartesian coordinate of the surface source (or line source, point source) voxel is (x) i ，y i ，0)。
(2) Determining a linear equation of a three-dimensional space by taking the central body voxel and the surface source voxel as two points on a straight line:
(x-x i )/(x 0 -x i )＝(y-y i )/(y 0 -y i )＝z/z 0
(3) according to the straight line equation, determining the corresponding Cartesian coordinates of all voxels through which the straight line between the central body voxel and the surface source voxel passes. These voxels are grouped together with the central voxel and the area source voxel into a set.
(4) It is determined whether all voxels in the collection are of the same mineral composition or fluid type, that is, the same phase. If the two phases are the same, the straight-line path in the same phase exists between the central voxel and the source.
(5) And (4) replacing the surface source voxel, repeating the steps (1) to (4) and finding out other straight-line paths in the same phase between the central voxel and the source.
(6) From all the in-phase straight-line paths, the shortest path is selected as the in-phase straight-line path between the central voxel and the source.
In step S107 of this embodiment, after the calculation of the first arrival time of the longitudinal wave or the transverse wave of a single voxel is completed, the first arrival time of the longitudinal wave or the transverse wave needs to be calculated for all voxels in the three-dimensional digital core except for the source, and finally, the calculation of the longitudinal wave and the transverse wave velocity of the three-dimensional digital core is implemented, and the steps are as follows:
s503, calculating the first arrival time of all the voxel longitudinal waves and transverse waves except the source voxels in the three-dimensional digital core.
And S504, selecting the minimum first-arrival time value in voxels on the top surface of the three-dimensional digital core as the first-arrival time of propagation of longitudinal waves or transverse waves.
And S505, dividing the length of the three-dimensional digital core in the z direction by the first arrival time of the propagation of the longitudinal wave or the transverse wave to obtain the velocity of the longitudinal wave or the transverse wave of the three-dimensional digital core in the z direction.
S600, if a straight line path in the same phase exists, calculating time corresponding to the shortest path, setting the time as t1, comparing the time t0 with the time t1, and setting the minimum time as the first arrival time of a central voxel; if not, setting t0 as the first arrival time of the central voxel;
s700, calculating the time of the next voxel adjacent to the central voxel until all voxels are calculated; and taking the minimum first arrival time value in the top surface of the three-dimensional digital core as the first arrival time of the propagation of the longitudinal wave or the transverse wave, and calculating the velocity of the longitudinal wave or the transverse wave of the three-dimensional digital core.
For a clearer and more intuitive explanation of the method for determining the longitudinal and transverse wave velocities of the three-dimensional digital core, a specific example is described below, but it should be noted that the specific example is only for better explaining the present invention, and is not to be construed as limiting the present invention.
In connection with step S100, a three-dimensional digital core is a digitized rock to which a specific number corresponds for each mineral component and fluid type in the rock. Table 1 below gives the values of compressional and shear velocities given respectively for the mineral composition of the tight sandstone reservoir rock and the type of fluid in the pores. Since these values are the high-frequency results of the ultrasonic test, the longitudinal and transverse wave velocities of the three-dimensional digital core calculated this time are also values under the high-frequency condition.
Table 1 sets forth compressional and shear wave velocity values for the mineral composition of tight sandstone reservoir rock and the type of fluid in the pore space, respectively, and their corresponding digitized labels
In connection with step S200, each minimized cell in the three-dimensional digital core is called a voxel, corresponding to a pixel in the two-dimensional image. The voxel is a cube with the side length being the resolution, and the resolution of the three-dimensional digital core selected in this embodiment is 3.83 μm. Each square in fig. 2 a-2 c is a voxel, where the grey voxels represent the starting points for the propagation of the acoustic wave, and different types of starting points may be set, for example, fig. 2a is a point source, consisting of a single voxel. Fig. 2b is a line source, consisting of several voxels on the same line. Fig. 2c is a surface source, consisting of several voxels on the same surface. In this example, a planar source was selected, consisting of 81 voxels in total, 9 × 9. The longitudinal wave propagation first arrival time and the transverse wave propagation first arrival time of all the area source voxels are set to be 0.
Combining step S300 and step S400, for each non-boundary voxel in the three-dimensional digital core, three types of voxels adjacent to it can be always found: face-neighbors, edge-neighbors, and point-neighbors. Fig. 3 a-3 c are schematic diagrams of these three classes of neighboring voxels, respectively, where neighboring voxels are all represented in gray and the central voxel is represented in white. Fig. 3a is a schematic diagram of voxels adjacent to the surface, and there are 6 voxels adjacent to the central voxel surface in fig. 3 a. The distance that the acoustic wave travels from any one of the face-adjacent voxel centers to the center voxel center is the voxel resolution, which in this embodiment is 3.84 μm. The travel time is calculated by the formula in step S401. Fig. 3b is a schematic diagram of edge-adjacent voxels, and there are 12 voxels in fig. 3b that edge-adjacent to the central voxel. The distance of the sound wave from the center of any edge-adjacent voxel to the center of the central voxel is the voxel resolution multiplied by
In this example 5.43 μm. The travel time is calculated by the formula in step S402. FIG. 3c is a schematic diagram of point-adjacent voxels, the volume in FIG. 3c that is point-adjacent to the central body elementThere are 8 total elements. The distance of the sound wave from the center of the adjacent voxel to the center of the central voxel at any point is the voxel resolution multiplied by
In this example 6.65 μm. The propagation time is calculated by the formula in step S403. And after the time of all 26 adjacent voxels propagating to the central voxel is calculated, selecting the minimum value from the time as the time of propagating to the central voxel, and calculating the time as t0.
Combining step S500 and step S600, the white voxel in the bottom surface of fig. 4 is a surface source voxel, and a single gray voxel P represents any voxel except the surface source voxel in the three-dimensional digital core. Because the core can form a discretized regular cube unit in the process of digitization, when the propagation time between a surface source voxel and any non-surface source voxel is actually calculated, the used distance is in the form of a broken line, and is not the shortest straight line between two points. Therefore, it is necessary to determine whether voxels through which a straight line passes between a surface-source voxel and any non-surface-source voxel are the same phase, that is, whether voxels through which a straight line passes in fig. 4 are the same quartz (or clay, feldspar, natural gas). If a straight line passing through the same phase exists, the distance between the surface source voxel and any voxel at the moment is calculated by adopting a distance formula between two points, then the distance formula is divided by the longitudinal wave velocity or the transverse wave velocity of the phase to calculate the propagation time which is marked as t1, and in general, t1 is less than or equal to t0. At this point t1 is taken as the shortest time to propagate from the source to the central voxel. If there is no straight line through the same phase, t0 is taken as the shortest time to travel from the source to the central voxel.
With reference to step S700, fig. 5 is a diagram of a three-dimensional digital core longitudinal wave first arrival time field finally obtained in the present embodiment. Fig. 6 is a three-dimensional digital core shear wave first arrival time field finally obtained in this embodiment. The differences in first arrival times are indicated by the shades of colors in fig. 5 and 6; the darker the color, the shorter the first arrival time; the lighter the color, the longer the first arrival time. And selecting the minimum first arrival time value in voxels on the top surface of the three-dimensional digital core as the first arrival time of the propagation of longitudinal waves or transverse waves. And dividing the length of the three-dimensional digital core in the z direction by the first arrival time of the propagation of the longitudinal wave or the transverse wave to obtain the velocity of the longitudinal wave or the transverse wave of the three-dimensional digital core in the z direction.
In order to verify the accuracy of the method provided by the invention, the longitudinal and transverse wave speeds measured by an ultrasonic laboratory for three-dimensionally printing a crack sample (the printing material is photosensitive resin) are compared with the longitudinal and transverse wave speeds obtained by the method provided by the invention, and the specific results are shown in fig. 7a and 7b. FIG. 7a is a plot of calculated longitudinal wave velocity versus experimentally tested longitudinal wave velocity; FIG. 7b is a graph of calculated shear wave velocity versus experimentally tested shear wave velocity. It can be seen from fig. 7a and 7b that the calculated longitudinal wave velocity and transverse wave velocity of the proposed method are close to those of laboratory ultrasonic measurement, which illustrates the reliability of the proposed method.
The method for determining the longitudinal and transverse wave speeds of the three-dimensional digital core, provided by the invention, has the advantages of small calculated amount, small occupied memory and calculation speed block, can be used for calculating the longitudinal and transverse wave speeds of the large-scale three-dimensional digital core and calculating the longitudinal and transverse wave speeds under different frequency conditions, and provides a calculation means for developing frequency dispersion research and rock acoustic response mechanism research based on the three-dimensional digital core. The method can also be popularized to the calculation of the longitudinal and transverse wave speeds of the digital core of the standard plunger rock sample and the digital cores of other scales.
It should be understood that the above-described embodiments of the present invention are examples for clearly illustrating the invention, and are not to be construed as limiting the embodiments of the present invention, and it will be obvious to those skilled in the art that various changes and modifications can be made on the basis of the above description, and it is not intended to exhaust all embodiments, and obvious changes and modifications can be made on the basis of the technical solutions of the present invention.
Claims (10)
1. A method for determining longitudinal and transverse wave speeds of a three-dimensional digital core is characterized by comprising the following steps:
imparting compressional and shear wave velocities to each mineral component and fluid in the three-dimensional digital core;
setting the bottom surface of the three-dimensional digital core as a sound wave propagation starting point;
setting a voxel adjacent to the acoustic wave propagation starting point voxel in the digital rock core as a central voxel from the acoustic wave propagation starting point voxel, and finding out the voxel adjacent to the central voxel;
determining a shortest time for an acoustic wave to propagate from the neighboring voxels to the central voxel;
determining whether a straight-line path in the same phase exists between the central voxel and the acoustic wave propagation starting point;
if a straight-line path in the same phase exists, determining the shorter time of the time corresponding to the straight-line path and the shortest time of the sound wave from the adjacent voxels to the central voxel as the first arrival time of the central voxel; if no straight-line path in the same phase exists, determining the shortest time of the sound wave from the adjacent voxels to the central voxel as the first arrival time of the central voxel;
then determining the first arrival time of the next voxel adjacent to the central voxel until all voxels are traversed;
and taking the minimum value of the first arrival time in the top surface of the three-dimensional digital core as the first arrival time of the propagation of the longitudinal wave or the transverse wave, and further determining the velocity of the longitudinal wave or the transverse wave of the three-dimensional digital core.
2. The method of determining according to claim 1, wherein in the step of assigning a compressional wave velocity and a shear wave velocity to each mineral component and fluid in the three-dimensional digital core, compressional wave velocity and shear wave velocity are assigned to each mineral component and fluid according to the mineral component and pore fluid type of the three-dimensional digital core skeleton, respectively.
3. The determination method according to claim 1, wherein in the step of setting the bottom surface of the three-dimensional digital core as the acoustic wave propagation starting point, the acoustic wave propagation starting point is set as a point source, a line source or a plane source according to actual needs.
4. The determination method according to claim 3, wherein when the starting point of the sound wave propagation is a point source, setting the first arrival time of a voxel where the point source is located on the bottom surface of the three-dimensional digital core to be 0;
when the initial point of the acoustic wave propagation is a line source, setting the first arrival time of all voxels on the line source on the bottom surface of the three-dimensional digital core to be 0;
and when the starting point of the sound wave propagation is a surface source, setting the first arrival time of all voxels on the surface source on the bottom surface of the three-dimensional digital rock core to be 0.
5. The determination method according to claim 4, wherein the voxels adjacent to the central voxel comprise: all voxels adjacent to the central body voxel face, adjacent to the edge, and adjacent to the point.
6. The method of claim 5, wherein the step of finding voxels neighboring the center voxel comprises:
setting the Cartesian coordinates of the central voxel to (x) 0 ，y 0 ，z 0 )；
Finding 6 voxels adjacent to the central body element plane with cartesian coordinates: (x) 0 +1，y 0 ，z 0 )、(x 0 -1，y 0 ，z 0 )、(x 0 ，y 0 +1，z 0 )、(x 0 ，y 0 -1，z 0 )、(x 0 ，y 0 ，z 0 +1)、(x 0 ，y 0 ，z 0 -1)；
Finding 12 voxels adjacent to the central voxel edge, whose cartesian coordinates are: (x) 0 +1，y 0 +1，z 0 )、(x 0 +1，y 0 -1，z 0 )、(x 0 -1，y 0 +1，z 0 )、(x 0 -1，y 0 -1，z 0 )、(x 0 +1，y 0 ，z 0 +1)、(x 0 +1，y 0 ，z 0 -1)、(x 0 -1，y 0 ，z 0 +1)、(x 0 -1，y 0 ，z 0 -1)、(x 0 ，y 0 +1，z 0 +1)、(x 0 ，y 0 +1，z 0 -1)、(x 0 ，y 0 -1，z 0 +1)、(x 0 ，y 0 -1，z 0 -1)；
Finding 8 voxels adjacent to the centrosome element point with cartesian coordinates: (x) 0 +1，y 0 +1，z 0 +1)、(x 0 +1，y 0 +1，z 0 -1)、(x 0 +1，y 0 -1，z 0 +1)、(x 0 +1，y 0 -1，z 0 -1)、(x 0 -1，y 0 +1，z 0 +1)、(x 0 -1，y 0 +1，z 0 -1)、(x 0 -1，y 0 -1，z 0 +1)、(x 0 -1，y 0 -1，z 0 -1)。
7. The method of determining according to claim 6, wherein said step of determining the shortest time for an acoustic wave to travel from said neighboring voxels to said central voxel is performed according to the Fermat principle.
8. The method of determining according to claim 7, wherein the step of determining the shortest time for the acoustic wave to propagate from the neighboring voxels to the central voxel comprises:
setting the longitudinal wave first arrival time of voxels adjacent to one surface as t for voxels adjacent to the central body voxel surface pf The time t for the propagation of the longitudinal wave from the voxel to the central voxel pf0 Comprises the following steps:
in the formula, a is the resolution of the three-dimensional digital core; v. of p0 The longitudinal wave velocity of the central voxel; v. of pf The longitudinal wave velocity of the adjacent voxel of the surface;
setting the longitudinal wave first arrival time of one edge adjacent voxel as t for the voxels adjacent to the edge of the central voxel pl The time t at which the longitudinal wave propagates from the voxel to the central voxel pl0 Comprises the following steps:
in the formula, v pl The longitudinal wave velocity of the adjacent voxel of the edge;
setting the longitudinal wave first arrival time of the voxels adjacent to one point as t for the voxels adjacent to the central body pixel point pp The time t at which the longitudinal wave propagates from the voxel to the central voxel pp0 Comprises the following steps:
in the formula, v pp The longitudinal wave velocity of the adjacent voxel of the point;
according to the Fermat principle, taking the shortest time of the longitudinal wave from all 26 surface-adjacent voxels, edge-adjacent voxels and point-adjacent voxels to the central voxel as the shortest time of the longitudinal wave to the central voxel;
and changing the longitudinal wave velocity into the transverse wave velocity to obtain the shortest time for the transverse wave to propagate the central voxel.
9. The method of determining according to claim 8, wherein the step of determining whether a straight-line path in the same phase exists between the central voxel and the acoustic wave propagation starting point comprises:
for voxels in the same base plane as the acoustic wave propagation starting point, the determination method is as follows:
let the central voxel Cartesian coordinate be (x) 0 ，y 0 0), the acoustic propagation starting point voxel has cartesian coordinates of (x) i ，y i ，0)；
Calculating the slope k and the intercept b of the straight line by taking the central voxel and the acoustic wave propagation starting point voxel as two points on the straight line, wherein the slope k and the intercept b are respectively as follows:
k＝(y 0 -y i )/(x 0 -x i )x 0 ≠x i
b＝y i -k·x i
determining Cartesian coordinates corresponding to all voxels through which a straight line between the central voxel and the voxel at the acoustic propagation starting point passes according to the slope and the intercept; these voxels together with the central voxel and the acoustic propagation start point voxel form a set;
determining whether all voxels in the set are of the same mineral composition or fluid type, i.e. are of the same phase; if the two phases are the same, a straight line path in the same phase exists between the central voxel and the sound wave propagation starting point;
aiming at the fact that the sound wave propagation starting point is a surface source or a line source, replacing the voxel of the sound wave propagation starting point, repeating the steps, and finding out straight-line paths in other same phases between the central voxel and the sound wave propagation starting point; selecting the shortest straight line path from all straight line paths in the same phase as the straight line path in the same phase between the central voxel and the sound wave propagation starting point;
for voxels that are not in the same base plane as the acoustic wave propagation starting point, the method of determination is as follows:
let the central voxel Cartesian coordinate be (x) 0 ，y 0 ，z 0 ) The acoustic wave propagation starting point voxel has a Cartesian coordinate of (x) i ，y i ，0)；
Determining a linear equation of a three-dimensional space by taking the central voxel and the acoustic wave propagation starting point voxel as two points on a straight line:
(x-x i )/(x 0 -x i )＝(y-y i )/(y 0 -y i )＝z/z 0 ；
according to the linear equation, determining Cartesian coordinates corresponding to all voxels through which a straight line between the central voxel and the voxel at the acoustic propagation starting point passes; these voxels together with the central voxel and the acoustic propagation start point voxel form a set;
determining whether all voxels in the set are of the same mineral composition or fluid type, i.e. are of the same phase; if the central voxel is in the same phase, a straight-line path in the same phase exists between the central voxel and the sound wave propagation starting point;
aiming at the fact that the acoustic wave propagation starting point is a surface source or a line source, replacing the acoustic wave propagation starting point voxel, repeating the steps, and finding out straight line paths in other same phases between the central voxel and the acoustic wave propagation starting point; from all the straight-line paths in the same phase, the shortest straight-line path is selected as the straight-line path in the same phase between the central voxel and the acoustic wave propagation starting point.
10. The method for determining according to claim 9, wherein the step of further determining the velocity of the longitudinal wave or the transverse wave of the three-dimensional digital core comprises:
and dividing the length of the three-dimensional digital core in the z direction by the first arrival time of the propagation of the longitudinal wave or the transverse wave to obtain the velocity of the longitudinal wave or the transverse wave of the three-dimensional digital core in the z direction.
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