CN110671100B - Method for manufacturing chessboard-like simulator in device for simulating rock heterogeneity - Google Patents
Method for manufacturing chessboard-like simulator in device for simulating rock heterogeneity Download PDFInfo
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- 238000000034 method Methods 0.000 title claims abstract description 31
- 239000011435 rock Substances 0.000 title claims abstract description 29
- 238000004519 manufacturing process Methods 0.000 title claims abstract description 15
- 230000035699 permeability Effects 0.000 claims abstract description 252
- 238000009826 distribution Methods 0.000 claims abstract description 50
- 238000004088 simulation Methods 0.000 claims abstract description 31
- 239000003822 epoxy resin Substances 0.000 claims description 10
- 229920000647 polyepoxide Polymers 0.000 claims description 10
- 239000006185 dispersion Substances 0.000 claims description 9
- 238000004364 calculation method Methods 0.000 claims description 8
- 239000006004 Quartz sand Substances 0.000 claims description 6
- VYPSYNLAJGMNEJ-UHFFFAOYSA-N Silicium dioxide Chemical compound O=[Si]=O VYPSYNLAJGMNEJ-UHFFFAOYSA-N 0.000 claims description 6
- 238000007619 statistical method Methods 0.000 claims description 6
- FFBHFFJDDLITSX-UHFFFAOYSA-N benzyl N-[2-hydroxy-4-(3-oxomorpholin-4-yl)phenyl]carbamate Chemical compound OC1=C(NC(=O)OCC2=CC=CC=C2)C=CC(=C1)N1CCOCC1=O FFBHFFJDDLITSX-UHFFFAOYSA-N 0.000 claims description 5
- 235000019580 granularity Nutrition 0.000 claims description 4
- NAWXUBYGYWOOIX-SFHVURJKSA-N (2s)-2-[[4-[2-(2,4-diaminoquinazolin-6-yl)ethyl]benzoyl]amino]-4-methylidenepentanedioic acid Chemical compound C1=CC2=NC(N)=NC(N)=C2C=C1CCC1=CC=C(C(=O)N[C@@H](CC(=C)C(O)=O)C(O)=O)C=C1 NAWXUBYGYWOOIX-SFHVURJKSA-N 0.000 claims description 2
- 238000002474 experimental method Methods 0.000 description 6
- 238000002347 injection Methods 0.000 description 4
- 239000007924 injection Substances 0.000 description 4
- 239000007788 liquid Substances 0.000 description 4
- 239000003921 oil Substances 0.000 description 4
- 230000006866 deterioration Effects 0.000 description 3
- 238000006073 displacement reaction Methods 0.000 description 3
- 238000000605 extraction Methods 0.000 description 3
- 238000005266 casting Methods 0.000 description 2
- 238000010586 diagram Methods 0.000 description 2
- 210000002445 nipple Anatomy 0.000 description 2
- 239000002245 particle Substances 0.000 description 2
- 208000035126 Facies Diseases 0.000 description 1
- 230000009286 beneficial effect Effects 0.000 description 1
- 230000015572 biosynthetic process Effects 0.000 description 1
- 230000015556 catabolic process Effects 0.000 description 1
- 239000010779 crude oil Substances 0.000 description 1
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- 230000008021 deposition Effects 0.000 description 1
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- E—FIXED CONSTRUCTIONS
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- E21B—EARTH OR ROCK DRILLING; OBTAINING OIL, GAS, WATER, SOLUBLE OR MELTABLE MATERIALS OR A SLURRY OF MINERALS FROM WELLS
- E21B49/00—Testing the nature of borehole walls; Formation testing; Methods or apparatus for obtaining samples of soil or well fluids, specially adapted to earth drilling or wells
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- G—PHYSICS
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- G01N—INVESTIGATING OR ANALYSING MATERIALS BY DETERMINING THEIR CHEMICAL OR PHYSICAL PROPERTIES
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- G01N15/00—Investigating characteristics of particles; Investigating permeability, pore-volume or surface-area of porous materials
- G01N15/08—Investigating permeability, pore-volume, or surface area of porous materials
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- Y02A—TECHNOLOGIES FOR ADAPTATION TO CLIMATE CHANGE
- Y02A10/00—TECHNOLOGIES FOR ADAPTATION TO CLIMATE CHANGE at coastal zones; at river basins
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Abstract
A device for simulating rock heterogeneity by using a chessboard-like simulator and a manufacturing method thereof. The main aim is to realize accurate simulation of rock plane heterogeneity in a laboratory. The method is characterized in that: the device consists of an ISCO constant pressure pump, an electronic pressure gauge, a five-way valve, a guide pipe, units with different permeability of 2 multiplied by 10cm, a pouring heterogeneous simulation body and a measuring cylinder. The manufacturing of the device depends on the permeability distribution condition of actual rocks, firstly collects each layer of permeability data of all well points in the region to be simulated, and then disperses the permeability data through a variation function to obtain the permeability value of any point on a plane, so that the plane heterogeneity of the rocks can be fully embodied in a simulation body, the simulation of the plane heterogeneity of the rocks in a laboratory becomes possible, and the influence of the plane heterogeneity on oil deposit development can be conveniently researched.
Description
The technical field is as follows:
the invention relates to a simulator device for simulating rock heterogeneity in an oil displacement experiment.
Technical background:
the oil field in China mainly takes a continental facies clastic rock reservoir as a main part, the geological condition complexity is high, the heterogeneity is strong, the property difference of crude oil is large, and the exploitation efficiency is low. Therefore, there is a need for a comprehensive study of the heterogeneity. Because the reservoir is influenced by deposition, diagenesis and tectonic effects in the forming process, the spatial distribution and various attributes in the reservoir are changed, the heterogeneity of the reservoir is mainly researched by an experimental method at present, but the heterogeneity of the reservoir is simulated by simply connecting cores with different permeabilities in parallel. Because experiment conditions are limited, the number of cores connected in parallel cannot be too many, and meanwhile, the permeability value of each core is made by using the average value of the permeability of a certain research block, so that the heterogeneity difference between the core and an actual reservoir is large, the reservoir cannot be well simulated, and the result of a laboratory oil displacement experiment sometimes cannot well guide field development.
The invention content is as follows:
in order to solve the technical problems mentioned in the technical background, the invention provides a device for simulating rock heterogeneity by using a chessboard-like simulator. Heterogeneity research is an important content of reservoir description, and the spatial distribution of parameters of the heterogeneity research not only has randomness, but also has structural property. The invention takes the permeability data of all wells in a research area as the basis, and based on the basic theory of geostatistics about a variation function, the known permeability data are dispersed through the variation function according to some known permeability distribution data, so that the permeability value of any point on a plane can be obtained, and a chessboard-shaped simulation body model is formed to reflect the plane heterogeneous characteristics of rocks. The model is based on actual permeability distribution, discretized through a variation function, and simulated by a permeability unit of 2 multiplied by 10cm, so that the distribution rule of the permeability in the rock can be fully embodied in a chessboard-shaped simulation body. Meanwhile, a single five-point method well group is arranged on the chessboard-shaped simulation body which finely describes the permeability distribution of the rock, so that the simulation of the heterogeneous oil displacement experiment of the rock in a laboratory is closer to the actual situation, and a better experimental basis can be provided for field development.
The technical scheme of the invention is as follows: the utility model provides a device that utilizes pouring heterogeneous emulation body simulation rock heterogeneity, includes ISCO constant pressure pump, pipe, electronic pressure gauge, five-way valve, first screwed joint, flow regulator, second screwed joint and graduated flask, its unique character lies in:
the device also comprises a pouring heterogeneous simulation body; the casting heterogeneous simulation body consists of a plurality of unit bodies with different permeabilities, wherein the length, the width and the height of each unit body are respectively 2 cm, 2 cm and 10cm, and the plurality of unit bodies with different permeabilities form a square body; the different permeability of the unit bodies is obtained by discrete simulation of the numerical value of the actual stratum permeability.
And an epoxy resin pouring layer is poured on the outer layer of the poured heterogeneous simulation body, a single five-point method well group is arranged on the poured heterogeneous simulation body through the epoxy resin pouring layer, and the single five-point method well group adopts a mode that a central well is positioned in four diagonal wells.
And the two ends of the second threaded joint are simultaneously provided with threads, the lower end of the second threaded joint is connected with a threaded through hole of a single five-point method well group on the poured heterogeneous simulation body through screwing, and the upper end of the second threaded joint is connected with the threaded through hole of the flow regulator through screwing.
The first threaded joint is provided with threads only at one end, wherein the threaded end of the first threaded joint is connected with the threaded through hole of the flow regulator through screwing, and the unthreaded other end is connected with the second conduit.
The flow regulator is provided with two threaded through holes and a knob, the two threaded through holes are respectively connected with the first threaded joint and the second threaded joint, and the knob is used for controlling and simulating the injection speed and the extraction speed of an actual injection well and an actual extraction well.
The electronic pressure gauge is connected between the ISCO constant pressure pump and the liquid flow input port of the five-way valve through a first conduit; the four liquid flow output ports of the five-way valve are respectively connected with the non-threaded end of the first threaded joint connected into the four diagonal wells through the second conduit; the unthreaded end of the first nipple which opens into a central well is connected to the inlet of the measuring cylinder by means of a second conduit.
There are two methods for making the chessboard-like simulated mass simulating heterogeneous rock, the first method comprising the steps of:
firstly, limiting the simulated plane size of unit bodies (11) with different permeabilities to be 50 multiplied by 50m, the length of a region to be simulated to be L and the width of the region to be simulated to be D, and calculating the number of units with different permeabilities of each layer to be N according to a formula (1);
secondly, collecting permeability data of all well points of the area to be simulated, establishing a known permeability database, wherein the number of wells is Q, the number of layers is P, the coordinates of each well on an XOY plane are (i, j), and the permeability value of each well on the z-th layer is K z (i，j)；
Thirdly, dispersing the first layer permeability data obtained in the second step to obtain the permeability value of any point on the first layer plane, namely knowing the distribution condition of the permeability on the first layer, and specifically calculating according to the following process:
firstly, according to the permeability value of the mth row of each well on the first layer, the permeability variation function between two wells with the distance h is calculated to be K by using a formula (2) z (h)；
Wherein, the formula (2) is:
in the formula:
n (h) -the logarithm of two wells at a distance h.
Introduction of an intermediate replacement variable x for facilitating the expression of a computational process 1 、x 2 And y and b 0 ，b 1 And b 2 . Based on the result of formula (2), a series of x can be obtained using formula (3), formula (4) and formula (5) 1 、x 2 And y;
wherein, formula (3), formula (4) and formula (5) are respectively:
x 1 ＝h (3)
x 2 ＝-h 3 (4)
y＝K z (h) (5)
then, the obtained x 1 、x 2 Substituting y into equation (6), fitting the data by linear programming method to obtain b 0 ，b 1 ，b 2 ；
Wherein, the formula (6) is:
y＝b 0 +b 1 x 1 +b 2 x 2 (6)
by comparing equation (6) and equation (7), equations (8), (9) and (10) can be obtained as follows:
C 0 ＝b 0 (9)
finally, a variation function equation of the permeability of the mth row on the first layer can be determined, as shown in formula (11), namely, half of the variance of the permeability of any two points on the mth row on the first layer is obtained, so that the permeability value after dispersion on the mth row on the first layer can be obtained, and the distribution condition of the permeability on the mth row on the first layer can be obtained;
wherein, formula (11) is:
in the formula:
a-range with correlation between permeabilities within this range and no correlation between permeability outside the range;
C 0 -a block value reflecting the variation amplitude of the permeability variation function;
C 1 the base station value, which varies greatly over short distances due to a number of factors;
h is the distance between two points;
obtaining a variation function equation of any row of the known partial permeability on the first layer by using the same method, thereby obtaining the permeability value after dispersion on the row, namely obtaining the distribution situation of the permeability on the row; then, based on the permeability value of each row in the transverse direction, solving a variation function equation of any column in the longitudinal direction, so that the permeability value of each point on the first layer can be known, and the permeability distribution condition of the first layer can be obtained;
fourthly, repeating the third step to obtain the permeability value of each point on the second layer, namely obtaining the permeability distribution condition of the second layer, and obtaining the permeability values and the permeability distribution conditions of all the layers until the permeability value of each point on the P layer is obtained;
fifthly, in order to reduce the manufacturing number of permeability units, simplify the manufacturing steps of the simulation body, and divide different permeability intervals for statistical analysis within the allowable range of experimental error; performing statistical analysis on the permeability data of each layer obtained in the third step and the fourth step, and determining the number of the permeability data distributed to different permeability intervals, so that the number of units distributed to different permeability intervals can be determined;
and sixthly, cementing quartz sand with different granularities and epoxy resin to form permeability units distributed in different permeability intervals according to the number of the permeability units distributed in different permeability intervals obtained in the fifth step, arranging N units with different permeability in each layer according to the distribution conditions of the permeability calculated in the third step and the fourth step, and sequentially arranging the P layers to enable the simulated rock to better accord with the actual conditions.
The second method for manufacturing the chessboard-like simulated body for simulating the heterogeneous rock comprises the following steps:
firstly, the simulated plane size of the unit bodies (11) with different permeabilities is limited to be 50 x 50m, the length of the area to be simulated is L, the width of the area to be simulated is D, and the number of the units with different permeabilities in each layer is calculated to be N according to the formula (1).
Secondly, collecting permeability data of all well points of the area to be simulated, establishing a known permeability database, wherein the number of wells is Q, the number of layers is P, the coordinates of each well on an XOY plane are (i, j), and the permeability value of each well on the z-th layer is K z (i，j)。
And thirdly, dispersing the first layer permeability data obtained in the second step to obtain the permeability value of any point on the plane of the first layer, namely knowing the distribution condition of the permeability on the first layer, and specifically calculating according to the following process.
Firstly, according to the permeability value of the mth row of each well on the first layer, the variation function of the permeability between two wells with the distance h is obtained as K by using a formula (2) z (h)。
Wherein, the formula (2) is:
in the formula:
n (h) -the logarithm of two wells at a distance h.
Introduction of an intermediate replacement variable x for facilitating the expression of a computational process 1 、x 2 And y and b 0 ，b 1 And b 2 . Based on the result of formula (2), a series of x can be obtained using formula (3), formula (4) and formula (5) 1 、x 2 And y.
Wherein, formula (3), formula (4) and formula (5) are respectively:
x 1 ＝h (3)
x 2 ＝-h 3 (4)
y＝K z (h) (5)
then, the obtained x 1 、x 2 Substituting y into equation (6), fitting the data by linear programming method to obtain b 0 ，b 1 ，b 2 。
Wherein, the formula (6) is:
y＝b 0 +b 1 x 1 +b 2 x 2 (6)
by comparing equation (6) and equation (7), equations (8), (9) and (10) can be obtained as follows:
C 0 ＝b 0 (9)
finally, a function equation of the permeability variation of the mth row on the first layer can be determined, as shown in formula (11), that is, half of the permeability variance of any two points on the mth row on the first layer is obtained, so that the permeability value after dispersion on the mth row on the first layer can be obtained, that is, the distribution situation of the permeability on the mth row on the first layer can be obtained.
Wherein, formula (11) is:
in the formula:
a-range with correlation between permeabilities within this range and no correlation between permeability outside the range;
C 0 -a block value reflecting the variation amplitude of the permeability variation function;
C 1 the base station value, due to many factors, causes large variations in permeability over short distances;
h-the distance between two points.
By using the same method, the deterioration function equation of any line of the known partial permeability of the first layer is obtained, so that the permeability value after dispersion on the line can be obtained, namely the distribution situation of the permeability on the line can be obtained. Then, based on the permeability value of each row in the transverse direction, the deterioration function equation of any column in the longitudinal direction is obtained, so that the permeability value of each point on the first layer can be known, and the permeability distribution condition of the first layer can be obtained.
And fourthly, repeating the third step to obtain the permeability value of each point on the second layer, namely obtaining the permeability distribution condition of the second layer, and obtaining the permeability values and the permeability distribution conditions of all the layers until the permeability value of each point on the P layer is obtained.
And fifthly, according to the permeability value of each point on all the layers obtained in the third step and the fourth step and the distribution condition of the permeability, cementing quartz sand and epoxy resin with different granularities to form M units with different permeabilities, wherein M is calculated by a formula (12).
Wherein, the formula (12) is:
M＝NP (12)
and then arranging the N units with different permeabilities of each layer according to the permeability distribution obtained by calculation in the third step and the fourth step, and sequentially arranging the P layers to enable the simulated rock to better accord with the actual situation.
The invention has the following beneficial effects: the method is based on the permeability data of all the layers of the well points of the area to be simulated, and based on the basic theory of the geostatistics about the variation function, the known permeability data are dispersed through the variation function according to the known permeability distribution data, so that the permeability data of any point on a plane can be obtained, and compared with a plurality of rock cores which are connected in parallel and only represent the average permeability of a certain research block in the current experiment, the method is more consistent with the heterogeneity of the reservoir, and provides more reliable experimental basis for field development.
Description of the drawings:
FIG. 1 is a schematic diagram of an integrated device for simulating rock heterogeneity using a checkerboard phantom.
FIG. 2 is a schematic view of a tessellated phantom.
FIG. 3 is a transverse cross-sectional view of a tessellated phantom.
FIG. 4 is a longitudinal cross-sectional view of a tessellated phantom.
FIG. 5 is a schematic view of the conduit, first and second threaded fittings, and flow regulator components.
Fig. 6 is a sectional view of the first threaded joint coupled to the flow regulator.
Fig. 7 is a sectional view of the second threaded joint coupled to the flow regulator.
FIG. 8 is a schematic view of an ISCO constant pressure pump.
Fig. 9 is a schematic view of an electronic pressure gauge.
FIG. 10 is a schematic of the five way valve.
FIG. 11 is a diagram of a square area well to be simulated.
In the figure, 1-ISCO constant pressure pump, 2-conduit, 3-electronic pressure gauge, 4-five-way valve, 5-first threaded joint, 6-flow regulator, 7-second threaded joint, 8-pouring heterogeneous chessboard-like simulation body, 9-measuring cylinder, 10-epoxy resin, 11-2 multiplied by 10cm different permeability units and 12-knob.
The specific implementation mode is as follows:
the invention will be further described with reference to the accompanying drawings in which:
as shown in fig. 1 to 10, the device for simulating rock heterogeneity by pouring heterogeneous simulation body comprises an ISCO constant pressure pump 1, a conduit 2, an electronic pressure gauge 3, a five-way valve 4, a first threaded joint 5, a flow regulator 6, a second threaded joint 7 and a measuring cylinder 9, and is characterized in that:
the device also comprises a pouring heterogeneous simulation body 8.
The casting heterogeneous simulation body 8 is composed of a plurality of unit bodies 11 with different permeabilities, wherein the length, the width and the height of each unit body 11 are respectively 2 cm, 2 cm and 10cm, and the plurality of unit bodies 11 with different permeabilities form a square body; the different permeability of the unit body 11 is obtained by discrete simulation of the actual formation permeability value.
And an epoxy resin pouring layer 10 is poured on the outer layer of the poured heterogeneous simulation body 8, and a single five-point method well group is arranged on the poured heterogeneous simulation body 8 through the epoxy resin pouring layer, wherein the single five-point method well group adopts a mode that one well is arranged in the center and four wells are arranged on four opposite corners.
And the two ends of the second threaded joint 7 are simultaneously provided with threads, the lower end of the second threaded joint 7 is connected with a threaded through hole of a single five-point well group on the poured heterogeneous simulation body 8 through screwing, and the upper end of the second threaded joint 7 is connected with a threaded through hole of the flow regulator 6 through screwing.
The first screw joint 5 is provided with threads only at one end, wherein the threaded end of the first screw joint 5 is connected with the threaded through hole of the flow regulator 6 by screwing, and the unthreaded other end is connected with the second conduit.
The flow regulator 6 is provided with two threaded through holes which are respectively connected with the first threaded joint 5 and the second threaded joint 7, and a knob 12 which is used for controlling the injection speed and the extraction speed of a simulated actual injection well and a simulated actual production well.
An electronic pressure gauge 3 is connected between the ISCO constant pressure pump 1 and a liquid flow input port of the five-way valve 4 through a first conduit 2; the four liquid flow output ports of the five-way valve 4 are respectively connected with the non-threaded end of a first threaded joint 5 which is connected into the four diagonal wells through a second conduit; the unthreaded end of the first nipple 5, which is connected to a central well, is connected to the inlet of the measuring cylinder 9 via a second conduit.
A specific embodiment of the first method for making the chessboard-like simulated mass simulating heterogeneous rock is given below: the method comprises the following steps:
firstly, the simulated plane size of the permeability units is limited to 50 x 50m, the length L of the area to be simulated is 1500m, the width D of the area to be simulated is 1470m, and the number N of different permeability units of each layer is 900 according to the formula (1).
Secondly, the number Q of wells in the area to be simulated is 37, the number P of layers is 3, and since each well is a vertical well, the coordinates of each well in each layer plane are the same, the well position of the square area to be simulated is shown in fig. 11, and the plane coordinates corresponding to each well are shown in table 1. Permeability data for each layer of all well sites in the area were collected and a database of known permeabilities was created as shown in table 2.
Table 1 per well plane coordinate statistical table
| Number of well | Plane coordinates | Number of well | Plane coordinates | Number of well | Plane coordinates | Number of well | Plane coordinates |
| W1 | (4,26) | W11 | (14,21) | W21 | (24,16) | W31 | (4,6) |
| W2 | (8,26) | W12 | (18,21) | W22 | (28,16) | W32 | (8,6) |
| W3 | (12,26) | W13 | (22,21) | W23 | (2,11) | W33 | (12,6) |
| W4 | (16,26) | W14 | (26,21) | W24 | (6,11) | W34 | (16,6) |
| W5 | (20,26) | W15 | (30,21) | W25 | (10,11) | W35 | (20,6) |
| W6 | (24,26) | W16 | (4,16) | W26 | (14,11) | W36 | (24,6) |
| W7 | (28,26) | W17 | (8,16) | W27 | (18,11) | W37 | (28,6) |
| W8 | (2,21) | W18 | (12,16) | W28 | (22,11) | ||
| W9 | (6,21) | W19 | (16,16) | W29 | (26,11) | ||
| W10 | (10,21) | W20 | (20,16) | W30 | (30,11) |
TABLE 2 database of known permeabilities
And thirdly, dispersing the first layer permeability data obtained in the second step to obtain the permeability value of any point on the plane of the first layer, namely, knowing the distribution condition of the permeability on the first layer, and calculating the permeability value and the permeability distribution condition of the 26 th row on the first layer according to the following process.
Firstly, according to the permeability value of 26 th row of each well on the first layer, the permeability variation function between two wells with the distance h is obtained as K by using the formula (2) 1 (h) Let the distance between two adjacent permeability cells be 1, and the calculation results thereof are shown in table 3.
Wherein, the formula (2) is:
TABLE 3 variation function calculation results
| Distance (h) | Variation function (K) 1 (h)) | Distance (h) | Variation function (K) 1 (h)) |
| 4 | 372.57 | 16 | 286.92 |
| 8 | 480.79 | 20 | 36.07 |
| 12 | 468.31 | 24 | 397.90 |
Introduction of an intermediate replacement variable x for facilitating the expression of a computational process 1 、x 2 And y and b 0 ，b 1 And b 2 . Based on the calculation results of Table 3, a series of x can be obtained by using formula (3), formula (4) and formula (5) 1 、x 2 And y, the calculation results are shown in table 4.
Wherein, formula (3), formula (4) and formula (5) are respectively:
x 1 ＝h (3)
x 2 ＝-h 3 (4)
y＝K 1 (h) (5)
TABLE 4x 1 、x 2 And the result of y
| x 1 | x 2 | y | x 1 | x 2 | y |
| 4 | -64 | 372.57 | 16 | -4096 | 286.92 |
| 8 | -512 | 480.79 | 20 | -8000 | 36.07 |
| 12 | -1728 | 468.31 | 24 | -13824 | 397.90 |
Then, the obtained x 1 、x 2 Substituting y into equation (6), fitting the data by linear programming method to obtain b 0 ＝204，b 1 ＝44.66，b 2 When the value is 0.16, the fitting formula is finally obtained as follows:
y＝204+44.66x 1 +0.16x 2 (6)
b is to 0 ＝204，b 1 ＝44.66，b 2 Substituting 0.16 into equation (8), equation (9), and equation (10) may yield C 0 ＝204、C 1 287.19 and a 9.65.
Wherein, the formula (8), the formula (9) and the formula (10) are respectively:
C 0 ＝b 0 ＝204 (9)
finally, the equation for the permeability degradation function for line 26 on the first layer can be determined as:
that is, knowing half of the variance of permeability at any two points on the 26 th row on the first layer, the permeability value after dispersion of the 26 th row on the first layer can be obtained, that is, the permeability distribution of the 26 th row on the first layer is obtained, as shown in the 26 th row (from bottom to top) in table 1. The permeability values and permeability distributions of all permeability units on the first layer on lines 6, 11, 16 and 21 were determined in the same manner. Then, based on the permeability values already obtained on the 6 th, 11 th, 16 th, 21 th and 26 th rows, the deterioration function equation of any column is obtained in the longitudinal direction, so that the permeability value and the permeability distribution of each permeability unit on the first layer can be known, as shown in table 5.
TABLE 5 Permeability distribution on first layer plane
| 85 | 81 | 98 | 87 | 62 | 73 | 56 | 85 | 84 | 94 | 82 | 10 8 | 13 1 | 12 8 | 90 | 10 1 | 10 8 | 11 6 | 11 9 | 12 3 | 10 | 90 | 85 | 88 | 75 | 118 | 90 | 71 | 80 | 85 |
| 88 | 76 | 69 | 84 | 80 | 64 | 86 | 55 | 78 | 11 6 | 90 | 11 2 | 10 0 | 13 1 | 11 7 | 10 1 | 91 | 97 | 11 0 | 11 1 | 11 5 | 81 | 85 | 64 | 85 | 85 | 81 | 84 | 50 | 73 |
| 69 | 50 | 71 | 79 | 10 6 | 87 | 92 | 61 | 11 4 | 79 | 10 7 | 74 | 10 8 | 10 2 | 11 1 | 96 | 10 3 | 11 0 | 13 2 | 11 6 | 10 5 | 10 6 | 63 | 10 1 | 45 | 101 | 74 | 94 | 89 | 71 |
| 88 | 71 | 10 3 | 11 0 | 57 | 46 | 42 | 99 | 97 | 76 | 59 | 98 | 10 0 | 11 8 | 11 1 | 97 | 95 | 87 | 12 3 | 88 | 77 | 71 | 58 | 52 | 75 | 61 | 96 | 97 | 82 | 102 |
| 74 | 84 | 78 | 99 | 64 | 86 | 46 | 59 | 63 | 77 | 62 | 65 | 94 | 83 | 83 | 10 7 | 71 | 54 | 83 | 93 | 10 8 | 50 | 94 | 99 | 51 | 107 | 89 | 71 | 71 | 60 |
| 82 | 75 | 58 | 50 | 45 | 60 | 58 | 88 | 53 | 86 | 91 | 60 | 44 | 75 | 75 | 74 | 57 | 65 | 78 | 11 7 | 11 1 | 73 | 59 | 61 | 98 | 89 | 84 | 90 | 54 | 81 |
| 74 | 75 | 65 | 50 | 62 | 25 | 52 | 45 | 49 | 63 | 58 | 62 | 43 | 59 | 53 | 56 | 59 | 65 | 61 | 84 | 10 5 | 69 | 66 | 88 | 68 | 64 | 70 | 70 | 95 | 56 |
| 10 5 | 53 | 68 | 77 | 45 | 52 | 1 | 53 | 59 | 37 | 60 | 42 | 57 | 39 | 44 | 35 | 55 | 54 | 83 | 61 | 63 | 46 | 46 | 49 | 78 | 64 | 71 | 80 | 58 | 42 |
| 97 | 61 | 35 | 10 1 | 64 | 43 | 20 | 49 | 65 | 35 | 45 | 43 | 53 | 46 | 33 | 46 | 51 | 95 | 87 | 79 | 63 | 72 | 51 | 45 | 70 | 68 | 67 | 71 | 41 | 54 |
| 88 | 35 | 80 | 54 | 51 | 46 | 48 | 38 | 43 | 62 | 35 | 59 | 44 | 55 | 69 | 59 | 55 | 67 | 63 | 45 | 53 | 49 | 11 1 | 39 | 33 | 53 | 44 | 54 | 49 | 63 |
| 65 | 49 | 55 | 94 | 42 | 51 | 50 | 64 | 44 | 70 | 44 | 55 | 36 | 56 | 69 | 50 | 87 | 96 | 71 | 76 | 45 | 84 | 52 | 54 | 73 | 68 | 59 | 66 | 68 | 95 |
| 94 | 56 | 46 | 10 4 | 42 | 43 | 68 | 39 | 64 | 32 | 50 | 63 | 64 | 46 | 58 | 50 | 74 | 76 | 89 | 58 | 62 | 48 | 60 | 73 | 29 | 79 | 60 | 52 | 68 | 54 |
| 97 | 80 | 99 | 71 | 39 | 68 | 36 | 61 | 65 | 64 | 46 | 58 | 43 | 88 | 45 | 58 | 79 | 78 | 38 | 96 | 83 | 73 | 60 | 44 | 61 | 65 | 72 | 49 | 44 | 71 |
| 97 | 87 | 48 | 53 | 59 | 54 | 58 | 50 | 74 | 56 | 58 | 70 | 73 | 68 | 73 | 73 | 83 | 10 6 | 10 7 | 84 | 10 4 | 80 | 97 | 58 | 68 | 77 | 82 | 72 | 82 | 72 |
| 93 | 70 | 62 | 54 | 37 | 74 | 49 | 51 | 56 | 67 | 66 | 51 | 76 | 69 | 53 | 77 | 75 | 10 1 | 93 | 77 | 10 3 | 78 | 85 | 85 | 97 | 59 | 83 | 72 | 101 | 54 |
| 63 | 80 | 62 | 65 | 56 | 70 | 34 | 33 | 39 | 70 | 60 | 82 | 10 3 | 63 | 77 | 44 | 87 | 11 4 | 10 6 | 76 | 12 6 | 86 | 96 | 68 | 95 | 72 | 78 | 72 | 90 | 117 |
| 64 | 99 | 80 | 64 | 70 | 83 | 35 | 61 | 45 | 57 | 91 | 11 1 | 48 | 83 | 75 | 90 | 78 | 90 | 78 | 95 | 80 | 75 | 93 | 76 | 63 | 61 | 76 | 79 | 79 | 110 |
| 65 | 65 | 75 | 81 | 78 | 65 | 63 | 54 | 33 | 64 | 64 | 11 0 | 98 | 57 | 71 | 88 | 10 1 | 77 | 71 | 10 6 | 10 5 | 98 | 78 | 86 | 100 | 59 | 81 | 104 | 72 | 66 |
| 70 | 78 | 96 | 64 | 70 | 69 | 68 | 63 | 79 | 10 3 | 11 9 | 75 | 84 | 70 | 69 | 62 | 11 5 | 95 | 89 | 11 4 | 99 | 94 | 66 | 79 | 104 | 93 | 64 | 75 | 72 | 81 |
| 10 0 | 90 | 81 | 84 | 85 | 62 | 73 | 77 | 91 | 10 0 | 95 | 95 | 11 0 | 79 | 83 | 83 | 82 | 12 1 | 83 | 10 1 | 11 4 | 58 | 77 | 91 | 81 | 89 | 10 3 | 99 | 89 | 79 |
| 58 | 77 | 56 | 64 | 11 4 | 56 | 50 | 68 | 99 | 10 6 | 10 2 | 13 0 | 12 0 | 98 | 79 | 98 | 91 | 11 0 | 99 | 12 1 | 11 3 | 11 0 | 89 | 87 | 99 | 76 | 94 | 113 | 106 | 78 |
| 85 | 97 | 81 | 92 | 87 | 70 | 68 | 99 | 10 3 | 97 | 10 4 | 90 | 92 | 11 3 | 10 5 | 86 | 74 | 10 5 | 68 | 12 7 | 13 1 | 10 4 | 11 7 | 56 | 112 | 92 | 10 6 | 102 | 104 | 66 |
| 79 | 76 | 66 | 57 | 91 | 63 | 86 | 11 3 | 81 | 10 4 | 95 | 98 | 94 | 10 1 | 68 | 77 | 84 | 10 5 | 10 4 | 91 | 78 | 10 5 | 78 | 10 1 | 96 | 105 | 12 8 | 94 | 104 | 115 |
| 90 | 10 9 | 97 | 74 | 87 | 10 1 | 10 1 | 84 | 88 | 89 | 82 | 87 | 93 | 83 | 80 | 11 0 | 10 6 | 90 | 10 2 | 87 | 10 8 | 10 5 | 85 | 82 | 118 | 119 | 11 2 | 110 | 102 | 81 |
| 10 8 | 95 | 90 | 80 | 81 | 82 | 83 | 73 | 81 | 72 | 88 | 98 | 11 9 | 10 3 | 11 5 | 13 8 | 11 6 | 16 | 10 9 | 91 | 11 0 | 80 | 79 | 91 | 79 | 115 | 11 8 | 133 | 98 | 93 |
| 12 2 | 76 | 10 5 | 72 | 84 | 81 | 84 | 10 9 | 97 | 83 | 10 9 | 11 7 | 87 | 91 | 91 | 13 9 | 11 4 | 11 4 | 13 3 | 12 2 | 10 9 | 12 2 | 11 0 | 12 5 | 104 | 115 | 11 4 | 118 | 122 | 85 |
| 10 5 | 10 4 | 81 | 95 | 11 2 | 10 4 | 10 0 | 10 5 | 87 | 89 | 90 | 97 | 96 | 11 5 | 13 0 | 13 6 | 10 9 | 14 6 | 11 8 | 10 3 | 10 0 | 12 6 | 12 1 | 10 9 | 102 | 102 | 87 | 118 | 62 | 100 |
| 12 8 | 13 2 | 77 | 10 7 | 10 9 | 12 4 | 11 7 | 11 6 | 81 | 11 0 | 90 | 12 5 | 13 1 | 11 2 | 12 9 | 11 5 | 11 2 | 13 8 | 95 | 11 3 | 66 | 73 | 11 4 | 75 | 109 | 85 | 11 6 | 82 | 79 | 54 |
| 10 3 | 12 2 | 11 7 | 11 3 | 12 2 | 12 1 | 11 3 | 10 1 | 85 | 70 | 80 | 11 3 | 11 7 | 13 7 | 13 4 | 11 6 | 11 4 | 11 6 | 10 8 | 11 8 | 82 | 93 | 99 | 95 | 100 | 112 | 97 | 80 | 81 | 101 |
| 12 3 | 12 3 | 14 9 | 12 1 | 11 4 | 12 8 | 11 4 | 10 0 | 10 9 | 12 1 | 11 7 | 11 6 | 83 | 11 7 | 13 1 | 10 5 | 12 0 | 13 6 | 87 | 10 9 | 10 5 | 11 6 | 92 | 10 6 | 84 | 100 | 11 2 | 98 | 111 | 93 |
And fourthly, repeating the third step to obtain the permeability value of each point on the second layer, namely the permeability distribution condition of the second layer, and sequentially obtaining the permeability value of each point on the third layer, namely the permeability values and the permeability distribution conditions of all the layers, wherein the permeability values and the permeability distribution conditions of each permeability unit on the second layer and the third layer are shown in tables 6 and 7.
TABLE 6 permeability distribution in the plane of the second layer
TABLE 7 Permeability distribution on third layer plane
| 56 | 73 | 54 | 57 | 57 | 60 | 70 | 81 | 65 | 78 | 65 | 63 | 53 | 60 | 60 | 67 | 47 | 61 | 36 | 37 | 37 | 46 | 42 | 43 | 46 | 42 | 50 | 55 | 35 | 28 |
| 74 | 51 | 62 | 51 | 65 | 58 | 71 | 76 | 66 | 66 | 48 | 58 | 59 | 54 | 48 | 61 | 43 | 53 | 56 | 37 | 50 | 43 | 47 | 52 | 38 | 52 | 49 | 38 | 30 | 32 |
| 58 | 72 | 66 | 82 | 68 | 81 | 72 | 69 | 57 | 74 | 54 | 55 | 48 | 45 | 65 | 48 | 60 | 63 | 38 | 42 | 43 | 59 | 60 | 39 | 41 | 53 | 38 | 41 | 36 | 36 |
| 87 | 81 | 75 | 72 | 76 | 65 | 69 | 68 | 60 | 71 | 56 | 62 | 54 | 61 | 57 | 56 | 66 | 44 | 34 | 50 | 48 | 59 | 63 | 47 | 47 | 42 | 48 | 46 | 34 | 40 |
| 73 | 65 | 79 | 79 | 83 | 79 | 72 | 73 | 81 | 50 | 48 | 65 | 67 | 43 | 54 | 70 | 58 | 50 | 34 | 37 | 45 | 35 | 65 | 51 | 62 | 51 | 61 | 62 | 37 | 31 |
| 62 | 74 | 79 | 83 | 81 | 77 | 67 | 70 | 61 | 50 | 71 | 60 | 37 | 57 | 52 | 56 | 47 | 49 | 36 | 32 | 39 | 31 | 44 | 33 | 41 | 45 | 46 | 37 | 47 | 48 |
| 77 | 73 | 85 | 68 | 70 | 67 | 76 | 61 | 63 | 59 | 68 | 45 | 67 | 48 | 53 | 33 | 51 | 40 | 52 | 43 | 43 | 46 | 46 | 48 | 28 | 61 | 46 | 26 | 40 | 35 |
| 80 | 84 | 87 | 80 | 60 | 72 | 64 | 65 | 58 | 53 | 57 | 73 | 73 | 72 | 56 | 49 | 46 | 54 | 32 | 54 | 51 | 52 | 49 | 43 | 32 | 42 | 43 | 25 | 32 | 32 |
| 79 | 64 | 76 | 66 | 61 | 69 | 55 | 53 | 57 | 63 | 80 | 62 | 52 | 59 | 38 | 45 | 33 | 51 | 45 | 44 | 46 | 56 | 44 | 46 | 43 | 52 | 25 | 42 | 34 | 29 |
| 69 | 81 | 77 | 76 | 79 | 77 | 60 | 63 | 59 | 58 | 73 | 68 | 53 | 72 | 53 | 42 | 55 | 47 | 33 | 46 | 56 | 51 | 48 | 51 | 58 | 52 | 34 | 39 | 32 | 32 |
| 67 | 64 | 66 | 61 | 62 | 73 | 56 | 66 | 51 | 59 | 47 | 59 | 62 | 71 | 60 | 51 | 71 | 41 | 51 | 59 | 64 | 40 | 43 | 41 | 37 | 38 | 34 | 48 | 42 | 51 |
| 81 | 67 | 67 | 56 | 61 | 61 | 47 | 54 | 51 | 55 | 75 | 48 | 53 | 67 | 61 | 52 | 52 | 54 | 63 | 31 | 49 | 51 | 31 | 42 | 36 | 47 | 42 | 45 | 55 | 45 |
| 68 | 88 | 60 | 76 | 59 | 58 | 57 | 59 | 61 | 60 | 52 | 52 | 58 | 61 | 60 | 70 | 66 | 48 | 45 | 47 | 50 | 25 | 49 | 46 | 41 | 43 | 60 | 32 | 34 | 50 |
| 72 | 71 | 62 | 55 | 60 | 64 | 59 | 66 | 67 | 41 | 57 | 42 | 46 | 60 | 79 | 64 | 60 | 73 | 53 | 31 | 45 | 28 | 43 | 46 | 53 | 44 | 39 | 40 | 40 | 51 |
| 72 | 70 | 54 | 62 | 56 | 63 | 64 | 59 | 63 | 66 | 65 | 55 | 60 | 45 | 46 | 53 | 68 | 53 | 64 | 45 | 39 | 52 | 44 | 43 | 51 | 39 | 50 | 41 | 42 | 60 |
| 57 | 76 | 81 | 62 | 62 | 69 | 64 | 47 | 67 | 56 | 73 | 62 | 52 | 33 | 51 | 66 | 63 | 68 | 54 | 50 | 37 | 52 | 57 | 42 | 32 | 45 | 42 | 43 | 52 | 51 |
| 63 | 63 | 66 | 49 | 58 | 65 | 64 | 50 | 49 | 48 | 58 | 55 | 57 | 44 | 59 | 57 | 55 | 58 | 43 | 47 | 61 | 53 | 55 | 50 | 48 | 41 | 40 | 51 | 46 | 68 |
| 71 | 55 | 50 | 75 | 64 | 66 | 72 | 60 | 53 | 42 | 42 | 47 | 50 | 62 | 58 | 57 | 60 | 54 | 43 | 63 | 43 | 50 | 60 | 44 | 50 | 58 | 47 | 55 | 46 | 44 |
| 49 | 62 | 59 | 59 | 59 | 58 | 60 | 56 | 53 | 46 | 64 | 53 | 66 | 46 | 41 | 72 | 55 | 60 | 45 | 59 | 61 | 56 | 47 | 42 | 44 | 42 | 48 | 43 | 48 | 44 |
| 68 | 49 | 64 | 79 | 71 | 63 | 56 | 50 | 50 | 49 | 57 | 57 | 53 | 64 | 47 | 52 | 60 | 58 | 77 | 56 | 52 | 58 | 39 | 56 | 34 | 46 | 47 | 50 | 41 | 29 |
| 50 | 42 | 39 | 56 | 57 | 55 | 38 | 55 | 54 | 27 | 58 | 34 | 50 | 42 | 63 | 60 | 58 | 74 | 63 | 53 | 55 | 50 | 49 | 57 | 42 | 74 | 62 | 48 | 39 | 54 |
| 68 | 54 | 43 | 45 | 49 | 49 | 64 | 51 | 58 | 54 | 48 | 55 | 61 | 68 | 67 | 61 | 53 | 53 | 60 | 47 | 41 | 57 | 72 | 61 | 62 | 57 | 39 | 35 | 21 | 45 |
| 48 | 45 | 55 | 36 | 49 | 49 | 54 | 62 | 35 | 58 | 42 | 56 | 44 | 69 | 56 | 53 | 66 | 64 | 56 | 43 | 43 | 55 | 47 | 57 | 53 | 42 | 56 | 32 | 41 | 44 |
| 67 | 56 | 51 | 41 | 46 | 63 | 34 | 37 | 52 | 61 | 53 | 81 | 61 | 74 | 72 | 56 | 58 | 54 | 69 | 54 | 64 | 48 | 51 | 46 | 47 | 38 | 43 | 43 | 29 | 43 |
| 64 | 39 | 64 | 44 | 63 | 69 | 50 | 34 | 40 | 52 | 56 | 63 | 65 | 64 | 65 | 63 | 71 | 41 | 58 | 65 | 51 | 49 | 51 | 38 | 51 | 39 | 41 | 48 | 41 | 45 |
| 63 | 56 | 59 | 56 | 60 | 50 | 52 | 57 | 43 | 56 | 54 | 65 | 57 | 77 | 53 | 66 | 63 | 57 | 65 | 49 | 46 | 65 | 61 | 52 | 48 | 59 | 52 | 55 | 43 | 47 |
| 74 | 56 | 45 | 54 | 64 | 52 | 44 | 49 | 45 | 54 | 56 | 70 | 74 | 77 | 83 | 64 | 73 | 75 | 60 | 59 | 44 | 58 | 47 | 62 | 49 | 50 | 51 | 28 | 45 | 50 |
| 69 | 80 | 78 | 59 | 74 | 67 | 56 | 42 | 58 | 67 | 63 | 61 | 70 | 51 | 68 | 83 | 58 | 75 | 58 | 76 | 54 | 70 | 67 | 57 | 68 | 48 | 41 | 43 | 52 | 64 |
| 70 | 78 | 64 | 76 | 74 | 62 | 48 | 54 | 58 | 77 | 60 | 59 | 72 | 63 | 75 | 60 | 76 | 47 | 68 | 51 | 61 | 46 | 62 | 70 | 62 | 58 | 41 | 49 | 55 | 56 |
| 80 | 67 | 78 | 67 | 61 | 67 | 66 | 41 | 55 | 61 | 68 | 57 | 73 | 58 | 65 | 73 | 67 | 72 | 72 | 59 | 50 | 61 | 42 | 54 | 53 | 28 | 40 | 62 | 50 | 45 |
And fifthly, in order to reduce the manufacturing number of permeability units, simplify the manufacturing steps of the simulation body, and divide different permeability intervals for statistical analysis within the allowable range of experimental errors. And (3) performing statistical analysis on the permeability data of each layer obtained in the third step and the fourth step, and determining the number of the permeability data distributed to different permeability intervals, so that the number of units distributed to different permeability intervals can be determined, and the statistical conditions of the different permeability intervals of each layer are shown in tables 8 to 10.
TABLE 8 statistical table for different permeability intervals of first layer
TABLE 9 statistical table for different permeability intervals of the second layer
TABLE 10 third layer different permeability interval statistical table
And sixthly, filling quartz sand with different particle sizes and numbers according to the number of the permeability units distributed in different permeability intervals obtained in the fifth step in different arrangement modes, and cementing by using different cementing modes, so that the permeability units distributed in different permeability intervals can be prepared.
As can be seen from the statistical results in table 8, the number of permeability units distributed in the permeability interval of 41 to 45mD in the first layer is 31, a simulated body with a size of 12 × 12 × 10cm and permeability distributed between 41 to 45mD is made by selecting quartz sand with a certain particle size and number according to a certain arrangement mode and cementing mode, and then 31 permeability units of 2 × 2 × 10cm are obtained by cutting, that is, the permeability units distributed in the permeability interval of 41 to 45mD are made, and the permeability units of all the permeability intervals of the first layer are made sequentially. And finishing the manufacture of the permeability units of the second layer and the third layer with different permeability intervals according to the statistical results of the tables 9 and 10.
The grid coordinates of the lower left corner of tables 5, 6 and 7 are defined as (1,1) and the grid coordinates of the upper right corner are defined as (30,30) according to the rectangular coordinate system. As can be seen from table 5, the permeability of the grid with coordinates of (1,1) in the first layer is 123mD, which corresponds to the permeability interval of table 8 being 121-125mD, and the permeability units that have been fabricated are selected from the permeability interval and arranged at the original positions of the grid, i.e. the coordinates of the permeability units are (1, 1). The permeability of the grid with coordinates of (1,2) in the first layer is 103mD, which corresponds to the permeability interval of table 8 being 101-105mD, and the prepared permeability units are selected from the permeability interval and arranged at the original positions of the grid, i.e. the coordinates of the permeability units are (1,2), thus completing the arrangement of all permeability units in the first layer in sequence. The arrangement of all permeability units in the second and third layers can be accomplished according to tables 6 and 7, and in combination with tables 9 and 10. Thus, 900 permeability units in each layer are arranged according to the permeability distribution obtained by calculation in the third step and the fourth step, and 3 layers are sequentially arranged, so that the simulated rock is more in line with the actual situation.
And then cementing the outer layer of the formed simulation body by epoxy resin, arranging a single five-point well group on the simulation body, installing a first threaded joint, a flow regulator, a second threaded joint and other devices, and finally forming a device for simulating the rock heterogeneity by using the checkerboard-shaped simulation body.
Claims (2)
1. A method of making a checkerboard simulation in a device for simulating rock heterogeneity, comprising the steps of:
firstly, limiting the simulated plane size of unit bodies (11) with different permeabilities to be 50 multiplied by 50m, the length of a region to be simulated to be L and the width of the region to be simulated to be D, and calculating the number of units with different permeabilities of each layer to be N according to a formula (1);
secondly, collecting permeability data of all well points of the area to be simulated, establishing a known permeability database, wherein the number of wells is Q, the number of layers is P, the coordinates of each well on an XOY plane are (i, j), and the permeability value of each well on the z-th layer is K z (i，j)；
Thirdly, dispersing the first layer permeability data obtained in the second step to obtain the permeability value of any point on the plane of the first layer, namely, knowing the distribution condition of the permeability on the first layer, and specifically calculating according to the following process:
firstly, according to the permeability value of the mth row of each well on the first layer, the permeability variation function between two wells with the distance h is calculated to be K by using a formula (2) z (h)；
Wherein, the formula (2) is:
in the formula:
n (h) -the logarithm of two wells at a distance h;
introduction of an intermediate replacement variable x for facilitating the expression of a computational process 1 、x 2 And y and b 0 ，b 1 And b 2 (ii) a Based on the result of formula (2), a series of x can be obtained by using formula (3), formula (4) and formula (5) 1 、x 2 And y;
wherein, formula (3), formula (4) and formula (5) are respectively:
x 1 ＝h (3)
x 2 ＝-h 3 (4)
y＝K z (h) (5)
then, the obtained x 1 、x 2 Substituting y into equation (6), fitting the data by linear programming method to obtain b 0 ，b 1 ，b 2 ；
Wherein, the formula (6) is:
y＝b 0 +b 1 x 1 +b 2 x 2 (6)
by comparing equation (6) and equation (7), equations (8), (9) and (10) can be obtained as follows:
C 0 ＝b 0 (9)
finally, a variation function equation of the permeability of the mth line on the first layer can be determined, as shown in formula (11), namely, half of the permeability variance of any two points on the mth line of the first layer is obtained, so that the permeability value after the dispersion on the mth line of the first layer can be solved, namely, the distribution condition of the permeability on the mth line of the first layer can be obtained;
wherein, formula (11) is:
in the formula:
a-variation, with a correlation between permeabilities within this range and no correlation between permeability outside the variation;
C 0 -a block value reflecting the variation amplitude of the permeability variation function;
C 1 the base station value, due to many factors, causes large variations in permeability over short distances;
h is the distance between two points;
the same method is used for obtaining a variation function equation of any line of the known partial permeability on the first layer, so that the permeability value after dispersion on the line can be obtained, namely the distribution situation of the permeability on the line can be obtained; then, based on the permeability value of each row in the transverse direction, solving a variation function equation of any column in the longitudinal direction, so that the permeability value of each point on the first layer can be known, and the permeability distribution condition of the first layer can be obtained;
fourthly, repeating the third step to obtain the permeability value of each point on the second layer, namely obtaining the permeability distribution condition of the second layer, and obtaining the permeability value and the permeability distribution condition of all the layers until the permeability value of each point on the P layer is obtained;
fifthly, in order to reduce the manufacturing number of permeability units, simplify the manufacturing steps of the simulation body, and divide different permeability intervals for statistical analysis within the allowable range of experimental error; performing statistical analysis on the permeability data of each layer obtained in the third step and the fourth step, and determining the number of the permeability data distributed to different permeability intervals, so that the number of units distributed to different permeability intervals can be determined;
and sixthly, cementing quartz sand with different granularities and epoxy resin to form permeability units distributed in different permeability intervals according to the number of the permeability units distributed in different permeability intervals obtained in the fifth step, arranging N units with different permeability in each layer according to the distribution conditions of the permeability calculated in the third step and the fourth step, and sequentially arranging the P layers to enable the simulated rock to better accord with the actual conditions.
2. A method of making a checkerboard simulation in a device for simulating rock heterogeneity, comprising the steps of:
firstly, limiting the simulated plane size of unit bodies (11) with different permeabilities to be 50 multiplied by 50m, the length of a region to be simulated to be L and the width of the region to be simulated to be D, and calculating the number of units with different permeabilities of each layer to be N according to a formula (1);
secondly, collecting permeability data of all well points of the area to be simulated, establishing a known permeability database, wherein the number of wells is Q, the number of layers is P, the coordinates of each well on an XOY plane are (i, j), and the permeability value of each well on the z-th layer is K z (i，j)；
Thirdly, dispersing the first layer permeability data obtained in the second step to obtain the permeability value of any point on the plane of the first layer, namely, knowing the distribution condition of the permeability on the first layer, and specifically calculating according to the following process;
firstly, according to the permeability value of the mth row of each well on the first layer, the permeability variation function between two wells with the distance h is calculated to be K by using a formula (2) z (h)；
Wherein, the formula (2) is:
in the formula:
n (h) -the logarithm of two wells at a distance h;
introduction of an intermediate replacement variable x for facilitating the expression of a computational process 1 、x 2 And y and b 0 ，b 1 And b 2 (ii) a Based on the result of formula (2), a series of x can be obtained by using formula (3), formula (4) and formula (5) 1 、x 2 And y;
wherein, formula (3), formula (4) and formula (5) are respectively:
x 1 ＝h (3)
x 2 ＝-h 3 (4)
y＝K z (h) (5)
then, the obtained x 1 、x 2 Substituting y into equation (6), fitting data by linear programming method to obtain b 0 ，b 1 ，b 2 ；
Wherein, the formula (6) is:
y＝b 0 +b 1 x 1 +b 2 x 2 (6)
by comparing the formula (6) and the formula (7), the formula (8), the formula (9), and the formula (10) can be respectively:
C 0 ＝b 0 (9)
finally, a variation function equation of the permeability of the mth line on the first layer can be determined, as shown in formula (11), namely, half of the variance of the permeability of any two points on the mth line on the first layer is obtained, so that the permeability value after dispersion on the mth line on the first layer can be obtained, namely, the distribution condition of the permeability on the mth line on the first layer can be obtained;
wherein, formula (11) is:
in the formula:
a-variation, with a correlation between permeabilities within this range and no correlation between permeability outside the variation;
C 0 -a block value reflecting the variation amplitude of the permeability variation function;
C 1 the base station value, due to many factors, causes large variations in permeability over short distances;
h is the distance between two points;
the same method is used for obtaining a variation function equation of any line of the known partial permeability on the first layer, so that the permeability value after dispersion on the line can be obtained, namely the distribution situation of the permeability on the line can be obtained; then, based on the permeability value of each row in the transverse direction, solving a variation function equation of any column in the longitudinal direction, so that the permeability value of each point on the first layer can be known, and the permeability distribution condition of the first layer can be obtained;
fourthly, repeating the third step to obtain the permeability value of each point on the second layer, namely obtaining the permeability distribution condition of the second layer, and obtaining the permeability value and the permeability distribution condition of all the layers until the permeability value of each point on the P layer is obtained;
fifthly, according to the permeability values of all points on all the layers obtained in the third step and the fourth step and the distribution condition of the permeability, cementing quartz sand and epoxy resin with different granularities to form M units with different permeability, wherein M is obtained by calculation of a formula (12);
wherein, the formula (12) is:
M＝NP (12)
and then arranging the N units with different permeabilities of each layer according to the permeability distribution obtained by calculation in the third step and the fourth step, and sequentially arranging the P layers to enable the simulated rock to better conform to the actual situation.
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