CN110671100B - Method for manufacturing chessboard-like simulator in device for simulating rock heterogeneity - Google Patents

Abstract

A device and a manufacturing method for simulating rock heterogeneity using a chessboard-shaped simulation body. The main purpose is to accurately simulate rock plane heterogeneity in the laboratory. It is characterized in that: the device consists of an ISCO constant pressure pump, an electronic pressure gauge, a five-way valve, a conduit, a 2×2×10cm unit of different permeability, a casting heterogeneous simulation body and a graduated cylinder. The manufacture of the device depends on the permeability distribution of the actual rock. First, the permeability data of each layer of all well points in the area to be simulated are collected, and then these permeability data are discretized by the variogram to obtain the permeability of any point on the plane. In this way, the plane heterogeneity of the rock can be fully reflected in the simulation body, making it possible to simulate the plane heterogeneity of the rock in the laboratory, so that it can be more convenient to study the effect of plane heterogeneity on reservoir development. Impact.

Description

A method for manufacturing a chessboard-shaped simulation body in a device for simulating rock heterogeneity

Technical field:

The invention relates to a simulation body device for simulating rock heterogeneity in oil displacement experiments.

technical background:

my country's oilfields are mainly dominated by continental clastic rock reservoirs, with high complexity of geological conditions, strong heterogeneity, and relatively large differences in the properties of crude oil, so the extraction efficiency is relatively low. Therefore, it is necessary to conduct a comprehensive study of heterogeneity. Due to the influence of sedimentation, diagenesis and tectonic action in the formation process of the reservoir, its spatial distribution and various properties within it vary. At present, the research on the heterogeneity of the reservoir is mainly an experimental method. The method simply simulates the heterogeneity of the reservoir by a simple parallel connection of cores of different permeability. Due to the limited experimental conditions, the number of cores connected in parallel should not be too many. At the same time, the permeability value of each core is made by using the average value of the permeability of a certain research block, which is not uniform with the actual reservoir. The quality gap is large, and the reservoir cannot be simulated well, so that the results of the laboratory oil flooding experiment sometimes cannot guide the field development very well.

Invention content:

In order to solve the technical problems mentioned in the technical background, the present invention provides a device for simulating rock heterogeneity by using a chessboard-shaped simulation body. Heterogeneity research is an important part of reservoir description, and the spatial distribution of its parameters is not only random but also structural. The present invention is based on the permeability data of all wells in the research area, starting from the basic theory of geostatistics about the variogram, and according to some known permeability distribution data, the known permeability data are processed by the variogram function. In this way, the permeability value of any point on the plane can be obtained, thus forming a checkerboard simulation model to reflect the plane heterogeneity of the rock. The model is based on the actual permeability distribution, which is discretized by the variogram, and simulated with a 2×2×10cm permeability unit, so that the distribution law of permeability in the rock can be displayed in a checkerboard simulation body. fully reflected in. At the same time, a single five-point method well group is arranged on a checkerboard-shaped simulation body that has a fine description of the rock permeability distribution, so that the simulated rock heterogeneous oil displacement experiment in the laboratory is closer to the actual situation, which can be used for field development. Provide a better experimental basis.

The technical scheme of the present invention is: a device for simulating rock heterogeneity by using a casting heterogeneous simulation body, comprising an ISCO constant pressure pump, a conduit, an electronic pressure gauge, a five-way valve, a first threaded joint, a flow regulator, The second threaded joint and the measuring cylinder are unique in that:

The device also includes a casting heterogeneous simulation body; the casting heterogeneous simulation body is composed of several units with different permeability, each of which is 2 cm, 2 cm and 10 cm in length, width and height. Each unit body with different permeability forms a square body; the different permeability of the unit body is obtained by the numerical simulation of the actual formation permeability after discretization.

An epoxy resin casting layer is cast on the outer layer of the casting heterogeneous simulation body, and a single five-point method well group is arranged on the casting heterogeneous simulation body through the epoxy resin casting layer. The one-five-point well group adopts the pattern of one well in the center and four wells in four diagonal corners.

Both ends of the second threaded joint are provided with threads at the same time, the lower end of the second threaded joint is connected with the threaded through hole of the single five-point method well group on the casting heterogeneous simulation body by screwing, and the upper end of the second threaded joint is connected by screwing. Connect with the threaded through hole of the flow regulator by 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 by screwing, and the unthreaded other end is connected with the second conduit.

The flow regulator has 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 to control the injection speed and production rate of the simulated actual injection well and production well. out speed.

The electronic pressure gauge is connected between the ISCO constant pressure pump and the liquid flow input port of the five-way valve through the first conduit; The unthreaded end of the threaded joint is connected; the unthreaded end of the first threaded joint connected to a central well is connected with the inlet of the measuring cylinder through the second conduit.

There are two methods for making the chessboard simulation body for simulating heterogeneous rocks, the first method includes the following steps:

In the first step, the plane size simulated by the unit body (11) with different permeability is defined as 50×50m, the length of the area to be simulated is L, and the width is D. According to formula (1), calculate the unit with different permeability for each layer The number is N;

The second step is to collect the permeability data of each layer of all wells in the area to be simulated, and establish a known permeability database, in which the number of wells is Q, the number of layers is P, and the coordinates of each well on the XOY plane are (i , j), then the permeability value of each well in the z-th layer is K _z (i, j);

In the third step, by discretizing the permeability data of the first layer obtained in the second step, the permeability value of any point on the plane of the first layer can be obtained, that is, the distribution of the permeability on the first layer can be known. The calculation is performed as follows:

First, according to the permeability value of each well in the mth row on the first layer, the variogram of the permeability between two wells with a distance of h is obtained by using formula (2) as K _z (h);

Among them, formula (2) is:

where:

N(h) - the logarithm of two wells with distance h.

In order to make the expression of the calculation process more convenient, intermediate substitution variables x ₁ , x ₂ and y and b ₀ , b ₁ and b ₂ are introduced. Based on the result of formula (2), a series of x ₁ , x ₂ and y can be obtained by using formula (3), formula (4) and formula (5);

Among them, formula (3), formula (4) and formula (5) are respectively:

x ₁ = h (3)

x ₂ = -h ³ (4)

y=K _z (h) (5)

Then, substitute the obtained x ₁ , x ₂ and y into the belt formula (6), and use the linear programming method to fit the data to obtain b ₀ , b ₁ , b ₂ ;

Among them, formula (6) is:

y=b ₀ +b ₁ x ₁ +b ₂ x ₂ (6)

By comparing formula (6) and formula (7), formula (8), formula (9) and formula (10) can be obtained as:

C ₀ =b ₀ (9)

Finally, the variogram equation of the permeability of the m-th 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 m-th row of the first layer can be obtained. The discrete permeability value on the mth row of the first layer, that is, the distribution of the permeability on the mth row of the first layer can be obtained;

Among them, formula (11) is:

where:

a - variable range, there is a correlation between the permeability within this range, but there is no correlation between the permeability outside the variable range;

C ₀ — nugget value, reflecting the variation range of the permeability variation function;

C ₁ ——The value of the abutment, due to the influence of many factors, the permeability has a large variation in a short distance;

h - the distance between two points;

Using the same method to obtain the variogram equation of any row of the known partial permeability on the first layer, the discrete permeability value of the row can be obtained, that is, the permeability distribution of the row can be obtained; Then, based on the permeability value of each row in the horizontal direction, the variogram equation of any column in the vertical direction is obtained, so that the permeability value of each point on the first layer can be known, and the permeability distribution of the first layer can be obtained. ;

The fourth step, repeating the third step can obtain the permeability value of each point on the second layer, that is, the permeability distribution of the second layer can be obtained, until the permeability value of each point on the P-th layer is obtained, that is, The permeability value and permeability distribution of all layers can be obtained;

The fifth step, in order to reduce the number of permeability units, simplify the manufacturing steps of the simulation body, and at the same time, within the allowable range of experimental errors, divide different permeability intervals for statistical analysis; The obtained permeability data of each layer is statistically analyzed to determine the number of units distributed to different permeability ranges, so that the number of units distributed to different permeability ranges can be determined;

In the sixth step, according to the number of permeability units distributed in different permeability intervals obtained in the fifth step, the permeability units distributed in different permeability intervals are formed by cementing quartz sand and epoxy resin with different particle sizes. The N units with different permeability in the layer are arranged according to the distribution of permeability calculated in the third and fourth steps, and the P layers are arranged in sequence to make the simulated rocks more in line with the actual situation.

The second method of making the chessboard simulation body for simulating heterogeneous rocks includes the following steps:

In the first step, the plane size simulated by the unit body (11) with different permeability is defined as 50×50m, the length of the area to be simulated is L, and the width is D. According to formula (1), calculate the unit with different permeability for each layer The number is N.

The second step is to collect the permeability data of each layer of all wells in the area to be simulated, and establish a known permeability database, in which the number of wells is Q, the number of layers is P, and the coordinates of each well on the XOY plane are (i , j), then the permeability value of each well in the z-th layer is K _z (i, j).

In the third step, by discretizing the permeability data of the first layer obtained in the second step, the permeability value of any point on the plane of the first layer can be obtained, that is, the distribution of the permeability on the first layer can be known. The calculation is performed as follows.

First, according to the permeability values of the m-th row of each well on the first layer, the variogram of the permeability between two wells separated by h is obtained by using formula (2) as K _z (h).

Among them, formula (2) is:

where:

N(h) - the logarithm of two wells with distance h.

In order to make the expression of the calculation process more convenient, intermediate substitution variables x ₁ , x ₂ and y and b ₀ , b ₁ and b ₂ are introduced. Based on the result of formula (2), a series of x ₁ , x ₂ and y can be obtained using formula (3), formula (4) and formula (5).

Among them, 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 and y are substituted into the belt formula (6), and the linear programming method is used to fit the data to obtain b ₀ , b ₁ , and b ₂ .

Among them, formula (6) is:

y=b ₀ +b ₁ x ₁ +b ₂ x ₂ (6)

By comparing formula (6) and formula (7), formula (8), formula (9) and formula (10) can be obtained as:

C ₀ =b ₀ (9)

Finally, the variogram equation of the permeability of the m-th 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 m-th row of the first layer can be obtained. The discrete permeability value on the mth row of the first layer can obtain the permeability distribution on the mth row of the first layer.

Among them, formula (11) is:

where:

a - variable range, there is a correlation between the permeability within this range, but there is no correlation between the permeability outside the variable range;

C ₀ — nugget value, reflecting the variation range of the permeability variation function;

C ₁ ——The value of the abutment, due to the influence of many factors, the permeability has a large variation in a short distance;

h - the distance between two points.

Using the same method to obtain the variogram equation of any line of known partial permeability on the first layer, the discrete permeability value on the line can be obtained, that is, the permeability distribution on the line can be obtained. Then, based on the permeability value of each row in the horizontal direction, the variogram equation of any column in the vertical direction is obtained, so that the permeability value of each point on the first layer can be known, and the permeability distribution of the first layer can be obtained. .

The fourth step, repeating the third step can obtain the permeability value of each point on the second layer, that is, the permeability distribution of the second layer can be obtained, until the permeability value of each point on the P-th layer is obtained, that is, Permeability values and permeability distributions for all layers can be obtained.

In the fifth step, according to the permeability value of each point on all the layers obtained in the third and fourth steps and the distribution of permeability, M units of different permeability are formed by cementing quartz sand and epoxy resin with different particle sizes, where M is calculated by formula (12).

Among them, formula (12) is:

M=NP (12)

Then, the N units with different permeability in each layer are arranged according to the distribution of permeability calculated in the third and fourth steps, and the P layers are arranged in sequence to make the simulated rocks more in line with the actual situation.

The present invention has the following beneficial effects: the present invention is based on the permeability data of each layer of all well points in the area to be simulated, starting from the basic theory of geostatistics about variogram, and according to some known permeability distribution data, These known permeability data are discretized by the variogram, so that the permeability data of any point on the plane can be obtained, which is more in line with the current experiments in parallel with several cores that only represent the average permeability of a certain research block. The heterogeneity of the reservoir provides a more reliable experimental basis for field development.

Description of drawings:

Figure 1 is a schematic diagram of a comprehensive device for simulating rock heterogeneity using a checkerboard-shaped simulation body.

FIG. 2 is a schematic diagram of a checkerboard-shaped simulation body.

FIG. 3 is a transverse cross-sectional view of a checkerboard-shaped simulation body.

FIG. 4 is a longitudinal cross-sectional view of a checkerboard-shaped simulation body.

Figure 5 is a schematic diagram of the conduit, the first and second threaded joints, and the flow regulator parts.

FIG. 6 is a sectional view of the connection between the first threaded joint and the flow regulator.

FIG. 7 is a sectional view of the connection between the second threaded joint and the flow regulator.

Figure 8 is a schematic diagram of an ISCO constant pressure pump.

Figure 9 is a schematic diagram of an electronic pressure gauge.

Figure 10 is a schematic diagram of a five-way valve.

Figure 11 is a well map of the square area to be simulated.

In the picture 1-ISCO constant pressure pump, 2-duct, 3-electronic pressure gauge, 4-five-way valve, 5-first threaded joint, 6-flow regulator, 7-second threaded joint, 8-pouring non-uniform Quality checkerboard simulation body, 9-grading cylinder, 10-epoxy resin, 11-2×2×10cm units of different permeability, 12-knob.

Detailed ways:

The present invention will be further described below in conjunction with the accompanying drawings:

As shown in Figure 1 to Figure 10, this device for simulating rock heterogeneity by using a casting heterogeneous simulation body includes an ISCO constant pressure pump 1, a conduit 2, an electronic pressure gauge 3, a five-way valve 4, a first thread The joint 5, the flow regulator 6, the second threaded joint 7 and the measuring cylinder 9 are unique in that:

The device also includes a casting heterogeneous simulation body 8 .

The casting heterogeneous simulation body 8 is composed of several units 11 with different permeability, each of which is 2 cm, 2 cm, and 10 cm in length, width, and height, and the several units 11 with different permeability form one unit. Square body; the different permeability of the unit body 11 is obtained by discrete simulation of the actual formation permeability value.

An epoxy resin casting layer 10 is cast on the outer layer of the casting heterogeneous simulation body 8, and a single five-point method well group is arranged on the casting heterogeneous simulation body 8 through the epoxy resin casting layer, The single five-point method well group adopts the pattern of one well in the center and four wells in four diagonal corners.

Both ends of the second threaded joint 7 are provided with threads at the same time. The upper end of the joint 7 is connected with the threaded through hole of the flow regulator 6 by screwing.

The first threaded joint 5 is provided with threads only at one end, wherein the threaded end of the first threaded 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 has two threaded through holes and a knob 12. The two threaded through holes are respectively connected with the first threaded joint 5 and the second threaded joint 7. The knob 12 is used to control the simulated actual injection well and production well. injection rate and extraction rate.

The electronic pressure gauge 3 is connected between the ISCO constant pressure pump 1 and the liquid flow input port of the five-way valve 4 through the first conduit 2; the four liquid flow output ports of the five-way valve 4 are connected to four The unthreaded end of the first threaded joint 5 of the diagonal wells is connected; the unthreaded end of the first threaded joint 5 connected to a central well is connected to the inlet of the measuring cylinder 9 through the second conduit.

A specific embodiment of the first method for making the chessboard-shaped simulation body for simulating heterogeneous rocks is given below: including the following steps:

In the first step, the plane size simulated by the permeability unit is 50×50m, the length L of the area to be simulated is 1500m, and the width D is 1470m. According to formula (1), the number N of different permeability units in each layer is calculated as 900.

In the second step, the number of wells Q in the area to be simulated is 37, and the number of layers P is 3. Since each well is a vertical well, the coordinates of each well in each layer plane are the same, and the wells in the square area to be simulated are The positions are shown in Figure 11, and the plane coordinates corresponding to each well are shown in Table 1. Collect the permeability data of each layer of all wells in this area, and establish a database of known permeability, as shown in Table 2.

Table 1 Statistical table of plane coordinates of each well

Hashtag plane coordinates Hashtag plane coordinates Hashtag plane coordinates Hashtag 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 Known permeability database

In the third step, by discretizing the permeability data of the first layer obtained in the second step, the permeability value of any point on the plane of the first layer can be obtained, that is, the distribution of the permeability on the first layer can be known, and the first The permeability value and permeability distribution of the 26th row on the first layer are calculated according to the following process.

First, according to the permeability value of each well on the 26th row of the first layer, the variogram of the permeability between two wells with a distance of h is obtained by using formula (2) as K ₁ (h). The distance between the two permeability units is 1, and the calculation results are shown in Table 3.

Among them, formula (2) is:

Table 3 Variation function calculation results

Distance (h) Variogram (K₁(h)) Distance (h) Variogram (K₁(h)) 4 372.57 16 286.92 8 480.79 20 36.07 12 468.31 twenty four 397.90

In order to make the expression of the calculation process more convenient, intermediate substitution variables x ₁ , x ₂ and y and b ₀ , b ₁ and b ₂ are introduced. Based on the calculation results in Table 3, a series of x ₁ , x ₂ and y can be obtained by using formula (3), formula (4) and formula (5). The calculation results are shown in Table 4.

Among them, formula (3), formula (4) and formula (5) are respectively:

x ₁ = h (3)

x ₂ = -h ³ (4)

y=K ₁ (h) (5)

Table 4 Calculation results of x ₁ , x ₂ and y

x₁ x₂ y x₁ x₂ y 4 -64 372.57 16 -4096 286.92 8 -512 480.79 20 -8000 36.07 12 -1728 468.31 twenty four -13824 397.90

Then, substituting the obtained x ₁ , x ₂ and y into the belt formula (6), and using the linear programming method to fit the data, we can obtain b ₀ =204, b ₁ =44.66, b ₂ =0.16, The final fitting formula is:

y=204+44.66x ₁ +0.16x ₂ (6)

Substituting b ₀ =204, b ₁ =44.66, b ₂ =0.16 into formula (8), formula (9) and formula (10), one can obtain C ₀ =204, C ₁ =287.19 and a=9.65.

Among them, formula (8), formula (9) and formula (10) are respectively:

C ₀ =b ₀ =204 (9)

Finally, it can be determined that the variogram equation of the permeability on the 26th line on the first layer is:

That is, half of the permeability variance of any two points on the 26th line on the first layer is known, so that the discrete permeability value of the 26th line on the first layer can be obtained, that is, the permeability of the 26th line on the first layer can be obtained. The distribution is shown in row 26 of Table 1 (counting from bottom to top). Use the same method to obtain the permeability values and permeability distributions of all permeability cells on the first layer on the 6th row, 11th row, 16th row and 21st row. Then, based on the permeability values that have been obtained on the 6th, 11th, 16th, 21st and 26th lines, the variogram equation of any column is obtained in the longitudinal direction, so that the first layer can be known. The permeability value and permeability distribution of each permeability unit are shown in Table 5.

Table 5 Permeability distribution table on the first layer plane

85 81 98 87 62 73 56 85 84 94 82 108 131 128 90 101 108 116 119 123 10 90 85 88 75 118 90 71 80 85 88 76 69 84 80 64 86 55 78 116 90 112 100 131 117 101 91 97 110 111 115 81 85 64 85 85 81 84 50 73 69 50 71 79 106 87 92 61 114 79 107 74 108 102 111 96 103 110 132 116 105 106 63 101 45 101 74 94 89 71 88 71 103 110 57 46 42 99 97 76 59 98 100 118 111 97 95 87 123 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 83 107 71 54 83 93 108 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 78 117 111 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 84 105 69 66 88 68 64 70 70 95 56 105 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 35 101 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 49 111 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 46 104 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 83 106 107 84 104 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 75 101 93 77 103 78 85 85 97 59 83 72 101 54 63 80 62 65 56 70 34 33 39 70 60 82 103 63 77 44 87 114 106 76 126 86 96 68 95 72 78 72 90 117 64 99 80 64 70 83 35 61 45 57 91 111 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 64 110 98 57 71 88 101 77 71 106 105 98 78 86 100 59 81 104 72 66 70 78 96 64 70 69 68 63 79 103 119 75 84 70 69 62 115 95 89 114 99 94 66 79 104 93 64 75 72 81 100 90 81 84 85 62 73 77 91 100 95 95 110 79 83 83 82 121 83 101 114 58 77 91 81 89 103 99 89 79 58 77 56 64 114 56 50 68 99 106 102 130 120 98 79 98 91 110 99 121 113 110 89 87 99 76 94 113 106 78 85 97 81 92 87 70 68 99 103 97 104 90 92 113 105 86 74 105 68 127 131 104 117 56 112 92 106 102 104 66 79 76 66 57 91 63 86 113 81 104 95 98 94 101 68 77 84 105 104 91 78 105 78 101 96 105 128 94 104 115 90 109 97 74 87 101 101 84 88 89 82 87 93 83 80 110 106 90 102 87 108 105 85 82 118 119 112 110 102 81 108 95 90 80 81 82 83 73 81 72 88 98 119 103 115 138 116 16 109 91 110 80 79 91 79 115 118 133 98 93 122 76 105 72 84 81 84 109 97 83 109 117 87 91 91 139 114 114 133 122 109 122 110 125 104 115 114 118 122 85 105 104 81 95 112 104 100 105 87 89 90 97 96 115 130 136 109 146 118 103 100 126 121 109 102 102 87 118 62 100 128 132 77 107 109 124 117 116 81 110 90 125 131 112 129 115 112 138 95 113 66 73 114 75 109 85 116 82 79 54 103 122 117 113 122 121 113 101 85 70 80 113 117 137 134 116 114 116 108 118 82 93 99 95 100 112 97 80 81 101 123 123 149 121 114 128 114 100 109 121 117 116 83 117 131 105 120 136 87 109 105 116 92 106 84 100 112 98 111 93

The fourth step, repeating the third step, the permeability value of each point on the second layer can be obtained, that is, the permeability distribution of the second layer can be obtained, and the permeability value of each point on the third layer can be obtained in turn, that is, The permeability values and permeability distributions of all layers are obtained. The permeability values and permeability distributions of each permeability unit on the second and third layers are shown in Tables 6 and 7.

Table 6 Permeability distribution table on the second layer plane

Table 7 Permeability distribution on the 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 twenty one 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

In the fifth step, in order to reduce the number of permeability units and simplify the manufacturing steps of the simulation body, at the same time, within the allowable range of experimental errors, different permeability intervals are divided for statistical analysis. Statistical analysis is performed on the permeability data of each layer obtained in the third and fourth steps to determine the number of them distributed to different permeability intervals, so that the number of units distributed to different permeability intervals can be determined, and each layer is different. The statistics of permeability interval are shown in Table 8 to Table 10.

Table 8 Statistical table of different permeability intervals of the first layer

Table 9 Statistical table of different permeability intervals of the second layer

Table 10 Statistical table of different permeability intervals of the third layer

In the sixth step, according to the number of permeability units distributed in different permeability intervals obtained in the fifth step, use quartz sand with different particle sizes and numbers to fill in different arrangements, and use different cementation methods for cementation, so that Permeability cells distributed in different permeability intervals can be prepared.

From the statistical results in Table 8, it can be seen that the number of permeability units distributed in the 41-45mD permeability range in the first layer is 31. Select a certain particle size and number of quartz sand to make permeability according to a certain arrangement and cementation method. The simulation volume with a size of 12×12×10cm distributed between 41-45mD, and then 31 permeability units of 2×2×10cm are obtained by cutting, that is, the permeability units distributed in the 41-45mD permeability range are completed. The production of permeability units in all permeability ranges of the first layer is completed in turn. According to the statistical results in Table 9 and Table 10, the fabrication of permeability units in different permeability intervals of the second layer and the third layer is completed.

According to the Cartesian coordinate system, the grid coordinates of the lower left corner of Table 5, Table 6 and Table 7 are defined as (1,1), and the grid coordinates of the upper right corner are (30,30). It can be seen from Table 5 that the permeability of the grid with coordinates (1, 1) in the first layer is 123mD, which corresponds to the permeability range of Table 8 of 121-125mD. The permeability unit is arranged at the original position of the grid, that is, the coordinate of the permeability unit is (1,1). In the first layer, the permeability of the grid with coordinates (1,2) is 103mD, and the permeability range corresponding to Table 8 is 101-105mD. Select the prepared permeability units from this permeability range and arrange them in the In the original position of the grid, that is, the coordinates of the permeability unit are (1, 2), so that the arrangement of all permeability units in the first layer is completed in turn. According to Tables 6 and 7, and in combination with Tables 9 and 10, the arrangement of all permeability cells in the second and third layers can be completed. In this way, 900 permeability units in each layer are arranged according to the distribution of permeability calculated in the third and fourth steps, and 3 layers are arranged in sequence, so that the simulated rocks are more in line with the actual situation.

The outer layer of the simulation body to be formed is glued with epoxy resin, and a single five-point method well group is arranged on it, and the first threaded joint, flow regulator, second threaded joint and other devices are installed on it, and finally a checkerboard shape is formed. A device for simulating rock heterogeneity.

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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