An efficient well flow unit application method for simulating decompression wellbore in three-dimensional finite element

Abstract

The present invention specifically discloses an efficient well flow unit application method for simulating pressure relief wells in a three-dimensional finite element method, and relates to the technical field of civil engineering dewatering. The method first determines the model calculation boundary and boundary conditions, the permeability coefficient of each soil layer, the location of the pressure relief well, and the water head and other parameters; secondly, a three-dimensional model is established to divide the Delaunay tetrahedral unit grid, and the three-dimensional pressure relief well is simplified into a one-dimensional well flow unit during modeling; then, based on the geometric properties of the tetrahedral grid around the well flow unit and the unit flow weight coefficient, the numerical solution and the analytical solution flow are made equal, and the water conduction matrix of the well flow unit is derived; finally, the water conduction matrix of the well flow unit is incorporated into the total rigid matrix to solve and obtain the high-precision flow of the pressure relief well and the water head of the model unit node. This method greatly improves the calculation efficiency and calculation accuracy, and the accuracy remains unchanged in large grid size models, greatly shortening the calculation time and reducing the investment in computing resources.

Description

Technical Field

[0001] The invention relates to the technical field of civil engineering dewatering, in particular to an efficient well flow unit application method for simulating a decompression wellbore in a three-dimensional finite element. Background Art

[0002] The size of a well differs from the scale of the seepage field by several orders of magnitude. When using the equal-dimensional method for 3D finite element simulation, reasonable accuracy can only be achieved when the mesh size around the well is smaller than its characteristic size. However, this approach is inefficient and consumes excessive computing resources. Otherwise, simulations of well flow within a constant head boundary will result in significant flow rate errors. To improve computational efficiency, well flow simulations are typically performed using equivalent or dimensionality reduction techniques.

[0003] At present, the research on equivalent dimensionality reduction and simplification of well flow simulation is mainly divided into the following categories:

[0004] The first type is the drainage substructure method, which accurately reflects the dimensions of drainage wells in the finite element method. By condensing the substructure stiffness matrix, this method can, to a certain extent, address the problem of overly dense meshes and inefficient well flow calculations in confined aquifers. However, when the wells are located in a phreatic zone, the outflow surface must be determined iteratively. In this case, the substructure matrix must be re-condensed with each iteration, which does not improve computational efficiency. The second type is the rod element method, which connects rod elements to the nodes of the well row section. Only the contribution of the rod element's permeability matrix to the nodes of the well row section is considered, eliminating the need for iterations to directly solve for flow. The third type is the stacked element method, which targets structures with drainage holes. Its core concept is to divide such structures into two main mesh components: a global mesh that covers the entire structure but excludes the drainage holes, and a local mesh surrounding each drainage hole. The fourth type is the composite element method, which models drainage holes and discontinuities. This method extends the air element method based on the variational principle and implicitly incorporates discontinuities into the composite element, dividing the rock mass element into multiple rock block sub-elements. The fifth category is the dimensionality reduction equivalent method, including the point-replacing-well method, which reduces the dimension of the well into a grid node. The grid size has little effect on the flow calculation results. For the analysis of the seepage flow of horizontal wells in dual-porosity media, the uniform convergence line method is used to regard the horizontal well as a line source composed of a finite number of point sources. The point source model is first solved, and then the line source solution is obtained by superimposing and integrating the point source solutions.

[0005] For simplified three-dimensional finite element simulations of well flow, existing techniques consider the problem of singular points caused by ignoring the wellbore diameter. The wellbore is equivalently divided into four isosceles right triangles. By comparing the analytical solution and the finite element expression to equalize the flow rate, the head difference between the equivalent radius and the actual well radius is obtained. By correcting the head difference, the actual head distribution can be reflected. However, the above research targets regular tetrahedral meshes, which brings inconvenience to its application. Currently, the virtual bypass element method is used to simplify and correct the wellbore. By comparing the analytical solution and the finite element expression, the head difference between the equivalent radius and the actual well radius is obtained while ensuring the consistency of the flow rate. By correcting the head difference, the actual head distribution can be reflected. This method has the advantage of ensuring calculation accuracy while greatly reducing the number of elements required for modeling. However, its scope of application is limited to quasi-three-dimensional finite element meshes, that is, three-dimensional cylindrical finite element meshes formed by stretching two-dimensional plane meshes. It is not applicable to three-dimensional finite element meshes divided by general linear tetrahedrons. Summary of the Invention

[0006] The purpose of the present invention is to propose an efficient well flow unit application method for simulating decompression wellbores in three-dimensional finite elements. By reducing the three-dimensional wellbore into a one-dimensional well flow unit and using a well point water level correction method to correct the flow rate, a simplified well flow simulation method is adopted to effectively and conveniently realize well flow simulation in three-dimensional finite elements. At the same time, without losing global accuracy, a large grid is used to simulate the well, avoiding iterative calculations and greatly improving the efficiency of simulating well flow using three-dimensional finite elements.

[0007] To achieve the above objectives, the present invention proposes an efficient well flow unit application method for simulating a decompression wellbore in a three-dimensional finite element method, the steps of which are as follows:

[0008] Step S1, determining basic model parameters, including model boundary positions and boundary conditions, control point positions and conditions, relief well layout positions, and physical parameters of each soil layer and relief well;

[0009] Step S2: read the basic parameters of the model into a three-dimensional finite element seepage calculation program to perform modeling, and perform Delaunay tetrahedron unit division on the model to obtain a total stiffness matrix;

[0010] Step S3: Based on the geometric properties of the tetrahedral units surrounding the well flow unit and the unit flow weight coefficient, the numerical solution and the analytical solution flow are made equal, and an explicit solution for the relationship between the wellbore head correction and the unit flow of a single tetrahedral unit is derived;

[0011] Step S4: Consider all tetrahedral units around the well line unit, and obtain the calculation relationship between the well line unit head correction amount and flow rate based on the unit flow weight coefficient and the relationship explicit solution;

[0012] Step S5, forming a well flow unit water conduction matrix according to the resistance coefficient;

[0013] Step S6: Considering the effect of pipe flow in the wellbore, the well flow unit water conduction matrix and the pipe flow effect matrix are merged into the total rigidity matrix;

[0014] Step S7: Solve the final matrix to obtain high-precision well flow and water head at each node of the model.

[0015] Preferably, in step S1, the physical parameters of the soil layer and the relief well include the thickness, position and permeability coefficient of each soil layer. , Relief Well Radius .

[0016] Preferably, in step S2, a zero-volume one-dimensional well flow unit is used to simulate a three-dimensional wellbore, and the model is divided into Delaunay tetrahedron units.

[0017] Preferably, in step S3, an explicit solution for the relationship between the wellbore hydraulic head correction amount and the unit flow rate of a single tetrahedron unit is derived, and the formula is as follows:

[0018] ;

[0019] ;

[0020] in, is the wellbore head correction, is the flow rate of the well perimeter unit for a single well line, is the unit flow weight coefficient, is the flow area, is the length between two nodes of the well line, 、 is an intermediate variable.

[0021] Preferably, the flow The calculation formula is as follows:

[0022] When the well perimeter unit has only one point When the flow rate coincides with the well line, the unit flow is weighted by length and distributed to the well line unit. and :

[0023] ;

[0024] in, is the shared unit traffic weight, then , and Well line unit and length; The flow direction well line node of the well perimeter unit of traffic.

[0025] When a tetrahedral element has an edge When coincident with the well axis:

[0026] ;

[0027] in, The flow direction well line node of the well perimeter unit Traffic volume;

[0028] 、 The calculation formula is as follows:

[0029] When only one node of the element coincides with the well axis:

[0030] ;

[0031] ;

[0032] in, Well perimeter unit node The equivalent seepage diameter, Well perimeter unit node The equivalent seepage diameter, Well perimeter unit node The equivalent seepage diameter; For unit The first OK The single column, ;

[0033] When one edge of a cell coincides with the well axis:

[0034] ;

[0035] ;

[0036] in, For unit The first OK The single column, .

[0037] Preferably, the unit flow weight coefficient The calculation formula is as follows:

[0038] Assuming the well overflow level ,but:

[0039] ;

[0040] ;

[0041] in, Well line unit The sum of the uncorrected flow rates of all cells around the well, 、 、 Well line unit nodes , well line unit node Well line unit The flow rate before correction, 、 、 are the water heads of nodes 1, 2, and 3 around the well, For unit The first OK The single column, .

[0042] Preferably, in step S4, the calculation relationship between the well line unit head correction amount and the flow rate is as follows:

[0043] ;

[0044] in, is the water head correction value of the well line unit, is the number of unit nodes around the well;

[0045] for The linear function of is as follows:

[0046] ;

[0047] in, is the drag coefficient.

[0048] Preferably, in step S5, the calculation formula of the well flow unit water conductance matrix is ​​as follows:

[0049] The well flow unit with an additional seepage path is introduced at the well source node, and the head difference at both ends is adjusted to , the flow rate expression of the well flow unit at the wellbore line element is:

[0050] ;

[0051] in, 、 Well line unit nodes The drag coefficient, 、 Well line unit nodes The corrected head, 、 Well flow unit nodes Water head, its value is equal to the water head at the overflow surface of the well;

[0052] 、 The calculation formula is as follows:

[0053] ;

[0054] Converted into matrix form:

[0055] ;

[0056] in, Well line unit node Well flow unit node The outflow flow, Well line unit node Well flow unit node outflow traffic.

[0057] Preferably, in step S6, the well flow unit water conduction matrix and the pipe flow interaction matrix are incorporated into the total rigidity matrix, and the formula is as follows:

[0058] ;

[0059] in, is the total stiffness matrix of the model water conduction OK The total strength of the column, ,…, , ,…, ; is the permeability coefficient of water flow in a cylindrical conduit, For model nodes c The water head, For model nodes c of traffic, c =1,…, , , , ,…, ;

[0060] When the node is the node of the well perimeter unit, then:

[0061] ;

[0062] in, Well perimeter unit node The water head, Well perimeter unit node The equivalent seepage diameter.

[0063] Preferably, it is applicable when the 3D finite element grid size is greater than 5 times the well radius. Sometimes, there are , the unit flow correction matrix is ​​a non-positive definite matrix, which leads to a negative correlation between flow and head difference and a singular calculation; among them, is the equivalent radius, is the unit size.

[0064] Therefore, the present invention proposes an efficient well flow unit application method for simulating decompression wellbore in three-dimensional finite element method, which has the following beneficial effects:

[0065] The present invention adopts a simplified method of simulating three-dimensional wellbores using zero-volume one-dimensional line elements, effectively and conveniently realizing well flow simulation in three-dimensional finite elements. At the same time, without losing global accuracy, it uses a large grid to simulate the well, avoiding iterative calculations and greatly improving the efficiency of using three-dimensional finite elements to simulate well flow.

[0066] The technical solution of the present invention is further described in detail below through the accompanying drawings and embodiments. BRIEF DESCRIPTION OF THE DRAWINGS

[0067] Figure 1 This is a flow chart of a method for applying an efficient well flow unit to simulate a decompression wellbore in a three-dimensional finite element system according to the present invention;

[0068] Figure 2 Schematic diagram of reducing the dimensionality of a three-dimensional wellbore into a one-dimensional well flow unit;

[0069] Figure 3 This is a schematic diagram of the unit types around the well line unit;

[0070] Figure 4 This is a schematic diagram of the method for determining the flow weight coefficient;

[0071] Figure 5 The flow error line graph of the flow weight coefficient determination method at different aquifer thicknesses;

[0072] Figure 6 It is a schematic diagram of a one-dimensional well flow unit;

[0073] Figure 7 Schematic diagram of the four mesh size divisions of the model;

[0074] Figure 8 Schematic diagram of the cross-section location for well point distribution and results display;

[0075] Figure 9 This is the hydraulic head distribution curve for a single well example;

[0076] Figure 10 This is a comparison chart of flow rate errors for a single well example;

[0077] Figure 11 This is the hydraulic head distribution curve for the multi-well example;

[0078] Figure 12 Comparison chart of flow rate errors for boundary and well spacing sensitivity analysis. DETAILED DESCRIPTION

[0079] To make the technical solutions, advantages, and objectives of the present invention more clear, the technical solutions of the embodiments of the present invention will be clearly and completely described below. The described embodiments are part of the embodiments of the present invention, not all of them. Based on the described embodiments of the present invention, all other embodiments obtained by ordinary technicians in this field without creative work are within the scope of protection of the present invention.

[0080] Unless otherwise defined, technical or scientific terms used in the present invention shall have the same meaning as commonly understood by one of ordinary skill in the art to which the present invention belongs.

[0081] like Figure 1 FIG. 1 is a flow chart of an efficient well flow unit application method for simulating a decompression wellbore in a three-dimensional finite element system according to the present invention. The specific steps are as follows:

[0082] S1. Determine the basic parameters of the model, including the model boundary location and boundary conditions, control point location and conditions, relief well layout location, and physical parameters of each soil layer and relief well;

[0083] Physical parameters of soil layers and relief wells include thickness, location and permeability of each soil layer , Relief Well Radius .

[0084] S2, such as Figure 2 As shown, the basic parameters of the model are read into the three-dimensional finite element seepage calculation program for modeling, and the model is divided into Delaunay tetrahedron units to obtain the total stiffness matrix as follows:

[0085] (1);

[0086] in, is the total stiffness matrix of the model water conduction OK The total strength of the column, ,…, ,…, ; Well perimeter unit node c The water head, Well perimeter unit node c of traffic, c =1,…, ,…, ; is the number of unit nodes around the well.

[0087] S3. Based on the geometric properties of the tetrahedral units around the well flow unit and the unit flow weight coefficient, the numerical solution and the analytical solution flow are made equal, and the explicit solution of the relationship between the wellbore head correction and the unit flow of a single tetrahedral unit is derived;

[0088] Based on the well point water level correction method, the wellbore head correction value of a tetrahedron unit is and unit flow The derivation of the explicit solution of the relationship is as follows:

[0089] 1) Finite element calculation formula for tetrahedron unit flow:

[0090] For tetrahedral elements The general form of the flow conduction matrix is:

[0091] (2);

[0092] in, For unit The first OK The single column, For unit nodes o The water head, For unit nodes o of traffic, .

[0093] 1. Such as Figure 3 Units in , for some tetrahedral elements of the wellbore line source, there is a point that coincides with the well axis:

[0094] (3);

[0095] in, Well line unit node Traffic volume; Well line unit node The corrected head, Well perimeter unit node The water head, Well perimeter unit node The water head, Well perimeter unit node head of water.

[0096] 2. Such as Figure 3 Units in , for some tetrahedral elements of the wellbore line source, there is a side that coincides with the well axis:

[0097] (4);

[0098] in, Well line unit node and The sum of the traffic, For unit The first OK The single column, , Well line unit node Corrected head.

[0099] 2) Basic assumptions and formulas for well flow analytical solution:

[0100] 1. Basic assumptions: permeability is isotropic; seepage field is constant seepage.

[0101] 2. The analytical solution of the well flow that satisfies the above assumptions is:

[0102] (5);

[0103] in, For traffic, is the permeability coefficient, is the hydraulic gradient, A is the flow area, is the water head of the unit node around the well, is the water head at the well outlet; in the axisymmetric flow of the wellbore, , ; is the equivalent seepage diameter, is the radius of the relief well; Figure 3 As shown, is the projection length from the node to the wellbore line source, is the length between two nodes, that is length.

[0104] 3) Let the numerical solution and analytical solution flow be equal:

[0105] 1. According to the analytical solution formula (5), we have:

[0106] For the case where only one point of the cell coincides with the well axis:

[0107] (6);

[0108] For the case where one edge of the element coincides with the well axis:

[0109] (7);

[0110] 2. Let the traffic weight coefficient , after substituting it into formula (6) and formula (7), we have:

[0111] (8);

[0112] in, is the water head corresponding to the node around the well, is the equivalent seepage path of the corresponding node around the well, Well line unit node The head correction amount; is the flow rate of the well perimeter unit for a single well line.

[0113] When only one point coincides with the well line, , is the shared unit traffic weight, such as Figure 6 As shown in the figure, when a point of the tetrahedron unit coincides with the well axis, the unit flow is weighted by length to the well line unit. and ,but , and Well line unit and Length; when one edge of the tetrahedron unit coincides with the well axis, .

[0114] 3. Substitute formulas (6), (7), and (8) into formulas (4) and (3) to obtain the head difference With unit flow Relationship:

[0115] (9);

[0116] in, 、 is an intermediate variable;

[0117] 、 The calculation is as follows:

[0118] The case where only one point of the cell coincides with the well axis:

[0119] (10);

[0120] When one edge of a cell coincides with the well axis:

[0121] (11);

[0122] in, Well perimeter unit node The equivalent seepage diameter, Well perimeter unit node The equivalent seepage diameter, Well perimeter unit node The equivalent seepage diameter.

[0123] like Figure 4 As shown, the flow weight coefficient in the cylindrical surface =Equal to the ratio of unit flow to total flow when simple dimensionality reduction is not corrected. According to formula (3) and formula (4), the well line unit The total flow of all surrounding units is:

[0124] (12);

[0125] in, 、 、 Well line unit nodes , well line unit node Well line unit The flow rate before correction, Well line unit node Shared unit traffic weight, Well line unit node The shared unit traffic weight.

[0126] by Figure 4 For example, let the overflow head of the well be 0, and the flow weight coefficient of the unit is the flow before correction. and The sum of uncorrected flow rates of all units around the well line The ratio of , that is:

[0127] (13);

[0128] in, For unit The first OK The single column, , 、 、 are the water heads of nodes 1, 2, and 3 around the well, respectively. For the water head of the well-surrounding unit, according to the analytical solution formula (5), we get:

[0129] (14);

[0130] in, is the water head of the node around the well, is the equivalent seepage path of the node, For the node.

[0131] The accuracy of the method for determining the value of the weight coefficient is verified by the flow error through a complete well calculation example. The entire model in the calculation is a cylinder, a single soil layer is used, and the permeability coefficient Well radius ; Outer boundary The well head is 0 m and is located at the center of the cylinder; the outer boundary head is 1 m.

[0132] like Figure 5 As shown in the figure, the error compared with the flow analytical solution shows that the flow error is extremely large under the method of simple dimensionality reduction without correction. When the unit size is 10 times the well diameter, there is a 15% error. When the unit size is 100 times the well diameter, the error is as high as 70%. The method of the present invention has good flow calculation accuracy under the conditions of different aquifer thicknesses and different unit sizes, and its error is within 2%.

[0133] S4. Consider all tetrahedral units around the well line unit, and obtain the calculation relationship between the well line unit head correction and flow rate based on the unit flow weight coefficient and the relationship explicit solution;

[0134] Formula (9) is the correction value of the well water level obtained based on a unit around the well. When all surrounding units It can be obtained by superimposing each unit and weighting it by the corresponding traffic contribution ratio, that is:

[0135] (15);

[0136] It can be seen from formula (15) that yes The linear function of . is the resistance coefficient, which is a constant related to the division of units around the well.

[0137] S5. forming a well flow unit water conduction matrix according to the resistance coefficient;

[0138] like Figure 6 As shown, the finite element program is used to explain the head loss of the corrected water level. dH , it is necessary to introduce an additional seepage path well flow unit at the well source node. One end of the unit is the average water head of the well line section ( Node), is the water head to be determined, one end is the well water head ( Node), the water head difference at both ends is adjusted to Therefore, the flow expression of the virtual bypass unit at the wellbore line element is:

[0139] (16);

[0140] Its matrix expression is:

[0141] (17);

[0142] The drag coefficient is obtained by formula (15):

[0143] (18);

[0144] in, 、 Well line unit nodes The drag coefficient, 、 Well line unit nodes Corrected head; 、 Well flow unit nodes The water head is equal to the water head at the overflow surface of the well; Well line node Well flow unit node The outflow flow, Well line node Well flow unit node outflow traffic.

[0145] S6. Considering the effect of pipe flow in the wellbore, the well flow unit water conduction matrix and the pipe flow effect matrix are merged into the total rigidity matrix;

[0146] like Figure 6 As shown, considering the well flow unit node and There is a pipe flow effect between nodes, and its matrix form is:

[0147] (19);

[0148] in, is the water permeability coefficient of the cylindrical conduit;

[0149] Incorporating the well flow unit water conduction matrix formula (17) and the pipe flow action matrix formula (19) into the total rigidity matrix yields:

[0150] (20);

[0151] When the node When it is a node of the well perimeter unit, its hydraulic head can be derived according to the analytical solution formula (5): , the same as formula (14).

[0152] By solving the matrix formula (20), we can obtain the high-precision well flow rate of the pressure relief well and the water head of each node of the model.

[0153] S7. Solve the final matrix to obtain high-precision well flow and water head at each node of the model.

[0154] The following analysis of the efficiency and accuracy of the simplified method is carried out through the sensitivity analysis of single well, multiple wells, boundaries and well spacing of complete wells.

[0155] Example 1

[0156] Single well example: The entire model is a cylinder, with a single soil layer, a permeability coefficient, and a 1m thick aquifer. The well radius is 0m; the outer boundary is 1m. The well head is 0m and is located at the center of the cylinder; the outer boundary head is 1m. The model grid is divided into four grid sizes, with grid size s being 0.1, 10, 50, and 100 times, respectively. Figure 7 shown.

[0157] Example 2

[0158] Multi-well example: The entire model is a cuboid with a length and width of 60m and a height of 1m. A single soil layer with a permeability coefficient and a 1m thick aquifer is used. The well radius and well head are 0m, the left boundary head is 1m, and the right boundary head is 2m. The well point arrangement and the head result are shown in the cross section as follows: Figure 8 shown.

[0159] The flow calculation results are shown in Table 1.

[0160] Table 1 Flow rate results and error comparison of multiple well examples

[0161] ;

[0162] Example 3

[0163] Boundary and well spacing sensitivity analysis: The two influencing factors of well distance model boundary and well spacing were analyzed. The range of flow error convergence of the simplified method was found by controlling variables. The entire model was a rectangular parallelepiped, with a single soil layer, permeability coefficient, aquifer thickness of 1m, well radius, well head of 0m, model left boundary head of 1m, and right boundary head of 2m. The well boundary model is based on the well distance model boundary. d With point source radius r The ratio is used as a variable; the well spacing model is based on the well spacing distance d With point source radius r Ratio as a variable.

[0164] The calculation results obtained by the method of the present invention in the above example are as follows Figures 9-12 As shown:

[0165] The water head distribution results of Example 1 are as follows Figure 9 As shown;

[0166] The flow error comparison of Example 1 is as follows: Figure 10 As shown;

[0167] The water head distribution results of Example 2 are as follows: Figure 11 As shown;

[0168] The flow error comparison of Example 3 is as follows: Figure 12 shown.

[0169] Analysis of the results of each case:

[0170] 1) Example 1: Single well example uses the analytical solution as the reference standard value: Figure 9 As shown in the figure, by comparing the hydraulic head distribution of the four methods with different grid divisions, under the condition of the same multiple of the well diameter unit size, the hydraulic head distribution of the simplified method is more accurate than that of the conventional method and the uncorrected method, and the hydraulic head is basically consistent with the analytical solution after the first node. Figure 10 As shown in the figure, by comparing the relative error between the well flow rate and the analytical solution, the conventional method requires subdividing the cell size to approximately 0.1 times the well diameter to reduce the error to less than 3%, indicating that the conventional method's mesh density has a significant impact on the results. However, the simplified method's cell size has little effect on the flow rate calculation error, with the overall maximum error not exceeding 5.24%. Comparing the cell sizes that most closely approximate the analytical solution flow rate for the conventional and simplified methods, the simplified method maintains a very close relative error to the analytical solution even at a cell size of 100 times the well diameter, significantly outperforming the conventional method's 0.1 times the well diameter.

[0171] 2) Example 2, Multi-well Example 1 Conventional 0.1 times well diameter grid division results without dimensionality reduction are reference standard values: Figure 11 As shown, the water head after the first node almost coincides with the reference value, showing the advantages of the simplified method in terms of high efficiency and high precision. As shown in Table 1, by comparing the flow calculation results of the three grid sizes vertically, it can be seen that the flow calculation results of the conventional method have a huge gap. When the grid size is large, the error is very large. It can be seen that the conventional method has high requirements for grid density. The difference is that when the simplified method of the present invention is used for complete well seepage calculation, the size of the grid division has little effect. At the same time, through horizontal comparison, the error of the simplified method of the present invention is small under the same unit size, and still maintains a high precision.

[0172] 3) Example 3: Figure 12 As shown, when the distance is greater than five times the well diameter, the error due to the model boundary and well spacing converges to within ±5% and stabilizes. Therefore, it is important to note that when using the simplified analysis method for flow rate calculations, the error is minimal when the distance between the well and the model boundary, or the distance between wells, is greater than five times the well diameter. In actual projects, the distance between wells is often greater than ten or even a hundred times the well diameter, satisfying the assumption of axisymmetric flow near the wellbore. Therefore, using the simplified analysis method, flow rate calculations can meet actual project requirements.

[0173] The present invention is applicable when the three-dimensional finite element grid size is greater than 5 times the well radius. Sometimes, there are , the unit flow correction matrix is ​​non-positive definite, resulting in a negative correlation between flow and head difference, and singular calculations. It should be noted that the grid used in actual projects is usually much larger than five times the well radius, so this does not affect the application in actual projects.

[0174] It is worth noting that the contents not elaborated in detail in the present invention are all prior art and are well known to those skilled in the art.

[0175] Therefore, the present invention provides an efficient well flow unit application method for simulating decompression wellbores in three-dimensional finite elements. By adopting a simplified method of simulating three-dimensional wellbores using zero-volume one-dimensional line elements, the well flow simulation in three-dimensional finite elements is effectively and conveniently realized. At the same time, without losing global accuracy, the well is simulated using a large grid, avoiding iterative calculations, and greatly improving the efficiency of simulating well flow using three-dimensional finite elements.

[0176] Finally, it should be noted that the above embodiments are only used to illustrate the technical solutions of the present invention rather than to limit the same. Although the present invention has been described in detail with reference to the preferred embodiments, those skilled in the art should understand that they can still modify or replace the technical solutions of the present invention with equivalents, and these modifications or equivalent replacements cannot cause the modified technical solutions to deviate from the spirit and scope of the technical solutions of the present invention.

Claims

1. A high-efficiency well flow unit application method for simulating a decompression wellbore in a three-dimensional finite element method, characterized in that: The three-dimensional decompression wellbore is reduced to a one-dimensional well flow unit to reduce the number of model units while ensuring the accuracy of the flow calculation results. The specific steps are as follows: Step S1, determining basic model parameters, including model boundary positions and boundary conditions, control point positions and conditions, relief well layout positions, and physical parameters of each soil layer and relief well; Physical parameters of soil layers and relief wells include thickness, location and permeability of each soil layer , Relief Well Radius ; Step S2: read the basic parameters of the model into a three-dimensional finite element seepage calculation program to perform modeling, and perform Delaunay tetrahedron unit division on the model to obtain a total stiffness matrix; Step S3: Based on the geometric properties of the tetrahedral units surrounding the well flow unit and the unit flow weight coefficient, the numerical solution and the analytical solution flow are made equal, and an explicit solution for the relationship between the wellbore head correction and the unit flow of a single tetrahedral unit is derived; The explicit solution of the relationship between the wellbore head correction and unit flow rate of a single tetrahedron unit is derived as follows: ； ； in, is the wellbore head correction, is the flow rate of the well perimeter unit for a single well line, is the unit flow weight coefficient, is the flow area, is the length between two nodes of the well line, 、 is an intermediate variable; Step S4: Consider all tetrahedral units around the well line unit, and obtain the calculation relationship between the well line unit head correction amount and flow rate based on the unit flow weight coefficient and the relationship explicit solution; The calculation relationship between the well line unit head correction and flow rate is as follows: ； in, is the water head correction value of the well line unit, is the number of unit nodes around the well, Well line unit The sum of the uncorrected flow rates of all cells around the well, The flow direction well line node of the well perimeter unit Traffic volume; for The linear function of is as follows: ； in, is the drag coefficient; Step S5, forming a well flow unit water conduction matrix according to the resistance coefficient; Step S6: Considering the effect of pipe flow in the wellbore, the well flow unit water conduction matrix and the pipe flow effect matrix are merged into the total rigidity matrix; Step S7: Solve the final matrix to obtain high-precision well flow and water head at each node of the model.

2. The method for applying an efficient well flow unit for simulating a decompression wellbore in a three-dimensional finite element according to claim 1, characterized in that: In step S2, a zero-volume one-dimensional well flow unit is used to simulate a three-dimensional wellbore, and the model is divided into Delaunay tetrahedron units.

3. The method for applying an efficient well flow unit for simulating a decompression wellbore in a three-dimensional finite element according to claim 1, characterized in that: flow The calculation formula is as follows: When the well perimeter unit has only one point When the flow rate coincides with the well line, the unit flow is weighted by length and distributed to the well line unit. and : ； in, is the shared unit traffic weight, then , and Well line unit and length; The flow direction well line node of the well perimeter unit Traffic volume; When a tetrahedral element has an edge When coincident with the well axis: ； in, The flow direction well line node of the well perimeter unit Traffic volume; 、 The calculation formula is as follows: When only one node of the element coincides with the well axis: ； ； in, Well perimeter unit node The equivalent seepage diameter, Well perimeter unit node The equivalent seepage diameter, Well perimeter unit node The equivalent seepage diameter; For unit The first OK The single column, ; When a cell has an edge that coincides with the well axis: ； in, For unit The first OK The single column, .

4. The method for applying an efficient well flow unit for simulating a decompression wellbore in a three-dimensional finite element according to claim 1, characterized in that: Unit flow weight coefficient The calculation formula is as follows: Assuming the well overflow level ,but: ； ； in, Well line unit The sum of the uncorrected flow rates of all cells around the well, 、 、 Well line unit nodes , well line unit node Well line unit The flow rate before correction, 、 、 are the water heads of nodes 1, 2, and 3 around the well, For unit The first OK The single column, , is the shared unit traffic weight, Well perimeter unit node The equivalent seepage diameter.

5. The method for applying an efficient well flow unit for simulating a decompression wellbore in a three-dimensional finite element according to claim 1, characterized in that: In step S5, the calculation formula of the well flow unit water conductance matrix is ​​as follows: The well flow unit with an additional seepage path is introduced at the well source node, and the head difference at both ends is adjusted to , the flow rate expression of the well flow unit at the wellbore line element is: ； in, 、 Well line unit nodes The drag coefficient, 、 Well line unit nodes The corrected head, 、 Well flow unit nodes 、 Water head, its value is equal to the water head at the overflow surface of the well; 、 The calculation formula is as follows: ； Converted into matrix form: ； in, 、 Well line unit nodes , well line unit node The flow rate before correction, Well line unit node Well flow unit node The outflow flow, Well line unit node Well flow unit node The outflow flow, is the number of unit nodes around the well.

6. The method for applying an efficient well flow unit for simulating a decompression wellbore in a three-dimensional finite element according to claim 1, characterized in that: In step S6, the well flow unit water conduction matrix and the pipe flow action matrix are incorporated into the total rigidity matrix, and the formula is as follows: ； in, is the total stiffness matrix of the model water conduction OK The total strength of the column, ,…, , ,…, ; is the permeability coefficient of water flow in a cylindrical conduit, For model nodes The water head, For model nodes of traffic, ,…, , , , ,…, , 、 Well line unit nodes The drag coefficient; When the node is the node of the well perimeter unit, then: ； in, Well perimeter unit node The water head, Well perimeter unit node The equivalent seepage diameter.

7. The method for applying an efficient well flow unit for simulating a decompression wellbore in a three-dimensional finite element according to claim 1, characterized in that: Applicable when the 3D finite element mesh size is greater than 5 times the well radius. Sometimes, there are , the unit flow correction matrix is ​​a non-positive definite matrix, which leads to a negative correlation between flow and head difference and a singular calculation; among them, is the equivalent radius, is the unit size.

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