Application method of efficient well flow unit for simulating decompression wellbore in three-dimensional finite element

Abstract

The invention particularly discloses an application method of an efficient well flow unit for simulating a decompression wellbore in a three-dimensional finite element, and relates to the technical field of civil engineering precipitation. The method comprises the steps of firstly determining parameters such as a model calculation boundary, boundary conditions, permeability coefficients of soil layers, the position of a relief well and a water head; secondly, establishing a three-dimensional model to divide a delaunay tetrahedron unit grid, and simplifying a three-dimensional relief well into a one-dimensional well flow unit during modeling; then, on the basis of geometric properties of a tetrahedral mesh around a well flow unit and a unit flow weight coefficient, making a numerical solution equal to an analytical solution flow, and deducing to obtain a well flow unit water guide matrix; and finally, merging the well flow unit water guide matrix into the total stiffness matrix, and solving to obtain the high-precision flow of the decompression wellbore and the node water head of the model unit. According to the method, the calculation efficiency and the calculation precision are greatly improved, the precision is not changed in a large-grid-size model, the calculation time is greatly shortened, and the investment of calculation resources is reduced.

Description

Technical Field

[0001] The present invention relates to the technical field of civil engineering dewatering, and in particular to an application method of an efficient well flow unit for simulating a pressure relief shaft in three-dimensional finite elements. Background Art

[0002] The size of the well differs from the scale of the seepage field by several orders of magnitude. When using an equal-dimensional method for simulation in three-dimensional finite elements, only when the grid size around the well is smaller than its characteristic size can reasonable accuracy be achieved, but the efficiency is too low and excessive computing resources are consumed. Otherwise, large flow errors will occur in the simulation of well flow with a constant head boundary. To improve the computing efficiency, equivalent or dimensionality reduction processing is usually performed on the well flow simulation.

[0003] Currently, in the research on equivalent dimensionality reduction and simplification of well flow simulation, it is mainly divided into the following categories of methods: The first category is the drainage substructure method, which truly reflects the size of the drainage well in the finite element. Through the condensation calculation of the substructure stiffness matrix, the problem of over-dense grids and low efficiency in well flow calculation in the confined aquifer is solved to a certain extent. However, when the well is in the phreatic layer, the overflow surface needs to be determined by iterative calculation. At this time, the substructure matrix needs to be condensed again each time for iteration, and the computing efficiency cannot be improved. The second category is the rod element method, which connects the rod element with the nodes of the well column section. Only the contribution of the permeability matrix of the rod element to the nodes of the well column section needs to be considered, and the flow rate can be directly solved without iteration. The third category is the stacked element method, which is aimed at structures containing drainage holes. Its core concept is to divide such structures into two main grid parts: one is the overall grid covering the entire structure but not including the drainage holes, and the other is the local grid around the area near each drainage hole. The fourth category is the composite element method for simulating drainage holes and discontinuous surfaces, which expands the air element method based on the variational principle. This method implicitly includes the discontinuous surface in the composite element and divides the rock mass element into multiple rock block sub-elements. The fifth category is the dimensionality reduction equivalent method, including the method of replacing the well with a point, which reduces the well to a grid node for processing, and the grid size has little influence on the flow rate calculation result; for the analysis of the seepage flow rate of horizontal wells in dual-porosity media, the uniform sink line method is used to regard the horizontal well as a line source composed of a finite number of point sources. First, the point source model is solved, and then the solution of the line source is obtained by superimposing and integrating along the solution of the point source.

[0004] For the three-dimensional finite element simplified simulation of well flow, the prior art has considered the problem of singular points caused by neglecting the well diameter. The area around the well is equivalently divided into four isosceles right triangles. By comparing the analytical solution and the finite element expression to make the flow rates equal, the head difference between the equivalent radius and the actual well radius is obtained. The actual head distribution can be reflected by correcting the head difference. However, the above research is aimed at 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 on the basis of ensuring the same flow rate. The actual head distribution can be reflected by correcting the head difference. Its advantage is that while ensuring the calculation accuracy, it greatly reduces the number of elements required for modeling. However, the applicable range is for quasi-three-dimensional finite element meshes, that is, three-dimensional columnar finite element meshes formed by stretching two-dimensional plane meshes, and it is not applicable to three-dimensional finite element meshes divided by general linear tetrahedrons. Summary of the Invention

[0005] The object of the present invention is to propose an efficient well flow unit application method for simulating a pressure-relief wellbore in three-dimensional finite elements. By reducing the three-dimensional wellbore to a one-dimensional well flow unit and simultaneously using the well point water level correction method to correct the flow rate, a simplified well flow simulation method is provided, which can effectively and conveniently realize the well flow simulation in three-dimensional finite elements. At the same time, under the condition of not losing the global accuracy, a large grid is used to simulate the well, avoiding iterative calculations and greatly improving the efficiency of using three-dimensional finite elements to simulate well flow.

[0006] To achieve the above object, the present invention proposes an efficient well flow unit application method for simulating a pressure-relief wellbore in three-dimensional finite elements, and the steps are as follows: Step S1: Determine the basic parameters of the model, including the model boundary position and boundary conditions, the control point position and conditions, the arrangement position of the relief wells, and the physical parameters of each soil layer and the relief wells; Step S2: Read the basic parameters of the model into the three-dimensional finite element seepage calculation program for modeling, and perform delaunay tetrahedral element division on the model to obtain the total stiffness matrix; Step S3: Based on the geometric properties of the tetrahedral elements around the well flow unit and the element flow weight coefficient, make the numerical solution and the analytical solution flow rates equal, and deduce the explicit solution of the relationship between the wellbore head correction amount of a single tetrahedral element and the element flow rate; Step S4: Consider all the tetrahedral elements around the well line unit, and according to the element flow weight coefficient and the explicit solution of the relationship, obtain the calculation relationship between the well line unit head correction amount and the flow rate; Step S5: Compose the water conductivity matrix of the well flow unit according to the resistance coefficient; Step S6: Considering the effect of the pipe flow in the wellbore, incorporate the water conductivity matrix of the well flow unit and the pipe flow action matrix into the total stiffness matrix; Step S7: Solve the final matrix to obtain the well discharge with high precision and the water heads at each node of the model.

[0007] 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 , the radius of the relief well .

[0008] Preferably, in step S2, a zero-volume one-dimensional well flow element is used to simulate the three-dimensional wellbore, and the model is divided into Delaunay tetrahedral elements.

[0009] Preferably, in step S3, an explicit solution of the relationship between the wellbore water head correction amount and the element flow rate of a single tetrahedral element is derived, and the formula is as follows: ; ; where is the wellbore water head correction amount, is the flow rate of the element around the well with respect to a single section of the well line, is the element flow rate weight coefficient, is the flow-through area, is the length between two nodes of the well line, , are intermediate variables.

[0010] Preferably, the flow rate is calculated by the following formula: When there is only one point in the element around the well that coincides with the well line, the element flow rate is weighted and distributed to the well line elements and : ; where is the shared element flow rate weight, then , and are the lengths of the well line elements and respectively; is the flow rate of the element around the well flowing towards the well line node .

[0011] When an edge of the tetrahedral element coincides with the well axis: ; where is the flow rate of the element around the well flowing towards the well line node ; , The calculation formula is as follows: When only one node of the unit coincides with the well axis: ; ; Among them, is the equivalent seepage path of the node around the well of the unit, is the equivalent seepage path of the node around the well of the unit, is the equivalent seepage path of the node around the well of the unit; is the element the single stiffness of the th row and th column of the conductivity matrix, When one side of the unit coincides with the well axis: ; ; Among them, is the element the single stiffness of the th row and .

[0012] Preferably, the unit flow weight coefficient is calculated as follows: Assume the water level of the well overflow surface , then: ; ; Among them, is the sum of the uncorrected flows of all the well-perimeter units of the well-line unit , , , are the flows of the well-line unit nodes , the well-line unit node and the well-line unit before correction, , , are the water heads of the well-perimeter unit nodes 1, 2, and 3 respectively, is the element the single stiffness of the th row and .

[0013] Preferably, in step S4, the calculation relationship between the head correction amount and the flow rate of the well line unit is as follows: ; wherein, is the head correction amount of the well line unit, is the number of node points of the unit around the well; is a linear function of, and the formula is as follows: ; wherein, is the resistance coefficient.

[0014] Preferably, in step S5, the calculation formula of the water conductivity matrix of the well flow unit is as follows: For the well flow unit with an additional seepage path introduced at the well source node, the head difference at both ends is adjusted to , and the flow rate expression of the well flow unit at the wellbore line element is: ; wherein, , are the resistance coefficients of the well line unit node respectively, , are the corrected heads of the well line unit node respectively, , are the heads of the well flow unit node , and their values are equal to the head of the well overflow surface; , The calculation formulas of are as follows: ; Converted into matrix form as: ; wherein, is the outflow flow rate from the well line unit node to the well flow unit node , is the outflow flow rate from the well line unit node to the well flow unit node .

[0015] Preferably, in step S6, the water conductivity matrix of the well flow unit and the pipe flow action matrix are incorporated into the total stiffness matrix, and the formula is as follows: ; wherein, is the total stiffness of the th row th column of the total water conductivity stiffness matrix of the model, , …, , , …, ; is the water flow permeability coefficient of the cylindrical conduit, is the model node c 's water head, is the model node c 's flow rate, c = 1, …, , , , , …, ; When the node is the node of the well - perimeter element, then: ; Among them, is the water head of the well - perimeter element node , is the equivalent seepage path of the well - perimeter element node .

[0016] Preferably, when applicable to a three - dimensional finite - element grid size greater than 5 times the well radius, when , there is , the element flow correction matrix is a non - positive definite matrix, resulting in a negative correlation between the flow rate and the head difference, and the calculation shows singularity; among them, is the equivalent radius, is the element size.

[0017] Therefore, the present invention proposes an efficient well - flow element application method for simulating a pressure - reducing wellbore in three - dimensional finite elements, and its beneficial effects are as follows: The present invention adopts a simplified method of using a zero - volume one - dimensional line element to simulate a three - dimensional wellbore, effectively and conveniently realizing well - flow simulation in three - dimensional finite elements. At the same time, under the condition of not losing global accuracy, the well is simulated using large grids, avoiding iterative calculations, and greatly improving the efficiency of simulating well flow using three - dimensional finite elements.

[0018] Next, through the drawings and embodiments, the technical solutions of the present invention will be further described in detail. Description of the Drawings

[0019] Figure 1 is the flow chart of an efficient well - flow element application method for simulating a pressure - reducing wellbore in three - dimensional finite elements according to the present invention; Figure 2 is the schematic diagram of reducing a three - dimensional wellbore to a one - dimensional well - flow element; Figure 3 is the schematic diagram of the types of elements around the well - line element; Figure 4Schematic diagram of the method for determining the flow weight coefficient; Figure 5 Flow error broken line graph of the method for determining the flow weight coefficient at different aquifer thicknesses; Figure 6 Schematic diagram of a one - dimensional well flow unit; Figure 7 Schematic diagram of the four grid size divisions of the model; Figure 8 Schematic diagram of the well point distribution and the position of the result display section; Figure 9 Head distribution curve graph of a single - well example; Figure 10 Flow error comparison graph of a single - well example; Figure 11 Head distribution curve graph of a multi - well example; Figure 12 Flow error comparison graph for the sensitivity analysis of boundaries and well spacing. Detailed implementation manners

[0020] To make the technical solutions, advantages and objectives of the present invention clearer, the technical solutions of the embodiments of the present invention will be described clearly and completely below. The described embodiments are part of the embodiments of the present invention, rather than all of the embodiments. Based on the described embodiments of the present invention, all other embodiments obtained by those of ordinary skill in the art without creative efforts fall within the protection scope of the present invention.

[0021] Unless otherwise defined, the technical terms or scientific terms used in the present invention shall have the ordinary meanings understood by those of ordinary skill in the art to which the present invention pertains.

[0022] As Figure 1 shown, the following is a flowchart of an efficient well flow unit application method for simulating a pressure - reducing wellbore in a three - dimensional finite element of the present invention, and the specific steps are as follows: S1. Determine the basic parameters of the model, including the model boundary position and boundary conditions, the control point position and conditions, the layout position of the pressure - reducing wells, and the physical parameters of each soil layer and the pressure - reducing wells; The physical parameters of the soil layer and the pressure - reducing wells include the thickness, position and permeability coefficient of each soil layer , the radius of the pressure - reducing well .

[0023] S2. As Figure 2 shown, read the basic parameters of the model into the three - dimensional finite element seepage calculation program for modeling, and perform delaunay tetrahedral element division on the model to obtain the total stiffness matrix, as follows: (1); Among them, is the total stiffness of the th row and th column of the total stiffness matrix for the model's water conduction, , …, ; is the water head of the c node of the element around the well, is the flow rate of the c node of the element around the well, c = 1, …, , …, ; is the number of nodes of the element around the well.

[0024] S3. Based on the geometric properties of the tetrahedral elements and the element flow weight coefficients around the well flow unit, equate the numerical solution and the analytical solution of the flow rate, and derive the explicit solution of the relationship between the wellbore water head correction amount and the element flow rate for a single tetrahedral element; Based on the well point water level correction method, the derivation of the explicit solution of the relationship between the wellbore water head correction amount and the element flow rate is as follows: 1) The finite element calculation formula for the flow rate of the tetrahedral element: For the tetrahedral element the general form of the flow rate water conduction matrix is: (2); where is the single stiffness of the th row and th column in the water conduction matrix of the element, is the water head of the o node of the element, is the flow rate of the o node of the element, .

[0025] 1. For example, for the Figure 3 element in , in the case where a part of the tetrahedral elements of the wellbore line source has a point coinciding with the well axis: (3); where is the flow rate of the node of the well line element; is the corrected water head of the node of the well line element, is the water head of the node of the element around the well, is the water head of the node of the element around the well, is the water head of the The water head.

[0026] 2. As Figure 3 the unit in , for some tetrahedral elements of the wellbore line source, there is a case where one edge coincides with the well axis: (4); Among them, is the sum of the fluxes of well line unit nodes and , is the element the single stiffness of the th row and is the modified water head of well line unit node .

[0027] 2) Basic assumptions and formulas for the analytical solution of well flow: 1. Basic assumptions: The permeability is isotropic; the seepage field is a steady seepage.

[0028] 2. The analytical solution of well flow satisfying the above assumptions is: (5); Among them, is the flux, is the permeability coefficient, is the hydraulic gradient, A is the cross-sectional area of flow, is the water head of the unit nodes around the well, is the water head of the well discharge surface; in the axisymmetric flow of the wellbore, , ; is the equivalent seepage path, is the radius of the relief well; as Figure 3 shown, is the projection length from the node to the wellbore line source, is the length between two nodes, that is, the length of.

[0029] 3) Make the numerical solution and the analytical solution fluxes equal: 1. According to the analytical solution formula (5), there is: For the case where only one point of the unit coincides with the well axis: (6); For the case where one edge of the unit coincides with the well axis: (7); 2. Let the flux weight coefficient , after substituting it into Formula (6) and Formula (7), we get: (8); where, is the water head of the node corresponding to the well perimeter element, is the equivalent seepage path of the node corresponding to the well perimeter element, is the water head correction of the node of the well line element ; is the flow rate of the well perimeter element for a single section of the well line.

[0030] When there is only one point coinciding with the well line, , is the flow rate weight of the shared element. As Figure 6 shows, when a tetrahedron element has one point coinciding with the well axis, the element flow rate is weighted and distributed to the well line elements and , then , and are the lengths of the well line elements and respectively; when a tetrahedron element has one edge coinciding with the well axis, .

[0031] 3. Substitute Formulas (6), (7), and (8) into Formulas (4) and (3) to obtain the relationship between the water head difference and the element flow rate : (9); where, , are intermediate variables; , The calculation methods are as follows: For the case where the element has only one point coinciding with the well axis: (10); For the case where the element has one edge coinciding with the well axis: (11); where, is the equivalent seepage path of the node of the well perimeter element, is the equivalent seepage path of the node of the well perimeter element, is the equivalent seepage path of the node of the well perimeter element.

[0032] As Figure 4 shows, the flow rate weight coefficient in the cylindrical surface It is equal to the ratio of the unit flow rate to the total flow rate when only dimensional reduction is performed without correction. According to formulas (3) and (4), for the well-line unit The total flow rate of all units around is: (12); Among them, 、 、 are respectively the flow rates of the well-line unit nodes 、the well-line unit node and the well-line unit before correction, is the shared unit flow weight of the well-line unit node , is the shared unit flow weight of the well-line unit node .

[0033] Taking the A unit in Figure 4 as an example, let the well discharge surface water head be 0. The flow weight coefficient of this unit is the ratio of the flow rate of this unit before correction to the sum of the uncorrected flow rates of all units around the well line , that is: (13); Among them, is the single stiffness of the row and column in the conductivity matrix of the unit , , , are respectively the water heads of the well perimeter unit nodes 1, 2, and 3; for the water heads of the well perimeter units, according to the analytical solution formula (5), we have: (14); Among them, is the water head of the well perimeter unit node, is the equivalent seepage path of the node, is the node.

[0034] Verify the accuracy of the method for determining the weight coefficient value by verifying the flow error through a complete well example. In the calculation, the entire model is a cylinder, using a single soil layer with a permeability coefficient . The well radius ; the outer boundary . The well water head is 0m, located at the center of the cylinder; the outer boundary water head is 1m.

[0035] Such as Figure 5As can be seen from the error compared with the flow analytical solution, the flow error is extremely large under the method of simple dimensionality reduction without correction. When the element size is 10 times the well diameter, there is already a 15% error, and when the element size is 100 times the well diameter, the error is as high as 70%. However, under the conditions of different aquifer thicknesses and different element sizes, the flow calculation accuracy of the method of the present invention performs well, and the error is within 2%.

[0036] S4. Consider all tetrahedral elements around the well line element, and obtain the calculation relationship between the head correction amount and the flow rate of the well line element according to the element flow rate weight coefficient and the explicit solution of the relationship; Formula (9) is the well water level correction amount obtained according to a single element around the well. When considering all the elements around the well line element it can be obtained by superimposing each element and weighting by the proportion of the corresponding flow contribution degree, that is: That is: (15); It can be seen from formula (15) that is a linear function of, and can be expressed as . is the resistance coefficient, which is a constant related to the division of the elements around the well.

[0037] S5. Compose the water conductivity matrix of the well flow element according to the resistance coefficient; As Figure 6 shown, in the finite element program, in order to explain the head loss of the corrected water level dH , it is necessary to introduce a well flow element with an additional seepage path at the well source node. One end of the element is the average head of the well line section ( node), which is the head to be solved, and one end is the well water head ( node), and the head difference between the two ends is adjusted to . Therefore, the flow rate expression of the virtual bypass element at the wellbore line element is: (16); Its matrix expression is: (17); The resistance coefficient is obtained through formula (15) as: (18); Among them, , are the resistance coefficients of the well line element nodes respectively, , are the corrected water heads of the well line element nodes respectively; , are the well flow element nodes respectively The water head, the value of which is equal to the water head of the well overflow surface; is the well line node The outflow discharge of the node of the flow unit towards the well of is the well line node The outflow discharge of the node of the flow unit towards the well of

[0038] S6. Considering the effect of the pipe flow in the wellbore, incorporate the water conductivity matrix of the well flow unit and the pipe flow effect matrix into the global stiffness matrix; As Figure 6 shown, considering the pipe flow effect between the node and nodes of the well flow unit, its matrix form is: (19); Among them, is the seepage coefficient of the water flow in the cylindrical conduit; Incorporate the water conductivity matrix formula (17) of the well flow unit and the pipe flow effect matrix formula (19) into the global stiffness matrix to obtain: (20); When the node is the node of the element around the well, its water head can be derived according to the analytical solution formula (5) , the same as formula (14).

[0039] Solve the matrix formula (20) to obtain the well discharge with high precision and the water heads of each node of the model.

[0040] S7. Solve the final matrix to obtain the well discharge with high precision and the water heads of each node of the model.

[0041] The efficiency and accuracy of the simplified method are analyzed through the single-well, multi-well, boundary, and well-spacing sensitivity analysis examples of a complete well below.

[0042] Example 1 Single-well example: In the calculation, the entire model is a cylinder, with a single soil layer, a permeability coefficient, and an aquifer thickness of 1 m. The well radius; the outer boundary. The well water head is 0 m, located at the center of the cylinder; the outer boundary water head is 1 m. The model grid is divided into 4 grid sizes, and the grid size s is 0.1, 10, 50, and 100 times, as Figure 7 shown.

[0043] Example 2 Multi-well example: In the calculation, the entire model is a cuboid with a length and width of 60 m and a height of 1 m, with a single soil layer, a permeability coefficient, and an aquifer thickness of 1 m. The well radius, the well water head is 0 m, the water head of the left boundary of the model is 1 m, and the water head of the right boundary is 2 m. The well point layout and the cross-section of the water head result are asFigure 8 as shown

[0044] The flow rate calculation results are shown in Table 1.

[0045] Table 1 Comparison of flow rate results and errors for multi-well examples ;

[0046] Example 3 Boundary and well spacing sensitivity analysis: Analyze two influencing factors, namely the well distance from the model boundary and the well spacing. Find the range of convergence of the flow rate error of the simplified method by controlling variables. In the calculation, the entire model is a cuboid, with a single soil layer, a permeability coefficient, an aquifer thickness of 1 m, a well radius, a well head of 0 m, a head of 1 m at the left boundary of the model, and a head of 2 m at the right boundary. The well boundary model takes the ratio of the well distance from the model boundary d to the point source radius r as a variable; the well spacing model takes the ratio of the well spacing distance d to the point source radius r as a variable.

[0047] The calculation results obtained by the method of the present invention for the foregoing examples are as Figures 9 - 12 shown: The head distribution result of Example 1 is as Figure 9 shown; The comparison of the flow rate error of Example 1 is as Figure 10 shown; The head distribution result of Example 2 is as Figure 11 shown; The comparison of the flow rate error of Example 3 is as Figure 12 shown.

[0048] Analysis of the results of each example: 1) For Example 1, the single-well example uses the analytical solution as the reference standard value: As Figure 9 shown, by comparing the head distribution of different mesh divisions of the four methods, under the condition of the same multiple of the well diameter unit size, the head distribution of the simplified method is more accurate than that of the conventional method and the uncorrected method, and the head basically coincides with the analytical solution after the first node. As Figure 10 shown, by comparing and analyzing the relative error between the well flow rate and the analytical solution, the conventional method needs to subdivide the unit size to about 0.1 times the well diameter to reduce the error to less than 3%, indicating that the mesh density of the conventional method has a great influence on the results. The relationship between the unit size of the simplified method and the flow rate calculation error is small, and the overall maximum error does not exceed 5.24%. By comparing the unit sizes of the conventional method and the simplified method when they are closest to the flow rate of the analytical solution, even when the unit size of the simplified method is 100 times the well diameter, the flow rate relative error is still very close to the analytical solution, which is more advantageous than 0.1 times the well diameter of the conventional method.

[0049] 2) Example 2. The mesh division result of the first multi-well example with the conventional non-dimension reduction of 0.1 times the well diameter is used as the reference standard value: As Figure 11 shown, the water head almost coincides with the reference value after the first node, showing the advantages of high calculation efficiency and high accuracy of the simplified method. As shown in Table 1, by longitudinally comparing the flow calculation results of three mesh sizes, it can be seen that the flow calculation results of the conventional method vary greatly, and the error is very large when the mesh size is large, indicating that the conventional method has a high requirement for the mesh density. In contrast, when the simplified method of the present invention is used for the seepage calculation of a complete well, the influence of the mesh division size is small. At the same time, through horizontal comparison, the error of the simplification of the present invention is smaller under the same element size, and still maintains a high accuracy.

[0050] 3) Example 3: As Figure 12 shown, when the distance is greater than five times the well diameter, the error effects caused by the model boundary and well spacing converge to within plus or minus 5% and tend to be stable. Therefore, it should be noted that when using the simplified analysis method for calculation, the error is small when the flow rate is in the applicable range where the distance between the well and the model boundary or the distance between the well and the well is more than five times the well diameter. In actual engineering, the well spacing is usually more than ten times or even a hundred times the well diameter, meeting the assumption of axisymmetric flow near the wellbore. Therefore, by using the simplified analysis method, the flow calculation can meet the actual engineering requirements.

[0051] The present invention is applicable when the three-dimensional finite element mesh size is greater than 5 times the well radius. When it is the case, there is , and the unit flow correction matrix is a non-positive definite matrix, resulting in a negative correlation between the flow rate and the head difference, and the calculation shows singularity. It should be noted that the meshes used in actual engineering are usually much larger than five times the well radius, so it does not affect the application in actual engineering.

[0052] It should be noted that the content not elaborated in detail in the present invention is all prior art and is well known to those skilled in the art.

[0053] Therefore, the present invention provides an efficient well flow unit application method for simulating a pressure-reducing wellbore in three-dimensional finite elements. By adopting the simplified method of using a zero-volume one-dimensional line element to simulate a three-dimensional wellbore, the well flow simulation in three-dimensional finite elements can be effectively and conveniently realized. At the same time, under the condition of not losing the global accuracy, the well is simulated using large meshes, avoiding iterative calculations, and greatly improving the efficiency of simulating well flow using three-dimensional finite elements.

[0054] Finally, it should be noted that the above embodiments are only used to illustrate the technical solutions of the present invention and are not intended to limit them. Although the present invention has been described in detail with reference to the preferred embodiments, those of ordinary skill in the art should understand that they can still modify or equivalently replace the technical solutions of the present invention, and these modifications or equivalent replacements do not cause the modified technical solutions to deviate from the spirit and scope of the technical solutions of the present invention.

Claims

1. An efficient well flow unit application method for simulating a pressure-relief wellbore in three-dimensional finite elements, characterized in that, Reduce the three-dimensional decompression wellbore to a one-dimensional well flow unit, while reducing the number of model units and ensuring that the accuracy of the flow calculation results does not decrease. The specific steps are as follows: Step S1: Determine the basic parameters of the model, including the model boundary position and boundary conditions, the control point position and conditions, the arrangement position of the decompression wells, and the physical parameters of each soil layer and decompression wells; Step S2: Read the basic parameters of the model into a three-dimensional finite element seepage calculation program for modeling, and perform delaunay tetrahedral element division on the model to obtain the total stiffness matrix; Step S3: Based on the geometric properties of the tetrahedral elements around the well flow unit and the element flow weight coefficient, make the numerical solution equal to the analytical solution flow, and derive the explicit solution of the relationship between the wellbore head correction amount of a single tetrahedral element and the element flow; Step S4: Consider all the tetrahedral elements around the well line unit, and according to the element flow weight coefficient and the explicit solution of the relationship, obtain the calculation relationship between the well line unit head correction amount and the flow; Step S5: Compose the water conductivity matrix of the well flow unit according to the resistance coefficient; Step S6: Considering the effect of the pipe flow in the wellbore, incorporate the water conductivity matrix of the well flow unit and the pipe flow effect matrix into the total stiffness matrix; Step S7: Solve the final matrix to obtain the high-precision well flow rate and the water head of each node of the model.

2. The efficient well flow unit application method for simulating a pressure-relief wellbore in three-dimensional finite elements according to claim 1, wherein 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 , the radius of the relief well .

3. The efficient well flow unit application method for simulating a pressure-relief wellbore in 3D finite elements according to claim 1, wherein In step S2, use a zero-volume one-dimensional well flow unit to simulate the three-dimensional wellbore, and perform delaunay tetrahedral element division on the model.

4. The efficient well flow unit application method for simulating a pressure-relief wellbore in a three-dimensional finite element according to claim 2, wherein In step S3, derive the explicit solution of the relationship between the wellbore head correction amount of a single tetrahedral element and the element flow. The formula is as follows: ； ； Among them, is the correction amount of the wellbore water head, is the flow rate of the unit around the well to the single-section well line, is the unit flow rate weight coefficient, is the flow-through area, is the length between two nodes of the well line, and are intermediate variables.

5. The application method of an efficient well flow unit for simulating a pressure-relief wellbore in 3D finite element according to claim 4, characterized in that, Flow rate The calculation formula is as follows: When there is only one point in the wellbore perimeter unit coinciding with the well line, the unit flow rate is weighted by length and distributed to the well line unit and : ； Among them, is the flow weight of the shared unit, then , and are the lengths of the well line units and respectively; is the flow rate of the well perimeter unit flowing towards the well line node ; When a tetrahedral element has an edge coinciding with the well axis: ； Among them, is the flow rate from the wellbore perimeter unit to the well line node ; , The calculation formula is as follows: When only one node of the element coincides with the well axis: ； ； Among them, is the equivalent seepage path of the well perimeter unit node , is the equivalent seepage path of the well perimeter unit node , is the equivalent seepage path of the well perimeter unit node ; is the th row and th column of the single stiffness of the water conductivity matrix of the unit ; When one edge of the element coincides with the well axis: ； ； Among them, is the single stiffness of the row and column in the water conduction matrix.

6. The efficient well flow unit application method for simulating a pressure-relieving wellbore in three-dimensional finite elements according to claim 4, characterized in that, Unit flow weight coefficient The calculation formula is as follows: Assume the water level of the well overflow surface , then: ； ； Among them, is the well line unit is the sum of the uncorrected flows of all the well perimeter units, , , are the node of the well line unit , the node of the well line unit and the flow of the well line unit before correction, , , are the water heads of the well perimeter unit nodes 1, 2, and 3 respectively, is the unit the row column single stiffness in the conductivity matrix, .

7. A method for applying an efficient well flow unit for simulating a pressure-relief wellbore in three-dimensional finite elements according to claim 1, characterized in that, In step S4, the calculation relationship between the well line unit head correction amount and the flow is as follows: ； Among them, is the head correction amount of the well line unit, is the number of nodal points of the unit around the well; is a linear function of, and the formula is as follows: ； Among them, is the drag coefficient.

8. A method for applying an efficient well flow unit for simulating a pressure-relief wellbore in a three-dimensional finite element, characterized in that, In step S5, the calculation formula of the water conductivity matrix of the well flow unit is as follows: The well flow unit introducing an additional seepage path at the well source node, with the head difference at both ends adjusted to , the flow rate expression of the well flow unit at the wellbore line element is as follows: ； Among them, and are the resistance coefficients of the well line unit nodes respectively, and are the corrected water heads of the well line unit nodes respectively, and are the water heads of the well flow unit nodes respectively, and their values are equal to the water head of the well overflow surface; , The calculation formula is as follows: ； Converted into matrix form: ； Among them, is the outflow rate of the well line unit node to the well flow unit node ; is the outflow rate of the well line unit node to the well flow unit node .

9. The efficient well flow unit application method for simulating a pressure-relief wellbore in three-dimensional finite elements according to claim 1, characterized in that, In step S6, incorporate the water conductivity matrix of the well flow unit and the pipe flow effect matrix into the total stiffness matrix. The formula is as follows: ； Among them, is the overall stiffness of the th row and th column of the overall stiffness matrix for model water conduction, , …, , ; is the water flow permeability coefficient of the cylindrical conduit, is the water head of model node c , is the flow rate of model node c , c = 1, …, , , , , …, ; When the node is a node of the wellbore perimeter element, then: ； Among them, is the head of the node of the well perimeter unit , is the equivalent seepage path of the node of the well perimeter unit .

10. A method for applying an efficient well flow unit for simulating a pressure-relief wellbore in three-dimensional finite elements according to claim 2, characterized in that, Applicable when the three-dimensional finite element mesh size is greater than 5 times the well radius. When holds, there is . The element flow correction matrix is non-positive definite, resulting in a negative correlation between the flow rate and the head difference, and singularities occur in the calculation. Among them, is the equivalent radius, and is the element size.

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