WO2016192077A1 - Method for establishing and solving numerical well-testing model of horizontal well for tight gas hydraulic fracturing - Google Patents

Method for establishing and solving numerical well-testing model of horizontal well for tight gas hydraulic fracturing Download PDF

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WO2016192077A1
WO2016192077A1 PCT/CN2015/080767 CN2015080767W WO2016192077A1 WO 2016192077 A1 WO2016192077 A1 WO 2016192077A1 CN 2015080767 W CN2015080767 W CN 2015080767W WO 2016192077 A1 WO2016192077 A1 WO 2016192077A1
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wellbore
pressure
dimensionless
crack
curve
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PCT/CN2015/080767
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French (fr)
Chinese (zh)
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欧阳伟平
张冕
袁冬蕊
李杉杉
杨燕
孙贺东
池小明
高红平
刘欢
徐俊芳
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中国石油集团川庆钻探工程有限公司长庆井下技术作业公司
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Priority to PCT/CN2015/080767 priority Critical patent/WO2016192077A1/en
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    • G—PHYSICS
    • G06—COMPUTING; CALCULATING OR COUNTING
    • G06F—ELECTRIC DIGITAL DATA PROCESSING
    • G06F30/00—Computer-aided design [CAD]
    • G06F30/20—Design optimisation, verification or simulation
    • G06F30/23—Design optimisation, verification or simulation using finite element methods [FEM] or finite difference methods [FDM]

Definitions

  • the invention relates to a method for establishing a numerical well test model for a tight gas pressure crack horizontal well, and belongs to the field of oil and gas well test in the petroleum industry.
  • tight gas is rich in resources and has great development potential.
  • Tight gas reservoirs have the characteristics of low permeability, low pressure, low abundance, etc.
  • the natural productivity of gas wells is low, and it is necessary to have industrial exploitation value after the reservoir reform measures.
  • Hydraulic fracturing technology and horizontal well technology are effective ways to increase the productivity of tight gas reservoirs.
  • the exploitation of tight gas reservoirs generally uses multi-stage fracturing horizontal well technology.
  • Well test interpretation of tight gas fracturing horizontal wells is an important means to obtain post-press fracture parameters and reservoir parameters, and is also an effective method for direct verification of seepage mechanism. Due to the seepage mechanism and well-type complexity of multi-stage fracturing horizontal wells in tight gas reservoirs, there is no well test interpretation model for fractured horizontal wells in tight gas reservoirs in China, mainly using the multi-section provided by conventional commercial software Saphir and EPS software. The fractured horizontal well analytical model is used for interpretation analysis, which seriously affects the correct interpretation of the well test data of the tight gas fracture horizontal well.
  • the currently used well test interpretation model does not consider nonlinear seepage mechanisms such as stress sensitivity and starting pressure gradient of tight gas reservoirs.
  • Conventional well testing models based on the Darcy linear seepage mechanism are not suitable for tight gas reservoirs. If the conventional fracturing horizontal well test model is used to interpret and analyze the well test data of the tight gas fracturing horizontal well, it will bring difficulties to the fitting interpretation, and the results obtained by the fitting may also be very large. error.
  • the conventional well test analytical model assumes that the reservoir is a homogeneous medium and cannot consider the heterogeneity of the reservoir.
  • the actual reservoir has obvious heterogeneity, and the reservoir heterogeneity is bound to be It has an important influence on the tight gas seepage and the bottomhole pressure response. Therefore, the reservoir heterogeneity is not considered at present, which will also have an impact on the well test curve fitting and interpretation results.
  • the pressure measured by the pressure gauge is usually regarded as the pressure of the horizontal wellbore section, which will inevitably cause errors in the well test interpretation.
  • the best way to solve this problem is to build a fractured horizontal well test model that considers the wellbore multiphase flow and the actual wellbore trajectory.
  • the object of the present invention is to provide a method for solving a numerical well test model of a compact gas pressure crack horizontal well with a fast calculation speed, a good curve fitting and an accurate interpretation result.
  • the technical solution adopted by the present invention is: a method for establishing a numerical well test model for a dense gas pressure crack horizontal well, comprising the following steps:
  • Step 1 Formation of two-dimensional geological bodies and three-dimensional geological bodies in horizontal wells in tight gas reservoirs;
  • Step 2 Perform grid separation on the generated two-dimensional geological body and three-dimensional geological body of the horizontal well in the tight gas reservoir;
  • Step 3 Calculation of seepage model without pressure difference in the wellbore
  • Step 4 Establish a coupling model, and solve the established coupling model, and generate a well test theoretical curve by the obtained solution;
  • Step 5 The theoretical curve obtained in step 4 is fitted to the measured curve to obtain the parameters of the well test interpretation.
  • the two-dimensional geological body and the three-dimensional geological body of the horizontal well in the tight gas reservoir are generated, and the specific steps are as follows:
  • the geometrical Boolean operation is used to generate the three-dimensional geological body.
  • the internal and external boundary genus in the 2D geological body and the 3D geological body are respectively formed into a 2D mesh file and a 3D mesh file according to the requirements of the Netgen mesh file format, and then the mesh discrete step is performed according to the mesh discrete step set by Netgen. .
  • the mixed finite element method is used to solve the transformed formation and fracture seepage equations.
  • the finite element equations of the stratum and fracture system are decomposed into the finite element equation of the formation region (the first term on the right side of Equation 9) and the finite element representing the fracture system. Equation (the second term on the right side of Equation 9).
  • the finite element equations (10) ⁇ (15) are combined to form the system stiffness matrix.
  • the parallelized SuperLU numerical solver is used to solve the large linear equations, and the pressure field distribution and the inner boundary normal pressure gradient of the whole reservoir can be obtained. Then calculate the production flow of each crack:
  • the coupling model is established in the fourth step, and the established coupling model is solved according to the following steps:
  • the multi-phase flow calculation formula of the wellbore is used to calculate, and the dimensionless differential pressure MP iD of each point of the wellbore is obtained.
  • the specific formula is as follows:
  • the liquid holdup rate H L and the frictional resistance coefficient ⁇ are calculated by the Beggs-Brill method.
  • the wellbore pressure gradient is obtained according to formula (17), and then the pressure difference between each point and the bottom hole standard point is obtained according to the relative distance of the inner boundary of the wellbore:
  • the dimensionless differential pressure MP iD at each point can be obtained.
  • step B The pressure difference MP iD of the inner boundary obtained in step A is brought into the seepage model to calculate the wellbore pressure p' WD and the crack flow Q' fi .
  • the coupling conditions of the wellbore multiphase flow model and the seepage model are as follows :
  • step D the p' WD determined in step C and the corresponding Q' fi are recorded. If the time step k ⁇ total time step n, then the calculation of the next time step is continued, according to the current wellbore pressure p WD , the crack flow rate Q fi , starting from step A, a new round of p' WD and Q' fi is calculated;
  • the fifth step is mainly to compare and compare the theoretical curve and the measured curve in the double logarithmic curve, the semi-logarithmic curve and the full historical pressure curve. According to the fitting degree of the curve, the fitting parameters can be adjusted, and finally The theoretical curve and the measured curve can be well matched in the double logarithmic curve, the semi-logarithmic curve and the full historical pressure curve, and the curve fitting is completed; after the curve fitting is completed, the well test can be obtained. Interpreted parameters, including crack parameters and reservoir parameters.
  • the invention adopts the above technical solutions and has the following advantages, and has the advantages of fast calculation speed, good curve fitting and accurate interpretation result.
  • Figure 1 Three-dimensional geological body and grid dispersion of fractured horizontal wells considering well trajectory and reservoir heterogeneity
  • Figure 2 is a flow chart for the establishment and solution of the coupled model.
  • a method for solving a numerical well test model of a dense gas-fractured horizontal well includes the following steps:
  • Step 1 Formation of two-dimensional geological bodies and three-dimensional geological bodies in horizontal wells in tight gas reservoirs;
  • the geometrical Boolean operation is used to generate the three-dimensional geological body.
  • Step 2 As shown in Figure 1, the generated tight gas reservoir fracturing horizontal well two-dimensional geological body and three-dimensional geological body grid discrete; first, the Netgen open source software package is successfully compiled to build the operating environment;
  • the internal and external boundary genus in the 2D geological body and the 3D geological body are respectively formed into a 2D mesh file and a 3D mesh file according to the requirements of the Netgen mesh file format, and then the mesh discrete step is performed according to the mesh discrete step set by Netgen. .
  • Step 3 Calculation of seepage model without horizontal pressure difference in horizontal wellbore
  • the mixed finite element method is used to solve the transformed formation and fracture seepage equations.
  • the finite element equations of the stratum and fracture system are decomposed into the finite element equation of the formation region (the first term on the right side of Equation 9) and the finite element representing the fracture system. Equation (the second term on the right side of Equation 9).
  • the finite element equations (10) ⁇ (15) are combined to form the system stiffness matrix.
  • the parallelized SuperLU numerical solver is used to solve the large linear equations, and the pressure field distribution and the inner boundary normal pressure gradient of the whole reservoir can be obtained. Then calculate the production flow of each crack:
  • Step 4 Establish a coupling model, solve the established coupling model, and generate the test well theory curve by solving the obtained solution; and solve the established coupling model according to the following steps:
  • the multi-phase flow calculation formula of the wellbore is used to calculate, and the dimensionless differential pressure MP iD of each point of the wellbore is obtained.
  • the specific formula is as follows:
  • the liquid holdup rate H L and the frictional resistance coefficient ⁇ are calculated by the Beggs-Brill method.
  • the wellbore pressure gradient is obtained according to formula (17), and then the pressure difference between each point and the bottom hole standard point is obtained according to the relative distance of the inner boundary of the wellbore:
  • the dimensionless differential pressure MP iD at each point can be obtained.
  • step B The pressure difference MP iD at the inner boundary obtained in step A is brought into the seepage model to calculate the wellbore pressure p' WD and the crack flow Q' fi .
  • the coupling conditions of the wellbore multiphase flow model and the seepage model are as follows :
  • step D the p' WD determined in step C and the corresponding Q' fi are recorded. If the time step k ⁇ total time step n, then the calculation of the next time step is continued, according to the current wellbore pressure p WD , the crack flow rate Q fi , starting from step A, a new round of p' WD and Q' fi is calculated;
  • Step 5 Fitting the theoretical curve obtained in step 4 with the measured curve to obtain the parameters of the well test interpretation;
  • the fifth step is mainly to compare and compare the theoretical curve and the measured curve in the double logarithmic curve, the semi-logarithmic curve and the full historical pressure curve. According to the fitting degree of the curve, the fitting parameters can be adjusted, and finally The theoretical curve and the measured curve can be well matched in the double logarithmic curve, the semi-logarithmic curve and the full historical pressure curve, and the curve fitting is completed; after the curve fitting is completed, the well test can be obtained. Interpreted parameters, including crack parameters and reservoir parameters.
  • a two-dimensional geological body is built, and then a two-dimensional geological body is converted into a three-dimensional geological body.
  • the outer boundary of the geological body where the fracturing horizontal well is located the inner boundary of the wellbore, the crack and the composite zone are realized, and then the inner and outer boundaries and the crack properties are determined.
  • the specific size and shape of the geological body can quickly establish a two-dimensional geological body. From the two-dimensional geological body, combined with the well trajectory and the position of the upper and lower boundaries of the reservoir, the geometric Boolean operation can be used to directly generate the three-dimensional geological body, and the OpenCasCade tool is used to display the three-dimensional view, as shown in Figure 1.
  • the Netgen open source software package is successfully compiled, the running environment is set up, and then the internal and external boundary attributes in the 2D geological body are formed into a 2D mesh file according to the requirements of the Netgen grid file format, and then the mesh discrete steps set by Netgen are performed.
  • Grid discrete The discrete process of a 3D geological body is similar to the discrete process of a 2D geological body. The difference is that the 3D mesh discretization first needs to output the 3D geological body into a common format (such as STEP format), and then use Netgen to network the output format file.
  • Discrete The discrete time of the two-dimensional geological body is relatively short, and the time required is generally between 10s and 30s.
  • the discrete time of the three-dimensional geological body is long, and it needs to be determined according to the density of the discrete mesh. Usually, the discrete time is less than 5 minutes. Discrete grid nodes and grid lines are automatically displayed after the grid is discrete, as shown in Figure 1.
  • a well test interpretation model considering multi-factor coupling is established.
  • the parameters involved in the model are divided into known parameters and unknown parameters (parameters to be interpreted).
  • the known parameters and unknown parameters should be set different input interfaces to avoid confusion.
  • the known parameters are entered according to the actual situation, and the unknown parameters can be determined after the curve fitting is completed.
  • the numerical solution algorithm of the design model is designed, and the computer code of the model numerical solution is compiled, as shown in the model solution flow chart shown in FIG. 2 .
  • the basic data is input, the geological body model is established, and the geological body model is meshed.
  • the initial step is to calculate the seepage model according to the method of no pressure difference in the wellbore, and calculate the initial bottomhole flow pressure and the distribution of each crack flow.
  • the wellbore multiphase flow calculation model is used to calculate the differential pressure distribution of the wellbore, and then the differential pressure is used.
  • the seepage model is calculated to obtain a new bottom hole pressure and crack flow distribution, and compared with the previous calculation results to determine whether the iteration of the time step is over. If the difference between the two is less than the small amount ⁇ , the next time step is calculated, otherwise the iteration is continued until the next time is stabilized. The calculation of the step. Using this method, the calculation of all the set time steps is finally completed, that is, the solution of the coupled model is completed.
  • the well test theory curve is automatically generated, and the theoretical curve and the measured curve are compared and fitted in a double logarithmic curve, a semi-logarithmic curve and a full historical pressure curve.
  • the double logarithmic graph is in the main view, while the semi-log graph and the full historical pressure graph are in the auxiliary view region, and the fitting parameters can be adjusted according to the degree of fitting of the curve.
  • the theoretical curve and the measured curve can be well matched in the double logarithmic curve, the semi-logarithmic curve and the full historical pressure curve, and the curve fitting is completed. After the curve fitting is completed, the test can be obtained.
  • Well explained parameters including crack parameters and reservoir parameters.
  • a two-dimensional geological body is built, and then a two-dimensional geological body is converted into a three-dimensional geological body.
  • the heterogeneous characteristics of the reservoir including porosity, gas saturation and initial permeability distribution, are divided into different regions in the geological body, each region representing a homogeneous body, each The homogeneous bodies have different porosity, water saturation and initial permeability, and the heterogeneity of the entire geological system is composed of many different homogeneous bodies.
  • the two-dimensional geological body combined with the well trajectory and the position of the upper and lower boundaries of the reservoir, can directly generate three-dimensional geological bodies;
  • Better display of 3D geological bodies based on OpenCasCade tools for 3D view display, including 3D geological bodies, grid discrete maps, and computational cloud maps.
  • the generated geological body is converted into a STEP format file, an IGES format file or a BREP format file, and then the Netgen open source tool is used to realize the automatic mesh discrete function of the two-dimensional geological body and the three-dimensional geological body, and the two-dimensional mesh is a triangular mesh, three-dimensional The mesh is a tetrahedral mesh.
  • the grid around the wellbore and the crack is automatically encrypted by setting the number of cracks and discrete nodes of the wellbore, and the discrete quality of the grid is controlled by setting the discrete parameters of the grid.
  • the denser the mesh the more the mesh volume, the longer the mesh discrete time, the longer the calculation time, and the smaller the mesh size will affect the calculation accuracy. Therefore, the actual mesh density should be selected.
  • the amount of two-dimensional grid is between 10,000 and 30,000, and the amount of three-dimensional grid is between 100,000 and 500,000.
  • the tight gas fracturing horizontal well is divided into three flow areas: the wellbore, the fracture and the formation.
  • the flow mechanism is different in different regions.
  • the wellbore is a gas-liquid two-phase flow
  • the fracture is a high-speed non-Darcy flow
  • the formation is a stress-sensitive nonlinear seepage.
  • the fracture zone is regarded as the high-permeability high-speed non-Darcy flow zone. Since the crack width is small, the fluid flow in the fracture zone is regarded as two-dimensional flow, and a fracturing horizontal well is established.
  • Two-dimensional model is mainly used for completion of horizontal wellbore in casing form, and three-dimensional model is used for horizontal wellbore completion in open hole; in the basis of the seepage model Considering the gas-liquid two-phase flow in the wellbore, the Beggs-Brill method is used to establish the flow resistance calculation method of the gas-liquid two-phase flow in the wellbore.
  • the seepage model and the wellbore multiphase flow model are coupled according to the continuous pressure of the formation and the wellbore contact surface.
  • the model is numerically solved by the hybrid finite element method, and the seepage model and the wellbore gas-liquid two-phase flow calculation model are coupled and iteratively calculated.
  • the calculation time node is set to logarithmic distribution, and 10 to 20 calculation points are set in each logarithmic period.
  • the calculated start time and end time can be adjusted according to actual conditions.
  • the condition for the end of each time step is that the calculation results satisfy both the seepage model and the wellbore multiphase flow calculation model.
  • the SuperLU solver The linear equations of the two-dimensional model are solved, and the linear equations of the three-dimensional model are solved by the parallelized SuperLU solver.
  • the number of threads used for parallel computing is determined according to the calculated grid amount. Under normal circumstances, the number of parallel threads is set. 6 to 10 can meet the computing needs.
  • the well test theory curve is automatically generated, and the theoretical curve and the measured curve are compared and fitted in a double logarithmic curve, a semi-logarithmic curve and a full historical pressure curve.
  • the double logarithmic graph is in the main view, while the semi-log graph and the full historical pressure graph are in the auxiliary view region, and the fitting parameters can be adjusted according to the degree of fitting of the curve.
  • the theoretical curve and the measured curve can be well matched in the double logarithmic curve, the semi-logarithmic curve and the full historical pressure curve, and the curve fitting is completed. After the curve fitting is completed, the test can be obtained.
  • Well explained parameters including crack parameters and reservoir parameters.

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Abstract

A method for establishing and solving a numerical well testing model of a horizontal well for tight gas hydraulic fracturing. The method comprises the following steps: (1) generating two-dimensional and three-dimensional geological body models of a horizontal well for tight gas reservoir hydraulic fracturing; (2) performing grid discretization on the generated two-dimensional and three-dimensional geological body models of the horizontal well for tight gas reservoir hydraulic fracturing; (3) computing a percolation model of a horizontal wellbore having no pressure difference; (4) establishing a coupling model, solving the established coupling model, and generating a well testing theoretical curve from the acquired solution; and (5) fitting the theoretical curve acquired in the step (4) and a measured curve to acquire well testing interpretation parameters. The present invention has the advantages of fast computation, good curve fitting, and accurate interpretation results.

Description

一种致密气压裂水平井数值试井模型建立求解方法A method for solving numerical well test model of dense gas pressure cracking horizontal well 技术领域Technical field
本发明涉及一种致密气压裂水平井数值试井模型建立求解的方法，属于石油工业油气井试井领域。The invention relates to a method for establishing a numerical well test model for a tight gas pressure crack horizontal well, and belongs to the field of oil and gas well test in the petroleum industry.
背景技术Background technique
致密气作为三大非常规天然气之一，资源量丰富，开发潜力大。致密气藏具有低渗、低压、低丰度等特点，气井自然生产能力低，需要经过储层改造措施后才具有工业开采价值。水力压裂技术和水平井技术是提高致密气藏产能的有效方法。目前致密气藏的开采普遍采用多段压裂水平井技术。As one of the three unconventional natural gas, tight gas is rich in resources and has great development potential. Tight gas reservoirs have the characteristics of low permeability, low pressure, low abundance, etc. The natural productivity of gas wells is low, and it is necessary to have industrial exploitation value after the reservoir reform measures. Hydraulic fracturing technology and horizontal well technology are effective ways to increase the productivity of tight gas reservoirs. At present, the exploitation of tight gas reservoirs generally uses multi-stage fracturing horizontal well technology.
致密气藏压裂水平井试井解释是获取压后裂缝参数和储层参数的重要手段，也是对渗流机理进行直接验证的有效方法。由于致密气藏多段压裂水平井渗流机理和井型的复杂性，目前国内还没有专门针对致密气藏压裂水平井的试井解释模型，主要采用常规商业软件Saphir和EPS软件所提供的多段压裂水平井解析模型来进行解释分析，这严重影响到致密气压裂水平井试井资料的正确解释。Well test interpretation of tight gas fracturing horizontal wells is an important means to obtain post-press fracture parameters and reservoir parameters, and is also an effective method for direct verification of seepage mechanism. Due to the seepage mechanism and well-type complexity of multi-stage fracturing horizontal wells in tight gas reservoirs, there is no well test interpretation model for fractured horizontal wells in tight gas reservoirs in China, mainly using the multi-section provided by conventional commercial software Saphir and EPS software. The fractured horizontal well analytical model is used for interpretation analysis, which seriously affects the correct interpretation of the well test data of the tight gas fracture horizontal well.
目前致密气压裂水平井试井解释主要存在的问题：At present, the main problems in the well test interpretation of tight gas-fractured horizontal wells are:
1)储层渗流机理方面，目前采用的试井解释模型没有考虑致密气藏的应力敏感、启动压力梯度等非线性渗流机理。基于达西线性渗流机理的常规试井模型不适用于致密气藏。倘若直接采用常规压裂水平井试井模型对致密气藏压裂水平井试井资料进行解释分析，将会给试井解释的拟合带来困难，拟合得到的结果也可能会存在很大误差。1) In terms of reservoir seepage mechanism, the currently used well test interpretation model does not consider nonlinear seepage mechanisms such as stress sensitivity and starting pressure gradient of tight gas reservoirs. Conventional well testing models based on the Darcy linear seepage mechanism are not suitable for tight gas reservoirs. If the conventional fracturing horizontal well test model is used to interpret and analyze the well test data of the tight gas fracturing horizontal well, it will bring difficulties to the fitting interpretation, and the results obtained by the fitting may also be very large. error.
2)储层非均质方面，常规试井解析模型假设储层为均匀介质，无法考虑储层的非均质性，然而实际储层具有明显的非均质性，储层非均质势必会对致密气渗流及井底压力响应产生重要影响，因此目前没考虑储层非均质性也会对试井曲线拟合及解释结果带来一定影响。2) In terms of reservoir heterogeneity, the conventional well test analytical model assumes that the reservoir is a homogeneous medium and cannot consider the heterogeneity of the reservoir. However, the actual reservoir has obvious heterogeneity, and the reservoir heterogeneity is bound to be It has an important influence on the tight gas seepage and the bottomhole pressure response. Therefore, the reservoir heterogeneity is not considered at present, which will also have an impact on the well test curve fitting and interpretation results.
3)裂缝分布方面，常规压裂水平井试井解析模型目前无法处理裂缝非 等间距的情况，而实际情况的压裂的位置几乎都是不等间距的，这也给实际应用带了不小的误差。3) In terms of crack distribution, the conventional fracturing horizontal well test analysis model is currently unable to deal with crack non- In the case of equal spacing, the actual position of the fracturing is almost unequal spacing, which also brings a lot of error to the practical application.
4)井筒多相流及井眼轨迹方面，目前在试井解释模型中几乎都没有考虑到井筒多相流和井眼轨迹的影响。致密气的开采通常伴随着水的产出，造成井筒内为气液两相流，气液两相流会加大井筒内流体的流动阻力，引起井筒内较大的压差，从而影响到试井解释结果。此外，目前水平井试井测试中压力计通常下入在造斜点以上10～20m的位置，距离水平井段有500m以上的距离。而在试井解释中，通常将压力计所测得的压力当作水平井筒段的压力，这势必会引起试井解释的误差。解决这一问题的最好方法就是建立考虑井筒多相流以及真实的井眼轨迹的压裂水平井试井模型。4) In terms of wellbore multiphase flow and wellbore trajectory, the influence of wellbore multiphase flow and wellbore trajectory is not considered in the well test interpretation model. The exploitation of tight gas is usually accompanied by the production of water, resulting in a gas-liquid two-phase flow in the wellbore. The gas-liquid two-phase flow will increase the flow resistance of the fluid in the wellbore, causing a large pressure difference in the wellbore, thus affecting the test. Well explained the result. In addition, in the current horizontal well test, the pressure gauge is usually placed at a position 10 to 20 m above the slanting point, and a distance of 500 m or more from the horizontal section. In the well test interpretation, the pressure measured by the pressure gauge is usually regarded as the pressure of the horizontal wellbore section, which will inevitably cause errors in the well test interpretation. The best way to solve this problem is to build a fractured horizontal well test model that considers the wellbore multiphase flow and the actual wellbore trajectory.
发明内容Summary of the invention
为了克服上述现有技术的缺点，本发明的目的在于提供一种计算速度快、曲线拟合好、解释结果准确的致密气压裂水平井数值试井模型建立求解的方法。In order to overcome the above disadvantages of the prior art, the object of the present invention is to provide a method for solving a numerical well test model of a compact gas pressure crack horizontal well with a fast calculation speed, a good curve fitting and an accurate interpretation result.
为了达到上述目的，本发明采取的技术方案为：一种致密气压裂水平井数值试井模型建立求解方法，包括以下步骤：In order to achieve the above object, the technical solution adopted by the present invention is: a method for establishing a numerical well test model for a dense gas pressure crack horizontal well, comprising the following steps:
步骤一：致密气藏压裂水平井的二维地质体和三维地质体的生成；Step 1: Formation of two-dimensional geological bodies and three-dimensional geological bodies in horizontal wells in tight gas reservoirs;
步骤二：对生成的致密气藏压裂水平井二维地质体和三维地质体进行网格离散；Step 2: Perform grid separation on the generated two-dimensional geological body and three-dimensional geological body of the horizontal well in the tight gas reservoir;
步骤三：井筒无压差的渗流模型计算；Step 3: Calculation of seepage model without pressure difference in the wellbore;
步骤四：建立耦合模型，并对建立的耦合模型进行求解，并把得到的解生成试井理论曲线；Step 4: Establish a coupling model, and solve the established coupling model, and generate a well test theoretical curve by the obtained solution;
步骤五：讲步骤四中得到的理论曲线与实测曲线进行拟合，得到试井解释的参数。Step 5: The theoretical curve obtained in step 4 is fitted to the measured curve to obtain the parameters of the well test interpretation.
所述的步骤一中生成致密气藏压裂水平井的二维地质体和三维地质体，具体步骤如下：In the first step, the two-dimensional geological body and the three-dimensional geological body of the horizontal well in the tight gas reservoir are generated, and the specific steps are as follows:
1)根据压裂水平井所处地质体的外边界，井筒内边界、裂缝以及复合区，再通过设置内外边界以及裂缝属性确定地质体的具体大小及形状，绘 制建立二维地质体；1) According to the outer boundary of the geological body where the horizontal well is fractured, the inner boundary of the wellbore, the crack and the composite area, and then determine the specific size and shape of the geological body by setting the inner and outer boundaries and the properties of the crack. Establish a two-dimensional geological body;
2)根据建立的二维体质和井眼轨迹以及储层上下边界的位置，利用几何体布尔运算生成三维地质体。2) According to the established two-dimensional physical and wellbore trajectory and the position of the upper and lower boundary of the reservoir, the geometrical Boolean operation is used to generate the three-dimensional geological body.
所述的步骤二中的二维地质体和三维地质体进行网格离散的具体步骤如下：The specific steps of the grid dispersion of the two-dimensional geological body and the three-dimensional geological body in the second step are as follows:
首先，将Netgen开源软件包成功进行编译，搭建运行环境；First, the Netgen open source software package is successfully compiled to build the operating environment;
然后，将二维地质体和三维地质体中的内外边界属分别按照Netgen网格文件格式的要求形成二维网格文件和三维网格文件，再按照Netgen设置的网格离散步骤进行网格离散。Then, the internal and external boundary genus in the 2D geological body and the 3D geological body are respectively formed into a 2D mesh file and a 3D mesh file according to the requirements of the Netgen mesh file format, and then the mesh discrete step is performed according to the mesh discrete step set by Netgen. .
所述的水平井筒无压差的渗流模型计算具体方法为：The specific method for calculating the seepage model of the horizontal wellbore without pressure difference is:
1)考虑应力敏感的地层和裂缝渗流方程1) Consider stress-sensitive formation and fracture seepage equations
地层渗流方程：Stratigraphic flow equation:
Figure PCTCN2015080767-appb-000001
Figure PCTCN2015080767-appb-000001
裂缝渗流方程：Crack seepage equation:
Figure PCTCN2015080767-appb-000002
Figure PCTCN2015080767-appb-000002
初始条件：Initial conditions:
pD(x,y,z,0)＝0     (3)p D (x, y, z, 0) = 0 (3)
内边界条件：Internal boundary conditions:
Figure PCTCN2015080767-appb-000003
Figure PCTCN2015080767-appb-000003
Figure PCTCN2015080767-appb-000004
Figure PCTCN2015080767-appb-000004
外边界条件： Outer boundary conditions:
封闭：
Figure PCTCN2015080767-appb-000005
 Closed:
Figure PCTCN2015080767-appb-000005
定压：
Figure PCTCN2015080767-appb-000006
 Constant pressure:
Figure PCTCN2015080767-appb-000006
式中符号含义：The meaning of the symbol in the formula:
pDR为地层区域的无量纲压力；pDf为裂缝区域的无量纲压力；tD为无量纲时间；CDL为无量纲井筒储存系数；KxD为x方向无量纲渗透率；KyD为y方向无量纲渗透率；KzD为z方向无量纲渗透率；KfD为无量纲裂缝渗透率；γD为无量纲渗透率模量；pwD为第一条裂缝与井筒交点处的无量纲压力；MPjD为j点无量纲压力与pwD之间的差值；Aj为内边界三角形无量纲面积；hD为无量纲储层厚度；St为井筒表皮系数；p DR is the dimensionless pressure of the stratigraphic region; p Df is the dimensionless pressure of the fracture zone; t D is the dimensionless time; C DL is the dimensionless wellbore storage coefficient; K xD is the dimensionless permeability in the x direction; K yD is y Directional dimensionless permeability; K zD is the dimensionless permeability in the z direction; K fD is the dimensionless fracture permeability; γ D is the dimensionless permeability modulus; p wD is the dimensionless pressure at the intersection of the first fracture and the wellbore MP jD is the difference between the dimensionless pressure of j point and p wD ; A j is the dimensionless area of the inner boundary triangle; h D is the dimensionless reservoir thickness; and S t is the wellbore skin factor;
2)方程求解2) Solving the equation
首先引入变换，将非线性渗流方程线性化，再采用有限元方法进行求解，变换公式为：First, the transformation is introduced, and the nonlinear seepage equation is linearized, and then solved by the finite element method. The transformation formula is:
Figure PCTCN2015080767-appb-000007
Figure PCTCN2015080767-appb-000007
采用混合有限元法将变换后的地层和裂缝渗流方程联立进行求解,地层和裂缝系统的有限元方程分解为地层区域的有限元方程(式9右边第一项)和代表裂缝系统的有限元方程(式9右边第二项)。The mixed finite element method is used to solve the transformed formation and fracture seepage equations. The finite element equations of the stratum and fracture system are decomposed into the finite element equation of the formation region (the first term on the right side of Equation 9) and the finite element representing the fracture system. Equation (the second term on the right side of Equation 9).
Figure PCTCN2015080767-appb-000008
Figure PCTCN2015080767-appb-000008
A.地层区域三维有限元方程为：A. The three-dimensional finite element equation of the stratigraphic zone is:
Figure PCTCN2015080767-appb-000009
Figure PCTCN2015080767-appb-000009
Figure PCTCN2015080767-appb-000010
Figure PCTCN2015080767-appb-000010
Figure PCTCN2015080767-appb-000011
Figure PCTCN2015080767-appb-000011
B.裂缝面二维有限元方程为：B. The two-dimensional finite element equation of the fracture surface is:
Figure PCTCN2015080767-appb-000012
Figure PCTCN2015080767-appb-000012
Figure PCTCN2015080767-appb-000013
Figure PCTCN2015080767-appb-000013
Figure PCTCN2015080767-appb-000014
Figure PCTCN2015080767-appb-000014
将有限元方程(10)～(15)联立组成系统刚度矩阵，利用并行化的SuperLU数值求解器对大型线性方程组进行求解，可以得到整个储层的压力场分布以及内边界法向压力梯度，再由此计算各裂缝生产流量：The finite element equations (10)~(15) are combined to form the system stiffness matrix. The parallelized SuperLU numerical solver is used to solve the large linear equations, and the pressure field distribution and the inner boundary normal pressure gradient of the whole reservoir can be obtained. Then calculate the production flow of each crack:
Figure PCTCN2015080767-appb-000015
Figure PCTCN2015080767-appb-000015
式中符号含义：The meaning of the symbol in the formula:
η为线性化变换参数；ηw为无量纲井底压力值所对应的变换参数；wf为裂缝宽度，m；wfD为无量纲裂缝宽度；LjD为裂缝内边界单元线长度；V为四面体体积；b，c，d为有限元系数；i，j，k，m为有限元四面体四个顶点序号；Qfi为第i条裂缝的流量，m3/d；Qsc为标况下气井的流量，m3/d。 η is the linear transformation parameter; η w is the transformation parameter corresponding to the dimensionless bottom hole pressure value; w f is the crack width, m; w fD is the dimensionless crack width; L jD is the crack inner boundary unit line length; Tetrahedral volume; b, c, d are finite element coefficients; i, j, k, m are four vertex numbers of finite element tetrahedron; Q fi is the flow of the ith crack, m 3 /d; Q sc is the standard The flow rate of the gas well, m 3 /d.
所述的步骤四中的建立耦合模型，并对建立的耦合模型进行求解按照以下步骤进行的：The coupling model is established in the fourth step, and the established coupling model is solved according to the following steps:
A，根据步骤四计算出的井筒压力pWD和裂缝流量Qfi，采用井筒多相流计算公式进行计算，得到井筒各点的无量纲压差MPiD，具体的公式如下：A. According to the wellbore pressure p WD and the crack flow Q fi calculated in the fourth step, the multi-phase flow calculation formula of the wellbore is used to calculate, and the dimensionless differential pressure MP iD of each point of the wellbore is obtained. The specific formula is as follows:
井筒多相流计算的基础方程为：The basic equation for the calculation of wellbore multiphase flow is:
Figure PCTCN2015080767-appb-000016
Figure PCTCN2015080767-appb-000016
式中符号含义：The meaning of the symbol in the formula:
ρL为液体密度，kg/m3；ρg为气体密度，kg/m3；G为气液混合物质量流量，kg/s；vm为混合物流动速度，m/s；vsg为气体表观流速，m/s；A为井筒油管截面积，m2；D为油管内径，m。ρ L is the liquid density, kg/m 3 ; ρ g is the gas density, kg/m 3 ; G is the mass flow rate of the gas-liquid mixture, kg / s; v m is the mixture flow velocity, m / s; v sg is the gas table Observe the flow rate, m/s; A is the cross-sectional area of the wellbore tubing, m 2 ; D is the inner diameter of the tubing, m.
其中持液率HL和摩擦阻力系数λ采用Beggs-Brill方法计算，根据公式(17)得到井筒压力梯度，再根据井筒内边界相对距离累加得到各点与井底标准点间的压差值：The liquid holdup rate H L and the frictional resistance coefficient λ are calculated by the Beggs-Brill method. The wellbore pressure gradient is obtained according to formula (17), and then the pressure difference between each point and the bottom hole standard point is obtained according to the relative distance of the inner boundary of the wellbore:
Figure PCTCN2015080767-appb-000017
Figure PCTCN2015080767-appb-000017
将得到的各点压差MPi进行无量纲化，即可获得各点无量纲压差MPiD。By obtaining the dimensionless difference MP i at each point, the dimensionless differential pressure MP iD at each point can be obtained.
B，把步骤A中求出的内边界各点压差MPiD，带入到渗流模型中计算出井筒压力p’WD和裂缝流量Q’fi，井筒多相流模型与渗流模型的耦合条件如下：B. The pressure difference MP iD of the inner boundary obtained in step A is brought into the seepage model to calculate the wellbore pressure p' WD and the crack flow Q' fi . The coupling conditions of the wellbore multiphase flow model and the seepage model are as follows :
地层与井筒交接面上：The interface between the formation and the wellbore:
Figure PCTCN2015080767-appb-000018
Figure PCTCN2015080767-appb-000018
裂缝与井筒交接面上：Crack and wellbore interface:
Figure PCTCN2015080767-appb-000019
Figure PCTCN2015080767-appb-000019
C，把前后迭代步计算得到的p’WD和pWD进行相减，当两者之间差的绝对值小于ε，则继续下一时间步的计算，当两者之差的绝对值大于或等于ε， 则把当前得到的p’WD和Q’fi与前一步的值取平均后得到新的井筒压力pWD和裂缝流量Qfi，并带入到步骤A中进行迭代，直到得到的p’WD与pWD进行相减之差的绝对值小于ε，ε一般取值为10-4；C, subtracting p' WD and p WD calculated from the previous iteration step. When the absolute value of the difference between the two is less than ε, the calculation of the next time step is continued, when the absolute value of the difference between the two is greater than or Equal to ε, the current obtained p' WD and Q' fi are averaged with the value of the previous step to obtain a new wellbore pressure p WD and crack flow Q fi , and brought into step A for iteration until the obtained p ' The absolute value of the difference between WD and p WD is less than ε, and ε is generally 10 -4 ;
D，把步骤C确定的p’WD和对应的Q’fi进行记录，若此时时间步k<总时间步n，则继续下一时间步的计算，根据当前的井筒压力pWD，裂缝流量Qfi，从步骤A开始计算得到新一轮的p’WD和Q’fi；D, the p' WD determined in step C and the corresponding Q' fi are recorded. If the time step k < total time step n, then the calculation of the next time step is continued, according to the current wellbore pressure p WD , the crack flow rate Q fi , starting from step A, a new round of p' WD and Q' fi is calculated;
E，把步骤D中n次计算中所得到p’WD和Q’fi的值生成试井理论曲线。E. Generate a well test theoretical curve by the values of p' WD and Q' fi obtained in the n calculations in step D.
所述步骤五主要是理论曲线与实测曲线在双对数曲线图、半对数曲线图和全历史压力曲线图中对比拟合，根据曲线的拟合程度，可进行拟合参数的调整，最终使理论曲线与实测曲线在双对数曲线图、半对数曲线图和全历史压力曲线图中都能够得到较好的吻合，曲线拟合才完成；曲线拟合完成后，即可以得到试井解释的参数，包括裂缝参数和储层参数。The fifth step is mainly to compare and compare the theoretical curve and the measured curve in the double logarithmic curve, the semi-logarithmic curve and the full historical pressure curve. According to the fitting degree of the curve, the fitting parameters can be adjusted, and finally The theoretical curve and the measured curve can be well matched in the double logarithmic curve, the semi-logarithmic curve and the full historical pressure curve, and the curve fitting is completed; after the curve fitting is completed, the well test can be obtained. Interpreted parameters, including crack parameters and reservoir parameters.
本发明采用以上技术方案，具有以下优点，具有计算速度快、曲线拟合好、解释结果准确。The invention adopts the above technical solutions and has the following advantages, and has the advantages of fast calculation speed, good curve fitting and accurate interpretation result.
附图说明DRAWINGS
图1考虑井眼轨迹及储层非均质性的压裂水平井三维地质体及网格离散；Figure 1 Three-dimensional geological body and grid dispersion of fractured horizontal wells considering well trajectory and reservoir heterogeneity;
图2耦合模型建立及求解的流程图。Figure 2 is a flow chart for the establishment and solution of the coupled model.
具体实施方式detailed description
下面结合附图和实施例对本发明进行详细的描述。The invention will now be described in detail in conjunction with the drawings and embodiments.
实施例1Example 1
如图2所示一种致密气压裂水平井数值试井模型建立求解方法，包括以下步骤：As shown in Figure 2, a method for solving a numerical well test model of a dense gas-fractured horizontal well includes the following steps:
步骤一：致密气藏压裂水平井的二维地质体和三维地质体的生成；主要Step 1: Formation of two-dimensional geological bodies and three-dimensional geological bodies in horizontal wells in tight gas reservoirs;
1)根据压裂水平井所处地质体的外边界，井筒内边界、裂缝以及复合区，再通过设置内外边界以及裂缝属性确定地质体的具体大小及形状，绘制建立二维地质体； 1) According to the outer boundary of the geological body where the horizontal well is fractured, the inner boundary of the wellbore, the crack and the composite zone, and then determine the specific size and shape of the geological body by setting the inner and outer boundaries and the properties of the fracture, and draw a two-dimensional geological body;
2)根据建立的二维体质和井眼轨迹以及储层上下边界的位置，利用几何体布尔运算生成三维地质体。2) According to the established two-dimensional physical and wellbore trajectory and the position of the upper and lower boundary of the reservoir, the geometrical Boolean operation is used to generate the three-dimensional geological body.
步骤二：如图1所示对生成的致密气藏压裂水平井二维地质体和三维地质体进行网格离散；首先，将Netgen开源软件包成功进行编译，搭建运行环境；Step 2: As shown in Figure 1, the generated tight gas reservoir fracturing horizontal well two-dimensional geological body and three-dimensional geological body grid discrete; first, the Netgen open source software package is successfully compiled to build the operating environment;
然后，将二维地质体和三维地质体中的内外边界属分别按照Netgen网格文件格式的要求形成二维网格文件和三维网格文件，再按照Netgen设置的网格离散步骤进行网格离散。Then, the internal and external boundary genus in the 2D geological body and the 3D geological body are respectively formed into a 2D mesh file and a 3D mesh file according to the requirements of the Netgen mesh file format, and then the mesh discrete step is performed according to the mesh discrete step set by Netgen. .
步骤三：水平井筒无压差的渗流模型计算；Step 3: Calculation of seepage model without horizontal pressure difference in horizontal wellbore;
1)考虑应力敏感的地层和裂缝渗流方程1) Consider stress-sensitive formation and fracture seepage equations
地层渗流方程：Stratigraphic flow equation:
Figure PCTCN2015080767-appb-000020
Figure PCTCN2015080767-appb-000020
裂缝渗流方程：Crack seepage equation:
Figure PCTCN2015080767-appb-000021
Figure PCTCN2015080767-appb-000021
初始条件：Initial conditions:
pD(x,y,z,0)＝0    (3)p D (x, y, z, 0) = 0 (3)
内边界条件：Internal boundary conditions:
Figure PCTCN2015080767-appb-000022
Figure PCTCN2015080767-appb-000022
Figure PCTCN2015080767-appb-000023
Figure PCTCN2015080767-appb-000023
外边界条件： Outer boundary conditions:
封闭：
Figure PCTCN2015080767-appb-000024
 Closed:
Figure PCTCN2015080767-appb-000024
定压：
Figure PCTCN2015080767-appb-000025
 Constant pressure:
Figure PCTCN2015080767-appb-000025
式中符号含义：The meaning of the symbol in the formula:
pDR为地层区域的无量纲压力；pDf为裂缝区域的无量纲压力；tD为无量纲时间；CDL为无量纲井筒储存系数；KxD为x方向无量纲渗透率；KyD为y方向无量纲渗透率；KzD为z方向无量纲渗透率；KfD为无量纲裂缝渗透率；γD为无量纲渗透率模量；pwD为第一条裂缝与井筒交点处的无量纲压力；MPjD为j点无量纲压力与pwD之间的差值；Aj为内边界三角形无量纲面积；hD为无量纲储层厚度；St为井筒表皮系数；p DR is the dimensionless pressure of the stratigraphic region; p Df is the dimensionless pressure of the fracture zone; t D is the dimensionless time; C DL is the dimensionless wellbore storage coefficient; K xD is the dimensionless permeability in the x direction; K yD is y Directional dimensionless permeability; K zD is the dimensionless permeability in the z direction; K fD is the dimensionless fracture permeability; γ D is the dimensionless permeability modulus; p wD is the dimensionless pressure at the intersection of the first fracture and the wellbore MP jD is the difference between the dimensionless pressure of j point and p wD ; A j is the dimensionless area of the inner boundary triangle; h D is the dimensionless reservoir thickness; and S t is the wellbore skin factor;
2)方程求解2) Solving the equation
首先引入变换，将非线性渗流方程线性化，再采用有限元方法进行求解，变换公式为：First, the transformation is introduced, and the nonlinear seepage equation is linearized, and then solved by the finite element method. The transformation formula is:
Figure PCTCN2015080767-appb-000026
Figure PCTCN2015080767-appb-000026
采用混合有限元法将变换后的地层和裂缝渗流方程联立进行求解,地层和裂缝系统的有限元方程分解为地层区域的有限元方程(式9右边第一项)和代表裂缝系统的有限元方程(式9右边第二项)。The mixed finite element method is used to solve the transformed formation and fracture seepage equations. The finite element equations of the stratum and fracture system are decomposed into the finite element equation of the formation region (the first term on the right side of Equation 9) and the finite element representing the fracture system. Equation (the second term on the right side of Equation 9).
Figure PCTCN2015080767-appb-000027
Figure PCTCN2015080767-appb-000027
A.地层区域三维有限元方程为： A. The three-dimensional finite element equation of the stratigraphic zone is:
Figure PCTCN2015080767-appb-000028
Figure PCTCN2015080767-appb-000028
Figure PCTCN2015080767-appb-000029
Figure PCTCN2015080767-appb-000029
Figure PCTCN2015080767-appb-000030
Figure PCTCN2015080767-appb-000030
B.裂缝面二维有限元方程为：B. The two-dimensional finite element equation of the fracture surface is:
Figure PCTCN2015080767-appb-000031
Figure PCTCN2015080767-appb-000031
Figure PCTCN2015080767-appb-000032
Figure PCTCN2015080767-appb-000032
Figure PCTCN2015080767-appb-000033
Figure PCTCN2015080767-appb-000033
将有限元方程(10)～(15)联立组成系统刚度矩阵，利用并行化的SuperLU数值求解器对大型线性方程组进行求解，可以得到整个储层的压力场分布以及内边界法向压力梯度，再由此计算各裂缝生产流量： The finite element equations (10)~(15) are combined to form the system stiffness matrix. The parallelized SuperLU numerical solver is used to solve the large linear equations, and the pressure field distribution and the inner boundary normal pressure gradient of the whole reservoir can be obtained. Then calculate the production flow of each crack:
Figure PCTCN2015080767-appb-000034
Figure PCTCN2015080767-appb-000034
式中符号含义：The meaning of the symbol in the formula:
η为线性化变换参数；ηw为无量纲井底压力值所对应的变换参数；wf为裂缝宽度，m；wfD为无量纲裂缝宽度；LjD为裂缝内边界单元线长度；V为四面体体积；b，c，d为有限元系数；i，j，k，m为有限元四面体四个顶点序号；Qfi为第i条裂缝的流量，m3/d；Qsc为标况下气井的流量，m3/d。η is the linear transformation parameter; η w is the transformation parameter corresponding to the dimensionless bottom hole pressure value; w f is the crack width, m; w fD is the dimensionless crack width; L jD is the crack inner boundary unit line length; Tetrahedral volume; b, c, d are finite element coefficients; i, j, k, m are four vertex numbers of finite element tetrahedron; Q fi is the flow of the ith crack, m 3 /d; Q sc is the standard The flow rate of the gas well, m 3 /d.
步骤四：建立耦合模型，并对建立的耦合模型进行求解，并把得到的解生成试井理论曲线；并对建立的耦合模型进行求解按照以下步骤进行的：Step 4: Establish a coupling model, solve the established coupling model, and generate the test well theory curve by solving the obtained solution; and solve the established coupling model according to the following steps:
A，根据步骤四计算出的井筒压力pWD和裂缝流量Qfi，采用井筒多相流计算公式进行计算，得到井筒各点的无量纲压差MPiD，具体的公式如下：A. According to the wellbore pressure p WD and the crack flow Q fi calculated in the fourth step, the multi-phase flow calculation formula of the wellbore is used to calculate, and the dimensionless differential pressure MP iD of each point of the wellbore is obtained. The specific formula is as follows:
井筒多相流计算的基础方程为：The basic equation for the calculation of wellbore multiphase flow is:
Figure PCTCN2015080767-appb-000035
Figure PCTCN2015080767-appb-000035
式中符号含义：The meaning of the symbol in the formula:
ρL为液体密度，kg/m3；ρg为气体密度，kg/m3；G为气液混合物质量流量，kg/s；vm为混合物流动速度，m/s；vsg为气体表观流速，m/s；A为井筒油管截面积，m2；D为油管内径，m。ρ L is the liquid density, kg/m 3 ; ρ g is the gas density, kg/m 3 ; G is the mass flow rate of the gas-liquid mixture, kg / s; v m is the mixture flow velocity, m / s; v sg is the gas table Observe the flow rate, m/s; A is the cross-sectional area of the wellbore tubing, m 2 ; D is the inner diameter of the tubing, m.
其中持液率HL和摩擦阻力系数λ采用Beggs-Brill方法计算，根据公式(17)得到井筒压力梯度，再根据井筒内边界相对距离累加得到各点与井底标准点间的压差值：The liquid holdup rate H L and the frictional resistance coefficient λ are calculated by the Beggs-Brill method. The wellbore pressure gradient is obtained according to formula (17), and then the pressure difference between each point and the bottom hole standard point is obtained according to the relative distance of the inner boundary of the wellbore:
Figure PCTCN2015080767-appb-000036
Figure PCTCN2015080767-appb-000036
将得到的各点压差MPi进行无量纲化，即可获得各点无量纲压差MPiD。By obtaining the dimensionless difference MP i at each point, the dimensionless differential pressure MP iD at each point can be obtained.
B，把步骤A中求出的内边界各点压差MPiD，带入到渗流模型中计算出 井筒压力p’WD和裂缝流量Q’fi，井筒多相流模型与渗流模型的耦合条件如下：B. The pressure difference MP iD at the inner boundary obtained in step A is brought into the seepage model to calculate the wellbore pressure p' WD and the crack flow Q' fi . The coupling conditions of the wellbore multiphase flow model and the seepage model are as follows :
地层与井筒交接面上：The interface between the formation and the wellbore:
Figure PCTCN2015080767-appb-000037
Figure PCTCN2015080767-appb-000037
裂缝与井筒交接面上：Crack and wellbore interface:
Figure PCTCN2015080767-appb-000038
Figure PCTCN2015080767-appb-000038
C，把前后迭代步计算得到的p’WD和pWD进行相减，当两者之间差的绝对值小于ε，则继续下一时间步的计算，当两者之差的绝对值大于或等于ε，则把当前得到的p’WD和Q’fi与前一步的值取平均后得到新的井筒压力pWD和裂缝流量Qfi，并带入到步骤A中进行迭代，直到得到的p’WD与pWD进行相减之差的绝对值小于ε，ε一般取值为10-4；C, subtracting p' WD and p WD calculated from the previous iteration step. When the absolute value of the difference between the two is less than ε, the calculation of the next time step is continued, when the absolute value of the difference between the two is greater than or Equal to ε, the current obtained p' WD and Q' fi are averaged with the value of the previous step to obtain a new wellbore pressure p WD and crack flow Q fi , and brought into step A for iteration until the obtained p ' The absolute value of the difference between WD and p WD is less than ε, and ε is generally 10 -4 ;
D，把步骤C确定的p’WD和对应的Q’fi进行记录，若此时时间步k<总时间步n，则继续下一时间步的计算，根据当前的井筒压力pWD，裂缝流量Qfi，从步骤A开始计算得到新一轮的p’WD和Q’fi；D, the p' WD determined in step C and the corresponding Q' fi are recorded. If the time step k < total time step n, then the calculation of the next time step is continued, according to the current wellbore pressure p WD , the crack flow rate Q fi , starting from step A, a new round of p' WD and Q' fi is calculated;
E，把步骤D中n次计算中所得到p’WD和Q’fi的值生成试井理论曲线。步骤五：讲步骤四中得到的理论曲线与实测曲线进行拟合，得到试井解释的参数；E. Generate a well test theoretical curve by the values of p' WD and Q' fi obtained in the n calculations in step D. Step 5: Fitting the theoretical curve obtained in step 4 with the measured curve to obtain the parameters of the well test interpretation;
所述步骤五主要是理论曲线与实测曲线在双对数曲线图、半对数曲线图和全历史压力曲线图中对比拟合，根据曲线的拟合程度，可进行拟合参数的调整，最终使理论曲线与实测曲线在双对数曲线图、半对数曲线图和全历史压力曲线图中都能够得到较好的吻合，曲线拟合才完成；曲线拟合完成后，即可以得到试井解释的参数，包括裂缝参数和储层参数。The fifth step is mainly to compare and compare the theoretical curve and the measured curve in the double logarithmic curve, the semi-logarithmic curve and the full historical pressure curve. According to the fitting degree of the curve, the fitting parameters can be adjusted, and finally The theoretical curve and the measured curve can be well matched in the double logarithmic curve, the semi-logarithmic curve and the full historical pressure curve, and the curve fitting is completed; after the curve fitting is completed, the well test can be obtained. Interpreted parameters, including crack parameters and reservoir parameters.
实施例2Example 2
1.实现致密气藏压裂水平井地质体快速生成1. Realize rapid generation of geological bodies in tight gas wells in tight gas reservoirs
首先建立二维地质体，再由二维地质体转换为三维地质体。通过编写软件几何图形绘制的代码，实现绘制压裂水平井所处地质体的外边界，井筒内边界、裂缝以及复合区等功能，再通过设置内外边界以及裂缝属性确定 地质体的具体大小及形状，通过这种方式可快速建立二维地质体。由二维地质体，结合井眼轨迹以及储层上下边界的位置，利用几何体布尔运算可直接生成三维地质体，采用OpenCasCade工具进行三维视图显示，如图1所示的三维地质体。First, a two-dimensional geological body is built, and then a two-dimensional geological body is converted into a three-dimensional geological body. By writing the code drawn by the software geometry, the outer boundary of the geological body where the fracturing horizontal well is located, the inner boundary of the wellbore, the crack and the composite zone are realized, and then the inner and outer boundaries and the crack properties are determined. The specific size and shape of the geological body can quickly establish a two-dimensional geological body. From the two-dimensional geological body, combined with the well trajectory and the position of the upper and lower boundaries of the reservoir, the geometric Boolean operation can be used to directly generate the three-dimensional geological body, and the OpenCasCade tool is used to display the three-dimensional view, as shown in Figure 1.
2.实现二维地质体和三维地质体网格自动离散功能2. Realize the automatic discrete function of 2D geological body and 3D geological body grid
首先将Netgen开源软件包成功进行编译，搭建运行环境，然后将二维地质体中的内外边界属性按照Netgen网格文件格式的要求形成二维网格文件，再按照Netgen设置的网格离散步骤进行网格离散。三维地质体的离散过程与二维地质体的离散过程类似，不同的是三维网格离散首先需将三维地质体输出为常用格式(如STEP格式)，再采用Netgen对该输出格式的文件进行网格离散。二维地质体的离散时间比较短，所需时间一般在10s～30s之间，三维地质体的离散时间较长，需根据网格离散的密度而定，通常离散时间不超过5分钟。网格离散后自动显示离散的网格结点及网格线，如图1所示。Firstly, the Netgen open source software package is successfully compiled, the running environment is set up, and then the internal and external boundary attributes in the 2D geological body are formed into a 2D mesh file according to the requirements of the Netgen grid file format, and then the mesh discrete steps set by Netgen are performed. Grid discrete. The discrete process of a 3D geological body is similar to the discrete process of a 2D geological body. The difference is that the 3D mesh discretization first needs to output the 3D geological body into a common format (such as STEP format), and then use Netgen to network the output format file. Discrete. The discrete time of the two-dimensional geological body is relatively short, and the time required is generally between 10s and 30s. The discrete time of the three-dimensional geological body is long, and it needs to be determined according to the density of the discrete mesh. Usually, the discrete time is less than 5 minutes. Discrete grid nodes and grid lines are automatically displayed after the grid is discrete, as shown in Figure 1.
3.建立试井解释模型，划分模型参数的类型3. Establish a well test interpretation model and classify the model parameters
根据压裂水平井所涉及到的流动方式，建立考虑多因素耦合的试井解释模型。将模型中所涉及到的参数分为已知参数和未知参数(待解释参数)，已知参数与未知参数应该设置不同的输入接口，以免混淆。已知参数根据实际情况输入，而未知参数可在曲线拟合完成后确定。Based on the flow patterns involved in fracturing horizontal wells, a well test interpretation model considering multi-factor coupling is established. The parameters involved in the model are divided into known parameters and unknown parameters (parameters to be interpreted). The known parameters and unknown parameters should be set different input interfaces to avoid confusion. The known parameters are entered according to the actual situation, and the unknown parameters can be determined after the curve fitting is completed.
4.编制模型数值求解的代码，实现模型快速求解4. Compile the code of the model numerical solution to realize the rapid solution of the model
建立完试井解释模型后，根据模型特点，设计模型的数值求解算法，编制模型数值求解的计算机代码，如图2所示的模型求解流程图。首先输入基础数据，建立地质体模型，将地质体模型进行网格离散。初始步按照井筒无压差的方式进行渗流模型计算，计算得到初始的井底流压和各裂缝流量分布，根据此结果利用井筒多相流计算模型计算井筒的压差分布，再由此压差进行渗流模型计算，获取新的井底压力和裂缝流量分布，与之前的计算结果对比判断该时间步的迭代是否结束。若两者之差小于小量ε则进行下个时间步的计算，反之则继续迭代，直到稳定为止后再进行下一时间 步的计算。利用此方法最终完成所有设定时间步的计算，即完成对耦合模型的求解。After the well test interpretation model is established, according to the characteristics of the model, the numerical solution algorithm of the design model is designed, and the computer code of the model numerical solution is compiled, as shown in the model solution flow chart shown in FIG. 2 . First, the basic data is input, the geological body model is established, and the geological body model is meshed. The initial step is to calculate the seepage model according to the method of no pressure difference in the wellbore, and calculate the initial bottomhole flow pressure and the distribution of each crack flow. According to the result, the wellbore multiphase flow calculation model is used to calculate the differential pressure distribution of the wellbore, and then the differential pressure is used. The seepage model is calculated to obtain a new bottom hole pressure and crack flow distribution, and compared with the previous calculation results to determine whether the iteration of the time step is over. If the difference between the two is less than the small amount ε, the next time step is calculated, otherwise the iteration is continued until the next time is stabilized. The calculation of the step. Using this method, the calculation of all the set time steps is finally completed, that is, the solution of the coupled model is completed.
5.进行实测曲线与理论曲线拟合5. Fitting the measured curve with the theoretical curve
模型求解完成后，自动生成试井理论曲线，将理论曲线与实测曲线在双对数曲线图、半对数曲线图和全历史压力曲线图中对比拟合。双对数曲线图在主视图中，而半对数曲线图和全历史压力曲线图在辅助视图区中，根据曲线的拟合程度，可进行拟合参数的调整。最终使理论曲线与实测曲线在双对数曲线图、半对数曲线图和全历史压力曲线图中都能够得到较好的吻合，曲线拟合才完成，曲线拟合完成后，即可以得到试井解释的参数，包括裂缝参数和储层参数。After the model is solved, the well test theory curve is automatically generated, and the theoretical curve and the measured curve are compared and fitted in a double logarithmic curve, a semi-logarithmic curve and a full historical pressure curve. The double logarithmic graph is in the main view, while the semi-log graph and the full historical pressure graph are in the auxiliary view region, and the fitting parameters can be adjusted according to the degree of fitting of the curve. Finally, the theoretical curve and the measured curve can be well matched in the double logarithmic curve, the semi-logarithmic curve and the full historical pressure curve, and the curve fitting is completed. After the curve fitting is completed, the test can be obtained. Well explained parameters, including crack parameters and reservoir parameters.
实施例3Example 3
1)致密气藏压裂水平井二维和三维地质体快速生成及显示方法；1) Rapid generation and display methods for two-dimensional and three-dimensional geological bodies of tight gas wells in tight gas reservoirs;
首先建立二维地质体，再由二维地质体转换为三维地质体。根据水平井测井解释结果设置储层的非均质特征，包括孔隙度、含气饱和度以及初始渗透率分布，在地质体中划分不同的区域，每个区域代表一个均质体，每个均质体具有不同的孔隙度、含水饱和度和初始渗透率，由许多个不同均质体组成整个地质系统的非均质性。均质体数目越多，参数差异越大，则地质体的非均质性越强；由二维地质体，再结合井眼轨迹以及储层上下边界的位置，可直接生成三维地质体；为了更好地进行三维地质体的显示，基于OpenCasCade工具进行三维视图的全方位显示，显示内容包括三维地质体、网格离散图、计算云图等。First, a two-dimensional geological body is built, and then a two-dimensional geological body is converted into a three-dimensional geological body. According to the results of horizontal well logging interpretation, the heterogeneous characteristics of the reservoir, including porosity, gas saturation and initial permeability distribution, are divided into different regions in the geological body, each region representing a homogeneous body, each The homogeneous bodies have different porosity, water saturation and initial permeability, and the heterogeneity of the entire geological system is composed of many different homogeneous bodies. The more the number of homogeneous bodies, the greater the difference in parameters, the stronger the heterogeneity of the geological body; the two-dimensional geological body, combined with the well trajectory and the position of the upper and lower boundaries of the reservoir, can directly generate three-dimensional geological bodies; Better display of 3D geological bodies, based on OpenCasCade tools for 3D view display, including 3D geological bodies, grid discrete maps, and computational cloud maps.
2)致密气藏压裂水平井网格自动离散的实现；2) Implementation of automatic dispersion of horizontal well grids in tight gas reservoirs;
将生成的地质体转换为STEP格式文件、IGES格式文件或者BREP格式文件，然后采用Netgen开源工具实现二维地质体和三维地质体的网格自动离散功能，二维网格为三角形网格，三维网格为四面体网格。针对压裂 水平井试井问题的特点，在网格离散过程中通过设置裂缝及井筒离散结点的数量来自动加密井筒及裂缝附近的网格，通过设置网格离散参数来控制网格离散的质量。网格越密集，网格量越多，网格离散的时间越长，计算所需时间也越长，而网格量过小会影响到计算精度，因此实际情况应该选择适中的网格密度。通常情况下二维网格量为1万～3万之间，三维网格量为10万～50万之间。The generated geological body is converted into a STEP format file, an IGES format file or a BREP format file, and then the Netgen open source tool is used to realize the automatic mesh discrete function of the two-dimensional geological body and the three-dimensional geological body, and the two-dimensional mesh is a triangular mesh, three-dimensional The mesh is a tetrahedral mesh. For fracturing The characteristics of the horizontal well test problem, in the grid discrete process, the grid around the wellbore and the crack is automatically encrypted by setting the number of cracks and discrete nodes of the wellbore, and the discrete quality of the grid is controlled by setting the discrete parameters of the grid. The denser the mesh, the more the mesh volume, the longer the mesh discrete time, the longer the calculation time, and the smaller the mesh size will affect the calculation accuracy. Therefore, the actual mesh density should be selected. Usually, the amount of two-dimensional grid is between 10,000 and 30,000, and the amount of three-dimensional grid is between 100,000 and 500,000.
3)致密气藏压裂水平井地层渗流及井筒多相流耦合模型的建立；3) Establishment of formation seepage and wellbore multiphase flow coupling model for tight gas wells in tight gas reservoirs;
将致密气藏压裂水平井划分为三个流动区域：井筒、裂缝和地层。不同区域的流动机理不同，井筒为气液两相流，裂缝为高速非达西渗流，地层为具有应力敏感的非线性渗流。首先基于致密气压裂水平井渗流特征，将裂缝区看作为高渗透高速非达西渗流区域，由于裂缝宽度很小，裂缝区流体的流动视为二维流动，建立一种压裂水平井二维数值试井模型和三维数值试井模型；二维模型主要用于水平井筒以套管形式完井的情况，而三维模型用于水平井筒以裸眼方式完井的情况；在该渗流模型的基础上再考虑井筒气液两相流，采用Beggs-Brill方法建立井筒气液两相流的流动阻力计算方法；渗流模型与井筒多相流模型根据地层与井筒接触面上压力连续的方式耦合。The tight gas fracturing horizontal well is divided into three flow areas: the wellbore, the fracture and the formation. The flow mechanism is different in different regions. The wellbore is a gas-liquid two-phase flow, the fracture is a high-speed non-Darcy flow, and the formation is a stress-sensitive nonlinear seepage. Firstly, based on the seepage characteristics of the horizontal wells with dense gas pressure cracking, the fracture zone is regarded as the high-permeability high-speed non-Darcy flow zone. Since the crack width is small, the fluid flow in the fracture zone is regarded as two-dimensional flow, and a fracturing horizontal well is established. Dimensional numerical well test model and three-dimensional numerical well test model; two-dimensional model is mainly used for completion of horizontal wellbore in casing form, and three-dimensional model is used for horizontal wellbore completion in open hole; in the basis of the seepage model Considering the gas-liquid two-phase flow in the wellbore, the Beggs-Brill method is used to establish the flow resistance calculation method of the gas-liquid two-phase flow in the wellbore. The seepage model and the wellbore multiphase flow model are coupled according to the continuous pressure of the formation and the wellbore contact surface.
4)致密气藏压裂水平井耦合模型的快速求解方法。4) A fast solution method for the coupling model of tight gas wells in tight gas reservoirs.
采用混合有限元方法对模型进行数值求解，将渗流模型与井筒气液两相流计算模型进行耦合迭代计算。根据试井渗流模型的特点，将计算时间节点设置为对数分布，每个对数周期内设置10～20个计算点，计算的起始时间和终止时间可以根据实际情况调整。每个时间步迭代结束的条件是计算结果既满足渗流模型又满足井筒多相流计算模型。利用SuperLU求解器 对二维模型的线性方程组进行求解，利用并行化的SuperLU求解器对三维模型的线性方程组进行求解，并行计算采用的线程数根据计算的网格量来确定，通常情况下并行线程数设置为6～10个即可满足计算需求。The model is numerically solved by the hybrid finite element method, and the seepage model and the wellbore gas-liquid two-phase flow calculation model are coupled and iteratively calculated. According to the characteristics of the well test seepage model, the calculation time node is set to logarithmic distribution, and 10 to 20 calculation points are set in each logarithmic period. The calculated start time and end time can be adjusted according to actual conditions. The condition for the end of each time step is that the calculation results satisfy both the seepage model and the wellbore multiphase flow calculation model. Using the SuperLU solver The linear equations of the two-dimensional model are solved, and the linear equations of the three-dimensional model are solved by the parallelized SuperLU solver. The number of threads used for parallel computing is determined according to the calculated grid amount. Under normal circumstances, the number of parallel threads is set. 6 to 10 can meet the computing needs.
5.进行实测曲线与理论曲线拟合5. Fitting the measured curve with the theoretical curve
模型求解完成后，自动生成试井理论曲线，将理论曲线与实测曲线在双对数曲线图、半对数曲线图和全历史压力曲线图中对比拟合。双对数曲线图在主视图中，而半对数曲线图和全历史压力曲线图在辅助视图区中，根据曲线的拟合程度，可进行拟合参数的调整。最终使理论曲线与实测曲线在双对数曲线图、半对数曲线图和全历史压力曲线图中都能够得到较好的吻合，曲线拟合才完成，曲线拟合完成后，即可以得到试井解释的参数，包括裂缝参数和储层参数。After the model is solved, the well test theory curve is automatically generated, and the theoretical curve and the measured curve are compared and fitted in a double logarithmic curve, a semi-logarithmic curve and a full historical pressure curve. The double logarithmic graph is in the main view, while the semi-log graph and the full historical pressure graph are in the auxiliary view region, and the fitting parameters can be adjusted according to the degree of fitting of the curve. Finally, the theoretical curve and the measured curve can be well matched in the double logarithmic curve, the semi-logarithmic curve and the full historical pressure curve, and the curve fitting is completed. After the curve fitting is completed, the test can be obtained. Well explained parameters, including crack parameters and reservoir parameters.
以上例举仅仅是对本发明的举例说明，并不构成对本发明的保护范围的限制，凡是与本发明相同或相似的设计均属于本发明的保护范围之内。 The above exemplifications are merely illustrative of the invention and are not intended to limit the scope of the invention. Any design that is identical or similar to the invention is within the scope of the invention.

Claims (6)

  1. 一种致密气压裂水平井数值试井模型建立求解方法，其特征在于，包括以下步骤：A method for solving a numerical well testing model for a tight gas-fractured horizontal well is characterized in that it comprises the following steps:
    步骤一：致密气藏压裂水平井的二维地质体和三维地质体的生成；Step 1: Formation of two-dimensional geological bodies and three-dimensional geological bodies in horizontal wells in tight gas reservoirs;
    步骤二：对生成的致密气藏压裂水平井二维地质体和三维地质体进行网格离散；Step 2: Perform grid separation on the generated two-dimensional geological body and three-dimensional geological body of the horizontal well in the tight gas reservoir;
    步骤三：井筒无压差的渗流模型计算；Step 3: Calculation of seepage model without pressure difference in the wellbore;
    步骤四：建立耦合模型，并对建立的耦合模型进行求解，并把得到的解生成试井理论曲线；Step 4: Establish a coupling model, and solve the established coupling model, and generate a well test theoretical curve by the obtained solution;
    步骤五：讲步骤四中得到的理论曲线与实测曲线进行拟合，得到试井解释的参数。Step 5: The theoretical curve obtained in step 4 is fitted to the measured curve to obtain the parameters of the well test interpretation.
  2. 根据权利要求1所述的一种致密气压裂水平井数值试井模型建立求解方法，其特征在于，所述的步骤一中生成致密气藏压裂水平井的二维地质体和三维地质体，具体步骤如下：The method for establishing a numerical well test model for a compact gas pressure crack horizontal well according to claim 1, wherein the step 2 generates a two-dimensional geological body and a three-dimensional geological body of a horizontal well in a tight gas reservoir. ,Specific steps are as follows:
    1)根据压裂水平井所处地质体的外边界，井筒内边界、裂缝以及复合区，再通过设置内外边界以及裂缝属性确定地质体的具体大小及形状，绘制建立二维地质体；1) According to the outer boundary of the geological body where the horizontal well is fractured, the inner boundary of the wellbore, the crack and the composite zone, and then determine the specific size and shape of the geological body by setting the inner and outer boundaries and the properties of the fracture, and draw a two-dimensional geological body;
    2)根据建立的二维体质和井眼轨迹以及储层上下边界的位置，利用几何体布尔运算生成三维地质体。2) According to the established two-dimensional physical and wellbore trajectory and the position of the upper and lower boundary of the reservoir, the geometrical Boolean operation is used to generate the three-dimensional geological body.
  3. 根据权利要求1所述的一种致密气压裂水平井数值试井模型建立求解方法，其特征在于，所述的步骤二中的二维地质体和三维地质体进行网格离散的具体步骤如下：The method for establishing a numerical well test model for a dense gas pressure crack horizontal well according to claim 1, wherein the specific steps of the two-dimensional geologic body and the three-dimensional geological body in the second step are as follows: :
    首先，将Netgen开源软件包成功进行编译，搭建运行环境；First, the Netgen open source software package is successfully compiled to build the operating environment;
    然后，将二维地质体和三维地质体中的内外边界属分别按照Netgen网格文件格式的要求形成二维网格文件和三维网格文件，再按照Netgen设置的网格离散步骤进行网格离散。Then, the internal and external boundary genus in the 2D geological body and the 3D geological body are respectively formed into a 2D mesh file and a 3D mesh file according to the requirements of the Netgen mesh file format, and then the mesh discrete step is performed according to the mesh discrete step set by Netgen. .
  4. 根据权利要求1所述的一种致密气压裂水平井数值试井模型建立求解方法，其特征在于，所述的水平井筒无压差的渗流模型计算具体方法为：The method for establishing a numerical well test model for a dense gas pressure cracking horizontal well according to claim 1, wherein the specific method for calculating the seepage model of the horizontal wellbore without pressure difference is:
    1)考虑应力敏感的地层和裂缝渗流方程 1) Consider stress-sensitive formation and fracture seepage equations
    地层渗流方程：Stratigraphic flow equation:
    Figure PCTCN2015080767-appb-100001
    Figure PCTCN2015080767-appb-100001
    裂缝渗流方程：Crack seepage equation:
    Figure PCTCN2015080767-appb-100002
    Figure PCTCN2015080767-appb-100002
    初始条件：Initial conditions:
    pD(x,y,z,0)＝0   (3)p D (x, y, z, 0) = 0 (3)
    内边界条件：Internal boundary conditions:
    Figure PCTCN2015080767-appb-100003
    Figure PCTCN2015080767-appb-100003
    Figure PCTCN2015080767-appb-100004
    Figure PCTCN2015080767-appb-100004
    外边界条件：Outer boundary conditions:
    封闭：
    Figure PCTCN2015080767-appb-100005
         Closed:
    Figure PCTCN2015080767-appb-100005
    定压：
    Figure PCTCN2015080767-appb-100006
         Constant pressure:
    Figure PCTCN2015080767-appb-100006
    式中符号含义：The meaning of the symbol in the formula:
    pDR为地层区域的无量纲压力；pDf为裂缝区域的无量纲压力；tD为无量纲时间；CDL为无量纲井筒储存系数；KxD为x方向无量纲渗透率；KyD为y方向无量纲渗透率；KzD为z方向无量纲渗透率；KfD为无量纲裂缝渗透率；γD为无量纲渗透率模量；pwD为第一条裂缝与井筒交点处的无量纲压力；MPjD为j点无量纲压力与pwD之间的差值；Aj为内边界三角形无量纲面积；hD为无量纲储层厚度；St为井筒表皮系数； p DR is the dimensionless pressure of the stratigraphic region; p Df is the dimensionless pressure of the fracture zone; t D is the dimensionless time; C DL is the dimensionless wellbore storage coefficient; K xD is the dimensionless permeability in the x direction; K yD is y Directional dimensionless permeability; K zD is the dimensionless permeability in the z direction; K fD is the dimensionless fracture permeability; γ D is the dimensionless permeability modulus; p wD is the dimensionless pressure at the intersection of the first fracture and the wellbore MP jD is the difference between the dimensionless pressure of j point and p wD ; A j is the dimensionless area of the inner boundary triangle; h D is the dimensionless reservoir thickness; and S t is the wellbore skin factor;
    2)方程求解2) Solving the equation
    首先引入变换，将非线性渗流方程线性化，再采用有限元方法进行求解，变换公式为：First, the transformation is introduced, and the nonlinear seepage equation is linearized, and then solved by the finite element method. The transformation formula is:
    Figure PCTCN2015080767-appb-100007
    Figure PCTCN2015080767-appb-100007
    采用混合有限元法将变换后的地层和裂缝渗流方程联立进行求解,地层和裂缝系统的有限元方程分解为地层区域的有限元方程(式9右边第一项)和代表裂缝系统的有限元方程(式9右边第二项)。The mixed finite element method is used to solve the transformed formation and fracture seepage equations. The finite element equations of the stratum and fracture system are decomposed into the finite element equation of the formation region (the first term on the right side of Equation 9) and the finite element representing the fracture system. Equation (the second term on the right side of Equation 9).
    Figure PCTCN2015080767-appb-100008
    Figure PCTCN2015080767-appb-100008
    A.地层区域三维有限元方程为：A. The three-dimensional finite element equation of the stratigraphic zone is:
    Figure PCTCN2015080767-appb-100009
    Figure PCTCN2015080767-appb-100009
    Figure PCTCN2015080767-appb-100010
    Figure PCTCN2015080767-appb-100010
    Figure PCTCN2015080767-appb-100011
    Figure PCTCN2015080767-appb-100011
    B.裂缝面二维有限元方程为：B. The two-dimensional finite element equation of the fracture surface is:
    Figure PCTCN2015080767-appb-100012
    Figure PCTCN2015080767-appb-100012
    Figure PCTCN2015080767-appb-100013
    Figure PCTCN2015080767-appb-100013
    Figure PCTCN2015080767-appb-100014
    Figure PCTCN2015080767-appb-100014
    将有限元方程(10)～(15)联立组成系统刚度矩阵，利用并行化的SuperLU数值求解器对大型线性方程组进行求解，可以得到整个储层的压力场分布以及内边界法向压力梯度，再由此计算各裂缝生产流量：The finite element equations (10)~(15) are combined to form the system stiffness matrix. The parallelized SuperLU numerical solver is used to solve the large linear equations, and the pressure field distribution and the inner boundary normal pressure gradient of the whole reservoir can be obtained. Then calculate the production flow of each crack:
    Figure PCTCN2015080767-appb-100015
    式中符号含义：
    Figure PCTCN2015080767-appb-100015
     The meaning of the symbol in the formula:
    η为线性化变换参数；ηw为无量纲井底压力值所对应的变换参数；wf为裂缝宽度，m；wfD为无量纲裂缝宽度；LjD为裂缝内边界单元线长度；V为四面体体积；b，c，d为有限元系数；i，j，k，m为有限元四面体四个顶点序号；Qfi为第i条裂缝的流量，m3/d；Qsc为标况下气井的流量，m3/d。η is the linear transformation parameter; η w is the transformation parameter corresponding to the dimensionless bottom hole pressure value; w f is the crack width, m; w fD is the dimensionless crack width; L jD is the crack inner boundary unit line length; Tetrahedral volume; b, c, d are finite element coefficients; i, j, k, m are four vertex numbers of finite element tetrahedron; Q fi is the flow of the ith crack, m 3 /d; Q sc is the standard The flow rate of the gas well, m 3 /d.
  5. 根据权利要求1所述的一种致密气压裂水平井数值试井模型建立求解方法，其特征在于，所述的步骤四中的建立耦合模型，并对建立的耦合模型进行求解按照以下步骤进行的：The method for establishing a numerical well test model for a dense gas pressure crack horizontal well according to claim 1, wherein the coupling model is established in the fourth step, and the coupled model is solved according to the following steps. of:
    A，根据步骤四计算出的井筒压力pWD和裂缝流量Qfi，采用井筒多相流计算公式进行计算，得到井筒各点的无量纲压差MPiD，具体的公式如下：A. According to the wellbore pressure p WD and the crack flow Q fi calculated in the fourth step, the multi-phase flow calculation formula of the wellbore is used to calculate, and the dimensionless differential pressure MP iD of each point of the wellbore is obtained. The specific formula is as follows:
    井筒多相流计算的基础方程为：The basic equation for the calculation of wellbore multiphase flow is:
    Figure PCTCN2015080767-appb-100016
    Figure PCTCN2015080767-appb-100016
    式中符号含义：The meaning of the symbol in the formula:
    ρL为液体密度，kg/m3；ρg为气体密度，kg/m3；G为气液混合物质量流 量，kg/s；vm为混合物流动速度，m/s；vsg为气体表观流速，m/s；A为井筒油管截面积，m2；D为油管内径，m。ρ L is the liquid density, kg/m 3 ; ρ g is the gas density, kg/m 3 ; G is the mass flow of the gas-liquid mixture, kg/s; v m is the mixture flow velocity, m/s; v sg is the gas meter Observe the flow rate, m/s; A is the cross-sectional area of the wellbore tubing, m 2 ; D is the inner diameter of the tubing, m.
    持液率HL和摩擦阻力系数λ采用Beggs-Brill方法计算，根据公式(17)得到井筒压力梯度，再根据井筒内边界相对距离累加得到各点与井底标准点间的压差值：The liquid holdup rate H L and the frictional resistance coefficient λ are calculated by the Beggs-Brill method. The wellbore pressure gradient is obtained according to formula (17), and then the pressure difference between each point and the bottom hole standard point is obtained according to the relative distance of the inner boundary of the wellbore:
    Figure PCTCN2015080767-appb-100017
    Figure PCTCN2015080767-appb-100017
    将得到的各点压差MPi进行无量纲化，即可获得各点无量纲压差MPiD。By obtaining the dimensionless difference MP i at each point, the dimensionless differential pressure MP iD at each point can be obtained.
    B，把步骤A中求出的内边界各点压差MPiD，带入到渗流模型中计算出井筒压力p’WD和裂缝流量Q’fi，井筒多相流模型与渗流模型的耦合条件如下：B. The pressure difference MP iD of the inner boundary obtained in step A is brought into the seepage model to calculate the wellbore pressure p' WD and the crack flow Q' fi . The coupling conditions of the wellbore multiphase flow model and the seepage model are as follows :
    地层与井筒交接面上：The interface between the formation and the wellbore:
    Figure PCTCN2015080767-appb-100018
    Figure PCTCN2015080767-appb-100018
    裂缝与井筒交接面上：Crack and wellbore interface:
    Figure PCTCN2015080767-appb-100019
    Figure PCTCN2015080767-appb-100019
    C，把前后迭代步计算得到的p’WD和pWD进行相减，当两者之间差的绝对值小于ε，则继续下一时间步的计算，当两者之差的绝对值大于或等于ε，则把当前得到的p’WD和Q’fi与前一步的值取平均后得到新的井筒压力pWD和裂缝流量Qfi，并带入到步骤A中进行迭代，直到得到的p’WD与pWD进行相减之差的绝对值小于ε，ε一般取值为10-4；C, subtracting p' WD and p WD calculated from the previous iteration step. When the absolute value of the difference between the two is less than ε, the calculation of the next time step is continued, when the absolute value of the difference between the two is greater than or Equal to ε, the current obtained p' WD and Q' fi are averaged with the value of the previous step to obtain a new wellbore pressure p WD and crack flow Q fi , and brought into step A for iteration until the obtained p ' The absolute value of the difference between WD and p WD is less than ε, and ε is generally 10 -4 ;
    D，把步骤C确定的p’WD和对应的Q’fi进行记录，若此时时间步k<总时间步n，则继续下一时间步的计算，根据当前的井筒压力pWD，裂缝流量Qfi，从步骤A开始计算得到新一轮的p’WD和Q’fi；D, the p' WD determined in step C and the corresponding Q' fi are recorded. If the time step k < total time step n, then the calculation of the next time step is continued, according to the current wellbore pressure p WD , the crack flow rate Q fi , starting from step A, a new round of p' WD and Q' fi is calculated;
    E，把步骤D中n次计算中所得到p’WD和Q’fi的值生成试井理论曲线。E. Generate a well test theoretical curve by the values of p' WD and Q' fi obtained in the n calculations in step D.
  6. 根据权利要求1所述的一种致密气压裂水平井数值试井模型建立求解方法，其特征在于，所述步骤五主要是理论曲线与实测曲线在双对数曲线图、半对数曲线图和全历史压力曲线图中对比拟合，根据曲线的拟合程度， 可进行拟合参数的调整，最终使理论曲线与实测曲线在双对数曲线图、半对数曲线图和全历史压力曲线图中都能够得到较好的吻合，曲线拟合才完成；曲线拟合完成后，即可以得到试井解释的参数，包括裂缝参数和储层参数。 The method for establishing a numerical well test model for a dense gas pressure crack horizontal well according to claim 1, wherein the step 5 is mainly a double logarithmic curve and a semi-logarithmic curve of the theoretical curve and the measured curve. Contrast fitting with the full historical pressure curve, according to the degree of fitting of the curve, The fitting parameters can be adjusted, and finally the theoretical curve and the measured curve can be well matched in the double logarithmic curve, the semi-logarithmic curve and the full historical pressure curve, and the curve fitting is completed; After the completion of the joint, the parameters of the well test interpretation, including the crack parameters and the reservoir parameters, can be obtained.
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CN117371361A (en) * 2023-12-08 2024-01-09 中国石油大学(华东) Dynamic simulation monitoring method for production of tight oil and gas reservoir fracturing horizontal well transformation system
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