CN104895550B - A kind of tight gas pressure break horizontal well numerical well testing model establishes method for solving - Google Patents

A kind of tight gas pressure break horizontal well numerical well testing model establishes method for solving Download PDF

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CN104895550B
CN104895550B CN201510308810.8A CN201510308810A CN104895550B CN 104895550 B CN104895550 B CN 104895550B CN 201510308810 A CN201510308810 A CN 201510308810A CN 104895550 B CN104895550 B CN 104895550B
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CN104895550A (en
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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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China National Petroleum Corp
CNPC Chuanqing Drilling Engineering Co Ltd
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Changqing Downhole Operation Co of CNPC Chuanqing Drilling Engineering Co Ltd
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Abstract

The invention provides a kind of tight gas pressure break horizontal well numerical well testing model to establish method for solving, comprises the following steps:Step 1:The two-dimentional geologic body of tight gas reservoir pressure break horizontal well and the generation of three-dimensional geologic;Step 2:To the tight gas reservoir pressure break horizontal well of generation, two-dimensionally to carry out grid discrete for plastid and three-dimensional geologic;Step 3:Flow model in porous media of the horizontal wellbore without pressure difference calculates;Step 4:Coupling model is established, and the coupling model of foundation is solved, and obtained solution is generated Well Testing Theory curve;Step 5:The theoretical curve obtained in step 4 is fitted with measured curve, obtains the parameter of well test analysis;With calculating speed is fast, curve matching is good, explanation results are accurate.

Description

A kind of tight gas pressure break horizontal well numerical well testing model establishes method for solving
Technical field
The method solved is established the present invention relates to a kind of tight gas pressure break horizontal well numerical well testing model, belongs to petroleum industry Oil/gas Well well testing field.
Background technology
Tight gas are as one of three big Unconventional gas, and stock number is enriched, and potentiality to be exploited is big.Tight gas reservoir has low Ooze, low pressure, low abundance the features such as, gas well natural production ability is low, it is necessary to just have commercial mining after reservoir reconstruction measure Value.Hydraulic fracturing technology and horizontal well technology are to improve the effective ways of tight gas reservoir production capacity.The exploitation of tight gas reservoir at present Generally use multistage pressure break horizontal well technology.
Tight gas reservoir pressure break horizontal well well test analysis is to obtain the important means of fracture parameters and reservoir parameter after pressure, and The effective ways directly verified to seepage flow mechanism.Due to answering for tight gas reservoir multistage pressure break horizontal well seepage flow mechanism and well type Polygamy, the country is not also specifically for the WELL TEST INTERPRETATION MODEL of tight gas reservoir pressure break horizontal well at present, mainly using routine business The multistage pressure break horizontal well analytic modell analytical model that software Saphir and EPS software is provided is analyzed to explain, and this is seriously affected The correct explanation of tight gas pressure break horizontal well well test data.
The problem of tight gas pressure break horizontal well well test analysis at present is primarily present:
1) in terms of Reservoir Seepage mechanism, the WELL TEST INTERPRETATION MODEL used at present do not account for tight gas reservoir stress sensitive, The non linear fluid flow through porous medium mechanism such as free-boundary problem.Conventional well test model based on Darcy linear seepage flow mechanism is not suitable for tight gas Hide.If directly tight gas reservoir pressure break horizontal well well test data is explained point using conventional pressure break horizontal well test model Analysis, it will the fitting to well test analysis brings difficulty, and the result for being fitted to obtain may also can have very big error.
2) in terms of reservoir, conventional well testing analytic modell analytical model assumes that reservoir is uniform dielectric, can not consider the non-of reservoir Homogenieity, but actual reservoir has obvious anisotropism, reservoir will certainly be to tight gas seepage flow and bottom pressure Response produces material impact, therefore does not consider that reservoir heterogeneity also can bring one to well test curve match and explanation results at present It is fixing to ring.
3) in terms of fractue spacing, conventional pressure break horizontal well well testing analytic modell analytical model can not handle the non-equidistant feelings in crack at present Condition, and the position of the pressure break of actual conditions is nearly all not equidistant, this also gives practical application band no small error.
4) pit shaft multiphase flow and well track aspect, it is more not account for pit shaft nearly all in WELL TEST INTERPRETATION MODEL at present The mutually influence of stream and well track.The exploitation of tight gas is generally with the output of dampening, and it is biphase gas and liquid flow in pit shaft to cause, gas Liquid two-phase can increase the flow resistance of downhole well fluid, cause pressure difference larger in pit shaft, so as to have influence on well test analysis knot Fruit.In addition, in the test of horizontal well well testing at present the usual tripping in of pressure gauge 10~20m more than kickoff point (KOP) position, distance is horizontal Well section has more than 500m distance.And in well test analysis, generally by the pressure measured by pressure gauge as horizontal wellbore section Pressure, this will certainly cause the error of well test analysis.The best method for solving this problem is exactly to establish to consider pit shaft multiphase flow And the pressure break horizontal well test model of real well track.
The content of the invention
The shortcomings that in order to overcome above-mentioned prior art, it is an object of the invention to provide a kind of calculating speed is fast, curve is intended Get togather, the accurate tight gas pressure break horizontal well numerical well testing model of explanation results establishes the method solved.
In order to achieve the above object, the technical scheme taken of the present invention is:A kind of tight gas pressure break horizontal well numerical well testing Model establishes method for solving, comprises the following steps:
Step 1:The two-dimentional geologic body of tight gas reservoir pressure break horizontal well and the generation of three-dimensional geologic;
Step 2:To the tight gas reservoir pressure break horizontal well of generation, two-dimensionally to carry out grid discrete for plastid and three-dimensional geologic;
Step 3:Flow model in porous media of the pit shaft without pressure difference calculates;
Step 4:Coupling model is established, and the coupling model of foundation is solved, and obtained solution generation well testing reason By curve;
Step 5:Say that the theoretical curve obtained in step 4 is fitted with measured curve, obtain the parameter of well test analysis.
The two-dimentional geologic body and three-dimensional geologic of tight gas reservoir pressure break horizontal well, specific steps are generated in described step one It is as follows:
1) according to residing for pressure break horizontal well geologic body external boundary, pit shaft inner boundary, crack and recombination region, then by setting Put inner and outer boundary and crack attribute determines the specific size and shape of geologic body, two-dimentional geologic body is established in drafting;
2) according to the two-dimentional constitution and well track of foundation and the position of reservoir up-and-down boundary, transported using solid boolean Calculate generation three-dimensional geologic.
Two-dimentional geologic body in described step two and three-dimensional geologic carry out that grid is discrete to be comprised the following steps that:
First, Netgen open source softwares are bundled into work(to be compiled, build running environment;
Then, the inner and outer boundary in two-dimentional geologic body and three-dimensional geologic is belonged to respectively according to Netgen grid file forms Requirement form two-dimensional grid file and three-dimensional grid file, according still further to the grid discrete step that Netgen is set carry out grid from Dissipate.
Flow model in porous media of the described horizontal wellbore without pressure difference calculates specific method:
1) stratum and the fisstured flow equation of stress sensitive are considered
Stratum filtration equation:
Fisstured flow equation:
Primary condition:
pD(x, y, z, 0)=0 (3)
Internal boundary condition:
Outer Boundary Conditions:
Closing:
Level pressure:
Symbol implication in formula:
pDRFor the dimensionless pressure of subterranean formation zone;pDfFor the dimensionless pressure of crack area;tDFor nondimensional time;CDL For dimensionless wellbore storage constant;KxDFor x directions dimensionless permeability;KyDFor y directions dimensionless permeability;KzDFor z directions without Dimension permeability;KfDFor dimensionless fracture permeabgility;γDFor dimensionless permeability modules;pwDHanded over for the first crack and pit shaft Dimensionless pressure at point;MPjDFor j point dimensionless pressures and pwDBetween difference;AjFor inner boundary triangle dimensionless area; hDFor dimensionless reservoir thickness;StFor wellbore skin coefficient;
2) equation solution
Conversion is firstly introduced into, nonlinear filtration equation is linearized, then is solved using finite element method, transformation for mula For:
The stratum after conversion and fisstured flow equations simultaneousness are solved using mixed finite element method, stratum and crack system The finite element equation of system is decomposed into the finite element equation (the right Section 1 of formula 9) of subterranean formation zone and represents the finite element of Fracture System Equation (the right Section 2 of formula 9).
A. subterranean formation zone three-dimensional finite element equation is:
B. fracture surface two dimensional finite element equation is:
By finite element equation (10)~(15) simultaneous composition system stiffness matrix, asked using the SuperLU numerical value of parallelization Solution device solves to large linear systems, can obtain the pressure field distribution and inner boundary normal pressure ladder of whole reservoir Degree, then thus calculate each crack production flow:
Symbol implication in formula:
η is transformation to linearity parameter;ηwFor the transformation parameter corresponding to dimensionless bottom pressure value;wfFor fracture width, m; wfDFor dimensionless fracture width;LjDFor crack inner boundary unit line length;V is tetrahedron volume;B, c, d are finite element coefficient; I, j, k, m are limited four summit sequence numbers of elementary tetrahedron;QfiFor the flow of the i-th crack, m3/d;QscFor the stream of gas well under mark condition Amount, m3/d。
Coupling model is established in described step four, and the coupling model of foundation is solved to enter according to following steps Capable:
A, the wellbore pressure p calculated according to step 4WDWith crack flow Qfi, entered using pit shaft multiphase flow calculation formula Row calculates, and obtains the dimensionless pressure difference MP of pit shaft each pointiD, specific formula is as follows:
The basic equation of pit shaft multiphase stream calculation is:
Symbol implication in formula:
ρLFor fluid density, kg/m3;ρgFor gas density, kg/m3;G is gas-liquid mixture mass flow, kg/s;vmIt is mixed Compound flowing velocity, m/s;vsgFor gas superficial flow velocity, m/s;A is pit shaft oil pipe sectional area, m2;D is pipe aperture, m.
Wherein liquid holdup HLCalculated with coefficient of frictional resistance λ using Beggs-Brill methods, well is obtained according to formula (17) Cylinder barometric gradient, the pressure difference between each point and shaft bottom standard point is obtained further according to pit shaft inner boundary relative distance is cumulative:
The each point pressure difference MP that will be obtainediCarry out nondimensionalization, you can obtain each point dimensionless pressure difference MPiD
B, the inner boundary each point pressure difference MP obtained in step AiD, it is brought into flow model in porous media and calculates wellbore pressure p 'WD With crack flow Q 'fi, the coupling condition of pit shaft multiphase flow model and flow model in porous media is as follows:
On stratum and pit shaft interface:
On crack and pit shaft interface:
C, the p ' that front and rear iteration step is calculatedWDAnd pWDSubtracted each other, when absolute value poor between the two is less than ε, then Continue the calculating of future time step, when the absolute value of both differences is more than or equal to ε, then currently available p 'WDAnd Q 'fiWith The value of back obtains new wellbore pressure pWD and crack flow Q after being averagedfi, and be brought into step A and be iterated, directly To obtained p 'WDWith pWDThe absolute value of the difference subtract each other is less than ε, and the general values of ε are 10-4
D, the p ' that step C is determinedWDWith corresponding Q 'fiRecorded, if now time step k<Total time walks n, then continues The calculating of future time step, according to current wellbore pressure pWD, crack flow Qfi, a new round is calculated since step A p’WDAnd Q 'fi
E, resulting p ' in n computations in step DWDAnd Q 'fiValue generation Well Testing Theory curve.
The step 5 is mainly theoretical curve and measured curve in log-log graph, semilogarithmic plot and full history In pressue-graph contrast fitting, according to the fitting degree of curve, the adjustment of parameter can be fitted, finally make theoretical curve with Measured curve can access in log-log graph, semilogarithmic plot and full historical pressures curve map preferably to coincide, Curve matching is just completed;After the completion of curve matching, you can to obtain the parameter of well test analysis, including fracture parameters and reservoir ginseng Number.
The present invention uses above technical scheme, has advantages below, with calculating speed is fast, curve matching is good, explains knot Fruit is accurate.
Brief description of the drawings
Fig. 1 considers that the pressure break horizontal well three-dimensional geologic and grid of well track and reservoir heterogeneity are discrete;
The flow chart that Fig. 2 coupling models are established and solved.
Embodiment
The present invention is described in detail with reference to the accompanying drawings and examples.
Embodiment 1
A kind of tight gas pressure break horizontal well numerical well testing model as shown in Figure 2 establishes method for solving, comprises the following steps:
Step 1:The two-dimentional geologic body of tight gas reservoir pressure break horizontal well and the generation of three-dimensional geologic;Mainly
1) according to residing for pressure break horizontal well geologic body external boundary, pit shaft inner boundary, crack and recombination region, then by setting Put inner and outer boundary and crack attribute determines the specific size and shape of geologic body, two-dimentional geologic body is established in drafting;
2) according to the two-dimentional constitution and well track of foundation and the position of reservoir up-and-down boundary, transported using solid boolean Calculate generation three-dimensional geologic.
Step 2:As shown in Figure 1 to tight gas reservoir pressure break horizontal well two-dimensionally plastid and the three-dimensional geologic progress of generation Grid is discrete;First, Netgen open source softwares are bundled into work(to be compiled, build running environment;
Then, the inner and outer boundary in two-dimentional geologic body and three-dimensional geologic is belonged to respectively according to Netgen grid file forms Requirement form two-dimensional grid file and three-dimensional grid file, according still further to the grid discrete step that Netgen is set carry out grid from Dissipate.
Step 3:Flow model in porous media of the horizontal wellbore without pressure difference calculates;
1) stratum and the fisstured flow equation of stress sensitive are considered
Stratum filtration equation:
Fisstured flow equation:
Primary condition:
pD(x, y, z, 0)=0 (3)
Internal boundary condition:
Outer Boundary Conditions:
Closing:
Level pressure:
Symbol implication in formula:
pDRFor the dimensionless pressure of subterranean formation zone;pDfFor the dimensionless pressure of crack area;tDFor nondimensional time;CDL For dimensionless wellbore storage constant;KxDFor x directions dimensionless permeability;KyDFor y directions dimensionless permeability;KzDFor z directions without Dimension permeability;KfDFor dimensionless fracture permeabgility;γDFor dimensionless permeability modules;pwDHanded over for the first crack and pit shaft Dimensionless pressure at point;MPjDFor j point dimensionless pressures and pwDBetween difference;AjFor inner boundary triangle dimensionless area; hDFor dimensionless reservoir thickness;StFor wellbore skin coefficient;
2) equation solution
Conversion is firstly introduced into, nonlinear filtration equation is linearized, then is solved using finite element method, transformation for mula For:
The stratum after conversion and fisstured flow equations simultaneousness are solved using mixed finite element method, stratum and crack system The finite element equation of system is decomposed into the finite element equation (the right Section 1 of formula 9) of subterranean formation zone and represents the finite element of Fracture System Equation (the right Section 2 of formula 9).
A. subterranean formation zone three-dimensional finite element equation is:
B. fracture surface two dimensional finite element equation is:
By finite element equation (10)~(15) simultaneous composition system stiffness matrix, asked using the SuperLU numerical value of parallelization Solution device solves to large linear systems, can obtain the pressure field distribution and inner boundary normal pressure ladder of whole reservoir Degree, then thus calculate each crack production flow:
Symbol implication in formula:
η is transformation to linearity parameter;ηwFor the transformation parameter corresponding to dimensionless bottom pressure value;wfFor fracture width, m; wfDFor dimensionless fracture width;LjDFor crack inner boundary unit line length;V is tetrahedron volume;B, c, d are finite element coefficient; I, j, k, m are limited four summit sequence numbers of elementary tetrahedron;QfiFor the flow of the i-th crack, m3/d;QscFor the stream of gas well under mark condition Amount, m3/d。
Step 4:Coupling model is established, and the coupling model of foundation is solved, and obtained solution generation well testing reason By curve;And the coupling model of foundation is carried out solving what is followed the steps below:
A, the wellbore pressure p calculated according to step 4WDWith crack flow Qfi, entered using pit shaft multiphase flow calculation formula Row calculates, and obtains the dimensionless pressure difference MP of pit shaft each pointiD, specific formula is as follows:
The basic equation of pit shaft multiphase stream calculation is:
Symbol implication in formula:
ρLFor fluid density, kg/m3;ρgFor gas density, kg/m3;G is gas-liquid mixture mass flow, kg/s;vmIt is mixed Compound flowing velocity, m/s;vsgFor gas superficial flow velocity, m/s;A is pit shaft oil pipe sectional area, m2;D is pipe aperture, m.
Wherein liquid holdup HLCalculated with coefficient of frictional resistance λ using Beggs-Brill methods, well is obtained according to formula (17) Cylinder barometric gradient, the pressure difference between each point and shaft bottom standard point is obtained further according to pit shaft inner boundary relative distance is cumulative:
The each point pressure difference MP that will be obtainediCarry out nondimensionalization, you can obtain each point dimensionless pressure difference MPiD
B, the inner boundary each point pressure difference MP obtained in step AiD, it is brought into flow model in porous media and calculates wellbore pressure p 'WD With crack flow Q 'fi, the coupling condition of pit shaft multiphase flow model and flow model in porous media is as follows:
On stratum and pit shaft interface:
On crack and pit shaft interface:
C, the p ' that front and rear iteration step is calculatedWDAnd pWDSubtracted each other, when absolute value poor between the two is less than ε, then Continue the calculating of future time step, when the absolute value of both differences is more than or equal to ε, then currently available p 'WDAnd Q 'fiWith The value of back obtains new wellbore pressure p after being averagedWDWith crack flow Qfi, and be brought into step A and be iterated, directly To obtained p 'WDWith pWDThe absolute value of the difference subtract each other is less than ε, and the general values of ε are 10-4
D, the p ' that step C is determinedWDWith corresponding Q 'fiRecorded, if now time step k<Total time walks n, then continues The calculating of future time step, according to current wellbore pressure pWD, crack flow Qfi, a new round is calculated since step A p’WDAnd Q 'fi
E, resulting p ' in n computations in step DWDAnd Q 'fiValue generation Well Testing Theory curve.Step 5:Say step The theoretical curve obtained in four is fitted with measured curve, obtains the parameter of well test analysis;
The step 5 is mainly theoretical curve and measured curve in log-log graph, semilogarithmic plot and full history In pressue-graph contrast fitting, according to the fitting degree of curve, the adjustment of parameter can be fitted, finally make theoretical curve with Measured curve can access in log-log graph, semilogarithmic plot and full historical pressures curve map preferably to coincide, Curve matching is just completed;After the completion of curve matching, you can to obtain the parameter of well test analysis, including fracture parameters and reservoir ginseng Number.
Embodiment 2
1. realize that tight gas reservoir pressure break horizontal well geologic body quickly generates
Two-dimentional geologic body is initially set up, then three-dimensional geologic is converted to by two-dimentional geologic body.By writing software geometric graph The code that shape is drawn, realize the external boundary, pit shaft inner boundary, crack and recombination region etc. for drawing geologic body residing for pressure break horizontal well Function, then by setting inner and outer boundary and crack attribute to determine the specific size and shape of geologic body, in this way may be used Quickly establish two-dimentional geologic body.By two-dimentional geologic body, with reference to the position of well track and reservoir up-and-down boundary, solid is utilized Boolean calculation can directly generate three-dimensional geologic, and carrying out 3-D view using OpenCasCade instruments shows, as shown in Figure 1 Three-dimensional geologic.
2. realize two-dimentional geologic body and the automatic discrete functionality of three-dimensional geological volume mesh
Netgen open source softwares are bundled into work(first to be compiled, build running environment, then by two-dimentional geologic body Inner and outer boundary attribute forms two-dimensional grid file according to the requirement of Netgen grid file forms, the net set according still further to Netgen It is discrete that lattice discrete step carries out grid.The departure process of three-dimensional geologic is similar with the departure process of two-dimentional geologic body, different It is that three-dimensional grid is discrete to need three-dimensional geologic output to be common format (such as STEP forms) first, then it is defeated to this using Netgen The file progress grid for going out form is discrete.The discrete time of two-dimentional geologic body is shorter, required time typically 10s~30s it Between, the discrete time of three-dimensional geologic is longer, need to be depending on the discrete density of grid, and usual discrete time is no more than 5 minutes. Automatically discrete mesh node and grid lines are shown after grid is discrete, as shown in Figure 1.
3. WELL TEST INTERPRETATION MODEL is established, the type of partitioning model parameter
According to the type of flow involved by pressure break horizontal well, the WELL TEST INTERPRETATION MODEL for considering various factors coupling is established.Will Involved parameter is divided into known parameters and unknown parameter (parameter to be explained) in model, it is known that parameter should with unknown parameter Different input interfaces is set, in order to avoid obscure.Known parameters input according to actual conditions, and unknown parameter can be complete in curve matching Into rear determination.
4. the code of compiling model numerical solution, implementation model rapid solving
After having established WELL TEST INTERPRETATION MODEL, according to model feature, the numerical solution algorithm to design a model, compiling model numerical value The computer code of solution, model solution flow chart as shown in Figure 2.Basic data is inputted first, establishes model of geological structure body, will It is discrete that model of geological structure body carries out grid.Initial step carries out flow model in porous media calculating in the way of pit shaft is without pressure difference, is calculated just The flowing bottomhole pressure (FBHP) of beginning and each crack flow distribution, the pressure difference point of pit shaft is calculated using pit shaft multiphase flow calculation model according to this result Cloth, then thus pressure difference carries out flow model in porous media calculating, new bottom pressure and crack flow distribution is obtained, with result of calculation before Contrast judges whether the iteration of the time step terminates.The calculating of next time step is carried out if both differences are less than a small amount of ε, it is on the contrary Then continue iteration, untill stabilization after carry out the calculating of future time step again.When being finally completed all settings using the method The calculating of spacer step, that is, complete the solution to coupling model.
5. carry out measured curve to be fitted with theoretical curve
After the completion of model solution, Well Testing Theory curve is automatically generated, by theoretical curve and measured curve in double logarithmic curve Fitting is contrasted in figure, semilogarithmic plot and full historical pressures curve map.Log-log graph is in front view, and semilog is bent Line chart and full historical pressures curve map, according to the fitting degree of curve, can be fitted the adjustment of parameter in auxiliary view area. It is final to make theoretical curve in log-log graph, semilogarithmic plot and full historical pressures curve map with measured curve Preferably it is coincide, curve matching is just completed, after the completion of curve matching, you can to obtain the parameter of well test analysis, including split Stitch parameter and reservoir parameter.
Embodiment 3
1) tight gas reservoir pressure break horizontal well two and three dimensions geologic body quickly generates and display methods;
Two-dimentional geologic body is initially set up, then three-dimensional geologic is converted to by two-dimentional geologic body.According to Horizontal Well Log Interpretation As a result the Heterogeneous Characteristics of reservoir, including porosity, gas saturation and original permeability distribution are set, drawn in geologic body Point different regions, each one isotropic body of Regional Representative, each isotropic body have different porositys, water saturation and just Beginning permeability, the anisotropism of whole geological system is made up of many different isotropic bodies.Isotropic body number is more, parameter differences Bigger, then the anisotropism of geologic body is stronger;By two-dimentional geologic body, in conjunction with the position of well track and reservoir up-and-down boundary Put, three-dimensional geologic can be directly generated;In order to preferably carry out the display of three-dimensional geologic, entered based on OpenCasCade instruments The comprehensive display of row 3-D view, display content include three-dimensional geologic, the discrete figure of grid, calculate cloud atlas etc..
2) the automatic discrete realization of tight gas reservoir pressure break horizontal well grid;
The geologic body of generation is converted into STEP formatted files, IGES formatted files or BREP formatted files, then adopted The automatic discrete functionality of the grid of two-dimentional geologic body and three-dimensional geologic is realized with Netgen Open-Source Tools, two-dimensional grid is triangle Grid, three-dimensional grid are tetrahedral grid.The characteristics of for pressure break horizontal well well testing problem, by setting in grid departure process The grid near the next automatic Encryption Well cylinder of quantity and crack in crack and the discrete node of pit shaft is put, by setting grid discrete parameter To control the discrete quality of grid.Grid is more intensive, and grid amount is more, and the grid discrete time is longer, the time required to calculating It is longer, and grid amount is too small influences whether computational accuracy, therefore actual conditions should select moderate mesh-density.Normal conditions Between lower two-dimensional grid amount is 10,000~30,000, between three-dimensional grid amount is 100,000~500,000.
3) foundation of tight gas reservoir pressure break horizontal well stratum filtration and pit shaft multiphase flow coupling model;
Tight gas reservoir pressure break horizontal well is divided into three flow regions:Pit shaft, crack and stratum.The flowing of different zones Mechanism is different, and pit shaft is biphase gas and liquid flow, and crack be high speed non-darcy flow, and stratum is that non-linear with stress sensitive oozes Stream.Tight gas pressure break horizontal well seepage flow characteristics are primarily based on, see crack area as Thief zone high speed non-darcy flow region, by In fracture width very little, the flowing of crack area fluid is considered as two-dimensional flow, establishes a kind of pressure break horizontal well two Dimension Numerical Value well testing mould Type and three-dimensional numerical value well test model;Two dimensional model is mainly used in horizontal wellbore with the situation of barrel forms completion, and threedimensional model Situation for horizontal wellbore completion in a manner of bore hole;Pit shaft biphase gas and liquid flow is considered further that on the basis of the flow model in porous media, is adopted The flow resistance computational methods of pit shaft biphase gas and liquid flow are established with Beggs-Brill methods;Flow model in porous media and pit shaft multiphase flow mould Type couples according to stratum with the continuous mode of pressure on pit shaft contact surface.
4) fast solution method of tight gas reservoir pressure break horizontal well coupling model.
Numerical solution is carried out to model using mixed finite element method, by flow model in porous media and pit shaft gas-liquid two-phase stream calculation mould Type carries out coupling iterative calculation.According to the characteristics of well testing flow model in porous media, timing node will be calculated and be arranged to log series model, it is each right 10~20 calculating points are set in one number time, and the initial time of calculating and termination time can adjust according to actual conditions.Each The condition that time step iteration terminates is that result of calculation had not only met flow model in porous media but also met pit shaft multiphase flow calculation model.Utilize SuperLU solvers solve to the system of linear equations of two dimensional model, using the SuperLU solvers of parallelization to three-dimensional mould The system of linear equations of type is solved, and the Thread Count that parallel computation uses determines according to the grid amount of calculating, under normal circumstances Parallel line number of passes, which is arranged to 6~10, can meet calculating demand.
5. carry out measured curve to be fitted with theoretical curve
After the completion of model solution, Well Testing Theory curve is automatically generated, by theoretical curve and measured curve in double logarithmic curve Fitting is contrasted in figure, semilogarithmic plot and full historical pressures curve map.Log-log graph is in front view, and semilog is bent Line chart and full historical pressures curve map, according to the fitting degree of curve, can be fitted the adjustment of parameter in auxiliary view area. It is final to make theoretical curve in log-log graph, semilogarithmic plot and full historical pressures curve map with measured curve Preferably it is coincide, curve matching is just completed, after the completion of curve matching, you can to obtain the parameter of well test analysis, including split Stitch parameter and reservoir parameter.
It is exemplified as above be only to the present invention for example, do not form the limitation to protection scope of the present invention, it is all It is to be belonged to the same or analogous design of the present invention within protection scope of the present invention.

Claims (5)

1. a kind of tight gas pressure break horizontal well numerical well testing model establishes method for solving, it is characterised in that comprises the following steps:
Step 1:The two-dimentional geologic body of tight gas reservoir pressure break horizontal well and the generation of three-dimensional geologic;
Step 2:To the tight gas reservoir pressure break horizontal well of generation, two-dimensionally to carry out grid discrete for plastid and three-dimensional geologic;
Step 3:Flow model in porous media of the pit shaft without pressure difference calculates;
Step 4:Coupling model is established, and the coupling model of foundation is solved, and obtained solution is generated Well Testing Theory song Line;
Step 5:The Well Testing Theory curve obtained in step 4 is fitted with measured curve, obtains the parameter of well test analysis;
Flow model in porous media calculating specific method of the pit shaft without pressure difference is in described step three:
1) stratum and the fisstured flow equation of stress sensitive are considered
Stratum filtration equation:
<mrow> <mtable> <mtr> <mtd> <mrow> <msub> <mi>K</mi> <mrow> <mi>x</mi> <mi>D</mi> </mrow> </msub> <mfrac> <mrow> <msup> <mo>&amp;part;</mo> <mn>2</mn> </msup> <msub> <mi>p</mi> <mrow> <mi>D</mi> <mi>R</mi> </mrow> </msub> </mrow> <mrow> <mo>&amp;part;</mo> <msubsup> <mi>x</mi> <mi>D</mi> <mn>2</mn> </msubsup> </mrow> </mfrac> <mo>+</mo> <msub> <mi>K</mi> <mrow> <mi>y</mi> <mi>D</mi> </mrow> </msub> <mfrac> <mrow> <msup> <mo>&amp;part;</mo> <mn>2</mn> </msup> <msub> <mi>p</mi> <mrow> <mi>D</mi> <mi>R</mi> </mrow> </msub> </mrow> <mrow> <mo>&amp;part;</mo> <msubsup> <mi>y</mi> <mi>D</mi> <mn>2</mn> </msubsup> </mrow> </mfrac> <mo>+</mo> <msub> <mi>K</mi> <mrow> <mi>z</mi> <mi>D</mi> </mrow> </msub> <mfrac> <mrow> <msup> <mo>&amp;part;</mo> <mn>2</mn> </msup> <msub> <mi>p</mi> <mrow> <mi>D</mi> <mi>R</mi> </mrow> </msub> </mrow> <mrow> <mo>&amp;part;</mo> <msubsup> <mi>z</mi> <mi>D</mi> <mn>2</mn> </msubsup> </mrow> </mfrac> <mo>-</mo> <msub> <mi>K</mi> <mrow> <mi>x</mi> <mi>D</mi> </mrow> </msub> <msub> <mi>&amp;gamma;</mi> <mi>D</mi> </msub> <msup> <mrow> <mo>(</mo> <mfrac> <mrow> <mo>&amp;part;</mo> <msub> <mi>p</mi> <mrow> <mi>D</mi> <mi>R</mi> </mrow> </msub> </mrow> <mrow> <mo>&amp;part;</mo> <msub> <mi>x</mi> <mi>D</mi> </msub> </mrow> </mfrac> <mo>)</mo> </mrow> <mn>2</mn> </msup> </mrow> </mtd> </mtr> <mtr> <mtd> <mrow> <mo>-</mo> <msub> <mi>K</mi> <mrow> <mi>y</mi> <mi>D</mi> </mrow> </msub> <msub> <mi>&amp;gamma;</mi> <mi>D</mi> </msub> <msup> <mrow> <mo>(</mo> <mfrac> <mrow> <mo>&amp;part;</mo> <msub> <mi>p</mi> <mrow> <mi>D</mi> <mi>R</mi> </mrow> </msub> </mrow> <mrow> <mo>&amp;part;</mo> <msub> <mi>y</mi> <mi>D</mi> </msub> </mrow> </mfrac> <mo>)</mo> </mrow> <mn>2</mn> </msup> <mo>-</mo> <msub> <mi>K</mi> <mrow> <mi>z</mi> <mi>D</mi> </mrow> </msub> <msub> <mi>&amp;gamma;</mi> <mi>D</mi> </msub> <msup> <mrow> <mo>(</mo> <mfrac> <mrow> <mo>&amp;part;</mo> <msub> <mi>p</mi> <mrow> <mi>D</mi> <mi>R</mi> </mrow> </msub> </mrow> <mrow> <mo>&amp;part;</mo> <msub> <mi>z</mi> <mi>D</mi> </msub> </mrow> </mfrac> <mo>)</mo> </mrow> <mn>2</mn> </msup> <mo>=</mo> <mfrac> <msup> <mi>e</mi> <mrow> <msub> <mi>&amp;gamma;</mi> <mi>D</mi> </msub> <msub> <mi>p</mi> <mrow> <mi>D</mi> <mi>R</mi> </mrow> </msub> </mrow> </msup> <msub> <mi>K</mi> <mrow> <mi>l</mi> <mi>D</mi> </mrow> </msub> </mfrac> <mfrac> <mrow> <mo>&amp;part;</mo> <msub> <mi>p</mi> <mrow> <mi>D</mi> <mi>R</mi> </mrow> </msub> </mrow> <mrow> <mo>&amp;part;</mo> <msub> <mi>t</mi> <mi>D</mi> </msub> </mrow> </mfrac> </mrow> </mtd> </mtr> </mtable> <mo>-</mo> <mo>-</mo> <mo>-</mo> <mrow> <mo>(</mo> <mn>1</mn> <mo>)</mo> </mrow> </mrow>
Fisstured flow equation:
<mrow> <mfrac> <mrow> <msup> <mo>&amp;part;</mo> <mn>2</mn> </msup> <msub> <mi>p</mi> <mrow> <mi>D</mi> <mi>f</mi> </mrow> </msub> </mrow> <mrow> <mo>&amp;part;</mo> <msubsup> <mi>y</mi> <mi>D</mi> <mn>2</mn> </msubsup> </mrow> </mfrac> <mo>+</mo> <mfrac> <mrow> <msup> <mo>&amp;part;</mo> <mn>2</mn> </msup> <msub> <mi>p</mi> <mrow> <mi>D</mi> <mi>f</mi> </mrow> </msub> </mrow> <mrow> <mo>&amp;part;</mo> <msubsup> <mi>z</mi> <mi>D</mi> <mn>2</mn> </msubsup> </mrow> </mfrac> <mo>=</mo> <mfrac> <mn>1</mn> <msub> <mi>K</mi> <mrow> <mi>f</mi> <mi>D</mi> </mrow> </msub> </mfrac> <mfrac> <mrow> <mo>&amp;part;</mo> <msub> <mi>p</mi> <mrow> <mi>D</mi> <mi>f</mi> </mrow> </msub> </mrow> <mrow> <mo>&amp;part;</mo> <msub> <mi>t</mi> <mi>D</mi> </msub> </mrow> </mfrac> <mo>-</mo> <mo>-</mo> <mo>-</mo> <mrow> <mo>(</mo> <mn>2</mn> <mo>)</mo> </mrow> </mrow>
Primary condition:
pD(x, y, z, 0)=0 (3)
Internal boundary condition:
<mrow> <munderover> <mo>&amp;Sigma;</mo> <mrow> <mi>j</mi> <mo>=</mo> <mn>1</mn> </mrow> <mi>N</mi> </munderover> <msub> <mi>A</mi> <mi>j</mi> </msub> <msub> <mi>K</mi> <mrow> <mi>j</mi> <mi>D</mi> </mrow> </msub> <msup> <mi>e</mi> <mrow> <mo>-</mo> <msub> <mi>&amp;gamma;</mi> <mi>D</mi> </msub> <msub> <mi>p</mi> <mrow> <mi>j</mi> <mi>D</mi> </mrow> </msub> </mrow> </msup> <mrow> <mo>(</mo> <mfrac> <mrow> <mo>&amp;part;</mo> <msub> <mi>p</mi> <mrow> <mi>j</mi> <mi>D</mi> </mrow> </msub> </mrow> <mrow> <mo>&amp;part;</mo> <msup> <mi>n</mi> <mo>&amp;prime;</mo> </msup> </mrow> </mfrac> <mo>)</mo> </mrow> <msub> <mo>|</mo> <msub> <mi>&amp;Gamma;</mi> <mrow> <mi>i</mi> <mi>n</mi> </mrow> </msub> </msub> <mo>=</mo> <mn>2</mn> <msub> <mi>&amp;pi;h</mi> <mi>D</mi> </msub> <mrow> <mo>(</mo> <mn>1</mn> <mo>-</mo> <msub> <mi>C</mi> <mrow> <mi>D</mi> <mi>L</mi> </mrow> </msub> <mfrac> <mrow> <msub> <mi>dp</mi> <mrow> <mi>w</mi> <mi>D</mi> </mrow> </msub> </mrow> <mrow> <msub> <mi>dt</mi> <mi>D</mi> </msub> </mrow> </mfrac> <mo>)</mo> </mrow> <mo>-</mo> <mo>-</mo> <mo>-</mo> <mrow> <mo>(</mo> <mn>4</mn> <mo>)</mo> </mrow> </mrow>
<mrow> <msub> <mi>p</mi> <mrow> <mi>w</mi> <mi>D</mi> </mrow> </msub> <mrow> <mo>(</mo> <msub> <mi>t</mi> <mi>D</mi> </msub> <mo>)</mo> </mrow> <mo>=</mo> <msub> <mi>p</mi> <mrow> <mi>j</mi> <mi>D</mi> </mrow> </msub> <mo>-</mo> <msub> <mi>S</mi> <mi>t</mi> </msub> <mfrac> <mrow> <munderover> <mo>&amp;Sigma;</mo> <mrow> <mi>j</mi> <mo>=</mo> <mn>1</mn> </mrow> <mi>N</mi> </munderover> <msub> <mi>A</mi> <mrow> <mi>j</mi> <mi>D</mi> </mrow> </msub> <msub> <mi>K</mi> <mrow> <mi>j</mi> <mi>D</mi> </mrow> </msub> <msup> <mi>e</mi> <mrow> <mo>-</mo> <msub> <mi>&amp;gamma;</mi> <mi>D</mi> </msub> <msub> <mi>p</mi> <mrow> <mi>j</mi> <mi>D</mi> </mrow> </msub> </mrow> </msup> </mrow> <mrow> <mn>2</mn> <msub> <mi>&amp;pi;h</mi> <mi>D</mi> </msub> </mrow> </mfrac> <mrow> <mo>(</mo> <mfrac> <mrow> <mo>&amp;part;</mo> <msub> <mi>p</mi> <mrow> <mi>j</mi> <mi>D</mi> </mrow> </msub> </mrow> <mrow> <mo>&amp;part;</mo> <msup> <mi>n</mi> <mo>&amp;prime;</mo> </msup> </mrow> </mfrac> <mo>)</mo> </mrow> <mo>-</mo> <msub> <mi>MP</mi> <mrow> <mi>j</mi> <mi>D</mi> </mrow> </msub> <mo>-</mo> <mo>-</mo> <mo>-</mo> <mrow> <mo>(</mo> <mn>5</mn> <mo>)</mo> </mrow> </mrow>
Outer Boundary Conditions:
Closing:
Level pressure:
Symbol implication in formula:
pDRFor the dimensionless pressure of subterranean formation zone;pDfFor the dimensionless pressure of crack area;tDFor nondimensional time;CDLTo be immeasurable Guiding principle wellbore storage constant;KxDFor x directions dimensionless permeability;KyDFor y directions dimensionless permeability;KzDOozed for z directions dimensionless Saturating rate;KfDFor dimensionless fracture permeabgility;γDFor dimensionless permeability modules;pwDFor the first crack and pit shaft point of intersection Dimensionless pressure;MPjDFor j point dimensionless pressures and pwDBetween difference;AjFor inner boundary triangle dimensionless area;hDFor nothing Dimension reservoir thickness;StFor wellbore skin coefficient;
2) equation solution
Conversion is firstly introduced into, nonlinear filtration equation is linearized, then is solved using finite element method, transformation for mula is:
<mrow> <msub> <mi>p</mi> <mi>D</mi> </msub> <mo>=</mo> <mo>-</mo> <mfrac> <mn>1</mn> <msub> <mi>&amp;gamma;</mi> <mi>D</mi> </msub> </mfrac> <mi>l</mi> <mi>n</mi> <mrow> <mo>(</mo> <mn>1</mn> <mo>-</mo> <msub> <mi>&amp;gamma;</mi> <mi>D</mi> </msub> <mi>&amp;eta;</mi> <mo>)</mo> </mrow> <mo>-</mo> <mo>-</mo> <mo>-</mo> <mrow> <mo>(</mo> <mn>8</mn> <mo>)</mo> </mrow> </mrow>
The stratum after conversion and fisstured flow equations simultaneousness are solved using mixed finite element method, stratum and Fracture System Finite element equation is decomposed into the right Section 1 of finite element equation formula 9 of subterranean formation zone and represents the finite element equation formula of Fracture System 9 the right Section 2;
<mrow> <mo>&amp;Integral;</mo> <mo>&amp;Integral;</mo> <msub> <mo>&amp;Integral;</mo> <mi>&amp;Omega;</mi> </msub> <mi>F</mi> <mi>E</mi> <mi>Q</mi> <mi>d</mi> <mi>&amp;Omega;</mi> <mo>=</mo> <mo>&amp;Integral;</mo> <mo>&amp;Integral;</mo> <msub> <mo>&amp;Integral;</mo> <msub> <mi>&amp;Omega;</mi> <mi>m</mi> </msub> </msub> <msub> <mi>FEQd&amp;Omega;</mi> <mi>m</mi> </msub> <mo>+</mo> <msub> <mi>w</mi> <mi>f</mi> </msub> <mo>&amp;CenterDot;</mo> <mo>&amp;Integral;</mo> <msub> <mo>&amp;Integral;</mo> <mover> <msub> <mi>&amp;Omega;</mi> <mi>f</mi> </msub> <mo>&amp;OverBar;</mo> </mover> </msub> <mi>F</mi> <mi>E</mi> <mi>Q</mi> <mi>d</mi> <mover> <msub> <mi>&amp;Omega;</mi> <mi>f</mi> </msub> <mo>&amp;OverBar;</mo> </mover> <mo>-</mo> <mo>-</mo> <mo>-</mo> <mrow> <mo>(</mo> <mn>9</mn> <mo>)</mo> </mrow> </mrow>
A. subterranean formation zone three-dimensional finite element equation is:
<mrow> <mtable> <mtr> <mtd> <mrow> <msub> <mi>VK</mi> <mrow> <mi>L</mi> <mi>D</mi> </mrow> </msub> <mrow> <mo>(</mo> <msub> <mi>K</mi> <mrow> <mi>x</mi> <mi>D</mi> </mrow> </msub> <msubsup> <mi>b</mi> <mi>i</mi> <mn>2</mn> </msubsup> <mo>+</mo> <msub> <mi>K</mi> <mrow> <mi>y</mi> <mi>D</mi> </mrow> </msub> <msubsup> <mi>c</mi> <mi>i</mi> <mn>2</mn> </msubsup> <mo>+</mo> <msub> <mi>K</mi> <mrow> <mi>z</mi> <mi>D</mi> </mrow> </msub> <msubsup> <mi>d</mi> <mi>i</mi> <mn>2</mn> </msubsup> <mo>+</mo> <mfrac> <mn>1</mn> <mrow> <mn>10</mn> <msub> <mi>K</mi> <mrow> <mi>L</mi> <mi>D</mi> </mrow> </msub> <msub> <mi>&amp;Delta;t</mi> <mi>D</mi> </msub> </mrow> </mfrac> <mo>)</mo> </mrow> <msubsup> <mi>&amp;eta;</mi> <mi>i</mi> <mrow> <mi>e</mi> <mo>,</mo> <mi>n</mi> <mo>+</mo> <mn>1</mn> </mrow> </msubsup> <mo>+</mo> <msub> <mi>VK</mi> <mrow> <mi>L</mi> <mi>D</mi> </mrow> </msub> <mfenced open = "(" close = ")"> <mtable> <mtr> <mtd> <mrow> <msub> <mi>K</mi> <mrow> <mi>x</mi> <mi>D</mi> </mrow> </msub> <msub> <mi>b</mi> <mi>i</mi> </msub> <msub> <mi>b</mi> <mi>j</mi> </msub> <mo>+</mo> <msub> <mi>K</mi> <mrow> <mi>y</mi> <mi>D</mi> </mrow> </msub> <msub> <mi>c</mi> <mi>i</mi> </msub> <msub> <mi>c</mi> <mi>j</mi> </msub> <mo>+</mo> <msub> <mi>K</mi> <mrow> <mi>z</mi> <mi>D</mi> </mrow> </msub> <msub> <mi>d</mi> <mi>i</mi> </msub> <msub> <mi>d</mi> <mi>j</mi> </msub> </mrow> </mtd> </mtr> <mtr> <mtd> <mrow> <mo>+</mo> <mfrac> <mn>1</mn> <mrow> <mn>20</mn> <msub> <mi>K</mi> <mrow> <mi>L</mi> <mi>D</mi> </mrow> </msub> <msub> <mi>&amp;Delta;t</mi> <mi>D</mi> </msub> </mrow> </mfrac> </mrow> </mtd> </mtr> </mtable> </mfenced> <msubsup> <mi>&amp;eta;</mi> <mi>j</mi> <mrow> <mi>e</mi> <mo>,</mo> <mi>n</mi> <mo>+</mo> <mn>1</mn> </mrow> </msubsup> </mrow> </mtd> </mtr> <mtr> <mtd> <mrow> <mo>+</mo> <msub> <mi>VK</mi> <mrow> <mi>L</mi> <mi>D</mi> </mrow> </msub> <mrow> <mo>(</mo> <msub> <mi>K</mi> <mrow> <mi>x</mi> <mi>D</mi> </mrow> </msub> <msub> <mi>b</mi> <mi>i</mi> </msub> <msub> <mi>b</mi> <mi>k</mi> </msub> <mo>+</mo> <msub> <mi>K</mi> <mrow> <mi>y</mi> <mi>D</mi> </mrow> </msub> <msub> <mi>c</mi> <mi>i</mi> </msub> <msub> <mi>c</mi> <mi>k</mi> </msub> <mo>+</mo> <msub> <mi>K</mi> <mrow> <mi>z</mi> <mi>D</mi> </mrow> </msub> <msub> <mi>d</mi> <mi>i</mi> </msub> <msub> <mi>d</mi> <mi>k</mi> </msub> <mo>+</mo> <mfrac> <mn>1</mn> <mrow> <mn>20</mn> <msub> <mi>K</mi> <mrow> <mi>L</mi> <mi>D</mi> </mrow> </msub> <msub> <mi>&amp;Delta;t</mi> <mi>D</mi> </msub> </mrow> </mfrac> <mo>)</mo> </mrow> <msubsup> <mi>&amp;eta;</mi> <mi>k</mi> <mrow> <mi>e</mi> <mo>,</mo> <mi>n</mi> <mo>+</mo> <mn>1</mn> </mrow> </msubsup> <mo>+</mo> <msub> <mi>VK</mi> <mi>L</mi> </msub> <mfenced open = "(" close = ")"> <mtable> <mtr> <mtd> <mrow> <msub> <mi>K</mi> <mrow> <mi>x</mi> <mi>D</mi> </mrow> </msub> <msub> <mi>b</mi> <mi>i</mi> </msub> <msub> <mi>b</mi> <mi>m</mi> </msub> <mo>+</mo> <msub> <mi>K</mi> <mrow> <mi>y</mi> <mi>D</mi> </mrow> </msub> <msub> <mi>c</mi> <mi>i</mi> </msub> <msub> <mi>c</mi> <mi>m</mi> </msub> <mo>+</mo> </mrow> </mtd> </mtr> <mtr> <mtd> <mrow> <msub> <mi>K</mi> <mrow> <mi>z</mi> <mi>D</mi> </mrow> </msub> <msub> <mi>d</mi> <mi>i</mi> </msub> <msub> <mi>d</mi> <mi>m</mi> </msub> <mo>+</mo> <mfrac> <mn>1</mn> <mrow> <mn>20</mn> <msub> <mi>K</mi> <mrow> <mi>L</mi> <mi>D</mi> </mrow> </msub> <msub> <mi>&amp;Delta;t</mi> <mi>D</mi> </msub> </mrow> </mfrac> </mrow> </mtd> </mtr> </mtable> </mfenced> <msubsup> <mi>&amp;eta;</mi> <mi>m</mi> <mrow> <mi>e</mi> <mo>,</mo> <mi>n</mi> <mo>+</mo> <mn>1</mn> </mrow> </msubsup> </mrow> </mtd> </mtr> <mtr> <mtd> <mrow> <mo>-</mo> <mfrac> <mrow> <msub> <mi>AK</mi> <mrow> <mi>L</mi> <mi>D</mi> </mrow> </msub> </mrow> <mn>6</mn> </mfrac> <mfrac> <mrow> <mo>&amp;part;</mo> <msubsup> <mi>&amp;eta;</mi> <mi>i</mi> <mrow> <mi>e</mi> <mo>,</mo> <mi>n</mi> <mo>+</mo> <mn>1</mn> </mrow> </msubsup> </mrow> <mrow> <mo>&amp;part;</mo> <msup> <mi>n</mi> <mo>&amp;prime;</mo> </msup> </mrow> </mfrac> <mo>-</mo> <mfrac> <mrow> <msub> <mi>AK</mi> <mrow> <mi>L</mi> <mi>D</mi> </mrow> </msub> </mrow> <mn>12</mn> </mfrac> <mfrac> <mrow> <mo>&amp;part;</mo> <msubsup> <mi>&amp;eta;</mi> <mrow> <mi>j</mi> <mo>/</mo> <mi>k</mi> <mo>/</mo> <mi>m</mi> </mrow> <mrow> <mi>e</mi> <mo>,</mo> <mi>n</mi> <mo>+</mo> <mn>1</mn> </mrow> </msubsup> </mrow> <mrow> <mo>&amp;part;</mo> <msup> <mi>n</mi> <mo>&amp;prime;</mo> </msup> </mrow> </mfrac> <mo>-</mo> <mfrac> <mrow> <msub> <mi>AK</mi> <mrow> <mi>L</mi> <mi>D</mi> </mrow> </msub> </mrow> <mn>12</mn> </mfrac> <mfrac> <mrow> <mo>&amp;part;</mo> <msubsup> <mi>&amp;eta;</mi> <mrow> <mi>k</mi> <mo>/</mo> <mi>m</mi> <mo>/</mo> <mi>j</mi> </mrow> <mrow> <mi>e</mi> <mo>,</mo> <mi>n</mi> <mo>+</mo> <mn>1</mn> </mrow> </msubsup> </mrow> <mrow> <mo>&amp;part;</mo> <msup> <mi>n</mi> <mo>&amp;prime;</mo> </msup> </mrow> </mfrac> </mrow> </mtd> </mtr> <mtr> <mtd> <mrow> <mo>=</mo> <mfrac> <mi>V</mi> <mrow> <mn>10</mn> <msub> <mi>&amp;Delta;t</mi> <mi>D</mi> </msub> </mrow> </mfrac> <msubsup> <mi>&amp;eta;</mi> <mi>i</mi> <mrow> <mi>e</mi> <mo>,</mo> <mi>n</mi> </mrow> </msubsup> <mo>+</mo> <mfrac> <mi>V</mi> <mrow> <mn>20</mn> <msub> <mi>&amp;Delta;t</mi> <mi>D</mi> </msub> </mrow> </mfrac> <msubsup> <mi>&amp;eta;</mi> <mi>j</mi> <mrow> <mi>e</mi> <mo>,</mo> <mi>n</mi> </mrow> </msubsup> <mo>+</mo> <mfrac> <mi>V</mi> <mrow> <mn>20</mn> <msub> <mi>&amp;Delta;t</mi> <mi>D</mi> </msub> </mrow> </mfrac> <msubsup> <mi>&amp;eta;</mi> <mi>k</mi> <mrow> <mi>e</mi> <mo>,</mo> <mi>n</mi> </mrow> </msubsup> <mo>+</mo> <mfrac> <mi>V</mi> <mrow> <mn>20</mn> <msub> <mi>&amp;Delta;t</mi> <mi>D</mi> </msub> </mrow> </mfrac> <msubsup> <mi>&amp;eta;</mi> <mi>m</mi> <mrow> <mi>e</mi> <mo>,</mo> <mi>n</mi> </mrow> </msubsup> </mrow> </mtd> </mtr> </mtable> <mo>-</mo> <mo>-</mo> <mo>-</mo> <mrow> <mo>(</mo> <mn>10</mn> <mo>)</mo> </mrow> </mrow>
<mrow> <mfrac> <mrow> <munderover> <mi>&amp;Sigma;</mi> <mrow> <mi>j</mi> <mo>=</mo> <mn>1</mn> </mrow> <mi>N</mi> </munderover> <msub> <mi>A</mi> <mrow> <mi>j</mi> <mi>D</mi> </mrow> </msub> <msub> <mi>K</mi> <mrow> <mi>j</mi> <mi>D</mi> </mrow> </msub> <mrow> <mo>(</mo> <mfrac> <mrow> <mo>&amp;part;</mo> <msub> <mi>&amp;eta;</mi> <mrow> <mi>j</mi> <mi>D</mi> </mrow> </msub> </mrow> <mrow> <mo>&amp;part;</mo> <msup> <mi>n</mi> <mo>&amp;prime;</mo> </msup> </mrow> </mfrac> <mo>)</mo> </mrow> <msub> <mo>|</mo> <msub> <mi>&amp;Gamma;</mi> <mrow> <mi>i</mi> <mi>n</mi> </mrow> </msub> </msub> </mrow> <mrow> <mn>2</mn> <msub> <mi>&amp;pi;h</mi> <mi>D</mi> </msub> </mrow> </mfrac> <mo>+</mo> <mfrac> <msub> <mi>C</mi> <mrow> <mi>D</mi> <mi>L</mi> </mrow> </msub> <mrow> <msub> <mi>&amp;Delta;t</mi> <mi>D</mi> </msub> </mrow> </mfrac> <msubsup> <mi>&amp;eta;</mi> <mi>w</mi> <mrow> <mi>e</mi> <mo>,</mo> <mi>n</mi> <mo>+</mo> <mn>1</mn> </mrow> </msubsup> <mo>=</mo> <mn>1</mn> <mo>+</mo> <mfrac> <msub> <mi>C</mi> <mrow> <mi>D</mi> <mi>L</mi> </mrow> </msub> <mrow> <msub> <mi>&amp;Delta;t</mi> <mi>D</mi> </msub> </mrow> </mfrac> <msubsup> <mi>&amp;eta;</mi> <mi>w</mi> <mrow> <mi>e</mi> <mo>,</mo> <mi>n</mi> </mrow> </msubsup> <mo>-</mo> <mo>-</mo> <mo>-</mo> <mrow> <mo>(</mo> <mn>11</mn> <mo>)</mo> </mrow> </mrow>
<mrow> <msub> <mi>&amp;eta;</mi> <mi>w</mi> </msub> <mrow> <mo>(</mo> <msub> <mi>t</mi> <mi>D</mi> </msub> <mo>)</mo> </mrow> <mo>=</mo> <mi>&amp;eta;</mi> <msub> <mo>|</mo> <msub> <mi>&amp;Gamma;</mi> <mrow> <mi>i</mi> <mi>n</mi> </mrow> </msub> </msub> <mo>-</mo> <msub> <mi>S</mi> <mi>t</mi> </msub> <mfrac> <mrow> <munderover> <mo>&amp;Sigma;</mo> <mrow> <mi>j</mi> <mo>=</mo> <mn>1</mn> </mrow> <mi>N</mi> </munderover> <msub> <mi>A</mi> <mrow> <mi>j</mi> <mi>D</mi> </mrow> </msub> <msub> <mi>K</mi> <mrow> <mi>j</mi> <mi>D</mi> </mrow> </msub> </mrow> <mrow> <mn>2</mn> <msub> <mi>&amp;pi;h</mi> <mi>D</mi> </msub> </mrow> </mfrac> <mrow> <mo>(</mo> <mfrac> <mrow> <mo>&amp;part;</mo> <msub> <mi>&amp;eta;</mi> <mi>j</mi> </msub> </mrow> <mrow> <mo>&amp;part;</mo> <msup> <mi>n</mi> <mo>&amp;prime;</mo> </msup> </mrow> </mfrac> <mo>)</mo> </mrow> <mo>-</mo> <mo>-</mo> <mo>-</mo> <mrow> <mo>(</mo> <mn>12</mn> <mo>)</mo> </mrow> </mrow>
B. fracture surface two dimensional finite element equation is:
<mrow> <mtable> <mtr> <mtd> <mrow> <mi>A</mi> <mrow> <mo>(</mo> <msubsup> <mi>b</mi> <mi>i</mi> <mn>2</mn> </msubsup> <mo>+</mo> <msubsup> <mi>c</mi> <mi>i</mi> <mn>2</mn> </msubsup> <mo>+</mo> <mfrac> <mn>1</mn> <mrow> <mn>6</mn> <msub> <mi>K</mi> <mrow> <mi>f</mi> <mi>D</mi> </mrow> </msub> <msub> <mi>&amp;Delta;t</mi> <mi>D</mi> </msub> </mrow> </mfrac> <mo>)</mo> </mrow> <msubsup> <mi>&amp;eta;</mi> <mi>i</mi> <mrow> <mi>e</mi> <mo>,</mo> <mi>n</mi> <mo>+</mo> <mn>1</mn> </mrow> </msubsup> <mo>+</mo> <mi>A</mi> <mrow> <mo>(</mo> <msub> <mi>b</mi> <mi>i</mi> </msub> <msub> <mi>b</mi> <mi>j</mi> </msub> <mo>+</mo> <msub> <mi>c</mi> <mi>i</mi> </msub> <msub> <mi>c</mi> <mi>j</mi> </msub> <mo>+</mo> <mfrac> <mn>1</mn> <mrow> <mn>12</mn> <msub> <mi>K</mi> <mrow> <mi>f</mi> <mi>D</mi> </mrow> </msub> <msub> <mi>&amp;Delta;t</mi> <mi>D</mi> </msub> </mrow> </mfrac> <mo>)</mo> </mrow> <msubsup> <mi>&amp;eta;</mi> <mi>j</mi> <mrow> <mi>e</mi> <mo>,</mo> <mi>n</mi> <mo>+</mo> <mn>1</mn> </mrow> </msubsup> </mrow> </mtd> </mtr> <mtr> <mtd> <mrow> <mo>+</mo> <mi>A</mi> <mrow> <mo>(</mo> <msub> <mi>b</mi> <mi>i</mi> </msub> <msub> <mi>b</mi> <mi>k</mi> </msub> <mo>+</mo> <msub> <mi>c</mi> <mi>i</mi> </msub> <msub> <mi>c</mi> <mi>k</mi> </msub> <mo>+</mo> <mfrac> <mn>1</mn> <mrow> <mn>12</mn> <msub> <mi>K</mi> <mrow> <mi>f</mi> <mi>D</mi> </mrow> </msub> <msub> <mi>&amp;Delta;t</mi> <mi>D</mi> </msub> </mrow> </mfrac> <mo>)</mo> </mrow> <msubsup> <mi>&amp;eta;</mi> <mi>k</mi> <mrow> <mi>e</mi> <mo>,</mo> <mi>n</mi> <mo>+</mo> <mn>1</mn> </mrow> </msubsup> <mo>-</mo> <mfrac> <mi>l</mi> <mn>3</mn> </mfrac> <mfrac> <mrow> <mo>&amp;part;</mo> <msubsup> <mi>&amp;eta;</mi> <mi>i</mi> <mrow> <mi>e</mi> <mo>,</mo> <mi>n</mi> <mo>+</mo> <mn>1</mn> </mrow> </msubsup> </mrow> <mrow> <mo>&amp;part;</mo> <msup> <mi>n</mi> <mo>&amp;prime;</mo> </msup> </mrow> </mfrac> <mo>-</mo> <mfrac> <mi>l</mi> <mn>6</mn> </mfrac> <mfrac> <mrow> <mo>&amp;part;</mo> <msubsup> <mi>&amp;eta;</mi> <mrow> <mi>j</mi> <mo>,</mo> <mi>k</mi> </mrow> <mrow> <mi>e</mi> <mo>,</mo> <mi>n</mi> <mo>+</mo> <mn>1</mn> </mrow> </msubsup> </mrow> <mrow> <mo>&amp;part;</mo> <msup> <mi>n</mi> <mo>&amp;prime;</mo> </msup> </mrow> </mfrac> </mrow> </mtd> </mtr> <mtr> <mtd> <mrow> <mo>=</mo> <mfrac> <mi>A</mi> <mrow> <mn>6</mn> <msub> <mi>&amp;Delta;t</mi> <mi>D</mi> </msub> </mrow> </mfrac> <msubsup> <mi>&amp;eta;</mi> <mi>i</mi> <mrow> <mi>e</mi> <mo>,</mo> <mi>n</mi> </mrow> </msubsup> <mo>+</mo> <mfrac> <mi>A</mi> <mrow> <mn>12</mn> <msub> <mi>&amp;Delta;t</mi> <mi>D</mi> </msub> </mrow> </mfrac> <msubsup> <mi>&amp;eta;</mi> <mi>j</mi> <mrow> <mi>e</mi> <mo>,</mo> <mi>n</mi> </mrow> </msubsup> <mo>+</mo> <mfrac> <mi>A</mi> <mrow> <mn>12</mn> <msub> <mi>&amp;Delta;t</mi> <mi>D</mi> </msub> </mrow> </mfrac> <msubsup> <mi>&amp;eta;</mi> <mi>k</mi> <mrow> <mi>e</mi> <mo>,</mo> <mi>n</mi> </mrow> </msubsup> </mrow> </mtd> </mtr> </mtable> <mo>-</mo> <mo>-</mo> <mo>-</mo> <mrow> <mo>(</mo> <mn>13</mn> <mo>)</mo> </mrow> </mrow>
<mrow> <mfrac> <mrow> <munderover> <mi>&amp;Sigma;</mi> <mrow> <mi>j</mi> <mo>=</mo> <mn>1</mn> </mrow> <mi>N</mi> </munderover> <msub> <mi>L</mi> <mrow> <mi>j</mi> <mi>D</mi> </mrow> </msub> <msub> <mi>K</mi> <mrow> <mi>j</mi> <mi>D</mi> </mrow> </msub> <mrow> <mo>(</mo> <mfrac> <mrow> <mo>&amp;part;</mo> <msub> <mi>&amp;eta;</mi> <mrow> <mi>j</mi> <mi>D</mi> </mrow> </msub> </mrow> <mrow> <mo>&amp;part;</mo> <msup> <mi>n</mi> <mo>&amp;prime;</mo> </msup> </mrow> </mfrac> <mo>)</mo> </mrow> </mrow> <mrow> <mn>2</mn> <mi>&amp;pi;</mi> </mrow> </mfrac> <mo>+</mo> <mfrac> <msub> <mi>C</mi> <mrow> <mi>D</mi> <mi>L</mi> </mrow> </msub> <mrow> <msub> <mi>&amp;Delta;t</mi> <mi>D</mi> </msub> </mrow> </mfrac> <msubsup> <mi>&amp;eta;</mi> <mi>w</mi> <mrow> <mi>e</mi> <mo>,</mo> <mi>n</mi> <mo>+</mo> <mn>1</mn> </mrow> </msubsup> <mo>=</mo> <mn>1</mn> <mo>+</mo> <mfrac> <msub> <mi>C</mi> <mrow> <mi>D</mi> <mi>L</mi> </mrow> </msub> <mrow> <msub> <mi>&amp;Delta;t</mi> <mi>D</mi> </msub> </mrow> </mfrac> <msubsup> <mi>&amp;eta;</mi> <mi>w</mi> <mrow> <mi>e</mi> <mo>,</mo> <mi>n</mi> </mrow> </msubsup> <mo>-</mo> <mo>-</mo> <mo>-</mo> <mrow> <mo>(</mo> <mn>14</mn> <mo>)</mo> </mrow> </mrow>
<mrow> <msub> <mi>&amp;eta;</mi> <mi>w</mi> </msub> <mrow> <mo>(</mo> <msub> <mi>t</mi> <mi>D</mi> </msub> <mo>)</mo> </mrow> <mo>=</mo> <msub> <mi>&amp;eta;</mi> <mi>j</mi> </msub> <mo>-</mo> <msub> <mi>S</mi> <mi>t</mi> </msub> <mfrac> <mrow> <munderover> <mo>&amp;Sigma;</mo> <mrow> <mi>j</mi> <mo>=</mo> <mn>1</mn> </mrow> <mi>N</mi> </munderover> <msub> <mi>L</mi> <mrow> <mi>j</mi> <mi>D</mi> </mrow> </msub> <msub> <mi>K</mi> <mrow> <mi>L</mi> <mi>D</mi> </mrow> </msub> </mrow> <mrow> <mn>2</mn> <msub> <mi>&amp;pi;h</mi> <mi>D</mi> </msub> </mrow> </mfrac> <mrow> <mo>(</mo> <mfrac> <mrow> <mo>&amp;part;</mo> <msub> <mi>&amp;eta;</mi> <mi>j</mi> </msub> </mrow> <mrow> <mo>&amp;part;</mo> <msup> <mi>n</mi> <mo>&amp;prime;</mo> </msup> </mrow> </mfrac> <mo>)</mo> </mrow> <mo>-</mo> <mo>-</mo> <mo>-</mo> <mrow> <mo>(</mo> <mn>15</mn> <mo>)</mo> </mrow> </mrow>
By finite element equation (10)~(15) simultaneous composition system stiffness matrix, the SuperLU numerical solvers of parallelization are utilized Large linear systems are solved, obtain the pressure field distribution and inner boundary normal pressure gradient of whole reservoir, then by This calculates each crack production flow:
<mrow> <msub> <mi>Q</mi> <mrow> <mi>f</mi> <mi>i</mi> </mrow> </msub> <mo>=</mo> <msub> <mi>Q</mi> <mrow> <mi>s</mi> <mi>c</mi> </mrow> </msub> <mfrac> <mrow> <msub> <mi>w</mi> <mrow> <mi>f</mi> <mi>D</mi> </mrow> </msub> <msub> <mi>L</mi> <mrow> <mi>i</mi> <mi>D</mi> </mrow> </msub> <msub> <mi>K</mi> <mrow> <mi>f</mi> <mi>D</mi> </mrow> </msub> <msup> <mi>e</mi> <mrow> <mo>-</mo> <msub> <mi>&amp;gamma;</mi> <mi>D</mi> </msub> <msub> <mi>p</mi> <mrow> <mi>i</mi> <mi>D</mi> </mrow> </msub> </mrow> </msup> </mrow> <mrow> <mn>2</mn> <msub> <mi>&amp;pi;h</mi> <mi>D</mi> </msub> </mrow> </mfrac> <mrow> <mo>(</mo> <mfrac> <mrow> <mo>&amp;part;</mo> <msub> <mi>p</mi> <mrow> <mi>i</mi> <mi>D</mi> </mrow> </msub> </mrow> <mrow> <mo>&amp;part;</mo> <msup> <mi>n</mi> <mo>&amp;prime;</mo> </msup> </mrow> </mfrac> <mo>)</mo> </mrow> <msub> <mo>|</mo> <msub> <mi>&amp;Gamma;</mi> <mrow> <mi>i</mi> <mi>n</mi> </mrow> </msub> </msub> <mo>-</mo> <mo>-</mo> <mo>-</mo> <mrow> <mo>(</mo> <mn>16</mn> <mo>)</mo> </mrow> </mrow>
Symbol implication in formula:
η is transformation to linearity parameter;ηwFor the transformation parameter corresponding to dimensionless bottom pressure value;wfFor fracture width, m;wfDFor Dimensionless fracture width;LjDFor crack inner boundary unit line length;V is tetrahedron volume;B, c, d are finite element coefficient;I, j, K, m are limited four summit sequence numbers of elementary tetrahedron;QfiFor the flow of the i-th crack, m3/d;QscTo mark the flow of gas well under condition, m3/d。
2. a kind of tight gas pressure break horizontal well numerical well testing model according to claim 1 establishes method for solving, its feature It is, the two-dimentional geologic body and three-dimensional geologic of tight gas reservoir pressure break horizontal well is generated in described step one, specific steps are such as Under:
1) according to residing for pressure break horizontal well geologic body external boundary, pit shaft inner boundary, crack and recombination region, then by setting External boundary and crack attribute determine the specific size and shape of geologic body, and two-dimentional geologic body is established in drafting;
2) according to the two-dimentional constitution and well track of foundation and the position of reservoir up-and-down boundary, given birth to using solid Boolean calculation Into three-dimensional geologic.
3. a kind of tight gas pressure break horizontal well numerical well testing model according to claim 1 establishes method for solving, its feature It is, two-dimentional geologic body in described step two and three-dimensional geologic carry out that grid is discrete to be comprised the following steps that:
First, Netgen open source softwares are bundled into work(to be compiled, build running environment;
Then, by the inner and outer boundary attribute in two-dimentional geologic body and three-dimensional geologic respectively according to Netgen grid file forms It is required that form two-dimensional grid file and three-dimensional grid file, according still further to the grid discrete step that Netgen is set carry out grid from Dissipate.
4. a kind of tight gas pressure break horizontal well numerical well testing model according to claim 1 establishes method for solving, its feature It is, coupling model is established in described step four, and solution is carried out to the coupling model of foundation and followed the steps below 's:
A, the wellbore pressure p calculated according to step 4WDWith crack flow Qfi, counted using pit shaft multiphase flow calculation formula Calculate, obtain the dimensionless pressure difference MP of pit shaft each pointiD, specific formula is as follows:
The basic equation of pit shaft multiphase stream calculation is:
<mrow> <mo>-</mo> <mfrac> <mrow> <msub> <mi>dp</mi> <mi>w</mi> </msub> </mrow> <mrow> <mi>d</mi> <mi>Z</mi> </mrow> </mfrac> <mo>=</mo> <mfrac> <mrow> <mo>(</mo> <msub> <mi>&amp;rho;</mi> <mi>l</mi> </msub> <msub> <mi>H</mi> <mi>L</mi> </msub> <mo>+</mo> <msub> <mi>&amp;rho;</mi> <mi>g</mi> </msub> <mo>(</mo> <mrow> <mn>1</mn> <mo>-</mo> <msub> <mi>H</mi> <mi>L</mi> </msub> </mrow> <mo>)</mo> <mo>)</mo> <mi>s</mi> <mi>i</mi> <mi>n</mi> <mi>&amp;theta;</mi> <mo>+</mo> <mfrac> <mrow> <msub> <mi>&amp;lambda;Gv</mi> <mi>m</mi> </msub> </mrow> <mrow> <mn>2</mn> <mi>A</mi> <mi>D</mi> </mrow> </mfrac> </mrow> <mrow> <mn>1</mn> <mo>-</mo> <mo>{</mo> <mo>&amp;lsqb;</mo> <msub> <mi>&amp;rho;</mi> <mi>l</mi> </msub> <msub> <mi>H</mi> <mi>L</mi> </msub> <mo>+</mo> <msub> <mi>&amp;rho;</mi> <mi>g</mi> </msub> <mrow> <mo>(</mo> <mn>1</mn> <mo>-</mo> <msub> <mi>H</mi> <mi>L</mi> </msub> <mo>)</mo> </mrow> <mo>&amp;rsqb;</mo> <msub> <mi>v</mi> <mi>m</mi> </msub> <msub> <mi>v</mi> <mrow> <mi>s</mi> <mi>g</mi> </mrow> </msub> <mo>}</mo> <mo>/</mo> <mi>p</mi> </mrow> </mfrac> <mo>-</mo> <mo>-</mo> <mo>-</mo> <mrow> <mo>(</mo> <mn>17</mn> <mo>)</mo> </mrow> </mrow>
Symbol implication in formula:
ρLFor fluid density, kg/m3;ρgFor gas density, kg/m3;G is gas-liquid mixture mass flow, kg/s;vmFor mixture Flowing velocity, m/s;vsgFor gas superficial flow velocity, m/s;A is pit shaft oil pipe sectional area, m2;D is pipe aperture, m;
Liquid holdup HLCalculated with coefficient of frictional resistance λ using Beggs-Brill methods, wellbore pressure ladder is obtained according to formula (17) Degree, the pressure difference between each point and shaft bottom standard point is obtained further according to pit shaft inner boundary relative distance is cumulative:
<mrow> <msub> <mi>MP</mi> <mi>i</mi> </msub> <mo>=</mo> <munderover> <mo>&amp;Sigma;</mo> <mrow> <mi>j</mi> <mo>=</mo> <mn>0</mn> </mrow> <mi>i</mi> </munderover> <msub> <mrow> <mo>(</mo> <mo>-</mo> <mfrac> <mrow> <msub> <mi>dp</mi> <mi>w</mi> </msub> </mrow> <mrow> <mi>d</mi> <mi>Z</mi> </mrow> </mfrac> <mo>)</mo> </mrow> <mi>i</mi> </msub> <msub> <mi>&amp;Delta;Z</mi> <mi>j</mi> </msub> <mo>-</mo> <mo>-</mo> <mo>-</mo> <mrow> <mo>(</mo> <mn>18</mn> <mo>)</mo> </mrow> </mrow>
The each point pressure difference MP that will be obtainediNondimensionalization is carried out, that is, obtains each point dimensionless pressure difference MPiD
B, the inner boundary each point pressure difference MP obtained in step AiD, it is brought into flow model in porous media and calculates wellbore pressure p 'WDWith split Stitch flow Q 'fi, the coupling condition of pit shaft multiphase flow model and flow model in porous media is as follows:
On stratum and pit shaft interface:
<mrow> <msub> <mi>p</mi> <mrow> <mi>D</mi> <mi>R</mi> <mi>i</mi> </mrow> </msub> <msub> <mo>|</mo> <msub> <mi>&amp;Gamma;</mi> <mrow> <mi>i</mi> <mi>n</mi> </mrow> </msub> </msub> <mo>=</mo> <msub> <mi>p</mi> <mrow> <mi>w</mi> <mi>D</mi> </mrow> </msub> <mo>+</mo> <msub> <mi>MP</mi> <mrow> <mi>i</mi> <mi>D</mi> </mrow> </msub> <mo>-</mo> <mo>-</mo> <mo>-</mo> <mrow> <mo>(</mo> <mn>19</mn> <mo>)</mo> </mrow> </mrow>
On crack and pit shaft interface:
<mrow> <msub> <mi>p</mi> <mrow> <mi>D</mi> <mi>f</mi> <mi>j</mi> </mrow> </msub> <msub> <mo>|</mo> <msub> <mi>&amp;Gamma;</mi> <mrow> <mi>i</mi> <mi>n</mi> </mrow> </msub> </msub> <mo>=</mo> <msub> <mi>p</mi> <mrow> <mi>w</mi> <mi>D</mi> </mrow> </msub> <mo>+</mo> <msub> <mi>MP</mi> <mrow> <mi>j</mi> <mi>D</mi> </mrow> </msub> <mo>-</mo> <mo>-</mo> <mo>-</mo> <mrow> <mo>(</mo> <mn>20</mn> <mo>)</mo> </mrow> </mrow>
C, the p ' that front and rear iteration step is calculatedWDAnd pWDSubtracted each other, when absolute value poor between the two is less than ε, then continued The calculating of future time step, when the absolute value of both differences is more than or equal to ε, then currently available p 'WDAnd Q 'fiWith it is previous The value of step obtains new wellbore pressure p after being averagedWDWith crack flow Qfi, and be brought into step A and be iterated, until The p ' arrivedWDWith pWDThe absolute value of the difference subtract each other is less than ε, and the general values of ε are 10-4
D, the p ' that step C is determinedWDWith corresponding Q 'fiRecorded, if now time step k<Total time walks n, then continues next The calculating of time step, according to current wellbore pressure pWD, crack flow Qfi, the p ' of a new round is calculated since step AWD And Q 'fi
E, resulting p ' in n computations in step DWDAnd Q fiValue generation Well Testing Theory curve.
5. a kind of tight gas pressure break horizontal well numerical well testing model according to claim 1 establishes method for solving, its feature It is, the step 5 is mainly theoretical curve and measured curve in log-log graph, semilogarithmic plot and full history pressure Fitting is contrasted in force curve figure, according to the fitting degree of curve, is fitted the adjustment of parameter, finally makes theoretical curve and actual measurement Curve can access in log-log graph, semilogarithmic plot and full historical pressures curve map preferably to coincide, curve Fitting is just completed;After the completion of curve matching, that is, obtain the parameter of well test analysis, including fracture parameters and reservoir parameter.
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* Cited by examiner, † Cited by third party
Publication number Priority date Publication date Assignee Title
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CN109446649B (en) * 2018-10-29 2019-07-26 西安石油大学 The method for building up of compact oil reservoir volume fracturing horizontal well three dimensional seepage model
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Citations (5)

* Cited by examiner, † Cited by third party
Publication number Priority date Publication date Assignee Title
US6549879B1 (en) * 1999-09-21 2003-04-15 Mobil Oil Corporation Determining optimal well locations from a 3D reservoir model
CN101446196A (en) * 2008-04-14 2009-06-03 中国石油大学(北京) Well test analysis method and device of treble medium oil pool branch horizontal well
CN102243680A (en) * 2011-07-21 2011-11-16 中国科学技术大学 Grid partitioning method and system
CN103266881A (en) * 2013-05-22 2013-08-28 中国石化集团华北石油局 Method for predicting yield of compact hypotonic gas field multistage fracturing horizontal well
CN104594872A (en) * 2015-01-04 2015-05-06 西南石油大学 Method for optimizing fracture conductivity of tight gas-reservoir fractured horizontal well

Patent Citations (5)

* Cited by examiner, † Cited by third party
Publication number Priority date Publication date Assignee Title
US6549879B1 (en) * 1999-09-21 2003-04-15 Mobil Oil Corporation Determining optimal well locations from a 3D reservoir model
CN101446196A (en) * 2008-04-14 2009-06-03 中国石油大学(北京) Well test analysis method and device of treble medium oil pool branch horizontal well
CN102243680A (en) * 2011-07-21 2011-11-16 中国科学技术大学 Grid partitioning method and system
CN103266881A (en) * 2013-05-22 2013-08-28 中国石化集团华北石油局 Method for predicting yield of compact hypotonic gas field multistage fracturing horizontal well
CN104594872A (en) * 2015-01-04 2015-05-06 西南石油大学 Method for optimizing fracture conductivity of tight gas-reservoir fractured horizontal well

Non-Patent Citations (1)

* Cited by examiner, † Cited by third party
Title
水平井分段压裂在特低渗透油藏开发中的应用;李春芹;《西南石油大学学报(自然科学版)》;20111231;85-86 *

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