CN105840187B - Compactness reservoir horizontal well staged fracturing Productivity - Google Patents
Compactness reservoir horizontal well staged fracturing Productivity Download PDFInfo
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- E—FIXED CONSTRUCTIONS
- E21—EARTH DRILLING; MINING
- E21B—EARTH DRILLING, e.g. DEEP DRILLING; OBTAINING OIL, GAS, WATER, SOLUBLE OR MELTABLE MATERIALS OR A SLURRY OF MINERALS FROM WELLS
- E21B49/00—Testing the nature of borehole walls; Formation testing; Methods or apparatus for obtaining samples of soil or well fluids, specially adapted to earth drilling or wells
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Abstract
The present invention relates to oil fracturing technical fields, and in particular to a kind of compactness reservoir horizontal well staged fracturing Productivity.Compactness reservoir horizontal well staged fracturing Productivity, it is characterised in that: the following steps are included: flow through oil reservoir region is divided into four parts by (1), (2) obtain the equivalent equivalent radius of every crack；(3) yield of each crack when multiple cracking interference is obtained；(4) yield for each crack that step (3) obtains is coupled with the waterpower pressure drop flow model in horizontal wellbore, obtain one group of bottom pressure, until iterative solution to the bottom pressure difference of two step of front and back is less than tolerance i.e. convergence, the one group of yield determined at this time is the seam control yield of every crack, and the sum of each crack seam control yield is horizontal well total output.Calculated result of the present invention is more true and reliable, and application effect is preferable.
Description
Technical field
The present invention relates to oil fracturing technical fields, and in particular to a kind of compactness reservoir horizontal well staged fracturing production capacity meter
Calculation method.
Background technique
Horizontal productivity size be fractured horizontal well parameter preferably with the foundation of development response evaluation.At present both at home and abroad about
The calculating of productivity of fractured horizontal well is all based on greatly the darcy flow model in reservoir matrix, and mining site production practices and interior are real
Test the result shows that, Oil in Super-low Permeability Reservoirs matrix seepage flow does not meet classical Darcy's law, and there are stronger non linear fluid flow through porous medium phenomenons.
Both at home and abroad for productivity of fractured horizontal well calculating carried out a series of researchs, mainly have Deng Yinger etc. establish it is each to
The non-darcy elliptical porous flow model of vertically fractured well two-phase in anisotropic Double Porosity Reservoir, analyze sorptivety, non-Darcy effects and
Influence of the injection rate to the pressure break horizontal well water breakthrough time；Duan Yonggang etc. considers the resistance of fluid mill, momentum change, wellbore wall inflow
Mixing interference etc. complicated factors, application boundary integration method establish horizontal wellbore and oil reservoir model for coupling；The scholars such as Chen Wei
It is non-homogeneous flow rate computation model by uniform flow rate model refinement, obtains horizontal well unsteady state flow in the method for half numerical value of semi analytic
The parameters such as rate distribution and wellbore pressure；The scholars such as Lian Peiqing establish oil reservoir and frac water using Green's function and Newman product principle
The new model of horizontal well pit shaft coupling, establishes the pressure break horizontal well unsteady Model that box oil reservoir is coupled with horizontal wellbore；Grandson sea etc.
Scholar establishes pit shaft and couples pressure break horizontal well unsteady Model with oil reservoir and give the optimization algorithm of model solution.
The research of the above scholar is evaluated horizontal productivity and dynamic prediction plays an important role, but is primarily present following ask
Topic: (1) most of productivity model assumed condition is more harsh at present, it is not comprehensive to consider the factor for influencing production capacity, answers
It is not satisfactory with effect；(2) about staged fracturing horizontal well parameter optimization method, it is mostly based on physical analogy and numerical value at present
What simulation carried out, it is less that the research of fracturing parameter rapid Optimum is carried out using reservoir engineering method；(3) at present about staged fracturing water
Horizontal well production capacity and percolation law research are based primarily upon seepage flow in matrix and meet the expansion of " Darcy linear percolation law " this premise,
Consider that the research of non linear fluid flow through porous medium phenomenon in low permeability reservoir matrix does not have substantially.
Summary of the invention
The present invention is directed in view of the above-mentioned problems, considering the non-linear flowing in staged fracturing horizontal well matrix, in crack
Waterpower pressure drop flowing in Darcy Flow, horizontal well pit shaft proposes that a kind of compactness oil reservoir segmented pressure break calculates production capacity method.
Technical program of the present invention lies in:
Include the following steps:
(1) flow through oil reservoir region is divided into four parts, i.e. far-field zone non linear fluid flow through porous medium, linear flow, crack in crack
Part is flowed in waterpower pressure drop in face into pit shaft radial flow and horizontal wellbore, and establishes the computation model of each section；
Wherein, the 1) computation model of far field non linear fluid flow through porous medium part are as follows:
It is tested by rock core flowing test, obtains fluid in hypotonic non-darcy flow, different displacement pressure gradients
Lower apparent permeability establishes the nonlinear mathematics equation for accurately reflecting percolation law in extra-low-permeability reservoir:
；
；(1)
Wherein, a is the impact factor of non linear fluid flow through porous medium concave curve section, and b is that Nonlinear Quasi starting pressure gradient is reciprocal；
On the basis of the non linear fluid flow through porous medium model of above-mentioned foundation, fluid is non-thread in matrix in the presence of considering monolete
Property elliptical porous flow, establishes elliptical coordinate system,
Rectangular coordinate system and elliptical coordinate system transformation relation are as follows:
(2)
Elliptic Cylinder volume are as follows:(3)
In the area approximation of the direction y cylindroid flow section are as follows:
(4)
Then its mass flow rate:(5)
Average semi-minor axis radius are as follows:(6)
By non linear fluid flow through porous medium law:(7)
(8)
(9)
It solves:) (10)
Fracture end-face pressure is integrated to obtain from supply boundary to fracture end-face pressureP 1 :
；(11)
Wherein,KFor reservoir matrix permeability, mD；μFor viscosity of crude, mPas；ξFor elliptic coordinates；H is that oil reservoir is thick
Degree, m；X f For fracture half-length, m；P 1 For fracture end-face pressure, MPa；P e For strata pressure, MPa；Q 1 For non linear fluid flow through porous medium in matrix
Field flow amount, m3/s。
2) in crack Darcy linear stream part computation model are as follows:
In fracture surface flowing be considered as with a thickness ofW f , length be (X f -h/2), pressure difference isP 1 -P 2 Linear seepage flow, seepage flow is micro-
Divide equation and boundary condition are as follows:
It solves:(12)
Wherein,k f For fracture permeabgility, mD；W f For fracture width, m；P 2 It is radially poly- for crack Darcy linear seepage flow and pit shaft
Collection flowing intersection pressure, MPa；Q 2 For Darcy linear seepage flow flow, m in fracture surface3/s；
3) to the computation model of pit shaft radial flow portion in fracture surface are as follows:
In fracture surface after the linear flowing of fluid again to pit shaft assemble, be considered as with a thickness ofW f , radius ish/2Planar radial
Stream, basis partial differential equation and boundary condition are as follows:
(13)
It solves:(14)
In formula:r w For wellbore radius, m；Q 3 Flow, m are moved for aggregate flow radial in fracture surface3/s；
4) computation model of the waterpower pressure drop flowing part in horizontal wellbore are as follows:
Horizontal well enters horizontal wellbore by crack and is divided into two parts pressure drop: first is that crack is radially injected in impact-level pit shaft
Main stream line caused by acceleration pressure drop.The caused friction pressure drop second is that horizontal well tube stream and wellbore wall rub.For simplify with
Horizontal well is divided into N-1 sections (only considering friction pressure drop as N=1) for N hydraulically created fracture by the coupling of crack yield.
For jth section, friction pressure drop caused by pipe stream are as follows:
(15)
Acceleration pressure drop caused by fluid is radially injected are as follows:
(16)
For jth section overall presure drop are as follows:(17)
In formula: ρ is oil density Kg/m3；D is mineshaft diameter, m；D is segmentation spacing, m；q t(j-1) It is flowed into for first j-1 sections
This section of integrated flux, m3/s；q j For this section of crack injection rate, m3/s；F is the coefficient of friction resistance, zero dimension.
(2) assume one group of equivalent well bottom pressure value, linear flow, crack in coupling far-field zone non linear fluid flow through porous medium, crack
The equivalent equivalent diameter for obtaining straight well in face to the computation model of pit shaft radial flow, obtains the equivalent equivalent radius of every crack:
Well bottom pressure equivalent for each crack is coupled with horizontal wellbore internal fissure with the pressure of junction in pit shaft,
It solves and calculates:
(18)
Joint type (15)-(18) formula obtains each equivalent well bottom pressure value.
Its flow in the presence of monoleteQMeet the condition of continuity:(19)
(20)
Formula (11) is brought into and can be obtained: corresponding equivalent equivalent radius Requ(i)
(21)
It is one givenp w(i) , solution aboutQ(i)Integral transcendental equation, obtain corresponding equivalent equivalent radiusR equ(i) 。
(3) a plurality of fracturing fracture is equivalent at equivalent straight well, progress pressure drop superposition show that each item when multiple cracking interference is split
The yield of seam；
(22)
Wherein,R ij For the distance between crack i and crack j, m；q i For the seam control yield of crack i, m3/s；p wi For crack i
Equivalent well bottom pressure, Pa(i, j=1,2,3 ... N)；It is right since each equivalent well spacing is different with a distance from supply boundary
Drainage radius amendment；
For eccentric well, image well inverting is utilized:； (23)
Pressure drop is superimposed the drainage radius amendment in equation group are as follows:； (24)
WhereinR e For drainage radius, m；；R’ e (i)Drainage radius, m are corrected for equivalent well；d(i)It is eccentric for each equivalent straight well
Away from m；
(4) yield for each crack that (3) obtain is coupled with the waterpower pressure drop flow model in horizontal wellbore, obtains one
Group bottom pressure iteratively solves the one group of production determined at this time until the bottom pressure difference of two step of front and back is less than tolerance i.e. convergence
Amount is the seam control yield of every crack, and the sum of each crack seam control yield is horizontal well total output.For withq f (t)Production
Crack, the drop of pressure caused by space are as follows:
(25)
In formula
(26)。
The technical effects of the invention are that:
The present invention considers staged fracturing on the basis of current staged fracturing horizontal well stable state, unsteady Model both at home and abroad
Non-linear flowing in horizontal well matrix, the Darcy Flow in crack, the waterpower pressure drop flowing in horizontal well pit shaft, propose one kind
Coupled Numerical solves the computation model of horizontal productivity, and calculated result is more true and reliable, and application effect is preferable.The model can
There is weight for horizontal productivity evaluation and the parameter designing of site operation production as pressure break horizontal well parameter optimization tool
Want directive significance.
Detailed description of the invention
Fig. 1 is a plurality of traversed by crack fractured horizontal well's productivity model schematic.
Fig. 2 is zero dimension apparent permeability and displacement pressure gradient relation curve.
Fig. 3 is rectangular coordinate system and elliptical coordinate system relational graph.
Fig. 4 is low-permeability oil deposit nonlinear of the fluid percolation curve.
Fig. 5 is the Darcy linear seepage flow schematic diagram in fracture surface.
Fig. 6 is the radial aggregation schematic diagram in fracture surface.
Fig. 7 is waterpower pressure drop flow schematic diagram in horizontal wellbore.
Fig. 8 is equivalent straight well bias well schematic diagram.
Fig. 9 is model solution flow chart.
Figure 10 is flow effect schematic diagram in crack.
Figure 11 flow effect schematic diagram between crack.
Figure 12 is crack outer radial stream effect diagram.
Figure 13 is the pressure field distribution figure for not considering pit shaft internal drop.
Figure 14 is the pressure field distribution figure after coupling.
Figure 15 is productivity model and ECLIPSE numerical simulation result comparison diagram.
Specific embodiment
It is as follows that mathematical model establishes assumed condition:
(1) drive type of reservoir is the drive of hydraulic pressure elasticity, i.e. supply rim pressure is constant；
(2) fluid flows the effects of belonging to isothermal steady seepage, not considering gravity, capillary force influence in reservoir matrix；
(3) fluid is single-phase flow in oil reservoir and crack；
(4) rectangular vertical crack complete penetration payzone；
(5) fluid first uniformly flows into crack along crack wall surface, then flows into horizontal wellbore by crack.
Wherein, the 1) computation model of far field non linear fluid flow through porous medium part are as follows:
The experiment of rock core flowing test is carried out by high precision flow, permeability is obtained and displacement pressure gradient relationship is bent
Line is shown in Fig. 2, establishes the state equation of permeability:
(1)
Wherein, a is the impact factor of non linear fluid flow through porous medium concave curve section, and b is that Nonlinear Quasi starting pressure gradient is reciprocal；
Fig. 4 is non linear fluid flow through porous medium indicatrix: the corresponding barometric gradient of a, c two o'clock is true starting pressure gradient and intends opening
Dynamic pressure force gradient.D is the transition point by non linear fluid flow through porous medium to pseudo-linear flow, and the corresponding flow event of curve ad is non-linear infiltration
Stream.It can be seen from Fig. 2 that liquid phase effective permeability is no longer constant when fluid flows in low permeability reservoir matrix, but displacement pressure
The function of force gradient.
This model can preferably describe barometric gradient and be in front of true starting pressure gradient and maximum starting pressure gradient
The non-linear flow phenomenon that fluid shows.As a=0,As quasi-threshold pressure gradient model；
When b infinity, reflection quasi-threshold pressure gradient is infinitely small, and the effect of fluid and solid is weak,It drills
Become Darcy linear flow model in porous media.The model can describe the stream that each barometric gradient section fluid is in low permeability reservoir matrix
It is dynamic.The relational expression for going out permeability and starting pressure gradient by laboratory core fitting experimental data, by taking rock sample 12-3 as an example, depth
For 2166.2m, core permeability 0.633mD, true starting pressure gradient 0.0517MPa, quasi-threshold pressure gradient is
0.1449MPa, match value a=0.268, b=6.90.
On the basis of above-mentioned state equation, non linear elliptic seepage flow of the fluid in matrix in the presence of monolete is considered.It builds
Vertical elliptical coordinate system, is shown in Fig. 3:
Rectangular coordinate system and elliptical coordinate system transformation relation are as follows:
(2)
Elliptic Cylinder volume are as follows:(3)
In the area approximation of the direction y cylindroid flow section are as follows:
(4)
Then its mass flow rate:(5)
Average semi-minor axis radius are as follows:(6)
By non linear fluid flow through porous medium law:(7)
(8)
(9)
It solves:(10)
Fracture end-face pressure is integrated to obtain from supply boundary to fracture end-face pressureP 1 :
；(11)
Wherein,KFor reservoir matrix permeability, mD；μFor viscosity of crude, mPas；ξFor elliptic coordinates；H is that oil reservoir is thick
Degree, m；X f For fracture half-length, m；P 1 For fracture end-face pressure, MPa；P e For strata pressure, MPa；Q 1 For non linear fluid flow through porous medium in matrix
Field flow amount, m3/s。
2) in crack linear stream part computation model are as follows:
Fig. 5 is the Darcy linear seepage flow schematic diagram in fracture surface, in fracture surface flowing can be considered with a thickness ofW f , length is
(X f -h/2), pressure difference isP 1 -P 2 Linear seepage flow, basis partial differential equation and boundary condition are as follows:
It solves:(12)
Wherein,k f For fracture permeabgility, mD；W f For fracture width, m；P 2 It is radially poly- for crack Darcy linear seepage flow and pit shaft
Collection flowing intersection pressure, MPa；Q 2 For Darcy linear seepage flow flow, m in fracture surface3/s；
3) to the computation model of pit shaft radial flow portion in fracture surface are as follows:
Fig. 6 is the radial aggregation schematic diagram in fracture surface, is assembled again to pit shaft after the linear flowing of fluid in fracture surface, can
Be considered as with a thickness ofW f , radius ish/2Radial fluid flow, basis partial differential equation and boundary condition are as follows:
(13)
It solves:(14)
In formula:r w For wellbore radius, m；Q 3 Flow, m are moved for aggregate flow radial in fracture surface3/s；
4) computation model of the waterpower pressure drop flowing part in pit shaft are as follows:
Fig. 7 is waterpower pressure drop flow schematic diagram in horizontal wellbore, and horizontal well enters horizontal wellbore by crack and is divided into two parts
Pressure drop: first is that crack is radially injected acceleration pressure drop caused by the main stream line in impact-level pit shaft.Second is that horizontal well tube stream with
Friction pressure drop caused by wellbore wall rubs.It is coupled for simplification with crack yield, for N hydraulically created fracture, by horizontal well
It is divided into N-1 sections (only considering friction pressure drop as N=1).
For jth section, friction pressure drop caused by pipe stream are as follows:
(15)
Acceleration pressure drop caused by fluid is radially injected are as follows:
(16)
For jth section overall presure drop are as follows:(17)
In formula: ρ is oil density Kg/m3；D is mineshaft diameter, m；D is segmentation spacing, m；q t(j-1) It is flowed into for first j-1 sections
This section of integrated flux, m3/s；q j For this section of crack injection rate, m3/s；F is the coefficient of friction resistance, zero dimension.
(2) assume one group of equivalent well bottom pressure value, linear flow, crack in coupling far-field zone non linear fluid flow through porous medium, crack
The equivalent equivalent diameter for obtaining straight well in face to the computation model of pit shaft radial flow, obtains the equivalent equivalent radius of every crack:
Well bottom pressure equivalent for each crack is coupled with horizontal wellbore internal fissure with the pressure of junction in pit shaft,
It solves and calculates:
(18)
Joint type (15)-(18) formula obtains each equivalent well bottom pressure value.
Its flow in the presence of monoleteQMeet the condition of continuity:(19)
(20)
Formula (11) is brought into and can be obtained: corresponding equivalent equivalent radius Requ(i)
(21)
It is one givenp w(i) , solution aboutQ(i)Integral transcendental equation, obtain corresponding equivalent equivalent radiusR equ(i) 。
(3) a plurality of fracturing fracture is equivalent at equivalent straight well, progress pressure drop superposition show that each item when multiple cracking interference is split
The yield of seam；
(22)
Wherein,R ij For the distance between crack i and crack j, m；q i For the seam control yield of crack i, m3/s；p wi For crack i
Equivalent well bottom pressure, Pa(i, j=1,2,3 ... N)；It is right since each equivalent well spacing is different with a distance from supply boundary
Drainage radius amendment；
For eccentric well, image well inverting is utilized:； (23)
Pressure drop is superimposed the drainage radius amendment in equation group are as follows:； (24)
WhereinR e For drainage radius, m；；R’ e (i)Drainage radius, m are corrected for equivalent well；d(i)It is eccentric for each equivalent straight well
Away from m；
(4) yield for each crack that (3) obtain is coupled with the waterpower pressure drop flow model in horizontal wellbore, obtains one
Group bottom pressure iteratively solves the one group of production determined at this time until the bottom pressure difference of two step of front and back is less than tolerance i.e. convergence
Amount is the seam control yield of every crack, and the sum of each crack seam control yield is horizontal well total output；
For withq f (t)The crack of production, the drop of pressure caused by space are as follows:
(25)
In formula
(26)。
When the physical significance of F function is that crack j is produced with specific yield, in 0 ~ t time interior pressure generated at the i of crack
Drop.What this model considered is the unstable state production decline rule under the conditions of determining bottom pressure.
The solution procedure of this model is shown in Fig. 9.
It is as follows to method validation provided by the invention:
(1) method for numerical simulation is verified
For the application effect for verifying model, reservoir parameter shown in table 1 is taken to be calculated.It is soft in ECLIPSE numerical simulation
Part Imitating calculates 180d, obtains yield and changes over time data, comparison productivity model calculated result and ECLIPSE numerical simulation
Calculated result such as Figure 10.
1 W block segmentation pressure break horizontal well underlying parameter table of table
Table 1 staged fracturing of horizontal well base parameter in W
blocks
As shown in Figure 15, the calculating data with Field Production Data of productivity model are coincide, and property is preferable, and demonstrate model can
By property.
(2) field test application
Long 9 oil reservoir, the four mouthfuls of water of oil field ultra-low penetration W block are extended to Ordos Basin using method provided by the invention
Horizontal well carries out AOF calculation, and compares with practical production capacity.The basic data and calculated result of the horizontal well such as table 2.
2 W block of table grows 9 oil reservoir, four mouthfuls of water horizontal well AOF calculation results
Table1 four horizontal well productivity calculation results of chang
9 reservoir in W block
(oil density: 0.75g/cm3).
The different productivity model calculation result data tables of table 3
Table2 Calculation result of different production models
According to the model calculation: the actual production at long 9 oil reservoir, the four mouthfuls of water horizontal well scenes of W block is 6.45t/d-
11.87t/d, calculating horizontal well production using new productivity model is 6.12t/d-11.37t/d, and coincidence rate is up to 85.21%-
94.25%, average out to 91.03%, it was demonstrated that the model has preferable practicability, demonstrates the accuracy of model.Due to novel production
Energy model considers the non linear fluid flow through porous medium feature in low permeability reservoir, so that calculated result meets the actual conditions in oil field, is applicable in
Property it is stronger, prediction result is more true and reliable, thus can be used as such reservoir-level well fracturing parameter optimization foundation.
Claims (3)
1. compactness reservoir horizontal well staged fracturing Productivity, it is characterised in that: the following steps are included:
(1) flow through oil reservoir region is divided into four parts, i.e., far-field zone non linear fluid flow through porous medium, linear flow in crack, in fracture surface
Part is flowed in waterpower pressure drop into pit shaft radial flow and horizontal wellbore, and establishes the computation model of each section；
Wherein, the computation model of far-field zone non linear fluid flow through porous medium part 1) is established:
It is tested by rock core flowing test, obtains fluid in hypotonic non-darcy flow, regarded under different displacement pressure gradients
Permeability establishes the nonlinear mathematics equation for accurately reflecting percolation law in extra-low-permeability reservoir:
；
；
Wherein, a is the impact factor of non linear fluid flow through porous medium concave curve section, and b is that Nonlinear Quasi starting pressure gradient is reciprocal；
On the basis of the non linear fluid flow through porous medium model of above-mentioned foundation, fluid is non-linear ellipse in matrix in the presence of considering monolete
Circle seepage flow, establishes elliptical coordinate system, obtains integrating to obtain fracture end-face pressure P from supply boundary to fracture end-face pressure1:
；
2) computation model of Darcy linear stream part in crack is established:
In fracture surface flowing be considered as with a thickness ofW f , length be (X f -h/2), pressure difference isP 1 -P 2 Linear seepage flow, seepage flow differential side
Journey and boundary condition are as follows:
It solves:
Wherein,k f For fracture permeabgility, mD；W f For fracture width, m；P 2 For crack Darcy linear seepage flow and pit shaft radial direction aggregate flow
Dynamic intersection pressure, MPa；Q 2 For Darcy linear seepage flow flow, m in fracture surface3/s；
3) computation model in fracture surface to pit shaft radial flow portion is established:
In fracture surface after the linear flowing of fluid again to pit shaft assemble, be considered as with a thickness ofW f , radius ish/2Radial fluid flow,
Basis partial differential equation and boundary condition are as follows:
It solves:
In formula:r w For wellbore radius, m；Q 3 Flow, m are moved for aggregate flow radial in fracture surface3/s；
4) computation model of the waterpower pressure drop flowing part in horizontal wellbore is established:
Crack is radially injected the overall presure drop in impact-level pit shaft are as follows:
；
Wherein, △ ρ1(j) friction pressure drop caused by rubbing for horizontal well tube stream and wellbore wall, △ ρ2(j) it is radially injected for crack
Acceleration pressure drop caused by main stream line in impact-level pit shaft；Wherein, ρ is oil density, Kg/m3；
(2) assume one group of equivalent well bottom pressure value, coupling far-field zone non linear fluid flow through porous medium, linear flow in crack, in fracture surface
The equivalent equivalent diameter that straight well is obtained to the computation model of pit shaft radial flow obtains the equivalent equivalent radius of every crack:
Each equivalent well bottom pressure in crack is coupled with horizontal wellbore internal fissure with the pressure of junction in pit shaft, solves meter
It calculates:
Each equivalent well bottom pressure value is calculated；
In the presence of monolete, flow meets the condition of continuity:
By formula
Bring to obtain corresponding equivalent equivalent radius intoR equ(i) ;
；
(3) a plurality of fracturing fracture is equivalent at equivalent straight well, progress pressure drop superposition obtains each crack when multiple cracking interference
Yield；
Wherein,R ij For the distance between crack i and crack j, m；q i For the seam control yield of crack i, m3/s；For the equivalent well of crack i
Bottom pressure, Pa(i, j=1,2,3 ... N)；It, be to drainage radius since each equivalent well spacing is different with a distance from supply boundary
Amendment；
For eccentric well, image well inverting is utilized:；
Pressure drop is superimposed the drainage radius amendment in equation group are as follows:；
WhereinR e For drainage radius, m；R’ e (i)Drainage radius, m are corrected for equivalent well；d(i)For each equivalent straight well eccentricity, m；
(4) yield for each crack that step (3) obtains is coupled with the waterpower pressure drop flow model in horizontal wellbore, obtains one
Group bottom pressure iteratively solves the one group of production determined at this time until the bottom pressure difference of two step of front and back is less than tolerance i.e. convergence
Amount is the seam control yield of every crack, and the sum of each crack seam control yield is horizontal well total output；
Forq f (t)With the crack of production, the drop of pressure caused by space are as follows:
In formula
；
Wherein,KFor reservoir matrix permeability, mD；μFor viscosity of crude, mPas；ξFor elliptic coordinates；H is core intersection, m；X f
For fracture half-length, m；P 1 For fracture end-face pressure, MPa；P e For strata pressure, MPa；Q 1 For non linear fluid flow through porous medium field flow amount in matrix,
m3/s。
2. compactness reservoir horizontal well staged fracturing Productivity according to claim 1, it is characterised in that: establish
Elliptical coordinate system, obtain integrating from supply boundary to fracture end-face pressure fracture end-face pressure method are as follows:
Rectangular coordinate system and elliptical coordinate system transformation relation are as follows:
Elliptic Cylinder volume are as follows:
In the area approximation of the direction y cylindroid flow section are as follows:
Then its mass flow rate:
Average semi-minor axis radius are as follows:
By non linear fluid flow through porous medium law:
It solves:
Fracture end-face pressure is integrated to obtain from supply boundary to fracture end-face pressureP 1 :
。
3. compactness reservoir horizontal well staged fracturing Productivity according to claim 2, it is characterised in that: described
The overall presure drop that is radially injected in impact-level pit shaft of crack include that friction pressure drop caused by pipe stream and fluid are radially injected and draw
The acceleration pressure drop risen, in which:
Friction pressure drop caused by pipe stream are as follows:；
Acceleration pressure drop caused by fluid is radially injected are as follows:。
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