CN105840187A - Method for calculating staged fracturing productivity of compact reservoir horizontal well - Google Patents

Method for calculating staged fracturing productivity of compact reservoir horizontal well Download PDF

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CN105840187A
CN105840187A CN201610387971.5A CN201610387971A CN105840187A CN 105840187 A CN105840187 A CN 105840187A CN 201610387971 A CN201610387971 A CN 201610387971A CN 105840187 A CN105840187 A CN 105840187A
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flow
crack
pressure
fracture
well
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CN105840187B (en
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石立华
赵习森
高海龙
席天德
严茹波
党海龙
刘滨
薛颖
白远
田丰
龚娟
丁磊
柳朝阳
李刚
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Shaanxi Yanchang Petroleum Group Co Ltd
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    • E—FIXED CONSTRUCTIONS
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    • 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 invention relates to the technical field of oil fracturing, in particular to a method for calculating the staged fracturing productivity of a compact reservoir horizontal well. The method is characterized by including the steps of firstly, dividing a reservoir infiltration area into four parts; secondly, obtaining the equivalent hole diameter of each fracture; thirdly, obtaining the yield of each fracture during multiple fracture disturbance; fourthly, coupling the yield of each fracture with the hydraulic pressure drop flow model in a horizontal wellbore to obtain a group of bottom hole pressure, iteratively solving until the bottom hole pressure difference of the previous step and the next step is smaller than tolerance, namely convergence, and taking the determined group of yield as the fracture-control yield of each fracture and the sum of the fracture-control yield of the fractures as the total yield of the horizontal well. The method is real and reliable in calculation result and good in application effect.

Description

Compactness reservoir horizontal well staged fracturing Productivity
Technical field
The present invention relates to oil fracturing technical field, be specifically related to a kind of compactness reservoir horizontal well staged fracturing production capacity meter Calculation method.
Background technology
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 indoor are real Testing result to show, Oil in Super-low Permeability Reservoirs matrix seepage flow does not meets the Darcy's law of classics, there is stronger non linear fluid flow through porous medium phenomenon.
Calculate for productivity of fractured horizontal well both at home and abroad and carried out a series of research, mainly have Deng Yinger etc. establish each to The opposite sex Double Porosity Reservoir in vertically fractured well two-phase non-darcy elliptical porous flow model, analyze sorptivety, non-Darcy effects and The injection rate impact on the frac water horizontal well water breakthrough time；Duan Yonggang etc. consider fluid mill resistance, momentum change, wellbore wall inflow The complicated factor such as mixing interference, application boundary integration method sets up 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, draws horizontal well unsteady state flow with the method for semi analytic half numerical value The parameters such as rate distribution and wellbore pressure；The scholars such as Lian Peiqing utilize Green's function and Newman to amass principle, set up oil reservoir and frac water The new model of horizontal well pit shaft coupling, sets up the frac water horizontal well unsteady Model that box oil reservoir couples with horizontal wellbore；Sun Hai etc. Scholar sets up pit shaft and couples frac water horizontal well unsteady Model with oil reservoir and give the optimized algorithm of model solution.
Horizontal productivity evaluation and dynamic prediction are played an important role by the research of above scholar, but are primarily present following asking Topic: (1) major part productivity model assumed condition at present is more harsh, it is not comprehensive to consider the factor affecting production capacity, should Not ideal by effect；(2) about staged fracturing horizontal well parameter optimization method, physical analogy and numerical value it are mostly based at present Simulation is carried out, and utilizes reservoir engineering method to carry out fracturing parameter rapid Optimum research less；(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 what " Darcy linear percolation law " this premise was launched, Consider in low permeability reservoir matrix there there is no substantially the research of non linear fluid flow through porous medium phenomenon.
Summary of the invention
It is contemplated that for the problems referred to above, it is considered in non-linear flowing in staged fracturing horizontal well matrix, crack Waterpower pressure drop flowing in Darcy Flow, horizontal well pit shaft, proposes a kind of compactness oil reservoir segmented pressure break and calculates production capacity method.
Technical program of the present invention lies in:
Comprise the steps:
(1) flow through oil reservoir region is divided into four parts, i.e. in far-field zone non linear fluid flow through porous medium, crack internal linear stream, fracture surface Waterpower pressure drop flowing part in pit shaft radial flow and horizontal wellbore, and set up the computation model of each several part；
Wherein, 1) computation model of far field non linear fluid flow through porous medium part is:
Tested by rock core flowing test, obtain fluid in the case of hypotonic non-darcy flow, regard under different displacement pressure gradients Permeability, sets up and accurately reflects the nonlinear mathematics equation of percolation law in extra-low-permeability reservoir:
；
；(1)
Wherein,For the factor of influence of non linear fluid flow through porous medium concave curve section,Reciprocal for quasi-threshold pressure gradient；
On the basis of non linear fluid flow through porous medium model according to above-mentioned foundation, it is considered to non-linear ellipse in matrix of fluid in the presence of monolete Circle seepage flow, sets up elliptical coordinate system,
Rectangular coordinate system and elliptical coordinate system transformation relation be:
(2)
Elliptic Cylinder volume is:(3)
?The area approximation of direction cylindroid flow section is:
(4)
Then its mass flow rate:(5)
Average semi-minor axis radius is:(6)
By non linear fluid flow through porous medium law:(7)
(8)
(9)
Solve:) (10)
Fracture end-face pressure is obtained to fracture end-face pressure integration from supply boundary:
；(11)
Wherein, K is reservoir matrix permeability, mD；For viscosity of crude, mPa s；A is nonlinear parameter, zero dimension；B is non- Linear dimensions, zero dimension；Measured by laboratory experiment；For elliptic coordinates；H is core intersection, m；For fracture half-length, m； For fracture end-face pressure, MPa；For strata pressure, MPa；For non linear fluid flow through porous medium field flow amount, m in matrix3/s。
2) in crack, the computation model of Darcy linear stream part is:
The interior flowing of fracture surface is considered as thickness and is, a length of, pressure reduction isLinear seepage flow, its seepage flow differential Equation and boundary condition be:
Solve:(12)
Wherein,For fracture permeabgility, mD；For fracture width, m；Radially assemble for crack Darcy linear seepage flow and pit shaft Flowing intersection pressure, MPa；For Darcy linear seepage flow flow, m in fracture surface3/s；
3) in fracture surface to the computation model of pit shaft radial flow portion it is:
Assembling to pit shaft after the linear flowing of fluid in fracture surface, being considered as thickness is again, radius isRadial fluid flow, Its basis partial differential equation and boundary condition be:
(13)
Solve:(14)
In formula:For wellbore radius, m；Flow, m is moved for radial direction aggregate flow in fracture surface3/s；
4) computation model of the waterpower pressure drop flowing part in horizontal wellbore is:
Horizontal well is entered horizontal wellbore by crack and is divided into two parts pressure drop: one is the master that crack is radially injected in impact-level pit shaft The acceleration pressure drop that streamline causes.Two is the friction pressure drop that horizontal well tube stream causes with wellbore wall friction.For simplifying and crack Yield couples, and for N bar hydraulically created fracture, horizontal well is divided into N-1 section (only considering friction pressure drop as N=1).
For jth section, the friction pressure drop that pipe stream causes is:
(15)
Fluid is radially injected the acceleration pressure drop caused:
(16)
Jth section stagnation pressure is reduced to:(17)
In formula:For oil density Kg/m3；D is mineshaft diameter, m；D is sublevel interval, m；This section is flowed into for front j-1 section Integrated flux, m3/s；For this section of crack injection rate, m3/s；F is the coefficient of friction resistance, zero dimension.
(2) suppose one group of equivalence well bottom pressure value, couple far-field zone non linear fluid flow through porous medium, crack internal linear stream, crack In face, computation model to pit shaft radial flow draws the equivalent equivalent diameter of straight well, draws the equivalent equivalent radius of every crack:
Each crack equivalence well bottom pressure is coupled with the pressure of junction in pit shaft with horizontal wellbore internal fissure, solves Calculate:
(18)
Simultaneous formula (15)-(18) formula, draws each equivalence well bottom pressure value.
Its flow in the presence of monoleteMeet the condition of continuity:(19)
(20)
Formula (11) is brought into and can be obtained: corresponding equivalent equivalent radius Requ(i)
(21)
Given one, solution aboutIntegration transcendental equation, obtain correspondence equivalent equivalent radius。
(3) a plurality of fracturing fracture equivalence is become equivalent straight well, carry out pressure drop superposition, show that each bar when multiple cracking disturbs splits The yield of seam；
(22)
Wherein,For the distance between crack i and crack j, m；For the seam control yield of crack i, m3/s；For crack i etc. Effect well bottom pressure, Pa(i, j=1,2,3 ... N)；Owing to each equivalence well spacing is different from supply boundary distance, therefore will be to supply Radius correction；
For eccentric well, utilize image well inverting:； (23)
Drainage radius in pressure drop superposition equation group is modified to:； (24)
WhereinFor drainage radius, m；For equivalence well correction drainage radius, m；For each equivalence straight well eccentric throw, m；
(4) yield of each crack (3) drawn couples with the waterpower pressure drop flow model in horizontal wellbore, draws one group of well Bottom pressure, the bottom pressure difference of iterative to front and back two step i.e. restrains less than tolerance, the one group of yield now determined is i.e. For the seam control yield of every crack, each crack seam control yield sum is horizontal well total output.For withProduce splits Seam, its drop of pressure caused in space is:
(25)
In formula
(26)
The method have technical effect that:
The present invention is on the basis of staged fracturing horizontal well stable state, unsteady Model the most both at home and abroad, it is considered to staged fracturing level Waterpower pressure drop flowing in non-linear flowing in well matrix, the Darcy Flow in crack, horizontal well pit shaft, proposes one coupling The computation model of numerical solution horizontal productivity, its result of calculation is more true and reliable, and application effect is preferable.This model can be made For frac water horizontal well parameter optimization instrument, the horizontal productivity evaluation produced for site operation and parameter designing have important finger Lead meaning.
Accompanying drawing explanation
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 graph of a relation.
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 that the radial direction in fracture surface assembles schematic diagram.
Fig. 7 is waterpower pressure drop flow schematic diagram in horizontal wellbore.
Fig. 8 is equivalence straight well bias well schematic diagram.
Fig. 9 is model solution flow chart.
Figure 10 is flow effect schematic diagram in crack.
Figure 11 is flow effect schematic diagram between crack.
Figure 12 is crack outer radial stream effect schematic diagram.
Figure 13 is the pressure field distribution figure 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.
Detailed description of the invention
Mathematical Models assumed condition is as follows:
(1) drive type of reservoir is that hydraulic pressure elasticity is driven, i.e. supply rim pressure is constant；
(2) fluid flows in reservoir matrix and belongs to isothermal steady seepage, does not consider the function influence such as gravity, capillary force；
(3) in oil reservoir and crack, fluid is single-phase flow；
(4) rectangular vertical crack completely penetrates through payzone；
(5) fluid first uniformly flows into crack along crack wall, then is flowed into horizontal wellbore by crack.
Wherein, 1) computation model of far field non linear fluid flow through porous medium part is:
Carry out rock core flowing test experiment by high precision flow, obtain permeability and displacement pressure gradient relation curve, see Fig. 2, sets up the state equation of permeability:
(1)
Wherein,For the factor of influence of non linear fluid flow through porous medium concave curve section,Reciprocal for quasi-threshold pressure gradient；
Fig. 4 is non linear fluid flow through porous medium indicatrix: 2 corresponding barometric gradients of a, c are true free-boundary problem and intend starting pressure Power gradient.D is by the transition point of non linear fluid flow through porous medium to pseudo-linear flow, and flow event corresponding for curve ad is non linear fluid flow through porous medium. Being found out by Fig. 2, when fluid flows in low permeability reservoir matrix, its liquid phase effective permeability is no longer constant, but displacement pressure The function of gradient.
This model can preferably describe before barometric gradient is in true free-boundary problem and maximum free-boundary problem The non-linear flow phenomenon that fluid presents.WhenTime,It is starting pressure ladder Degree model；WhenTime infinitely great, reflection quasi-threshold pressure gradient is infinitely small, and fluid is weak with the effect of solid,Develop into Darcy linear flow model in porous media.This model can describe in low permeability reservoir matrix and be in The flowing of each barometric gradient interval fluid.The pass of permeability and free-boundary problem is gone out by laboratory core fitting experimental data Being formula, as a example by rock sample 12-3, the degree of depth is 2166.2m, core permeability 0.633mD, true free-boundary problem 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, it is considered to fluid non linear elliptic seepage flow in matrix in the presence of monolete.Build Vertical elliptical coordinate system, is shown in Fig. 3:
Rectangular coordinate system and elliptical coordinate system transformation relation be:
(2)
Elliptic Cylinder volume is:(3)
?The area approximation of direction cylindroid flow section is:
(4)
Then its mass flow rate:(5)
Average semi-minor axis radius is:(6)
By non linear fluid flow through porous medium law:(7)
(8)
(9)
Solve:) (10)
Fracture end-face pressure is obtained to fracture end-face pressure integration from supply boundary:
；(11)
Wherein, K is reservoir matrix permeability, mD；For viscosity of crude, mPa s；A is nonlinear parameter, zero dimension；B is non- Linear dimensions, m/MPa；Measured by laboratory experiment；For elliptic coordinates；H is core intersection, m；For fracture half-length, m； For fracture end-face pressure, MPa；For strata pressure, MPa；For non linear fluid flow through porous medium field flow amount, m in matrix3/s。
2) computation model of crack internal linear stream part is:
Fig. 5 is the Darcy linear seepage flow schematic diagram in fracture surface, and in fracture surface, flowing can be considered that thickness is, a length of, pressure reduction isLinear seepage flow, its basis partial differential equation and boundary condition be:
Solve:(12)
Wherein,For fracture permeabgility, mD；For fracture width, m；Radially assemble for crack Darcy linear seepage flow and pit shaft Flowing intersection pressure, MPa；For Darcy linear seepage flow flow, m in fracture surface3/s；
3) in fracture surface to the computation model of pit shaft radial flow portion it is:
Fig. 6 is that the radial direction in fracture surface assembles schematic diagram, assembles to pit shaft again, can be considered in fracture surface after the linear flowing of fluid Thickness is, radius isRadial fluid flow, its basis partial differential equation and boundary condition be:
(13)
Solve:(14)
In formula:For wellbore radius, m；Flow, m is moved for radial direction aggregate flow in fracture surface3/s；
4) computation model of the waterpower pressure drop flowing part in pit shaft is:
Fig. 7 is waterpower pressure drop flow schematic diagram in horizontal wellbore, and horizontal well is entered horizontal wellbore by crack and is divided into two parts pressure drop: One is the acceleration pressure drop that the main stream line that crack is radially injected in impact-level pit shaft causes.Two is horizontal well tube stream and well bore wall The friction pressure drop that face friction causes.Couple with crack yield for simplifying, for N bar hydraulically created fracture, horizontal well is divided into N-1 Section (only considering friction pressure drop as N=1).
For jth section, the friction pressure drop that pipe stream causes is:
(15)
Fluid is radially injected the acceleration pressure drop caused:
(16)
Jth section stagnation pressure is reduced to:(17)
In formula:For oil density Kg/m3；D is mineshaft diameter, m；D is sublevel interval, m；This section is flowed into for front j-1 section Integrated flux, m3/s；For this section of crack injection rate, m3/s；F is the coefficient of friction resistance, zero dimension.
(2) suppose one group of equivalence well bottom pressure value, couple far-field zone non linear fluid flow through porous medium, crack internal linear stream, crack In face, computation model to pit shaft radial flow draws the equivalent equivalent diameter of straight well, draws the equivalent equivalent radius of every crack:
Each crack equivalence well bottom pressure is coupled with the pressure of junction in pit shaft with horizontal wellbore internal fissure, solves Calculate:
(18)
Draw each equivalence well bottom pressure value；
Its flow in the presence of monoleteMeet the condition of continuity:(19)
(20)
Formula (11) is brought into and can be obtained: corresponding equivalent equivalent radius Requ(i)
(21)
Given one, solution aboutIntegration transcendental equation, obtain correspondence equivalent equivalent radius；
(3) a plurality of fracturing fracture equivalence is become equivalent straight well, carry out pressure drop superposition, draw each crack when multiple cracking disturbs Yield；
(22)
Wherein,For the distance between crack i and crack j, m；For the seam control yield of crack i, m3/s；For crack i etc. Effect well bottom pressure, Pa(i, j=1,2,3 ... N)；Owing to each equivalence well spacing is different from supply boundary distance, therefore will be to supply Radius correction；
For eccentric well, utilize image well inverting:； (23)
Drainage radius in pressure drop superposition equation group is modified to:； (24)
WhereinFor drainage radius, m；For equivalence well correction drainage radius, m；For each equivalence straight well eccentric throw, m；
(4) yield in (3) being coupled with the waterpower pressure drop flow model in horizontal wellbore, draw one group of bottom pressure, iteration is asked Solution to the bottom pressure difference of front and back two step i.e. restrains less than tolerance, the one group of yield now determined is the seam of every crack Control yield, each crack seam control yield sum is horizontal well total output；
For withThe crack produced, its drop of pressure caused in space is:
(25)
In formula
(26)
The physical significance of F function is crack j when producing with specific yield, the pressure drop produced at the i of crack within 0 ~ t time. This model is it is considered that unstable state production decline rule under the conditions of determining bottom pressure.
The solution procedure of this model is shown in Fig. 9.
The method validation providing the present invention is as follows:
(1) method for numerical simulation checking
For verifying the application effect of model, take the reservoir parameter shown in table 1 and calculate.Under ECLIPSE numerical simulation software Simulation calculates 180d, obtains yield and changes over data, contrast productivity model result of calculation and ECLIPSE numerical simulation calculation Result such as Figure 10.
Table 1 W block segmentation frac water horizontal well underlying parameter table
Table 1 staged fracturing of horizontal well base parameter in W blocks
As shown in Figure 15, the calculating data of productivity model are preferable with coincideing property of Field Production Data, demonstrate the reliability of model.
(2) field test application
The method utilizing the present invention to provide extends oil field ultra-low penetration W four mouthfuls of water horizontal wells of block length 9 oil reservoir to Ordos Basin Carry out AOF calculation, and contrast with actual production capacity.The basic data of this horizontal well and result of calculation such as table 2.
Four mouthfuls of water horizontal well AOF calculation results of table 2 W block length 9 oil reservoir
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 table of table 3
Table2 Calculation result of different production models
According to the model calculation: the actual production at four mouthfuls of water horizontal wells scenes of W block length 9 oil reservoir is 6.45t/d- 11.87t/d, utilizes new productivity model to calculate horizontal well production for 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 this model has preferable practicality, demonstrate the accuracy of model.Due to novel product The non linear fluid flow through porous medium feature in low permeability reservoir can be considered by model so that result of calculation meets the actual conditions in oil field, be suitable for Property higher, it was predicted that result is more true and reliable, therefore can as such reservoir-level well fracturing parameter optimize foundation.

Claims (3)

1. compactness reservoir horizontal well staged fracturing Productivity, it is characterised in that: comprise the following steps:
(1) flow through oil reservoir region is divided into four parts, i.e. in far-field zone non linear fluid flow through porous medium, crack internal linear stream, fracture surface Waterpower pressure drop flowing part in pit shaft radial flow and horizontal wellbore, and set up the computation model of each several part；
Wherein, the computation model of far-field zone non linear fluid flow through porous medium part 1) is set up:
Tested by rock core flowing test, obtain fluid in the case of hypotonic non-darcy flow, regard under different displacement pressure gradients Permeability, sets up and accurately reflects the nonlinear mathematics equation of percolation law in extra-low-permeability reservoir:
；
；
Wherein,For the factor of influence of non linear fluid flow through porous medium concave curve section, b is that quasi-threshold pressure gradient is reciprocal；
On the basis of non linear fluid flow through porous medium model according to above-mentioned foundation, it is considered to non-linear ellipse in matrix of fluid in the presence of monolete Circle seepage flow, sets up elliptical coordinate system, obtains obtaining fracture end-face pressure P from supply boundary to fracture end-face pressure integration1:
；
2) computation model of Darcy linear stream part in crack is set up:
The interior flowing of fracture surface is considered as thickness and is, a length of, pressure reduction isLinear seepage flow, its seepage flow differential Equation and boundary condition be:
Solve:
Wherein,For fracture permeabgility, mD；For fracture width, m；For crack Darcy linear seepage flow and pit shaft radially aggregate flow Dynamic intersection pressure, MPa；For Darcy linear seepage flow flow, m in fracture surface3/s；
3) fracture surface is set up interior to the computation model of pit shaft radial flow portion:
Assembling to pit shaft after the linear flowing of fluid in fracture surface, being considered as thickness is again, radius isRadial fluid flow, Its basis partial differential equation and boundary condition be:
Solve:
In formula:For wellbore radius, m；Flow, m is moved for radial direction aggregate flow in fracture surface3/s；
4) computation model of waterpower pressure drop flowing part in horizontal wellbore is set up:
The stagnation pressure that crack is radially injected in impact-level pit shaft is reduced to:
；
Wherein, △ 1J () is the friction pressure drop that horizontal well tube stream causes with wellbore wall friction, △ 2J () is crack radially note Enter the acceleration pressure drop that the main stream line in impact-level pit shaft causes;Wherein,For oil density, Kg/m3;
(2) one group of equivalence well bottom pressure value is supposed, in coupling far-field zone non linear fluid flow through porous medium, crack internal linear stream, fracture surface Computation model to pit shaft radial flow draws the equivalent equivalent diameter of straight well, draws the equivalent equivalent radius of every crack:
Each crack equivalence well bottom pressure couples with the pressure of junction in pit shaft with horizontal wellbore internal fissure, solves meter Calculate:
Calculate each equivalence well bottom pressure value；
In the presence of monolete, its flowMeet the condition of continuity:
By formulaBring into right The equivalent equivalent radius answered；
；
(3) a plurality of fracturing fracture equivalence is become equivalent straight well, carry out pressure drop superposition, draw each crack when multiple cracking disturbs Yield；
Wherein,For the distance between crack i and crack j, m；For the seam control yield of crack i, m3/s；For crack i etc. Effect well bottom pressure, Pa(i, j=1,2,3 ... N)；Owing to each equivalence well spacing is different from supply boundary distance, therefore will be to supply Radius correction；
For eccentric well, utilize image well inverting:；
Drainage radius in pressure drop superposition equation group is modified to:；
WhereinFor drainage radius, m；For equivalence well correction drainage radius, m；For each equivalence straight well eccentric throw, m；
(4) yield of each crack step (3) drawn couples with the waterpower pressure drop flow model in horizontal wellbore, draws one Group bottom pressure, the bottom pressure difference of iterative to front and back two step i.e. restrains less than tolerance, the one group of product now determined Amount is the seam control yield of every crack, and each crack seam control yield sum is horizontal well total output；
For withThe crack produced, its drop of pressure caused in space is:
In formula
。
Compactness reservoir horizontal well staged fracturing Productivity the most according to claim 1, it is characterised in that: set up Elliptical coordinate system, obtaining the method from supply boundary obtains fracture end-face pressure to fracture end-face pressure integration is:
Rectangular coordinate system and elliptical coordinate system transformation relation be:
Elliptic Cylinder volume is:
?The area approximation of direction cylindroid flow section is:
Then its mass flow rate:
Average semi-minor axis radius is:
By non linear fluid flow through porous medium law:
Solve:
Fracture end-face pressure is obtained to fracture end-face pressure integration from supply boundary:
；
Wherein, K is reservoir matrix permeability, mD；For viscosity of crude, mPa s；A is nonlinear parameter, zero dimension；B is non- Linear dimensions, zero dimension；Measured by laboratory experiment；For elliptic coordinates；H is core intersection, m；For fracture half-length, m；For fracture end-face pressure, MPa；For strata pressure, MPa；For non linear fluid flow through porous medium field flow amount, m in matrix3/s。
Compactness reservoir horizontal well staged fracturing Productivity the most according to claim 2, it is characterised in that: described The crack overall presure drop that is radially injected in impact-level pit shaft include that friction pressure drop that pipe stream causes and fluid are radially injected and draw The acceleration pressure drop risen, wherein:
The friction pressure drop that pipe stream causes is:；
Fluid is radially injected the acceleration pressure drop caused:。
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