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 PDFInfo
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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
Technical Field
The invention relates to the technical field of petroleum fracturing, in particular to a staged fracturing productivity calculation method for a horizontal well of a compact oil reservoir.
Background
The horizontal well productivity is the basis for optimizing the fracturing parameters of the horizontal well and evaluating the development effect. At present, the calculation of the fracturing capacity of the horizontal well at home and abroad is mostly based on a Darcy seepage model in a reservoir matrix, and the production practice of a mining field and the results of indoor experiments show that the seepage of the ultra-low permeability reservoir matrix does not accord with the classic Darcy law and has stronger nonlinear seepage phenomenon.
A series of researches are carried out at home and abroad aiming at the calculation of the fracturing capacity of the horizontal well, a vertical fractured well two-phase non-Darcy elliptical seepage model in the anisotropic dual-medium oil reservoir is mainly established by Dengyl and the like, and the influence of the suction seepage, the non-Darcy effect and the injection rate on the water breakthrough time of the fractured horizontal well is analyzed; segment permanent rigidity and the like consider complex factors such as fluid abrasion resistance, momentum change, mixing interference of borehole wall surface inflow and the like, and a boundary integration method is applied to establish a horizontal borehole and oil reservoir coupling calculation model; the scholars such as Chengwei and the like improve the uniform flow rate model into a non-uniform flow rate calculation model, and parameters such as horizontal well unsteady flow rate distribution, wellbore pressure and the like are obtained by a semi-analytic half-value method; the method comprises the following steps that a new model of coupling of an oil reservoir and a fractured horizontal well shaft is established by a student in the field of Ringqing and the like by utilizing a Green function and the Newman product principle, and a fractured horizontal well unsteady state model of coupling of a box-type oil reservoir and the horizontal well shaft is established; sunhai et al establishes a non-steady-state model of a shaft and oil reservoir coupled fractured horizontal well and provides an optimization algorithm for solving the model.
The research of the scholars plays an important role in evaluating and dynamically predicting the productivity of the horizontal well, but the problems are mainly as follows: (1) at present, most capacity calculation models are harsh in assumed conditions, the factors influencing the capacity are not considered comprehensively, and the application effect is not ideal; (2) regarding the staged fracturing horizontal well parameter optimization method, most of the methods are performed based on physical simulation and numerical simulation at present, and the rapid optimization research of fracturing parameters by using an oil reservoir engineering method is less; (3) at present, researches on the productivity and the seepage rule of the staged fracturing horizontal well are mainly developed on the premise that the seepage in a matrix conforms to the Darcy linear seepage rule, and the researches considering the nonlinear seepage phenomenon in the matrix of a hypotonic reservoir are basically not available.
Disclosure of Invention
Aiming at the problems, the invention provides a method for calculating the productivity of the compact oil reservoir by sectional fracturing, which considers the nonlinear flow in a substrate of a sectional fracturing horizontal well, the Darcy flow in a crack and the hydraulic pressure drop flow in a shaft of the horizontal well.
The technical scheme of the invention is as follows:
the method comprises the following steps:
(1) dividing an oil reservoir seepage area into four parts, namely a far field zone nonlinear seepage part, a fracture internal linear flow part, a fracture surface internal wellbore radial flow part and a horizontal wellbore hydraulic pressure drop flow part, and establishing a calculation model of each part;
wherein, 1) the calculation model of the far-field nonlinear seepage part is as follows:
through a core flow test experiment, the apparent permeability of the fluid under the condition of low-permeability non-Darcy seepage and different displacement pressure gradients is obtained, and a nonlinear mathematical equation which accurately reflects the seepage rule in the ultra-low permeability reservoir is established:
；
； （1）
wherein,is the influence factor of the non-linear seepage concave curve segment,is the inverse of the pressure gradient to be started;
based on the established nonlinear seepage model, the nonlinear elliptical seepage of the fluid in the matrix when the single fracture exists is considered, an elliptical coordinate system is established,
the rectangular coordinate system and the elliptical coordinate system have the following transformation relations:
（2）
the volume of the elliptic cylinder is as follows:（3）
in thatThe area of the flow cross section of the directional elliptic cylinder is approximately as follows:
（4）
its average mass flow rate is:（5）
the average minor semi-axis radius is:（6）
from the nonlinear percolation law:（7）
（8）
（9）
obtaining by solution:） （10）
integrating the pressure from the supply boundary to the fracture end face to obtain the fracture end face pressure：
； （11）
Wherein K is the reservoir matrix permeability, mD;crude oil viscosity, mPa · s; a is a nonlinear parameter without dimension; b is a non-linear parameter without dimension; determined by laboratory experiments;is an elliptical coordinate; h is the oil layer thickness, m;m is the half-length of the crack;the pressure of the end face of the crack is MPa;is the formation pressure, MPa;is the flow rate of a nonlinear seepage field in a matrix, m3/s。
2) The computational model of the darcy linear flow portion within the fracture is:
the flow in the fracture plane is regarded as the thicknessLength ofDifferential pressure ofThe seepage differential equation and the boundary conditions of the linear seepage of (1) are as follows:
obtaining by solution:（12）
wherein,fracture permeability, mD;is the crack width, m;the pressure at the junction of the fracture Darcy linear seepage and the radial aggregation flow of the shaft is MPa;is Darcy's linear seepage flow in the fracture surface, m3/s；
3) The calculation model of the radial flow part of the inner direction of the fracture surface to the shaft is as follows:
the fluid in the fracture surface is linearly flowed and then is gathered towards the shaftIs of thickness ofRadius ofThe seepage differential equation and the boundary conditions of the planar radial flow of (2) are as follows:
（13）
obtaining by solution:（14）
in the formula:is the wellbore radius, m;for radially concentrating the flow in the fracture plane, m3/s；
4) The calculation model of the hydraulic pressure drop flow section in the horizontal wellbore is:
the horizontal well is divided into two pressure drops when the cracks enter the horizontal shaft, namely the pressure drop caused by the fact that the cracks are injected radially to impact a main flow line in the horizontal shaft. And the second is the friction pressure drop caused by the friction between the horizontal well pipe flow and the wall surface of the well bore. To simplify the coupling to fracture production, for N hydraulic fractures, the horizontal well was divided into N-1 sections (only frictional pressure drop was considered when N = 1).
For section j, the frictional pressure drop caused by the pipe flow is:
（15）
the acceleration pressure drop caused by the radial injection of the fluid is as follows:
（16）
for the j-th section the total pressure drop is:（17）
in the formula:is crude oil density Kg/m3(ii) a D is the diameter of the shaft, m; d is the segment spacing, m;cumulative flow into this section for the first j-1 section, m3/s；M is the amount of crack injected in this section3S; f is the friction coefficient and has no dimension.
(2) Assuming a group of equivalent well bottom pressure values, coupling a calculation model of nonlinear seepage in a far-field zone, linear flow in a crack and radial flow of a crack surface to a shaft to obtain the equivalent diameter of a straight well, and obtaining the equivalent well diameter of each crack:
for each fracture equivalent well bottom pressure and the pressure of the fracture in the horizontal shaft and the connection part in the shaft are coupled, solving and calculating:
（18）
and (4) obtaining the bottom pressure value of each equivalent well by the joint formulas (15) - (18).
Flow rate of single crack in existenceThe continuity condition is satisfied:（19）
（20）
formula (11) is substituted into available: corresponding equivalent well diameter Requ(i)
（21）
Is given oneRelate toThe integral transcendental equation of the equivalent well diameter is obtained。
(3) Equivalent vertical wells are equivalently formed by a plurality of fracturing fractures, and pressure drop superposition is carried out to obtain the yield of each fracture when the fractures are interfered;
(22)
wherein,is the distance between crack i and crack j, m;gap control yield for gap i, m3/s；Pa (i, j =1,2,3 … … N) which is the equivalent bottom hole pressure of fracture i; because each equivalent well is at a different distance from the supply boundary, the supply radius is corrected;
for an eccentric well, inversion is performed using an image well:； (23)
the feed radius in the pressure drop stack equation is modified as:； (24)
whereinTo supply radius, m;correcting the supply radius, m, for the equivalent well;is the eccentricity of each equivalent vertical well, m;
(4) and (3) coupling the yield of each crack obtained in the step (3) with a hydraulic pressure drop flow model in the horizontal shaft to obtain a group of bottom hole pressures, and iteratively solving until the bottom hole pressure difference of the previous step and the next step is smaller than the tolerance, namely convergence is achieved, the determined group of yields are the crack control yields of each crack, and the sum of the crack control yields is the total yield of the horizontal well. To in relation toA fracture produced which has a spatially induced pressure drop of:
（25）
in the formula
(26)
The invention has the technical effects that:
on the basis of steady-state and unsteady-state models of the staged fracturing horizontal well at home and abroad at present, nonlinear flow in a staged fracturing horizontal well matrix, Darcy flow in cracks and hydraulic pressure drop flow in a horizontal well shaft are considered, the invention provides the calculation model for solving the horizontal well productivity by coupling numerical values, and the calculation result is more real and reliable and has better application effect. The model can be used as a fracturing horizontal well parameter optimization tool, and has important guiding significance for horizontal well productivity evaluation and parameter design of field construction production.
Drawings
FIG. 1 is a schematic diagram of a productivity model of a horizontal well fractured by a plurality of transverse fractures.
FIG. 2 is a graph of dimensionless permeability versus displacement pressure gradient.
Fig. 3 is a relationship diagram of a rectangular coordinate system and an elliptical coordinate system.
FIG. 4 is a non-linear seepage curve for low permeability reservoir fluids.
FIG. 5 is a schematic view of Darcy's linear seepage in the fracture plane.
FIG. 6 is a schematic view of radial concentration in the fracture face.
Fig. 7 is a schematic diagram of hydraulic pressure drop flow in a horizontal wellbore.
FIG. 8 is a schematic diagram of an equivalent vertical offset well.
FIG. 9 is a flow chart of model solution.
FIG. 10 is a schematic diagram of the flow effect in a fracture.
FIG. 11 is a schematic view showing the effect of flow between cracks.
FIG. 12 is a schematic view of the effect of radial flow outside the fracture.
FIG. 13 is a pressure field profile without regard to pressure drop within the wellbore.
Fig. 14 is a coupled pressure field profile.
FIG. 15 is a graph comparing a throughput model with ECLIPSE numerical simulation results.
Detailed Description
The mathematical model establishes the following assumptions:
(1) the oil deposit driving type is hydraulic elastic driving, namely the supply edge pressure is unchanged;
(2) fluid flows in a reservoir matrix and belongs to isothermal stable seepage, and the influence of gravity, capillary force and the like is not considered;
(3) the fluid in the oil reservoir and the crack is single-phase flow;
(4) the rectangular vertical cracks completely penetrate the producing zone;
(5) the fluid flows into the fracture uniformly along the fracture wall surface and then flows into the horizontal wellbore from the fracture.
Wherein, 1) the calculation model of the far-field nonlinear seepage part is as follows:
performing a core flow test experiment through the high-precision flowmeter to obtain a relation curve of permeability and displacement pressure gradient, and establishing a state equation of permeability as shown in figure 2:
(1)
wherein,is the influence factor of the non-linear seepage concave curve segment,is the inverse of the pressure gradient to be started;
FIG. 4 is a non-linear seepage characteristic curve: a. and c, the pressure gradients corresponding to the two points are a real starting pressure gradient and a simulated starting pressure gradient. d is the transition point from the nonlinear seepage to the quasi-linear seepage, and the seepage process corresponding to the curve ad is the nonlinear seepage. As can be seen from fig. 2, the effective permeability of the fluid in the liquid phase is no longer a constant but a function of the displacement pressure gradient as it flows in the hypotonic reservoir matrix.
The model can better describe the nonlinear flow phenomenon of the fluid before the pressure gradient is between the real starting pressure gradient and the maximum starting pressure gradient. When in useWhen the temperature of the water is higher than the set temperature,namely a pressure gradient model to be started; when in useWhen infinite, the pressure gradient of the starting is infinitesimal, the action of the fluid and the solid is weak,evolved into a darcy linear seepage model. The model can describe the flow of fluid in the hypotonic reservoir matrix at various pressure gradient intervals. Fitting a relation between permeability and starting pressure gradient through indoor core experiment data to obtain a rock sample 12-3 for example, depth of 2166.2m, core permeability of 0.633mD, true start pressure gradient of 0.0517MPa, pseudo start pressure gradient of 0.1449MPa, fit a =0.268, b = 6.90.
On the basis of the equation of state above, consider the nonlinear elliptical seepage of fluid in a matrix in the presence of a single fracture. An elliptical coordinate system is established, see fig. 3:
the rectangular coordinate system and the elliptical coordinate system have the following transformation relations:
（2）
the volume of the elliptic cylinder is as follows:（3）
in thatThe area of the flow cross section of the directional elliptic cylinder is approximately as follows:
（4）
its average mass flow rate is:（5）
the average minor semi-axis radius is:（6）
from the nonlinear percolation law:（7）
（8）
（9）
obtaining by solution:） （10）
integrating the pressure from the supply boundary to the fracture end face to obtain the fracture end face pressure：
； （11）
Wherein K is the reservoir matrix permeability, mD;crude oil viscosity, mPa · s; a is a nonlinear parameter without dimension; b is a nonlinear parameter, m/MPa; determined by laboratory experiments;is an elliptical coordinate; h is the oil layer thickness, m;m is the half-length of the crack;the pressure of the end face of the crack is MPa;is the formation pressure, MPa;is the flow rate of a nonlinear seepage field in a matrix, m3/s。
2) The computational model of the linear flow portion within the fracture is:
FIG. 5 is a schematic view of Darcy's linear seepage in the fracture plane, where the flow in the fracture plane can be considered as thicknessLength ofDifferential pressure ofThe seepage differential equation and the boundary conditions of the linear seepage of (1) are as follows:
obtaining by solution:（12）
wherein,fracture permeability, mD;is the crack width, m;the pressure at the junction of the fracture Darcy linear seepage and the radial aggregation flow of the shaft is MPa;is Darcy's linear seepage flow in the fracture surface, m3/s；
3) The calculation model of the radial flow part of the inner direction of the fracture surface to the shaft is as follows:
FIG. 6 is a schematic view of radial convergence in the fracture plane, in which the fluid in the fracture plane converges toward the wellbore after flowing linearly, which can be considered as having a thickness ofRadius ofThe seepage differential equation and the boundary conditions of the planar radial flow of (2) are as follows:
（13）
obtaining by solution:（14）
in the formula:is the wellbore radius, m;for radially concentrating the flow in the fracture plane, m3/s；
4) The computational model of the hydraulic pressure drop flow section in the wellbore is:
FIG. 7 is a schematic diagram of hydraulic pressure drop flow in a horizontal wellbore, wherein the horizontal well is divided into two pressure drops when entering the horizontal wellbore from a fracture, namely, the pressure drop due to acceleration caused by radial injection of the fracture to impact a main flow line in the horizontal wellbore. And the second is the friction pressure drop caused by the friction between the horizontal well pipe flow and the wall surface of the well bore. To simplify the coupling to fracture production, for N hydraulic fractures, the horizontal well was divided into N-1 sections (only frictional pressure drop was considered when N = 1).
For section j, the frictional pressure drop caused by the pipe flow is:
（15）
the acceleration pressure drop caused by the radial injection of the fluid is as follows:
（16）
for the j-th section the total pressure drop is:（17）
in the formula:is crude oil density Kg/m3(ii) a D is the diameter of the shaft, m; d is the segment spacing, m;cumulative flow into this section for the first j-1 section, m3/s；M is the amount of crack injected in this section3S; f is the friction coefficient and has no dimension.
(2) Assuming a group of equivalent well bottom pressure values, coupling a calculation model of nonlinear seepage in a far-field zone, linear flow in a crack and radial flow of a crack surface to a shaft to obtain the equivalent diameter of a straight well, and obtaining the equivalent well diameter of each crack:
for each fracture equivalent well bottom pressure and the pressure of the fracture in the horizontal shaft and the connection part in the shaft are coupled, solving and calculating:
（18）
obtaining bottom pressure values of all equivalent wells;
flow rate of single crack in existenceThe continuity condition is satisfied:（19）
（20）
formula (11) is substituted into available: corresponding equivalent well diameter Requ(i)
（21）
Is given oneRelate toThe integral transcendental equation of the equivalent well diameter is obtained；
(3) Equivalent vertical wells are equivalently formed by a plurality of fracturing fractures, and pressure drop superposition is carried out to obtain the yield of each fracture when the fractures are interfered;
(22)
wherein,is the distance between crack i and crack j, m;gap control yield for gap i, m3/s；Pa (i, j =1,2,3 … … N) which is the equivalent bottom hole pressure of fracture i; because each equivalent well is at a different distance from the supply boundary, the supply radius is corrected;
for an eccentric well, inversion is performed using an image well:； (23)
the feed radius in the pressure drop stack equation is modified as:； (24)
whereinTo supply radius, m;correcting the supply radius, m, for the equivalent well;is the eccentricity of each equivalent vertical well, m;
(4) coupling the yield in the step (3) with a hydraulic pressure drop flow model in a horizontal shaft to obtain a group of bottom hole pressures, and iteratively solving until the bottom hole pressure difference of the previous step and the next step is smaller than a tolerance, namely convergence is carried out, wherein the determined group of yields are seam control yields of each crack, and the sum of the seam control yields of all cracks is the total yield of the horizontal shaft;
to in relation toA fracture produced which has a spatially induced pressure drop of:
（25）
in the formula
(26)
The physical significance of the F function is the pressure drop at fracture i in 0-t time when fracture j is produced at unit production. The model considers the unsteady production decrement law under the condition of fixed bottom hole pressure.
The solving process of the model is shown in figure 9.
The method provided by the invention is verified as follows:
(1) verification by numerical simulation method
In order to verify the application effect of the model, the reservoir parameters shown in table 1 were taken for calculation. The simulation calculation 180d is performed under ECLIPSE numerical simulation software to obtain the data of the change of the yield with time, and the comparison between the calculation result of the capacity model and the calculation result of the ECLIPSE numerical simulation is shown in FIG. 10.
TABLE 1W Block staged fracturing horizontal well basic parameter Table
Table 1 staged fracturing of horizontal well base parameter in W blocks
As can be seen from FIG. 15, the calculated data of the capacity model and the field production data are well matched, and the reliability of the model is verified.
(2) Mine site test application
The method provided by the invention is used for carrying out capacity calculation on four horizontal wells of an ultra-low permeability W block length 9 oil layer of an Eldos basin, and comparing the capacity calculation with the actual capacity. The basic data and the calculation results of this horizontal well are shown in table 2.
TABLE 2W Block Length 9 reservoir four horizontal wells productivity calculation results
Table1 four horizontal well productivity calculation results of chang 9reservoir in W block
(crude oil Density: 0.75 g/cm)3）。
TABLE 3 data table of calculation results of different productivity models
Table2 Calculation result of different production models
According to the model calculation result, the following results are obtained: the actual yield of the W block with the length of 9 oil layers on four horizontal wells is 6.45t/d-11.87t/d, the yield of the horizontal well is calculated to be 6.12t/d-11.37t/d by using the new productivity model, the coincidence rate is up to 85.21% -94.25%, the average yield is 91.03%, and the model is proved to have better practicability and the accuracy of the model is verified. The novel capacity model considers the nonlinear seepage characteristics in the low-permeability reservoir, so that the calculation result accords with the actual condition of the oil field, the applicability is stronger, and the prediction result is more real and reliable, so that the novel capacity model can be used as the basis for optimizing the fracturing parameters of the horizontal well of the reservoir.
Claims (3)
1. The staged fracturing productivity calculation method of the compact oil reservoir horizontal well is characterized by comprising the following steps of: the method comprises the following steps:
(1) dividing an oil reservoir seepage area into four parts, namely a far field zone nonlinear seepage part, a fracture internal linear flow part, a fracture surface internal wellbore radial flow part and a horizontal wellbore hydraulic pressure drop flow part, and establishing a calculation model of each part;
wherein, 1) establishing a calculation model of the far-field zone nonlinear seepage part:
through a core flow test experiment, the apparent permeability of the fluid under the condition of low-permeability non-Darcy seepage and different displacement pressure gradients is obtained, and a nonlinear mathematical equation which accurately reflects the seepage rule in the ultra-low permeability reservoir is established:
；
；
wherein,the influence factor of the nonlinear seepage concave curve segment is shown, and b is the reciprocal of the pressure gradient to be started;
on the basis of the established nonlinear seepage model, the nonlinear elliptical seepage of the fluid in the matrix when the single fracture exists is considered, an elliptical coordinate system is established, and the pressure integral from the supply boundary to the fracture end face is obtained to obtain the fracture end face pressure P1：
；
2) Establishing a calculation model of Darcy linear flow part in the crack:
the flow in the fracture plane is regarded as the thicknessLength ofDifferential pressure ofThe seepage differential equation and the boundary conditions of the linear seepage of (1) are as follows:
obtaining by solution:
wherein,fracture permeability, mD;is the crack width, m;the pressure at the junction of the fracture Darcy linear seepage and the radial aggregation flow of the shaft is MPa;is Darcy's linear seepage flow in the fracture surface, m3/s；
3) Establishing a calculation model of a radial flow part of the inward wellbore of the fracture surface:
the fluid in the fracture surface is linearly flowed and then gathered towards the shaft, and the thickness is regarded asRadius ofThe seepage differential equation and the boundary conditions of the planar radial flow of (2) are as follows:
obtaining by solution:
in the formula:is the wellbore radius, m;for radially concentrating the flow in the fracture plane, m3/s；
4) Establishing a calculation model of the hydraulic pressure drop flow part in the horizontal well shaft:
the total pressure drop in the fracture radial injection horizontal wellbore is:
；
wherein, △ 1(j) For frictional pressure drop caused by friction between horizontal well pipe flow and wellbore wall, △ 2(j) The fracture is radially injected with an acceleration pressure drop that impinges on the primary flow line within the horizontal wellbore, wherein,is crude oil density, Kg/m3;
(2) Assuming a group of equivalent well bottom pressure values, coupling a calculation model of nonlinear seepage in a far-field zone, linear flow in a crack and radial flow of a crack surface to a shaft to obtain the equivalent diameter of a straight well, and obtaining the equivalent well diameter of each crack:
the bottom hole pressure of each fracture equivalent well is coupled with the pressure of the fracture in the horizontal shaft and the connecting part in the shaft, and the solution calculation is as follows:
calculating to obtain the bottom pressure value of each equivalent well;
when a single crack exists, the flow rate of the single crackThe continuity condition is satisfied:
general formulaBring the equivalent well diameter into correspondence；
；
(3) Equivalent vertical wells are equivalently formed by a plurality of fracturing fractures, and pressure drop superposition is carried out to obtain the yield of each fracture when the fractures are interfered;
wherein,is the distance between crack i and crack j, m;gap control yield for gap i, m3/s；Pa (i, j =1,2,3 … … N) which is the equivalent bottom hole pressure of fracture i;because each equivalent well is at a different distance from the supply boundary, the supply radius is corrected;
for an eccentric well, inversion is performed using an image well:；
the feed radius in the pressure drop stack equation is modified as:；
whereinTo supply radius, m;correcting the supply radius, m, for the equivalent well;is the eccentricity of each equivalent vertical well, m;
(4) coupling the yield of each crack obtained in the step (3) with a hydraulic pressure drop flow model in a horizontal shaft to obtain a group of bottom hole pressures, and iteratively solving until the bottom hole pressure difference of the previous step and the next step is smaller than a tolerance, namely convergence is achieved, wherein the determined group of yields are the seam control yields of each crack, and the sum of the seam control yields of all cracks is the total yield of the horizontal shaft;
to in relation toA fracture produced which has a spatially induced pressure drop of:
in the formula
。
2. The staged fracturing productivity calculation method for the horizontal well of the tight oil reservoir according to claim 1, which is characterized by comprising the following steps of: the method for establishing an elliptical coordinate system and obtaining the fracture end face pressure obtained by integrating the pressure from the supply boundary to the fracture end face comprises the following steps:
the rectangular coordinate system and the elliptical coordinate system have the following transformation relations:
the volume of the elliptic cylinder is as follows:
in thatThe area of the flow cross section of the directional elliptic cylinder is approximately as follows:
its average mass flow rate is:
the average minor semi-axis radius is:
from the nonlinear percolation law:
obtaining by solution:
integrating the pressure from the supply boundary to the fracture end face to obtain the fracture end face pressure：
；
Wherein K is the reservoir matrix permeability, mD;crude oil viscosity, mPa · s; a is a nonlinear parameter without dimension; b is a non-linear parameter without dimension; determined by laboratory experiments;is an elliptical coordinate; h is the oil layer thickness, m;m is the half-length of the crack;the pressure of the end face of the crack is MPa;is the formation pressure, MPa;is the flow rate of a nonlinear seepage field in a matrix, m3/s。
3. The staged fracturing productivity calculation method for the horizontal well of the tight reservoir according to claim 2, which is characterized by comprising the following steps: the total pressure drop of the fracture radial injection in the horizontal impact wellbore comprises pipe flow-induced friction pressure drop and fluid radial injection-induced acceleration pressure drop, wherein:
the frictional pressure drop caused by the pipe flow is:；
the acceleration pressure drop caused by the radial injection of the fluid is as follows:。
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