CN113987862A - Optimal well spacing estimation method - Google Patents

Optimal well spacing estimation method Download PDF

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CN113987862A
CN113987862A CN202111190282.2A CN202111190282A CN113987862A CN 113987862 A CN113987862 A CN 113987862A CN 202111190282 A CN202111190282 A CN 202111190282A CN 113987862 A CN113987862 A CN 113987862A
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cluster
fracture
well
fracturing
optimal
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魏晓琛
柳曈
刘向君
梁利喜
施雷庭
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Southwest Petroleum University
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    • G—PHYSICS
    • G06—COMPUTING; CALCULATING OR COUNTING
    • G06F—ELECTRIC DIGITAL DATA PROCESSING
    • G06F30/00—Computer-aided design [CAD]
    • G06F30/20—Design optimisation, verification or simulation
    • G06F30/23—Design optimisation, verification or simulation using finite element methods [FEM] or finite difference methods [FDM]
    • 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
    • E21B43/00—Methods or apparatus for obtaining oil, gas, water, soluble or meltable materials or a slurry of minerals from wells
    • E21B43/30—Specific pattern of wells, e.g. optimizing the spacing of wells
    • G—PHYSICS
    • G06—COMPUTING; CALCULATING OR COUNTING
    • G06F—ELECTRIC DIGITAL DATA PROCESSING
    • G06F30/00—Computer-aided design [CAD]
    • G06F30/20—Design optimisation, verification or simulation
    • G06F30/28—Design optimisation, verification or simulation using fluid dynamics, e.g. using Navier-Stokes equations or computational fluid dynamics [CFD]
    • G—PHYSICS
    • G06—COMPUTING; CALCULATING OR COUNTING
    • G06F—ELECTRIC DIGITAL DATA PROCESSING
    • G06F2113/00—Details relating to the application field
    • G06F2113/08—Fluids
    • G—PHYSICS
    • G06—COMPUTING; CALCULATING OR COUNTING
    • G06F—ELECTRIC DIGITAL DATA PROCESSING
    • G06F2119/00—Details relating to the type or aim of the analysis or the optimisation
    • G06F2119/14—Force analysis or force optimisation, e.g. static or dynamic forces

Abstract

The invention discloses an optimal well spacing estimation method, which comprises the following steps: establishing a single-section single-cluster geomechanical model considering fluid-solid coupling and fracturing fluid flow and filtration loss in a fracture by an extended finite element method; performing single-cluster fracturing simulation, and determining the optimal cluster spacing according to the stress difference distribution of the horizontal section in the single-cluster fracturing simulation result; constructing a single-stage multi-cluster fracturing model according to the optimal cluster spacing; and performing single-stage multi-cluster fracturing simulation, and determining an interference limit according to the horizontal minimum principal stress distribution in the single-stage multi-cluster fracturing simulation result, wherein the value of the interference limit is the optimal well spacing. The method can estimate and obtain the optimal well spacing, provides a theoretical basis for horizontal well subdivision cutting fracturing and three-dimensional well pattern design optimization, and has important significance for efficient development of unconventional oil and gas resources.

Description

Optimal well spacing estimation method
Technical Field
The invention relates to the technical field of oil and gas reservoir development, in particular to an optimal well spacing estimation method.
Background
The efficient development of unconventional oil and gas resources has important significance for the balance of energy supply and demand and the optimization of energy structure in China. Since unconventional oil and gas reservoirs generally have low pore and low permeability characteristics, efficient development is difficult to achieve without modification. At present, under a platform well-logging mode and a 'well factory' development mode, a horizontal well staged fracturing technology is one of key technologies for unconventional oil and gas reservoir transformation. Unconventional oil and gas well spacing design is the key of gas field development technical policy design, is related to the maximum utilization of resources, and is closely related to geological characteristics and fracturing process technology. However, in the current multistage hydraulic fracturing process, multi-fracture non-uniform expansion is often generated under the condition of small well spacing, the effective modification volume of a reservoir is influenced, pressure channeling and sand blocking between wells can be caused, and the scale and the effect of fracturing modification are severely restricted.
Disclosure of Invention
In view of the above problems, the present invention aims to provide an optimal well spacing estimation method.
The technical scheme of the invention is as follows:
an optimal well spacing estimation method, comprising the steps of:
establishing a single-section single-cluster geomechanical model considering fluid-solid coupling and fracturing fluid flow and filtration loss in a fracture by an extended finite element method;
performing single-cluster fracturing simulation, and determining the optimal cluster spacing according to the stress difference distribution of the horizontal section in the single-cluster fracturing simulation result;
constructing a single-stage multi-cluster fracturing model according to the optimal cluster spacing;
and performing single-stage multi-cluster fracturing simulation, and determining an interference limit according to the horizontal minimum principal stress distribution in the single-stage multi-cluster fracturing simulation result, wherein the value of the interference limit is the optimal well spacing.
Preferably, the fluid-solid coupling and the fracturing fluid flow and fluid loss in the fracture are realized by fluid-solid coupling equations, wherein the fluid-solid coupling equations comprise:
(1) equation characterizing reservoir rock linear elastic strain and pore pressure variation:
σ＝σ′+αP0 (1)
in the formula: sigma and sigma' are total stress and effective stress respectively, MPa; alpha is a Biao coefficient; p0Pore pressure, MPa;
(2) stress balance equation based on virtual work principle:
∫V(σ′+P0I)：δεvdV＝∫VγδVvdS+∫VfδVvdV (2)
in the formula: v is the cumulative amount of deformation, m3(ii) a I is an identity matrix; deltaεIs the rate of deformation of the virtual work; v is the deformation rate of the reservoir matrix, m/s; gamma is surface tension per unit area, MPa/m2；δVIs a reservoir matrix virtual velocity field, m/s; s is the area of load application, m2(ii) a f is unit volume physical strength, MPa/m3；
(3) Continuity equation for fluid flow in reservoir:
Figure BDA0003300698840000021
in the formula: rhofIs the rock density of the reservoir in kg/m3(ii) a Phi is the reservoir rock porosity; n is the surface S external normal vector; q. q.smFor the fluid injection rate, m3/s；
(4) Flow equation of the fracturing fluid inside the fracture:
Figure BDA0003300698840000022
in the formula: q. q.stIs the flow velocity, m/s; w is the crack opening, mm; mu is the viscosity of the fracturing fluid, mPa & s; v ^ pfIs the fluid pressure gradient in the fracture, MPa;
(5) fluid mass conservation equation in hydraulic fracture:
Figure BDA0003300698840000023
in the formula: t is time, s; v1M is the fluid loss per unit area of fracturing fluid3/(m2·s)；
(6) Fluid loss equation for fracturing fluid in fracture to matrix:
V1＝cV(pf-pm) (6)
in the formula: c. CVThe filtration loss coefficient of the fracturing fluid is m/(MPa.s); p is a radical offFluid pressure in the fracture, MPa; p is a radical ofmThe pore pressure near the fracture surface, MPa.
Preferably, when the single-segment single-cluster geomechanical model is established by an extended finite element method, fracture initiation and extension criteria of the single-segment single-cluster geomechanical model are as follows:
(1) the global shift approximation solution is:
uapp(x)＝∑iNi(x)∑jβijpj(x) (7)
in the formula: u. ofapp(x) A displacement approximation solution for the universe; x is a spatial coordinate; subscripts i, j denote node impact domains; n is a radical ofi(x) Solving a set of unit decomposition functions over the domain; p is a radical ofj(x) A set of bases in a local approximation space; when p isj(x) When only constant terms are included, βijIs the node displacement;
(2) judging the initiation process of the hydraulic fracture by adopting a maximum principal stress criterion, namely:
Figure BDA0003300698840000024
in the formula: f is the maximum principal stress ratio;
Figure BDA0003300698840000031
critical maximum principal stress;<σmax>is defined as: when sigma ismaxAt time < 0<σmax>0, and when σmaxWhen is greater than 0<σmax>＝σmax；
When the maximum main stress ratio f is more than or equal to 1, the hydraulic fracture starts to crack;
(3) and judging the expansion of the hydraulic fracture by adopting the energy release rate, namely:
Figure BDA0003300698840000032
in the formula:
Figure BDA0003300698840000033
normal fracture energy release rate, N/mm;
Figure BDA0003300698840000034
the tangential fracture energy release rate is N/mm; gSAnd GTNormal and tangential displacements, respectively; eta is a material characteristic constant; gCThe composite fracture energy release rate is N/mm;
the unit characterizes the hydraulic fracture propagation process by a damage variable D defined as:
Figure BDA0003300698840000035
in the formula:
Figure BDA0003300698840000036
the maximum displacement is mm corresponding to the rock destruction process;
Figure BDA0003300698840000037
corresponding maximum displacement, mm, for complete destruction of the unit;
Figure BDA0003300698840000038
corresponding displacement, mm, for initial destruction of the unit;
the damage variable D is 0-1, and when D is equal to 0, the unit is not damaged; when D is equal to 1, the cell stiffness is completely degraded and the crack begins to propagate;
(4) the unit damage evolution process is characterized by unit stiffness degradation, namely:
Figure BDA0003300698840000039
in the formula: sigman'、σS' and σtThe' respectively is the stress, MPa, obtained by a unit normal direction and two tangent directions according to a traction separation criterion; sigman、σSAnd σtStress in three corresponding directions, MPa.
Preferably, the determining of the optimal cluster spacing according to the stress difference distribution of the horizontal section specifically comprises: and defining the distance from the fracture starting point when the difference between the horizontal maximum principal stress and the horizontal minimum principal stress is minimum along the center horizontal direction of the shaft as the optimal cluster spacing of the single well fracturing.
Preferably, the interference limit is determined from the horizontal minimum principal stress distribution by: and defining the maximum distance of the area with the horizontal minimum principal stress reduction larger than the reduction threshold value from the shaft as the single well fracturing interference limit.
Preferably, the reduction threshold is 1 MPa.
Preferably, the method further comprises the step of establishing a multi-well multi-cluster fracturing model to verify whether the optimal well spacing is correct.
Preferably, the step of establishing a multi-well multi-cluster fracture model to verify whether the optimal well spacing is correct specifically comprises the following substeps:
establishing a plurality of multi-well multi-cluster fracturing models with different well spacing, wherein the different well spacing comprises the optimal well spacing, at least one well spacing smaller than the optimal well spacing and at least one well spacing larger than the optimal well spacing;
and performing multi-well multi-cluster fracturing simulation on the multi-well multi-cluster fracturing models with different well distances, and analyzing the influence of the well distances on the inter-well interference according to the simulation result.
Preferably, the influence of the well spacing on the interference among wells is analyzed by adopting the fracture asymmetry coefficient, when the fracture asymmetry coefficient reaches the maximum, the stress shielding of the outer-side fracture on the middle-cluster fracture reaches the maximum, and the well spacing corresponding to the fracture asymmetry coefficient is the optimal well spacing.
Preferably, the fracture asymmetry factor is calculated by the following formula:
Figure BDA0003300698840000041
in the formula: lambda is the fracture asymmetry coefficient; k is the number of crack clusters;
Figure BDA0003300698840000042
the length of the single-cluster crack is longer than that of the long wing;
Figure BDA0003300698840000043
the length of the single-cluster crack short and long wing.
The invention has the beneficial effects that:
the invention relates to a finite element expanding method based on fluid-solid coupling, which fully considers the flowing and filtration loss of fracturing fluid in fractures, carries out systematic research on hydraulic fracture disturbance stress from aspects such as the lithologic characteristics of unconventional oil and gas reservoirs, the distribution of ground stress fields, the construction process and the like, discloses a single-well subsection multi-cluster hydraulic fracture expanding mechanism and stress disturbance characteristics, researches the inter-well pressure fracture interference law of multiple wells on the basis, estimates and obtains the optimal well spacing, provides a theoretical basis for horizontal well subdivision cutting fracturing and three-dimensional well network design optimization, and has important significance for the efficient development of unconventional oil and gas resources.
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In order to more clearly illustrate the embodiments of the present invention or the technical solutions in the prior art, the drawings used in the description of the embodiments or the prior art will be briefly described below, and it is obvious that the drawings in the following description are only some embodiments of the present invention, and for those skilled in the art, other drawings can be obtained according to these drawings without creative efforts.
FIG. 1 is a schematic diagram of a single-segment, single-cluster geomechanical model in accordance with an embodiment of the present invention;
FIG. 2 is a schematic diagram of horizontal maximum principal stress distribution of a single cluster fracture simulation result according to an embodiment of the present invention;
FIG. 3 is a diagram illustrating a single cluster fracture simulation result level minimum principal stress distribution according to an embodiment of the present invention;
FIG. 4 is a schematic diagram of a single-stage multi-cluster fracture model according to an embodiment of the invention;
FIG. 5 is a schematic diagram of a single-stage multi-cluster fracture simulation result according to an embodiment of the present invention;
FIG. 6 is a schematic view of a fracture propagation model for a well according to an embodiment of the present invention 2;
FIG. 7 shows an embodiment 1 of the present invention#Sigma after completion of well fracturinghReduction of area greater than 1MPa results are shown;
FIG. 8 shows an embodiment 1 of the present invention#Sigma after completion of well fracturinghSchematic diagram of the results of the region with an increase of more than 1 MPa;
FIG. 9 shows an embodiment 2 of the present invention#Well fracturing 45s time sigmahReduction of area greater than 1MPa results are shown;
FIG. 10 shows an embodiment 2 of the present invention#Well fracturing 45s time sigmahSchematic diagram of the results of the region with an increase of more than 1 MPa;
FIG. 11 shows an embodiment 2 of the present invention#Sigma after completion of well fracturinghReduction of area greater than 1MPa results are shown;
FIG. 12 shows an embodiment 2 of the present invention#Sigma after completion of well fracturinghSchematic diagram of the results of the region with an increase of more than 1 MPa;
FIG. 13 shows the well spacing 2 at 30m#A fracture form and stress distribution result schematic diagram after well fracturing is completed;
FIG. 14 shows a well spacing of 40m 2#A fracture form and stress distribution result schematic diagram after well fracturing is completed;
FIG. 15 shows the well spacing 2 at 50m#A fracture form and stress distribution result schematic diagram after well fracturing is completed;
FIG. 16 shows the well spacing 2 at 60m#Well pressureThe shape of the crack and the stress distribution result are shown schematically after the crack is finished;
FIG. 17 shows the well spacing of 70m 2#A fracture form and stress distribution result schematic diagram after well fracturing is completed;
FIG. 18 shows an embodiment 2 of the present invention#And (3) a schematic diagram of fracture asymmetric coefficient results under different well spacing conditions of wells.
Detailed Description
The invention is further illustrated with reference to the following figures and examples. It should be noted that, in the present application, the embodiments and the technical features of the embodiments may be combined with each other without conflict. It is noted that, unless otherwise indicated, all technical and scientific terms used herein have the same meaning as commonly understood by one of ordinary skill in the art to which this application belongs. The use of the terms "comprising" or "including" and the like in the present disclosure is intended to mean that the elements or items listed before the term cover the elements or items listed after the term and their equivalents, but not to exclude other elements or items.
The invention provides an optimal well spacing estimation method, which comprises the following steps:
s1: and establishing a single-section single-cluster geomechanical model considering fluid-solid coupling and fracturing fluid flow and fluid loss in the fracture by an extended finite element method.
The method can avoid the grid reconstruction and encryption of the conventional finite element method by adopting an expanded finite element method, and can describe the fracture expansion rule in the turning fracturing process in the hydraulic fracturing simulation by improving the interpolation shape function and releasing the degree of freedom of the reinforced node to describe the problem of discontinuous displacement.
In a particular embodiment, the consideration of fluid-solid coupling and fracturing fluid flow and fluid loss in the fracture is specifically achieved by fluid-solid coupling equations comprising:
(1) equation characterizing reservoir rock linear elastic strain and pore pressure variation:
σ＝σ′+αP0 (1)
in the formula: sigma and sigma' are total stress and effective stress respectively, MPa; alpha is a ratio(ii) an austenite coefficient; p0Pore pressure, MPa;
(2) stress balance equation based on virtual work principle:
∫V(σ′+P0I)：δεvdV＝∫VγδVvdS+∫VfδVvdV (2)
in the formula: v is the cumulative amount of deformation, m3(ii) a I is an identity matrix; deltaεIs the rate of deformation of the virtual work; v is the deformation rate of the reservoir matrix, m/s; gamma is surface tension per unit area, MPa/m2；δVIs a reservoir matrix virtual velocity field, m/s; s is the area of load application, m2(ii) a f is unit volume physical strength, MPa/m3；
(3) Continuity equation for fluid flow in reservoir:
Figure BDA0003300698840000061
in the formula: rhofIs the rock density of the reservoir in kg/m3(ii) a Phi is the reservoir rock porosity; n is the surface S external normal vector; q. q.smFor the fluid injection rate, m3/s；
(4) The flow equation of the fracturing fluid (assuming it is an incompressible newtonian fluid) inside the fracture:
Figure BDA0003300698840000062
in the formula: q. q.stIs the flow velocity, m/s; w is the crack opening, mm; mu is the viscosity of the fracturing fluid, mPa & s; v ^ pfIs the fluid pressure gradient in the fracture, MPa;
(5) fluid mass conservation equation in hydraulic fracture:
Figure BDA0003300698840000063
in the formula: t is time, s; v1M is the fluid loss per unit area of fracturing fluid3/(m2·s)；
(6) Fluid loss equation for fracturing fluid in fracture to matrix:
V1＝cV(pf-pm) (6)
in the formula: c. CVThe filtration loss coefficient of the fracturing fluid is m/(MPa.s); p is a radical offFluid pressure in the fracture, MPa; p is a radical ofmThe pore pressure near the fracture surface, MPa.
In a specific embodiment, when the single-segment single-cluster geomechanical model is built by an extended finite element method, fracture initiation and extension criteria of the single-segment single-cluster geomechanical model are as follows:
(1) the global shift approximation solution is:
uapp(x)＝∑iNi(x)∑jβijpj(x) (7)
in the formula: u. ofapp(x) A displacement approximation solution for the universe; x is a spatial coordinate; subscripts i, j denote node impact domains; n is a radical ofi(x) Solving a set of unit decomposition functions over the domain; p is a radical ofj(x) A set of bases in a local approximation space; when p isj(x) When only constant terms are included, βijIs the node displacement;
(2) judging the initiation process of the hydraulic fracture by adopting a maximum principal stress criterion, namely:
Figure BDA0003300698840000071
in the formula: f is the maximum principal stress ratio;
Figure BDA0003300698840000072
critical maximum principal stress;<σmax>is defined as: when sigma ismaxAt time < 0<σmax>0, and when σmaxWhen is greater than 0<σmax>＝σmax；
When the maximum main stress ratio f is more than or equal to 1, the hydraulic fracture starts to crack;
(3) and judging the expansion of the hydraulic fracture by adopting the energy release rate, namely:
Figure BDA0003300698840000073
in the formula:
Figure BDA0003300698840000074
normal fracture energy release rate, N/mm;
Figure BDA0003300698840000075
the tangential fracture energy release rate is N/mm; gSAnd GTNormal and tangential displacements, respectively; eta is a material characteristic constant; gCThe composite fracture energy release rate is N/mm;
the unit characterizes the hydraulic fracture propagation process by a damage variable D defined as:
Figure BDA0003300698840000076
in the formula:
Figure BDA0003300698840000077
the maximum displacement is mm corresponding to the rock destruction process;
Figure BDA0003300698840000078
corresponding maximum displacement, mm, for complete destruction of the unit;
Figure BDA0003300698840000079
corresponding displacement, mm, for initial destruction of the unit;
the damage variable D is 0-1, and when D is equal to 0, the unit is not damaged; when D is equal to 1, the cell stiffness is completely degraded and the crack begins to propagate;
(4) the unit damage evolution process is characterized by unit stiffness degradation, namely:
Figure BDA00033006988400000710
in the formula: sigman'、σS' and σtThe' respectively is the stress, MPa, obtained by a unit normal direction and two tangent directions according to a traction separation criterion; sigman、σSAnd σtStress in three corresponding directions, MPa.
S2: and performing single-cluster fracturing simulation, and determining the optimal cluster spacing according to the stress difference distribution of the horizontal section in the single-cluster fracturing simulation result.
In a specific embodiment, the determining the optimal cluster spacing according to the horizontal segment stress difference distribution specifically includes: and defining the distance from the fracture starting point when the difference between the horizontal maximum principal stress and the horizontal minimum principal stress is minimum along the center horizontal direction of the shaft as the optimal cluster spacing of the single well fracturing.
S3: and constructing a single-section multi-cluster fracturing model according to the optimal cluster spacing.
S4: and performing single-stage multi-cluster fracturing simulation, and determining an interference limit according to the horizontal minimum principal stress distribution in the single-stage multi-cluster fracturing simulation result, wherein the value of the interference limit is the optimal well spacing.
In a particular embodiment, the determination of the disturbance limit from the horizontal minimum principal stress distribution is in particular: and defining the maximum distance of the area with the horizontal minimum principal stress reduction larger than the reduction threshold value from the shaft as the single well fracturing interference limit. Optionally, the reduction threshold is 1 MPa.
In a specific embodiment, the present invention further includes a step S5 of establishing a multi-well multi-cluster fracture model to verify whether the optimal well spacing is correct, where the step S5 specifically includes the following sub-steps:
s51: and establishing a plurality of multi-well multi-cluster fracturing models with different well spacing, wherein the different well spacing comprises the optimal well spacing, at least one well spacing smaller than the optimal well spacing and at least one well spacing larger than the optimal well spacing.
S52: and performing multi-well multi-cluster fracturing simulation on the multi-well multi-cluster fracturing models with different well distances, and analyzing the influence of the well distances on the inter-well interference according to the simulation result.
In a specific embodiment, analyzing the influence of well spacing on inter-well interference by using a fracture asymmetry coefficient, wherein when the fracture asymmetry coefficient reaches the maximum, the stress shielding of the outer fracture on the middle cluster fracture reaches the maximum, and the well spacing corresponding to the fracture asymmetry coefficient is the optimal well spacing; the fracture asymmetry factor is calculated by:
Figure BDA0003300698840000081
in the formula: lambda is the fracture asymmetry coefficient; k is the number of crack clusters;
Figure BDA0003300698840000082
the length of the single-cluster crack is longer than that of the long wing;
Figure BDA0003300698840000083
the length of the single-cluster crack short and long wing.
In a specific embodiment, taking an unconventional reservoir in the northwest region as an example, the rock mechanics parameters, the ground stress state and the fracturing construction parameters of the reservoir are shown in table 1:
TABLE 1 reservoir rock mechanics parameters and fracturing construction parameters
Figure BDA0003300698840000084
The method for estimating the optimal well spacing of the reservoir disclosed by the invention is used for estimating the optimal well spacing of the reservoir, and specifically comprises the following steps of:
(1) establishing a single-section single-cluster geomechanical model considering fluid-solid coupling and fracturing fluid flow and fluid loss in a fracture by an extended finite element method, wherein the result is shown in figure 1;
(2) performing single-cluster fracturing simulation, wherein the single-cluster fracturing simulation result is shown in fig. 2-3, and determining the optimal cluster spacing according to the stress difference distribution of the horizontal section in the single-cluster fracturing simulation result, wherein the optimal cluster spacing is 15 m;
(3) constructing a single-section multi-cluster fracturing model according to the optimal cluster spacing, wherein the result is shown in FIG. 4;
(4) and performing single-stage multi-cluster fracturing simulation, wherein the single-stage multi-cluster fracturing simulation result is shown in fig. 5, and an interference limit is determined according to the horizontal minimum principal stress distribution in the single-stage multi-cluster fracturing simulation result, wherein the result is 52.5m, and the value is the optimal well spacing.
In this embodiment, the inter-well interference effect of the optimal well spacing is also verified by the following steps, which prove the accuracy thereof:
firstly, on the basis of the single-well model shown in fig. 4, a fracture propagation model of 2 wells is established, and the result is shown in fig. 6, the mechanical parameters and the ground stress state of the model reservoir rock are as shown in table 1, the well spacing is D, wherein 1 is 1# Well head 2#The well is fractured, and the single-section displacement of two wells is 1.56m3Min, fracturing time 120 s.
1#The fracture morphology after well fracturing is shown in FIG. 7, the fracture disturbance zone is shown in FIG. 8, and it can be seen from FIGS. 7-8 that the hydraulic fractures are in-between and normal to σhRising, in the direction of crack propagation σhAnd decreases.
When well spacing D is 52.5m, 2#Stress distribution after 45s well fracturing is shown in FIGS. 9-10, 2#Fracture morphology and stress distribution after well fracturing is complete are shown in figures 11-12. As can be seen from FIGS. 9-10, receiver 1#Well fracture disturbance stress effect, 1#Well and 2#Well-to-well zone sigmahLower, 2#Outside-well fractures are more prone to y+The directional expansion is asymmetrically expanded, resulting in 2#Outside well fracture at y+The length of the directional slit is longer, and y-The length of the direction seam is shorter; in addition, 2#Outside well fracture at y+The preferential extension in direction forming an inter-slit stress disturbance, sigma between slitshThe increase of about 3MPa forms stress shielding on the middle cluster cracks, so that the middle cluster cracks tend to be in the y direction-And (4) expanding the direction. As can be seen from FIGS. 11-12, 2# Well 3 clusters of fractures are significantly asymmetric about the wellbore, mainly manifested as an outside fracture 1#The influence of the well fracturing disturbance area is expanded to the interwell area of the two wells, and the middle cluster cracks are shielded by the stress of the outer cracks to influence the two wellsThe side area is expanded.
When the well spacing D is 30m, 40m, 50m, 60m and 70m, under the condition of different well spacings D, the well spacing D is 2 m#Fracture morphology and stress distribution after well fracturing is shown in figures 13-17. As can be seen from fig. 13, the two well hydraulic fractures communicate in the interwell region, with interwell fracture crosstalk occurring; as can be seen from FIGS. 14-17, no interwell pressure channeling has occurred, 2#The outside-of-the-well fractures propagate toward the wellbore and the middle cluster fractures tend to propagate toward the outside of the wellbore. Counting 2 under different distances D#The well fracture asymmetry factor results are shown in figure 18. When D is less than the interference limit (52.5m), 2#The cracking positions of three clusters of cracks in the well are positioned at 1#Inside the well fracture interference area, the outer hydraulic fractures tend to expand towards the well space, the middle fractures expand towards the outer areas of the two wells under the influence of stress shielding generated by preferential expansion of the outer fractures, and the stress shielding effect is enhanced along with the increase of D. When D is equal to R, the stress shielding of the outer cracks to the middle cluster cracks reaches the maximum, the asymmetric coefficient reaches the maximum at the moment, and the value is 2#The well is most well-to-well modified, but the asymmetry of the fracture wings may result in insufficient reservoir mobilization. And finally, when D is larger than R, the stress shielding of the outer cracks to the middle cluster cracks is gradually reduced along with the increase of D, and the crack asymmetry coefficient is reduced along with the reduction of D.
In conclusion, the invention selects the crack induced stress calculation model for researching single well and multiple wells, which is established by the finite element expansion method based on fluid-solid coupling, and the interference boundary obtained by the method is used as the optimal well spacing result to be accurate, thereby providing a theoretical basis for horizontal well subdivision cutting and fracturing and three-dimensional well pattern design optimization, and having important significance for the efficient development of unconventional oil and gas resources.
Although the present invention has been described with reference to a preferred embodiment, it should be understood that various changes, substitutions and alterations can be made herein without departing from the spirit and scope of the invention as defined by the appended claims.

Claims (10)

1. A method for optimal well spacing estimation, comprising the steps of:
establishing a single-section single-cluster geomechanical model considering fluid-solid coupling and fracturing fluid flow and filtration loss in a fracture by an extended finite element method;
performing single-cluster fracturing simulation, and determining the optimal cluster spacing according to the stress difference distribution of the horizontal section in the single-cluster fracturing simulation result;
constructing a single-stage multi-cluster fracturing model according to the optimal cluster spacing;
and performing single-stage multi-cluster fracturing simulation, and determining an interference limit according to the horizontal minimum principal stress distribution in the single-stage multi-cluster fracturing simulation result, wherein the value of the interference limit is the optimal well spacing.
2. The optimal well spacing estimation method according to claim 1, wherein the taking into account fluid-solid coupling and fracture fluid flow and fluid loss within the fracture is specifically achieved by a fluid-solid coupling equation comprising:
(1) equation characterizing reservoir rock linear elastic strain and pore pressure variation:
σ＝σ′+αP0 (1)
in the formula: sigma and sigma' are total stress and effective stress respectively, MPa; alpha is a Biao coefficient; p0Pore pressure, MPa;
(2) stress balance equation based on virtual work principle:
∫V(σ′+P0I)：δεvdV＝∫VγδVvdS+∫VfδVvdV (2)
in the formula: v is the cumulative amount of deformation, m3(ii) a I is an identity matrix; deltaεIs the rate of deformation of the virtual work; v is the deformation rate of the reservoir matrix, m/s; gamma is surface tension per unit area, MPa/m2；δVIs a reservoir matrix virtual velocity field, m/s; s is the area of load application, m2(ii) a f is unit volume physical strength, MPa/m3；
(3) Continuity equation for fluid flow in reservoir:
Figure FDA0003300698830000011
in the formula: rhofIs the rock density of the reservoir in kg/m3(ii) a Phi is the reservoir rock porosity; n is the surface S external normal vector; q. q.smFor the fluid injection rate, m3/s；
(4) Flow equation of the fracturing fluid inside the fracture:
Figure FDA0003300698830000012
in the formula: q. q.stIs the flow velocity, m/s; w is the crack opening, mm; mu is the viscosity of the fracturing fluid, mPa & s;
Figure FDA0003300698830000013
is the fluid pressure gradient in the fracture, MPa;
(5) fluid mass conservation equation in hydraulic fracture:
Figure FDA0003300698830000014
in the formula: t is time, s; v1M is the fluid loss per unit area of fracturing fluid3/(m2·s)；
(6) Fluid loss equation for fracturing fluid in fracture to matrix:
V1＝cV(pf-pm) (6)
in the formula: c. CVThe filtration loss coefficient of the fracturing fluid is m/(MPa.s); p is a radical offFluid pressure in the fracture, MPa; p is a radical ofmThe pore pressure near the fracture surface, MPa.
3. The optimal well spacing estimation method according to claim 1, wherein when the single-segment single-cluster geomechanical model is established by an extended finite element method, fracture initiation and extension criteria of the single-segment single-cluster geomechanical model are as follows:
(1) the global shift approximation solution is:
uapp(x)＝∑iNi(x)∑jβijpj(x) (7)
in the formula: u. ofapp(x) A displacement approximation solution for the universe; x is a spatial coordinate; subscripts i, j denote node impact domains; n is a radical ofi(x) Solving a set of unit decomposition functions over the domain; p is a radical ofj(x) A set of bases in a local approximation space; when p isj(x) When only constant terms are included, βijIs the node displacement;
(2) judging the initiation process of the hydraulic fracture by adopting a maximum principal stress criterion, namely:
Figure FDA0003300698830000021
in the formula: f is the maximum principal stress ratio;
Figure FDA0003300698830000022
critical maximum principal stress;<σmax>is defined as: when sigma ismaxAt time < 0<σmax>0, and when σmaxWhen is greater than 0<σmax>＝σmax；
When the maximum main stress ratio f is more than or equal to 1, the hydraulic fracture starts to crack;
(3) and judging the expansion of the hydraulic fracture by adopting the energy release rate, namely:
Figure FDA0003300698830000023
in the formula:
Figure FDA0003300698830000024
normal fracture energy release rate, N/mm;
Figure FDA0003300698830000025
the tangential fracture energy release rate is N/mm; gSAnd GTNormal and tangential displacements, respectively; eta is a material characteristic constant; gCThe composite fracture energy release rate is N/mm;
the unit characterizes the hydraulic fracture propagation process by a damage variable D defined as:
Figure FDA0003300698830000026
in the formula:
Figure FDA0003300698830000027
the maximum displacement is mm corresponding to the rock destruction process;
Figure FDA0003300698830000028
corresponding maximum displacement, mm, for complete destruction of the unit;
Figure FDA0003300698830000029
corresponding displacement, mm, for initial destruction of the unit;
the damage variable D is 0-1, and when D is equal to 0, the unit is not damaged; when D is equal to 1, the cell stiffness is completely degraded and the crack begins to propagate;
(4) the unit damage evolution process is characterized by unit stiffness degradation, namely:
Figure FDA0003300698830000031
in the formula: sigman'、σS' and σt' cell normal and two tangential directions according to traction, respectivelyStress obtained by separation criterion, MPa; sigman、σSAnd σtStress in three corresponding directions, MPa.
4. The optimal well spacing estimation method according to claim 1, wherein determining the optimal cluster spacing according to the horizontal segment stress difference distribution specifically comprises: and defining the distance from the fracture starting point when the difference between the horizontal maximum principal stress and the horizontal minimum principal stress is minimum along the center horizontal direction of the shaft as the optimal cluster spacing of the single well fracturing.
5. The optimal well spacing estimation method according to claim 1, wherein determining the disturbance margin from the horizontal minimum principal stress distribution is specifically: and defining the maximum distance of the area with the horizontal minimum principal stress reduction larger than the reduction threshold value from the shaft as the single well fracturing interference limit.
6. The optimal well spacing estimation method according to claim 5, characterized in that the lowering threshold is 1 MPa.
7. The optimal well spacing estimation method according to claim 1, further comprising the step of establishing a multi-well multi-cluster fracture model to verify whether the optimal well spacing is correct.
8. The optimal well spacing estimation method according to claim 7, wherein the step of establishing a multi-well and multi-cluster fracture model to verify whether the optimal well spacing is correct specifically comprises the following sub-steps:
establishing a plurality of multi-well multi-cluster fracturing models with different well spacing, wherein the different well spacing comprises the optimal well spacing, at least one well spacing smaller than the optimal well spacing and at least one well spacing larger than the optimal well spacing;
and performing multi-well multi-cluster fracturing simulation on the multi-well multi-cluster fracturing models with different well distances, and analyzing the influence of the well distances on the inter-well interference according to the simulation result.
9. The optimal well spacing estimation method according to claim 8, wherein the influence of well spacing on inter-well interference is analyzed by using fracture asymmetry coefficients, when the fracture asymmetry coefficients reach the maximum, the stress shielding of outer fractures on middle cluster fractures reaches the maximum, and the well spacing corresponding to the fracture asymmetry coefficients is the optimal well spacing.
10. The optimal well spacing estimation method according to claim 9, wherein the fracture asymmetry factor is calculated by:
Figure FDA0003300698830000032
in the formula: lambda is the fracture asymmetry coefficient; k is the number of crack clusters;
Figure FDA0003300698830000041
the length of the single-cluster crack is longer than that of the long wing;
Figure FDA0003300698830000042
the length of the single-cluster crack short and long wing.
CN202111190282.2A 2021-10-13 2021-10-13 Optimal well spacing estimation method Pending CN113987862A (en)

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Cited By (1)

* Cited by examiner, † Cited by third party
Publication number Priority date Publication date Assignee Title
CN115270559A (en) * 2022-07-25 2022-11-01 中国科学院武汉岩土力学研究所 Optimal well spacing determination method for shallow layer gas ground disaster prevention and control advanced exhaust well

Cited By (2)

* Cited by examiner, † Cited by third party
Publication number Priority date Publication date Assignee Title
CN115270559A (en) * 2022-07-25 2022-11-01 中国科学院武汉岩土力学研究所 Optimal well spacing determination method for shallow layer gas ground disaster prevention and control advanced exhaust well
CN115270559B (en) * 2022-07-25 2023-07-18 中国科学院武汉岩土力学研究所 Optimal well spacing determination method for advanced exhaust well for shallow gas-ground disaster prevention

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