CN112177598B - Stratum cracking pressure prediction method considering compressibility of fracturing fluid - Google Patents
Stratum cracking pressure prediction method considering compressibility of fracturing fluid Download PDFInfo
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Abstract
The invention provides a stratum fracture initiation pressure prediction method considering the compressibility of fracturing fluid, and belongs to the technical field of shale gas development. The method comprises the following steps: s1: establishing a discretized shaft model of shaft fracturing fluid flow, and obtaining a law of time change of bottom hole pressure and a law of time change of wellhead pressure; s2: establishing a shaft-cement ring-near-well wall stratum three-dimensional fluid-solid coupling mechanical model under perforation conditions, and obtaining a distribution rule of near-well wall stress fields and a distribution rule of seepage fields in a shaft pressure holding process; s3: inversion of the formation initiation time and wellhead initiation pressure. The invention establishes a calculation model of a shaft pressure field and a speed field in the pressure holding process, and on the basis, the calculation method of the hydraulic fracturing initiation pressure and the hydraulic fracturing initiation time of the shale gas well is perfected by combining related knowledge such as rock mechanics and the like, so that further theoretical basis and design basis are provided for deep understanding of the initiation mechanism of the hydraulic fracturing of the shale gas well and development of fracturing design to a certain extent.
Description
Technical Field
The invention belongs to the technical field of shale gas development, and particularly relates to a stratum fracture initiation pressure prediction method considering the compressibility of fracturing fluid.
Background
The shale gas resources in China are rich. Through preliminary evaluation, the geological resource potential of the land shale gas in China is 134.42 trillion cubic meters, and the recoverable resource potential is 25.08 trillion cubic meters (without containing Tibet areas). But shale matrix has low permeability and low pore size, and industrial gas flow can be obtained through hydraulic fracturing operation. At present, the conventional fracturing mode in China is horizontal sectional multi-shower hole fracturing, and the method is relatively mature in process due to simple operation, and is widely applied to shale gas resource development in China.
However, the hydraulic fracturing operation of deep and ultra-deep shale gas reservoirs is found, and the hydraulic fracturing operation of the deep and ultra-deep shale gas reservoirs is extremely high in fracture pressure and extremely difficult to construct due to the fact that the deep and ultra-deep shale gas reservoirs are buried in part of areas, the rock is compact, the closing pressure is high, and great difficulty is brought to shale gas reservoir transformation. Therefore, the cause of formation of high fracture pressure and means for reducing the fracture pressure need to be studied from the standpoint of physical and mechanical properties of shale gas reservoirs. The prediction model of the hydraulic fracture initiation of the shale gas well is particularly important.
For this, many scholars have developed studies on a predictive model of cracking pressure. The research method is mainly based on an analytic method, a finite element method, a boundary element method and the like, for example, chinese patent publication CN107609258B discloses a calculation method of shale repeated fracturing steering fracture initiation pressure, and the technical scheme is different from the application range of the method; the Chinese patent publication CN106555575A discloses a calculation method of the formation cracking pressure of deep shale, wherein the influence of fluid fracturing fluid, viscosity, resistivity reduction and the like on the cracking pressure is not considered in the calculation, and the method has certain technical limitations in predicting the cracking time and the cracking pressure; chinese patent publication CN107587867B discloses a repeated fracturing process design method for improving the complexity of shale fracture network, and the technical scheme is different from the application range of the invention.
In addition, most models simplify the loading modes of the pressure in the hole and the shaft to constant pressure, in fact, the pressure in the shaft does not rise immediately at the initial stage of fracturing, but gradually rises, the pressurization rate is influenced by the displacement, viscosity and compressibility of the fracturing fluid, and the cracking pressure and the cracking time of the shale gas well are directly influenced. Therefore, the existing shale gas well cracking pressure prediction model is difficult to directly consider the influence of fracturing fluid parameters such as displacement, viscosity and the like on the cracking pressure, so that the method has certain technical limitations in predicting the cracking pressure and time, and a cracking pressure calculation model considering the compressibility of the fracturing fluid of a well bore is required to be established.
Disclosure of Invention
The invention aims to solve the problems in the prior art and provides a stratum cracking pressure prediction method considering the compressibility of a fracturing fluid, so as to realize the prediction of the cracking pressure and the cracking time of the hydraulic fracturing of a shale gas well.
The invention is realized by the following technical scheme:
the method comprises the following steps:
s1: establishing a discretized shaft model of shaft fracturing fluid flow, and obtaining a law of time change of bottom hole pressure and a law of time change of wellhead pressure;
s2: establishing a shaft-cement ring-near-well wall stratum three-dimensional fluid-solid coupling mechanical model under perforation conditions, and obtaining a distribution rule of near-well wall stress fields and a distribution rule of seepage fields in a shaft pressure holding process;
s3: inversion of the formation initiation time and wellhead initiation pressure.
The operation of establishing the discretized wellbore model of the wellbore fracturing fluid flow in the step S1 comprises the following steps:
edge sleeveThe casing is divided into n shaft micro-element sections in the axial direction of the pipe, and the length of each shaft micro-element section is deltaz i The method comprises the steps of carrying out a first treatment on the surface of the The first shaft micro-element section corresponds to a wellhead, and the nth shaft micro-element section corresponds to a bottom of a well;
the discretized wellbore model for establishing wellbore fracturing fluid flow is as follows:
wherein,the quality of the fracturing fluid of the ith shaft micro-element section at the moment t is calculated by adopting the following formula:
p is the pressure, v is the average flow rate,represents the cross section of the intersection of the ith shaft micro-element section and the (i+1) th shaft micro-element section,>representing the cross section of the intersection of the ith shaft micro-element section and the ith-1 th shaft micro-element section, wherein deltat is the unit time step length, alpha is the included angle between the shaft micro-element section and the vertical direction, d is the diameter of the inner wall of the casing, g is the gravity acceleration, rho 0 Is the density of the fracturing fluid under standard atmospheric pressure, p 0 Is the standard atmospheric pressure, C is the fracturing fluid pressure coefficient; τ w Is the friction resistance of the wall surface of the shaft.
The operation of obtaining the law of the change of the bottom hole pressure with time and the law of the change of the wellhead pressure with time in the step S1 includes:
(1) Solving a discretized shaft model of the shaft fracturing fluid flow under a unit time step length to obtain bottom hole pressure and wellhead pressure under the unit time step length; the bottom hole pressure is correspondingly solved to obtain the pressure p of the nth shaft micro-element section under the unit time step n The pressure p of the 1 st shaft micro-element section under the unit time step is obtained by corresponding solving of the wellhead pressure 1 ；
(2) Judgment of p n Whether or not is equal to or greater than Y times the maximum horizontal principal stress, if not, then
t=t+Δt, then returning to step (1), if yes, turning to step (3);
(3) Outputting a law of time change of bottom hole pressure and a law of time change of wellhead pressure: the law of the change of the bottom hole pressure along with the time corresponds to p n The value of the pressure at the well head is corresponding to p along with the time change law of the pressure at the well head at each unit time step 1 Values at each unit time step.
In the step (1), solving a discretized shaft model of the shaft fracturing fluid flow under each unit time step by adopting a Newton iteration method;
y in the step (2) is 1.5.
The operation of step S2 includes:
step 201: acquiring the sizes of a casing, a cement sheath and a borehole, and establishing a three-dimensional fluid-solid coupling mechanical model of the casing-cement sheath-near-borehole wall stratum under perforation conditions by using a finite element method in combination with perforation construction parameters;
step 202: endowing a sleeve and a cement sheath in the three-dimensional fluid-solid coupling mechanical model of the shaft-cement sheath-near-well wall stratum under the perforation condition with material properties; imparting physical and mechanical properties to shale in a three-dimensional fluid-solid coupling mechanical model of a shaft-cement sheath-near-well wall stratum under the perforation condition;
step 203: applying far-field boundary load to the three-dimensional fluid-solid coupling mechanical model of the sleeve, the cement sheath and the near-well wall stratum under the perforation condition;
step 204: applying hydraulic load to the inner wall of the sleeve and the hole of the three-dimensional fluid-solid coupling mechanical model of the sleeve-cement sheath-near-well wall stratum under the perforation condition, wherein the hydraulic load is the bottom hole pressure obtained in the step S1;
step 205: and calculating to obtain the distribution rule of the stress field of the near-well wall shale in the pressure holding process and the distribution rule of the seepage field.
In the step 201, a three-dimensional hexahedral reduction integral pore pressure unit is adopted to divide grids of the three-dimensional mechanical model of the sleeve, the cement ring and the near-well wall stratum, and the grids are encrypted at the positions of the holes.
The physico-mechanical properties in step 202 include: permeability, porosity, elastic modulus, poisson's ratio.
The operation of step S3 includes:
step 301: inputting the law of the change of the bottom hole pressure obtained in the step S1 along with time; calculating to obtain the maximum main stress of near-well wall rock under different construction times according to the distribution rule of the stress field obtained in the step S2;
step 302: inverting the stratum cracking time according to the maximum principal stress of near-wall rock under different construction times;
step 303: inverting the wellhead cracking pressure according to the stratum cracking time and the law of the wellhead pressure change along with time, which is obtained in the step S1.
The operation of step 302 includes:
taking the maximum principal stress of near-wall rock under different construction times as interpolation basic data, and interpolating the basic data to obtain the construction time when the maximum principal stress of the wall shale reaches the tensile strength of the rock, wherein the construction time is the stratum cracking time.
The operation of step 303 includes:
taking the value of each wellhead pressure in the law of the change of the wellhead pressure along with time obtained in the step S1 as interpolation basic data, interpolating the basic data, and then calculating the wellhead pressure when the construction time is the formation cracking time, wherein the wellhead pressure is the wellhead cracking pressure.
Compared with the prior art, the invention has the beneficial effects that: the invention establishes a calculation model of a shaft pressure field and a speed field in the pressure holding process based on the related knowledge of fluid mechanics, and on the basis, the calculation method of the hydraulic fracturing initiation pressure and the hydraulic fracturing initiation time of the shale gas well is perfected by combining the related knowledge of rock mechanics and the like, so that further theoretical basis and design basis are provided for deep understanding of the hydraulic fracturing initiation mechanism of the shale gas well and development of fracturing design to a certain extent.
Drawings
FIG. 1 is a basic flow chart of the present invention;
FIG. 2 is a basic flow chart of a wellbore pressure field in the process of calculating a hold-down pressure according to the present invention;
FIG. 3 is a basic flow chart of the calculation of near-wellbore wall stress field and seepage field of the present invention;
FIG. 4 is a basic flow chart of the calculation of the cracking pressure and time of the present invention;
FIG. 5 is a comparison of wellhead pressure calculations and measured values in an example;
FIG. 6 is a three-dimensional finite element model of a casing-cement sheath-formation under perforating conditions;
fig. 7 is a graph showing the maximum principal stress of near-wellbore shale as a function of holding time.
Detailed Description
The invention is described in further detail below with reference to the attached drawing figures:
as shown in fig. 1 to 4, the method of the present invention includes:
s1: establishing a discretized shaft model of shaft fracturing fluid flow, and obtaining a law of time change of bottom hole pressure and a law of time change of wellhead pressure: acquiring construction displacement and well opening pressure, combining parameters such as resistivity reduction, viscosity, compressibility and the like of fracturing fluid, establishing a mathematical model of wellbore fracturing fluid flowing in the pressure holding process, and solving the change rule of well bottom and wellhead pressure along with time;
s2: establishing a shaft-cement ring-near-well wall stratum three-dimensional fluid-solid coupling mechanical model under perforation conditions, and obtaining a distribution rule of near-well wall stress fields and a distribution rule of seepage fields in a shaft holding process: based on the related knowledge of seepage mechanics and rock mechanics, combining perforation parameters and mechanical parameters of a shaft, a cement ring and a stratum, establishing a three-dimensional fluid-solid coupling mechanical model of the shaft, the cement ring and a near-well wall stratum, and calculating distribution rules of a near-well wall stress field and a seepage field in the process of suppressing pressure of the shaft;
s3: inversion of formation initiation time and wellhead initiation pressure: and analyzing a change rule of the maximum main stress of shale in the well shaft holding process by combining a calculation result, and inverting the formation cracking time and the wellhead cracking pressure by combining a maximum horizontal main stress criterion.
Preferably, the mathematical model of the wellbore fracturing fluid flowing in the build-up pressure holding process in step S1 specifically includes the following contents:
step 101: preparing calculation parameters: obtaining compression coefficient, viscosity, density, resistivity reduction rate, construction displacement, well opening pressure, well track and perforation position of the fracturing fluid;
step 102: numerical simulation was performed: based on the related knowledge of fluid mechanics, a physical model of wellbore fluid flow in the fracturing pressure-holding process is established, a numerical simulation method is adopted to carry out numerical simulation of a wellbore pressure field and a speed field in the fracturing pressure-holding process, the fluid pressure distribution of fracturing fluid in a wellbore in each time step is solved by adopting a Newton iteration method, the flow speed field distribution is solved on the basis, and next time step calculation is carried out until the bottom hole pressure reaches more than 1.5 times of the maximum horizontal main stress; the method comprises the following steps:
calculating a wellbore fluid pressure field in the pressure holding process by adopting a mathematical model, wherein the mathematical model of wellbore fracturing fluid flow in the pressure holding process is shown as formulas (1) to (4):
fluid compressibility equation:
wherein, C is the compression coefficient of fracturing fluid; ρ is the fracturing fluid density; p is the open-hole pressure (obtainable from the adjacent well).
The method comprises the following steps:
wherein: ρ 0 Is the density of the fracturing fluid under standard atmospheric pressure, p 0 Is at standard atmospheric pressure;
mass conservation equation:
wherein z is the position of the tube in the longitudinal direction; u is the flow rate of the fracturing fluid in the tube.
Equation of wellbore pressure drop:
wherein d is the diameter of the inner wall of the casing, alpha is the included angle between the shaft unit and the vertical direction, g is the gravitational acceleration, f is the friction coefficient, and beta is the resistivity.
The wellbore fluid flow model described requires a discretized wellbore model (the model refers to formulas (5) and (6)) that is pre-formed with wellbore fracturing fluid flow by:
dividing the sleeve into n shaft micro-element sections along the axial direction of the sleeve at equal distance, wherein the length of each shaft micro-element section is deltaz i 。
Taking a single shaft micro-element section as a research object, the mass conservation equation can be discretized into:
in the method, in the process of the invention,the quality of fracturing fluid of the ith shaft micro-element section at the moment t;
according to equation (2), the fracturing fluid density is a function of pressure, so the pressure is included in equation (5).For the average flow velocity on the cross section at the intersection of the ith and (i+1) th well micro-element sections,/for the (i) th well micro-element section>Represents the average flow velocity of the section at the intersection of the ith shaft micro-element section and the (i-1) th shaft micro-element section, and deltat is the unit time step.
Meanwhile, the wellbore pressure drop equation may be discretized as:
wherein τ w Representing the wellbore wall friction resistance.
Notably, because the model takes the compressibility of the fluid into consideration, the fracturing fluid density of the micro-element section of the shaft is as follows according to the fluid compressibility equation:
further, it is necessary to define the boundary conditions of the wellbore fracturing fluid flow model during the hold-down process. Firstly, the wellhead pressure at the beginning of the fracturing is defined, and then, the injection displacement of the wellhead during the hold-down is defined, which displacement can be a fixed value or a function of time.
Further, the well bore is divided into n well bore micro-segments, each well bore micro-segment including two unknowns, namely 2n unknowns. Each wellbore microcell can establish a continuity equation and 2 equations (i.e., equations (5) and (6)) for wellbore pressure drop equations, together 2n equations can be established. Therefore, the number of equations is the same as the number of unknowns, and can be solved. And solving by adopting a Newton iteration method in view of the fact that the continuity equation and the shaft pressure drop equation are all implicit nonlinear equations.
Further, calculating the bottom hole pressure (corresponding to the pressure value p of the last shaft micro-element section) at different times in the pressure holding process n ) When the size of the well isAnd stopping calculation when the bottom pressure reaches more than 1.5 times of the maximum horizontal main stress (which can be obtained through logging or rock core acoustic emission experiments).
Step 103: outputting a calculation result: outputting parameters required by calculating the cracking pressure and the cracking time according to the requirements, namely: step 102 solves 2n equations to obtain flow velocity and pressure of n shaft micro-element sections under different time, wherein the law of the change of the bottom hole pressure along with time corresponds to the pressure p of the last shaft micro-element section (namely the nth shaft micro-element section) obtained by solving the law of the change of the bottom hole pressure along with time n The value of each unit time step length is that the rule of the change of the wellhead pressure along with the time corresponds to the pressure p of the first shaft micro-element section obtained by solving 1 Values at each unit time step.
The step S2 of establishing a three-dimensional fluid-solid coupling mechanical model of a sleeve, a cement sheath and a near-well wall stratum comprises the following specific contents:
step 201: acquiring the sizes of a casing, a cement sheath and a borehole, and establishing a three-dimensional fluid-solid coupling mechanical model of the casing-cement sheath-near-borehole wall stratum under perforation conditions based on a finite element method by combining perforation construction parameters; dividing the grid into three-dimensional hexahedron reduced integral pore pressure units by the model, and locally encrypting the grid at the hole in order to ensure the accuracy of the calculation result;
step 202: and (3) endowing the casing pipe and the cement sheath in the model with material properties: inputting material parameters of the sleeve and the cement sheath; imparting physical mechanical properties to shale in the model: the physical and mechanical properties of shale are obtained through logging data and an indoor core experiment, and the physical and mechanical parameters of shale are input; the physical and mechanical parameters of the shale include, but are not limited to, permeability, porosity, elastic modulus, poisson's ratio and other parameters; the mechanical constitutive model (namely elastoplastic mechanical equation) of shale can be adjusted according to the mechanical properties of shale, including but not limited to transverse isotropy elastoplastic mechanical model, elastoplastic mechanical model based on D-P criterion;
step 203: applying far-field boundary load to the three-dimensional fluid-solid coupling mechanical model of the sleeve-cement sheath-near-well wall stratum under the jet hole condition: injecting vertical main stress in the vertical direction, inputting maximum horizontal main stress in the direction of the maximum horizontal main stress, inputting minimum horizontal main stress in the direction of the minimum horizontal main stress, and applying a pore pressure boundary on the outer boundary of the rock; the shale boundary conditions mainly comprise a stratum initial stress field and a seepage field, and displacement constraint conditions and pore pressure boundary conditions are applied to the outer boundary of the model.
Step 204: applying hydraulic load to the inner wall of the sleeve and the position of the hole of the sleeve-cement sheath-near-well wall stratum three-dimensional mechanical model under the condition of the jet hole, wherein the hydraulic load is the output result in the step 103, namely a bottom hole pressure change value related to the construction time;
step 205: calculating stress field and seepage field distribution of near-wellbore wall shale in the pressure holding process: may be calculated by a discrete element method, a finite element method, or a boundary element method. Taking a finite element method as an example, establishing a shale reservoir fluid-solid coupling mechanical equation based on a rock mechanical balance mechanical equation and a seepage mechanical equation, dispersing the mechanical equation to obtain a finite element calculation format of the coupling equation, and solving the finite element calculation format by a numerical method.
Preferably, the calculating the cracking pressure and the cracking time in the step S3 specifically includes the following:
step 301: based on the step 103 and the step 205, the bottom hole pressure (i.e. the law of time variation of the bottom hole pressure obtained in the step 103) and the maximum main stress of the near-wall rock at different construction times in the pressure holding process are analyzed and determined. The stress field of the near-wellbore wall shale is obtained in step 205, and the maximum principal stress can be calculated by adopting a conventional mechanical formula through the stress field calculated in step 205.
Step 302: based on the maximum horizontal principal stress criterion, inverting the cracking time according to the calculation result of the maximum principal stress of near-wall rock under different construction times, wherein the method comprises the following steps: s2, obtaining the shale maximum principal stress under different construction times; and taking the calculation result as basic data of interpolation, interpolating the data, and calculating the construction time when the maximum main stress of the well wall shale reaches the tensile strength of the rock. According to the maximum horizontal principal stress criterion, when the maximum principal stress of the rock reaches the tensile strength of the rock, the rock starts to break, and thus the construction time is the initiation time.
Step 303: inverting the cracking pressure according to wellhead pressure calculation results (namely, the rule of wellhead pressure change along with time obtained in the step S1) under different construction times, wherein the method comprises the following steps of: step S1, acquiring wellhead pressure under different construction times; and taking the calculation result as interpolation basic data, interpolating the data, and calculating the wellhead pressure when the construction time is the cracking time, namely the wellhead cracking pressure.
The embodiment of the invention relates to a 1 st stage test fracturing of a shale gas well in southeast of Sichuan province. As shown in fig. 1, the method specifically comprises the following steps:
s1: establishing a discretized shaft model of shaft fracturing fluid flow, and obtaining a law of time change of bottom hole pressure and a law of time change of wellhead pressure: acquiring construction displacement and well opening pressure, combining parameters such as resistivity reduction, viscosity, compressibility and the like of fracturing fluid, establishing a mathematical model of wellbore fracturing fluid flowing in the pressure holding process, and solving the change rule of well bottom and wellhead pressure along with time;
s2: establishing a shaft-cement ring-near-well wall stratum three-dimensional fluid-solid coupling mechanical model under perforation conditions, and obtaining a distribution rule of near-well wall stress fields and a distribution rule of seepage fields in a shaft holding process: based on the related knowledge of seepage mechanics and rock mechanics, combining perforation parameters and mechanical parameters of a shaft, a cement ring and a stratum, establishing a three-dimensional fluid-solid coupling mechanical model of the shaft, the cement ring and a near-well wall stratum, and calculating distribution rules of a near-well wall stress field and a seepage field in the process of suppressing pressure of the shaft;
s3: inversion of formation initiation time and wellhead initiation pressure: and analyzing a change rule of the maximum main stress of shale in the well shaft holding process by combining a calculation result, and inverting the formation cracking time and the wellhead cracking pressure by combining a maximum horizontal main stress criterion.
Step S1, as shown in fig. 2, specifically includes:
step 101: according to the fracturing design, the fracturing fluid designed and used in the section is slick water, and the viscosity, density and resistivity of the fracturing fluid can be obtained through an indoor experiment. In order to conveniently verify the accuracy of the model, parameters such as construction displacement, well opening pressure and the like in calculation come from on-site construction data;
step 102: dispersing a shaft into 80 shaft micro-element sections, wherein the length of each shaft micro-element section is 70m, and the unit time step length is 1s, namely: n=80; δz=80; δt=1;
the continuity equation and the shaft pressure drop equation of each shaft micro-element section are constructed as follows:
the step of solving the formulas (8) and (9) includes:
from equation (7), the unknown numberAs a function of pressure, in combination with equation (9), equation (8) can be a nonlinear equation for p, namely:
R(p)＝0 (10)
wherein R= [ R ] 1 ,R 2 ,…,R n ]，p＝[p 1 ,p 2 ,…,p n ]
And in each time step, taking the pressure distribution calculated in the previous step as an initial value, substituting the initial value into the formula (9), starting to solve the flow velocity distribution of the fracturing fluid in the shaft from the wellhead micro-element section through numerical methods such as a dichotomy method, a chord cutting method and the like, and substituting the initial value into the formula (10) to obtain R from the left of the equal sign. Meanwhile, the differential method is adopted to derive the pressure of each well barrel micro-element section in the nonlinear equation, and the pressure is obtained:
thus, the pressure distribution in the wellbore can be updated by newton-iteration, namely:
p * ＝Δp+p 0 (13)
wherein p is 0 To calculate the value p * To update the results.
When the calculation error is smaller than the set error, stopping calculation and entering calculation of the next step length; if not, the update is continued.
Step 103: the calculation result is shown in fig. 5, and it can be seen from the graph that the calculated wellhead pressure is relatively close to the actual construction value before the stratum is broken, which indicates that the established model has better accuracy and reliability, and can be used for calculating the cracking pressure. And outputting the bottom hole pressure and the wellhead pressure at different times in the pressure holding process.
Step S2, as shown in fig. 4, includes:
in step 201, a three-dimensional finite element model of the casing-cement sheath-formation is created under perforation conditions according to the well bore structure and fracture design parameters, as shown in fig. 6.
Step 202: endowing the casing pipe and the cement sheath in the mechanical model with material properties based on the material parameters of the casing pipe and the cement sheath; based on logging data and an indoor core experiment, acquiring physical and mechanical properties of shale, and endowing the shale with physical and mechanical properties;
step 203: applying a pore pressure boundary condition, namely a displacement boundary condition, to the three-dimensional mechanical model of the casing-cement sheath-near-wellbore wall stratum under the jet hole condition, wherein the pore pressure is derived from logging data and drilling data; an initial ground stress field is applied, and the ground stress field is derived from indoor acoustic emission experiment and logging related data;
step 204: applying hydraulic load to the inner wall of the sleeve and the position of the hole of the sleeve-cement sheath-near-well wall stratum three-dimensional mechanical model under the condition of the jet hole, wherein the hydraulic load is the output result in the step 103, namely the bottom hole pressure changing along with time in the pressure holding process;
step 205: and calculating the distribution of stress fields and seepage fields of the near-well wall shale in the pressured holding process.
The step S3 shown in fig. 5 includes:
step 301: on the basis of step 103 and step 205, analyzing and determining the bottom hole pressure and the maximum main stress of near-wall rock at different construction times in the pressure holding process; the maximum principal stress of near-wellbore shale over time for this condition is shown in figure 7.
Step 302: and extracting data of maximum horizontal main stress-holding time for inverting the cracking time from the calculation result. According to the indoor experimental result of the obtained core, the tensile strength of shale is 8.23MPa. And combining cubic spline interpolation, and when the maximum horizontal main stress reaches 8.23MPa, the cracking time is 147.0941s.
Step 303: and extracting data of the holding time-wellhead pressure for inverting the cracking pressure from the calculation result. According to the inversion result of the last step, the cracking time is 147.0941s. And combining cubic spline interpolation, wherein the wellhead cracking pressure is 81.9403MPa.
According to the actual construction result of the test fracturing, the cracking time is 149s, and the cracking pressure is 81.42MPa. The error between the calculated result of the method and the actual calculated result is 0.64% on the cracking pressure, and the error between the calculated result and the actual calculated result is 1.28% on the cracking time. The calculation method and the established model of the method are reliable, the crack initiation mechanism of the hydraulic fracturing of the shale gas well can be accurately reflected, and a theoretical basis is provided for the hydraulic fracturing design of the shale gas well.
The method improves the prediction method of the cracking pressure and the cracking time of the shale gas well cracking crack, and provides a theoretical basis for the hydraulic fracturing design of the shale gas well.
The foregoing technical solution is only one embodiment of the present invention, and various modifications and variations can be easily made by those skilled in the art based on the application methods and principles disclosed in the present invention, not limited to the methods described in the foregoing specific embodiments of the present invention, so that the foregoing description is only preferred and not in a limiting sense.
Claims (8)
1. A stratum cracking pressure prediction method considering the compressibility of a fracturing fluid is characterized in that: the method comprises the following steps:
s1: establishing a discretized shaft model of shaft fracturing fluid flow, and obtaining a law of time change of bottom hole pressure and a law of time change of wellhead pressure;
s2: establishing a shaft-cement ring-near-well wall stratum three-dimensional fluid-solid coupling mechanical model under perforation conditions, and obtaining a distribution rule of near-well wall stress fields and a distribution rule of seepage fields in a shaft pressure holding process;
s3: inverting the formation cracking time and wellhead cracking pressure;
the operation of establishing the discretized wellbore model of the wellbore fracturing fluid flow in the step S1 comprises the following steps:
dividing the sleeve into n shaft micro-element sections along the axial direction of the sleeve at equal distance, wherein the length of each shaft micro-element section is deltaz i The method comprises the steps of carrying out a first treatment on the surface of the The first shaft micro-element section corresponds to a wellhead, and the nth shaft micro-element section corresponds to a bottom of a well;
the discretized wellbore model for establishing wellbore fracturing fluid flow is as follows:
wherein,the quality of the fracturing fluid of the ith shaft micro-element section at the moment t is calculated by adopting the following formula:
p is the pressure, v is the average flow rate,represents the cross section of the intersection of the ith shaft micro-element section and the (i+1) th shaft micro-element section,representing the cross section of the intersection of the ith shaft micro-element section and the ith-1 th shaft micro-element section, wherein deltat is the unit time step length, alpha is the included angle between the shaft micro-element section and the vertical direction, d is the diameter of the inner wall of the casing, g is the gravity acceleration, rho 0 Is the density of the fracturing fluid under standard atmospheric pressure, p 0 Is the standard atmospheric pressure, C is the fracturing fluid pressure coefficient; τ w Friction resistance for the wall surface of the shaft;
the operation of step S2 includes:
step 201: acquiring the sizes of a casing, a cement sheath and a borehole, and establishing a three-dimensional fluid-solid coupling mechanical model of the casing-cement sheath-near-borehole wall stratum under perforation conditions by using a finite element method in combination with perforation construction parameters;
step 202: endowing a sleeve and a cement sheath in the three-dimensional fluid-solid coupling mechanical model of the shaft-cement sheath-near-well wall stratum under the perforation condition with material properties; imparting physical and mechanical properties to shale in a three-dimensional fluid-solid coupling mechanical model of a shaft-cement sheath-near-well wall stratum under the perforation condition;
step 203: applying far-field boundary load to the three-dimensional fluid-solid coupling mechanical model of the sleeve, the cement sheath and the near-well wall stratum under the perforation condition;
step 204: applying hydraulic load to the inner wall of the sleeve and the hole of the three-dimensional fluid-solid coupling mechanical model of the sleeve-cement sheath-near-well wall stratum under the perforation condition, wherein the hydraulic load is the bottom hole pressure obtained in the step S1;
step 205: and calculating to obtain the distribution rule of the stress field of the near-well wall shale in the pressure holding process and the distribution rule of the seepage field.
2. The method for predicting the formation fracture pressure considering the compressibility of the fracturing fluid according to claim 1, wherein: the operation of obtaining the law of the change of the bottom hole pressure with time and the law of the change of the wellhead pressure with time in the step S1 includes:
(1) Solving a discretized shaft model of the shaft fracturing fluid flow under a unit time step length to obtain bottom hole pressure and wellhead pressure under the unit time step length; the bottom hole pressure is correspondingly solved to obtain the pressure p of the nth shaft micro-element section under the unit time step n The pressure p of the 1 st shaft micro-element section under the unit time step is obtained by corresponding solving of the wellhead pressure 1 ；
(2) Judgment of p n Whether the maximum horizontal principal stress is greater than or equal to Y times of the maximum horizontal principal stress, if not, t=t+Δt, then returning to the step (1), and if so, turning to the step (3);
(3) Outputting a law of time change of bottom hole pressure and a law of time change of wellhead pressure: the law of the change of the bottom hole pressure along with the time corresponds to p n The value of the pressure at the well head is corresponding to p along with the time change law of the pressure at the well head at each unit time step 1 Values at each unit time step.
3. The method for predicting the formation fracture pressure considering the compressibility of the fracturing fluid according to claim 2, wherein: in the step (1), solving a discretized shaft model of the shaft fracturing fluid flow under each unit time step by adopting a Newton iteration method;
y in the step (2) is 1.5.
4. The method for predicting the formation fracture pressure considering the compressibility of the fracturing fluid according to claim 1, wherein: in the step 201, a three-dimensional hexahedral reduction integral pore pressure unit is adopted to divide grids of the three-dimensional mechanical model of the sleeve, the cement ring and the near-well wall stratum, and the grids are encrypted at the positions of the holes.
5. The method for predicting the formation fracture pressure considering the compressibility of the fracturing fluid according to claim 1, wherein: the physico-mechanical properties in step 202 include: permeability, porosity, elastic modulus, poisson's ratio.
6. The method for predicting the formation fracture pressure considering the compressibility of the fracturing fluid according to claim 1, wherein: the operation of step S3 includes:
step 301: inputting the law of the change of the bottom hole pressure obtained in the step S1 along with time; calculating to obtain the maximum main stress of near-well wall rock under different construction times according to the distribution rule of the stress field obtained in the step S2;
step 302: inverting the stratum cracking time according to the maximum principal stress of near-wall rock under different construction times;
step 303: inverting the wellhead cracking pressure according to the stratum cracking time and the law of the wellhead pressure change along with time, which is obtained in the step S1.
7. The method for predicting the formation fracture pressure considering the compressibility of the fracturing fluid according to claim 6, wherein: the operation of step 302 includes:
taking the maximum principal stress of near-wall rock under different construction times as interpolation basic data, and interpolating the basic data to obtain the construction time when the maximum principal stress of the wall shale reaches the tensile strength of the rock, wherein the construction time is the stratum cracking time.
8. The method for predicting the formation fracture pressure considering the compressibility of the fracturing fluid according to claim 6, wherein: the operation of step 303 includes:
taking the value of each wellhead pressure in the law of the change of the wellhead pressure along with time obtained in the step S1 as interpolation basic data, interpolating the basic data, and then calculating the wellhead pressure when the construction time is the formation cracking time, wherein the wellhead pressure is the wellhead cracking pressure.
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| CN115324560A (en) * | 2021-04-26 | 2022-11-11 | 中国石油天然气集团有限公司 | Method for determining fracturing-induced oil-gas casing deformation position by using ground stress field simulation |
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