Establishment of dynamic model for acid fracturing in long open hole section of horizontal well and prediction method of fracture pressure

Abstract

The present invention provides a method for establishing a dynamic model of acid fracturing and predicting fracture pressure of a long open hole section of a horizontal well. The model establishment method includes: establishing a physical model of a long open hole section of a horizontal well and a geological model distributed along the wellbore and performing grid division, confirming characteristic parameters and mechanical parameters of the corresponding depth according to logging data; establishing a fluid pressure model in the wellbore and a fluid pressure model in the matrix according to the above parameters; establishing an acid flow velocity model based on the acid injection port position in the wellbore according to the above pressure model; and establishing an acid fracturing dynamic model according to the acid flow velocity model, the fluid pressure model in the wellbore and the fluid pressure model in the matrix. The prediction method includes confirming the fracture pressure according to the above acid fracturing dynamic model and the rock failure criterion. The present invention takes into account the influence of acid on the mechanical and physical properties of the reservoir, and simply and accurately calculates the dynamic fracture pressure under different acid injection parameters, acid injection port positions, and reservoir conditions, providing a theoretical basis for the optimization of subsequent operations.

Description

Technical Field

[0001] The present invention relates to the technical field of petroleum engineering, and in particular to a method for establishing a dynamic model of acid fracturing in a long open hole section of a horizontal well and a method for predicting dynamic fracture pressure of acid fracturing in a long open hole section of a horizontal well. Background Art

[0002] Carbonate gas reservoirs are the main front for the current and future development of natural gas in China, and acid fracturing is one of the main means to achieve efficient development of such oil and gas reservoirs. In order to achieve efficient transformation of such reservoirs, it is necessary to inject acid under conditions greater than the reservoir fracture pressure to form artificial fractures and increase the seepage channels and flow capacity of oil and gas in the reservoir. With the development of exploration and development theory and the accumulation of field practical experience, long horizontal wells have become one of the main well types for efficient development of carbonate reservoirs, and segmented acid fracturing is an important transformation and development process for carbonate rocks in long open hole horizontal wells. However, due to the extremely strong heterogeneity of carbonate reservoirs and the long open hole section of horizontal wells, the acid absorption conditions of the reservoir sections vary greatly. In addition, the chemical reaction during the acid injection process affects the physical properties and mechanical characteristics of the reservoir, making it difficult to predict the dynamic situation of acid fracturing in the long open hole section of the horizontal well and the dynamic fracture pressure of acid fracturing.

[0003] At present, a relatively complete numerical model has been constructed for the prediction of horizontal well fracture pressure. However, most of these models are developed for hydraulic fracturing. For example, the invention patent with the publication number CN111219175A discloses a method for optimizing the matching of acid fracturing fractures in fractured carbonate rocks considering stress sensitivity. In this method, by inputting the natural fracture and hydraulic fracture etching width, the conductivity distribution of the acid-etched fractures and natural fractures calculated based on the initial effective closure stress of the formation and the NK model is assigned to the corresponding position grid in the reservoir model to obtain the permeability of the corresponding grid, and a fixed outlet is set in the reservoir model to simulate the production well, calculate the reservoir fluid pressure distribution at the end of each time step, and then complete the simulation and evaluation of the production process. However, for acid etching, this method simply takes the fracture etching data in the case with the smallest acid injection amount and acid injection displacement in all construction parameter cases as the reference etching form, and it does not fully consider the impact of the acid chemical reaction on the reservoir physical properties and mechanical characteristics. However, the existing acid fracturing fracture pressure prediction model does not consider coupling the flow model of the acid in the wellbore and the reservoir. For example, the invention patent with the publication number CN110094196A discloses a method for evaluating the effect of acid fracturing in carbonate open hole horizontal wells. This method uses the logging interpretation data of the acid fracturing well section to calculate the rock mechanics parameter profile, and by calculating the fracture pressure profile of the acid fracturing well section, it clarifies the fracture initiation point of the acid fracturing well section and determines the location of the acid fracturing fracture. It mainly obtains the conversion coefficient of dynamic and static rock mechanics parameters by fitting the indoor rock mechanics data with the rock mechanics data calculated by logging, and does not consider the overall influence of reservoir heterogeneity on the fracture pressure and the fracture initiation position. Therefore, there is a lack of a direct and simple method to calculate the dynamic fracture pressure of acid fracturing in long open hole sections of horizontal wells, which provides a reliable basis for the design and construction optimization of acid fracturing in long horizontal wells. Summary of the invention

[0004] The purpose of the present invention is to solve at least one of the above-mentioned deficiencies in the prior art. For example, one of the purposes of the present invention is to provide a method for establishing a dynamic model of acid fracturing of a long open hole section of a horizontal well, which can fully consider the influence of acid chemical reaction on reservoir physical properties and mechanical characteristics, and the flow of acid in the wellbore and reservoir on the overall heterogeneity of the reservoir and its influence on the fracture pressure and the fracture initiation position, and the dynamic model of acid fracturing can also be used to predict the dynamic fracture pressure of acid fracturing of a long open hole section of a horizontal well under different acid injection parameters, acid injection port locations, and reservoir conditions, so as to provide more accurate support for the design optimization and construction of acid fracturing of a long open hole section of a horizontal well in carbonate rock.

[0005] In order to achieve the above-mentioned object, the present invention provides, on one hand, a method for establishing a dynamic model of acid fracturing in a long open hole section of a horizontal well.

[0006] The method for establishing a dynamic model of acid fracturing in a long open hole section of a horizontal well comprises the following steps:

[0007] S1. Establish a physical model of a long open hole section of a horizontal well and a geological model distributed along the wellbore, and confirm the characteristic parameters and mechanical parameters of the corresponding depth based on the logging data, the physical model of the long open hole section of the horizontal well after gridding, and the geological model distributed along the wellbore.

[0008] S2. Establishing a wellbore fluid pressure model and a matrix fluid pressure model according to the characteristic parameters and mechanical parameters.

[0009] S3. Establishing an acid fluid flow velocity model based on the acid injection port position in the wellbore according to the wellbore fluid pressure model and the matrix fluid pressure model.

[0010] S4. Establishing an acid fracturing dynamic model according to the acid fluid flow velocity model, the wellbore fluid pressure model and the matrix fluid pressure model.

[0011] In an exemplary embodiment of the method for establishing a dynamic model of acid fracturing in a long open hole section of a horizontal well according to the present invention, the wellbore fluid internal pressure model may include:

[0012] Formula 1:

[0013] Formula 2:

[0014] Formula 3:

[0015] Wherein, n is the nth time step, dimensionless; is the bottom hole pressure at the n+1th time step, Pa; is the bottom hole pressure at the nth time step, Pa; the ΔP n is the pressure change caused by the compressibility of the fluid in the wellbore at the nth time step, Pa; ΔP is the pressure change caused by the compressibility of the fluid in the wellbore, Pa; ΔV acid is the volume increment of the acid fluid in the wellbore at the nth time step, m 3 ; The V well is the wellbore volume, m 3 ; The c1 is the fluid compressibility coefficient, Pa -1 ; Δt is the time step, s; is the acid flow rate injected into the wellbore in the nth time step, m 3 / min; is the acid flow rate out of the wellbore in the nth time step, m 3 / min, and when n=1, The Δx and Δy are the lengths of the cell in the x-axis and y-axis directions, m; the k y is the permeability of the cell in the y-axis direction, m2 ; r is the wellbore radius, m; μ is the fluid viscosity, Pa·s; is the reservoir fluid pressure in the first grid at the nth time step in the y-axis direction, Pa.

[0016] In an exemplary embodiment of the method for establishing a dynamic model of acid fracturing in a horizontal well long open hole section of the present invention, the time step Δt can be based on the average permeability k of the reservoir matrix. m Confirmation may specifically include: when the k m The value range is k m <10 -15 m 2 When the time step Δt=1s; when the k m The value range is 10 -15 m 2 ≤k m ≤10 -14 m 2 When the time step Δt = 1 to 10 s; when the k m The value range is 10 -14 m 2 ≤k m , the time step Δt=10s.

[0017] In an exemplary embodiment of the method for establishing a dynamic model of acid fracturing in a long open hole section of a horizontal well according to the present invention, the intra-matrix fluid pressure model may include:

[0018] Formula 4:

[0019] Wherein, ρ is the fluid density, kg / m 3 ; the k x , k y are the permeabilities of the cell in the x-axis and y-axis directions, m 2 ; μ is the fluid viscosity, Pa·s; P is the reservoir fluid pressure, Pa; φ is the reservoir porosity, dimensionless; c1 is the fluid compressibility, Pa -1 ; The t is the acid injection time, s.

[0020] In an exemplary embodiment of the method for establishing a dynamic model of acid fracturing in a long open hole section of a horizontal well of the present invention, the acid flow velocity model may include an upstream acid flow velocity model and a downstream acid flow velocity model, which may respectively include:

[0021] Formula 5:

[0022] Formula 6:

[0023] Among them, the ui上 is the flow rate of the upstream acid in the wellbore, m / s; i下 is the flow rate of the downstream acid in the wellbore, m / s; in is the position of the acid injection port, dimensionless; i is the unit cell position in the x-axis direction, dimensionless; m is the total number of units in the acid flow velocity model in the x-axis direction, dimensionless; x m is the position of the mth cell in the x-axis direction, dimensionless; Δx and Δy are the lengths of the cell in the x-axis and y-axis directions, m; P well,i is the fluid pressure in the wellbore at position i in the x-axis direction, Pa; r,i is the fluid pressure in the formation at position i in the x-axis direction, Pa; k y,i is the permeability of the reservoir at position i along the y-axis, m 2 ; μ is the fluid viscosity, Pa·s; D 井 is the borehole diameter, m.

[0024] In an exemplary embodiment of the method for establishing a dynamic model of acid fracturing in a long open hole section of a horizontal well of the present invention, the dynamic model of acid fracturing may include an acid concentration distribution model, and the acid concentration distribution model may include:

[0025] Formula 7:

[0026] Formula 8: v l,i =Q out,i / (πD 井 Δx).

[0027] Wherein, Δx is the length of the cell in the x-axis direction, m; D 井 is the borehole diameter, m; C is the acid concentration, mol / m 3 ; t is the injection time of acid solution, s; u is the flow rate of acid solution in the wellbore, m / s; k c Acid-rock reaction rate, m / s; v l is the acid flow rate from the wellbore into the reservoir, m / s; i is the unit cell position in the x-axis direction, dimensionless; v l,i is the acid flow rate from the wellbore into the reservoir at position i in the x-axis direction, m / s; Q out,i is the acid flow rate out of the wellbore per unit time at position i in the x-axis direction, m 3 / min.

[0028] In an exemplary embodiment of the method for establishing a dynamic model of acid fracturing in a long open hole section of a horizontal well of the present invention, the dynamic model of acid fracturing may include a porosity model and a permeability model after acid dissolution, and the porosity model and the permeability model may respectively include:

[0029] Formula 9:

[0030] Formula 10:

[0031] Among them, the φ n is the porosity at the nth time step, dimensionless; φ is the reservoir porosity, dimensionless; Δx and Δy are the lengths of the unit cell in the x-axis and y-axis directions, m; D 井 is the borehole diameter, m; n is the nth time step; t is the acid injection time, s; τ is the corresponding time step number of the acid front first reaching the cells at different positions in the wellbore; ΔV is the volume of rock dissolved by the acid, m 3 ; β is the solubility of the acid for rock minerals, kg / kg; M is the molar mass of the acid, kg / mol; k c Acid-rock reaction rate, m / s; C is the acid concentration, mol / m 3 ; said ρ S is the rock density, kg / m 3 ; the k n is the permeability after dissolution, m 2 ; k is the initial permeability, m 2 ; the β SG is the pore structure parameter, dimensionless.

[0032] In an exemplary embodiment of the method for establishing a dynamic model of acid fracturing in a long open hole section of a horizontal well of the present invention, the dynamic model of acid fracturing may include a well wall tangential stress model, and the well wall tangential stress model may include:

[0033] Formula 11:

[0034]

[0035] ν=5.89e [-(t-τ) / 6.47] -6.23,

[0036] Among them, the σ θ is the wellbore tangential stress, MPa; H , σ h and σ ν are the maximum horizontal principal stress, minimum horizontal principal stress and vertical stress, MPa respectively; the σ z is the tangential stress of the wellbore, MPa; θ, θ' are the well inclination angle, the angle from the wellbore axis to the tangential stress direction of the bottom of the hole on the wellbore, °; P wellis the fluid pressure in the wellbore, MPa; P is the reservoir fluid pressure, MPa; α is the Biot coefficient, dimensionless; ν is the rock Poisson's ratio, dimensionless; ω is the acid damage variable, dimensionless; φ is the reservoir porosity, dimensionless; φ n is the porosity at the nth time step, dimensionless; t is the acid injection time, s; τ is the corresponding time step number when the acid front first reaches the cells at different positions in the wellbore.

[0037] In an exemplary embodiment of the method for establishing a dynamic model of acid fracturing in a horizontal well long open hole section of the present invention, when the acid concentration at the cell position in the wellbore is greater than or equal to 301-903 mol / m 3 When , it can be determined that the acid front reaches the cell position for the first time.

[0038] On the other hand, the present invention provides a method for predicting the dynamic fracture pressure of acid fracturing in a long open hole section of a horizontal well. The method for predicting the dynamic fracture pressure of acid fracturing in a long open hole section of a horizontal well may include: using the acid fracturing dynamic model in any of the above-mentioned methods for establishing a dynamic model of acid fracturing in a long open hole section of a horizontal well to confirm whether the difference between the reservoir fluid pressure and the well wall tangential stress is greater than or equal to the rock tensile strength.

[0039] When the difference is greater than or equal to the rock tensile strength, the fracture location and fracture pressure can be confirmed.

[0040] When the difference is less than the rock tensile strength, the characteristic parameters and mechanical parameters may be updated, and steps S1 to S4 may be repeated until the difference is greater than or equal to the rock tensile strength.

[0041] When the acid injection process is completed and the difference is less than the rock tensile strength, the construction parameters can be redesigned.

[0042] Compared with the prior art, the beneficial effects of the present invention include at least one of the following:

[0043] (1) The method for establishing the acid fracturing dynamic model provided by the present invention takes into account the changes in mechanical characteristics and physical properties of reservoir sections with different physical property parameters caused by the chemical reaction of the acid during the acid fracturing of a horizontal well and a long open hole, as well as the influence of the overall reservoir heterogeneity on the fracture pressure and the fracture initiation position, and is coupled with the flow model of the acid in the wellbore and the reservoir. It can more accurately calculate and reflect the dynamic flow and reaction process of the acid in the wellbore and the reservoir in real time.

[0044] (2) The acid fracturing dynamic fracture pressure prediction method provided by the present invention can use the acid fracturing dynamic model to more accurately predict the acid fracturing dynamic fracture pressure of a long open hole section of a horizontal well under different acid injection parameters, acid injection port locations, and reservoir conditions.

[0045] (3) The calculation process of the acid fracturing dynamic model provided by the present invention is simple and does not require several iterations. At the same time, the calculation results are accurate, which can provide reliable support for the design optimization and construction of acid fracturing in long open hole sections of carbonate horizontal wells, and improve the completion efficiency. BRIEF DESCRIPTION OF THE DRAWINGS

[0046] The above and other objects and / or features of the present invention will become more apparent through the following description in conjunction with the accompanying drawings, in which:

[0047] Figure 1 A flow chart showing an exemplary embodiment of a method for establishing a dynamic model of acid fracturing in a long open hole section of a horizontal well according to the present invention.

[0048] Figure 2 A schematic diagram showing calculation results of fluid pressure in a reservoir of an example of a method for predicting dynamic fracture pressure of a horizontal well long open hole section by acid fracturing according to the present invention is shown.

[0049] Figure 3 A schematic diagram showing calculation results of acid fluid velocity distribution in a wellbore of an example of a method for predicting dynamic fracture pressure of a horizontal well long open hole section by acid fracturing according to the present invention.

[0050] Figure 4 A schematic diagram showing calculation results of acid concentration distribution in a wellbore of an example of a method for predicting dynamic fracture pressure of a horizontal well long open hole section by acid fracturing according to the present invention.

[0051] Figure 5 A schematic diagram of the fracture pressure judgment result of an example of the method for predicting the dynamic fracture pressure of a horizontal well long open hole section by acid fracturing according to the present invention is shown. DETAILED DESCRIPTION

[0052] Hereinafter, the method for establishing a dynamic model for acid fracturing in a long open hole section of a horizontal well and predicting the fracture pressure of the present invention will be described in detail in combination with exemplary embodiments. The fracture pressure is also called the initiation pressure.

[0053] It should be noted that the terms "S1", "S2", "S3", etc. used in the present invention are used to distinguish similar objects, and are not necessarily used to describe a specific order or sequence. "Upper", "lower", etc. are only used to facilitate description and to form a relative orientation or position relationship, and do not indicate or imply that the referred component must have such a specific orientation or position.

[0054] Acid fracturing (abbreviated as acid fracturing) refers to squeezing acid into the reservoir under conditions higher than the reservoir fracture pressure to form hydraulic fractures in the reservoir. At the same time, the acid reacts chemically with the rock on the fracture wall, non-uniformly etches the fracture wall rock, forming grooved or uneven etching shapes, so that the hydraulic fractures are not completely closed after the construction is completed, and finally form acid-etched fractures with certain geometric dimensions and conductivity, thereby increasing the production of oil and gas wells. Therefore, the dynamic flow and reaction process of the acid in the wellbore and reservoir during acid fracturing, as well as the prediction results of the dynamic fracture pressure, will affect the design of the acid fracturing scheme. The acid will not only cause chemical reactions to the mechanical characteristics and physical characteristics of the reservoir sections with different physical parameters, but will also flow inside the wellbore and reservoir, causing stress changes in the wellbore. However, the current models cannot consider the above changes at the same time.

[0055] In response to the above problems, the inventors proposed a method for establishing a dynamic model of acid fracturing in long open hole sections of horizontal wells and a method for predicting fracture pressure, which can accurately and simply calculate and reflect the acid fracturing dynamics of long open hole sections of horizontal wells under different acid injection parameters, acid injection port locations and reservoir conditions.

[0056] In order to achieve the above-mentioned object, the present invention provides, on one hand, a method for establishing a dynamic model of acid fracturing in a long open hole section of a horizontal well.

[0057] In an exemplary embodiment of the method for establishing a dynamic model of acid fracturing in a horizontal well long open hole section of the present invention, Figure 1 As shown in FIG. 1 , the method for establishing the dynamic model of acid fracturing in a long open hole section of a horizontal well includes the following steps:

[0058] S1. Establish a physical model of the long open hole section of a horizontal well and a geological model distributed along the wellbore. The direction along the wellbore is set as the x-axis, the direction of increasing depth is the positive direction of the x-axis, the direction perpendicular to the wellbore is set as the y-axis, and the direction away from the wellbore is the positive direction of the y-axis. According to the logging data, the physical model of the long open hole section of the horizontal well after grid division, and the geological model distributed along the wellbore, the characteristic parameters and mechanical parameters of the corresponding depth are confirmed.

[0059] In this embodiment, the wellbore fluid pressure model may include:

[0060] Formula 1:

[0061] Formula 2:

[0062] Formula 3:

[0063] Where n is the nth time step, dimensionless; is the bottom hole pressure at the n+1th time step, Pa; is the bottom hole pressure at the nth time step, Pa; ΔP nis the pressure change caused by the compressibility of the fluid in the wellbore at the nth time step, Pa; ΔP is the pressure change caused by the compressibility of the fluid in the wellbore, Pa; ΔV acid is the volume increment of acid fluid in the wellbore, m 3 ; V well is the wellbore volume, m 3 ; c1 is the fluid compressibility coefficient, Pa -1 ; Δt is the time step, s; is the acid flow rate injected into the wellbore in the nth time step, m 3 / min; is the acid flow rate out of the wellbore in the nth time step, m 3 / min, and when n=1, ; Δx, Δy are the lengths of the cell in the x-axis and y-axis directions, m; k y is the permeability of the cell in the y-axis direction, m 2 ; r is the wellbore radius, m; μ is the fluid viscosity, Pa·s; is the reservoir fluid pressure in the first grid at the nth time step in the y-axis direction, Pa.

[0064] In this embodiment, the time step Δt can be calculated based on the average permeability k of the reservoir matrix. m Confirmation may include: m The value range is k m <10 -15 m 2 When k m The value range is 10 -15 m 2 ≤k m ≤10 -14 m 2 When k m The value range is 10 -14 m 2 ≤k m When the time step is Δt=10s.

[0065] S2. Establish a fluid pressure model in the wellbore and a fluid pressure model in the matrix according to the characteristic parameters and mechanical parameters.

[0066] In this embodiment, the intra-matrix fluid pressure model may include:

[0067] Formula 4:

[0068] Where ρ is the fluid density, kg / m 3 ;k x , k yare the permeabilities of the cell in the x-axis and y-axis directions, m 2 ; μ is fluid viscosity, Pa·s; P is reservoir fluid pressure, Pa; φ is reservoir porosity, dimensionless; c1 is fluid compressibility, Pa -1 ; t is the acid injection time, s.

[0069] S3. Establishing an acid fluid flow velocity model based on the acid injection port position in the wellbore according to the wellbore fluid pressure model and the matrix fluid pressure model.

[0070] In this embodiment, the acid liquid flow velocity model may include an upstream acid liquid flow velocity model and a downstream acid liquid flow velocity model, which may respectively include:

[0071] Formula 5:

[0072] Formula 6:

[0073] Among them, u i上 is the flow rate of the upstream acid in the wellbore, m / s; u i下 is the flow rate of the downstream acid in the wellbore, m / s; x in is the location of the acid injection port, dimensionless; i is the cell location in the x-axis direction, dimensionless; m is the total number of cells in the acid flow velocity model in the x-axis direction, dimensionless; x m is the position of the mth cell in the x-axis direction, dimensionless; Δx and Δy are the lengths of the cell in the x-axis and y-axis directions, m; P well,i is the fluid pressure in the wellbore at position i in the x-axis direction, Pa; P r,i is the fluid pressure in the formation at position i in the x-axis direction, Pa; k y,i is the permeability of the reservoir at position i along the y-axis, m 2 ; μ is the fluid viscosity, Pa·s; D 井 is the borehole diameter, m.

[0074] S4. An acid fracturing dynamic model is established based on the acid flow velocity model, the wellbore fluid pressure model and the matrix fluid pressure model.

[0075] In this embodiment, the acid fracturing dynamic model may include an acid concentration distribution model, and the acid concentration distribution model may include:

[0076] Formula 7:

[0077] Formula 8: v l,i =Q out,i / (πD 井 Δx).

[0078] Where Δx is the length of the cell in the x-axis direction, m; D井 is the borehole diameter, m; C is the acid concentration, mol / m 3 ; t is the acid injection time, s; u is the acid flow rate in the wellbore, m / s; k c Acid-rock reaction rate, m / s; v l is the acid flow rate from the wellbore into the reservoir, m / s; i is the unit cell position in the x-axis direction, dimensionless; v l,i is the acid flow rate from the wellbore into the reservoir at position i in the x-axis direction, m / s; Q out,i is the acid flow rate out of the wellbore per unit time at position i in the x-axis direction, m 3 / min.

[0079] In this embodiment, the acid fracturing dynamic model may include a porosity model and a permeability model after acid dissolution, and the porosity model and the permeability model may include:

[0080] Formula 9:

[0081] Formula 10:

[0082] Among them, φ n is the porosity at the nth time step, dimensionless; φ is the reservoir porosity, dimensionless; Δx and Δy are the lengths of the unit cell in the x-axis and y-axis directions, m; D 井 is the borehole diameter, m; n is the nth time step, dimensionless; t is the acid injection time, s; τ is the corresponding time step number of the acid front reaching the cells at different positions in the wellbore for the first time; ΔV is the volume of rock dissolved by the acid, m 3 ; β is the solubility of the acid for rock minerals, kg / kg; M is the molar mass of the acid, kg / mol; k c Acid-rock reaction rate, m / s; C is acid concentration, mol / m 3 ; said ρ S is the rock density, kg / m 3 ;k n is the permeability after dissolution, m 2 ; k is the initial permeability, m 2 β SG is the pore structure parameter, dimensionless.

[0083] In this embodiment, the acid fracturing dynamic model may include a wellbore tangential stress model, and the wellbore tangential stress model may include:

[0084] Formula 11:

[0085]

[0086] ν=5.89e [-(t-τ) / 6.47] -6.23,

[0087] Among them, σ θ is the wellbore tangential stress, MPa; σ H , σ h and σ ν are the maximum horizontal principal stress, minimum horizontal principal stress and vertical stress, MPa; σ z is the tangential stress of the wellbore, MPa; θ, θ' are the well inclination angle, the angle from the wellbore axis to the tangential stress direction of the bottom of the hole on the wellbore, °; P well is the fluid pressure in the wellbore, MPa; P is the reservoir fluid pressure, MPa; α is the Biot coefficient, dimensionless; ν is the rock Poisson's ratio, dimensionless; ω is the acid damage variable, dimensionless; φ is the reservoir porosity, dimensionless; φ n is the porosity at the nth time step, dimensionless; t is the acid injection time, s; τ is the corresponding time step number when the acid front first reaches the cells at different positions in the wellbore.

[0088] In this embodiment, when the acid concentration at the cell position in the wellbore is greater than or equal to 301-903 mol / m 3 For example, 301, 602, 903 mol / m 3 , it can be determined that the acid front reaches the cell position for the first time. Among them, the acid concentration can also be confirmed according to the initial concentration of the injected acid, which can usually be 10% to 20% of the initial concentration. The specific value can also be confirmed according to the on-site conditions of the oil field.

[0089] In another aspect, the present invention provides a method for predicting dynamic fracture pressure of a long open hole section of a horizontal well by acid fracturing.

[0090] In an exemplary embodiment of the method for predicting the acid fracturing pressure of a long open hole section of a horizontal well of the present invention, the method for predicting the dynamic acid fracturing pressure of a long open hole section of a horizontal well includes the following steps: confirming whether the difference between the reservoir fluid pressure and the wellbore tangential stress is greater than or equal to the rock tensile strength through the acid fracturing dynamic model in any of the above-mentioned methods for establishing the dynamic acid fracturing model of a long open hole section of a horizontal well.

[0091] When the difference is greater than or equal to the rock tensile strength, the fracture location and fracture pressure can be confirmed.

[0092] When the difference is less than the rock tensile strength, the characteristic parameters and mechanical parameters can be updated, and the above steps S1 to S4 are repeated until the difference is greater than or equal to the rock tensile strength.

[0093] When the acid injection process is completed and the difference is less than the rock tensile strength, the construction parameters can be redesigned.

[0094] In order to better understand the above exemplary embodiments of the present invention, they are further described below in conjunction with specific examples and drawings, but the examples given are not intended to limit the present invention.

[0095] Example 1

[0096] In this example, the method for establishing the acid fracturing dynamic model for a long open hole section of a horizontal well can be achieved by the following steps:

[0097] S1. Establish a physical model of the long open hole section of a horizontal well and a geological model distributed along the wellbore. The direction along the wellbore is set as the x-axis, the direction of increasing wellbore depth is the positive direction of the x-axis, the direction perpendicular to the wellbore is set as the y-axis, and the direction away from the wellbore is the positive direction of the y-axis. According to the logging data, the physical model of the long open hole section of the horizontal well after grid division, and the geological model distributed along the wellbore, the characteristic parameters and mechanical parameters of the corresponding depth are confirmed.

[0098] S11. Establish a geological model distributed along the wellbore. The number of cells in the length direction of the geological model is m. According to the logging data, the reservoir porosity, permeability, formation pressure and other characteristic parameters of the corresponding depth are assigned to each cell.

[0099] S12. Calculate the mechanical parameter profile along the wellbore based on the logging data and indoor experimental results, including the maximum horizontal principal stress, minimum horizontal principal stress, vertical principal stress, Young's modulus, Poisson's ratio of the reservoir, and other mechanical parameters assigned to the corresponding depth in each cell.

[0100] S2. Establish a fluid pressure model in the wellbore and a fluid pressure model in the matrix according to the characteristic parameters and mechanical parameters.

[0101] S21, according to the volume V of the transformation section wellbore well , reservoir fluid pressure P, injection volume Q in Calculate the fluid pressure P in the wellbore using the same parameters well , as shown in formulas 1 to 3:

[0102] Formula 1:

[0103] Formula 2:

[0104] Formula 3:

[0105] In the above formula, n is the nth time step, dimensionless; is the bottom hole pressure at the n+1th time step, Pa; is the bottom hole pressure at the nth time step, Pa; ΔP nis the pressure change caused by the compressibility of the fluid in the wellbore at the nth time step, Pa; ΔP is the pressure change caused by the compressibility of the fluid in the wellbore, Pa; ΔV acid is the volume increment of acid fluid in the wellbore, m 3 ; V well is the wellbore volume, m 3 ; c1 is the fluid compressibility coefficient, Pa -1 ; Δt is the time step, s; is the acid flow rate injected into the wellbore in the nth time step, m 3 / min; is the acid flow rate out of the wellbore in the nth time step, m 3 / min, and when n=1, Δx and Δy are the lengths of the cell in the x-axis and y-axis directions, m; k y is the permeability of the cell in the y-axis direction, m 2 ; r is the wellbore radius, m; μ is the fluid viscosity, Pa·s; is the reservoir fluid pressure in the first grid at the nth time step in the y-axis direction, Pa.

[0106] S22. Determine the time step according to the average permeability of the reservoir matrix, including:

[0107] When k m The value range is k m <10 -15 m 2 When , the time step Δt = 1s.

[0108] When k m The value range is 10 -15 m 2 ≤k m ≤10 -14 m 2 When the time step is Δt=1~10s.

[0109] When k m The value range is 10 -14 m 2 ≤k m When the time step is Δt=10s.

[0110] S23, according to the time step wellbore fluid pressure P obtained in step S21 well Calculate the fluid pressure within the matrix as shown below:

[0111] Formula 4:

[0112] Where ρ is the fluid density, kg / m 3 ;k x , ky are the permeabilities of the cell in the x-axis and y-axis directions, m 2 ; μ is fluid viscosity, Pa·s; P is reservoir fluid pressure, Pa; φ is the porosity in the unit cell, dimensionless; c1 is the fluid compressibility, Pa -1 ; t is the acid injection time, s.

[0113] S3. Establishing an acid fluid flow velocity model based on the acid injection port position in the wellbore according to the wellbore fluid pressure model and the matrix fluid pressure model.

[0114] S31, the cell position x of the acid injection port in As a benchmark, the positive direction of the x-axis is the downstream, and the negative direction is the upstream. The acid flow velocities of the upstream and downstream of the acid injection port at different positions in the wellbore are calculated respectively.

[0115] Among them, the upstream acid flow velocity u i上 and downstream acid flow velocity u i下 This can be confirmed by calculation using the following formula 5 and formula 6, respectively.

[0116] Formula 5:

[0117] Formula 6:

[0118] Among them, u i上 is the flow rate of the upstream acid in the wellbore, m / s; u i下 is the flow rate of the downstream acid in the wellbore, m / s; x in is the location of the acid injection port, dimensionless; i is the cell location in the x-axis direction, dimensionless; m is the total number of cells in the acid flow velocity model in the x-axis direction, dimensionless; x m is the position of the mth cell in the x-axis direction, dimensionless; Δx and Δy are the lengths of the cell in the x-axis and y-axis directions, m; P well,i is the fluid pressure in the wellbore at position i in the x-axis direction, Pa; P r,i is the fluid pressure in the formation at position i in the x-axis direction, Pa; k y,i is the permeability of the reservoir at position i along the y-axis, m 2 ; μ is the fluid viscosity, Pa·s; D 井 is the borehole diameter, m.

[0119] S4. An acid fracturing dynamic model is established based on the acid flow velocity model, the wellbore fluid pressure model and the matrix fluid pressure model.

[0120] S41. Calculate the concentration distribution of the acid in the wellbore based on the flow rate of the acid in the wellbore, as shown in Formulas 7 and 8 below.

[0121] Formula 7:

[0122] Formula 8: v l ,i=Q out ,i / (πD 井 Δx).

[0123] Where Δx is the length of the cell in the x-axis direction, m; D 井 is the borehole diameter, m; C is the acid concentration, mol / m 3 ; t is the acid injection time, s; u is the acid flow rate in the wellbore, m / s; k c Acid-rock reaction rate, m / s; v l is the acid flow rate from the wellbore into the reservoir, m / s; i is the unit cell position in the x-axis direction, dimensionless; v l , i is the acid flow rate from the wellbore into the reservoir at position i in the x-axis direction, m / s; Q out , i is the acid flow rate out of the wellbore per unit time at position i in the x-axis direction, m 3 / min.

[0124] S42, according to the acid concentration of the cell position in the wellbore is greater than or equal to 301 ~ 903 mol / m 3 , it is determined that the acid front reaches the cell position for the first time.

[0125] S43. Based on the acid concentration distribution in the wellbore and the acid flow rate from the wellbore to the reservoir, starting from the corresponding position where the acid front first arrives in the wellbore, calculate the porosity after acid dissolution and the permeability after dissolution.

[0126] The calculation of porosity after acid dissolution is shown in Formula 9.

[0127] Formula 9:

[0128] The calculation of the permeability after dissolution is shown in Equation 10.

[0129] Formula 10:

[0130] In the above formula, φ n is the porosity at the nth time step, dimensionless; φ is the reservoir porosity, dimensionless; Δx and Δy are the lengths of the unit cell in the x-axis and y-axis directions, m; D 井 is the borehole diameter, m; n is the nth time step, dimensionless; t is the acid injection time, s; τ is the corresponding time step number of the acid front reaching the cells at different positions in the wellbore for the first time; ΔV is the volume of rock dissolved by the acid, m 3; β is the solubility of the acid for rock minerals, kg / kg; M is the molar mass of the acid, kg / mol; k c Acid-rock reaction rate, m / s; C is acid concentration, mol / m 3 ρ S is the rock density, kg / m 3 ;k n is the permeability after dissolution, m 2 ; k is the initial permeability, m 2 β SG is the pore structure parameter, dimensionless.

[0131] S44, according to the wellbore porosity φ n , reservoir fluid pressure P, bottom hole fluid pressure P well The tangential stress distribution along the wellbore is calculated based on the wellbore stress model and other parameters. The fracture position and fracture pressure can be determined based on the calculated tangential stress distribution along the wellbore.

[0132] The wellbore stress model can be expressed by the following formula 11:

[0133] Formula 11:

[0134]

[0135] ν=5.89e [-(t-τ) / 6.47] -6.23,

[0136] Among them, σ θ is the wellbore tangential stress, MPa; σ H , σ h and σ ν are the maximum horizontal principal stress, minimum horizontal principal stress and vertical stress, MPa; σ z is the tangential stress of the wellbore, MPa; θ, θ' are the well inclination angle, the angle from the wellbore axis to the tangential stress direction of the bottom of the hole on the wellbore, °; P well is the fluid pressure in the wellbore, MPa; P is the reservoir fluid pressure, MPa; α is the Biot coefficient, dimensionless; ν is the rock Poisson's ratio, dimensionless; ω is the acid damage variable, dimensionless; φ is the reservoir porosity, dimensionless; φ n is the porosity at the nth time step, dimensionless; t is the acid injection time, s; τ is the corresponding time step number when the acid front first reaches the cells at different positions in the wellbore.

[0137] Example 2

[0138] In this example, a method for predicting the dynamic fracture pressure of a horizontal well long open hole section by acid fracturing is provided, which can judge whether each position in the wellbore has reached the fracture pressure in turn according to the selected rock failure criterion. It should be noted that the fracture pressure calculation model that can be used here can select the corresponding fracture pressure model according to different well types, completion methods, and reservoir characteristics. For example, when the well is completed by casing perforation, a calculation model that takes casing perforation completion into consideration needs to be selected.

[0139] Among them, the rock failure criterion can be expressed by the following formula 12:

[0140] Formula 12: P-σ θ ≥σ t .

[0141] Where P is the reservoir fluid pressure, MPa; σ θ is the wellbore tangential stress, MPa; σ t is the rock tensile strength, MPa. The above-mentioned wellbore tangential stress can be obtained by the method of establishing the dynamic model of acid fracturing in the horizontal well long open hole section in Example 1. The rock tensile strength σ t It can also be obtained through indoor experiments.

[0142] A further solution is that if the condition satisfies the above formula 12, the calculation is stopped to obtain the fracture position and fracture pressure. If the fracture condition is not met, the reservoir permeability, porosity, fluid pressure in the wellbore, reservoir fluid pressure, and acid concentration distribution are updated, and steps S1 to S4 in the above example are repeated to obtain the fracture position and fracture pressure calculation. If the fracture condition is still not met after the acid injection process is completed, it is determined that the formation cannot be opened to form acid fractures under the corresponding acid injection conditions, and the construction parameters need to be redesigned.

[0143] Example 3

[0144] In this example, a method for predicting dynamic fracture pressure in a horizontal well with long open hole section during acid fracturing is provided, which is implemented by the following steps:

[0145] S1. Establish a physical model for calculating the long open hole section of a horizontal well (including the physical model of the long open hole section of a horizontal well in Example 1 and the geological model distributed along the wellbore), and assign parameters as shown in Table 1 below.

[0146] Table 1 Parameter assignment table

[0147]

[0148] S2. According to the parameters such as the wellbore volume of the reformed section, the reservoir fluid pressure, and the injection volume, a suitable time step is selected, and the fluid pressure in the wellbore is calculated according to equations 1 to 3 in Example 1.

[0149] S3, based on the fluid pressure in the wellbore, the fluid pressure in the reservoir at the time step, the reservoir permeability, the porosity and other parameters, the distribution of the fluid in the reservoir at the time step is calculated according to Formula 4 in Example 1. Figure 2 As shown, Figure 2 The calculation results of fluid pressure in the reservoir are shown. Figure 2 It can be seen that due to the heterogeneity of reservoir physical properties, the fluid pressure changes near the wellbore also show strong heterogeneity, which can provide a basis for the calculation of non-uniform filtration and heterogeneous flow of acid in the wellbore.

[0150] S4. Based on the calculated reservoir fluid pressure, the flow rate of the acid fluid in the wellbore is calculated according to Formulas 5 to 6 in Example 1. Figure 3 As shown, Figure 3 The calculation results of the acid flow velocity distribution in the wellbore are shown. Figure 3 The horizontal axis represents the well section, the unit is m, and the vertical axis represents the flow velocity in the wellbore, the unit is m / s. The broken line in the figure represents the flow velocity in the wellbore at different well section positions.

[0151] S5. Based on the reservoir fluid pressure calculated in S3, according to the acid concentration distribution in the wellbore at the current time step according to equations 7 to 8 in Example 1, as follows: Figure 4 As shown, Figure 4 The calculation results of acid concentration distribution in the wellbore are shown. Figure 4 The horizontal axis represents the wellbore cell position, the unit is m, and the vertical axis represents the HCL acid concentration, the unit is %. The broken line in the figure represents the HCL acid concentration at different wellbore cell positions.

[0152] The acid concentration at the cell position in the current wellbore is greater than or equal to 602 mol / m 3 As a judgment criterion, when the above criteria are met, the moment when the acid front first reaches cells at different positions in the wellbore is recorded.

[0153] S6. Based on the acid concentration distribution in the wellbore and the acid flow rate from the wellbore to the reservoir, starting from the time when the acid front first arrives at the corresponding position in the wellbore, calculate the porosity after acid dissolution and the permeability after dissolution according to Formulas 9 and 10 in Example 1.

[0154] S7, according to the parameters such as the wellbore porosity, reservoir fluid pressure, and bottom hole fluid pressure, the tangential stress distribution along the wellbore is calculated according to Formula 11 in Example 1, and further according to Formula 12 in Example 2, it is determined in turn whether each position in the wellbore has reached the fracture pressure, such as Figure 5 As shown, Figure 5 The burst pressure determination result is shown. Figure 5The horizontal axis represents time in seconds, and the vertical axis represents pressure in MPa. The broken line a in the figure represents the wellbore tangential stress at different times, the broken line b in the figure represents the reservoir pore pressure at different times, and the broken line c in the figure represents the bottom hole flow pressure at different times. Figure 5 It can be seen that due to the pressure loss accumulated during the flow of fluid from the wellbore to the reservoir, the fluid pressure in the wellbore is always greater than the reservoir fluid pressure. With the injection of fluid, the reservoir fluid pressure is at the intersection of the sum of the wellbore tangential stress and the tensile strength at 413s, at which time the fracture initiation condition is reached.

[0155] S8. If it is determined in S7 that any position along the wellbore meets the fracturing conditions, the calculation is stopped to obtain the fracturing position and fracturing pressure. If the fracturing conditions are not met, the reservoir permeability, porosity, wellbore fluid pressure, reservoir fluid pressure, and acid concentration distribution are updated, and steps S1 to S7 are repeated to obtain the fracturing position and fracturing pressure calculation. If the fracturing conditions are still not met after the acid injection process is completed, it is determined that the formation cannot be opened to form acid fracturing under the corresponding acid injection conditions, and the construction parameters need to be redesigned.

[0156] In summary, the beneficial effects of the present invention include: by real-time calculation of the dynamic flow and reaction process of the acid in the wellbore and reservoir, and considering the changes in mechanical characteristics and physical characteristics of the acid chemical reaction on the reservoir sections with different physical parameters, the dynamic fracture pressure in the acid fracturing process can be predicted. The model calculation process is simple and does not require iteration. It can accurately and simply calculate the dynamic fracture pressure of horizontal well long open hole acid fracturing under different acid injection parameters, acid injection port locations, and reservoir conditions, providing a theoretical basis for the optimization of acid fracturing process types, process parameters, supporting liquids and tools.

[0157] Although the present invention has been described above in conjunction with the exemplary embodiments and the accompanying drawings, it should be apparent to those skilled in the art that various modifications may be made to the above-described embodiments without departing from the spirit and scope of the claims.

Claims

1. A method for establishing a dynamic model of acid fracturing in a long open hole section of a horizontal well, characterized in that: The method comprises the following steps: S1. Establishing a physical model of a long open hole section of a horizontal well and a geological model distributed along the wellbore, and confirming characteristic parameters and mechanical parameters of corresponding depths according to the physical model of the long open hole section of the horizontal well after gridding and the geological model distributed along the wellbore; S2. Establishing a fluid pressure model in the wellbore and a fluid pressure model in the matrix according to the characteristic parameters and mechanical parameters; S3, establishing an acid fluid flow velocity model based on the acid injection port position in the wellbore according to the wellbore fluid pressure model and the matrix fluid pressure model; S4, establishing an acid fracturing dynamic model according to the acid fluid flow velocity model, the wellbore fluid pressure model and the matrix fluid pressure model; Wherein, the wellbore fluid pressure model includes: Formula 1: Formula 2: Formula 3: Wherein, n is the nth time step, dimensionless; is the bottom hole pressure at the n+1th time step, Pa; is the bottom hole pressure at the nth time step, Pa; the ΔP n is the pressure change caused by the compressibility of the fluid in the wellbore at the nth time step, Pa; ΔP is the pressure change caused by the compressibility of the fluid in the wellbore, Pa; ΔV acid is the volume increment of the acid fluid in the wellbore at the nth time step, m 3 ; The V well is the wellbore volume, m 3 ; The c1 is the fluid compressibility coefficient, Pa -1 ; Δt is the time step, s; is the acid flow rate injected into the wellbore in the nth time step, m 3 / min; is the acid flow rate out of the wellbore in the nth time step, m 3 / min, and when n=1, The Δx and Δy are the lengths of the cell in the x-axis and y-axis directions, m; the k y is the permeability of the cell in the y-axis direction, m 2 ; r is the wellbore radius, m; μ is the fluid viscosity, Pa·s; is the reservoir fluid pressure at the nth time step in the first grid in the y-axis direction, Pa; The matrix fluid pressure model includes: Formula 4: Wherein, ρ is the fluid density, kg / m 3 ; the k x , k y are the permeabilities of the cell in the x-axis and y-axis directions, m 2 ; μ is the fluid viscosity, Pa·s; P is the reservoir fluid pressure, Pa; φ is the reservoir porosity, dimensionless; c1 is the fluid compressibility, Pa -1 ; t is the acid injection time, s; The acid flow velocity model includes an upstream acid flow velocity model and a downstream acid flow velocity model, which respectively include: Formula 5: Formula 6: Among them, the u i上 is the flow rate of the upstream acid in the wellbore, m / s; i下 is the flow rate of the downstream acid in the wellbore, m / s; in is the position of the acid injection port, dimensionless; i is the unit cell position in the x-axis direction, dimensionless; m is the total number of units in the acid flow velocity model in the x-axis direction, dimensionless; x m is the position of the mth cell in the x-axis direction, dimensionless; Δx and Δy are the lengths of the cell in the x-axis and y-axis directions, m; P well,i is the fluid pressure in the wellbore at position i in the x-axis direction, Pa; r,i is the fluid pressure in the formation at position i in the x-axis direction, Pa; k y,i is the permeability of the reservoir at position i along the y-axis, m 2 ; μ is the fluid viscosity, Pa·s; D 井 is the borehole diameter, m.

2. The method for establishing a dynamic model of acid fracturing in a horizontal well long open hole section according to claim 1, characterized in that: The time step Δt is based on the average permeability k of the reservoir matrix. m Confirmation, specifically including: when the k m The value range is k m <10 -15 m 2 When the time step Δt=1s; when the k m The value range is 10 -15 m 2 ≤k m ≤10 -14 m 2 When the time step Δt = 1 to 10 s; when the k m The value range is 10 -14 m 2 ≤k m , the time step Δt=10s.

3. The method for establishing a dynamic model of acid fracturing in a long open hole section of a horizontal well according to claim 1, characterized in that: The acid fracturing dynamic model includes an acid concentration distribution model, and the acid concentration distribution model includes: Formula 7: Equation 8: v l , i = Q out , i / (πD 井 Δx); Wherein, Δx is the length of the cell in the x-axis direction, m; D 井 is the borehole diameter, m; C is the acid concentration, mol / m 3 ; t is the injection time of acid solution, s; u is the flow rate of acid solution in the wellbore, m / s; k c Acid-rock reaction rate, m / s; v l is the acid flow rate from the wellbore into the reservoir, m / s; i is the unit cell position in the x-axis direction, dimensionless; v l , i is the acid flow rate from the wellbore into the reservoir at position i in the x-axis direction, m / s; Q out , i is the acid flow rate out of the wellbore per unit time at position i in the x-axis direction, m 3 / min.

4. The method for establishing a dynamic model of acid fracturing in a horizontal well long open hole section according to claim 1, characterized in that: The acid fracturing dynamic model includes a porosity model and a permeability model after acid dissolution, and the porosity model and the permeability model respectively include: Formula 9: Formula 10: Among them, the φ n is the porosity at the nth time step, dimensionless; φ is the reservoir porosity, dimensionless; Δx and Δy are the lengths of the unit cell in the x-axis and y-axis directions, m; D 井 is the borehole diameter, m; n is the nth time step; t is the acid injection time, s; τ is the corresponding time step number of the acid front first reaching the cells at different positions in the wellbore; ΔV is the volume of rock dissolved by the acid, m 3 ; β is the solubility of the acid for rock minerals, kg / kg; M is the molar mass of the acid, kg / mol; k c Acid-rock reaction rate, m / s; C is the acid concentration, mol / m 3 ; said ρ S is the rock density, kg / m 3 ; the k n is the permeability after dissolution, m 2 ; k is the initial permeability, m 2 ; the β SG is the pore structure parameter, dimensionless.

5. The method for establishing a dynamic model of acid fracturing in a long open hole section of a horizontal well according to claim 1, characterized in that: The acid fracturing dynamic model includes a well wall tangential stress model, and the well wall tangential stress model includes: Formula 11: Among them, the σ θ is the wellbore tangential stress, MPa; H , σ h and σ ν are the maximum horizontal principal stress, minimum horizontal principal stress and vertical stress, MPa respectively; the σ z is the tangential stress of the wellbore, MPa; θ, θ' are the well inclination angle, the angle from the wellbore axis to the tangential stress direction of the bottom of the hole on the wellbore, °; P well is the fluid pressure in the wellbore, MPa; P is the reservoir fluid pressure, MPa; α is the Biot coefficient, dimensionless; ν is the rock Poisson's ratio, dimensionless; ω is the acid damage variable, dimensionless; φ is the reservoir porosity, dimensionless; φ n is the porosity at the nth time step, dimensionless; t is the acid injection time, s; τ is the corresponding time step number when the acid front first reaches the cells at different positions in the wellbore.

6. The method for establishing a dynamic model of acid fracturing in a long open hole section of a horizontal well according to claim 1, characterized in that: When the acid concentration at the cell position in the wellbore is greater than or equal to 301-903 mol / m 3 When , it is determined that the acid front reaches the cell position for the first time.

7. A method for predicting dynamic fracture pressure of a horizontal well long open hole section by acid fracturing, characterized in that: The prediction method comprises: using the acid fracturing dynamic model in the method for establishing an acid fracturing dynamic model for a long open hole section of a horizontal well according to any one of claims 1 to 6 to confirm whether the difference between the reservoir fluid pressure and the wellbore tangential stress is greater than or equal to the rock tensile strength; When the difference is greater than or equal to the rock tensile strength, the fracture position and fracture pressure are confirmed; When the difference is less than the rock tensile strength, the characteristic parameters and mechanical parameters are updated, and steps S1 to S4 are repeated until the difference is greater than or equal to the rock tensile strength; When the acid injection process is completed and the difference is less than the rock tensile strength, the construction parameters are redesigned.

Images