Method, device, medium and equipment for quickly simulating height of fracturing crack by using wellhead construction pressure

Abstract

The invention relates to a method, a device, a medium and equipment for quickly simulating the height of a fracturing crack by using wellhead construction pressure. The method comprises the following steps: establishing a relationship between wellhead pressure and net pressure; liquid column pressure in a shaft, perforation hole friction resistance and shaft friction resistance are calculated; based on the liquid column pressure in a shaft, the perforation hole friction resistance and the pipe column friction resistance, according to the relation between the wellhead pressure and the net pressure, the continuous crack opening pressure and the net pressure are obtained, and according to the change rule of the net pressure, the change rule of the crack height is preliminarily judged; according to the fracture pressure obtained through calculation of the wellhead pressure, the result that the fracture pressure is calculated through frictional resistance of liquid in a fracture is replaced, an algorithm suitable for simulating three-dimensional expansion of conventional reservoir fracturing fractures and calculating fracture parameters according to the fracture pressure is formed, and the filtration coefficient and the closing stress in the geologic model are updated according to the test fracturing result. And real-time seam pressure is introduced for constraint, and the width, the height and the length of a fitting crack are calculated.

Description

Technical Field

[0001] The present invention relates to a method, device, medium and equipment for rapidly simulating the height of a fracturing crack by utilizing wellhead construction pressure, and belongs to the technical field of liquefied natural gas. Background Art

[0002] Hydraulic fracturing is the process of creating fractures in formations by injecting proppants or high-pressure fluids. Since the 1940s, hydraulic fracturing has undergone a long journey from theory to practice, achieving considerable success. For low- or ultra-low-permeability reservoirs, hydraulic fracturing is an excellent way to achieve industrial flow rates. Hydraulic fracturing has become a crucial measure in oil and gas field development, particularly in the development of unconventional oil and gas fields, such as shale and tight oil and gas, and an essential reservoir stimulation measure. From a petroleum engineering perspective, drilling and fracturing represent the most expensive engineering steps, and the success of hydraulic fracturing determines the profitability of this investment. Rapid simulation of actual fracture heights based on operating pressure data facilitates the formulation of oil and gas development policies and ensures efficient and economical development. Fracturing technology has become a primary development tool and an indispensable process for low-permeability reservoirs, and has experienced rapid development in my country in recent years. With the continued advancement of unconventional natural gas exploration and development in my country, methods for calculating actual fracture parameters based on wellhead operating pressures have a broad market demand and promising prospects.

[0003] Net pressure analysis has become a key diagnostic method for fracturing operations. Accurate calculation and analysis of fracturing operation pressures form the foundation of real-time diagnostic technology, providing comprehensive guidance for fracturing operation decisions. Fracturing operation pressure qualitatively describes the dynamics of fracture extension, making fracturing pressure analysis a key tool for mitigating operational risks and ensuring fracturing quality. Fracture parameter calculations provide an effective basis for fracturing optimization and adjustment, and are crucial for determining the effectiveness of fracturing operations. Accurate net pressure calculations provide the foundation and basis for calculating fracture height, length, and width.

[0004] Implementing net pressure analysis requires clear and accurate curve plotting, but corresponding algorithmic tools are lacking. Numerous researchers have conducted extensive research on the propagation process of hydraulic fractures using the extended finite element method. However, most studies assume a fixed net pressure within the fracture, or calculate the net pressure based on previously established geological models, fracture shape, and construction process parameters. These calculations differ significantly from the actual propagation of hydraulic fractures in the reservoir, leading to large simulation errors and insufficient utilization of measured wellhead pressure data. This significantly constrains the calculation of fracture parameters. Furthermore, when calculating bottomhole pressure from wellhead pressure, conventional fracturing pressure calculation models often simplify the calculation of wellbore pressure by setting a unified frictional pressure drop gradient / coefficient, resulting in significant deviations in the results. This is because conventional fracturing pressure calculation models rarely comprehensively consider the influence of factors such as the perforation cluster opening degree and perforation abrasion on perforation pressure drop. Summary of the Invention

[0005] In response to the above technical problems, the present invention provides a method, device, medium and equipment for quickly simulating the height of hydraulic fracturing cracks using wellhead construction pressure. This method provides a strong foundation for real-time monitoring of net pressure, diagnosis of crack extension morphology, and crack morphology (especially diagnosis of crack height) during hydraulic fracturing construction.

[0006] To achieve the above object, the present invention adopts the following technical solutions:

[0007] A method for rapidly simulating the height of a hydraulic fracture using wellhead construction pressure, comprising:

[0008] S1: Establish the relationship between wellhead pressure and net pressure;

[0009] S2: Calculate the fluid column pressure in the wellbore, the friction resistance of the perforation holes and the friction resistance of the wellbore;

[0010] S3: Based on the fluid column pressure in the wellbore, the friction resistance of the perforation holes, and the friction resistance of the tubing string, and according to the relationship between the wellhead pressure and the net pressure, the continuous fracture mouth pressure and the net pressure are obtained. Based on the variation pattern of the net pressure, the variation pattern of the fracture height is preliminarily determined;

[0011] S4: The fracture pressure calculated based on the wellhead pressure replaces the result calculated using the friction resistance of the liquid in the fracture to form an algorithm suitable for simulating the three-dimensional expansion of conventional reservoir fracturing cracks and calculating the fracture parameters based on the fracture pressure. At the same time, combined with the fluid flow simulation algorithm, the fracture expansion simulation algorithm, and the stress-flow-extension coupling solution algorithm, the filtration coefficient and closure stress in the geological model are updated according to the test fracturing results, and the real-time fracture pressure is introduced for constraint to calculate the fitting fracture width, fracture height and length.

[0012] In the method for rapidly simulating the height of a fracturing crack using wellhead construction pressure, preferably, in step S2, when calculating the liquid column pressure in the wellbore, a density calculation method for the single-phase fracturing fluid between the fracturing fluid or proppant plugs under high temperature and high pressure conditions is established. With the addition of proppant, the liquid becomes a sand-carrying fluid, which will increase the local concentration and density of the fracturing fluid. Therefore, when calculating the liquid column pressure in the wellbore, the effect of the proppant on the density of the fracturing fluid must be considered, and a relationship between the density of the sand-carrying fluid and the sand ratio and particle composition must be established.

[0013] In the method for rapidly simulating the height of a fracturing crack using wellhead construction pressure, preferably, the fracturing fluid and proppant flow in solid-liquid two-phase in the crack, wherein the flow of the fracturing fluid in the crack is one-dimensional along the length of the crack, taking into account the filtration behavior from the crack to the matrix pores; and the proppant migrates two-dimensionally along the length of the crack and settles vertically.

[0014] In the method for rapidly simulating the height of a hydraulic fracture using wellhead construction pressure, preferably, in step S2, when calculating the friction resistance of the perforation holes, two situations are considered:

[0015] When there is no test fracturing data, a calculation model for perforation friction resistance is established. According to the perforation phase angle, the number of perforations is accurately assigned, and an empirical equation for perforation abrasion is established to calculate the changes in perforation diameter and flow coefficient, thereby dynamically calculating the perforation friction resistance.

[0016] When test fracturing data is available, the reduction rate method is used to obtain a regression formula for the sum of the hole friction resistance and the near-wellbore friction resistance, which are uniformly considered as the hole friction resistance, and then the initial flow coefficient is calculated. Then, according to the amount of fluid and sand injected, the changes in the hole diameter and flow coefficient are corrected during the construction process, thereby dynamically calculating the friction resistance of the perforation hole.

[0017] In the method for rapidly simulating the height of a fracturing crack using wellhead construction pressure, preferably, in step S2, when calculating the wellbore friction resistance, the viscosity of the liquid before and after cross-linking is taken into account, and the influence of the wellbore friction coefficient, the fluid Reynolds number, the pipe diameter, the roughness, and the fluid viscosity are taken into account, so as to accurately calculate the wellbore friction resistance.

[0018] The method for rapidly simulating the height of hydraulic fractures using wellhead construction pressure preferably comprises the following steps: in step S4, boundary element method, finite difference method, and finite volume method are used to establish a stress field simulation algorithm, a fluid flow simulation algorithm (see formula 30), a fracture extension simulation algorithm, and a stress-flow-extension coupling solution algorithm. The fracture mouth pressure calculated based on the wellhead pressure is introduced to replace the result of calculating the fracture mouth pressure using the friction resistance of the liquid in the fracture, thereby forming an algorithm suitable for simulating the three-dimensional extension of hydraulic fractures in conventional reservoirs and calculating the fracture parameters based on the fracture mouth pressure, and calculating the fitted fracture width, fracture height, and length.

[0019] In the method for rapidly simulating the height of a hydraulic fracture using wellhead construction pressure, preferably, in step S4, the closure stress and the fluid loss coefficient are obtained based on the interpretation of the post-fracture pressure drop curve to calibrate the geological model.

[0020] A second aspect of the present invention provides a device for rapidly simulating the height of a hydraulic fracturing crack using wellhead construction pressure, comprising:

[0021] a first processing unit for establishing a relationship between the wellhead pressure and the net pressure;

[0022] The second processing unit is used to calculate the fluid column pressure in the wellbore, the friction resistance of the perforation hole and the friction resistance of the wellbore;

[0023] The third processing unit is used to obtain the continuous fracture mouth pressure and net pressure based on the relationship between the wellhead pressure and the net pressure, based on the liquid column pressure in the wellbore, the friction resistance of the perforation hole and the friction resistance of the pipe string, and preliminarily determine the change pattern of the fracture height based on the change pattern of the net pressure;

[0024] The fourth processing unit is used to replace the result of calculating the fracture pressure using the friction resistance of the liquid in the fracture based on the fracture pressure calculated based on the fracture pressure calculated based on the wellhead pressure, to form an algorithm suitable for simulating the three-dimensional expansion of conventional reservoir fracturing cracks and calculating the fracture parameters based on the fracture pressure. At the same time, it combines the fluid flow simulation algorithm, the fracture expansion simulation algorithm, and the stress-flow-extension coupling solution algorithm, updates the filtration coefficient and closure stress in the geological model according to the test fracturing results, introduces real-time fracture pressure for constraint, and calculates the fitted fracture width, fracture height, and length.

[0025] A third aspect of the present invention provides a computer-readable storage medium having a computer program stored thereon, wherein the computer program, when executed by a processor, implements the steps of any one of the above-mentioned methods for rapidly simulating the height of a hydraulic fracture using wellhead construction pressure.

[0026] A fourth aspect of the present invention provides a computer device comprising a memory, a processor, and a computer program stored in the memory and executable on the processor. When the processor executes the computer program, the steps of any one of the above-mentioned methods for rapidly simulating the height of a fracturing crack using wellhead construction pressure are implemented.

[0027] The present invention has the following advantages due to the adoption of the above technical solution:

[0028] 1. The present invention uses the pressure drop test results to calibrate the geological model, including closure stress, filtration coefficient, etc.

[0029] 2. The present invention takes into account the delayed cross-linking time of the liquid and makes a detailed calculation of the viscosity of the fracturing fluid in the wellbore. The viscosity of the liquid before cross-linking is the viscosity of the original liquid, while the viscosity increases significantly after cross-linking.

[0030] 3. The present invention calculates the average density of different proppant combinations in detail, taking into account the change in proppant density within the wellbore.

[0031] 4. The present invention reversely calculates the bottom hole pressure based on the construction pressure or casing pressure measured at the wellhead, and further calculates the net pressure and the seam pressure based on the hole friction resistance and closing stress.

[0032] 5. The present invention establishes a precise model of perforation friction resistance. When no lift and displacement data is available, an initial model of perforation friction resistance is first established. During the fracturing process, sand addition is the process of polishing the perforations. During this sand addition process, the perforation friction resistance changes dynamically. As the amount of sand added and the amount of fluid flowing through increases, the perforation edges are polished, the perforation diameter increases, and the flow coefficient increases, reducing friction resistance. The actual, dynamic friction resistance of the perforations is calculated by taking into account perforation wear and the number of effective perforations. When test fracturing data is available, an initial expression for perforation friction resistance is derived based on lift and displacement tests. The initial flow coefficient is then inverted and the actual, dynamic friction resistance of the perforations is calculated, taking into account perforation wear and the number of effective perforations. After perforation in a vertical well, during fracture initiation, perforations closer to the ideal orientation initiate fractures first and connect together to form fractures. Perforations at a greater angle from the ideal orientation do not initiate fractures and cannot be fed with fluid on a large scale. Therefore, at a phase angle of 60°, the number of perforations with liquid flow is only 1 / 3 of the actual number of perforations. The above model takes into account the wear of the perforations and the number of effective perforations, and can calculate the true friction resistance of the perforations.

[0033] 6. The present invention calculates fracture parameters under the constraints of real fracture pressure. Unlike the conventional process of calculating fracture parameters, conventional simulation software calculates the net pressure based on the flow resistance of the fluid in the fracture, thereby constraining the calculation of fracture parameters. However, this patent calculates the net pressure based on the construction pressure measured at the wellhead, so the calculated fracture parameters are more in line with the actual situation, more reliable, and more reliable. For high-pressure fractures with controlled fractures, when the fracture height control effect is better, the net pressure will gradually increase. In other words, if the construction net pressure calculated by back-calculating the wellhead pressure has an upward trend, it means that the fracture height control effect is better. BRIEF DESCRIPTION OF THE DRAWINGS

[0034] Figure 1 Schematic diagram of the wellhead-wellbore-fracture system provided by the present invention;

[0035] Figure 2 The present invention provides a crack expansion solution process that introduces real-time crack pressure. DETAILED DESCRIPTION

[0036] To make the objectives, technical solutions, and advantages of the present invention more clear, the technical solutions of the present invention are described clearly and completely below. Obviously, the embodiments described are only some of the embodiments of the present invention, not all of them. All other embodiments derived by ordinary persons in this field based on the embodiments of the present invention without creative effort are within the scope of protection of the present invention.

[0037] Unless otherwise defined, the technical or scientific terms used in the present invention shall have the usual meanings understood by persons of ordinary skill in the field to which the present invention belongs. The words "first", "second", "third", "fourth" and similar terms used in the present invention do not indicate any order, quantity or importance, but are only used to distinguish different components. Words such as "include" or "comprise" mean that the elements or objects preceding the word include the elements or objects listed after the word and their equivalents, without excluding other elements or objects. Words such as "connect" or "connected" are not limited to physical or mechanical connections, but may include electrical connections, whether direct or indirect.

[0038] For ease of description, spatially relative terms may be used herein to describe the relationship of one element or feature relative to another element or feature as shown in the figures, such as "inside," "outside," "inner side," "outer side," "lower," "upper," etc. Such spatially relative terms are intended to encompass different orientations of the device in use or operation in addition to the orientation depicted in the figures.

[0039] Implementing net pressure analysis requires clear and accurate curve drawing, but the corresponding algorithmic tools are lacking. Numerous researchers have conducted extensive research on the expansion process of hydraulic fractures using the extended finite element method. However, most studies are based on the assumption of net pressure within a fixed fracture, or on the calculation of net fracture pressure based on earlier geological models, the shape of the fractures that expanded in the previous period, and construction process parameters. These studies differ significantly from the actual expansion of hydraulic fractures in the reservoir, resulting in large simulation errors and inadequate use of measured wellhead pressure data, which significantly restricts the calculation of fracture parameters. Furthermore, when calculating bottomhole pressure from wellhead pressure, conventional fracturing pressure calculation models often simplify the calculation of wellbore pressure by setting a unified friction pressure drop gradient / coefficient, resulting in large deviations in the results.

[0040] Based on the above technical problems, the present invention provides a method, device, medium and equipment for quickly simulating the height of hydraulic fracturing cracks using wellhead construction pressure. This method provides a strong foundation for real-time monitoring of net pressure, diagnosis of crack extension morphology, and crack morphology (especially diagnosis of crack height) during hydraulic fracturing construction.

[0041] like Figure 1As shown, the method provided by the present invention for rapidly simulating the height of a hydraulic fracture using wellhead construction pressure includes the following specific steps:

[0042] 1) Relationship between wellhead pressure and net pressure

[0043] According to the principles of fluid mechanics:

[0044] BHTP=p surf +p hyd -p fric (1)

[0045] p net =BHTP-p perf -σ c (2)

[0046] p f =p net +σ c (3)

[0047] Where: BHTP is the bottom hole pressure; p perf is the friction resistance of the perforation hole; p hyd is the pressure of the sand mixing liquid column; p surf is the wellhead pressure; p fric is the friction resistance of the pipe string; σ c is the closing stress; p net is the friction resistance of the pipe string; p f is the liquid pressure at the seam.

[0048] 2) Calculation of liquid column pressure in the wellbore

[0049] The pressure of the fluid column in a wellbore is typically expressed in a unified way. However, because oil and gas wells are deep, the high temperatures and pressures within the wellbore can significantly change the density and viscosity of the fracturing fluid. Consequently, the calculation of the fluid column pressure in the wellbore cannot be based solely on a constant fluid density. The first prerequisite for constructing a wellbore fluid flow model is to discretize the wellbore into N units. The pressure of the sand-mixed fluid column is as follows:

[0050]

[0051] Where: P hyd , ρ(h) are the sand mixing liquid column pressure (MPa), the sand mixing liquid density in the wellbore (g / cm 3 ).

[0052] ① The density of the single-phase fracturing fluid between the fracturing fluid or proppant plugs under high temperature and high pressure conditions is:

[0053] ρ(h)=ρ w (P,T)=D0+D1T+D2P (5)

[0054] Where: T is temperature, P is pressure; D0, D1, D2 are fitting coefficients, ρ w is the density of single-phase fracturing fluid under high temperature and high pressure conditions. The coefficients in the above formula vary with actual construction and reservoir conditions, and in actual case applications, they need to be fitted based on actual measured points.

[0055] ② Calculate the density of the sand-carrying fluid. With the addition of proppant, the fluid becomes a sand-carrying fluid, which increases the local concentration and density of the fracturing fluid. Therefore, when calculating the fluid column pressure within the wellbore, the effect of the proppant on the fracturing fluid density must be considered. The density of the sand-carrying fluid is related to the sand ratio and particle composition. The average density of different proppant combinations must be carefully calculated, taking into account the variation in proppant density within the wellbore. The specific expression for density is as follows:

[0056]

[0057] Where: ρ(h) is the density of the sand-carrying fluid, kg / m 3 ; ρ0 is the density of the fracturing fluid base fluid, kg / m 3 ρ t is the proppant bulk density, kg / m 3 ρ s is the apparent density of the proppant, kg / m 3 ; c is the sand ratio; C s It is the sand ratio, a decimal.

[0058] 3) Calculation of friction resistance of perforation holes

[0059] ① Calculation method of perforation friction resistance when there is no test fracturing data

[0060] Generally speaking, at the moment the first perforation ruptures, fluid enters the fracture. Due to the large relative strength of the perforation frictional resistance and the fracture extension pressure, the bottomhole pressure increases within a very short period of time, reaching the fracture pressure of the second perforation. Perforation frictional resistance is closely related to fluid density, the number of perforations per cluster, perforation diameter, and flow coefficient. The smaller the perforation diameter and the fewer the perforations, the greater the frictional resistance generated by flow through the perforations. At a 60° phase angle, the number of effective perforations for fluid inflow is only 1 / 3 of the actual number of perforations. The perforation frictional resistance equation is as follows:

[0061]

[0062] Among them, p perf is the hole friction, MPa; ρ f is the density of fracturing fluid, kg / m 3 ; q is the construction displacement, m 3 / min;n p is the number of effective perforations; d p is the perforation hole diameter, m; Cd is the hole flow coefficient (0.8~0.85).

[0063] First, take the perforation flow coefficient as a certain constant and calculate the perforation friction resistance. During the sand fracturing process, the perforation aperture and flow coefficient will change. In the field of perforation abrasion research during fracturing transformation, the main existing technology is numerical simulation. However, there is no experimental simulation device and simulation method for the abrasion phenomenon of wellbore perforations during hydraulic fracturing in the existing technology. Specifically, the existing technology cannot study the abrasive effect of solid proppant particles in the sand-carrying fluid on the wellbore perforations during hydraulic fracturing transformation through experimental simulation. The higher the proppant concentration, the more serious the perforation damage and the lower the perforation friction coefficient. In view of this, the perforation abrasion is often calculated using the following empirical equation. The perforation aperture changes are as follows:

[0064]

[0065] Where: Δd p is the change of perforation hole diameter, m; Δt is the construction time, min; α is the empirical coefficient; C e is the proppant concentration.

[0066] The perforation shape (discharge coefficient C d ) changes as follows:

[0067]

[0068] in, is the empirical coefficient.

[0069] The friction resistance formula considering the hole wear is:

[0070]

[0071] ②Calculation of perforation friction resistance when test pressure data is available

[0072] In the early stages of construction or small-scale fracturing tests, the friction resistance near the wellbore is solved. The characteristics of the resistance can be used to preliminarily determine the source of the resistance. The causes of friction resistance near the wellbore include perforation friction resistance, micro-annular friction resistance caused by improper perforation phase, fracture bending and turning friction resistance and friction resistance caused by multiple fractures, and additional friction resistance caused by unclean perforation holes. According to research, perforation friction resistance is proportional to the square of the construction displacement; for friction resistance near the wellbore, due to laminar flow through narrow channels in the pressure-sensitive area near the wellbore, it can be roughly expressed as Δp near =k near q β(In most engineering applications, the value is 0.5.) Therefore, the sum of the hole friction and the near-wellbore friction can be reduced to the following formula, which is uniformly considered as the perforation hole friction resistance:

[0073] P perf =k pf q 2 +k near q 0.5 (11)

[0074] Among them, k pf q 2 is the hole friction, k near q 0.5 is the friction resistance near the wellbore, k pf is the friction coefficient of the hole, k near is the near-wellbore friction coefficient.

[0075] The testing process involves reducing the flow rate in stages near the end of a small-scale fracturing test, each stage lasting 1-2 minutes. Once the pressure stabilizes, the flow rate is reduced to the next stage. This allows the change in bottomhole pressure at different flow rates to be determined. The pressure drop data is processed based on the frictional resistance of the perforations to develop a formula for the frictional resistance of the perforations.

[0076] According to the hole friction coefficient k pf The relationship between density, number of holes, pore size, and flow coefficient is used to calculate the initial C d , and then make corrections during the construction process based on the amount of liquid and sand fed during the construction process. According to the perforation hole friction resistance formula, the relationship between the hole friction resistance coefficient and the flow coefficient is:

[0077]

[0078] get

[0079]

[0080] During the sand adding construction process, the calculation formula for friction resistance is as follows:

[0081]

[0082] 4) Calculation of wellbore friction resistance

[0083] Wellbore frictional resistance refers to the resistance encountered by fluids when passing through pipelines. In actual engineering, fluids often need to be transported through pipelines, and the resistance in the pipelines will affect the flow speed and flow rate of the fluids.

[0084] Wellbore friction is related to fluid velocity, density, flow pattern, and wellbore dimensions. The greater the flow rate and the smaller the wellbore inner diameter or annulus diameter, the greater the wellbore friction. Calculating wellbore friction requires careful calculation of the fluid viscosity. Before crosslinking, the viscosity of the fluid is the original solution viscosity (guanidine collagen stock solution viscosity is 30-40 mPa.s). After crosslinking, the viscosity increases significantly, reaching the viscosity of the crosslinked fluid. The calculation method for wellbore friction is as follows.

[0085] Wellbore friction pressure drop:

[0086]

[0087] Wellbore friction coefficient f:

[0088]

[0089] Fluid Reynolds number Re:

[0090]

[0091] Fitting coefficient α f 、b f :

[0092]

[0093] Where ρ is the density of the fluid (kg / m3); v is the velocity of the fluid (m / s); L is the length of the string (m); D is the characteristic length (e.g., the diameter of the pipe, in meters); and μ is the dynamic viscosity of the fluid (usually in Pascals-seconds).

[0094] 5) Pressure drop analysis

[0095] A post-fracturing pressure drop curve is a plot showing the change in bottomhole or wellhead pressure over time after pumping is stopped during fracturing. Fracture closure data can be analyzed using derivatives of the G function to identify the filtration mechanism, and the characteristic morphology of the G function derivative and the superimposed derivative curves of the G function can be used to identify the filtration type. Using the first-order derivative dp / dG, the superimposed derivative ISIP-Gdp / dG, and the relationship between dp / dG and the G function, relevant formation parameters such as the filtration coefficient and closure stress can be determined, allowing for an update of the initial geological model, thus providing a basis for designing fracturing operation parameters.

[0096] 6) Mathematical model of fracturing fluid flow

[0097] The fracturing fluid and proppant flow in the fracture as solid-liquid two-phases. The fracturing fluid flows in the fracture in a one-dimensional manner along the fracture length, taking into account the filtration behavior from the fracture to the matrix pores; the proppant migrates in a two-dimensional manner along the fracture length and settles vertically.

[0098] ① Fracturing fluid flow rate equation (Poiseuille flow equation)

[0099] The smaller the viscosity of the fracturing fluid, the larger the crack width, the greater the pressure difference within the crack, and the faster the fracturing fluid flows within the crack.

[0100]

[0101] Where: q f is the flow velocity; w is the crack width; μ is the apparent viscosity of the fracturing fluid; p is the fluid pressure in the crack; and x is the distance along the length of the crack.

[0102] ②Fracturing fluid apparent viscosity equation

[0103] For non-Newtonian fracturing fluid, the power law model is used to characterize its apparent viscosity and indirectly modify the Poiseuille flow equation.

[0104] μ=Kγ n-1 (twenty one)

[0106] Where: K is the consistency coefficient; n is the fluidity index; μ is the apparent viscosity of the fracturing fluid; γ is the shear rate.

[0107] ③ Friction pressure drop equation of fracturing fluid fracture

[0108] The greater the viscosity of the fracturing fluid and the narrower the crack, the greater the frictional resistance of the fracturing fluid along the way.

[0109]

[0110] Where: p is the friction resistance along the way, which is equal to the net pressure.

[0111] ④ Fracturing fluid loss equation

[0112] The larger the contact area between the fracturing fluid and the rock, the greater the fracturing fluid loss; as the loss time increases, the loss rate gradually slows down. The loss rate is calculated as follows:

[0113]

[0114] Where: Q L is the filtration velocity; t is the total construction time; t′ is the time when filtration starts at a certain point; h is the reservoir thickness; C l is the filtration coefficient.

[0115] ⑤Fracturing fluid mass conservation equation

[0116]

[0117] Where: q f is the flow velocity; q i is the pumping fracturing fluid (inlet unit); q L is the volume of filtrate-lost fracturing fluid.

[0118] 7) Mathematical model of proppant migration and settlement

[0119] ① Proppant flow rate equation

[0120] Proppant concentration significantly affects proppant migration velocity, thereby indirectly affecting fracture propagation, final concentration distribution, and permeability of propped fractures after fracturing.

[0121]

[0122] Among them, q s is the liquid phase velocity of suspended sand fracturing fluid; q px is the solid phase velocity of suspended sand fracturing fluid; B(a) is the blockage correction factor; f s is the viscous drag correction factor; φ is the sand ratio.

[0123] ② Proppant sedimentation equation

[0124] The larger the proppant density and particle size, the faster it settles. Proppant settling affects the proppant concentration distribution, ultimately affecting the permeability of the propped fracture after fracturing.

[0125] q pz =V stokes B(a)f c (26)

[0126] Among them, q pz is the proppant settling velocity; V stokes is the free settling velocity; B(a) is the clogging correction factor; f c is the settlement correction factor.

[0127] 8) Crack propagation mathematical model

[0128] The pumped fracturing fluid flows at high speed within the hydraulic fracture, and the fluid pressure supports and expands the fracture walls. The hydraulic fracture expansion simulation calculates the hydraulic fracture width, fracture height, and fracture extension length.

[0129] ① Crack width w

[0130] Given the initial crack length, Young's modulus, Poisson's ratio, and closure stress, calculate the crack width.

[0131]

[0132] Among them, p f is the actual pressure in the crack; E is the elastic modulus; v is the Poisson's ratio.

[0133] ② Extension length of hydraulic fracture

[0134] Based on the calculated hydraulic fracture width and shear slip, the fracture extension length Δl is calculated. Whenever the cumulative fracture extension length Δl exceeds the preset length of the newly added fracture mesh, a new extended fracture mesh is added.

[0135]

[0136] Where K IC is the fracture toughness of the crack.

[0137] ③Multi-layer balanced crack height model

[0138] The fracture height h is calculated based on the calculated fluid pressure in the fracture and the known fluid density and longitudinal stress parameters.

[0139]

[0140] Among them, KI u，l is the stress intensity factor at the upper and lower ends of the crack; h is the crack height; h p is the pay zone thickness; h i is the height from the bottom of the crack to the top of the i-th layer; ΔKI u，l To characterize the apparent fracture toughness of the vertical flow of fracturing fluid; σ i is the closing stress of the i-th layer.

[0141] ④Solution process of hydraulic fracture extension height

[0142] (i) Determine the fracture width, fluid pressure, and fracture wall stress of each fracture grid cell.

[0143] (ii) Calculation of stress intensity factors KI at the upper and lower crack tips based on the crack extension height equation u KI l .

[0144] (iii) Compare the stress intensity factors at the upper and lower crack tips with the fracture toughness of the formation at the upper and lower crack tips. If the stress intensity factor is greater than or equal to the fracture toughness: KI u，l ≥K IC , then the corresponding preset length Δl of the crack upper / lower tip expansion crack height growth h .

[0145] (iv) Return to step (ii) and repeat the calculations (ii) to (iii) until the stress intensity factors of the upper and lower tips are both less than the fracture toughness of the formation at the location.

[0146] (v) Output current fracture height: The grid fracture height is simulated along the fracture length direction. Generally, the fracture height decreases with the distance from the wellbore.

[0147] 9) Discrete mathematical model

[0148] ① Flow within cracks

[0149] Fracture propagation simulation algorithms require solving the flow of fracturing fluid and proppant within the fracture. Common flow field discretization algorithms include the finite volume method. Based on a one-dimensional rectangular grid-based fluid flow model in the fracture, the finite volume method is used to discretize and simulate the fluid pressure field of fracturing fluid and proppant migration and sedimentation in the fracture. The process is as follows: the fracture grids within the current fracturing section are numbered from 1 to i; the fracturing fluid flow equation is substituted into the mass conservation equation, and the finite volume method discretization equation is constructed along the fracture grid as follows. Fracturing fluid mass conservation equation:

[0150]

[0151] Where w t is the unit width at time t; w t-1 is the unit crack width at time (t-1); Δt is the time period; For the Crack width at the node; For the Crack width at the node; p i+1 is the pressure of (i+1) unit; p i-1 is the pressure of (i-1) unit; p i is the pressure of unit i; Δx is the unit length; q I is the flow rate into the unit; q L is the filtration rate.

[0152] The proppant flow and sedimentation equations are substituted into the proppant mass conservation equation to construct the finite volume method discrete equations, including the proppant lateral mass conservation equation and the proppant longitudinal mass conservation equation.

[0153] ② Discretization mathematical model of crack extension:

[0154] The fracture propagation model is based on a one-dimensional rectangular grid and is discretized using boundary elements. The process for simulating fracture width is as follows: the fracture grids within the current fracturing section are numbered from 1 to i. The boundary element method discretization equation for fracture width is constructed along the fracture grids as follows. The fracture width equation group is:

[0155]

[0156] 10) Stress-flow-extension coupling solution algorithm

[0157] The dynamic fracture propagation simulation algorithm uses coupled and iterative solutions to achieve stress-flow-propagation coupling. The coupled solution is used for the fracture fluid flow equation and the fracture width equation (two sets of equations are solved simultaneously and coupled); the iterative solution is used for the fracture proppant flow equation, matrix flow equation, fracture height equation, and fracture extension length equation.

[0158] 11) Introducing a crack propagation simulation algorithm based on real-time crack pressure

[0159] In the process of stress-flow-extension coupling solution, the closing stress and filtration coefficient are obtained according to the interpretation of the pump-off pressure drop data, and the geological model is updated; the wellhead fluid pressure is monitored, and the bottom hole pressure, net pressure, and fracture pressure are calculated according to the calculation model proposed above; the calculated fracture pressure is used to replace the fracture pressure calculated by the friction resistance in the fracture, and the hydraulic fracture expansion simulation calculation is performed for constraint and reference to obtain the hydraulic fracture width, fracture height, and fracture extension length. The fracture expansion solution process with the introduction of real-time fracture pressure is as follows: Figure 2 shown.

[0160] One of the main tasks of the present invention is to establish a calculation method to calculate the bottom hole pressure based on the wellhead pressure analysis, calculate the net pressure, obtain the net pressure change curve, and then calculate the size of the crack. The pressure drop gradient along the wellbore will take into account the changes in different fracturing fluids, proppant properties, and proppant concentrations, and comprehensively consider the dynamic changes in proppant distribution under different pumping designs. The use of grid discretization of the wellbore and the calculation of the wellbore pressure drop gradient and pressure distribution can help to more accurately predict the pressure along the way. The friction resistance of the perforation will take into account the pressure loss effect of the perforation area, that is, the number of perforations opened and the perforation erosion effect. The stress-flow-extension coupling solution algorithm in the crack expansion process will introduce bottom hole pressure as a constraint to obtain the real crack parameters. After the implementation of the scheme, a real-time net pressure change curve and a real-time changing crack height will be obtained, based on which the real extension morphology of the crack can be judged, construction risks can be reduced, and the quality of fracturing construction can be guaranteed.

[0161] A second aspect of the present invention provides a device for rapidly simulating the height of a hydraulic fracturing crack using wellhead construction pressure, comprising:

[0162] a first processing unit for establishing a relationship between the wellhead pressure and the net pressure;

[0163] The second processing unit is used to calculate the fluid column pressure in the wellbore, the friction resistance of the perforation hole and the friction resistance of the wellbore;

[0164] The third processing unit is used to obtain the continuous fracture mouth pressure and net pressure based on the relationship between the wellhead pressure and the net pressure, based on the liquid column pressure in the wellbore, the friction resistance of the perforation hole and the friction resistance of the pipe string, and preliminarily determine the change pattern of the fracture height based on the change pattern of the net pressure;

[0165] The fourth processing unit is used to replace the result of calculating the fracture pressure using the friction resistance of the liquid in the fracture based on the fracture pressure calculated based on the fracture pressure calculated based on the wellhead pressure, to form an algorithm suitable for simulating the three-dimensional expansion of conventional reservoir fracturing cracks and calculating the fracture parameters based on the fracture pressure. At the same time, it combines the fluid flow simulation algorithm, the fracture expansion simulation algorithm, and the stress-flow-extension coupling solution algorithm, updates the filtration coefficient and closure stress in the geological model according to the test fracturing results, introduces real-time fracture pressure for constraint, and calculates the fitted fracture width, fracture height, and length.

[0166] A third aspect of the present invention provides a computer-readable storage medium having a computer program stored thereon, wherein the computer program, when executed by a processor, implements the steps of any one of the above-mentioned methods for rapidly simulating the height of a hydraulic fracture using wellhead construction pressure.

[0167] A fourth aspect of the present invention provides a computer device comprising a memory, a processor, and a computer program stored in the memory and executable on the processor. When the processor executes the computer program, the steps of any one of the above-mentioned methods for rapidly simulating the height of a fracturing crack using wellhead construction pressure are implemented.

[0168] The present invention is described in terms of flowcharts and / or block diagrams of methods, devices (systems), and computer program products according to specific embodiments. It should be understood that each process and / or block in the flowchart and / or block diagram, as well as a combination of processes and / or blocks in the flowchart and / or block diagram, can be implemented by computer program instructions. These computer program instructions can be provided to a processor of a general-purpose computer, a special-purpose computer, an embedded processor, or other programmable data processing device to generate a machine, so that the instructions executed by the processor of the computer or other programmable data processing device generate instructions for implementing the processes in the flowchart and / or block diagram. Figure 1 a process or multiple processes and / or boxes Figure 1 A device that provides the functions specified in a block or multiple blocks.

[0169] These computer program instructions may also be stored in a computer readable memory that can direct a computer or other programmable data processing device to work in a specific manner, so that the instructions stored in the computer readable memory produce an article of manufacture comprising an instruction device, which implements the process Figure 1 a process or multiple processes and / or boxes Figure 1 The function specified in one or more boxes.

[0170] These computer program instructions can also be loaded onto a computer or other programmable data processing device so that a series of operational steps are executed on the computer or other programmable device to produce a computer-implemented process, thereby providing the instructions executed on the computer or other programmable device for implementing the process. Figure 1a process or multiple processes and / or boxes Figure 1 A step that specifies a function in one or more boxes.

[0171] Finally, it should be noted that the above embodiments are only used to illustrate the technical solutions of the present invention, rather than to limit it. Although the present invention has been described in detail with reference to the aforementioned embodiments, those skilled in the art should understand that they can still modify the technical solutions described in the aforementioned embodiments, or make equivalent replacements for some of the technical features therein. However, these modifications or replacements do not deviate the essence of the corresponding technical solutions from the spirit and scope of the technical solutions of the various embodiments of the present invention.

Claims

1. A method for rapidly simulating the height of a hydraulic fracturing crack using wellhead construction pressure, characterized in that: include: S1: Establish the relationship between wellhead pressure and net pressure; S2: Calculate the fluid column pressure in the wellbore, the friction resistance of the perforation holes and the friction resistance of the wellbore; S3: Based on the fluid column pressure in the wellbore, the friction resistance of the perforation holes and the friction resistance of the tubing string, and according to the relationship between the wellhead pressure and the net pressure, the continuous fracture mouth pressure and net pressure are obtained. Based on the variation pattern of the net pressure, the variation pattern of the fracture height is preliminarily determined; S4: The fracture pressure calculated based on the wellhead pressure replaces the result calculated using the friction resistance of the liquid in the fracture to form an algorithm suitable for simulating the three-dimensional expansion of conventional reservoir fracturing fractures and calculating the fracture parameters based on the fracture pressure. At the same time, combined with the fluid flow simulation algorithm, the fracture expansion simulation algorithm, and the stress-flow-extension coupling solution algorithm, the filtration coefficient and closure stress in the geological model are updated according to the test fracturing results, and the real-time fracture pressure is introduced as a constraint to calculate the fitted fracture width, fracture height, and length.

2. The method for rapidly simulating the height of a hydraulic fracturing crack using wellhead construction pressure according to claim 1, characterized in that: In step S2, when calculating the fluid column pressure in the wellbore, a method for calculating the density of the fracturing fluid or the single-phase fracturing fluid between the proppant plugs under high temperature and high pressure conditions is established. With the addition of proppant, the liquid becomes a sand-carrying fluid, which will increase the local concentration and density of the fracturing fluid. Therefore, when calculating the fluid column pressure in the wellbore, the effect of the proppant on the fracturing fluid density must be considered, and the relationship between the sand-carrying fluid density and the sand ratio and particle composition must be established.

3. The method for rapidly simulating the height of a hydraulic fracturing crack using wellhead construction pressure according to claim 2, characterized in that: The fracturing fluid and proppant flow in the fracture as solid-liquid two-phases. The fracturing fluid flows in the fracture in a one-dimensional manner along the fracture length, taking into account the filtration behavior from the fracture to the matrix pores; the proppant migrates in a two-dimensional manner along the fracture length and settles vertically.

4. The method for rapidly simulating the height of a hydraulic fracturing crack using wellhead construction pressure according to claim 1, characterized in that: In step S2, when calculating the friction resistance of the perforation hole, there are two cases: When there is no test fracturing data, a calculation model for perforation friction resistance is established. According to the perforation phase angle, the number of perforations is accurately assigned, and an empirical equation for perforation abrasion is established to calculate the changes in perforation diameter and flow coefficient, thereby dynamically calculating the perforation friction resistance. When test fracturing data is available, the reduction rate method is used to obtain a regression formula for the sum of the hole friction resistance and the near-wellbore friction resistance, which are uniformly considered as the hole friction resistance, and then the initial flow coefficient is calculated. Then, according to the amount of fluid and sand injected, the changes in the hole diameter and flow coefficient are corrected during the construction process, thereby dynamically calculating the friction resistance of the perforation hole.

5. The method for rapidly simulating the height of a hydraulic fracturing crack using wellhead construction pressure according to claim 1, characterized in that: In step S2, when calculating the wellbore friction resistance, the viscosity of the liquid before and after cross-linking is taken into account, and the influence of the wellbore friction coefficient, fluid Reynolds number, pipe diameter, roughness, and fluid viscosity are taken into account, so as to accurately calculate the wellbore friction resistance.

6. The method for rapidly simulating the height of a hydraulic fracturing crack using wellhead construction pressure according to claim 1, characterized in that: In step S4, the boundary element method, finite difference method, and finite volume method are used to establish a stress field simulation algorithm, a fluid flow simulation algorithm, a fracture extension simulation algorithm, and a stress-flow-extension coupling solution algorithm. The fracture pressure calculated based on the wellhead pressure is introduced to replace the result of calculating the fracture pressure based on the friction resistance of the liquid in the fracture. This forms an algorithm suitable for simulating three-dimensional extension of conventional reservoir fracturing fractures and calculating fracture parameters based on the fracture pressure, and calculates the fitted fracture width, fracture height, and length.

7. The method for rapidly simulating the height of a hydraulic fracturing crack using wellhead construction pressure according to claim 1, characterized in that: In step S4, the closure stress and the fluid loss coefficient are obtained based on the interpretation of the post-fracturing pressure drop curve to calibrate the geological model.

8. A device for rapidly simulating the height of a hydraulic fracturing crack using wellhead construction pressure, characterized in that: include: a first processing unit for establishing a relationship between the wellhead pressure and the net pressure; The second processing unit is used to calculate the fluid column pressure in the wellbore, the friction resistance of the perforation hole and the friction resistance of the wellbore; The third processing unit is used to obtain the continuous fracture mouth pressure and net pressure based on the relationship between the wellhead pressure and the net pressure, based on the liquid column pressure in the wellbore, the friction resistance of the perforation hole and the friction resistance of the pipe string, and preliminarily determine the change pattern of the fracture height based on the change pattern of the net pressure; The fourth processing unit is used to replace the result of calculating the fracture pressure using the friction resistance of the liquid in the fracture based on the fracture pressure calculated based on the fracture pressure calculated based on the wellhead pressure, to form an algorithm suitable for simulating the three-dimensional expansion of conventional reservoir fracturing cracks and calculating the fracture parameters based on the fracture pressure. At the same time, it combines the fluid flow simulation algorithm, the fracture expansion simulation algorithm, and the stress-flow-extension coupling solution algorithm, updates the filtration coefficient and closure stress in the geological model according to the test fracturing results, introduces real-time fracture pressure for constraint, and calculates the fitted fracture width, fracture height, and length.

9. A computer-readable storage medium having a computer program stored thereon, characterized in that: When the computer program is executed by a processor, the steps of the method for rapidly simulating the height of a hydraulic fracture using wellhead construction pressure as described in any one of claims 1 to 7 are implemented.

10. A computer device comprising a memory, a processor, and a computer program stored in the memory and executable on the processor, wherein: When the processor executes the computer program, the steps of the method for rapidly simulating the height of a hydraulic fracture using wellhead construction pressure as described in any one of claims 1 to 7 are implemented.

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