A multi-fracture fluid loss analysis method based on embedded discrete fracture model
By analyzing the fracturing fluid loss in multi-fractured tight sandstone reservoirs using an embedded discrete fracture model, the problem of existing technologies being unable to accurately reflect fracturing fluid loss was solved, enabling accurate analysis of fracturing fluid loss and optimization of process parameters.
Patent Information
- Authority / Receiving Office
- CN · China
- Patent Type
- Patents(China)
- Current Assignee / Owner
- PETROCHINA CO LTD
- Filing Date
- 2022-08-04
- Publication Date
- 2026-07-31
AI Technical Summary
Existing filtration analysis methods cannot accurately reflect the filtration of fracturing fluid in horizontal well sections of tight sandstone reservoirs using multi-fracture fracturing technology, and cannot effectively analyze the filtration effect during the fracturing process.
An embedded discrete fracture model was adopted. By collecting reservoir and fracturing operation parameters of the well section, the width model and seepage model of N main fractures were established. Combining the law of conservation of mass and the seepage model, the filtration loss and filtration rate of fracturing fluid were calculated. A set of nonlinear equations was established, and the finite difference method and Newton's iteration method were used to solve for the filtration loss and filtration rate.
It provides a true reflection of the fracturing fluid loss during multi-fracture fracturing in tight sandstone reservoirs, offering more accurate loss analysis and guiding the optimization of fracturing process parameters.
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Figure CN117552779B_ABST
Abstract
Description
Technical Field
[0001] This invention relates to the field of tight sandstone reservoir stimulation, and specifically to a multi-fracture fracturing fluid loss analysis method based on an embedded discrete fracture model. Background Technology
[0002] Tight sandstone reservoirs are characterized by low porosity, low permeability, and low pressure, typically requiring reservoir stimulation for efficient development. Currently, multi-fracture fracturing technology within horizontal well sections is the primary method for efficient development of tight sandstone reservoirs. This involves injecting fracturing fluid to create multiple hydraulic fractures, which are then filled with proppant to provide conductivity, thus establishing flow channels between the reservoir and the wellbore. However, during the formation of artificial fractures, the fracturing fluid inevitably leaks into the formation due to the higher pressure within the fractures compared to the formation pressure. On one hand, fracturing fluid leakage reduces fluid efficiency, thereby decreasing fracture geometry; on the other hand, it can easily damage the reservoir, especially in tight sandstone reservoirs with low porosity, low permeability, and low pressure, leading to difficulties in subsequent fluid drainage and low production. Therefore, it is necessary to characterize the volume of fracturing fluid leakage during the fracturing process to analyze working fluid efficiency and the degree of reservoir damage.
[0003] The patent application number (2021112265520) entitled "A Method for Testing the Filtration Loss of Fracturing Fluid in Rough Natural Fractures," submitted by Zhang Wei, Xiao Jialin, Yi Zhaobo, Gao Ting, Liu Xiang, and Li Qin of the Petroleum Engineering Technology Research Institute of Jianghan Oilfield Branch, China Petroleum & Chemical Corporation, describes a method for testing the filtration loss of fracturing fluid in rough natural fractures. The method involves: manually drilling outcrops at the target oilfield construction site to obtain columnar core samples; processing the columnar core samples and then artificially creating fractures through artificial slitting; scanning the fractures in the columnar core samples to obtain fracture profiles; calculating the surface roughness of each fracture surface; conducting displacement experiments on the fractured columnar core samples; plotting the relationship between filtration loss time and the square root of time based on the filtration loss time and cumulative filtration loss; obtaining a linear relationship between filtration loss and the square root of time, along with the slope and intercept of the line; and calculating the filtration loss coefficient, filtration loss rate, and initial filtration loss based on the cross-sectional area of the core sample, the slope of the line, and the intercept. This invention can accurately obtain the filtration loss law of fracturing fluid in natural fractures, providing a basis for hydraulic fracturing during subsequent field operations. However, this invention cannot yet characterize the filtration loss of fracturing fluid in multi-fracture fracturing technology in horizontal well sections of tight sandstone reservoirs.
[0004] The existing technology has the following problems:
[0005] Existing filtration analysis methods cannot characterize the filtration of fracturing fluid in multi-fracture fracturing technology in horizontal well sections of tight sandstone reservoirs. They cannot accurately reflect the filtration of fracturing fluid during fracturing, thus failing to analyze the filtration effect during multi-fracture fracturing in tight sandstone reservoir sections. Summary of the Invention
[0006] The technical problem to be solved by this application is that existing filtration loss analysis methods cannot characterize the filtration loss of fracturing fluid in multi-fracture fracturing technology in horizontal well sections of tight sandstone reservoirs, and cannot truly reflect the filtration loss of fracturing fluid during fracturing. The purpose is to provide a multi-fracture fracturing fluid filtration loss analysis method based on an embedded discrete fracture model, which solves the problem that existing filtration loss analysis methods cannot analyze the filtration effect during multi-fracture fracturing in tight sandstone reservoir sections.
[0007] This application is achieved through the following technical solution:
[0008] A method for analyzing the filtration loss of fracturing fluid in multi-fracture systems based on an embedded discrete fracture model includes the following steps:
[0009] S1. Collect reservoir parameters and fracturing operation parameters in the well section; wherein, the fracturing operation parameters include cluster number and operation flow rate, and the cluster number corresponds to the number N of main fractures formed;
[0010] S2. Based on the PKN fracture extension model, establish width models for N main fractures respectively; wherein, the rock mechanics parameters in the PKN fracture extension model are provided by the reservoir parameters and the fracturing operation parameters;
[0011] S3. Based on the width model of each main fracture, calculate the fracturing fluid flow rate allocated to the N main fractures according to the construction displacement, and establish a fracture relationship model; wherein, the fracture relationship model includes the internal pressure model of the N main fractures themselves and the relationship model between the main fractures and multiple fractures, and the sum of the fracturing fluid flow rates of the N main fractures is equal to the construction displacement.
[0012] S4. Based on the pressure drop equations of the N main fractures, calculate the fracturing fluid that seeps into the formation from each main fracture and establish the seepage models between the N main fractures and the formation.
[0013] S5. Based on the seepage model of N main fractures and formation, calculate the pressure change in the formation caused by the fracturing fluid seeping into the formation, and establish a two-phase seepage model in the formation.
[0014] S6. Based on the fracture relationship model, the fracture-formation seepage model, and the formation two-phase seepage model, simulate the actual formation conditions and the true fracture extension state, and establish the boundary conditions and initial conditions for fracture extension and fracturing fluid loss.
[0015] S7. Based on the boundary conditions and initial conditions in step S6, substitute the relationship model between the main fracture and multiple fractures in step S2 into the internal pressure model of the N main fractures and the seepage model between the N main fractures and the formation. Establish a set of nonlinear equations about multiple fractures with fracture width and formation pressure as unknowns by the mass conservation law of fracturing fluid flow rate of the N main fractures formed during the fracturing process and the total fracturing fluid flow rate during construction.
[0016] S8. Based on the embedded discrete fracture model, the nonlinear equations in step S7 are calculated to obtain the filtration loss and filtration rate of the fracturing fluid in the fracture.
[0017] In the above technical solution, the degree of fracturing fluid loss in the fracture is analyzed by the amount and rate of fluid loss. By establishing the relationship between N main fractures and multiple fractures, the degree of fracturing fluid loss in multiple fractures within the tight sandstone section can be analyzed simultaneously.
[0018] Collecting reservoir parameters and fracturing parameters from the well section provides information for subsequent steps, as well as the number of main fractures formed during fracturing. Based on the number of main fractures, the mature fracture propagation software model PKN is selected to model each fracture and determine its width. PKN is easy to implement in the field, provides clear and simple simulation results, and its parameters can be obtained by collecting and / or calculating reservoir parameters and fracturing parameters from the well section.
[0019] First, a relationship model of the fractures was established to obtain their morphology and intra-fracture pressure, facilitating subsequent analysis of the fracture-formation relationship. Specifically, the fracture morphology was determined by establishing the relationship between the main fracture and multiple fractures using the law of mass conservation. The relationship between the main fracture and multiple fractures was established using the fracturing fluid flow rate. In subsequent steps, this relationship allows the model of N main fractures to be transformed into a multi-fracture model to meet the requirements of fracturing fluid loss analysis across multiple fractures. The sum of the fracturing fluid flow rates allocated to the N main fractures equals the operational discharge rate. During hydraulic fracturing, fracturing fluid enters the fractures, resulting in different intra-fracture pressures for fractures of varying widths. Establishing the pressure drop equation for each main fracture facilitates the subsequent analysis of the fracture-formation relationship during fracturing fluid infiltration.
[0020] Then, based on the principle that after fracture formation, fracturing fluid seeps into the formation through the narrow fracture layers, seepage models are established between the N main fractures and the formation. The seepage models include the fracturing fluid loss rate, loss velocity, and loss flow coefficient. The fracturing fluid loss situation in the fractures can be analyzed by analyzing the fracturing fluid loss rate and loss velocity.
[0021] After fracturing fluid seeps into the formation, it changes the pressure inside the formation. When analyzing the filtration of fracturing fluid in fractures, it is necessary to consider the pressure inside the formation to more realistically and reasonably reflect the filtration of fracturing fluid during the fracturing process. Therefore, a two-phase flow model inside the formation is established based on the fracture model and the seepage model between the fracture and the formation.
[0022] Based on the fracture model, the seepage model between the fracture and the formation, and the two-phase seepage model within the formation obtained in steps S3 to S5, the actual situation of the formation and the true extension state of the fractures can be derived. Based on the actual situation of the formation and the true extension state of the fractures, boundary conditions and initial conditions for fracture extension and fracturing fluid loss can be established, making the model closer to the actual situation during the fracturing process. The aforementioned boundary conditions and initial conditions can be applied to each main fracture.
[0023] Under the boundary and initial conditions of fracture extension and fracturing fluid loss, the fracture models in steps S3 to S5, the seepage model between the fracture and the formation, and the two-phase seepage model within the formation are combined. The relationship model between the main fracture and multiple fractures in step S2 is substituted into the internal pressure model of each main fracture and the seepage model between each main fracture and the formation. By applying the law of conservation of mass for the fracturing fluid flow rate of each main fracture formed during fracturing and the total fracturing fluid flow rate during construction, a nonlinear equation for multiple fractures can be established, with fracture width and formation pressure as unknowns. Based on the embedded discrete fracture model, the filtration rate and filtration volume of the multiple fractures can be obtained. These filtration rates and filtration durations can be used to analyze the degree of fracturing fluid loss within tight sandstone sections.
[0024] In one optional embodiment, step S2, based on the PKN crack propagation model assuming an elliptical crack cross-sectional shape, yields the following main crack width model:
[0025]
[0026] Among them, W f,k H represents the crack width, t represents the fracturing operation time, and H represents the fracture width. f x is the crack height. f E is the distance from the narrowest point within the fracture to the fracture opening, v is the Young's modulus of the formation, and P is the Poisson's ratio. f,k (x f ,t) represents the pressure inside the seam, σ n This represents the minimum horizontal principal stress.
[0027] In an optional embodiment, the relationship between the main fracture and multiple fractures in step S3 is based on the mass balance equation during hydraulic fracturing. Considering that the fracture cross-sectional shape is elliptical, the mass conservation equations for the main fracture and multiple fractures are established as follows:
[0028]
[0029]
[0030]
[0031] Where, q k Let v be the flow rate within the k-th crack. l,k Q represents the filtration velocity, Q represents the construction discharge rate, and k represents the label of the main crack.
[0032] In an optional embodiment, the cross-sectional shape of the crack in step S3 is elliptical. Based on the fact that the pressure drop of the fluid flow inside the elliptical tube is 16 / 3 times the pressure drop of the flow between the parallel plates, the pressure drop equation inside the main crack is obtained as follows:
[0033]
[0034] Where, μ l This refers to the viscosity of the fracturing fluid.
[0035] In an optional embodiment, the seepage model between the fracture and the formation in step S4 includes filtration loss, filtration velocity, and filtration flow coefficient, and the calculation equations for filtration loss, filtration velocity, and filtration flow coefficient are as follows:
[0036] q l,k (x f ,t)=T fm,k (x f ,t)(P f,k (x f ,t)-P ml (x,y,t)) (6)
[0037]
[0038]
[0039] Where, q l,k Let P be the filtration volume of the k-th fracture, E be the Young's modulus of the formation, and P be the filtration volume of the k-th fracture. ml A represents the liquid phase formation pressure within the reservoir. fm,k To avoid contact area with the crack, k fm,k The harmonized average permeability between the fracture and the formation. The characteristic distance between the fracture and the formation; summing the k fractures yields the total filtration loss: Q l This represents the total filtration loss for each crack.
[0040] In an optional embodiment, the two-phase flow model within the formation established in step S5, ignoring the effect of capillary forces, is as follows:
[0041]
[0042]
[0043] Where φ is the formation porosity, P ml P is the formation liquid phase pressure. mg k is the formation gas phase pressure. l k is the liquid phase permeability. g V is the gas phase permeability, k is the absolute permeability, and V is the gas phase permeability. b B is the matrix per unit volume. l B is the liquid volume coefficient. g S is the gas volume coefficient. w The water saturation level is μ. g δ represents the gas viscosity, and δ is the crack judgment factor.
[0044] Specifically, when δ = 1, the matrix network contains cracks; when δ = 0, the matrix network does not contain cracks.
[0045] In an optional embodiment, the boundary conditions and initial conditions for fracture propagation and fracturing fluid loss in step S6 are expressed as follows:
[0046]
[0047]
[0048] P ml (x,y)| t＝0 =P mg (x,y)| t＝0 =P e (13)
[0049] S wo =S wi (14)
[0050] Where G is the shear modulus, X f X is the dynamic fracture length, Y is the reservoir length, and P is the reservoir width. e Original formation pressure, S wo S represents the initial water saturation. wi To constrain water saturation.
[0051] In an optional embodiment, step S7 involves simultaneously solving equations (1) to (10), and under the conditions of equations (11) to (14), establishing a nonlinear system of equations, which is as follows:
[0052]
[0053]
[0054]
[0055] Among them, the crack width W f,k and formation gas phase pressure P mg Set as an unknown.
[0056] In one alternative embodiment, the steps of determining the filtration loss and filtration rate include:
[0057] S81. Discretize the nonlinear equations in S7 using the finite difference method based on grid elements, obtaining the discretized result. A system of nonlinear equations consisting of several equations;
[0058] S82. Solve the system of equations in step S81 using the Newton-Raphson iteration method to obtain N arrays of fracture widths and one formation pressure matrix for N fractures.
[0059] S83. Substitute the results of step S82 into the width model of the main fracture and the seepage model between the fracture and the formation to obtain the filtration loss and filtration rate.
[0060] In an optional embodiment, the grid cells in step S81 are dynamic multi-fracture and sandstone reservoir numerical simulation grids established based on the orthogonal structured grid partitioning method of the embedded discrete fracture model.
[0061] Compared with the prior art, this application has the following advantages and beneficial effects:
[0062] This application provides a multi-fracture fracturing fluid loss analysis method based on an embedded discrete fracture model. This method can overcome the shortcomings of existing loss analysis methods and more realistically and reasonably reflect the loss situation during fracturing. This enables the analysis of the loss effect during multi-fracture fracturing in tight sandstone reservoirs and provides certain guidance for the optimization of fracturing process parameters. Attached Figure Description
[0063] To more clearly illustrate the technical solutions of the exemplary embodiments of the present invention, the accompanying drawings used in the embodiments will be briefly described below. It should be understood that the following drawings only show some embodiments of the present invention and should not be considered as a limitation of the scope. For those skilled in the art, other related drawings can be obtained based on these drawings without creative effort. In the drawings:
[0064] Figure 1 A flowchart illustrating a multi-fracture fracturing fluid loss analysis method based on an embedded discrete fracture model, provided in an embodiment of this application;
[0065] Figure 2 This is a schematic diagram of the mesh division of the filtering region provided in an embodiment of this application;
[0066] Figure 3 A diagram showing the relationship between well section length, reservoir length, and formation pressure provided in an embodiment of this application;
[0067] Figure 4 The ratio of filtration volume to liquid efficiency for each crack provided in one embodiment of this application;
[0068] Figure 5 A graph showing the relationship between construction time, filtration rate, and filtration volume provided in an embodiment of this application. Detailed Implementation
[0069] To make the objectives, technical solutions, and advantages of the present invention clearer, the present invention will be further described in detail below with reference to the embodiments and accompanying drawings. The illustrative embodiments and descriptions of the present invention are only used to explain the present invention and are not intended to limit the present invention.
[0070] Example 1
[0071] A method for analyzing the filtration loss of fracturing fluid in multi-fracture systems based on an embedded discrete fracture model, such as... Figure 1 The steps include:
[0072] Step S1: Collect reservoir parameters and fracturing operation parameters in the well section.
[0073] A specific section within the well is selected, and its reservoir parameters and fracturing parameters are collected to facilitate parameter calculation in subsequent steps. The reservoir parameters include porosity, permeability, water saturation, formation pressure, Young's modulus, Poisson's ratio, gas viscosity, and gas volume factor. The fracturing parameters include the length of the operated section, the fracturing fluid flow rate, the fracturing fluid viscosity, the fluid volume factor, and the cluster number.
[0074] Step S2: Based on the PKN fracture extension model, establish the width model of the main fracture; wherein, the rock mechanics parameters in the PKN fracture extension model are provided by reservoir parameters and fracturing operation parameters.
[0075] The PKN model is a relatively mature crack propagation software model, commonly used in the optimization design of hydraulic fracturing construction. Currently, in actual construction, the crack shape is usually elliptical, and the crack shape generated by the PKN model is exactly elliptical. Here, by adopting the assumption of the PKN crack derivation model, a model that is closer to the real crack can be established.
[0076] Based on the assumptions of the PKN crack propagation model that the crack cross-section is elliptical, the width model of a single crack is established as follows:
[0077]
[0078] Among them, W f,k H represents the crack width, t represents the fracturing operation time, and H represents the fracture width. f x is the crack height. f E is the distance from the narrowest point within the fracture to the fracture opening, v is the Young's modulus of the formation, and P is the Poisson's ratio. f,k (x f ,t) represents the pressure inside the seam, σ n This represents the minimum horizontal principal stress.
[0079] The parameters related to rock mechanics in the model of a single fracture can be obtained through simple calculations using the reservoir parameters and fracturing operation parameters from step S1.
[0080] Step S3: Calculate the fracturing fluid flow rate in the fracture based on the width model of the main fracture and establish a fracture relationship model; wherein, the fracture relationship model includes the mass conservation equation of the main fracture and multiple fractures and the pressure drop equation of the main fracture.
[0081] Based on the fracturing parameters collected in step S1, the number of clusters within the fracturing section can be obtained. The number of clusters generated within the section corresponds to the number of main fractures formed. Based on the number of main fractures, and considering the mass balance equations in the hydraulic fracturing process, while also assuming an elliptical fracture cross-sectional shape according to the PKN fracture propagation model, mass conservation equations are established for the main fracture k and multiple fractures N, where N is the number of main fractures and k is the fracture number.
[0082] The mass conservation equations for the main crack and multiple cracks are:
[0083]
[0084]
[0085]
[0086] Where, q k Let v be the flow rate within the k-th crack. l,k Where Q is the filtration velocity and Q is the construction discharge rate.
[0087] Among them, the crack width W f,k Since it is an unknown, it needs to be solved in subsequent steps.
[0088] Equation (2) yields the mass of one crack, and equation (3) yields the mass of multiple cracks. Equation (3) represents the flow distribution within the cracks. Since the mass of the cracks is conserved, equations (2) to (4) can be used to make a preliminary prediction of the crack morphology and the number of cracks by applying the mass conservation equations between the main crack and multiple cracks.
[0089] Since the pressure drop of the fluid flow inside the elliptical tube is 16 / 3 times that of the fluid flow between the parallel plates, the pressure drop equation inside the crack can be established based on the pressure drop of the fluid flow between the parallel plates.
[0090] The equation for the pressure drop within the crack is:
[0091]
[0092] Where, μ l This refers to the viscosity of the fracturing fluid.
[0093] A new unknown, the pressure P inside the gap, is introduced into the pressure drop equation. f,k (x f ,t).
[0094] Step S4: Based on the pressure drop equation of the main fracture, calculate the fracturing fluid that seeps into the formation through the main fracture and establish a seepage model between the fracture and the formation.
[0095] The seepage model of fractures and formations includes filtration loss, filtration velocity, and filtration flow coefficient. The calculation equations for filtration loss, filtration velocity, and filtration flow coefficient are as follows:
[0096] q l,k (x f ,t)=T fm,k (x f ,t)(P f,k (x f ,t)-P ml (x,y,t)) (6)
[0097]
[0098]
[0099] Where, q l,k Let P be the filtration volume of the k-th fracture, E be the Young's modulus of the formation, and P be the filtration volume of the k-th fracture. ml A represents the liquid phase formation pressure within the reservoir. fm,k To avoid contact area with the crack, k fm,k The harmonized average permeability between the fracture and the formation. The characteristic distance between the fracture and the formation; summing the k fractures yields the total filtration loss: Q l Let K be the total filtration loss of the k cracks.
[0100] Formations have certain fissures. During construction, fracturing fluid gradually seeps into the formation through these fissures. One important factor in analyzing the quality of fracturing fluid in a fracture is the fluid loss volume. The relationship between fluid loss and fluid loss rate can be established using equations (6) to (8) above, such as... Figure 5 As shown, the filtration rate is highest and the filtration volume is lowest at the beginning of construction. As the construction time increases, the filtration rate gradually slows down while the filtration volume gradually increases.
[0101] Step S5: Based on the seepage model of fractures and formations, calculate the pressure change in the formation caused by the fracturing fluid seeping into the formation, and establish a two-phase seepage model in the formation.
[0102] After fracturing fluid leaks into the formation, it causes a change in formation pressure. Based on the fluid seepage mass balance relationship within the formation and neglecting the effect of capillary forces, the established two-phase flow model within the formation is as follows:
[0103]
[0104]
[0105] Where φ is the formation porosity, P ml P is the formation liquid phase pressure. mg k is the formation gas phase pressure. l k is the liquid phase permeability. g V is the gas phase permeability, k is the absolute permeability, and V is the gas phase permeability. b B is the matrix per unit volume. l B is the liquid volume coefficient. g S is the gas volume coefficient. w The water saturation level is μ. g δ represents the gas viscosity, and δ is the crack judgment factor.
[0106] Specifically, when δ = 1, the matrix network contains cracks; when δ = 0, the matrix network does not contain cracks.
[0107] Step S6: Based on the fracture relationship model, the fracture-formation seepage model, and the two-phase seepage model within the formation, simulate the actual formation conditions and the true extension state of the fractures, and establish the boundary conditions and initial conditions for fracture extension and fracturing fluid loss.
[0108] Based on the fracture model, the seepage model between the fracture and the formation, and the two-phase seepage model within the formation in steps S3 to S5, the actual situation of the formation and the true extension state of the fracture can be obtained.
[0109] Based on the actual formation conditions and the true extension state of the fractures, boundary conditions and initial conditions for fracture extension and fracturing fluid loss can be established.
[0110] The boundary conditions and initial conditions for fracture propagation and fracturing fluid loss are expressed as follows:
[0111]
[0112]
[0113] P ml (x,y)| t＝0 =P mg (x,y)| t＝0 =P e (13)
[0114] S wo =S wi (14)
[0115] Where G is the shear modulus, X f X is the dynamic fracture length, Y is the reservoir length, and P is the reservoir width. e Original formation pressure, S wo S represents the initial water saturation. wi To constrain water saturation.
[0116] Step S7: Based on the boundary conditions and initial conditions in Step S6, and combined with the models in Steps S2 to S5, establish nonlinear equations concerning fracture width and formation pressure.
[0117] Step S7: Solve equations (1) to (10) simultaneously. Under the conditions of equations (11) to (14), establish a nonlinear system of equations as follows:
[0118]
[0119]
[0120]
[0121] Among them, the crack width W f,k and formation gas phase pressure P mg Set as an unknown.
[0122] Equations (1) to (10) contain identical parameters in pairs, and a set of nonlinear equations can be formed by combining these identical parameters. Based on the actual formation conditions and the true extension state of the fractures, boundary conditions and initial conditions for fracture extension and fracturing fluid loss can be established, along with the collection of reservoir parameters and fracturing operation parameters within the well section in step S1. Through the above equations and conditions, the fracture width W can be determined. f,k and formation gas phase pressure P mg All parameters except for the crack width W. Ultimately, a system can be established with the crack width W as the parameter. f,k and formation gas phase pressure P mg The system of nonlinear equations has unknowns.
[0123] Step S8: Based on the embedded discrete crack model, obtain the filtration loss and filtration loss rate.
[0124] The steps for determining the filtration loss and filtration rate include:
[0125] S81. Discretize the nonlinear equations in S7 using the finite difference method based on grid elements, obtaining the discretized result. A system of nonlinear equations consisting of several equations;
[0126] S82. Solve the system of equations in step S91 using the Newton-Raphson iteration method to obtain N arrays of fracture widths and one formation pressure matrix for N fractures, where N is the total number of fractures.
[0127] S83. Substitute the results of step S92 into equations (2) and (6) to obtain the filtration loss amount and filtration loss rate.
[0128] In step S81, the grid cells are established as a dynamic main fracture and sandstone reservoir numerical simulation network based on the orthogonal structured network partitioning method of the embedded discrete fracture model.
[0129] like Figure 2 As shown, the filtration zone is divided into grids, where the two-dimensional reservoir grid cell is represented by (i,j), and the grid segment of the k-th fracture is represented by i. k This indicates that the k-th crack is the i-th crack. k The step size of each crack element is Δx ik The step sizes of reservoir grid cells (i,j) are Δy and Δx, respectively. In this embodiment, N = 3, k = 1, 2, 3.
[0130] Example 2
[0131] Taking a tight gas well (X210 well) in a certain area of Southwest China as an example, this application uses a multi-fracture fracturing fluid loss analysis method based on an embedded discrete fracture model to calculate the fracturing fluid loss volume and loss rate during fracturing operations in a certain section of the well. The calculation process is as follows:
[0132] Step S1: Collect reservoir parameters and fracturing operation parameters for one section of well X210.
[0133] Reservoir parameters include porosity, permeability, water saturation, formation pressure, Young's modulus, Poisson's ratio, gas viscosity, and gas volume factor. Fracturing parameters include well section length, fracturing fluid flow rate, and fracturing fluid viscosity and volume factor. The reservoir parameters and fracturing parameters for the second section of well X210 are shown in the table below:
[0134]
[0135] Step S2: Based on the assumptions of the PKN crack propagation model, establish the width model of the main crack.
[0136] Based on the assumptions of the PKN crack propagation model that the crack cross-section is elliptical, the width model of a single crack is established as follows:
[0137]
[0138] Among them, W f,k H represents the crack width, t represents the fracturing operation time, and H represents the fracture width. f x is the crack height. f E is the distance from the narrowest point within the fracture to the fracture opening, v is the Young's modulus of the formation, and P is the Poisson's ratio. f,k (x f ,t) represents the pressure inside the seam, σ n This represents the minimum horizontal principal stress.
[0139] Among them, the Young's modulus E and Poisson's ratio v of the formation are determined in step S1.
[0140] Step S3: Establish a crack relationship model, which includes the mass conservation equations for the main crack and multiple cracks, and the pressure reduction equation for the main crack.
[0141] In this embodiment, three clusters of fractures form three main fractures within the construction section. Based on the mass balance equations during hydraulic fracturing and considering the PKN fracture propagation model which assumes an elliptical fracture cross-section, mass conservation equations are established for the main fracture k and multiple fractures N, where N = 3 and k = 1, 2, 3.
[0142] The mass conservation equations for the main crack and multiple cracks are:
[0143]
[0144]
[0145]
[0146] Where, q k Let v be the flow rate within the k-th crack. l,k Where Q is the filtration velocity and Q is the construction discharge rate.
[0147] Among them, the crack width W f,k Since it is an unknown, it needs to be solved in subsequent steps.
[0148] Since the mass of a crack is conserved, the morphology and number of cracks can be preliminarily predicted by applying the mass conservation equations between the material in the main crack and multiple cracks.
[0149] Since the pressure drop of the fluid flow inside the elliptical tube is 16 / 3 times that of the fluid flow between the parallel plates, the pressure drop equation inside the crack can be established based on the pressure drop of the fluid flow between the parallel plates.
[0150] The equations for the pressure drop within the three cracks are:
[0151]
[0152] Where, μ l This refers to the viscosity of the fracturing fluid.
[0153] A new unknown, the pressure P inside the gap, is introduced into the pressure drop equation. f,k (x f ,t).
[0154] like Figure 2 As shown, the pressure within the fractures calculated in step S3 and presented by the computer in the form of a cloud map reveals the pressure in the three fractures and the surrounding strata. The three vertical white lines represent the three fractures, while the other parts represent the strata surrounding them. It can be seen from the figure that the pressure in the strata surrounding the three fractures is higher than the pressure in the strata farther away from the fractures.
[0155] Step S4: Based on the principle of flow exchange in the embedded discrete fracture model, establish a seepage model between the fracture and the formation.
[0156] The seepage model of fractures and formations includes filtration loss, filtration velocity, and filtration flow coefficient. The calculation equations for filtration loss, filtration velocity, and filtration flow coefficient are as follows:
[0157] q l,k (x f ,t)=T fm,k (x f ,t)(P f,k (x f ,t)-P ml (x,y,t)) (6)
[0158]
[0159]
[0160] Where, q l,k Let P be the filtration volume of the k-th fracture, E be the Young's modulus of the formation, and P be the filtration volume of the k-th fracture. ml A represents the liquid phase formation pressure within the reservoir. fm,k To avoid contact area with the crack, k fm,k The harmonized average permeability between the fracture and the formation. The characteristic distance between the fracture and the formation; summing the k fractures yields the total filtration loss: Ql Let K be the total filtration loss of the k cracks.
[0161] Formations have certain fissures. During construction, fracturing fluid gradually seeps into the formation through these fissures. One important factor in analyzing the quality of fracturing fluid in a fracture is the fluid loss volume. The relationship between fluid loss and fluid loss rate can be established using equations (6) to (8) above, such as... Figure 5 As shown, the filtration rate is highest and the filtration volume is lowest at the beginning of construction. As the construction time increases, the filtration rate gradually slows down while the filtration volume gradually increases.
[0162] Step S5: Based on the material balance relationship of fluid seepage within the formation, establish a two-phase seepage model within the formation.
[0163] After fracturing fluid leaks into the formation, it causes a change in formation pressure. Based on the fluid seepage mass balance relationship within the formation and neglecting the effect of capillary forces, the established two-phase flow model within the formation is as follows:
[0164]
[0165]
[0166] Where φ is the formation porosity, P ml P is the formation liquid phase pressure. mg k is the formation gas phase pressure. l k is the liquid phase permeability. g V is the gas phase permeability, k is the absolute permeability, and V is the gas phase permeability. b B is the matrix per unit volume. l B is the liquid volume coefficient. g S is the gas volume coefficient. w The water saturation level is μ. g δ represents the gas viscosity, and δ is the crack judgment factor.
[0167] Specifically, when δ = 1, the matrix network contains cracks; when δ = 0, the matrix network does not contain cracks.
[0168] Step S6: Based on the actual formation conditions and the true extension state of the fractures, establish the boundary conditions and initial conditions for fracture extension and fracturing fluid loss.
[0169] Based on the fracture model, the seepage model between the fracture and the formation, and the two-phase seepage model within the formation in steps S3 to S5, the actual situation of the formation and the true extension state of the fracture can be obtained.
[0170] Based on the actual formation conditions and the true extension state of the fractures, boundary conditions and initial conditions for fracture extension and fracturing fluid loss can be established.
[0171] The boundary conditions and initial conditions for fracture propagation and fracturing fluid loss are expressed as follows:
[0172]
[0173]
[0174] P ml (x,y)| t＝0 =P mg (x,y)| t＝0 =P e (13)
[0175] S wo =S wi (14)
[0176] Where G is the shear modulus, X f X is the dynamic fracture length, Y is the reservoir length, and P is the reservoir width. e Original formation pressure, S wo S represents the initial water saturation. wi To constrain water saturation.
[0177] Step S7: Based on the boundary conditions and initial conditions in Step S6, and combined with the models in Steps S2 to S5, establish nonlinear equations concerning fracture width and formation pressure.
[0178] Step S7: Solve equations (1) to (10) simultaneously. Under the conditions of equations (11) to (14), establish a nonlinear system of equations as follows:
[0179]
[0180]
[0181]
[0182] Among them, the crack width W f,k and formation gas phase pressure P mg Set as an unknown.
[0183] Equations (1) to (10) contain identical parameters in pairs, and a set of nonlinear equations can be formed by combining these identical parameters. Based on the actual formation conditions and the true fracture extension state, boundary conditions and initial conditions for fracture extension and fracturing fluid loss can be established, along with the collection of reservoir parameters and fracturing operation parameters within the X210 well section in step S1. Using the above equations and conditions, the fracture width W can be determined. f,k and formation gas phase pressure P mgAll parameters except for the crack width W. Ultimately, a system can be established with the crack width W as the parameter. f,k and formation gas phase pressure P mg The system of nonlinear equations has unknowns.
[0184] Step S8: Based on the embedded discrete crack model, obtain the filtration loss and filtration loss rate.
[0185] The steps for determining the filtration loss and filtration rate include:
[0186] S81. Discretize the nonlinear equations in S7 using the finite difference method based on grid elements, obtaining the discretized result. A system of nonlinear equations consisting of several equations;
[0187] S82. Solve the system of equations in step S91 using the Newton-Raphson iteration method to obtain N arrays of fracture widths and one formation pressure matrix for N fractures, where N is the total number of fractures.
[0188] S83. Substitute the results of step S92 into equations (2) and (6) to obtain the filtration loss amount and filtration loss rate.
[0189] In step S81, the grid cells are established as a dynamic main fracture and sandstone reservoir numerical simulation network based on the orthogonal structured network partitioning method of the embedded discrete fracture model.
[0190] like Figure 2 As shown, the filtration zone is divided into grids, where the two-dimensional reservoir grid cell is represented by (i,j), and the grid segment of the k-th fracture is represented by i. k This indicates that the k-th crack is the i-th crack. k The step size of each crack element is Δx ik The step sizes of reservoir grid cells (i,j) are Δy and Δx, respectively. In this embodiment, N = 3, k = 1, 2, 3.
[0191] Transform all the equations in steps (2) to (9) into equations that the computer can recognize, as follows:
[0192]
[0193]
[0194]
[0195]
[0196]
[0197]
[0198]
[0199]
[0200]
[0201]
[0202]
[0203]
[0204]
[0205]
[0206]
[0207]
[0208] Computer processing was used to analyze the filtrate loss of fracturing fluid in multiple fractures, and the results are as follows: Figure 3 As shown. The filtration loss can be obtained through calculations in steps (2) to (9). Figure 3 The bar chart showing the filtration volume versus liquid efficiency for the three fissures in this embodiment indicates that the filtration volumes for the three fissures are 27.65 m³ / s. 3 26.83m 3 The fluid volumes were 27.65 m3 and 72.35%, respectively, while the fluid efficiencies were 72.35%, 73.17%, and 72.35%. It can be seen that the smaller the fluid loss volume, the higher the fluid efficiency. Therefore, the filling efficiency of the fracturing fluid in the fracture can be analyzed by the fluid loss volume.
[0209] This application's embodiments establish fracture relationship models, fracture-formation seepage models, and formation two-phase seepage models to simulate actual formation conditions and the true extension state of fractures. This makes the PKN fracture extension model more closely resemble the actual fracture-formation situation during fracturing, thus more realistically and reasonably reflecting fluid loss during the fracturing process. The fracture relationship model establishes the relationship between single and multiple fractures, allowing simultaneous analysis of multiple fractures formed during fracturing. This overcomes the limitation of existing fluid loss analysis methods that can only analyze single fractures, providing guidance for optimizing fracturing process parameters. Simultaneously, the embedded discrete fracture model provides an orthogonal structured fracture and reservoir mesh partitioning format, enabling rapid and efficient fracture extension and reservoir numerical simulation solutions in multi-fracture fracturing fluid loss analysis, improving the efficiency of multi-fracture fracturing fluid loss analysis.
[0210] The specific embodiments described above further illustrate the purpose, technical solution, and beneficial effects of the present invention. It should be understood that the above description is only a specific embodiment of the present invention and is not intended to limit the scope of protection of the present invention. Any modifications, equivalent substitutions, improvements, etc., made within the spirit and principles of the present invention should be included within the scope of protection of the present invention.
Claims
1. A method for analyzing fluid loss of multi-fracture fracturing fluid based on embedded discrete fracture model, characterized in that, Includes the following steps: S1. Collect reservoir parameters and fracturing operation parameters in the well section; wherein, the fracturing operation parameters include cluster number and operation flow rate, and the cluster number corresponds to the number N of main fractures formed; S2. Based on the PKN fracture extension model, establish width models for N main fractures respectively; wherein, the rock mechanics parameters in the PKN fracture extension model are provided by the reservoir parameters and the fracturing operation parameters; S3. Based on the width model of each main fracture, calculate the fracturing fluid flow rate allocated to the N main fractures during the fracturing process and establish a fracture relationship model; wherein, the fracture relationship model includes the internal pressure model of the N main fractures themselves and the relationship model between the main fractures and multiple fractures, and the sum of the fracturing fluid flow rates allocated to the N main fractures is equal to the construction discharge rate. S4. Based on the pressure drop equations of the N main fractures, calculate the fracturing fluid that seeps into the formation from each main fracture and establish the seepage models between the N main fractures and the formation. S5. Based on the seepage model of N main fractures and formation, calculate the pressure change in the formation caused by the fracturing fluid seeping into the formation, and establish a two-phase seepage model in the formation. S6. Based on the fracture relationship model, the fracture-formation seepage model, and the formation two-phase seepage model, simulate the actual formation conditions and the true fracture extension state, and establish the boundary conditions and initial conditions for fracture extension and fracturing fluid loss. S7. Based on the boundary conditions and initial conditions in step S6, substitute the relationship model between the main fracture and multiple fractures in step S3 into the internal pressure model of the N main fractures and the seepage model between the N main fractures and the formation. Establish a set of nonlinear equations about multiple fractures with fracture width and formation pressure as unknowns by the mass conservation law of fracturing fluid flow rate of the N main fractures formed during the fracturing process and the total fracturing fluid flow rate during construction. S8. Based on the embedded discrete fracture model, the nonlinear equations in step S7 are calculated to obtain the filtration loss and filtration rate of the fracturing fluid in the fracture.
2. The method of claim 1, wherein, In step S2, based on the PKN crack propagation model, assuming the crack cross-sectional shape is elliptical, the obtained main crack width model is as follows: (1) in, The width of the crack. For fracturing operation time, The height of the crack. This is the distance from the narrow seam inside the seam to the seam opening. The Young's modulus of the formation. Poisson's ratio, For the pressure inside the seam, This represents the minimum horizontal principal stress.
3. The method for analyzing the filtration loss of fracturing fluid in multiple fractures based on an embedded discrete fracture model according to claim 2, characterized in that, In step S3, the relationship between the main fracture and multiple fractures is based on the mass balance equation in the hydraulic fracturing process. Considering that the fracture cross-section is elliptical, the relationship model between the main fracture and multiple fractures is established using the mass conservation equation of the discharge rate of each main fracture and the total discharge rate of fracturing fluid during construction: (2) (3) (4) in, The width of the crack. For fracturing operation time, The height of the crack. q represents the distance from the narrow seam inside the seam to the seam opening. k Let be the flow rate within the k-th crack. For filtration rate, The displacement during construction is represented by k, which indicates the designation of the main crack.
4. The method for analyzing the filtration loss of fracturing fluid in multiple fractures based on an embedded discrete fracture model according to claim 3, characterized in that, In step S3, the crack cross-section is elliptical. Based on the fact that the pressure drop of the fluid flow inside the elliptical tube is 16 / 3 times the pressure drop of the flow between the parallel plates, the pressure drop equation inside the main crack is obtained as follows: (5) in, This refers to the viscosity of the fracturing fluid. This refers to the pressure inside the seam.
5. The method for analyzing the filtration loss of fracturing fluid in multiple fractures based on an embedded discrete fracture model according to claim 1, characterized in that, The seepage model between the fracture and the formation in step S4 includes filtration loss, filtration velocity, and filtration flow coefficient. The calculation equations for filtration loss, filtration velocity, and filtration flow coefficient are as follows: (6) (7) (8) in, For the pressure inside the seam, Let K be the filtration volume of the k-th crack. The Young's modulus of the formation. This refers to the liquid phase formation pressure within the reservoir. To avoid contact area with cracks, The harmonized average permeability between the fracture and the formation. The characteristic distance between the fracture and the formation; the total filtration loss is obtained by adding up the values of each fracture: , This represents the total filtration loss for each crack.
6. The method for analyzing the filtration loss of fracturing fluid in multiple fractures based on an embedded discrete fracture model according to claim 1, characterized in that, The two-phase flow model within the formation established in step S5, ignoring capillary forces, is as follows: (9) (10) in, P represents formation porosity. ml Formation liquid phase pressure, Formation gas phase pressure, For liquid phase permeability, For gas phase permeability, For absolute penetration rate, per unit volume of matrix The volume coefficient of the liquid. The gas volume coefficient, Water saturation For gas viscosity, This is a factor for judging cracks; Among them, when At that time, the matrix network contains cracks; when At that time, the matrix network does not contain cracks.
7. The method for analyzing the filtration loss of fracturing fluid in multiple fractures based on an embedded discrete fracture model according to claim 1, characterized in that, The expressions for the boundary conditions and initial conditions for fracture propagation and fracturing fluid loss in step S6 are as follows: (11) (12) (13) (14) in, For construction displacement, This refers to the viscosity of the fracturing fluid. Shear modulus P represents the dynamic crack length. ml Formation liquid phase pressure, Formation gas phase pressure, For reservoir length, The reservoir width, Original formation pressure, The initial water saturation level, To restrict water saturation, The width of the crack.
8. A multi-fracture fracturing fluid loss analysis method based on an embedded discrete fracture model according to any one of claims 2 to 7, wherein in step S7, equations (1) to (10) are solved simultaneously, and under the conditions of equations (11) to (14), a nonlinear equation set is established, the nonlinear equation set being as follows: (15) (16) (17) in, Crack width and formation gas phase pressure Set as an unknown.
9. The method for analyzing the filtration loss of fracturing fluid in multiple fractures based on an embedded discrete fracture model according to claim 1, characterized in that, The steps for determining the filtration loss and filtration rate include: S81. Discretize the nonlinear equations in S7 using the finite difference method based on grid elements, obtaining the discretized result. A nonlinear system of equations consisting of +i*j equations; S82. Solve the system of equations in step S81 using the Newton-Raphson iteration method to obtain N arrays of fracture widths and one formation pressure matrix for N fractures. S83. Substitute the results of step S82 into the width model of N main fractures and the seepage model between the fractures and the formation to obtain the filtration loss and filtration rate of multiple fractures.
10. The method for analyzing the filtration loss of fracturing fluid in multiple fractures based on an embedded discrete fracture model according to claim 9, characterized in that, The grid cells in step S81 are dynamic multi-fracture and sandstone reservoir numerical simulation grids established based on the orthogonal structured grid generation method of the embedded discrete fracture model.