A fracturing productivity prediction method for complex fracture network of low permeability and tight reservoir

Abstract

The application provides a fracturing productivity prediction method for complex fracture networks of low-permeability and dense reservoirs, obtains a reservoir compressibility evaluation index based on a reservoir weak surface influence index, a fracture space physical model, a fracture symbolic index and a rock layer toughness index; obtains a fracture closure point based on a bottom hole pressure drop function, and identifies a main fracture filtration amount and a natural fracture filtration amount at the fracture closure point; establishes a reservoir fracturing fracture network seepage mathematical model based on reservoir DFIT test results, and establishes a fracturing well section complex fracture network numerical model according to the compressibility evaluation index and the natural fracture filtration amount. Finally, the fracturing well section complex fracture network numerical model is taken as a boundary condition to establish a single well productivity prediction model after fracturing. The application fully utilizes field and test data, lays a foundation for reasonable assumptions of a fracture geometric model, and the established complex fracture network mathematical model is closer to the actual situation, which is of great significance for fracturing evaluation and productivity prediction.

Description

Technical Field

[0001] This invention relates to the field of oil and gas well production enhancement and oil and gas field development technology, and in particular to a method for predicting fracturing production capacity for complex fracture networks in low-permeability tight reservoirs. Background Technology

[0002] As a guiding theory and practical method for modern oil and gas production enhancement and stimulation, volumetric fracturing operations expand natural fractures and shear and slip brittle rock layers, causing natural and artificial fractures to intertwine. During volumetric fracturing in horizontal wells, the continuously pumped fracturing fluid causes multiple branch fractures to form from the main artificial fracture, which in turn connect with natural fractures, creating a complex fracture network. This increases the "oil and gas reservoir-wellbore contact area" and the "oil and gas reservoir stimulation volume," enhancing the permeability of the oil and gas reservoir and forming a complex fracture network. Currently, post-fracturing productivity evaluation methods based on fracture geometry parameters and fracture conductivity mostly use symmetrical biplane fracture models, which are not suitable for the complex fracture networks formed after volumetric fracturing.

[0003] Therefore, in order to improve fracturing effect and increase single-well production after fracturing, it is of great significance to carry out evaluation and interpretation work for complex fracture networks. Summary of the Invention

[0004] To address the aforementioned issues, this invention provides a method for predicting fracturing productivity in complex fracture networks within low-permeability tight reservoirs. Based on the influence of weak surfaces, it incorporates the interconnected seepage between the main fracture and natural fractures, accurately describing various fracture parameters. Simultaneously, based on the filtration loss from natural fractures and the reservoir compressibility index, two numerical models for efficient fracture network extension and diversion storage are established to predict the productivity of a single well after fracturing.

[0005] The technical solution provided by this invention is a method for predicting fracturing productivity in complex fracture networks of low-permeability tight reservoirs. Since weak surfaces may exist in low-permeability tight reservoirs, affecting the propagation law of hydraulic fractures, this invention first considers the mechanical influence of weak surfaces, conducts research on the fracturing deformation and failure mechanism of low-permeability tight reservoir rocks, and establishes a new method for reservoir compressibility assessment based on three fracture network influence indices. Secondly, DFIT testing of the target reservoir is conducted to explore the reservoir compressibility law and establish a mathematical model of seepage in the fracture network. In the key steps, the traditional G-function method is improved to obtain a ΔP-G function chart, determine the fracture closure point, and finally establish a numerical model of complex fracture networks suitable for volumetric fracturing. The fracture conductivity is calculated from the fracture filtration situation. Using the numerical model of the complex fracture network in the fracturing section as boundary conditions, a single-well productivity prediction model is established to predict the post-fracturing single-well productivity.

[0006] Specifically, it includes the following steps:

[0007] S1. Based on the mechanical influence of weak surfaces in reservoirs, establish the weak surface influence index during reservoir fracturing.

[0008] S2. Based on the dynamic changes in crack width, establish a spatial physical model of the crack;

[0009] S3. Obtain the fracture symbolism index and rock toughness index;

[0010] S4. Based on the weak surface influence index, fracture spatial physical model, fracture symbol index and rock toughness index, obtain the reservoir compressibility assessment index.

[0011] S5. Based on the bottom hole pressure drop ΔP-G function, obtain the fracture closure point, thereby obtaining the main fracture filtration loss when the fracture closes after fracturing and the natural fracture filtration loss when the fracture closes after fracturing.

[0012] S6. Based on the reservoir DFIT test results, establish a mathematical model for seepage in the reservoir fracture network;

[0013] S7. Based on the compressibility assessment index and the filtration loss of natural fractures, establish a numerical model of complex fracture networks in the fractured well section;

[0014] S8. Obtain the conductivity after the fracture is closed, and establish a one-dimensional flow continuity equation for fluid along the fracture length in the fracturing fracture.

[0015] S9. Based on the mathematical model of seepage in the fractured network, the conductivity after fracture closure, and the one-dimensional flow continuity equation, a single-well productivity prediction model is established using the numerical model of the complex fractured network in the fractured well section as the boundary condition. The productivity of a single well after fracture can be predicted through the single-well productivity prediction model.

[0016] The benefits of this invention are as follows:

[0017] This method first studies the compressibility of low-permeability tight reservoirs based on the influence of weak surfaces, providing guidance for efficient staged fracturing operations. Furthermore, it fully utilizes field and experimental data to lay a solid foundation for reasonable assumptions in fracture geometry models. The resulting mathematical model of complex fracture networks is closer to reality and is of great significance for fracturing assessment. Attached Figure Description

[0018] Figure 1 The stress diagram of the weak surface AB is shown (a represents the stress state of the rock with cracks, and b represents the rock failure strength analysis).

[0019] Figure 2 This is a diagram illustrating the mechanical effects on weak surfaces.

[0020] Figure 3 This is a graph showing the variation of the minimum principal stress with the angle between the weak surfaces under multiple weak surfaces.

[0021] Figure 4 Here is a flowchart of the micro-injection pressure drop test.

[0022] Figure 5 The variation of the reservoir compressibility assessment index with fracturing time is shown.

[0023] Figure 6 This is a physical model diagram of the crack space (H represents the crack width, L represents the crack length);

[0024] Figure 7 A graph of the ΔP-G function;

[0025] Figure 8 A schematic diagram of a complex fracture network in a low-permeability tight reservoir;

[0026] Figure 9 This is a flowchart of the calculation process of the present invention. Detailed Implementation

[0027] The present invention will be further described in detail below with reference to the embodiments and accompanying drawings.

[0028] To make the objectives, technical solutions, and advantages of the embodiments of the present invention clearer, the technical solutions of the embodiments of the present invention will be clearly and completely described below with reference to the accompanying drawings. Obviously, the described embodiments are only a part of the embodiments of the present invention, not all of them. Based on the embodiments of the present invention, all other embodiments obtained by those skilled in the art without creative effort are within the scope of protection of the present invention. Therefore, the following detailed description of the embodiments of the present invention provided in the accompanying drawings is not intended to limit the scope of the claimed invention, but merely to illustrate selected embodiments of the invention.

[0029] Example 1

[0030] The technical solution of this embodiment is: a method for predicting fracturing productivity in complex fracture networks of low-permeability tight reservoirs. Since weak surfaces may exist in low-permeability tight reservoirs, affecting the propagation law of hydraulic fractures, the mechanical influence of weak surfaces is considered first. Research on the fracturing deformation and failure mechanism of low-permeability tight reservoir rocks is conducted, and a new method for reservoir compressibility assessment based on three fracture network influence indices is established. Secondly, DFIT testing of the target reservoir is carried out to explore the reservoir compressibility law and establish a pressure drop seepage mathematical model. In the key step, the traditional G-function method is improved to obtain a ΔP-G function chart, determine the fracture closure point, and finally establish a complex fracture network model suitable for volumetric fracturing. The fracture conductivity is calculated from the fracture filtration situation to predict the single-well productivity after fracturing.

[0031] Specifically, the following steps are included:

[0032] S1. Based on the mechanical influence of reservoir weak surfaces, establish the weak surface influence index under reservoir pressure;

[0033] A weak surface is a discontinuous surface with a certain directional extension formed in a rock mass during diagenesis by a large amount of low-strength material. Rock strata containing weak surfaces exhibit anisotropy, and these weak surfaces can lead to shear failure, causing wellbore collapse, wellbore abandonment, and other accidents. Wellbore instability in formations containing weak surfaces severely restricts the efficient exploitation of oil and gas resources.

[0034] Based on the single-structure plane theory, it is assumed that a weak plane AB exists in the reservoir rock. Figure 1 a) Define the angle β between the normal direction of surface AB and the direction of the maximum principal stress σ1. Analyze the normal and shear stresses acting on surface AB using the Mohr stress circle method, and then apply the MC criterion. The mechanical conditions for failure of the well wall rock along the weak surface AB were calculated.

[0035] The formulas for calculating the normal stress and shear stress on the AB surface are as follows:

[0036]

[0037] The mechanical conditions under which the wellbore rock fails along the weak surface AB are:

[0038]

[0039] In the formula: σ is the composite normal stress on the reservoir rock unit, MPa;

[0040] τ is the shear stress on the reservoir rock element, in MPa;

[0041] β is the angle between the normal direction of plane AB and the direction of maximum principal stress, in °;

[0042] C w The cohesion within the weak surface of the reservoir rock, MPa; The internal friction angle of the weak surface of the rock is °;

[0043] σ1 and σ3 represent the maximum principal stress and minimum principal stress, respectively, obtained from core tests, in MPa.

[0044] A further technical solution is to consider two scenarios when reservoir rocks undergo hydraulic fracturing failure: weak surface failure and bulk failure. Rock strength analysis is performed, the geometric relationship of the included angle β is calculated, and the variation law of the minimum principal stress of a single weak surface with the included angle is derived.

[0045] according to Figure 1 b, the geometric relationships involving the included angle β are:

[0046]

[0047] When considering failure along the weak surface, substituting the critical values ​​β1 and β2 respectively, the range of force angle distribution along the weak surface AB of the wellbore rock is obtained as follows:

[0048]

[0049] like Figure 2 As shown, the specific range of force angle distribution is as follows:

[0050] ① When β < β1 or β > β2, the rock does not fail along the weak surface, but rather fails along a certain direction within the rock body. At this moment, the angle between the failure surface and the maximum principal stress is .

[0051] ② Significant weak-plane failure only occurs when β1 < β < β2. Based on core test results, the variation of the minimum principal stress σ3 of a single weak plane with the included angle β was calculated (i.e., within this angle range, the minimum principal stress σ3 of a single weak plane first decreases and then increases with the increase of the included angle β). (When it reaches its minimum value).

[0052] A further technical solution is to make reasonable extrapolations based on the results of single weak surface analysis, assuming that there are two or more sets of weak surfaces in low-permeability tight reservoirs, and using the maximum and minimum stress values ​​of one set of weak surfaces as a benchmark, calculate the stress distribution of other sets of weak surfaces by grade difference, and derive the variation law of the minimum principal stress of multiple sets of weak surfaces with the included angle.

[0053] like Figure 3 The variation law of the minimum principal stress σ3 of multiple weak surfaces in the low-permeability tight reservoir rock with the included angle β is as follows:

[0054] (1) The minimum principal stress of low-permeability tight reservoirs varies with the weak plane angle β, and the trend of variation is nonlinear, which means that the rock strength exhibits a certain anisotropy.

[0055] (2) The strength of a low-permeability tight reservoir rock mass containing multiple sets of weak surfaces depends on the minimum strength of each set of weak surfaces, and the rock mass strength decreases as the number of weak surfaces increases.

[0056] (3) The strength of low-permeability tight reservoir rock mass will increase with increasing confining pressure under any circumstances.

[0057] The above-mentioned reservoir fracturing deformation and failure research results show that: compared with formations with a single weak surface or undeveloped weak surfaces, well sections encountering multiple weak surface formations are more prone to collapse and are unfavorable for opening fractures and seepage during fracturing stimulation.

[0058] A further technical solution is to select a stable well section with a reasonable well inclination angle based on the distribution range of the stress angle β of the well wall rock along the weak surface AB, adjust the corresponding fracturing process parameters for the well section, carry out efficient segmented fracturing operations, collect data, and lay the technical groundwork for the subsequent mathematical description of fracturing fractures.

[0059] Meanwhile, based on the mechanical influence of weak surfaces and its analysis process, an evaluation equation for the weak surface influence index is established, as follows:

[0060]

[0061] In the formula: Fβ() represents the evaluation auxiliary function, and the variables in parentheses are the independent variables of the evaluation target, which are dimensionless;

[0062] E represents the Young's modulus of core samples taken from any well section, in GPa;

[0063] E max E min These represent the maximum and minimum Young's modulus of the core sample from the fractured well section, in GPa.

[0064] μ is the Poisson's ratio of core samples taken from any well section, which is dimensionless;

[0065] μ max μ min These are the maximum and minimum Poisson's ratios of the core samples from the fractured well section, respectively, and are dimensionless.

[0066] F1 is the weak-area influence index, which is dimensionless.

[0067] S2. Based on the dynamic changes in crack width, establish a spatial physical model of the crack;

[0068] The selected fractured well sections are then subjected to reservoir identification, and DFIT testing is performed on the target reservoirs. DFIT testing, or micro-injection pressure drop testing (a fracturing diagnostic method), follows the procedure described below. Figure 4 .

[0069] The test process is as follows: a certain amount of fracturing fluid is pumped into the formation at a constant small displacement to generate micro-fractures in the formation and form a high-pressure periphery region (the pressure in this region is higher than the original formation pressure); then the well is shut in, and under the action of pressure differential, the fracturing fluid in the micro-fractures is filtered out into the formation, and the wellbore pressure gradually decreases to the original formation pressure.

[0070] Test results show that the inconsistent top and bottom ends of the hydraulic fracture cross section after fracturing will lead to irregular deformation of the fracture cross section. The resulting fracture width (referred to as the fracture width) is not a constant, but a dynamic variable.

[0071] A further technical solution is to consider the dynamic changes in crack width, make reasonable assumptions, and establish a physical model of crack space.

[0072] Reasonable assumptions made regarding the fracturing fractures include:

[0073] ① After the fracturing pump finishes pumping, the fracture length is positively correlated with the test time. The fluid inside the fracture flows in a one-dimensional steady state only along the direction of fracture extension, and the interface of dynamic change in fracture width is elliptical.

[0074] ②The Young's modulus and Poisson's ratio of the formation near the wellbore in the fractured section are assumed to be constant.

[0075] exist Figure 6 In the physical model of the fracture space, the fracture is an axisymmetric geometry along its length extension direction. At an initial moment T0 before fracturing, the fracture geometry parameters are: fracture length L0, fracture width 2H0, and the solid line indicated by T0 represents the fracture morphology at this moment. After a period T following fracturing, at moment T+T0, the fracture geometry parameters are: fracture length L(T), fracture width 2H(T), and the dashed line indicated by T+T0 represents the fracture morphology at this moment. During fracturing, the change in fracture length is ΔL = L(T) - L0, and the change in fracture width is ΔH = |H0 - H(T)|, with the absolute value of the change in width taken into account.

[0076] Based on the assumed conditions, the dynamic equation for crack width variation between crack propagation and minimum principal stress is obtained as follows:

[0077]

[0078] S3. Obtain the fracture symbolism index and rock toughness index;

[0079] Considering the current practice of using segmented fracturing in fracturing operations, and based on the concept of wellbore integrity, a new method for assessing the compressibility of low-permeability tight reservoirs based on the influence of weak surfaces is established for the selected fracturing sections. Reservoir compressibility is represented by three influence indices related to the physical state of the fracture network (weak surface influence index, fracture symbolism index, and formation toughness index). The calculation process of the fracture network influence index involves Young's modulus and Poisson's ratio, directly reflecting the ease or difficulty of reservoir fracturing.

[0080] A further technical solution is to consider that the fracturing network needs to overcome the tensile strength of the rock body, and to obtain the fracture symbolic index before fracturing based on the horizontal stress difference converted from the level surface, so as to help judge the feasibility of reservoir rock fracturing.

[0081] The established crack symbolic index model is as follows:

[0082]

[0083] In the formula: F2 is the crack symbol index, which is dimensionless;

[0084] α is the well inclination angle measured from the axis of the fractured well section, in °;

[0085] S t The uniaxial tensile strength of the rock body is measured experimentally in MPa.

[0086] A further technical solution is that the formation of the fracture network must ultimately consider the toughness of the rock strata near some weak surfaces. This is calculated using confining pressure and uniaxial tensile strength, and corrected using well logging data. The process for fitting the corrected rock strata toughness is as follows:

[0087]

[0088] In the formula: K1 and K2 are the toughness factors of type I and type II rock formations, respectively, which are obtained by core experiments and are dimensionless;

[0089] a1, a2, a3, a4, and a5 are the fitting coefficients for the toughness of Type I rock strata, with values ​​ranging from -0.34 to 0.52. Choose appropriate values ​​based on the accuracy of the solution and substitute them into the calculation.

[0090] b1, b2, and b3 are the toughness fitting coefficients for Type II rock strata, with values ​​ranging from -0.08 to 0.14. For Type I, select appropriate values ​​and substitute them into the calculation.

[0091] σ n For confining pressure, the triaxial rock mechanics experiment can be set to obtain a value in MPa;

[0092] F3 is the rock toughness index, which is dimensionless.

[0093] S4. Based on the weak surface influence index, fracture spatial physical model, fracture symbol index and rock toughness index, obtain the reservoir compressibility assessment index.

[0094] Based on the analysis process of the physical state of the fracture network, and by associating the timing of fracture initiation, a new method for assessing the compressibility of low-permeability tight reservoirs through segmented fracturing is developed, which includes the weak surface influence index, fracture symbolism index, and rock toughness index. A compressibility assessment model is then established.

[0095] The established model for assessing the compressibility of low-permeability tight reservoirs through staged fracturing is as follows:

[0096]

[0097] In the formula: EST is the compressibility assessment index. The higher the value, the easier it is to fracture a certain well section. It is dimensionless.

[0098] X1 is a dimensionless coefficient to be determined by the pressure drop test process.

[0099] T represents the fracturing operation time, H;

[0100] P fThis is the reservoir fracture pressure near the wellbore, which can be calculated from well logging data, in MPa.

[0101] P in The constant pumping pressure of fracturing fluid into the fracturing pump, in MPa;

[0102] R represents the distance from a point in the near-wellbore zone to the wellbore axis, in meters (m). w Let be the wellbore radius, in meters (m).

[0103] S5. Based on the bottom hole pressure drop ΔP-G function, obtain the fracture closure point, thereby obtaining the main fracture filtration loss when the fracture closes after fracturing and the natural fracture filtration loss when the fracture closes after fracturing.

[0104] Traditional algorithms for determining crack closure pressure and closure time use the G-function. However, the G-function method only considers a single artificial crack and is not suitable for analyzing complex crack networks. Therefore, an improved version of the G-function method will be developed.

[0105] Define the G function as:

[0106]

[0107] Introducing the bottom hole pressure drop ΔP-G function algorithm:

[0108]

[0109] Differentiate ΔP with respect to G and with respect to the logarithm lnG:

[0110]

[0111] In the formula: ΔT represents the fracturing time step, H; λ and δ are both calculation coefficients related to the bottom hole pressure drop, which are calculated from oil test and well test data and are dimensionless;

[0112] Based on literature review and practical production experience, it can be found that during the fracture initiation phase, using the G-function analysis overestimates the fracture filter vector during fracturing operations. Therefore, during the fracture closure phase after pump shutdown, we mainly observe the linear relationship between the bottom hole pressure P and the G-function, calculate the derivative DP / DG and the logarithmic derivative DP / D(lnG) of the ΔP-G function, solve for the extreme points of the linear relationship of the ΔP-G function based on the derivative relationship, and use these points as the fracture closure reference points to plot the ΔP-G function chart, as shown below. Figure 7 .

[0113] It is important to note that the ΔP-G function chart introduces a fitted regression line passing through the origin. This line should be as tangent as possible to the derivative curve. Points deviating from this line can be initially considered as fracture closure points. These points are then compared with the extreme points of the linear relationship of the ΔP-G function to calibrate the expression of the fitted regression line. Finally, representative fracture closure points are obtained, and the corresponding fracturing time step ΔT (based on the initial fracturing time T0, adding this time step ΔT gives the fracture closure time T0+ΔT) and fracture closure pressure P are recorded.

[0114] Low-permeability tight oil and gas reservoirs commonly exhibit natural fractures of various scales and microfractures. However, these microfractures are closed under formation conditions and lack conductivity. Hydraulic fractures generated during hydraulic fracturing connect with these natural fractures, forming a complex fracture network, such as... Figure 8 As shown.

[0115] Based on the ΔP-G function chart, the main fracture filtration loss at the fracture closure point after fracturing is calculated as follows:

[0116]

[0117] Based on the ΔP-G function chart, the natural fracture filtration loss at the fracture closure point after hydraulic fracturing is calculated as follows:

[0118]

[0119] In the formula: V major () represents the filtration loss of the main fracture at a certain moment, m 3 ;

[0120] r p This represents the ratio of crack filtration height to crack width, and is dimensionless.

[0121] C Lm This represents the filtration coefficient of the main fracture, in m / min. 0.5 ;

[0122] A fm The area of ​​filtration loss in the main crack is expressed in m. 2 ;

[0123] V nature () represents the filtration loss from natural cracks at a certain moment, in m. 3 ;

[0124] C Ln Represents the filtration coefficient of natural fractures, in m / min 0.5 ;

[0125] A fn The area of ​​natural crack filtration is expressed in m. 2 .

[0126] S6. Based on the reservoir DFIT test results, establish a mathematical model for seepage in the reservoir fracture network;

[0127] Based on the DFIT test results of the target reservoir, multiple sets of fracture geometric parameters (including fracture length, fracture width, etc.) are determined. Substitute them into Equation 9 to calculate the undetermined calculation coefficient X1. Calculate the reservoir compressibility EST value in the centripetal region near the wellbore of the low-permeability tight reservoir. The hydraulic fracturing variation law of the target reservoir is derived from the fracture spatial physical model.

[0128] The hydraulic fracturing variation law of the target reservoir is as follows: Figure 5 As shown: the rock compressibility of tight reservoirs with microfractures is not constant during the fracturing fluid pumping process; the initial compressibility assessment index is less than 0.4, and after a period of fracturing, the compressibility assessment index rises rapidly to nearly 0.7; as the dimensionless distance increases, the penetration depth of fracturing fluid in the near-wellbore zone gradually decreases, and the compressibility index of the formation rock gradually decreases to the initial value.

[0129] As fracturing fluid is continuously pumped into the wellbore, the pressure inside the well exceeds the reservoir fracturing pressure. Solid particles in the fracturing fluid penetrate the rock pore throats and microfractures, exhibiting certain hydration mechanics effects. This indicates that a fracture network forms relatively quickly after fracturing, reducing the strength of the tight reservoir rock and making it more susceptible to fracturing.

[0130] A further technical solution is to establish a mathematical model of seepage in the fracture network based on the formation process of the fracture network and the DFIT test results, taking the rock matrix and large-scale rock pores as the research objects (small-scale pores belong to the rock matrix type), considering the elastic storage capacity and compressibility of both, and based on the collected fractured well section data.

[0131] The mathematical model for seepage in the fractured mesh is as follows:

[0132]

[0133] Where: N f N s represents the large-scale rock pores and rock matrix permeability, respectively, in mD;

[0134] ω e φ represents the effective viscosity of the fracturing fluid, in mPa·s; φ represents the porosity, in %.

[0135] C t Represents the overall elastic coefficient of the formation, in MPa —1 ; n represents the fracturing fluid flow regime index, which is dimensionless;

[0136] biot represents the magnitude of the rock pore elastic coefficient, which is dimensionless;

[0137] Ω NThis represents the consistency coefficient of the fracturing fluid, in mPa·s. n ;

[0138] x and y represent two orthogonal sub-directions of the crack extension direction.

[0139] S7. Based on the compressibility assessment index and the filtration loss of natural fractures, establish a numerical model of complex fracture networks in the fractured well section;

[0140] Following the law of conservation of mass, the mass balance equation is derived from the mass balance within multiple fractures at any given time, which is also the fracturing mass balance of the complex fracture network as a whole, as follows:

[0141] ∑[V major (ΔT)+R major (ΔT)+V nature (ΔT)+R nature [(ΔT)]=V P (Equation 16)

[0142] In the formula: R major () represents the volume within the main fracture at a given moment, calculated from the dynamic fracture width H(T) using numerical simulation software, in meters. 3 ;

[0143] R nature () represents the volume within a natural fracture at a given moment, calculated by weighted averaging from core samples obtained from fractured well sections, in m. 3 ;

[0144] V P Indicates the amount of fracturing fluid loss, m 3 .

[0145] A further technical solution is to substitute the calculated filtration loss from the main fracture (Equation 13) and the calculated filtration loss from the natural fracture (Equation 14) into the material balance judgment equation (Equation 16) to determine whether the equation holds true. If the equation holds true, it proves that the ΔP-G function chart processing is accurate, and the relevant data can be used as a basis for predicting post-fracturing production capacity. If the equation does not hold true, it proves that the ΔP-G function chart has a large error, and it is necessary to re-establish the chart and redetermine the fracture closure point.

[0146] Therefore, in order to investigate whether fracturing fractures effectively connect with natural fractures and form favorable seepage channels, under the premise that the mass balance determination equation holds, considering the volumetric fracturing process, and based on the level of filtration loss from natural fractures and the reservoir compressibility index, we established two complex fracture network numerical models: efficient fracture network extension and diversion storage.

[0147] The physical model for the high-efficiency fracture network extension is as follows: the main fracture intersects with multiple natural fractures, and both the main fracture and the natural fractures simultaneously filter into the matrix, with the natural fractures in a high filtration condition, and the reservoir compressibility assessment index is greater than 0.51.

[0148] The numerical model for efficient mesh extension is as follows:

[0149]

[0150] In the formula: ζ s This is the ratio of the average static pressure in the fracture to the pressure in the wellbore, and it is dimensionless.

[0151] These are the fitting pressure and the fitting pressure drop, respectively, in MPa;

[0152] R f Let be the crack radius at the moment the crack closes, in mm;

[0153] h f x is the crack height at the moment the crack closes, in mm; f The median length of the crack at the point of crack closure is in mm;

[0154] g0 is the auxiliary calculation coefficient for fracturing pump injection, with a value range of 0 to 1 and is dimensionless.

[0155] The proposed redirection storage physical model is as follows: the main fracture does not effectively intersect with the natural fracture, resulting in minimal impact from the natural fracture filtration, the natural fracture is in a low filtration condition, and the reservoir compressibility assessment index is less than 0.5.

[0156] The numerical model for the redirection storage is as follows:

[0157]

[0158] It should be noted that when the natural fracture filtration index value is between 40% and 60%, the corresponding model should be selected from the two complex fracture network numerical models of efficient fracture network extension and diversion storage to study the fractured well section, depending on the size of the reservoir compressibility assessment index EST value. At the same time, the PKN type, KGD type, and Radial type auxiliary calculation parameters are selected from the fracture simulation space corresponding to the well section.

[0159] S8. Obtain the conductivity after the fracture is closed, and establish a one-dimensional flow continuity equation for fluid along the fracture length in the fracturing fracture.

[0160] Considering the impact of fracturing on rock pores and matrix, which introduces errors in permeability data, a conversion of fracture conductivity is introduced to make the entire calculation process closer to the actual situation of formation seepage after fracturing.

[0161] A further technical solution is to use a suitable finite element method (FEM) software (such as Petrel, Techlog, etc.) to model the formation properties based on the numerical model of the complex fracture network in the fractured well section. Fracture-related parameters are then set appropriately as boundary conditions. The mathematical model for seepage testing of the fracture network mentioned in Equation 10 is then solved using a differential method to inversely derive N. f N s Numerical values ​​refer to the distribution range of large-scale rock pores and rock matrix permeability in the strata.

[0162] The established equation for converting the conductivity of fracturing fractures is as follows:

[0163]

[0164] Where: FL CD The conductivity after the crack closes, in mD·mm;

[0165] FL CDO The initial fracture conductivity is calculated from core experimental data, in mD·mm;

[0166] ρ S The concentration of proppant sand is kg / m³. 2 .

[0167] A further technical solution is to ignore the influence of fluid flow along the width of the fracture while ensuring a certain level of accuracy, and only consider the fluid flow along the fracture extension direction (i.e., the fracture length direction) to establish a one-dimensional flow continuity equation for fluid along the fracture length direction in the fracturing fracture.

[0168] The established one-dimensional flow continuity equation is as follows:

[0169]

[0170] In the formula: ρ L The density of the fracturing fluid is kg / m³. 3 Q represents the single-well productivity after fracturing, m 3 / d;

[0171] W mf This is the mass exchange term between the rock matrix and the fracturing fracture, kg / (m 3 ×d).

[0172] S9. Based on the mathematical model of seepage in the fractured network, the conductivity after fracture closure, and the one-dimensional flow continuity equation, a single-well productivity prediction model is established using the numerical model of the complex fractured network in the fractured well section as the boundary condition. The productivity of a single well after fracture can be predicted through the single-well productivity prediction model.

[0173] Based on the selected complex fracture network numerical model, the fracture parameters are incorporated as boundary conditions into the seepage mathematical model of the fractured network. Using a finite difference solution approach, the analytical solution of the equation set composed of Equations 10 and 20 is derived, resulting in the formula for calculating the single-well productivity of a low-permeability tight reservoir after fracturing:

[0174]

[0175] In this embodiment, the specific computational process framework is as follows: Figure 9 As shown.

[0176] The above description is merely a preferred embodiment of the present invention, but the scope of protection of the present invention is not limited thereto. Any variations or substitutions that can be easily conceived by those skilled in the art within the technical scope disclosed in the embodiments of the present invention should be included within the scope of protection of the present invention. Therefore, the scope of protection of the present invention should be determined by the scope of the claims.

Claims

1. A method for predicting fracturing productivity in complex fracture networks of low-permeability tight reservoirs, characterized in that, Includes the following steps: S1. Based on the mechanical influence of weak surfaces in reservoirs, establish the weak surface influence index during reservoir fracturing. S2. Based on the dynamic changes in crack width, establish a spatial physical model of the crack; S3. Obtain the fracture symbolism index and rock toughness index; S4. Based on the weak surface influence index, fracture spatial physical model, fracture symbol index and rock toughness index, obtain the reservoir compressibility assessment index. S5, Based on bottom hole pressure drop The function obtains the fracture closure point, thereby obtaining the main fracture filtration loss and the natural fracture filtration loss when the fracture closes after fracturing. S6. Based on the reservoir DFIT test results, establish a mathematical model for seepage in the reservoir fracture network; S7. Based on the compressibility assessment index and the filtration loss of natural fractures, establish a numerical model of complex fracture networks in the fractured well section; S8. Obtain the conductivity after the fracture is closed, and establish a one-dimensional flow continuity equation for fluid along the fracture length in the fracturing fracture. S9. Based on the mathematical model of seepage in the fractured network, the conductivity after fracture closure, and the one-dimensional flow continuity equation, a single-well productivity prediction model after fracturing is established using the numerical model of the complex fractured network in the fracturing section as the boundary condition. The productivity of a single well after fracturing is then predicted using the single-well productivity prediction model. The weakness impact index is calculated using the following formula: In the formula: This represents the evaluation auxiliary function, with the independent variable of the evaluation target inside the parentheses. It is dimensionless. E Young's modulus of core samples taken from any well section. ; , These represent the maximum and minimum Young's modulus values ​​of the core samples from the fractured well section, respectively. ; for Surface normal direction and maximum principal stress The angle between directions is , The surface is a weak surface existing in the reservoir rock; For the cohesion of the weak surface of the reservoir rock, ; Poisson's ratio for core samples taken from any well section, dimensionless; , These are the maximum and minimum Poisson's ratios of the core samples from the fractured well section, respectively, and are dimensionless. The weak-side influence index is dimensionless. The physical model of the crack space is as follows: The cracks form an axisymmetric geometry along their length, at a certain initial moment before fracturing. The crack geometry parameters are: crack length is The seam width is ,by The solid line indicates the crack morphology at this moment; after a period of time following fracturing... T After that, this moment is The crack geometry parameters are: crack length is The seam width is ,by The dotted line indicates the shape of the crack at this moment; During hydraulic fracturing, the change in fracture length is Change in seam width The change in seam width is measured in absolute value. Based on the assumed conditions, the dynamic equation for crack width variation between crack propagation and minimum principal stress is obtained as follows: In the formula, This is the reservoir fracture pressure near the wellbore, calculated from well logging data; , These represent the maximum and minimum principal stresses, respectively, obtained from core tests. ; The coefficient to be calculated is determined by the pressure drop test process and is dimensionless.

2. The method according to claim 1, characterized in that, The fracture symbolism index and the rock toughness index are obtained through the following two equations: In the formula: The crack symbol is a dimensionless index. The well inclination angle measured from the axis of the fractured well section. ; The uniaxial tensile strength of the rock mass was measured experimentally. ; , These are the toughness factors for Type I and Type II rock formations, respectively, measured by core experiments and are dimensionless. , , , , The value is the fitting coefficient for the toughness of Type I rock strata, ranging from -0.34 to 0.

52. Choose an appropriate value based on the accuracy of the solution and substitute it into the calculation. , , The fitting coefficient for the toughness of type II rock strata is 0.08 to 0.

14. For type I, select an appropriate value and substitute it into the calculation. For confining pressure, triaxial rock mechanics experiments can be set to obtain numerical values. ; is the rock toughness index, dimensionless.

3. The method according to claim 2, characterized in that, The compressibility assessment index is obtained by the following formula: In the formula: EST It is a compressibility assessment index; the higher the value, the easier it is to fracture a certain well section. It is dimensionless. The coefficient to be calculated is determined by the pressure drop test process and is dimensionless; T Indicates the fracturing operation time. ; For confining pressure, triaxial rock mechanics experiments can be set to obtain numerical values. ; To maintain a constant pumping pressure of fracturing fluid into the fracturing pump, ; R This indicates the distance from a point in the near-wellbore zone to the wellbore axis. ; The radius of the wellbore. .

4. The method according to claim 1, characterized in that, The crack closure point was obtained in the following way: During the fracture closure period after pump shutdown, the linear relationship between the bottom hole pressure P and the G function was observed, and calculations were performed. derivative of a function Logarithmic derivative Solve using the derivative relationship The extreme points of the linear relationship of the function are used as the reference points for crack closure, and the following plots are drawn. Function graph; In the function graph, a fitted regression line passing through the origin is introduced, and it is made as tangent as possible to the derivative curve. Points deviating from the line can be initially considered as crack closure points. The extreme points of the linear relationship of the function are compared to each other to calibrate the expression of the fitted regression line; Finally, representative fracture closure points were identified, and the corresponding fracturing time steps were recorded. Crack closing pressure P ; based on The function graph shows the main fracture filtration loss at the fracture closure point after fracturing. based on The function graph shows the natural fracture filtration loss at the fracture closure point after hydraulic fracturing. In the formula: This represents the filtration loss of the main fracture at a certain moment. ; This represents the ratio of crack filtration height to crack width, and is dimensionless. Indicates the filtration coefficient of the main crack. ; Indicates the filtration area of ​​the main crack. ; This represents the amount of fluid lost through natural cracks at a given moment. ; Indicates the filtration loss coefficient of natural cracks. ; This represents the area of ​​filtration loss due to natural cracks. .

5. The method according to claim 1, characterized in that, The reservoir fracture network seepage mathematical model refers to: In the formula: , These represent the size of large-scale rock pores and the permeability of the rock matrix, respectively. ; This indicates the effective viscosity of the fracturing fluid. ; To maintain a constant pumping pressure of fracturing fluid into the fracturing pump, ; This represents the reservoir fracture pressure near the wellbore, calculated from well logging data. ; Indicates porosity. ; Indicates the overall elastic coefficient of the formation. ; n This represents the fracturing fluid flow regime index, which is dimensionless. biot This represents the magnitude of the rock pore elastic coefficient and is dimensionless. This represents the consistency coefficient of the fracturing fluid. ; x , y These represent the two orthogonal decomposition directions that indicate the direction of crack extension.

6. The method according to claim 1, characterized in that, The numerical model of complex fracture network in the fractured well section refers to: The efficient mesh extension model is as follows: The redirection storage model is as follows: In the formula: This is the ratio of the average static pressure in the fracture to the pressure in the wellbore, and it is dimensionless. , These are the fitting pressure and the fitting pressure drop, respectively. ; Let be the crack radius at the moment the crack closes. ; The crack height at the moment the crack closes. ; The median length of the crack at the point of crack closure. ; This is the auxiliary calculation coefficient for fracturing pump injection, with a value range of 0~1 and is dimensionless. This represents the amount of fluid lost through natural cracks at a given moment. ; This represents the fracturing time step. This represents the filtration loss of the main fracture at a certain moment. ; EST It is a compressibility assessment index; the higher the value, the easier it is to fracture a certain well section. It is dimensionless. This represents the ratio of crack filtration height to crack width, and is dimensionless. When the natural crack filtration index is between 40% and 60%, the compressibility assessment index is used. EST The numerical magnitude is determined by selecting the appropriate model from two complex fracture network numerical models: efficient fracture network extension and redirection storage, to study the fracturing well section. The selection is also based on the fracture simulation space corresponding to that section. PKN type, KGD type, Radial Type of auxiliary calculation parameters.

7. The method according to claim 1, characterized in that, The single-well productivity prediction model is as follows: In the formula: The initial fracture conductivity was calculated from core experimental data. ; The density of the fracturing fluid. ; This refers to the single-well production capacity after fracturing. ; This refers to the mass exchange term between the rock matrix and the fracturing fracture. ; Indicates porosity. ; This indicates the effective viscosity of the fracturing fluid. ; To maintain a constant pumping pressure of fracturing fluid into the fracturing pump, ; This represents the reservoir fracture pressure near the wellbore, calculated from well logging data. ; R This indicates the distance from a point in the near-wellbore zone to the wellbore axis. ; The radius of the wellbore. ; For fracturing fluid efficiency; This represents the ratio of crack filtration height to crack width, and is dimensionless. Indicates the filtration coefficient of the main crack. ; Indicates the filtration area of ​​the main crack. ; Indicates the filtration loss coefficient of natural cracks. ; This represents the area of ​​filtration loss due to natural cracks. ; This indicates the amount of fracturing fluid lost. .

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