Characteristic point fitting inversion method, electronic equipment and medium for volume fracturing horizontal well

Abstract

Disclosed are a method, electronic device and medium for fitting and inversion of characteristic points of volume fracturing horizontal wells. The method includes: establishing a mathematical model of volume fracturing horizontal well partition seepage; solving the mathematical model of volume fracturing horizontal well partition seepage, and then calculating the bottom hole pressure and the bottom hole pressure derivative; determining multiple characteristic points according to the bottom hole pressure derivative curve of the volume fracturing horizontal well; establishing a fitting expression for each characteristic point and the well test interpretation information; adjusting the characteristic points so that the pressure derivative curve and the pressure curve coincide with the corresponding actual test well curve, and then calculating the well test interpretation information. The present invention performs mathematical analysis based on the seepage characteristics corresponding to different regions in the volume fracturing horizontal well model, quickly and effectively fits the actual test well data of the volume fracturing horizontal well, and obtains the wellbore, reservoir and fracturing transformation parameters of the volume fracturing horizontal well, providing a basis for the well test interpretation and fracturing transformation effect evaluation of the volume fracturing horizontal well.

Description

Technical Field

[0001] The present invention relates to the technical field of well testing for oil reservoir engineering, and more specifically to a method for fitting and inverting characteristic points of a volume fracturing horizontal well, electronic equipment and a medium. Background Art

[0002] Volume fracturing of horizontal wells is an effective means for the industrial development of low-permeability and tight oil and gas reservoirs. Volume fracturing can achieve volume transformation of oil and gas reservoirs in three directions: X, Y, and Z. This technology can not only greatly increase the production of single wells in production wells, but also maximize the utilization degree and recovery rate of reservoirs. With the implementation of volume fracturing technology, how to use mathematical methods to describe the fracture network in the reservoir transformation area, evaluate the fracturing effect, and determine the reservoir, wellbore and fracturing transformation parameters of volume fracturing wells are some important issues currently faced. The present invention establishes a dynamic inversion method and device for fitting the characteristic points of volume fracturing horizontal well test, which can quickly fit the test data of volume fracturing horizontal well test, invert the test interpretation information of volume fracturing horizontal well test, and evaluate the transformation effect of volume fracturing in production wells.

[0003] The existing technologies include: a non-Darcy seepage mathematical model for volume fracturing horizontal wells, which is approximately solved by differential equations, but the solution speed is slow, and the test interpretation method is a conventional method, which cannot be fitted to obtain interpretation parameters simply and quickly; a test model for tight gas reservoir fracturing horizontal wells, which can be used for test interpretation of tight gas reservoir fracturing horizontal wells, but cannot be used for test interpretation of volume fracturing horizontal wells in oil reservoirs; an unstable test model for 2-zone composite reservoirs, which can be used for unstable test interpretation of horizontal wells in 2-zone composite reservoirs, but the model does not consider the influence of hydraulic fractures and transformation sealing nets in volume fracturing horizontal wells, and cannot solve the problem of well interpretation of volume fracturing horizontal wells; for multi-stage fracturing horizontal wells in shale oil reservoirs, a volume fracturing transformation test model that simultaneously considers primary fractures and secondary fracture networks is established based on the shape of the pressure difference derivative curve of actual well test data, but the model does not consider the fluid supply of the unfractured transformation area far away from the wellbore, but regards it as a closed boundary, and the pressure and pressure derivative fitting and wellbore and reservoir parameter inversion methods are conventional well test interpretation methods.

[0004] With the development of low-permeability tight oil reservoirs, horizontal well volume fracturing has become an effective means of developing such reservoirs. At present, it is urgent to solve the problems of pressure dynamic analysis of volume fracturing wells, acquisition of reservoir, fracture, wellbore parameters and evaluation of fracturing effects. In view of the above problems, there is currently a lack of well test models and fast dynamic inversion methods that can effectively describe the characteristics of horizontal well volume fracturing transformation. Therefore, it is necessary to develop a characteristic point fitting inversion method, electronic equipment and medium for volume fracturing horizontal wells.

[0005] The information disclosed in the background technology section of the present invention is only intended to deepen the understanding of the general background technology of the present invention, and should not be regarded as acknowledging or suggesting in any form that the information constitutes the prior art already known to those skilled in the art. Summary of the invention

[0006] The present invention proposes a method, device, electronic equipment and medium for fitting and inversion of characteristic points of volume fracturing horizontal wells, which can perform mathematical analysis according to the seepage characteristics corresponding to different regions in the volume fracturing horizontal well model, quickly and effectively fit the actual test well data of the volume fracturing horizontal well, and obtain the wellbore, reservoir and fracturing transformation parameters of the volume fracturing horizontal well, providing a basis for the well test interpretation and fracturing transformation effect evaluation of the volume fracturing horizontal well.

[0007] In a first aspect, an embodiment of the present disclosure provides a method for fitting and inversion of characteristic points of a volumetric fractured horizontal well, including: establishing a mathematical model of partitioned seepage of a volumetric fractured horizontal well; solving the mathematical model of partitioned seepage of a volumetric fractured horizontal well, and then calculating the bottom hole pressure and the bottom hole pressure derivative; drawing a bottom hole pressure curve of a volumetric fractured horizontal well and a bottom hole pressure derivative curve of a volumetric fractured horizontal well, and determining a plurality of characteristic points according to the bottom hole pressure derivative curve of the volumetric fractured horizontal well; establishing a fitting expression for each characteristic point and well test interpretation information; adjusting the plurality of characteristic points so that the pressure derivative curve and the pressure curve coincide with the corresponding actual test well curve, and calculating the well test interpretation information through the adjusted characteristic points and the fitting expression.

[0008] Preferably, the volume fracturing horizontal well partition seepage mathematical model includes a main fracture zone seepage mathematical model, a reformed zone seepage mathematical model, and a non-reformed zone seepage mathematical model.

[0009] Preferably, the mathematical model of seepage in the main fracture zone is:

[0010]

[0011] Among them, p lfD is the dimensionless pressure of the main crack; p lsfD x is the dimensionless pressure of microcracks at the main crack wall; D is the dimensionless distance in the x direction; y D is the dimensionless distance in the y direction; F CD is the dimensionless conductivity of the fracture.

[0012] Preferably, the mathematical model of seepage in the transformation zone is:

[0013]

[0014] Among them, p sfD is the dimensionless pressure of microcracks; p mDis the dimensionless pressure of the matrix; r D is the radial dimensionless radius; t D is dimensionless time; C D is the dimensionless wellbore storage coefficient; λ is the crossflow coefficient; ω is the storage capacity ratio.

[0015] Preferably, the mathematical model of seepage in the non-reconstructed area is:

[0016]

[0017] Among them, p 2D is the dimensionless pressure in the non-transformation area; γ D is the dimensionless permeability modulus; M 1,2 is the flow ratio between inner and outer zones, W is the ratio of the energy storage coefficients of the inner and outer zones, e is the natural logarithm.

[0018] Preferably, solving the mathematical model of the partitioned seepage of the volumetric fracturing horizontal well and then calculating the bottom hole pressure and the bottom hole pressure derivative includes: solving the general solution of the mathematical model of the seepage in the reformed area and the mathematical model of the seepage in the non-reformed area respectively; calculating the source function; combining the mathematical model of the seepage in the main fracture area with the source function to calculate the bottom hole pressure response; performing Laplace numerical inversion on the bottom hole pressure response by the Stehfest algorithm to obtain the bottom hole pressure; and derivatizing the bottom hole pressure to obtain the bottom hole pressure derivative.

[0019] Preferably, the source function is:

[0020]

[0021] Among them, G is the source function; A and B are coefficients; I0 is a type of zero-order modified Bessel function; K0 is a type of second-order zero-order modified Bessel function; u is a Laplace space variable.

[0022] Preferably, the bottom hole pressure response is:

[0023]

[0024] in, is the dimensionless bottom hole pressure including the wellbore reservoir effect in Laplace space; is the dimensionless bottom hole pressure in Laplace space.

[0025] As a specific implementation method of the embodiment of the present disclosure,

[0026] In a second aspect, an embodiment of the present disclosure further provides an electronic device, the electronic device comprising:

[0027] A memory storing executable instructions;

[0028] A processor runs the executable instructions in the memory to implement the volume fracturing horizontal well characteristic point fitting inversion method.

[0029] In a third aspect, an embodiment of the present disclosure further provides a computer-readable storage medium storing a computer program, which, when executed by a processor, implements the characteristic point fitting inversion method for volume fracturing horizontal wells.

[0030] Its beneficial effects are: according to the seepage characteristics corresponding to different areas in the volume fracturing horizontal well model, mathematical analysis is carried out to establish the seepage mathematical model of the volume fracturing horizontal well model. The seepage characteristics corresponding to different areas are comprehensively considered, which improves the accuracy of establishing the seepage mathematical model and provides an accurate data basis for subsequent well test interpretation. The solution of the seepage mathematical model is obtained by a semi-analytical method. According to the solution of the seepage mathematical model, the horizontal well test curve of the volume fracturing horizontal well model can be drawn, and the well test interpretation of the volume fracturing horizontal well can be carried out according to the obtained horizontal well test curve. Comprehensively considering the seepage characteristics corresponding to different geological characteristics makes the constructed seepage mathematical model more accurate, further improving the accuracy of the well test interpretation results.

[0031] The methods and apparatus of the present invention have other features and advantages that will be apparent from, or will be described in detail in, the accompanying drawings and subsequent detailed descriptions incorporated herein, which together serve to explain the specific principles of the present invention. BRIEF DESCRIPTION OF THE DRAWINGS

[0032] The above and other objects, features and advantages of the present invention will become more apparent through a more detailed description of exemplary embodiments of the present invention in conjunction with the accompanying drawings, wherein like reference numerals generally represent like components throughout the exemplary embodiments of the present invention.

[0033] Figure 1 A flow chart showing the steps of the method for fitting and inverting characteristic points of a volumetric fractured horizontal well according to the present invention.

[0034] Figure 2 A schematic diagram of a seepage physical model of a horizontal well with volume fracturing in a quasi-elliptical transformation zone according to an embodiment of the present invention is shown.

[0035] Figure 3 A schematic diagram of a bottom hole pressure curve of a volumetric fractured horizontal well and a bottom hole pressure derivative curve of a volumetric fractured horizontal well according to an embodiment of the present invention is shown.

[0036] Figure 4A schematic diagram of a pressure derivative characteristic curve of a volume fracturing horizontal well test model according to an embodiment of the present invention is shown.

[0037] Figure 5 shows different C according to one embodiment of the present invention De 2S Schematic diagram of the pressure derivative curve when .

[0038] Figure 6 shows the coordinate value of the feature point 2 and log(C De 2S ) values.

[0039] Figure 7 A schematic diagram showing pressure derivative curves at different crossflow coefficients according to an embodiment of the present invention is shown.

[0040] Figure 8 A relationship diagram between the abscissa value of the feature point 3 and the parameter group 1 according to an embodiment of the present invention is shown.

[0041] Fig. 9 A relationship diagram between the ordinate value of the feature point 3 and the parameter group 2 according to an embodiment of the present invention is shown.

[0042] Fig.10 A schematic diagram of pressure derivative curves for different numbers of cracks according to an embodiment of the present invention is shown.

[0043] Fig.11 A schematic diagram showing pressure derivative curves at different horizontal wellbore lengths according to an embodiment of the present invention is shown.

[0044] Fig.12 A relationship diagram between the ordinate value of the characteristic point 4 and the number of cracks according to an embodiment of the present invention is shown.

[0045] Fig.13 A relationship diagram between the horizontal coordinate value of the characteristic point 4 and the crack spacing according to an embodiment of the present invention is shown.

[0046] Fig.14 A relationship diagram between the abscissa value of the characteristic point 4 and the wellbore length according to an embodiment of the present invention is shown.

[0047] Fig.15 A schematic diagram showing pressure derivative curves at different transformation zone radii according to an embodiment of the present invention is shown.

[0048] Fig.16 A relationship diagram between the horizontal coordinate value of the characteristic point 6 and the square of the radius of the transformation area according to an embodiment of the present invention is shown.

[0049] Fig.17 A schematic diagram showing pressure derivative curves at different inner and outer zone flow rate ratios according to an embodiment of the present invention is shown.

[0050] Fig.18 The figure shows the relationship between the abscissa value of the characteristic point 7 and the flow rate ratio between the inner and outer zones according to an embodiment of the present invention. DETAILED DESCRIPTION

[0051] The present invention will be described in more detail below with reference to the accompanying drawings. Although preferred embodiments of the present invention are shown in the accompanying drawings, it should be understood that the present invention can be implemented in various forms and should not be limited by the embodiments set forth herein. On the contrary, these embodiments are provided to make the present invention more thorough and complete, and to fully convey the scope of the present invention to those skilled in the art.

[0052] Figure 1 A flow chart showing the steps of the method for fitting and inverting characteristic points of a volumetric fractured horizontal well according to the present invention.

[0053] In this embodiment, the characteristic point fitting inversion method for volume fracturing horizontal wells according to the present invention may include: step 101, establishing a mathematical model of partitioned seepage of volume fracturing horizontal wells; step 102, solving the mathematical model of partitioned seepage of volume fracturing horizontal wells, and then calculating the bottom hole pressure and the bottom hole pressure derivative; step 103, drawing the bottom hole pressure curve of the volume fracturing horizontal well and the bottom hole pressure derivative curve of the volume fracturing horizontal well, and determining multiple characteristic points according to the bottom hole pressure derivative curve of the volume fracturing horizontal well; step 104, establishing a fitting expression for each characteristic point and the well test interpretation information; step 105, adjusting multiple characteristic points so that the pressure derivative curve and the pressure curve coincide with the corresponding actual test well curve, and calculating the well test interpretation information through the adjusted characteristic points and the fitting expression.

[0054] In one example, the volumetric fractured horizontal well partitioned seepage mathematical model includes a main fracture zone seepage mathematical model, a reformed zone seepage mathematical model, and a non-reformed zone seepage mathematical model.

[0055] In one example, the mathematical model of seepage in the main fracture zone is:

[0056]

[0057] Among them, p lfD is the dimensionless pressure of the main crack; p lsfD x is the dimensionless pressure of microcracks at the main crack wall; D is the dimensionless distance in the x direction; y D is the dimensionless distance in the y direction; F CD is the dimensionless conductivity of the fracture.

[0058] In one example, the mathematical model of seepage in the reformed area is:

[0059]

[0060] Among them, p sfD is the dimensionless pressure of microcracks; p mD is the dimensionless pressure of the matrix; r D is the radial dimensionless radius; t D is dimensionless time; C D is the dimensionless wellbore storage coefficient; λ is the crossflow coefficient; ω is the storage capacity ratio.

[0061] In one example, the mathematical model of seepage in the non-reconstruction zone is:

[0062]

[0063] Among them, p 2D is the dimensionless pressure in the non-transformation area; γ D is the dimensionless permeability modulus; M 1,2 is the flow ratio between inner and outer zones, W is the ratio of the energy storage coefficients of the inner and outer zones, e is the natural logarithm.

[0064] In one example, solving the mathematical model of seepage in a volumetric fractured horizontal well partition and then calculating the bottom hole pressure and the bottom hole pressure derivative includes: solving the general solutions of the mathematical model of seepage in the reformed area and the mathematical model of seepage in the non-reformed area respectively; calculating the source function; combining the mathematical model of seepage in the main fracture area with the source function to calculate the bottom hole pressure response; performing Laplace numerical inversion on the bottom hole pressure response by the Stehfest algorithm to obtain the bottom hole pressure; and taking the derivative of the bottom hole pressure to obtain the bottom hole pressure derivative.

[0065] In one example, the source function is:

[0066]

[0067] Among them, G is the source function; A and B are coefficients; I0 is a type of zero-order modified Bessel function; K0 is a type of second-order zero-order modified Bessel function; u is a Laplace space variable.

[0068] In one example, the bottom hole pressure response is:

[0069]

[0070] in, is the dimensionless bottom hole pressure including the wellbore reservoir effect in Laplace space; is the dimensionless bottom hole pressure in Laplace space.

[0071] Specifically, the characteristic point fitting inversion method for volume fracturing horizontal wells according to the present invention may include:

[0072] By analyzing the fracturing construction parameters of volume fracturing wells and the results of microseismic monitoring, it is realized that horizontal well volume fracturing can not only form artificial fractures, but also open and communicate natural fracture networks, forming a certain range of transformation areas around the horizontal wells.

[0073] Figure 2 A schematic diagram of a seepage physical model of a horizontal well with volume fracturing in a quasi-elliptical transformation zone according to an embodiment of the present invention is shown.

[0074] Establish as Figure 2 The volume fracturing horizontal well partition seepage physical model shown in the figure analyzes the fracturing construction parameters and microseismic results of the volume fracturing horizontal well. According to the analysis results, after the volume fracturing of the horizontal well, while the main fractures are formed around the wellbore, secondary fractures are also generated and connect the natural fractures to form a fracture network, forming a transformation zone within a certain range around the wellbore. This area is characterized by the Warren-Root dual-porosity and single-permeability model; the area far away from the wellbore has not been transformed and is called the non-transformation zone. It is described by a single medium model, and the stress sensitivity characteristics of the reservoir are considered.

[0075] The formation and fluid satisfy the following assumptions:

[0076] (1) Fluid flow obeys Darcy's law, has a constant compressibility coefficient and viscosity, is single-phase compressible, and flows radially in an infinite reservoir plane;

[0077] (2) Ignoring the effects of capillary force and gravity, the fluid flows in the formation in a Darcy-like manner, and the flow process is isothermal;

[0078] (3) The vertically closed and horizontally infinite (or closed) reservoir has a thickness of h and is divided into two zones: the inner zone and the outer zone. The inner zone is the volume fracturing zone and is characterized by the Warren-Root dual-porosity and single-permeability model. It consists of a matrix system and a fracture system. The matrix system is the reservoir space for the fluid (with a permeability of k m , the porosity is φ m ), the fracture system acts as a seepage channel for the fluid (with a permeability of k sf , the porosity is φ sf ). The outer area is the non-transformed area (indicated by subscript 2), which is described by a single medium and takes into account the stress sensitivity of the reservoir;

[0079] (4) Under original conditions, reservoir pressure is equal everywhere, that is, the original formation pressure is p i ;

[0080] (5) The horizontal well is parallel to the x-axis and the length of the horizontal well is L h , the number of main fractures in hydraulic fracturing is nf , the crack half length is X f , the crack width is w f , the fracture permeability is k f , the crack spacing is L f , the transformation radius is r f ;

[0081] (6) The well is produced at a constant rate q, and the flow in the wellbore is infinite. The formation fluid first flows from the outer zone single-porous medium system into the inner zone dual-porous medium system, then flows from the inner zone dual-porous medium system into the hydraulic main fracture, and then flows from the hydraulic main fracture into the horizontal wellbore. There is a pressure drop along the main fracture, the pressure at the seepage interface between the inner and outer zones is continuous, and there is crossflow between the matrix and microfractures in the dual-porous medium system in the reformed zone.

[0082] Then, a mathematical model of the regional seepage of volume fracturing horizontal wells is established, including the mathematical model of the seepage in the main fracture zone, the mathematical model of the seepage in the reformed zone, and the mathematical model of the seepage in the non-reformed zone. The mathematical model of the seepage in the main fracture zone is formula (1), and the initial condition is:

[0083] p lfD (x D ,y D ,t D =0)=0 (6),

[0084] The bottom hole flow conditions are:

[0085]

[0086] The conditions for equal flow rates between crack and wall are:

[0087]

[0088] In the formula,

[0089] The material balance condition is

[0090]

[0091] The mathematical model of seepage in the transformation area is formula (2), and the initial conditions are:

[0092] p sfD (x D ,y D ,t D =0) =0 (10)

[0093] The coupling condition at the boundary between the inner and outer zones is:

[0094] The pressure is equal,

[0095] The flow rate is equal,

[0096] The mathematical model of seepage in the non-transformed area is formula (3), and the initial conditions are:

[0097] p 2D (x D ,y D ,t D =0) =0 (13)

[0098] The outer boundary conditions are: infinite boundary,

[0099] Solving the mathematical model of volumetric fractured horizontal well partition seepage and then calculating the bottom hole pressure and bottom hole pressure derivative includes:

[0100] The fractures are discretized, and the analytical solution of the reformed area (dual-porosity medium model) and the analytical solution of the non-reformed area (single-porosity medium model) are combined to obtain the solution of the mathematical model of seepage in the volume fractured horizontal well by using a coupled solution method.

[0101] Since the stress sensitivity of the reservoir is taken into account in the outer zone, the obtained seepage control equation is a highly nonlinear equation and cannot be solved directly. The perturbation transformation formula is introduced to linearize the model for solution. Based on the boundary conditions at the seepage interface between the reformed zone and the non-reformed zone, and the equal pressure and flow at the boundary, the general solution of the mathematical model of seepage in the reformed zone is:

[0102]

[0103] The general solution of the mathematical model of seepage in the non-reconstructed area is:

[0104]

[0105] According to the boundary conditions of the transformation area, the coupling conditions of equal pressure and equal flow at the boundary between the transformation area and the non-transformation area, the values ​​of A, B and C are obtained, and then the source function is calculated as formula (4).

[0106] Using the crack discretization mechanism, one wing of the crack L is divided into n small segments, with a total of NF = 2n × n f Assuming that the flow rate in each small segment is uniformly distributed, the center coordinates of the mth unit of the fracture L can be obtained as (x Dl(m) ,y Dl(m) ), half length is L fDl(m) , flow rate q Dl(m) , the definition methods of other micro-elements are similar. Then the m-th unit equation of crack L is:

[0107]

[0108] Where l = 1, 2, 3, ..., nf ; m = 1, 2, 3, ..., n;

[0109] Considering the mutual interference between multiple fractures during actual production, for a multi-stage fractured horizontal well in an infinite formation, the instantaneous source function is superimposed along the fractures, as shown in the following formula:

[0110]

[0111] Where, l,q=1,2,3,......,n f ; m, k = 1, 2, 3, ..., 2n;

[0112]

[0113] The flow constraints for fixed production are:

[0114]

[0115] In summary, since the fracture conductivity mainly affects the initial seepage curve shape and the fracture area is small, the combined formulas (17)-(19) are n f ×2n+1 equations can be solved numerically etc. f ×2n+1 unknowns, the bottom hole pressure response including the wellbore reservoir effect is calculated as formula (5); the bottom hole pressure response is numerically inverted by Laplace using the Stehfest algorithm to obtain the bottom hole pressure; the bottom hole pressure is differentiated to obtain the bottom hole pressure derivative.

[0116] Draw the bottom hole pressure curve of the volume fracturing horizontal well and the bottom hole pressure derivative curve of the volume fracturing horizontal well, divide the derivative curve into stages, and then determine multiple characteristic points on the bottom hole pressure derivative curve of the volume fracturing horizontal well according to the shape of the bottom hole pressure derivative curve of the volume fracturing horizontal well, mark the characteristic points at the corresponding positions of the bottom hole pressure curve of the volume fracturing horizontal well, the characteristic points may include maximum points, minimum points, inflection points, etc., and technical personnel in this field can set them according to specific circumstances; establish a fitting expression for each characteristic point and the well test interpretation information; adjust multiple characteristic points, first make the pressure derivative curve coincide with the pressure derivative curve in the actual test well curve, and then make the pressure curve coincide with the pressure curve in the actual test well curve, and calculate the well test interpretation information through the adjusted characteristic points and fitting expressions.

[0117] This method performs mathematical analysis based on the seepage characteristics corresponding to different areas in the volume fracturing horizontal well model, quickly and effectively fits the actual test well data of the volume fracturing horizontal well, and obtains the wellbore, reservoir and fracturing transformation parameters of the volume fracturing horizontal well, providing a basis for the well test interpretation and fracturing transformation effect evaluation of the volume fracturing horizontal well.

[0118] Application Examples

[0119] To facilitate understanding of the solution and effects of the embodiments of the present invention, a specific application example is given below. Those skilled in the art should understand that this example is only for facilitating understanding of the present invention, and any specific details thereof are not intended to limit the present invention in any way.

[0120] The method for fitting and inversion of characteristic points of volume fracturing horizontal wells according to the present invention may include:

[0121] A mathematical model for the regional seepage of volume fracturing horizontal wells is established, including the mathematical model for the seepage in the main fracture zone, the mathematical model for the seepage in the reformed zone, and the mathematical model for the seepage in the non-reformed zone. The mathematical model for the seepage in the main fracture zone is formula (1), the mathematical model for the seepage in the reformed zone is formula (2), and the mathematical model for the seepage in the non-reformed zone is formula (3).

[0122] Solving the mathematical model of seepage in the volume fracturing horizontal well partition and then calculating the bottom hole pressure and the bottom hole pressure derivative includes: respectively solving the general solutions of the mathematical model of seepage in the reformed area and the mathematical model of seepage in the non-reformed area as formula (15) and formula (16); according to the boundary conditions of the reformed area and the coupling conditions of equal pressure and equal flow at the boundary between the reformed area and the non-reformed area, calculating the source function as formula (4); combining the mathematical model of seepage in the main fracture area with the source function, and calculating the bottom hole pressure response as formula (5); performing Laplace numerical inversion on the bottom hole pressure response by the Stehfest algorithm to obtain the bottom hole pressure; and taking the derivative of the bottom hole pressure to obtain the bottom hole pressure derivative.

[0123] Figure 3 A schematic diagram of a bottom hole pressure curve of a volumetric fractured horizontal well and a bottom hole pressure derivative curve of a volumetric fractured horizontal well according to an embodiment of the present invention is shown.

[0124] Draw the bottom hole pressure curve of volume fracturing horizontal well and the bottom hole pressure derivative curve of volume fracturing horizontal well, such as Figure 3 As shown, the derivative curve is divided into stages:

[0125] In the first stage, the fracture bilinear flow stage, that is, the stage where the linear flow in the hydraulic fracture and the linear flow from the microfracture to the hydraulic fracture act simultaneously, the slope of the pressure derivative curve is 1 / 4; in the second stage, the linear flow stage perpendicular to the fracture, that is, the linear flow from the reservoir microfracture to the hydraulic fracture, the slope of the pressure derivative curve is 1 / 2; in the third stage, the fracture quasi-radial flow stage, the pressure derivative curve has a horizontal section, which appears for a very short time and may be difficult to observe; in the fourth stage, the cross-flow stage from the matrix to the microfracture, the pressure derivative curve has a concave feature; in the fifth stage, the reformed area system radial flow stage, the pressure derivative curve is a horizontal line with a value equal to 0.5; in the sixth stage, the transition stage from the reformed area to the non-reformed area, the pressure and pressure derivative curves are upturned; in the seventh stage, the reservoir system radial flow stage, the pressure derivative curve is a value equal to 0.5M 1,2 horizontal line.

[0126] Figure 4 A schematic diagram of a pressure derivative characteristic curve of a volume fracturing horizontal well test model according to an embodiment of the present invention is shown.

[0127] According to the shape of the bottom hole pressure derivative curve of the volume fracturing horizontal well, 7 characteristic points are determined on the bottom hole pressure derivative curve of the volume fracturing horizontal well, such as Figure 4 As shown: the first characteristic point is the starting point, the second characteristic point is the maximum point, the third characteristic point is the minimum point, the fourth characteristic point is the end point of the fracture radial flow, the fifth characteristic point is the horizontal line point of the radial flow in the transformation area, the sixth characteristic point is the end point of the radial flow in the transformation area, and the seventh characteristic point is the horizontal line point of the radial flow in the non-transformation area. The characteristic points are marked at the corresponding positions of the bottom hole pressure curve of the volume fracturing horizontal well; the fitting expression of each characteristic point and the well test interpretation information is established:

[0128] ① The first characteristic point is the starting point. When there is a wellbore reservoir effect, this characteristic point can be any point on the straight line segment with an initial slope of 1 for the pressure derivative:

[0129]

[0130] From formula (20), we can know that as long as we obtain the coordinate value of any point (Δp′1, t1) where the slope of the measured pressure derivative is 1 in the early stage, we can calculate the parameter C D :

[0131]

[0132] Figure 5 shows different C according to one embodiment of the present invention De 2S Schematic diagram of the pressure derivative curve when .

[0133] Figure 6shows the coordinate value of the feature point 2 and log(C De 2S ) values.

[0134] ②The second characteristic point is the maximum value point of the pressure derivative. This characteristic point is related to C D e 2S By giving different C D e 2S Value, find a set of pressure derivative curves, such as Figure 5 As shown. Plot the coordinates of the extreme points and log(C D e 2S ) value relationship diagram, such as Figure 6 As shown, the following expression can be obtained through linear regression:

[0135]

[0136] From formula (22), we can know that as long as the coordinates of the maximum point of the measured pressure derivative (Δp′2, t2) are obtained, the parameter cluster C can be calculated. D e 2S :

[0137]

[0138] Figure 7 A schematic diagram showing pressure derivative curves at different crossflow coefficients according to an embodiment of the present invention is shown.

[0139] Figure 8 A relationship diagram between the abscissa value of the feature point 3 and the parameter group 1 according to an embodiment of the present invention is shown.

[0140] Fig. 9 A relationship diagram between the ordinate value of the feature point 3 and the parameter group 2 according to an embodiment of the present invention is shown.

[0141] ③The third characteristic point is the minimum point of the pressure derivative. This characteristic point is related to the parameter group of storage capacity ratio, crossflow coefficient and wellbore storage coefficient. By giving different storage capacity ratio values, a set of pressure derivative curves is obtained, such as Figure 7 The horizontal coordinate value of feature point 3 and parameter group Like Figure 8 The relationship between the vertical coordinate value of feature point 3 and the parameter group Like Fig. 9 The relationship expression is as follows:

[0142]

[0143] It can be seen from formula (24) that as long as the coordinate value of the minimum point of the measured pressure derivative (Δp'3, t3) is obtained, the parameters ω and λ of the following transcendental equation can be solved by iteration:

[0144]

[0145] Fig.10 A schematic diagram of pressure derivative curves for different numbers of cracks according to an embodiment of the present invention is shown.

[0146] Fig.11 A schematic diagram showing pressure derivative curves at different horizontal wellbore lengths according to an embodiment of the present invention is shown.

[0147] Fig.12 A relationship diagram between the ordinate value of the characteristic point 4 and the number of cracks according to an embodiment of the present invention is shown.

[0148] Fig.13 A relationship diagram between the horizontal coordinate value of the characteristic point 4 and the crack spacing according to an embodiment of the present invention is shown.

[0149] Fig.14 A relationship diagram between the abscissa value of the characteristic point 4 and the wellbore length according to an embodiment of the present invention is shown.

[0150] ④The fourth characteristic point is the end point of the fracture radial flow and the starting point of the fracture interference. When the wellbore length is constant, the pressure derivative curves for different fracture numbers are as follows: Fig.10 When the number of fractures is constant, the pressure derivative curves at different wellbore lengths are shown in Fig.11 As shown in Figure 2, it can be seen that the ordinate of this feature point is only related to the number of cracks, and the relationship is as follows: Fig.12 The horizontal axis value is related to the number of fractures and the length of the wellbore, and the relationship is as follows: Fig.13 and Fig.14 The relationship between characteristic point 4, the number of fractures and the length of the wellbore is as follows:

[0151]

[0152] It can be seen from formula (26) that as long as the vertical coordinate value and the horizontal coordinate value of the end point of the radial flow of the measured pressure derivative fracture are obtained, the number of fractures and the horizontal wellbore length can be obtained by solving formula (26).

[0153] ⑤The fifth characteristic point is the horizontal line point of radial flow in the transformation area, and the vertical coordinate value of this characteristic point is 0.5:

[0154] (p' wD )5=0.5 (27)

[0155] From formula (27), we can know that as long as the ordinate value Δp'5 of the horizontal line point of the measured pressure derivative is obtained, the microfracture permeability k of the reservoir in the reformed area can be obtained. sf :

[0156]

[0157] Fig.15 A schematic diagram showing pressure derivative curves at different transformation zone radii according to an embodiment of the present invention is shown.

[0158] Fig.16 A relationship diagram between the horizontal coordinate value of the characteristic point 6 and the square of the radius of the transformation area according to an embodiment of the present invention is shown.

[0159] ⑥The sixth characteristic point is the end point of the radial flow in the reformed area. Given different reformed area radii, a set of pressure derivative curves are obtained such as Fig.15 The horizontal coordinate of the feature point and the square of the radius of the transformation area are as follows Fig.16 The relationship shown in the figure can be expressed as follows through linear regression:

[0160]

[0161] From formula (29), we can know that as long as we obtain the horizontal coordinate value t6 of the end point of the radial flow in the inner zone of the measured pressure derivative, we can get the radius r of the transformation zone: f :

[0162]

[0163] Fig.17 A schematic diagram showing pressure derivative curves at different inner and outer zone flow rate ratios according to an embodiment of the present invention is shown.

[0164] Fig.18 The figure shows the relationship between the abscissa value of the characteristic point 7 and the flow rate ratio between the inner and outer zones according to an embodiment of the present invention.

[0165] ⑦The seventh characteristic point is the horizontal line point of the radial flow in the non-transformed area. Given different flow ratios between the inner and outer zones, a set of pressure derivative curves are obtained, such as Fig.17 The relationship between the ordinate of the characteristic point and the flow ratio between the inner and outer zones is shown in Fig.18 As shown, the relationship expression is as follows:

[0166] (p' wD )7=0.5M 1,2 (31)

[0167] From formula (31), it can be seen that as long as the ordinate value Δp'7 of the measured pressure derivative horizontal line is obtained, the reservoir permeability k2 in the non-transformed area can be obtained:

[0168]

[0169] Adjust multiple characteristic points, first make the pressure derivative curve coincide with the pressure derivative curve in the actual test well curve, and then make the pressure curve coincide with the pressure curve in the actual test well curve, and calculate the well test interpretation information through the adjusted characteristic points and the fitting expression.

[0170] In summary, the present invention performs mathematical analysis based on the seepage characteristics corresponding to different areas in the volume fracturing horizontal well model, quickly and effectively fits the actual test well data of the volume fracturing horizontal well, and obtains the wellbore, reservoir and fracturing transformation parameters of the volume fracturing horizontal well, providing a basis for the well test interpretation and fracturing transformation effect evaluation of the volume fracturing horizontal well.

[0171] Those skilled in the art should understand that the purpose of the above description of the embodiments of the present invention is only to exemplarily illustrate the beneficial effects of the embodiments of the present invention, and is not intended to limit the embodiments of the present invention to any given examples.

[0172] An electronic device according to an embodiment of the present disclosure includes a memory and a processor.

[0173] The memory is used to store non-temporary computer-readable instructions. Specifically, the memory may include one or more computer program products, which may include various forms of computer-readable storage media, such as volatile memory and / or non-volatile memory. The volatile memory may, for example, include random access memory (RAM) and / or cache memory (cache), etc. The non-volatile memory may, for example, include read-only memory (ROM), hard disk, flash memory, etc.

[0174] The processor may be a central processing unit (CPU) or other forms of processing units having data processing capabilities and / or instruction execution capabilities, and may control other components in the electronic device to perform desired functions. In one embodiment of the present disclosure, the processor is used to run the computer-readable instructions stored in the memory.

[0175] Those skilled in the art should be able to understand that in order to solve the technical problem of how to obtain a good user experience, the present embodiment may also include well-known structures such as a communication bus and an interface, and these well-known structures should also be included in the protection scope of the present disclosure.

[0176] For detailed description of this embodiment, reference may be made to the corresponding descriptions in the aforementioned embodiments, which will not be repeated here.

[0177] An embodiment of the present disclosure provides a computer-readable storage medium storing a computer program. When the computer program is executed by a processor, the method for fitting and inverting characteristic points of a volumetric fracturing horizontal well is implemented.

[0178] According to the computer-readable storage medium of the embodiment of the present disclosure, non-transitory computer-readable instructions are stored thereon. When the non-transitory computer-readable instructions are executed by a processor, all or part of the steps of the above-mentioned methods of each embodiment of the present disclosure are executed.

[0179] The above-mentioned computer-readable storage media include, but are not limited to: optical storage media (e.g., CD-ROM and DVD), magneto-optical storage media (e.g., MO), magnetic storage media (e.g., magnetic tape or mobile hard disk), media with built-in rewritable non-volatile memory (e.g., memory card) and media with built-in ROM (e.g., ROM box).

[0180] The embodiments of the present invention have been described above, and the above description is exemplary, not exhaustive, and is not limited to the disclosed embodiments. Many modifications and changes will be apparent to those skilled in the art without departing from the scope and spirit of the described embodiments.

Claims

1. A method for fitting and inversion of characteristic points of volume fracturing horizontal wells, characterized in that: include: Establish a mathematical model of zoned seepage in volumetric fractured horizontal wells; Solving the mathematical model of partitioned seepage in the volumetric fractured horizontal well, and then calculating the bottom hole pressure and the bottom hole pressure derivative; Draw a volume fracturing horizontal well bottom hole pressure curve and a volume fracturing horizontal well bottom hole pressure derivative curve, and determine a plurality of characteristic points according to the volume fracturing horizontal well bottom hole pressure derivative curve; Establish a fitting expression between each characteristic point and the well test interpretation information; Adjusting the plurality of characteristic points so that the pressure derivative curve and the pressure curve coincide with the corresponding actual test well curve, and calculating the well test interpretation information through the adjusted characteristic points and the fitting expression; The volume fracturing horizontal well partition seepage mathematical model includes the main fracture zone seepage mathematical model, the transformation zone seepage mathematical model, and the non-transformation zone seepage mathematical model; Wherein, the mathematical model of seepage in the main fracture area is: Among them, p lfD is the dimensionless pressure of the main crack; p lsfD x is the dimensionless pressure of microcracks at the main crack wall; D is the dimensionless distance in the x direction; y D is the dimensionless distance in the y direction; F CD is the dimensionless conductivity of the fracture; X f The crack is half length.

2. The method for fitting and inversion of characteristic points of volume fracturing horizontal wells according to claim 1, wherein: The mathematical model of seepage in the transformation area is: Among them, p sfD is the dimensionless pressure of microcracks; p mD is the dimensionless pressure of the matrix; r D is the radial dimensionless radius; t D is dimensionless time; C D is the dimensionless wellbore storage coefficient; λ is the crossflow coefficient; ω is the storage capacity ratio.

3. The method for fitting and inversion of characteristic points of volume fracturing horizontal wells according to claim 1, wherein: The mathematical model of seepage in the non-transformation zone is: Among them, p 2D is the dimensionless pressure in the non-transformation area; γ D is the dimensionless permeability modulus; M 1,2 is the flow ratio between inner and outer zones, k f is the fracture permeability, k2 is the reservoir permeability in the non-transformed area; W is the energy storage coefficient ratio of the inner and outer zones, φ m is the porosity of the matrix system, φ sf is the porosity of the fracture system; e is the natural logarithm.

4. The method for fitting and inversion of characteristic points of volume fracturing horizontal wells according to claim 1, wherein: Solving the mathematical model of the volumetric fractured horizontal well partition seepage flow, and then calculating the bottom hole pressure and the bottom hole pressure derivative includes: Solve the general solutions of the mathematical model of seepage in the reformed area and the mathematical model of seepage in the non-reformed area respectively; Calculate source function; The mathematical model of seepage in the main fracture zone is combined with the source function to calculate the bottom hole pressure response; Performing Laplace numerical inversion on the bottom hole pressure response by using the Stehfest algorithm to obtain the bottom hole pressure; The bottom hole pressure is differentiated to obtain the bottom hole pressure derivative.

5. The method for fitting and inversion of characteristic points of volume fracturing horizontal wells according to claim 4, wherein: The source function is: Where G is the source function; A and B are coefficients; I0 is a first-order modified Bessel function; K0 is a second-order modified Bessel function; u is a Laplace space variable; r D is the radial dimensionless radius.

6. The method for fitting and inversion of characteristic points of volume fracturing horizontal wells according to claim 4, wherein: The bottom hole pressure response is: in, is the dimensionless bottom hole pressure including the wellbore reservoir effect in Laplace space; is the dimensionless bottom hole pressure in Laplace space; C D is the dimensionless wellbore storage coefficient; u is the Laplace space variable.

7. An electronic device, characterized in that: The electronic device comprises: A memory storing executable instructions; A processor, wherein the processor runs the executable instructions in the memory to implement the volume fracturing horizontal well characteristic point fitting inversion method according to any one of claims 1 to 6.

8. A computer-readable storage medium, characterized in that: The computer-readable storage medium stores a computer program, and when the computer program is executed by a processor, the method for fitting and inverting characteristic points of a volume fracturing horizontal well according to any one of claims 1 to 6 is implemented.

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