Production dynamic analysis method and equipment for fractured horizontal wells under inter-well interference conditions

Abstract

The present disclosure provides a method and apparatus for analyzing the production dynamics of fractured horizontal wells under inter-well interference conditions. The method comprises: constructing a mathematical model for analyzing the production dynamics of fractured horizontal wells under inter-well interference conditions; semi-analytically solving the mathematical model to obtain a production solution for the fractured horizontal wells under inter-well interference conditions; determining a pressure-normalized production curve under inter-well interference conditions based on the production solution; and performing a plate fit between the pressure-normalized production curve and actual oilfield production data to determine reservoir parameters. Implementing the technical solution of the present disclosure can quickly and accurately obtain reservoir parameters.

Description

Technical Field

[0001] The present invention relates to the technical field of oilfield development, and in particular to a production dynamic analysis method and equipment for a fractured horizontal well under inter-well interference conditions. Background Art

[0002] With the rapid and sustained development of the economy, the demand for oil and gas resources in my country has been increasing day by day. The development of conventional oil and gas resources has entered the middle and late stages, and the overall quality of domestic conventional oil and gas resources has declined. Therefore, the development and utilization of unconventional oil and gas resources has become a research focus for solving the shortage of oil and gas resources.

[0003] Unconventional oil and gas reservoirs, due to their low porosity and low permeability, are difficult to achieve effective development using conventional extraction technologies. The effective combination of horizontal well production and hydraulic fracturing is crucial for the successful development of tight reservoirs. Hydraulic fracturing can activate natural fractures in the reservoir, improve the formation's permeability, and increase the reservoir's effective permeability, making the development of unconventional oil and gas resources feasible. However, when oil and gas reservoirs reach a certain stage of development, field development plans must be adjusted to increase recoverable reserves and improve oil and gas recovery rates. Therefore, accurate understanding of reservoir conditions and fluid flow patterns is essential for maximizing the economic benefits of oil and gas reservoirs. Production performance analysis methods using oil and gas well production data can interpret basic formation parameters, evaluate the effectiveness of stimulation measures, and predict production and geological reserves, making them crucial for adjusting oil and gas field development plans. Therefore, a production performance analysis method for fractured horizontal wells that considers interwell interference is urgently needed. Summary of the Invention

[0004] In order to solve at least one technical problem in the prior art, the present disclosure provides a production dynamic analysis method and device for a fractured horizontal well under inter-well interference conditions;

[0005] According to a first aspect of the present disclosure, a method for analyzing production performance of a fractured horizontal well under inter-well interference conditions is provided, comprising:

[0006] Construct a mathematical model for production dynamic analysis and seepage of fractured horizontal wells under inter-well interference conditions;

[0007] A semi-analytical solution is obtained for the mathematical model of seepage for production dynamic analysis to obtain a production solution for a fractured horizontal well under inter-well interference conditions;

[0008] determining a pressure-normalized production curve under an inter-well interference condition according to the production solution;

[0009] The pressure normalized production curve is fitted with actual oilfield production data to determine reservoir parameters.

[0010] Optionally, constructing a mathematical model for production performance analysis and seepage of a fractured horizontal well under inter-well interference conditions includes:

[0011] Based on the physical model of fractured horizontal wells under inter-well interference conditions, a mathematical model for production dynamic analysis and seepage of fractured horizontal wells under inter-well interference conditions is constructed. The physical model is constructed according to the geological parameters of the formation, the physical properties of the fluid, the fracturing production increase method and the historical production data of the oil wells.

[0012] Optionally, the assumptions of the physical model include:

[0013] The reservoir has uniform water quality and thickness, the initial pressure at each point in the reservoir is the same, and the effect of temperature on fluid flow is ignored. The fluid in the reservoir is a single-phase slightly compressible fluid that satisfies Darcy's law. The multiple hydraulic fractures formed by artificial fracturing completely penetrate the formation, and the length of the fractures is much greater than the fracture height and width. The flow in the hydraulic fractures is one-dimensional and satisfies Darcy's law. Multiple fractured horizontal wells are all under constant flow pressure production conditions, the target well has a variable bottomhole flow pressure, and the commissioning time of adjacent wells and the target well is different or the same.

[0014] Optionally, constructing a mathematical model for production performance analysis of fractured horizontal wells under inter-well interference conditions includes:

[0015] The production dynamic analysis seepage mathematical model is constructed based on dimensionless variables, wherein the dimensionless variables include dimensionless production time, dimensionless bottom hole pressure and dimensionless production.

[0016] Optionally, the production dynamic analysis seepage mathematical model includes an oil reservoir seepage mathematical model and a hydraulic fracture seepage mathematical model;

[0017] The reservoir seepage mathematical model and its initial conditions and internal and external boundary conditions are as follows:

[0018]

[0019] Among them, p D is the dimensionless pressure of the reservoir system, r D is the dimensionless radial distance, u is the Laplace variable, t D is the dimensionless production time, q D is the dimensionless production of the reservoir system;

[0020] The mathematical model of hydraulic fracture seepage and its initial conditions and internal and external boundary conditions are as follows:

[0021]

[0022] Among them, p hfD is the dimensionless pressure of the hydraulic fracture system, x Dis the dimensionless distance in the direction of the hydraulic fracture, C hfD is the dimensionless hydraulic fracture conductivity, q hfD is the dimensionless production of the hydraulic fracture system, t D is the dimensionless production time, p wD is the dimensionless bottom hole pressure, L hfD is the half-length of the dimensionless hydraulic fracture.

[0023] Optionally, the semi-analytical solution of the seepage mathematical model for the production dynamic analysis to obtain the production solution of the fractured horizontal well under the inter-well interference condition includes:

[0024] Semi-analytically solving the production performance analysis seepage mathematical model using Laplace transform to obtain a general solution of the hydraulic fracture model contained in the production performance analysis seepage mathematical model and a general solution of the reservoir model contained in the production performance analysis seepage mathematical model;

[0025] Taking into account the influence of inter-well interference, the general solution of the hydraulic fracture model is coupled with the general solution of the reservoir model to obtain the production solution.

[0026] Optionally, the semi-analytical solution of the seepage mathematical model for the production dynamic analysis to obtain the production solution of the fractured horizontal well under the inter-well interference condition includes:

[0027] The production dynamic analysis mathematical model is solved according to the initial conditions, inner boundary conditions and outer boundary conditions to obtain the single well production solution. The pressure superposition term of the adjacent wells for the target well is calculated by utilizing the production ratio relationship and the superposition principle, and the pressure superposition term is superimposed and coupled with the flow rate and pressure term of the target well to obtain the production solution.

[0028] Optionally, the general solution of the hydraulic fracture model is:

[0029]

[0030] Among them, p i，D is the dimensionless pressure of each hydraulic fracture segment, i is the hydraulic fracture segment number, p wD is the dimensionless bottom hole pressure, subscript k represents the different hydraulic fractures in the multi-well model, C hfD is the dimensionless hydraulic fracture conductivity, ΔL D is the dimensionless hydraulic fracture segment length, q hfD is the dimensionless production of the hydraulic fracture system, σ is the number of fracture segments in each hydraulic fracture;

[0031] The general solution of the reservoir model pressure is:

[0032]

[0033] pD is the dimensionless pressure of the reservoir system, x D is the dimensionless distance in the direction of the hydraulic fracture, ΔL D is the dimensionless hydraulic fracture segment length, q D is the dimensionless production of the reservoir system, K0 is the second-order zero-order Bessel function, u is the Laplace variable, r D is the dimensionless radial distance, and l is the integration variable.

[0034] Optionally, determining a pressure-normalized production curve under an inter-well interference condition according to the production solution includes:

[0035] A dynamic analysis method for unstable production under inter-well interference is established by using multi-well material balance time and pressure-normalized production. A pressure-normalized production curve under inter-well interference conditions is drawn. The pressure-normalized production curve includes curves showing changes of pressure-normalized production under inter-well interference conditions and its integral and integral derivative with material balance time.

[0036] Optionally, performing plate fitting on the pressure-normalized production curve and actual oilfield production data to determine reservoir parameters includes:

[0037] Performing plate fitting on the pressure normalized production curve and actual oilfield production data to obtain fitting points;

[0038] Based on the fitting points, the reservoir parameters are calculated.

[0039] According to a second aspect of the present disclosure, an electronic device is provided, comprising:

[0040] processor; and

[0041] Memory for storing programs,

[0042] The program includes instructions, which, when executed by the processor, enable the processor to perform the method according to any one of the embodiments of the present disclosure.

[0043] One or more technical solutions provided in the embodiments of the present application construct a mathematical model for production dynamic analysis and seepage under the premise of considering inter-well interference, and determine the pressure-normalized production curve based on the production solution obtained from the mathematical model for production dynamic analysis and seepage, and determine the reservoir parameters by fitting the pressure-normalized production curve with the actual production data of the oil field. Therefore, accurate reservoir parameters can be obtained quickly. BRIEF DESCRIPTION OF THE DRAWINGS

[0044] The accompanying drawings illustrate exemplary embodiments of the present disclosure and together with the description serve to explain the principles of the present disclosure. These drawings are included to provide a further understanding of the present disclosure and are incorporated in and constitute a part of this specification.

[0045] Figure 1 A flow chart showing a method for analyzing production performance of a fractured horizontal well under inter-well interference conditions according to an exemplary embodiment of the present disclosure is shown;

[0046] Figure 2 A schematic diagram showing a physical model according to an exemplary embodiment of the present disclosure is shown;

[0047] Figure 3 A graph showing pressure-normalized production and its integral and integral derivative versus material balance time according to an exemplary embodiment of the present disclosure is shown;

[0048] Figure 4 FIG4 shows the fitting result of the target well production curve before the well-to-well interference in the presence of the well-to-well interference according to an exemplary embodiment of the present disclosure;

[0049] Figure 5 FIG2 shows the fitting result of the target well production curve after the well-to-well interference according to an exemplary embodiment of the present disclosure;

[0050] Figure 6 A structural block diagram of an electronic device according to an exemplary embodiment of the present disclosure is shown. DETAILED DESCRIPTION

[0051] The following describes embodiments of the present disclosure in more detail with reference to the accompanying drawings. Although certain embodiments of the present disclosure are shown in the accompanying drawings, it should be understood that the present disclosure can be implemented in various forms and should not be construed as limited to the embodiments described herein. Rather, these embodiments are provided to provide a more thorough and complete understanding of the present disclosure. It should be understood that the drawings and embodiments of the present disclosure are for illustrative purposes only and are not intended to limit the scope of protection of the present disclosure.

[0052] It should be understood that the various steps described in the method embodiments of the present disclosure may be performed in different orders and / or in parallel. In addition, the method embodiments may include additional steps and / or omit the steps shown. The scope of the present disclosure is not limited in this respect.

[0053] The term "including" and its variations used in this document are open inclusions, that is, "including but not limited to". The term "based on" means "based at least in part on". The term "one embodiment" means "at least one embodiment"; the term "another embodiment" means "at least one other embodiment"; the term "some embodiments" means "at least some embodiments". The relevant definitions of other terms will be given in the description below. It should be noted that the concepts of "first", "second", etc. mentioned in this disclosure are only used to distinguish different devices, modules or units, and are not used to limit the order or interdependence of the functions performed by these devices, modules or units.

[0054] It should be noted that the modifications of "one" and "multiple" mentioned in the present disclosure are illustrative rather than restrictive, and those skilled in the art should understand that unless otherwise clearly indicated in the context, they should be understood as "one or more".

[0055] The names of the messages or information exchanged between multiple devices in the embodiments of the present disclosure are only used for illustrative purposes and are not used to limit the scope of these messages or information.

[0056] The following describes the solution of the present disclosure with reference to the accompanying drawings:

[0057] See also Figure 1 , Figure 1 A production performance analysis method for a fractured horizontal well under inter-well interference conditions according to an exemplary embodiment of the present disclosure is shown, comprising:

[0058] S1, construct a mathematical model for production dynamic analysis and seepage of fractured horizontal wells under inter-well interference conditions;

[0059] In step S1, a mathematical model for production dynamic analysis and seepage of fractured horizontal wells under inter-well interference conditions can be constructed based on the physical model of the fractured horizontal wells under inter-well interference conditions. The physical model is constructed according to the geological parameters of the formation, the physical properties of the fluid, the fracturing production increase method and the historical production data of the oil wells.

[0060] For example, the target well block is located in the Ordos Basin in north-central China, covering a total area of 3.7 million km². The target well has an effective horizontal well length of 750 m, extending from 2070 m to 2820 m. The wellbore has a deflection depth of 2612 m and a vertical depth of 1935 m. Well logging data indicates a reservoir thickness of 8.08 m and a porosity of 5%. Fracturing production began in May 2011, with a target reservoir temperature of 57°C. The target well and the interference well had different production times. Basic parameters, including geological parameters, fluid physical properties, and fracturing stimulation methods, are shown in Table 1.

[0061] Table 1

[0062]

[0063] Among them, the physical model is Figure 2As shown in Figure 2, the assumptions of the physical model include: (1) the reservoir water quality and thickness are uniform, the initial pressure at each point in the reservoir is the same, and the effect of temperature on fluid flow is ignored; (2) the fluid in the reservoir is a single-phase slightly compressible fluid that satisfies Darcy's law; (3) the multiple hydraulic fractures formed by artificial fracturing completely penetrate the formation, the length of the fracture is much larger than the fracture height and fracture width, the flow in the hydraulic fracture is one-dimensional and satisfies Darcy's law; (4) multiple fractured horizontal wells are all under constant flow pressure production conditions, the target well has a variable bottomhole flow pressure, and the production time of adjacent wells is different or the same as that of the target well; (5) the target well has a variable bottomhole flow pressure, and the production time of adjacent wells can be different from that of the target well.

[0064] In step S1, a mathematical model for production dynamic analysis of seepage can be constructed based on dimensionless variables, wherein the dimensionless variables include dimensionless production time, dimensionless bottom hole pressure, and dimensionless production rate. The dimensionless variables may also include dimensionless bottom hole pressure ratio.

[0065] The mathematical model for production dynamic analysis seepage constructed includes a reservoir seepage mathematical model and a hydraulic fracture seepage mathematical model. For example, the definition of dimensionless variables and the construction of the mathematical model for production dynamic analysis are as follows:

[0066] Dimensionless production time t D :

[0067]

[0068] Where k is the permeability of the reservoir system, μ is the fluid viscosity, is the reservoir porosity, C t is the comprehensive compression coefficient, x f is the half length of hydraulic fracture, and t is the production time.

[0069] The dimensionless pressure p of the reservoir system D :

[0070]

[0071] Where k is the permeability of the reservoir system, h is the reservoir thickness, and q sc is the production under standard conditions, t represents the target well, μ is the fluid viscosity, B is the volume coefficient, and p i is the original formation pressure of the reservoir, and p is the pressure of the reservoir system.

[0072] Dimensionless pressure p of hydraulic fracture system hfD :

[0073]

[0074] Among them, k nf is the permeability of the hydraulic fracture system, h is the reservoir thickness, qsc is the production under standard conditions, t represents the target well, B is the volume coefficient, p i is the original formation pressure of the reservoir, p hf is the hydraulic fracture pressure.

[0075] Dimensionless bottomhole flowing pressure, which is assumed to be a dimensionless function of time in the complex internal boundary model:

[0076]

[0077] Among them, p wD is the dimensionless bottom hole pressure, k is the reservoir system permeability, h is the reservoir thickness, μ is the fluid viscosity, B is the volume coefficient, and p i is the original formation pressure of the reservoir, p w is the bottom hole flowing pressure, the subscript j represents different wells in the multi-well system, t represents the target well in the multi-well system, and 2, 3, 4…N represent the adjacent wells of the target well in the multi-well system.

[0078] The dimensionless production of the reservoir system q D :

[0079]

[0080] Where μ is the fluid viscosity, B is the volume coefficient, k is the reservoir system permeability, h is the reservoir thickness, and p i is the original formation pressure of the reservoir, p w is the bottom hole pressure, q sc is the production of the reservoir system under standard conditions.

[0081] Dimensionless production q of hydraulic fracture system hfD :

[0082]

[0083] Where μ is the fluid viscosity, B is the volume coefficient, k is the reservoir system permeability, h is the reservoir thickness, and p i is the original formation pressure of the reservoir, q hf,sc is the production under standard conditions of the hydraulic fracture system.

[0084] Dimensionless hydraulic fracture conductivity C hfD :

[0085]

[0086] Among them, k hf is the hydraulic fracture system permeability, w is the hydraulic fracture width, k is the reservoir system permeability, x f It is half the length of the hydraulic fracture.

[0087] Dimensionless hydraulic fracture half length LhfD :

[0088]

[0089] x f is the half length of hydraulic fracture:

[0090] Dimensionless radial distance:

[0091]

[0092] Where r is the radial distance, x f is the half length of the hydraulic fracture, and x, y are the distances in the rectangular coordinate system.

[0093] Dimensionless boundary distance r eD :

[0094]

[0095] Among them, r e is the supply frontier distance, x f It is half the length of the hydraulic fracture.

[0096] Dimensionless distance x in the direction of hydraulic fracture D :

[0097]

[0098] Among them, x is the rectangular coordinate system distance, x f It is half the length of the hydraulic fracture.

[0099] Dimensionless hydraulic fracture spacing H D :

[0100]

[0101] Where H is the hydraulic fracture interval of multi-stage fracturing; x f It is half the length of the hydraulic fracture.

[0102] Dimensionless well spacing d D :

[0103]

[0104] Where d is the distance from the adjacent well to the target well, x f It is half the length of the hydraulic fracture.

[0105] The mathematical model of reservoir seepage in the pull-type space and its initial conditions and internal and external boundary conditions are as follows:

[0106]

[0107] Among them, p Dis the dimensionless pressure of the reservoir system, r D is the dimensionless radial distance, u is the Laplace variable, t D is the dimensionless production time, q D is the dimensionless production of the reservoir system.

[0108] The first formula in the above model is the equation of the reservoir seepage mathematical model, the second formula is defined as the initial condition, the third formula is the outer boundary condition, and the fourth formula is the inner boundary condition.

[0109] The mathematical model of hydraulic fracture seepage and its initial conditions and internal and external boundary conditions are as follows:

[0110]

[0111] Among them, p hfD is the dimensionless pressure of the hydraulic fracture system, x D is the dimensionless distance in the direction of the hydraulic fracture, C hfD is the dimensionless hydraulic fracture conductivity, q hfD is the dimensionless production of the hydraulic fracture system, t D is the dimensionless production time, p wD is the dimensionless bottom hole pressure, L hfD is the half-length of the dimensionless hydraulic fracture.

[0112] In the above model, the first formula is the equation of the hydraulic fracture seepage mathematical model, the second formula is the initial condition, the third and fourth formulas are the inner boundary conditions, and the fifth formula is the outer boundary condition.

[0113] Among them, in the above formula:

[0114] p is the pressure of the reservoir system, MPa;

[0115] p i is the original formation pressure of the reservoir, MPa;

[0116] p w is the bottom hole flowing pressure, MPa;

[0117] k is the reservoir system permeability, D;

[0118] h is the reservoir thickness, m;

[0119] B is the volume coefficient, m 3 / m 3 ;

[0120] r is the radial distance, m;

[0121] μ is the fluid viscosity, mPa.s;

[0122] q scis the output under standard conditions, m 3 ;

[0123] t is the production time, h;

[0124] C t is the comprehensive compression coefficient, MPa -1 ;

[0125] is the reservoir porosity;

[0126] re is the supply frontier distance, m;

[0127] x f is the half length of hydraulic fracture, m;

[0128] H is the hydraulic fracture interval of multi-stage fracturing, m;

[0129] q is the oil well production, m3;

[0130] w is the width of the hydraulic fracture, m;

[0131] k hf is the permeability of the hydraulic fracture system, D;

[0132] p hf is the hydraulic fracture pressure, MPa;

[0133] x,y are the distances in the rectangular coordinate system, m;

[0134] u is the Laplace variable;

[0135] d Distance from adjacent well to target well, m.

[0136] S2, semi-analytically solves the mathematical model of seepage for production dynamic analysis and obtains the production solution of fractured horizontal wells under inter-well interference conditions.

[0137] In step S2, the production performance analysis seepage mathematical model can be semi-analyzed using a Laplace transform to obtain a general solution of the hydraulic fracture model contained in the production performance analysis seepage mathematical model and a general solution of the reservoir model contained in the production performance analysis seepage mathematical model (a dimensionless pressure solution of a line source in Laplace space). The general solution of the hydraulic fracture model is coupled with the general solution of the reservoir model to obtain a production solution, taking into account the influence of interwell interference. For example, the production performance analysis seepage mathematical model is a production performance analysis mathematical model for multi-stage fractured horizontal wells in a dense oil reservoir under interwell interference.

[0138] In step S2, the production performance analysis mathematical model is solved based on the initial conditions, internal boundary conditions, and external boundary conditions to obtain a single-well production solution. Using the production ratio relationship and the superposition principle, the pressure superposition term of the adjacent wells relative to the target well is calculated and superimposed with the flow rate and pressure terms of the target well to obtain the production solution. Here, the production solution can be understood as a production capacity equation, and the production solution obtained here is an unstable production solution.

[0139] Specifically, the general solution of the hydraulic fracture model (dimensionless partial differential equation in hydraulic fracture) is:

[0140]

[0141] Among them, p i，D is the dimensionless pressure of each hydraulic fracture segment, i is the hydraulic fracture segment number, p wD is the dimensionless bottom hole pressure, subscript k represents the different hydraulic fractures in the multi-well model, C hfD is the dimensionless hydraulic fracture conductivity, ΔL D is the dimensionless hydraulic fracture segment length, q hfD is the dimensionless production of the hydraulic fracture system, and σ is the number of fracture segments in each hydraulic fracture.

[0142] The length of the hydraulic fracture section and the node position of the hydraulic fracture section satisfy the formula:

[0143]

[0144] Here, the subscript k represents different hydraulic fractures in the multi-well model.

[0145] k=1,2,3,4,…m hf，total

[0146] m hf,total is the total number of hydraulic fractures.

[0147] The general solution of reservoir model pressure (in the form of line source integral) is:

[0148]

[0149] Among them, p D is the dimensionless pressure of the reservoir system, x D is the dimensionless distance in the direction of the hydraulic fracture, ΔL D is the dimensionless hydraulic fracture segment length, q D is the dimensionless production of the reservoir system, K0 is the second-order zero-order Bessel function, u is the Laplace variable, r D is the dimensionless radial distance, and l is the integral variable.

[0150] In order to take into account the arbitrary distribution characteristics of hydraulic fractures (such as hydraulic fracture length, inclination, number, etc.), the dimensionless distance r between different fracture segments is D It can be further viewed as a dimensionless function of well spacing and fracture spacing:

[0151] r D =f(d D ,H D )

[0152] Where: d D is the dimensionless well spacing, H D is the dimensionless hydraulic fracture interval.

[0153] The superposition between wells is achieved by using the pressure superposition on the line source of the general solution of the reservoir model, so it can be expressed as:

[0154]

[0155] Where j represents the different wells in the multi-well system, t represents the target well in the multi-well system, N is the number of wells in the multi-well system, mhf is the number of hydraulic fractures in each well, σ is the number of fracture segments in each hydraulic fracture, and subscript k represents the different hydraulic fractures in the multi-well model. σk is the number of crack segments of the K-th crack, is the dimensionless flow rate of the g-th crack segment of the k-th crack, x k,g,D is the dimensionless relative position of the gth crack segment of the kth crack on the kth crack, ΔL k,g,D is the dimensionless length of the gth crack segment of the kth crack, K0 is the second-order zero-order Bessel function, u is the Laplace variable, f(u) is 1, r k,g,D is the dimensionless position of the gth fracture segment of the kth fracture, l is the integration variable, and mhf,j is the number of hydraulic fractures in the jth well.

[0156] In the above formula: K0 is the second-order zero-order Bessel function;

[0157] σ is the number of fracture segments in each hydraulic fracture;

[0158] N hf is the number of hydraulic fracture segments;

[0159] N is the number of wells in the multi-well system;

[0160] mhf is the number of hydraulic fractures per well;

[0161] m hf,total is the total number of hydraulic fractures;

[0162] u is the Laplace variable;

[0163] l is the integral variable;

[0164] ΔL D is the dimensionless hydraulic fracture segment length;

[0165] f(t) is a time-dependent constant.

[0166] Specifically, the superposition method is used to couple the general solution of the hydraulic fracture model with the general solution of the reservoir model while considering the influence of inter-well interference to obtain the production solution:

[0167] The general solution of the reservoir model after considering pressure superposition is expressed in matrix form:

[0168]

[0169] Among them, A N,t This is the matrix form of the general solution of the reservoir of the target well for the Nth well. Similarly, the meanings of other parameters in the matrix can be known, which will not be described in detail here.

[0170] The general solution of hydraulic fracture is expressed in matrix form:

[0171]

[0172] Among them, B N,t This is the matrix form of the general solution of the hydraulic fracture of the target well for the Nth well. Similarly, the meanings of other parameters in the matrix can be known and will not be described in detail here.

[0173] Taking the i-th production well as an example, the pressure superposition matrix of the general solution of the reservoir model can be expressed as:

[0174]

[0175] The variables that need to be solved include the pressure and flow terms of each hydraulic fracture segment of the target well:

[0176]

[0177]

[0178] Where mhf,t represents the number of hydraulic fractures in the t-th well, σ g Indicates the number of crack segments of the g-th crack.

[0179] It also includes the pressure and flow terms of each hydraulic fracture segment of adjacent wells:

[0180]

[0181]

[0182] in, represents the total number of fracture segments, mhf,k represents the number of hydraulic fractures in the kth well, σ g represents the number of crack segments of the g-th crack, is the flow term of each hydraulic fracture segment, is the pressure term of each hydraulic fracture segment. In this embodiment, the upper horizontal line of the parameter represents that the corresponding parameter is the corresponding parameter in the Laplace space.

[0183] Dimensionless bottom hole flowing pressure of target well and adjacent wells:

[0184]

[0185] Under complex internal boundary conditions, the bottomhole pressure of the target well and adjacent wells is considered as a dimensionless time-varying function. For the target well, the bottomhole pressure at different time steps in Laplace space can be expressed as:

[0186]

[0187] in, It represents the dimensionless bottom hole flowing pressure of target well t from the first moment 1 to the nth moment.

[0188] For adjacent wells, the changing bottom hole pressure can be expressed as:

[0189]

[0190] in, represents the dimensionless bottom hole flowing pressure of adjacent well j from the first moment 1 to the nth moment.

[0191] Finally, the production term of the jth well in the Laplace domain is calculated by summing the flow terms of each hydraulic fracture segment. The production term of the jth well in the Laplace domain can be inverted into real space using the Stehfest numerical inversion algorithm to obtain the production Q of the jth well. j .

[0192]

[0193] in, is the flow term of the j-th fracture segment, is the production term of the jth well, mhf,j is the number of hydraulic fractures in the jth well, σ g is the number of fracture segments of the g-th hydraulic fracture in the j-th well.

[0194] S3, determining the pressure normalized production curve under the inter-well interference condition based on the production solution.

[0195] In step S3, a dynamic analysis method for unstable production under inter-well interference can be established by using the material balance time and pressure-normalized production of multiple wells, and a pressure-normalized production curve under inter-well interference conditions can be drawn. The pressure-normalized production curve includes curves showing how the pressure-normalized production under inter-well interference conditions and its integral and integral derivative change with material balance time.

[0196] The pressure and production data of any well in a multi-well production process can be expressed as pressure normalized production (PNR):

[0197]

[0198] Among them, Q j is the production term of the jth well, p i is the original formation pressure of the reservoir, p w is the bottom hole flowing pressure, subscript j is the well number j = t, 2, 3, 4…N, f(t) is a time-related constant, G is the geological reserve, C t is the comprehensive compression coefficient, Corrects material balance time for cumulative production from multiple wells.

[0199] Correcting material balance time using the cumulative production of multiple wells based on material balance of a multi-well system

[0200]

[0201] Among them, N p,total is the cumulative production of multiple wells, Q j is the production item of the jth well, Q i is the production term of the i-th well.

[0202] The dimensionless production and time in the quasi-steady-state flow stage under boundary influence can be defined as:

[0203]

[0204]

[0205] Among them, q D,BDF is the dimensionless production in the pseudo-steady-state flow stage under boundary influence, μ is the fluid viscosity, B is the volume coefficient, k is the permeability of the reservoir system, h is the reservoir thickness, Q j is the production term of the jth well, p i is the original formation pressure of the reservoir, p w is the bottom hole flowing pressure, subscript j is the well number, representing different wells in the multi-well system, j = t, 2, 3, 4…N, r eD is the dimensionless boundary distance, β D is the ratio of total production to target well production, t Dis the dimensionless production time, is the reservoir porosity, C t is the comprehensive compression coefficient, A is the reservoir supply area, is the time to correct material balance, and N is the number of production wells.

[0206] In the above formula:

[0207] G is geological reserves, m3;

[0208] N p,total is the cumulative production of multiple wells, m3;

[0209] q(t) is the daily production of the target well, m3 / d;

[0210] r eD is the dimensionless boundary distance;

[0211] N is the number of production wells;

[0212] β D is the ratio of total production to target well production;

[0213] r eD is the dimensionless boundary distance;

[0214] A is the reservoir supply area, m2;

[0215] f(t) is a time-dependent constant;

[0216] The subscript j is the well number, j = t, 2, 3, 4…N.

[0217] It can be known that the curves of pressure normalized production and its integral and integral derivative changing with material balance time under well-to-well interference conditions may include three curves: pressure normalized production, pressure normalized production integral, and pressure normalized production integral derivative. Figure 3 As shown, the curves from top to bottom on the far right are the pressure normalized production integral, the pressure normalized production integral derivative and the pressure normalized production curve.

[0218] S4, performing a plate fitting between the pressure normalized production curve and the actual production data of the oil field to determine the reservoir parameters.

[0219] In step S4, the pressure-normalized production curve and the actual production data of the oil field may be fitted to obtain fitting points, and the reservoir parameters may be calculated based on the fitting points.

[0220] Specifically, the actual production data of the oil field can be used, combined with chart fitting and automatic fitting to finally form a production dynamic analysis method under well interference. The model proposed by the present invention obtains parameters such as target well, adjacent well properties and formation physical properties by fitting the actual production data, including: initial reservoir pressure, permeability, crossflow coefficient, storage volume ratio, well spacing, hydraulic fracture length, boundary distance, boundary properties and control volume, etc. Parameters provide a reference for the study of production dynamic analysis methods under well interference. The fitting parameter results are shown in Table 2. The fitting results are as follows Figure 4 and Figure 5 As shown, Figure 4 is the fitting result of the target well production curve before the well-to-well interference. Figure 5 It is the fitting result of the target well production curve after inter-well interference in the presence of inter-well interference.

[0221] Table 2

[0222]

[0223] Exemplarily, the calculated reservoir parameters are as follows:

[0224]

[0225] Among them, the reservoir parameter k is the permeability of the reservoir system, μ is the fluid viscosity, B is the volume coefficient, h is the reservoir thickness, Q j is the production term of the jth well, p i is the original formation pressure of the reservoir, p w is the bottom hole pressure, subscript j is the well number j = t, 2, 3, 4…N, r eD is the dimensionless boundary distance, q D,BDF is the dimensionless production in the quasi-steady-state flow stage under boundary influence, M is the fitting point, r eD is the dimensionless boundary distance, β D is the ratio of total production to target well production.

[0226]

[0227] Among them, the reservoir parameter G is geological reserves, is the material equilibrium time, t D is the dimensionless production time, q j is the pressure term of each hydraulic fracture segment, p i is the original formation pressure of the reservoir, p w is the bottom hole pressure, subscript j is the well number j=t,2,3,4…N, q D,BDF Dimensionless production in the pseudo-steady-state flow stage under boundary influence, M is the fitting point, C t is the comprehensive compression coefficient,

[0228]

[0229] Among them, A is the reservoir supply area, G is the geological reserves, B is the volume coefficient, h is the reservoir thickness, is the porosity, S w is the water saturation,

[0230]

[0231] Where re is the supply frontier distance and A is the reservoir supply area.

[0232]

[0233] Among them, x f is the half length of hydraulic fracture, r eD is the dimensionless frontier distance, re is the supply frontier distance, S w is the water saturation.

[0234] The present invention provides a production dynamic analysis method for fractured horizontal wells considering inter-well interference. On the premise of considering inter-well interference, a production capacity calculation model for multi-stage fractured horizontal wells in tight oil reservoirs under constant / variable bottom hole pressure conditions is established to provide theoretical guidance for the production dynamic analysis of fractured horizontal wells in tight oil reservoirs.

[0235] Based on the clarification of unstable seepage characteristics, this paper establishes a mathematical model for unstable seepage under constant or variable bottomhole pressure for fractured horizontal wells, taking into account interwell interference. This model is used to develop a production model for fractured horizontal wells under interwell interference. This model is then solved to obtain the unstable production characteristic curve of the target well under the influence of adjacent wells. The pressure-normalized yield (PNR) and its derivative are then analyzed, resulting in a comprehensive method for analyzing the production performance of fractured horizontal wells under interwell interference.

[0236] The exemplary embodiments of the present disclosure further provide an electronic device including: at least one processor; and a memory communicatively connected to the at least one processor. The memory stores a computer program executable by the at least one processor, which, when executed by the at least one processor, causes the electronic device to perform a method according to an exemplary embodiment of the present disclosure.

[0237] Exemplary embodiments of the present disclosure also provide a non-transitory computer-readable storage medium storing a computer program, wherein the computer program, when executed by a processor of a computer, is used to cause the computer to perform the method according to an embodiment of the present disclosure.

[0238] Exemplary embodiments of the present disclosure further provide a computer program product, including a computer program, wherein when the computer program is executed by a processor of a computer, it is used to cause the computer to perform the method according to the embodiment of the present disclosure.

[0239] refer to Figure 6 , a block diagram of an electronic device 600 that can serve as a server or client of the present disclosure will now be described, which is an example of a hardware device that can be applied to various aspects of the present disclosure. The electronic device is intended to represent various forms of digital electronic computer devices, such as laptop computers, desktop computers, workstations, personal digital assistants, servers, blade servers, mainframe computers, and other suitable computers. The electronic device can also represent various forms of mobile devices, such as personal digital processing, cellular phones, smart phones, wearable devices and other similar computing devices. The components shown herein, their connections and relationships, and their functions are merely examples and are not intended to limit the implementation of the present disclosure described and / or required herein.

[0240] like Figure 6 As shown, the electronic device 600 includes a computing unit 601, which can perform various appropriate actions and processes according to a computer program stored in a read-only memory (ROM) 602 or a computer program loaded from a storage unit 608 into a random access memory (RAM) 603. Various programs and data required for the operation of the electronic device 600 can also be stored in the RAM 603. The computing unit 601, the ROM 602, and the RAM 603 are connected to each other via a bus 604. An input / output (I / O) interface 605 is also connected to the bus 604.

[0241] Multiple components within electronic device 600 are connected to I / O interface 605, including an input unit 606, an output unit 607, a storage unit 608, and a communication unit 609. Input unit 606 can be any type of device capable of inputting information into electronic device 600. Input unit 606 can receive input numeric or character information and generate key input signals related to user settings and / or function control of the electronic device. Output unit 607 can be any type of device capable of presenting information and may include, but is not limited to, a display, a speaker, a video / audio output terminal, a vibrator, and / or a printer. Storage unit 604 may include, but is not limited to, a magnetic disk or an optical disk. Communication unit 609 allows electronic device 600 to exchange information / data with other devices via computer networks such as the Internet and / or various telecommunication networks and may include, but is not limited to, a modem, a network card, an infrared communication device, a wireless communication transceiver and / or a chipset, such as a Bluetooth™ device, a WiFi device, a WiMax device, a cellular communication device, and / or the like.

[0242] The computing unit 601 may be a variety of general and / or special processing components with processing and computing capabilities. Some examples of the computing unit 601 include, but are not limited to, a central processing unit (CPU), a graphics processing unit (GPU), various dedicated artificial intelligence (AI) computing chips, various computing units that run machine learning model algorithms, digital signal processors (DSPs), and any appropriate processors, controllers, microcontrollers, etc. The computing unit 601 performs the various methods and processes described above. For example, in some embodiments, the method of the present embodiment may be implemented as a computer software program, which is tangibly included in a machine-readable medium, such as a storage unit 608. In some embodiments, part or all of the computer program may be loaded and / or installed on the electronic device 600 via the ROM 602 and / or the communication unit 609. In some embodiments, the computing unit 601 may be configured to perform the method of the present embodiment in any other appropriate manner (e.g., by means of firmware).

[0243] The program code for implementing the method of the present disclosure can be written in any combination of one or more programming languages. These program codes can be provided to a processor or controller of a general-purpose computer, a special-purpose computer, or other programmable data processing device so that when the program code is executed by the processor or controller, the functions / operations specified in the flow chart and / or block diagram are implemented. The program code can be executed entirely on the machine, partially on the machine, as a stand-alone software package, partially on the machine and partially on a remote machine, or entirely on a remote machine or server.

[0244] In the context of the present disclosure, a machine-readable medium can be a tangible medium that can contain or store a program for use by or in conjunction with an instruction execution system, device or equipment. A machine-readable medium can be a machine-readable signal medium or a machine-readable storage medium. A machine-readable medium can include, but is not limited to, an electronic, magnetic, optical, electromagnetic, infrared, or semiconductor system, device or equipment, or any suitable combination of the foregoing. A more specific example of a machine-readable storage medium can include an electrical connection based on one or more lines, a portable computer disk, a hard disk, a random access memory (RAM), a read-only memory (ROM), an erasable programmable read-only memory (EPROM or flash memory), an optical fiber, a portable compact disk read-only memory (CD-ROM), an optical storage device, a magnetic storage device, or any suitable combination of the foregoing.

[0245] As used in this disclosure, the terms "machine-readable medium" and "computer-readable medium" refer to any computer program product, apparatus, and / or device (e.g., a magnetic disk, an optical disk, a memory, a programmable logic device (PLD)) for providing machine instructions and / or data to a programmable processor, including machine-readable media that receive machine instructions as machine-readable signals. The term "machine-readable signal" refers to any signal used to provide machine instructions and / or data to a programmable processor.

[0246] To provide interaction with a user, the systems and techniques described herein can be implemented on a computer having: a display device (e.g., a CRT (cathode ray tube) or LCD (liquid crystal display) monitor) for displaying information to the user; and a keyboard and pointing device (e.g., a mouse or trackball) through which the user can provide input to the computer. Other types of devices can also be used to provide interaction with the user; for example, the feedback provided to the user can be any form of sensory feedback (e.g., visual feedback, auditory feedback, or tactile feedback); and input from the user can be received in any form (including acoustic input, voice input, or tactile input).

[0247] The systems and techniques described herein can be implemented in a computing system that includes back-end components (e.g., as a data server), or a computing system that includes middleware components (e.g., an application server), or a computing system that includes front-end components (e.g., a user computer having a graphical user interface or a web browser through which a user can interact with implementations of the systems and techniques described herein), or a computing system that includes any combination of such back-end components, middleware components, or front-end components. The components of the system can be interconnected by any form or medium of digital data communication (e.g., a communication network). Examples of communication networks include a local area network (LAN), a wide area network (WAN), and the Internet.

[0248] Computer systems may include clients and servers. A client and server are generally remote from each other and typically interact through a communication network. The client and server relationship arises through computer programs running on the respective computers and having a client-server relationship to each other.

Claims

1. A production dynamic analysis method for fractured horizontal wells under inter-well interference conditions, characterized in that: include: Construct a mathematical model for production dynamic analysis and seepage of fractured horizontal wells under inter-well interference conditions; A semi-analytical solution is obtained for the mathematical model of seepage for production dynamic analysis to obtain a production solution for a fractured horizontal well under inter-well interference conditions; determining a pressure-normalized production curve under an inter-well interference condition according to the production solution; Performing plate fitting on the pressure normalized production curve and actual production data of the oil field to determine reservoir parameters; The production dynamic analysis seepage mathematical model includes an oil reservoir seepage mathematical model and a hydraulic fracture seepage mathematical model; The reservoir seepage mathematical model and its initial conditions and internal and external boundary conditions are as follows: Among them, p D is the dimensionless pressure of the reservoir system, r D is the dimensionless radial distance, u is the Laplace variable, t D is the dimensionless production time, q D is the dimensionless production of the reservoir system; The mathematical model of hydraulic fracture seepage and its initial conditions and internal and external boundary conditions are as follows: Among them, p hfD is the dimensionless pressure of the hydraulic fracture system, x D is the dimensionless distance in the direction of the hydraulic fracture, C hfD is the dimensionless hydraulic fracture conductivity, q hfD is the dimensionless production of the hydraulic fracture system, t D is the dimensionless production time, p wD is the dimensionless bottom hole pressure, L hfD is the half-length of the dimensionless hydraulic fracture.

2. The method according to claim 1, characterized in that The construction of a mathematical model for production performance analysis and seepage of a fractured horizontal well under inter-well interference conditions includes: Based on the physical model of fractured horizontal wells under inter-well interference conditions, a mathematical model for production dynamic analysis and seepage of fractured horizontal wells under inter-well interference conditions is constructed. The physical model is constructed according to the geological parameters of the formation, the physical properties of the fluid, the fracturing production increase method and the historical production data of the oil wells.

3. The method according to claim 2, characterized in that The assumptions of the physical model include: The reservoir has uniform water quality and thickness, the initial pressure at each point in the reservoir is the same, and the effect of temperature on fluid flow is ignored. The fluid in the reservoir is a single-phase slightly compressible fluid that satisfies Darcy's law. The multiple hydraulic fractures formed by artificial fracturing completely penetrate the formation, and the length of the fractures is much greater than the fracture height and width. The flow in the hydraulic fractures is one-dimensional and satisfies Darcy's law. Multiple fractured horizontal wells are all under constant flow pressure production conditions, the target well has a variable bottomhole flow pressure, and the commissioning time of adjacent wells and the target well is different or the same.

4. The method according to claim 1, wherein The construction of a mathematical model for production performance analysis and seepage of a fractured horizontal well under inter-well interference conditions includes: The production dynamic analysis seepage mathematical model is constructed based on dimensionless variables, wherein the dimensionless variables include dimensionless production time, dimensionless bottom hole pressure and dimensionless production.

5. The method according to claim 1, wherein The semi-analytical solution of the mathematical model for the production dynamic analysis to obtain the production solution of the fractured horizontal well under the condition of inter-well interference includes: Semi-analytically solving the production performance analysis seepage mathematical model using Laplace transform to obtain a general solution of the hydraulic fracture model contained in the production performance analysis seepage mathematical model and a general solution of the reservoir model contained in the production performance analysis seepage mathematical model; Taking into account the influence of inter-well interference, the general solution of the hydraulic fracture model is coupled with the general solution of the reservoir model to obtain the production solution.

6. The method according to claim 1, characterized in that The semi-analytical solution of the mathematical model for the production dynamic analysis to obtain the production solution of the fractured horizontal well under the condition of inter-well interference includes: The production dynamic analysis seepage mathematical model is solved according to the initial conditions, inner boundary conditions and outer boundary conditions to obtain the single well production solution. The pressure superposition term of the adjacent wells for the target well is calculated by utilizing the production ratio relationship and the superposition principle, and the pressure superposition term is superimposed and coupled with the flow rate and pressure term of the target well to obtain the production solution.

7. The method according to claim 5, characterized in that The general solution of the hydraulic fracture model is: Among them, p i,D is the dimensionless pressure of each hydraulic fracture segment, i is the hydraulic fracture segment number, p wD is the dimensionless bottom hole pressure, subscript k represents the different hydraulic fractures in the multi-well model, C hfD is the dimensionless hydraulic fracture conductivity, ΔL D is the dimensionless hydraulic fracture length, q hfD is the dimensionless production of the hydraulic fracture system, σ is the number of fracture segments in each hydraulic fracture; The general solution of the reservoir model pressure is: p D is the dimensionless pressure of the reservoir system, x D is the dimensionless distance in the direction of the hydraulic fracture, ΔL D is the dimensionless hydraulic fracture segment length, q D is the dimensionless production of the reservoir system, K0 is the second-order zero-order Bessel function, u is the Laplace variable, r D is the dimensionless radial distance, and l is the integral variable.

8. The method according to claim 1, characterized in that Determining a pressure-normalized production curve under an inter-well interference condition according to the production solution includes: A dynamic analysis method for unstable production under inter-well interference is established by using multi-well material balance time and pressure-normalized production. A pressure-normalized production curve under inter-well interference conditions is drawn. The pressure-normalized production curve includes curves showing changes of pressure-normalized production under inter-well interference conditions and its integral and integral derivative with material balance time.

9. An electronic device, characterized in that include: processor; as well as Memory for storing programs, The program includes instructions, which, when executed by the processor, enable the processor to perform the production performance analysis method for fractured horizontal wells under inter-well interference conditions according to any one of claims 1-8.

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